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          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
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          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable" xlink:label="us-gaap_ScheduleOfStockByClassTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany" xlink:label="dei_EntityEmergingGrowthCompany"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentArrangementContractToPerformForOthersCompensationEarned_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Grant funds payment received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentArrangementContractToPerformForOthersCompensationEarned_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Arrangement, Contract to Perform for Others, Compensation Earned</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Exercise Price, Forfeited/expired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Weighted Average Exercise Price, Forfeited/expired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures and Expirations in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial Term Loan</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_WellcomeLeapAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Wellcome Leap Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_WellcomeLeapAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Wellcome Leap Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Accounts Payable, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Excluding Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Term loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USGovernmentAgenciesDebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Government Agencies Debt Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USGovernmentAgenciesDebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">US Government Agency Bonds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Short-term Investments, Unrealized Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Short-term investments, unrealized loss.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Short-term investments, Unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Short-term marketable securities, Unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashAndCashEquivalentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash And Cash Equivalents, Unrealized Gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashAndCashEquivalentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash and cash equivalents, unrealized gain.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashAndCashEquivalentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents, Unrealized gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value by Liability Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA2RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series A-2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA2RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A-2 Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA2RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A-2 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA2RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series A-2 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Stated Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate, stated percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Temporary equity beginning balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Temporary equity Ending balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LongTermMarketableSecuritiesContractualMaturityTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Marketable Securities Contractual Maturity Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LongTermMarketableSecuritiesContractualMaturityTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long term marketable securities contractual maturity term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LongTermMarketableSecuritiesContractualMaturityTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term marketable securities, Contractual Maturity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConvertibleDebtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Debt [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConvertibleDebtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible Notes</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentArrangementContractToPerformForOthersByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Arrangement, Contract to Perform for Others, Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfRedeemableConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfRedeemableConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from Series D issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandTwentyFourEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand Twenty-Four Employee Stock Purchase Plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandTwentyFourEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty-Four Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandTwentyFourEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2024 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Right-of-use assets obtained in exchange for lease obligation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RegulatoryLiabilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Regulatory Liability [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued interest receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average grant date fair value of stock options granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_WarrantLiabilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Warrant liability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_WarrantLiabilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrant Liability [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_WarrantLiabilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrant liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DeferredOfferingCostsIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Offering Costs Included In Accounts Payable, Accrued Expenses, And Other Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DeferredOfferingCostsIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred offering costs included in accounts payable, accrued expenses, and other current liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DeferredOfferingCostsIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred offering costs included in accounts payable, accrued expenses, and other current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrant [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrants to Purchase Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Warrants, Issued and Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_RisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risks and Uncertainties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_RisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Risks and uncertainties.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_RisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Risks and Uncertainties, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities and stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less current portion of Term loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of term loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Portion Attributable to Parent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Portion Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency translation adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFrequencyOfPeriodicPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Frequency of Periodic Payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFrequencyOfPeriodicPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, frequency of periodic payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Lease Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash lease expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentDateOfFirstRequiredPayment1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument payment commencement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentDateOfFirstRequiredPayment1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Date of First Required Payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cash equivalents, Fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and Cash Equivalents, Fair Value Disclosure, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Public offering price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommonStockAggregateOfferingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Aggregate Offering Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommonStockAggregateOfferingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock aggregate offering amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommonStockAggregateOfferingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock aggregate offering amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesCRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series C</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesCRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series C Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesCRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series C Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesCRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series C Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Effective Income Tax Rate Reconciliation, Percent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effective tax rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock Options, Issued and Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ScheduleOfCashEquivalentsAndShortTermAndLongTermMarketableSecuritiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Cash Equivalents And Short Term and Long Term Marketable Securities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ScheduleOfCashEquivalentsAndShortTermAndLongTermMarketableSecuritiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of Cash Equivalents And Short Term and Long Term Marketable Securities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ScheduleOfCashEquivalentsAndShortTermAndLongTermMarketableSecuritiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Company's Cash Equivalents and Marketable Securities' Amortized Costs, Gross Unrealized Gains, Gross Unrealized Losses and Estimated Fair Values by Significant Investment Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan, Employer Matching Contribution, Percent of Employees' Gross Pay</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of employer matching contribution</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockAmountConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of redeemable convertible preferred stock into common stock upon initial public offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockAmountConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Stock, Amount Converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShaneBartonMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shane Barton [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShaneBartonMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Shane Barton.