doi:10.1016/j.ifacol.2016.12.150

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IFAC-PapersOnLine 49-26 (2016) 344–349ScienceDirectAvailable online at www.sciencedirect.com2405-8963 © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Peer review under responsibility of International Federation of Automatic Control.10.1016/j.ifacol.2016.12.150© 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.OptimumExperimentalDesignforPatientSpecificMathematicalLeukopeniaModelsFelixJost∗KristineRinke∗ThomasFischer∗∗EnricoSchalk∗∗SebastianSager∗∗InstituteofMathematicalOptimization,Otto-von-GuerickeUniversity,Magdeburg,39106Germany(e-mail:felix.jost@ovgu.de).∗∗DepartmentofHematologyandOncology,Otto-von-GuerickeUniversity,Magdeburg,39120Germany.Abstract:Mathematicalmodelsareessentialforsimulation-drivendecisionsupportforclinicaldoctors.Foranestimationofparametersforpatientspecificmodels,valuessuchasthenumberofcertainbloodcellsneedtobemeasured.Inthispaperwefocusonleukopenia,aclinicallyimportantsideeffectarisingfromthetreatmentofleukemiawithchemotherapy.Amathematicalleukopeniamodelispresenteddescribingthedynamicsofleukocytesandweshowthatthestandarddeviationsoftheparameterestimatesdependstronglyonthetimingofthemeasurements.Wediscusstheissueofmeasurementtimepointsfortwopatientsbeingintheconsolidationphaseofacutemyeloidleukemiaandprovideoptimalsolutions.Optimizedmeasurementtimepointsandthethusenabledaccuratesimulationshavealargeimpact:drugtreatmentscanbeadaptedindividuallyandpatientsmaysafelyleavethehospitalforlongerandmoreconvenienttimeintervals.Thedynamicsofleukocytesaremodeledbyasystemofordinarydifferentialequationsandthechemotherapywithcytarabineisdescribedbyapharmacokinetics/pharmacodynamicsmodelconsistingoftwocompartmentsandalog-linearfunctionrepresentingthedrugeffect.Themeasurementtimepointsareoptimizedbyoptimalexperimentaldesign.Withoptimalexperimentaldesignanaverageparameteruncertaintyreductionof57%(Pa-tient1)and80%(Patient2)canbeachievedcomparedtotheclinicalexperimentaldesigns,withthesametotalnumberofmeasurements.Theseencouragingresultsmotivatefurtherresearchandanextensionofthedatabasistomorepatients.Keywords:Leukopenia,acutemyeloidleukemia,parameterestimation,optimumexperimentaldesign,samplingdecision.1.INTRODUCTIONAclinicallyimportantsideeffectarisingfromthetreat-mentofleukemiawithchemotherapyisleukopenia.Inthispaper,wefocusonacutemyeloidleukemia(AML),acancerofthemyeloidstem/progenitorcellcompartmentofthebonemarrow.Immatureneoplasticmyeloidblastsproliferaterapidlyandsuppressanynormal,maturedleukocytecells(c.f.Arellanoetal.(2011)).Theoverpro-ductionofimmaturedneoplasticwhitebloodcellsharmsthefunctionoftheimmunesystemandofotherorganseventuallyleadingtodeath,seee.g.Panoskaltsisetal.(2003).Thechemotherapyregimenisdividedintotwophases(inductionandconsolidationphase),eachconsist-ingofseveralcycles.Themaingoaloftheinductionphaseistheeliminationofcancercells(immaturedblastcellsandneoplasticstem/progenitorcells).Aftertheinductionphasethenumberofcancercellsisreducedtoalowlevel,butfurtherchemotherapycyclesintheconsolidationphaseThisprojecthasreceivedfundingfromtheEuropeanResearchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchandinnovationprogramme(grantagreementNo647573),whichisgratefullyacknowledged.areneededtopreventarelapseofthedisease.However,thechemotherapyapplieddoesnotonlystopthegrowthofcancercells,butalsothegrowthofhealthyleukocytes.Hence,thereisacriticaltimeforpatientsinwhichthenumberofleukocytesisverylowandtheriskofbacterialinfectionsishigh(c.f.Malkaetal.(2012)).Webelieveinmathematicalmodeling,simulationandopti-mizationbeingtheenablingtechnologyforindividualizedmedicine,whereriskassessmentandtiminganddosageofdrugtreatmentsarebasedondecisionsupport.Inthisparticularscenarioweuseittopredictthedynamicsofleukocytesandtheinfluenceofchemotherapytowardshealthycells.Withanappropriatemodelinsilicosimu-lationsandforecastsofthediseaseandpredictionsabouttheleukocytes’nadircanbemadeforeachpatient.Theonsetanddurationofnadir,definingthelowestnumberofleukocytesafterchemotherapy,isanindicatorfortheriskofinfections.1.1ContributionEachpatienthasadifferentresponsetowardschemother-apyandthusalsodifferentdynamicsandrecoveryrates6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1OptimumExperimentalDesignforPatientSpecificMathematicalLeukopeniaModelsFelixJost∗KristineRinke∗ThomasFischer∗∗EnricoSchalk∗∗SebastianSager∗∗InstituteofMathematicalOptimization,Otto-von-GuerickeUniversity,Magdeburg,39106Germany(e-mail:felix.jost@ovgu.de).