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<!-- Creation Date :2022-10-20T11:38:55.1765+00:00 -->
<!-- Copyright (c) 2022 Donnelly Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="pstv_ConsecutiveBusinessDays" name="ConsecutiveBusinessDays" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_ContractEffectiveDate" name="ContractEffectiveDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_ContractTerminationDate" name="ContractTerminationDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_CpritGrantFundingTerm" name="CpritGrantFundingTerm" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_DebtInstrumentFloatingInterestRatePercentage" name="DebtInstrumentFloatingInterestRatePercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="pstv_DebtPrincipalRepaymentStartDate" name="DebtPrincipalRepaymentStartDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_DeferredGrantLiabilityCurrent" name="DeferredGrantLiabilityCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="pstv_GrantFundingPeriod" name="GrantFundingPeriod" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_GrantFundingTerm" name="GrantFundingTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_GrossProceedsFromIssuanceOfCommonStock" name="GrossProceedsFromIssuanceOfCommonStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="pstv_IncreaseDecreaseInGrantReceivable" name="IncreaseDecreaseInGrantReceivable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="pstv_InitialCommitmentFee" name="InitialCommitmentFee" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="pstv_InitialCommitmentShares" name="InitialCommitmentShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="pstv_LeaseCommencementDate" name="LeaseCommencementDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_LongTermDebtOutstandingThresholdAmount" name="LongTermDebtOutstandingThresholdAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="pstv_MasterServicesAgreementDate" name="MasterServicesAgreementDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_MasterServicesAgreementInitialTerm" name="MasterServicesAgreementInitialTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_MasterServicesAgreementTermsDescription" name="MasterServicesAgreementTermsDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_MaximumGrantAmountToBeReceivedAsPerGrantContract" name="MaximumGrantAmountToBeReceivedAsPerGrantContract" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="pstv_MaximumSharesToBeIssuedUnderAgreement" name="MaximumSharesToBeIssuedUnderAgreement" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="pstv_MaximumValueOfSharesToBeIssuedUnderAgreement" name="MaximumValueOfSharesToBeIssuedUnderAgreement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="pstv_MinimumLiquidityCovenantAmount" name="MinimumLiquidityCovenantAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="pstv_NonCashLeaseExpense" name="NonCashLeaseExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="pstv_NumberOfMaximumCommonSharesCanBeResale" name="NumberOfMaximumCommonSharesCanBeResale" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="pstv_NumberOfPreferredStockSharesExercised" name="NumberOfPreferredStockSharesExercised" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_NumberOfWarrantsExercised" name="NumberOfWarrantsExercised" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_OperatingLeasesExpiryYear" name="OperatingLeasesExpiryYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_PercentageIssuanceOfCommonStock" name="PercentageIssuanceOfCommonStock" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_PercentageOfAggregateAmountOfProceedsAwardedUnderCpritGrant" name="PercentageOfAggregateAmountOfProceedsAwardedUnderCpritGrant" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_PercentageOfCommissionOnGrossProceedsFromSaleOfCommonStock" name="PercentageOfCommissionOnGrossProceedsFromSaleOfCommonStock" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_PercentageOfGrantProceedsWithInterestNotExceedAnnually" name="PercentageOfGrantProceedsWithInterestNotExceedAnnually" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_PeriodExercisableFromTheDateOfIssuance" name="PeriodExercisableFromTheDateOfIssuance" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_PeriodForRegainCompliance" name="PeriodForRegainCompliance" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_PreferredStockDividendRatePercentageEliminatedDate" name="PreferredStockDividendRatePercentageEliminatedDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_ProceedsFromWarrantExercises1" name="ProceedsFromWarrantExercises1" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="pstv_SalesOrderTerm" name="SalesOrderTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAggregateIntrinsicValueRollForward1" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAggregateIntrinsicValueRollForward1" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_StockIssuedDuringPeriodSharesWarrantsExercise" name="StockIssuedDuringPeriodSharesWarrantsExercise" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="pstv_StockIssuedDuringPeriodSharesWarrantsExerciseShares" name="StockIssuedDuringPeriodSharesWarrantsExerciseShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_UnpaidOfferingCosts" name="UnpaidOfferingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="pstv_WarrantsIssuedUnderwrittenPublicOfferingPeriod" name="WarrantsIssuedUnderwrittenPublicOfferingPeriod" type="xbrli:gYearMonthItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_AtTheMarketOfferingProgramMember" name="AtTheMarketOfferingProgramMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_CanaccordGenuityLLCMember" name="CanaccordGenuityLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_CancerPreventionAndResearchInstituteOfTexasContractMember" name="CancerPreventionAndResearchInstituteOfTexasContractMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_CharlottesvilleMember" name="CharlottesvilleMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_DistributionAgreementMember" name="DistributionAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_JanuaryTwoThousandAndTwentyTwoDistributionAgreementMember" name="JanuaryTwoThousandAndTwentyTwoDistributionAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_LincolnParkCapitalFundLLCMember" name="LincolnParkCapitalFundLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_LoanAndSecurityAgreementMember" name="LoanAndSecurityAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_LoremVascularPteLtdMember" name="LoremVascularPteLtdMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_MedidataSolutionsIncMember" name="MedidataSolutionsIncMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_OptionsMember" name="OptionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_PiramalPharmaSolutionsIncMember" name="PiramalPharmaSolutionsIncMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_PreClinicalResearchStudyObligationsMember" name="PreClinicalResearchStudyObligationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_RepresentativeSeriesUWarrantMember" name="RepresentativeSeriesUWarrantMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SaleOfJapaneseSubsidiaryAndCertainAssetsMember" name="SaleOfJapaneseSubsidiaryAndCertainAssetsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SalesAgreementMember" name="SalesAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SeptemberTwoThousandAndTwentyTwoDistributionAgreementMember" name="SeptemberTwoThousandAndTwentyTwoDistributionAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SeriesAConvertiblePreferredStockMember" name="SeriesAConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SeriesBConvertiblePreferredStockMember" name="SeriesBConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SeriesCConvertiblePreferredStockMember" name="SeriesCConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SeriesUWarrantsMember" name="SeriesUWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_ServicesAgreementMember" name="ServicesAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_StockBasedCompensation2015EquityIncentivePlan1Member" name="StockBasedCompensation2015EquityIncentivePlan1Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_StockBasedCompensation2020EquityIncentivePlanMember" name="StockBasedCompensation2020EquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_TermLoanMember" name="TermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_TwentyTwentyPurchaseAgreementMember" name="TwentyTwentyPurchaseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_TwoThousandAndTwentyTwoPurchaseAgreementMember" name="TwoThousandAndTwentyTwoPurchaseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_TwoThousandEighteenRightsOfferingMember" name="TwoThousandEighteenRightsOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_TwoThousandTwentyTwoDistributionAgreementMember" name="TwoThousandTwentyTwoDistributionAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_UTHSALicenseAgreementMember" name="UTHSALicenseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_DisclosureOfLiquidityTextBlock" name="DisclosureOfLiquidityTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_LicenseAgreementDisclosureTextBlock" name="LicenseAgreementDisclosureTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_UseOfEstimatesTextBlock" name="UseOfEstimatesTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
</xsd:schema>