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShaneBartonMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shane Barton</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computation of Basic and Diluted Net Loss per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DebtInstrumentConvertibleQualifiedMilestoneAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum qualified financing for conversion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DebtInstrumentConvertibleQualifiedMilestoneAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument, convertible, qualified milestone amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DebtInstrumentConvertibleQualifiedMilestoneAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Convertible Qualified Milestone Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash interest expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Interest Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share attributable to common stockholders, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IndirectResearchAndDevelopmentExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indirect Research And Development Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IndirectResearchAndDevelopmentExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Indirect research and development expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IndirectResearchAndDevelopmentExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Indirect research and development expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency translation adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Number of Options, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of Options, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock options outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SizeOfOfficeAndLabSpace_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Size of office and lab space.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SizeOfOfficeAndLabSpace_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Size Of Office And Lab Space</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SizeOfOfficeAndLabSpace_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Size of office and lab space</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AccruedResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AccruedResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued research and development expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AccruedResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Research And Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2031</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Changes in Fair Value of the Warrant Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_WarrantsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Warrants liability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_WarrantsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrants Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_WarrantsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrants liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance Initial Public Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock in initial public offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from initial public offering, net of underwriting discounts and commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intrinsic value of stock options exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_OneCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">One Customer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_OneCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">One customer.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_OneCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">One Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity stock issued during period shares new issues.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Stock Issued During Period Shares New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series D redeemable convertible preferred stock, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncomeTaxesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income taxes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncomeTaxesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationOperatingIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Information, Operating Income (Loss) [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationOperatingIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common Stock, Issued and Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update and Change in Accounting Principle [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Exercise Price, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Exercise price of options granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentArrangementContractToPerformForOthersTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Arrangement, Contract to Perform for Others, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Effective Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effective interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LeerinkPartnersLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leerink Partners LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LeerinkPartnersLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Leerink partners llc member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LeerinkPartnersLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leerink Partners LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Estimated Fair Value of Stock Options Granted Weighted Average Assumptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Temporary equity beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Temporary equity Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary equity value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, par value of $0.00001, 31,634,362 shares authorized as of December 31, 2023, and 31,465,128 shares issued and outstanding as of December 31, 2023; aggregate liquidation preference of $131,864 as of December 31, 2023; no shares issued and outstanding as of September 30, 2024</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Short-term Investments, Unrealized Gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Short-term investments, unrealized gain.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Short-term marketable securities, Unrealized gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashCashEquivalentsAndMarketableSecuritiesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash, Cash Equivalents, and Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashCashEquivalentsAndMarketableSecuritiesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalents, and Marketable Securities [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashCashEquivalentsAndMarketableSecuritiesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash, cash equivalents, and marketable securities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredLeaseRevenueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Lease Revenue [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredLeaseRevenueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfSharesConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of convertible promissory notes into Series D-1 redeemable convertible preferred stock, Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfSharesConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity conversion of shares convertible securities.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShortTermMarketableSecuritiesContractualMaturityTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Short Term Marketable Securities Contractual Maturity Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShortTermMarketableSecuritiesContractualMaturityTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Short term marketable securities contractual maturity term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShortTermMarketableSecuritiesContractualMaturityTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Short-term marketable securities, Contractual Maturity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SaleOfStockNumberOfSharesAvailableInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock Number of Shares Available in Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SaleOfStockNumberOfSharesAvailableInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of Stock Number of Shares Available in Transaction.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SaleOfStockNumberOfSharesAvailableInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares available</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LoanAndSecurityAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loan Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LoanAndSecurityAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loan And Security Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LoanAndSecurityAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loan And Security Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrimeRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prime Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrimeRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prime rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net increase (decrease) in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAdjustmentOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase in warrant liability</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAdjustmentOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesEmbeddedDerivativeLiabilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Convertible promissory notes embedded derivative liability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesEmbeddedDerivativeLiabilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Promissory Notes Embedded Derivative Liability [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesEmbeddedDerivativeLiabilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible promissory notes embedded derivative liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Potentially dilutive securities excluded from computation of diluted shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetRelatedDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Balance Sheet Related Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other comprehensive income(loss) :</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Base Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGrantedForPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Granted for Period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGrantedForPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Granted for Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGrantedForPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares Available to Grant, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGrantedForPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Shares Available to Grant, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Remaining Contractual Life (Years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Options, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of Options, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock option exercises, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Marketable Securities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandFifteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2015 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandFifteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand fifteen equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandFifteenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Fifteen Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RegulatoryLiabilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Regulatory Liability [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConvertibleNotesPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Qualified financing, maximum</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConvertibleNotesPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Notes Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Conversion of Convertible Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of convertible preferred stock into common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommonStockCapitalSharesReservedForFutureIssuanceAdditionalSharesReservedPercentageMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock, capital shares reserved for future issuance, additional shares reserved, percentage, maximum.