∗∗DepartmentofHematologyandOncology,Otto-von-GuerickeUniversity,Magdeburg,39120Germany.Abstract:Mathematicalmodelsareessentialforsimulation-drivendecisionsupportforclinicaldoctors.Foranestimationofparametersforpatientspecificmodels,valuessuchasthenumberofcertainbloodcellsneedtobemeasured.Inthispaperwefocusonleukopenia,aclinicallyimportantsideeffectarisingfromthetreatmentofleukemiawithchemotherapy.Amathematicalleukopeniamodelispresenteddescribingthedynamicsofleukocytesandweshowthatthestandarddeviationsoftheparameterestimatesdependstronglyonthetimingofthemeasurements.Wediscusstheissueofmeasurementtimepointsfortwopatientsbeingintheconsolidationphaseofacutemyeloidleukemiaandprovideoptimalsolutions.Optimizedmeasurementtimepointsandthethusenabledaccuratesimulationshavealargeimpact:drugtreatmentscanbeadaptedindividuallyandpatientsmaysafelyleavethehospitalforlongerandmoreconvenienttimeintervals.Thedynamicsofleukocytesaremodeledbyasystemofordinarydifferentialequationsandthechemotherapywithcytarabineisdescribedbyapharmacokinetics/pharmacodynamicsmodelconsistingoftwocompartmentsandalog-linearfunctionrepresentingthedrugeffect.Themeasurementtimepointsareoptimizedbyoptimalexperimentaldesign.Withoptimalexperimentaldesignanaverageparameteruncertaintyreductionof57%(Pa-tient1)and80%(Patient2)canbeachievedcomparedtotheclinicalexperimentaldesigns,withthesametotalnumberofmeasurements.Theseencouragingresultsmotivatefurtherresearchandanextensionofthedatabasistomorepatients.Keywords:Leukopenia,acutemyeloidleukemia,parameterestimation,optimumexperimentaldesign,samplingdecision.1.INTRODUCTIONAclinicallyimportantsideeffectarisingfromthetreat-mentofleukemiawithchemotherapyisleukopenia.Inthispaper,wefocusonacutemyeloidleukemia(AML),acancerofthemyeloidstem/progenitorcellcompartmentofthebonemarrow.Immatureneoplasticmyeloidblastsproliferaterapidlyandsuppressanynormal,maturedleukocytecells(c.f.Arellanoetal.(2011)).Theoverpro-ductionofimmaturedneoplasticwhitebloodcellsharmsthefunctionoftheimmunesystemandofotherorganseventuallyleadingtodeath,seee.g.Panoskaltsisetal.(2003).Thechemotherapyregimenisdividedintotwophases(inductionandconsolidationphase),eachconsist-ingofseveralcycles.Themaingoaloftheinductionphaseistheeliminationofcancercells(immaturedblastcellsandneoplasticstem/progenitorcells).Aftertheinductionphasethenumberofcancercellsisreducedtoalowlevel,butfurtherchemotherapycyclesintheconsolidationphaseThisprojecthasreceivedfundingfromtheEuropeanResearchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchandinnovationprogramme(grantagreementNo647573),whichisgratefullyacknowledged.areneededtopreventarelapseofthedisease.However,thechemotherapyapplieddoesnotonlystopthegrowthofcancercells,butalsothegrowthofhealthyleukocytes.Hence,thereisacriticaltimeforpatientsinwhichthenumberofleukocytesisverylowandtheriskofbacterialinfectionsishigh(c.f.Malkaetal.(2012)).Webelieveinmathematicalmodeling,simulationandopti-mizationbeingtheenablingtechnologyforindividualizedmedicine,whereriskassessmentandtiminganddosageofdrugtreatmentsarebasedondecisionsupport.Inthisparticularscenarioweuseittopredictthedynamicsofleukocytesandtheinfluenceofchemotherapytowardshealthycells.Withanappropriatemodelinsilicosimu-lationsandforecastsofthediseaseandpredictionsabouttheleukocytes’nadircanbemadeforeachpatient.Theonsetanddurationofnadir,definingthelowestnumberofleukocytesafterchemotherapy,isanindicatorfortheriskofinfections.1.1ContributionEachpatienthasadifferentresponsetowardschemother-apyandthusalsodifferentdynamicsandrecoveryrates6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1OptimumExperimentalDesignforPatientSpecificMathematicalLeukopeniaModelsFelixJost∗KristineRinke∗ThomasFischer∗∗EnricoSchalk∗∗SebastianSager∗∗InstituteofMathematicalOptimization,Otto-von-GuerickeUniversity,Magdeburg,39106Germany(e-mail:felix.jost@ovgu.de).