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  <xsd:element id="pstv_TaxCreditCarryforwardExpirationDate1" name="TaxCreditCarryforwardExpirationDate1" type="xbrli:stringItemType" 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_IncomeTaxesLineItems" name="IncomeTaxesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SummaryOfSignificantAccountingPoliciesLineItems" name="SummaryOfSignificantAccountingPoliciesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <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_BardaContractMember" name="BardaContractMember" 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_CommitmentFeeMember" name="CommitmentFeeMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_DevelopmentMember" name="DevelopmentMember" 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_NanoTxLicensesAgreementMember" name="NanoTxLicensesAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_OfficeLaboratoryAndStorageSpaceMember" name="OfficeLaboratoryAndStorageSpaceMember" 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_TwentyTwentyRepurchaseAgreementMember" name="TwentyTwentyRepurchaseAgreementMember" 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_IncomeTaxesTable" name="IncomeTaxesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="pstv_SummaryOfSignificantAccountingPoliciesTable" name="SummaryOfSignificantAccountingPoliciesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <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_ScheduleOfOperatingAndFinancingLeaseLiabilityMaturityTableTextBlock" name="ScheduleOfOperatingAndFinancingLeaseLiabilityMaturityTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="pstv_ScheduleOfRightOfUseAssetsAndLeaseLiabilitiesTableTextBlock" name="ScheduleOfRightOfUseAssetsAndLeaseLiabilitiesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
</xsd:schema>