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommonStockCapitalSharesReservedForFutureIssuanceAdditionalSharesReservedPercentageMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Capital Shares Reserved for Future Issuance, Additional Shares Reserved, Percentage, Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommonStockCapitalSharesReservedForFutureIssuanceAdditionalSharesReservedPercentageMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of additional shares reserved for issuance, percentage, maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities, Current</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_GrossProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gross Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_GrossProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gross proceeds from issuance of common stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_GrossProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross proceeds from issuance of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Sale and Maturity of Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maturities of marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 (excluding the three months ended March 31, 2026)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Revenue, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Revenue, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_EmployeeStockOptionAuthorizedForFutureIssuanceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee Stock Option Authorized for Future Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_EmployeeStockOptionAuthorizedForFutureIssuanceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Option Authorized for Future Issuance [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_EmployeeStockOptionAuthorizedForFutureIssuanceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock Options, Authorized for Future Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unamortized issuance costs and debt discounts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Presentation and Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation and Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA4RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series A-4 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA4RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series A-4</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA4RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A-4 Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA4RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A-4 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Expense, Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Instrument, Unamortized Discount, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Unamortized Discount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Unamortized debt discount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Option to Extend</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease, Extended</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, $0.00001 par value; 10,000,000 shares authorized as of March 31, 2026 and December 31, 2025; no shares issued or outstanding as of March 31, 2026 and December 31, 2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SummaryOfSignificantAccountingPoliciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Significant Accounting Policies [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SummaryOfSignificantAccountingPoliciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of Significant Accounting Policies.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SummaryOfSignificantAccountingPoliciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Fair Value Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_JanuaryTwoZeroTwoSixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">January 2026 Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_JanuaryTwoZeroTwoSixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">January Two Zero Two Six Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_JanuaryTwoZeroTwoSixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">January Two Zero Two Six Offering.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Financial Assets And Liabilities Measured at Fair Value on a Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashDeferredOfferingCostsIncludedInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred offering costs included in accounts payable and accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashDeferredOfferingCostsIncludedInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Deferred Offering Costs Included In Accounts Payable And Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashDeferredOfferingCostsIncludedInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash deferred offering costs included in accounts payable and accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesDRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series D Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesDRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series D Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesDRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series D</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesDRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series D Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Receivable, after Allowance for Credit Loss, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseRenewalTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Renewal Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseRenewalTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Option to extend the term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and Administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred grant income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term loan annual interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioForecastMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Forecast [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioForecastMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Forecast</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Cash, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DefinedContributionPlanMatchingContributionsByEmployer_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Defined contribution plan matching contributions by employer.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DefinedContributionPlanMatchingContributionsByEmployer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan Matching Contributions by Employer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DefinedContributionPlanMatchingContributionsByEmployer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Company's matching contributions to employees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerProductAndServiceExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer, Product and Service [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Equivalents and Marketable Securities, Unrealized Gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash equivalents and marketable securities, unrealized gain.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash equivalents and marketable securities, Unrealized gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents and marketable securities, Unrealized gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Including Disposal Group and Discontinued Operations, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effect of changes in exchange rate on cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Equivalents and Marketable Securities, Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash equivalents and marketable securities, amortized cost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash equivalents and marketable securities, Amortized cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedBenefitPlanTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Benefit Plan [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedBenefitPlanTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee Benefit Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average shares used to compute basic net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-average common shares outstanding, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementScenarioAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scenario [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommercialResearchFundingAgreementTerminationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commercial research funding agreement termination date.