∗∗DepartmentofHematologyandOncology,Otto-von-GuerickeUniversity,Magdeburg,39120Germany.Abstract:Mathematicalmodelsareessentialforsimulation-drivendecisionsupportforclinicaldoctors.Foranestimationofparametersforpatientspecificmodels,valuessuchasthenumberofcertainbloodcellsneedtobemeasured.Inthispaperwefocusonleukopenia,aclinicallyimportantsideeffectarisingfromthetreatmentofleukemiawithchemotherapy.Amathematicalleukopeniamodelispresenteddescribingthedynamicsofleukocytesandweshowthatthestandarddeviationsoftheparameterestimatesdependstronglyonthetimingofthemeasurements.Wediscusstheissueofmeasurementtimepointsfortwopatientsbeingintheconsolidationphaseofacutemyeloidleukemiaandprovideoptimalsolutions.Optimizedmeasurementtimepointsandthethusenabledaccuratesimulationshavealargeimpact:drugtreatmentscanbeadaptedindividuallyandpatientsmaysafelyleavethehospitalforlongerandmoreconvenienttimeintervals.Thedynamicsofleukocytesaremodeledbyasystemofordinarydifferentialequationsandthechemotherapywithcytarabineisdescribedbyapharmacokinetics/pharmacodynamicsmodelconsistingoftwocompartmentsandalog-linearfunctionrepresentingthedrugeffect.Themeasurementtimepointsareoptimizedbyoptimalexperimentaldesign.Withoptimalexperimentaldesignanaverageparameteruncertaintyreductionof57%(Pa-tient1)and80%(Patient2)canbeachievedcomparedtotheclinicalexperimentaldesigns,withthesametotalnumberofmeasurements.Theseencouragingresultsmotivatefurtherresearchandanextensionofthedatabasistomorepatients.Keywords:Leukopenia,acutemyeloidleukemia,parameterestimation,optimumexperimentaldesign,samplingdecision.1.INTRODUCTIONAclinicallyimportantsideeffectarisingfromthetreat-mentofleukemiawithchemotherapyisleukopenia.Inthispaper,wefocusonacutemyeloidleukemia(AML),acancerofthemyeloidstem/progenitorcellcompartmentofthebonemarrow.Immatureneoplasticmyeloidblastsproliferaterapidlyandsuppressanynormal,maturedleukocytecells(c.f.Arellanoetal.(2011)).Theoverpro-ductionofimmaturedneoplasticwhitebloodcellsharmsthefunctionoftheimmunesystemandofotherorganseventuallyleadingtodeath,seee.g.Panoskaltsisetal.(2003).Thechemotherapyregimenisdividedintotwophases(inductionandconsolidationphase),eachconsist-ingofseveralcycles.Themaingoaloftheinductionphaseistheeliminationofcancercells(immaturedblastcellsandneoplasticstem/progenitorcells).Aftertheinductionphasethenumberofcancercellsisreducedtoalowlevel,butfurtherchemotherapycyclesintheconsolidationphaseThisprojecthasreceivedfundingfromtheEuropeanResearchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchandinnovationprogramme(grantagreementNo647573),whichisgratefullyacknowledged.areneededtopreventarelapseofthedisease.However,thechemotherapyapplieddoesnotonlystopthegrowthofcancercells,butalsothegrowthofhealthyleukocytes.Hence,thereisacriticaltimeforpatientsinwhichthenumberofleukocytesisverylowandtheriskofbacterialinfectionsishigh(c.f.Malkaetal.(2012)).Webelieveinmathematicalmodeling,simulationandopti-mizationbeingtheenablingtechnologyforindividualizedmedicine,whereriskassessmentandtiminganddosageofdrugtreatmentsarebasedondecisionsupport.Inthisparticularscenarioweuseittopredictthedynamicsofleukocytesandtheinfluenceofchemotherapytowardshealthycells.Withanappropriatemodelinsilicosimu-lationsandforecastsofthediseaseandpredictionsabouttheleukocytes’nadircanbemadeforeachpatient.Theonsetanddurationofnadir,definingthelowestnumberofleukocytesafterchemotherapy,isanindicatorfortheriskofinfections.1.1ContributionEachpatienthasadifferentresponsetowardschemother-apyandthusalsodifferentdynamicsandrecoveryrates6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1OptimumExperimentalDesignforPatientSpecificMathematicalLeukopeniaModelsFelixJost∗KristineRinke∗ThomasFischer∗∗EnricoSchalk∗∗SebastianSager∗∗InstituteofMathematicalOptimization,Otto-von-GuerickeUniversity,Magdeburg,39106Germany(e-mail:felix.jost@ovgu.de).