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommercialResearchFundingAgreementTerminationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Research Funding Agreement Termination Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CommercialResearchFundingAgreementTerminationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial research funding agreement termination date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfValueConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity conversion of value convertible securities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfValueConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Conversion Of Value Convertible Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfValueConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of convertible promissory notes into Series D-1 redeemable convertible preferred stock, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingExpenseInformationUsedByCodmDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment reporting, expense information used by CODM, description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingExpenseInformationUsedByCodmDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Expense Information Used by CODM, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Private Placement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common shares through private placement, net of placement agent fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ReturnOfUnusedGrantFundsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Return Of Unused Grant Funds Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ReturnOfUnusedGrantFundsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Return of unused grant funds amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ReturnOfUnusedGrantFundsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Return of unused grant funds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CollaborativeArrangementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaboration Agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CollaborativeArrangementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedBenefitPlanDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Benefit Plan Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OverAllotmentOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Over-Allotment Option [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leasehold improvements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leasehold Improvements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationNonproduction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationNonproduction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Nonproduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accrued Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental non-cash disclosure:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental non-cash disclosure:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment reporting, CODM, individual title and position</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Exercise Price, Vested and Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrants outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Short-term Investments, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Short-term investments, fair value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Short-term marketable securities, Fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_BasisOfPresentationAndPrinciplesOfConsolidationPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Basis of presentation and principles of consolidation.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_BasisOfPresentationAndPrinciplesOfConsolidationPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Presentation and Principles of Consolidation, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_BasisOfPresentationAndPrinciplesOfConsolidationPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation and Principles of Consolidation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of reportable segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Investments, Unrealized Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long-term investments, unrealized loss.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term marketable securities, Unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Long-term marketable securities, Unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Principal loan balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Principal amount of Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Principal amount of Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Gross, Total</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Property, Plant and Equipment, Gross, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardIncreaseDecreaseInAuthorizedShares_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-Based Compensation Arrangement by Share-Based Payment Award, Increase Decrease in Authorized Shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardIncreaseDecreaseInAuthorizedShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Increase Decrease in Authorized Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardIncreaseDecreaseInAuthorizedShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares Available to Grant, Change in authorized shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashEquityIssuanceCostsIncludedInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Equity Issuance Costs Included In Accounts Payable And Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashEquityIssuanceCostsIncludedInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash equity issuance costs included in accounts payable and accrued expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NoncashEquityIssuanceCostsIncludedInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unpaid underwritten offering issuance costs included in accounts payable and accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Convertible promissory notes current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Promissory Notes Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible Promissory notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">OCI, Debt Securities, Available-for-Sale, Gain (Loss), after Adjustment, before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">OCI, Debt Securities, Available-for-Sale, Gain (Loss), after Adjustment, before Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized loss on marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NovartisPharmaAGMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Novartis Pharma AG [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NovartisPharmaAGMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Novartis pharma ag.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_NovartisPharmaAGMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Novartis Pharma AG</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCorporateDebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Security, Corporate, Non-US [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCorporateDebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign corporate debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable Convertible Preferred Stock, Issued and Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsNotSettleableInCashFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrants Not Settleable in Cash, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsNotSettleableInCashFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ComputerEquipmentAndSoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Computer equipment and software.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ComputerEquipmentAndSoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Computer Equipment And Software [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ComputerEquipmentAndSoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computer Equipment and Software</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_QualifiedFinancingAdjustedDiscountRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjusted discount rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_QualifiedFinancingAdjustedDiscountRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Qualified financing adjusted discount rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_QualifiedFinancingAdjustedDiscountRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Qualified Financing Adjusted Discount Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashCashEquivalentsAndMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Cash Equivalents And Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashCashEquivalentsAndMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash, cash equivalents, and marketable securities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashCashEquivalentsAndMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash, cash equivalents, and marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstandingMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrants and Rights Outstanding, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstandingMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrants, maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instruments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Deferred Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Short-term Investments, Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Short-term investments, amortized cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Short-term marketable securities, Amortized cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Short-TermInvestmentsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Short-term marketable securities, Amortized cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average of shares used to compute diluted net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-average common shares outstanding, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesD1RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series D-1 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesD1RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series D-1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesD1RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series D-1 Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesD1RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series D-1 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DirectOperatingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Direct Operating Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DirectOperatingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Direct Operating Costs, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DirectOperatingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Direct program costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized holding gains (losses) on available-for-sale investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsContractualMaturityTermDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Equivalents Contractual Maturity Term Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsContractualMaturityTermDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash equivalents contractual maturity term description.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsContractualMaturityTermDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents, Contractual Maturity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SalesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sales Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SalesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sales agreement member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SalesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sales Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_FinalPaymentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Final Payment Fee Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_FinalPaymentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Final payment fee, percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_FinalPaymentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Final payment fee percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalBalanceSheetDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Balance Sheet Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalBalanceSheetDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Balance Sheet Components</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Investments, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long-term investments, fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term marketable securities, Fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncreaseDecreaseInAccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase (decrease) in accrued expenses and other current liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncreaseDecreaseInAccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accrued Expenses and Other Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncreaseDecreaseInAccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses and other current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue Benchmark [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioUnspecifiedDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scenario [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Treasury Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Treasury bill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares authorized (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Reporting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">General and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLiquidationPreference_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Liquidation Preference</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLiquidationPreference_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, aggregate liquidation preference</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures and Expirations in Period, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures and Expirations in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options, Forfeited/expired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Options, Forfeited/expired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Extinguishment of Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Extinguishment of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Loss on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesForfeitedExpired_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Forfeited/Expired.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesForfeitedExpired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Forfeited/Expired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesForfeitedExpired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares Available to Grant, Forfeited/expired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Additional Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Remaining Contractual Term and Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Issued Accounting Pronouncements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Maturities of Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contract with Customer, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of convertible preferred stock into common stock, Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Conversion of convertible preferred stock into common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock options vesting period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Investments, Unrealized Gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long-term investments, unrealized gain.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term marketable securities, Unrealized gain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial term of lease</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Investments, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities, current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Less: current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total operating and segment expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Research and Development Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DebtInstrumentFinalFeeAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Final fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DebtInstrumentFinalFeeAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Final Fee Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DebtInstrumentFinalFeeAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument, final fee amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common shares, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock Option Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capital Structure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued expenses and other current liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Expenses and Other Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses and other current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AccruedExpensesAndOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total accrued expenses and other current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Loss Per Share Attributable to Common Stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Equivalents and Marketable Securities, Unrealized Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash equivalents and marketable securities, unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedLosses_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Cash equivalents and marketable securities, Unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedLosses_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Cash equivalents and marketable securities, Unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Segment and consolidated net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Aggregate Intrinsic Value, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Aggregate Intrinsic Value, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Dividend Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated dividend yield</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_FutureLongTermResearchDevelopmentAndCommercialMilestonePayment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Future long-term research, development, and commercial milestone payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_FutureLongTermResearchDevelopmentAndCommercialMilestonePayment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Future Long term research, development, and commercial milestone Payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_FutureLongTermResearchDevelopmentAndCommercialMilestonePayment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Future long term research, development, and commercial milestone payment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate Intrinsic Value, Vested and Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average risk-free interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Construction in Progress [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction-in-progress</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayments of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Term loan principal payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_PurchasesOfPropertyAndEquipmentInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Purchases Of Property And Equipment In Accounts Payable And Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_PurchasesOfPropertyAndEquipmentInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Purchases of property and equipment in accounts payable and accrued expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_PurchasesOfPropertyAndEquipmentInAccountsPayableAndAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchases of property and equipment in accounts payable and accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">INVESTING ACTIVITIES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Expense, Nonoperating, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_EmbeddedDerivativeLiabilityConvertedIntoRedeemableConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Embedded derivative liability converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_EmbeddedDerivativeLiabilityConvertedIntoRedeemableConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Embedded derivative liability converted into redeemable convertible preferred stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_EmbeddedDerivativeLiabilityConvertedIntoRedeemableConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Embedded Derivative Liability Converted Into Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Revenue, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Conversion, Converted Instrument, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of convertible promissory notes into Series D-1 redeemable convertible preferred stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Conversion of convertible promissory notes into Series D-1 redeemable convertible preferred stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Stock Options Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common shares upon stock option exercises</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_UpfrontPaymentsAndResearchFunding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Upfront Payments and Research Funding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_UpfrontPaymentsAndResearchFunding_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Upfront payments and research funding.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_UpfrontPaymentsAndResearchFunding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Upfront payments and research funding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Embedded Derivative, Fair Value of Embedded Derivative Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible promissory notes embedded derivative liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Withdrawn amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Line of Credit, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Line of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, after Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total fair value of financial assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series D redeemable convertible preferred stock, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration risk, percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrivatePlacementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Private Placement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrivatePlacementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private Placement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Money Market Funds [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Money Market Funds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Allowance for Credit Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Debt Securities, Available-for-Sale, Allowance for Credit Loss, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Debt Securities, Available-for-Sale, Allowance for Credit Loss, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Securities, Available-for-Sale, Allowance for Credit Loss, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Allowance for credit losses or impairments of its marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IssuanceCostsPaidOnInitialPublicOfferingAndPrivatePlacement_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Issuance costs paid on initial public offering and private placement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IssuanceCostsPaidOnInitialPublicOfferingAndPrivatePlacement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance Costs Paid on Initial Public Offering and Private Placement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IssuanceCostsPaidOnInitialPublicOfferingAndPrivatePlacement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance costs paid on initial public offering and private placement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncomeTaxesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income taxes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncomeTaxesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 (excluding the three months ended March 31, 2026)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandTwentyFourEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2024 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandTwentyFourEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">2024 equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TwoThousandTwentyFourEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Four Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in operating assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Components of Property and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted Average Exercise Price, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted Average Exercise Price, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized tax benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Unrecognized Tax Benefits, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Unrecognized Tax Benefits, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements or Change in Accounting Principle [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LesseeOperatingLeaseCommencedDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating Lease Commenced Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LesseeOperatingLeaseCommencedDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee Operating Lease Commenced Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_LesseeOperatingLeaseCommencedDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lessee, operating lease commenced date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payroll and related costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">FINANCING ACTIVITIES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected term of stock options (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recurring</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityExTransitionPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Ex Transition Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_USGovernmentBondsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Government Bonds [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_USGovernmentBondsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">US Government Bonds.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_USGovernmentBondsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">US Government Bonds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Remaining Contractual Life (Years), Vested and Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted average remaining lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other income (expense), net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest and other income (expense), net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_PercentageOfPrepaymentPremiumOfPrincipalAmountOutstandingPriorToMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of prepayment premium of principal amount outstanding prior to maturity date.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_PercentageOfPrepaymentPremiumOfPrincipalAmountOutstandingPriorToMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Prepayment Premium of Principal Amount Outstanding Prior to Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_PercentageOfPrepaymentPremiumOfPrincipalAmountOutstandingPriorToMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepayment premium outstanding amount , percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">IPO [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">IPO</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MajorCustomersAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock options term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Liabilities, Fair Value Disclosure, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Schedule of Common Stock Shares Reserved for Future Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Stock by Class [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Exercise Price, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contract with Customer, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.00001 par value; 500,000,000 shares authorized as of March 31, 2026 and December 31, 2025; 44,386,785 and 37,386,908 shares issued and outstanding as of March 31, 2026 and December 31, 2025, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SVBInnovativeCreditGrowthFundIXLPAndInnovativeCreditGrowthFundVIIIALPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lenders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SVBInnovativeCreditGrowthFundIXLPAndInnovativeCreditGrowthFundVIIIALPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">SVB Innovative Credit Growth Fund IX, LP and Innovative Credit Growth Fund VIII-A, LP.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SVBInnovativeCreditGrowthFundIXLPAndInnovativeCreditGrowthFundVIIIALPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">S V B Innovative Credit Growth Fund I X, L P and Innovative Credit Growth Fund V I I I A, L P [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrants and Rights Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Fair value at March 31, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Fair value at December 31, 2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lab Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive loss:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible Promissory Notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Convertible Promissory Notes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_ConvertiblePromissoryNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Promissory Notes [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense) [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other income (expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average expected stock price volatility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred stock, share authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Debt [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Components of Term Loan Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesBRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series B Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesBRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series B</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesBRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series B Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesBRedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series B Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashAndCashEquivalentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash And Cash Equivalents, Unrealized Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashAndCashEquivalentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash and cash equivalents, unrealized loss.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashAndCashEquivalentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents, Unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashAndCashEquivalentsUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Cash equivalents, Unrealized losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DirectorOrOfficersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Director or Officers [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DirectorOrOfficersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Director or Officers [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_DirectorOrOfficersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Director or Officers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in-capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Additional Paid in Capital, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">At-the-Market Program</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">At the Market Program [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">At the Market Program.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net proceeds from issuance of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from underwritten offering of common stock, net of underwriting discounts and commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares available for grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentrations of Credit Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Credit Risk, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByLiabilityClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liability Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Other Comprehensive Income (Loss), Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accumulated other comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated other comprehensive income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedBenefitPlanAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Benefit Plan [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Investments, Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long-term investments, amortized cost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term marketable securities, Amortized cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_Long-TermInvestmentsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-term marketable securities, Amortized cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_GainLossFromChangesInFairValueOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (loss) from changes in fair value of warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_GainLossFromChangesInFairValueOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gain (loss) from changes in fair value of warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncreaseDecreaseInDeferredGrantIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred grant income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncreaseDecreaseInDeferredGrantIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Deferred Grant Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_IncreaseDecreaseInDeferredGrantIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase decrease in deferred grant income.