∗∗DepartmentofHematologyandOncology,Otto-von-GuerickeUniversity,Magdeburg,39120Germany.Abstract:Mathematicalmodelsareessentialforsimulation-drivendecisionsupportforclinicaldoctors.Foranestimationofparametersforpatientspecificmodels,valuessuchasthenumberofcertainbloodcellsneedtobemeasured.Inthispaperwefocusonleukopenia,aclinicallyimportantsideeffectarisingfromthetreatmentofleukemiawithchemotherapy.Amathematicalleukopeniamodelispresenteddescribingthedynamicsofleukocytesandweshowthatthestandarddeviationsoftheparameterestimatesdependstronglyonthetimingofthemeasurements.Wediscusstheissueofmeasurementtimepointsfortwopatientsbeingintheconsolidationphaseofacutemyeloidleukemiaandprovideoptimalsolutions.Optimizedmeasurementtimepointsandthethusenabledaccuratesimulationshavealargeimpact:drugtreatmentscanbeadaptedindividuallyandpatientsmaysafelyleavethehospitalforlongerandmoreconvenienttimeintervals.Thedynamicsofleukocytesaremodeledbyasystemofordinarydifferentialequationsandthechemotherapywithcytarabineisdescribedbyapharmacokinetics/pharmacodynamicsmodelconsistingoftwocompartmentsandalog-linearfunctionrepresentingthedrugeffect.Themeasurementtimepointsareoptimizedbyoptimalexperimentaldesign.Withoptimalexperimentaldesignanaverageparameteruncertaintyreductionof57%(Pa-tient1)and80%(Patient2)canbeachievedcomparedtotheclinicalexperimentaldesigns,withthesametotalnumberofmeasurements.Theseencouragingresultsmotivatefurtherresearchandanextensionofthedatabasistomorepatients.Keywords:Leukopenia,acutemyeloidleukemia,parameterestimation,optimumexperimentaldesign,samplingdecision.1.INTRODUCTIONAclinicallyimportantsideeffectarisingfromthetreat-mentofleukemiawithchemotherapyisleukopenia.Inthispaper,wefocusonacutemyeloidleukemia(AML),acancerofthemyeloidstem/progenitorcellcompartmentofthebonemarrow.Immatureneoplasticmyeloidblastsproliferaterapidlyandsuppressanynormal,maturedleukocytecells(c.f.Arellanoetal.(2011)).Theoverpro-ductionofimmaturedneoplasticwhitebloodcellsharmsthefunctionoftheimmunesystemandofotherorganseventuallyleadingtodeath,seee.g.Panoskaltsisetal.(2003).Thechemotherapyregimenisdividedintotwophases(inductionandconsolidationphase),eachconsist-ingofseveralcycles.Themaingoaloftheinductionphaseistheeliminationofcancercells(immaturedblastcellsandneoplasticstem/progenitorcells).Aftertheinductionphasethenumberofcancercellsisreducedtoalowlevel,butfurtherchemotherapycyclesintheconsolidationphaseThisprojecthasreceivedfundingfromtheEuropeanResearchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchandinnovationprogramme(grantagreementNo647573),whichisgratefullyacknowledged.areneededtopreventarelapseofthedisease.However,thechemotherapyapplieddoesnotonlystopthegrowthofcancercells,butalsothegrowthofhealthyleukocytes.Hence,thereisacriticaltimeforpatientsinwhichthenumberofleukocytesisverylowandtheriskofbacterialinfectionsishigh(c.f.Malkaetal.(2012)).Webelieveinmathematicalmodeling,simulationandopti-mizationbeingtheenablingtechnologyforindividualizedmedicine,whereriskassessmentandtiminganddosageofdrugtreatmentsarebasedondecisionsupport.Inthisparticularscenarioweuseittopredictthedynamicsofleukocytesandtheinfluenceofchemotherapytowardshealthycells.Withanappropriatemodelinsilicosimu-lationsandforecastsofthediseaseandpredictionsabouttheleukocytes’nadircanbemadeforeachpatient.Theonsetanddurationofnadir,definingthelowestnumberofleukocytesafterchemotherapy,isanindicatorfortheriskofinfections.1.1ContributionEachpatienthasadifferentresponsetowardschemother-apyandthusalsodifferentdynamicsandrecoveryrates6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1

FelixJost

Felix Jost et al. / IFAC-PapersOnLine 49-26 (2016) 344–349 345OptimumExperimentalDesignforPatientSpecificMathematicalLeukopeniaModelsFelixJost∗KristineRinke∗ThomasFischer∗∗EnricoSchalk∗∗SebastianSager∗∗InstituteofMathematicalOptimization,Otto-von-GuerickeUniversity,Magdeburg,39106Germany(e-mail:felix.jost@ovgu.de).∗∗DepartmentofHematologyandOncology,Otto-von-GuerickeUniversity,Magdeburg,39120Germany.Abstract:Mathematicalmodelsareessentialforsimulation-drivendecisionsupportforclinicaldoctors.Foranestimationofparametersforpatientspecificmodels,valuessuchasthenumberofcertainbloodcellsneedtobemeasured.Inthispaperwefocusonleukopenia,aclinicallyimportantsideeffectarisingfromthetreatmentofleukemiawithchemotherapy.Amathematicalleukopeniamodelispresenteddescribingthedynamicsofleukocytesandweshowthatthestandarddeviationsoftheparameterestimatesdependstronglyonthetimingofthemeasurements.Wediscusstheissueofmeasurementtimepointsfortwopatientsbeingintheconsolidationphaseofacutemyeloidleukemiaandprovideoptimalsolutions.Optimizedmeasurementtimepointsandthethusenabledaccuratesimulationshavealargeimpact:drugtreatmentscanbeadaptedindividuallyandpatientsmaysafelyleavethehospitalforlongerandmoreconvenienttimeintervals.Thedynamicsofleukocytesaremodeledbyasystemofordinarydifferentialequationsandthechemotherapywithcytarabineisdescribedbyapharmacokinetics/pharmacodynamicsmodelconsistingoftwocompartmentsandalog-linearfunctionrepresentingthedrugeffect.Themeasurementtimepointsareoptimizedbyoptimalexperimentaldesign.Withoptimalexperimentaldesignanaverageparameteruncertaintyreductionof57%(Pa-tient1)and80%(Patient2)canbeachievedcomparedtotheclinicalexperimentaldesigns,withthesametotalnumberofmeasurements.Theseencouragingresultsmotivatefurtherresearchandanextensionofthedatabasistomorepatients.Keywords:Leukopenia,acutemyeloidleukemia,parameterestimation,optimumexperimentaldesign,samplingdecision.1.INTRODUCTIONAclinicallyimportantsideeffectarisingfromthetreat-mentofleukemiawithchemotherapyisleukopenia.Inthispaper,wefocusonacutemyeloidleukemia(AML),acancerofthemyeloidstem/progenitorcellcompartmentofthebonemarrow.Immatureneoplasticmyeloidblastsproliferaterapidlyandsuppressanynormal,maturedleukocytecells(c.f.Arellanoetal.(2011)).Theoverpro-ductionofimmaturedneoplasticwhitebloodcellsharmsthefunctionoftheimmunesystemandofotherorganseventuallyleadingtodeath,seee.g.Panoskaltsisetal.(2003).Thechemotherapyregimenisdividedintotwophases(inductionandconsolidationphase),eachconsist-ingofseveralcycles.Themaingoaloftheinductionphaseistheeliminationofcancercells(immaturedblastcellsandneoplasticstem/progenitorcells).Aftertheinductionphasethenumberofcancercellsisreducedtoalowlevel,butfurtherchemotherapycyclesintheconsolidationphaseThisprojecthasreceivedfundingfromtheEuropeanResearchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchandinnovationprogramme(grantagreementNo647573),whichisgratefullyacknowledged.areneededtopreventarelapseofthedisease.However,thechemotherapyapplieddoesnotonlystopthegrowthofcancercells,butalsothegrowthofhealthyleukocytes.Hence,thereisacriticaltimeforpatientsinwhichthenumberofleukocytesisverylowandtheriskofbacterialinfectionsishigh(c.f.Malkaetal.(2012)).Webelieveinmathematicalmodeling,simulationandopti-mizationbeingtheenablingtechnologyforindividualizedmedicine,whereriskassessmentandtiminganddosageofdrugtreatmentsarebasedondecisionsupport.Inthisparticularscenarioweuseittopredictthedynamicsofleukocytesandtheinfluenceofchemotherapytowardshealthycells.Withanappropriatemodelinsilicosimu-lationsandforecastsofthediseaseandpredictionsabouttheleukocytes’nadircanbemadeforeachpatient.Theonsetanddurationofnadir,definingthelowestnumberofleukocytesafterchemotherapy,isanindicatorfortheriskofinfections.1.1ContributionEachpatienthasadifferentresponsetowardschemother-apyandthusalsodifferentdynamicsandrecoveryrates6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1OptimumExperimentalDesignforPatientSpecificMathematicalLeukopeniaModelsFelixJost∗KristineRinke∗ThomasFischer∗∗EnricoSchalk∗∗SebastianSager∗∗InstituteofMathematicalOptimization,Otto-von-GuerickeUniversity,Magdeburg,39106Germany(e-mail:felix.jost@ovgu.de).∗∗DepartmentofHematologyandOncology,Otto-von-GuerickeUniversity,Magdeburg,39120Germany.Abstract:Mathematicalmodelsareessentialforsimulation-drivendecisionsupportforclinicaldoctors.Foranestimationofparametersforpatientspecificmodels,valuessuchasthenumberofcertainbloodcellsneedtobemeasured.Inthispaperwefocusonleukopenia,aclinicallyimportantsideeffectarisingfromthetreatmentofleukemiawithchemotherapy.Amathematicalleukopeniamodelispresenteddescribingthedynamicsofleukocytesandweshowthatthestandarddeviationsoftheparameterestimatesdependstronglyonthetimingofthemeasurements.Wediscusstheissueofmeasurementtimepointsfortwopatientsbeingintheconsolidationphaseofacutemyeloidleukemiaandprovideoptimalsolutions.Optimizedmeasurementtimepointsandthethusenabledaccuratesimulationshavealargeimpact:drugtreatmentscanbeadaptedindividuallyandpatientsmaysafelyleavethehospitalforlongerandmoreconvenienttimeintervals.Thedynamicsofleukocytesaremodeledbyasystemofordinarydifferentialequationsandthechemotherapywithcytarabineisdescribedbyapharmacokinetics/pharmacodynamicsmodelconsistingoftwocompartmentsandalog-linearfunctionrepresentingthedrugeffect.Themeasurementtimepointsareoptimizedbyoptimalexperimentaldesign.Withoptimalexperimentaldesignanaverageparameteruncertaintyreductionof57%(Pa-tient1)and80%(Patient2)canbeachievedcomparedtotheclinicalexperimentaldesigns,withthesametotalnumberofmeasurements.Theseencouragingresultsmotivatefurtherresearchandanextensionofthedatabasistomorepatients.Keywords:Leukopenia,acutemyeloidleukemia,parameterestimation,optimumexperimentaldesign,samplingdecision.1.INTRODUCTIONAclinicallyimportantsideeffectarisingfromthetreat-mentofleukemiawithchemotherapyisleukopenia.Inthispaper,wefocusonacutemyeloidleukemia(AML),acancerofthemyeloidstem/progenitorcellcompartmentofthebonemarrow.Immatureneoplasticmyeloidblastsproliferaterapidlyandsuppressanynormal,maturedleukocytecells(c.f.Arellanoetal.(2011)).Theoverpro-ductionofimmaturedneoplasticwhitebloodcellsharmsthefunctionoftheimmunesystemandofotherorganseventuallyleadingtodeath,seee.g.Panoskaltsisetal.(2003).Thechemotherapyregimenisdividedintotwophases(inductionandconsolidationphase),eachconsist-ingofseveralcycles.Themaingoaloftheinductionphaseistheeliminationofcancercells(immaturedblastcellsandneoplasticstem/progenitorcells).Aftertheinductionphasethenumberofcancercellsisreducedtoalowlevel,butfurtherchemotherapycyclesintheconsolidationphaseThisprojecthasreceivedfundingfromtheEuropeanResearchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchandinnovationprogramme(grantagreementNo647573),whichisgratefullyacknowledged.areneededtopreventarelapseofthedisease.However,thechemotherapyapplieddoesnotonlystopthegrowthofcancercells,butalsothegrowthofhealthyleukocytes.Hence,thereisacriticaltimeforpatientsinwhichthenumberofleukocytesisverylowandtheriskofbacterialinfectionsishigh(c.f.Malkaetal.(2012)).Webelieveinmathematicalmodeling,simulationandopti-mizationbeingtheenablingtechnologyforindividualizedmedicine,whereriskassessmentandtiminganddosageofdrugtreatmentsarebasedondecisionsupport.Inthisparticularscenarioweuseittopredictthedynamicsofleukocytesandtheinfluenceofchemotherapytowardshealthycells.Withanappropriatemodelinsilicosimu-lationsandforecastsofthediseaseandpredictionsabouttheleukocytes’nadircanbemadeforeachpatient.Theonsetanddurationofnadir,definingthelowestnumberofleukocytesafterchemotherapy,isanindicatorfortheriskofinfections.1.1ContributionEachpatienthasadifferentresponsetowardschemother-apyandthusalsodifferentdynamicsandrecoveryrates6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1OptimumExperimentalDesignforPatientSpecificMathematicalLeukopeniaModelsFelixJost∗KristineRinke∗ThomasFischer∗∗EnricoSchalk∗∗SebastianSager∗∗InstituteofMathematicalOptimization,Otto-von-GuerickeUniversity,Magdeburg,39106Germany(e-mail:felix.jost@ovgu.de).∗∗DepartmentofHematologyandOncology,Otto-von-GuerickeUniversity,Magdeburg,39120Germany.Abstract:Mathematicalmodelsareessentialforsimulation-drivendecisionsupportforclinicaldoctors.Foranestimationofparametersforpatientspecificmodels,valuessuchasthenumberofcertainbloodcellsneedtobemeasured.Inthispaperwefocusonleukopenia,aclinicallyimportantsideeffectarisingfromthetreatmentofleukemiawithchemotherapy.Amathematicalleukopeniamodelispresenteddescribingthedynamicsofleukocytesandweshowthatthestandarddeviationsoftheparameterestimatesdependstronglyonthetimingofthemeasurements.Wediscusstheissueofmeasurementtimepointsfortwopatientsbeingintheconsolidationphaseofacutemyeloidleukemiaandprovideoptimalsolutions.Optimizedmeasurementtimepointsandthethusenabledaccuratesimulationshavealargeimpact:drugtreatmentscanbeadaptedindividuallyandpatientsmaysafelyleavethehospitalforlongerandmoreconvenienttimeintervals.Thedynamicsofleukocytesaremodeledbyasystemofordinarydifferentialequationsandthechemotherapywithcytarabineisdescribedbyapharmacokinetics/pharmacodynamicsmodelconsistingoftwocompartmentsandalog-linearfunctionrepresentingthedrugeffect.Themeasurementtimepointsareoptimizedbyoptimalexperimentaldesign.Withoptimalexperimentaldesignanaverageparameteruncertaintyreductionof57%(Pa-tient1)and80%(Patient2)canbeachievedcomparedtotheclinicalexperimentaldesigns,withthesametotalnumberofmeasurements.Theseencouragingresultsmotivatefurtherresearchandanextensionofthedatabasistomorepatients.Keywords:Leukopenia,acutemyeloidleukemia,parameterestimation,optimumexperimentaldesign,samplingdecision.1.INTRODUCTIONAclinicallyimportantsideeffectarisingfromthetreat-mentofleukemiawithchemotherapyisleukopenia.Inthispaper,wefocusonacutemyeloidleukemia(AML),acancerofthemyeloidstem/progenitorcellcompartmentofthebonemarrow.Immatureneoplasticmyeloidblastsproliferaterapidlyandsuppressanynormal,maturedleukocytecells(c.f.Arellanoetal.