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Issuance of common shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquitySharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable convertible preferred stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share attributable to common stockholders, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Segment Net Loss, Including Significant Segment Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Segments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CollaborationAgreementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaboration Agreements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CollaborationAgreementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Collaboration agreements abstract.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Face Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Principal amount of Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Principal loan balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Debt instrument, principal amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loan borrowing, amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Benefit Plan [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average remaining lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseExpirationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease expired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseExpirationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Expiration Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options, Vested and Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Including Disposal Group and Discontinued Operations, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss from operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Loss from operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Payment Arrangement, Noncash Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Noncash Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Stock Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Underwriter fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Placement agent fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Underwritten offering issuance costs paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average discount rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating lease liability, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by (used in) financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfConvertibleSecuritiesValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity conversion of convertible securities, value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfConvertibleSecuritiesValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Conversion Of Convertible Securities, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfConvertibleSecuritiesValue_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Temporary equity, Conversion of convertible preferred stock into common stock, value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SizeOfAdditionalSpace_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Size of additional space.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SizeOfAdditionalSpace_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Size of Additional Space</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SizeOfAdditionalSpace_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Size of additional space</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrant liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computation of Potentially Dilutive Securities Outstanding Excluded from Computation of Diluted Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CorporateDebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Corporate Debt Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CorporateDebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Corporate Debt Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">OPERATING ACTIVITIES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Furniture and Fixtures [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Furniture and Fixtures</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RemovalCostsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reimbursable Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RemovalCostsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Removal Costs [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accretion of net investment discounts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfConvertibleSecuritiesShares_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity conversion of convertible securities, shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfConvertibleSecuritiesShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Conversion Of Convertible Securities, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TemporaryEquityConversionOfConvertibleSecuritiesShares_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Temporary equity, Conversion of convertible preferred stock into common stock, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash equivalents, Amortized cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Equivalents, at Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents, Amortized cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Equivalents and Marketable Securities, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash equivalents and marketable securities, fair value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash equivalents and marketable securities, Fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_CashEquivalentsAndMarketableSecuritiesFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents and marketable securities, Fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche two .</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche Two [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_TrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOrSaleOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds from Issuance or Sale of Equity, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOrSaleOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance or Sale of Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOrSaleOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Local Phone Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA3RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series A-3 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA3RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series A-3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA3RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A-3 Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA3RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A-3 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Denominator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Financing Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments of Financing Costs, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Deferred offering costs paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA1RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series A-1 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA1RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series A-1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA1RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A-1 Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="bioa_SeriesA1RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A-1 Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaboration revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Numerator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2030</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialPaperMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Paper [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialPaperMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial Paper</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares available for grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Shares Available to Grant, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Shares Available to Grant, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average period for recognize compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock, Class of Stock [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</link:label>
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          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bioa_TrancheOneMember" xlink:to="bioa_TrancheOneMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByTypeAxis" xlink:to="us-gaap_ConcentrationRiskByTypeAxis_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationStateCountryCode" xlink:to="dei_EntityIncorporationStateCountryCode_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesIssued" xlink:to="us-gaap_PreferredStockSharesIssued_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bioa_WellcomeLeapAgreementMember" xlink:to="bioa_WellcomeLeapAgreementMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsPayable" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable_lbl"/>
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          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpense" xlink:label="us-gaap_NonoperatingIncomeExpense"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss"/>
          <link:loc xlink:type="locator" xlink:href="bioa-20260331.xsd#bioa_IndirectResearchAndDevelopmentExpenses" xlink:label="bioa_IndirectResearchAndDevelopmentExpenses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense"/>
        </link:calculationLink>
      </link:linkbase>
    </xsd:appinfo>
  </xsd:annotation>
  <xsd:element id="bioa_TwoThousandTwentyFourEquityIncentivePlanMember" name="TwoThousandTwentyFourEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_FutureLongTermResearchDevelopmentAndCommercialMilestonePayment" name="FutureLongTermResearchDevelopmentAndCommercialMilestonePayment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardIncreaseDecreaseInAuthorizedShares" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardIncreaseDecreaseInAuthorizedShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_Short-TermInvestmentsFairValue" name="Short-TermInvestmentsFairValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_TemporaryEquityConversionOfSharesConvertibleSecurities" name="TemporaryEquityConversionOfSharesConvertibleSecurities" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_SeriesA3RedeemableConvertiblePreferredStockMember" name="SeriesA3RedeemableConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGrantedForPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGrantedForPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_SeriesA2RedeemableConvertiblePreferredStockMember" name="SeriesA2RedeemableConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_ShortTermMarketableSecuritiesContractualMaturityTerm" name="ShortTermMarketableSecuritiesContractualMaturityTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_TermLoanMember" name="TermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_ConvertiblePromissoryNotesMember" name="ConvertiblePromissoryNotesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_CashAndCashEquivalentsUnrealizedGain" name="CashAndCashEquivalentsUnrealizedGain" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_AccruedExpensesAndOtherCurrentLiabilities" name="AccruedExpensesAndOtherCurrentLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_CashCashEquivalentsAndMarketableSecurities" name="CashCashEquivalentsAndMarketableSecurities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