(2011)).Theoverpro-ductionofimmaturedneoplasticwhitebloodcellsharmsthefunctionoftheimmunesystemandofotherorganseventuallyleadingtodeath,seee.g.Panoskaltsisetal.(2003).Thechemotherapyregimenisdividedintotwophases(inductionandconsolidationphase),eachconsist-ingofseveralcycles.Themaingoaloftheinductionphaseistheeliminationofcancercells(immaturedblastcellsandneoplasticstem/progenitorcells).Aftertheinductionphasethenumberofcancercellsisreducedtoalowlevel,butfurtherchemotherapycyclesintheconsolidationphaseThisprojecthasreceivedfundingfromtheEuropeanResearchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchandinnovationprogramme(grantagreementNo647573),whichisgratefullyacknowledged.areneededtopreventarelapseofthedisease.However,thechemotherapyapplieddoesnotonlystopthegrowthofcancercells,butalsothegrowthofhealthyleukocytes.Hence,thereisacriticaltimeforpatientsinwhichthenumberofleukocytesisverylowandtheriskofbacterialinfectionsishigh(c.f.Malkaetal.(2012)).Webelieveinmathematicalmodeling,simulationandopti-mizationbeingtheenablingtechnologyforindividualizedmedicine,whereriskassessmentandtiminganddosageofdrugtreatmentsarebasedondecisionsupport.Inthisparticularscenarioweuseittopredictthedynamicsofleukocytesandtheinfluenceofchemotherapytowardshealthycells.Withanappropriatemodelinsilicosimu-lationsandforecastsofthediseaseandpredictionsabouttheleukocytes’nadircanbemadeforeachpatient.Theonsetanddurationofnadir,definingthelowestnumberofleukocytesafterchemotherapy,isanindicatorfortheriskofinfections.1.1ContributionEachpatienthasadifferentresponsetowardschemother-apyandthusalsodifferentdynamicsandrecoveryrates6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1OptimumExperimentalDesignforPatientSpecificMathematicalLeukopeniaModelsFelixJost∗KristineRinke∗ThomasFischer∗∗EnricoSchalk∗∗SebastianSager∗∗InstituteofMathematicalOptimization,Otto-von-GuerickeUniversity,Magdeburg,39106Germany(e-mail:felix.jost@ovgu.de).∗∗DepartmentofHematologyandOncology,Otto-von-GuerickeUniversity,Magdeburg,39120Germany.Abstract:Mathematicalmodelsareessentialforsimulation-drivendecisionsupportforclinicaldoctors.Foranestimationofparametersforpatientspecificmodels,valuessuchasthenumberofcertainbloodcellsneedtobemeasured.Inthispaperwefocusonleukopenia,aclinicallyimportantsideeffectarisingfromthetreatmentofleukemiawithchemotherapy.Amathematicalleukopeniamodelispresenteddescribingthedynamicsofleukocytesandweshowthatthestandarddeviationsoftheparameterestimatesdependstronglyonthetimingofthemeasurements.Wediscusstheissueofmeasurementtimepointsfortwopatientsbeingintheconsolidationphaseofacutemyeloidleukemiaandprovideoptimalsolutions.Optimizedmeasurementtimepointsandthethusenabledaccuratesimulationshavealargeimpact:drugtreatmentscanbeadaptedindividuallyandpatientsmaysafelyleavethehospitalforlongerandmoreconvenienttimeintervals.Thedynamicsofleukocytesaremodeledbyasystemofordinarydifferentialequationsandthechemotherapywithcytarabineisdescribedbyapharmacokinetics/pharmacodynamicsmodelconsistingoftwocompartmentsandalog-linearfunctionrepresentingthedrugeffect.Themeasurementtimepointsareoptimizedbyoptimalexperimentaldesign.Withoptimalexperimentaldesignanaverageparameteruncertaintyreductionof57%(Pa-tient1)and80%(Patient2)canbeachievedcomparedtotheclinicalexperimentaldesigns,withthesametotalnumberofmeasurements.Theseencouragingresultsmotivatefurtherresearchandanextensionofthedatabasistomorepatients.Keywords:Leukopenia,acutemyeloidleukemia,parameterestimation,optimumexperimentaldesign,samplingdecision.1.INTRODUCTIONAclinicallyimportantsideeffectarisingfromthetreat-mentofleukemiawithchemotherapyisleukopenia.Inthispaper,wefocusonacutemyeloidleukemia(AML),acancerofthemyeloidstem/progenitorcellcompartmentofthebonemarrow.Immatureneoplasticmyeloidblastsproliferaterapidlyandsuppressanynormal,maturedleukocytecells(c.f.Arellanoetal.