_IncreaseDecreaseInAccruedExpensesAndOtherCurrentLiabilities" name="IncreaseDecreaseInAccruedExpensesAndOtherCurrentLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_SeriesA4RedeemableConvertiblePreferredStockMember" name="SeriesA4RedeemableConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_NoncashLeaseExpense" name="NoncashLeaseExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_TemporaryEquityConversionOfConvertibleSecuritiesShares" name="TemporaryEquityConversionOfConvertibleSecuritiesShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_CollaborationAgreementsAbstract" name="CollaborationAgreementsAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_QualifiedFinancingAdjustedDiscountRate" name="QualifiedFinancingAdjustedDiscountRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_NoncashEquityIssuanceCostsIncludedInAccountsPayableAndAccruedExpenses" name="NoncashEquityIssuanceCostsIncludedInAccountsPayableAndAccruedExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_TwoThousandFifteenEquityIncentivePlanMember" name="TwoThousandFifteenEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_LeerinkPartnersLLCMember" name="LeerinkPartnersLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_CommonStockAggregateOfferingAmount" name="CommonStockAggregateOfferingAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_RisksAndUncertaintiesPolicyPolicyTextBlock" name="RisksAndUncertaintiesPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_SizeOfAdditionalSpace" name="SizeOfAdditionalSpace" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_UpfrontPaymentsAndResearchFunding" name="UpfrontPaymentsAndResearchFunding" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedGain" name="CashEquivalentsAndMarketableSecuritiesUnrealizedGain" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesForfeitedExpired" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesForfeitedExpired" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_ConvertiblePromissoryNotesEmbeddedDerivativeLiabilityMember" name="ConvertiblePromissoryNotesEmbeddedDerivativeLiabilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_CashCashEquivalentsAndMarketableSecuritiesPolicyTextBlock" name="CashCashEquivalentsAndMarketableSecuritiesPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_IncreaseDecreaseInDeferredGrantIncome" name="IncreaseDecreaseInDeferredGrantIncome" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_IssuanceCostsPaidOnInitialPublicOfferingAndPrivatePlacement" name="IssuanceCostsPaidOnInitialPublicOfferingAndPrivatePlacement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_IndirectResearchAndDevelopmentExpenses" name="IndirectResearchAndDevelopmentExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_SeriesDRedeemableConvertiblePreferredStockMember" name="SeriesDRedeemableConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_Long-TermInvestmentsFairValue" name="Long-TermInvestmentsFairValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_NoncashInterestExpense" name="NoncashInterestExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_DirectorOrOfficersMember" name="DirectorOrOfficersMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_PercentageOfPrepaymentPremiumOfPrincipalAmountOutstandingPriorToMaturityDate" name="PercentageOfPrepaymentPremiumOfPrincipalAmountOutstandingPriorToMaturityDate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_SeriesBRedeemableConvertiblePreferredStockMember" name="SeriesBRedeemableConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_Short-TermInvestmentsAmortizedCost" name="Short-TermInvestmentsAmortizedCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_SeriesA1RedeemableConvertiblePreferredStockMember" name="SeriesA1RedeemableConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_SummaryOfSignificantAccountingPoliciesPolicyTextBlock" name="SummaryOfSignificantAccountingPoliciesPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_CashEquivalentsAndMarketableSecuritiesUnrealizedLosses" name="CashEquivalentsAndMarketableSecuritiesUnrealizedLosses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_DefinedContributionPlanMatchingContributionsByEmployer" name="DefinedContributionPlanMatchingContributionsByEmployer" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_CommercialResearchFundingAgreementTerminationDate" name="CommercialResearchFundingAgreementTerminationDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_CashAndCashEquivalentsUnrealizedLoss" name="CashAndCashEquivalentsUnrealizedLoss" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_NoncashDeferredOfferingCostsIncludedInAccountsPayableAndAccruedExpenses" name="NoncashDeferredOfferingCostsIncludedInAccountsPayableAndAccruedExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_TemporaryEquityConversionOfConvertibleSecuritiesValue" name="TemporaryEquityConversionOfConvertibleSecuritiesValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_ConvertiblePromissoryNotesCurrent" name="ConvertiblePromissoryNotesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_SalesAgreementMember" name="SalesAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_WarrantsLiability" name="WarrantsLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_Long-TermInvestmentsAmortizedCost" name="Long-TermInvestmentsAmortizedCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_ShaneBartonMember" name="ShaneBartonMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_USGovernmentBondsMember" name="USGovernmentBondsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_Long-TermInvestmentsUnrealizedLoss" name="Long-TermInvestmentsUnrealizedLoss" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_DebtInstrumentFinalFeeAmount" name="DebtInstrumentFinalFeeAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_TemporaryEquityConversionOfValueConvertibleSecurities" name="TemporaryEquityConversionOfValueConvertibleSecurities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_WellcomeLeapAgreementMember" name="WellcomeLeapAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_WarrantLiabilityMember" name="WarrantLiabilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_SaleOfStockNumberOfSharesAvailableInTransaction" name="SaleOfStockNumberOfSharesAvailableInTransaction" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_SeriesCRedeemableConvertiblePreferredStockMember" name="SeriesCRedeemableConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_AccruedResearchAndDevelopmentExpense" name="AccruedResearchAndDevelopmentExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_NovartisPharmaAGMember" name="NovartisPharmaAGMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_LesseeOperatingLeaseCommencedDate" name="LesseeOperatingLeaseCommencedDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_GrossProceedsFromIssuanceOfCommonStock" name="GrossProceedsFromIssuanceOfCommonStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_IncomeTaxesTable" name="IncomeTaxesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_SVBInnovativeCreditGrowthFundIXLPAndInnovativeCreditGrowthFundVIIIALPMember" name="SVBInnovativeCreditGrowthFundIXLPAndInnovativeCreditGrowthFundVIIIALPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_CommonStockCapitalSharesReservedForFutureIssuanceAdditionalSharesReservedPercentageMaximum" name="CommonStockCapitalSharesReservedForFutureIssuanceAdditionalSharesReservedPercentageMaximum" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="bioa_TrancheTwoMember" name="TrancheTwoMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_DebtInstrumentConvertibleQualifiedMilestoneAmount" name="DebtInstrumentConvertibleQualifiedMilestoneAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_TrancheOneMember" name="TrancheOneMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_PurchasesOfPropertyAndEquipmentInAccountsPayableAndAccruedExpenses" name="PurchasesOfPropertyAndEquipmentInAccountsPayableAndAccruedExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_SeriesD1RedeemableConvertiblePreferredStockMember" name="SeriesD1RedeemableConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_ReturnOfUnusedGrantFundsAmount" name="ReturnOfUnusedGrantFundsAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_CashEquivalentsAndMarketableSecuritiesAmortizedCost" name="CashEquivalentsAndMarketableSecuritiesAmortizedCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_GainLossFromChangesInFairValueOfWarrants" name="GainLossFromChangesInFairValueOfWarrants" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_CashEquivalentsContractualMaturityTermDescription" name="CashEquivalentsContractualMaturityTermDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_Short-TermInvestmentsUnrealizedLoss" name="Short-TermInvestmentsUnrealizedLoss" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_IncomeTaxesLineItems" name="IncomeTaxesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_AtTheMarketProgramMember" name="AtTheMarketProgramMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_FinalPaymentFeePercentage" name="FinalPaymentFeePercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" name="TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_ComputerEquipmentAndSoftwareMember" name="ComputerEquipmentAndSoftwareMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_Short-TermInvestmentsUnrealizedGain" name="Short-TermInvestmentsUnrealizedGain" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_SizeOfOfficeAndLabSpace" name="SizeOfOfficeAndLabSpace" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_EmployeeStockOptionAuthorizedForFutureIssuanceMember" name="EmployeeStockOptionAuthorizedForFutureIssuanceMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_ScheduleOfCashEquivalentsAndShortTermAndLongTermMarketableSecuritiesTableTextBlock" name="ScheduleOfCashEquivalentsAndShortTermAndLongTermMarketableSecuritiesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_OneCustomerMember" name="OneCustomerMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_LongTermMarketableSecuritiesContractualMaturityTerm" name="LongTermMarketableSecuritiesContractualMaturityTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_CashEquivalentsAndMarketableSecuritiesFairValue" name="CashEquivalentsAndMarketableSecuritiesFairValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="bioa_EmbeddedDerivativeLiabilityConvertedIntoRedeemableConvertiblePreferredStock" name="EmbeddedDerivativeLiabilityConvertedIntoRedeemableConvertiblePreferredStock" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_Long-TermInvestmentsUnrealizedGain" name="Long-TermInvestmentsUnrealizedGain" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_DeferredOfferingCostsIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities" name="DeferredOfferingCostsIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="bioa_JanuaryTwoZeroTwoSixOfferingMember" name="JanuaryTwoZeroTwoSixOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_BasisOfPresentationAndPrinciplesOfConsolidationPolicyPolicyTextBlock" name="BasisOfPresentationAndPrinciplesOfConsolidationPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="bioa_LoanAndSecurityAgreementMember" name="LoanAndSecurityAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="bioa_TwoThousandTwentyFourEmployeeStockPurchasePlanMember" name="TwoThousandTwentyFourEmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