(2011)).Theoverpro-ductionofimmaturedneoplasticwhitebloodcellsharmsthefunctionoftheimmunesystemandofotherorganseventuallyleadingtodeath,seee.g.Panoskaltsisetal.(2003).Thechemotherapyregimenisdividedintotwophases(inductionandconsolidationphase),eachconsist-ingofseveralcycles.Themaingoaloftheinductionphaseistheeliminationofcancercells(immaturedblastcellsandneoplasticstem/progenitorcells).Aftertheinductionphasethenumberofcancercellsisreducedtoalowlevel,butfurtherchemotherapycyclesintheconsolidationphaseThisprojecthasreceivedfundingfromtheEuropeanResearchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchandinnovationprogramme(grantagreementNo647573),whichisgratefullyacknowledged.areneededtopreventarelapseofthedisease.However,thechemotherapyapplieddoesnotonlystopthegrowthofcancercells,butalsothegrowthofhealthyleukocytes.Hence,thereisacriticaltimeforpatientsinwhichthenumberofleukocytesisverylowandtheriskofbacterialinfectionsishigh(c.f.Malkaetal.(2012)).Webelieveinmathematicalmodeling,simulationandopti-mizationbeingtheenablingtechnologyforindividualizedmedicine,whereriskassessmentandtiminganddosageofdrugtreatmentsarebasedondecisionsupport.Inthisparticularscenarioweuseittopredictthedynamicsofleukocytesandtheinfluenceofchemotherapytowardshealthycells.Withanappropriatemodelinsilicosimu-lationsandforecastsofthediseaseandpredictionsabouttheleukocytes’nadircanbemadeforeachpatient.Theonsetanddurationofnadir,definingthelowestnumberofleukocytesafterchemotherapy,isanindicatorfortheriskofinfections.1.1ContributionEachpatienthasadifferentresponsetowardschemother-apyandthusalsodifferentdynamicsandrecoveryrates6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ofleukocytes.Fortheidentificationofpatient-specificpa-rameterswecomparedifferentmeasurementtimepointsconcerningtheassociateduncertaintyoftheparameterestimate.Theoptimalchoicecanbedeterminedusingoptimumexperimentaldesign(OED),K ̈orkel(2002).Insystemandcellbiology,themethodologyofOEDbecomesmorevisibleandstandardindesigningexperimentscom-paredtomedicalapplications.AsareviewseeKreutzandTimmer(2009)andforapplicationexamplesseeBangaandBalsa-Canto(2008)andBandaraetal.(2009).Toourknowledge,applyingOEDtomedicalapplicationsisonlyinvestigatedbyafewpublishedpapers(c.f.KiranandSamavedham(2013)andAaronsandOgungbenro(2010)).Duetoitslargebenefits,morestudiesarerequiredtotransferthesemethodintoclinicalpractice.2.MATHEMATICALMODELINGOFLEUKOPENIASeveralmathematicalmodelshavebeenpublishedthatdescribethedynamicsofleukocytesduringchemotherapy,e.g.,inShochatetal.(2007)thedynamicsofneutrophils(partoftheleukocytes)inthecirculatingbloodaremod-eled,andinR ̆adulescuetal.(2016)asystemofdelaydifferentialequationsisproposed.Ourmodelisbasedonasemi-mechanisticpopulationpharmacokinetics(PK)/pharmacodynamics(PD)modelformyelosuppressionpublishedbyFribergetal.(2002).Themodelconsistsofonecelllinerepresentingleucocytesmodeledbyseveralcompartments(Fig.1).Thecellmat-urationinthebonemarrowismodeledbyoneprolifer-ationcompartmentandseveraltransitioncompartments.Onecompartmentdescribesthecirculationofcellsintheblood.DifferingfromFribergetal.(2002),wedescribetheleukopoiesiswithtwocompartments,onerepresentingtheproliferationphaseandtheotheronerepresentingthewholematurationphase.Aftermaturationtheleukocytesmigratetotheperipheralblooddescribedbyathirdcompartment.AfeedbackdependingonthesteadystatevalueofcirculatingleukocytesdenotedbyBaseandthenumberofleukocytesattimetisintroduced,triggeringtheproliferationofleukocytes.BoneMarrowBloodProliferation(x3)Transition(x4)Circulation(x5)ktrktrkcircktrcelldeath(duetochemo)Feedback=(Basex5)γFig.1.Schematicmodelofleukocytecells’dynamicsInadditiontothemodelingofproliferation,maturationandcirculationofleukocytesweincludethechemotherapyanditsinfluenceonthecellcycles.Firstly,wethereforemodeledthePKoftheusedagent(herecytarabine)usingatwo-compartmentmodel(e.g.PilariandHuisinga(2010);Figure2).Sincewehadnoinformationaboutthecytarabineconcentrations,weusedpublisheddata(Kernetal.(1997)).Secondly,theinfluenceofchemotherapyonthenumberofleukocytesismodeledbyalog-linearfunctionwiththeslopevaluefromPefanietal.(2014).Central(x1)Tissue(x2)DrugDosagek10k12k21Fig.2.Two-compartmentmodeldescribingthepharma-cokineticsofthedrugcytarabine.Themathematicalmodelisdefinedbythefollowingequa-tions,withx1andx2theamountofcytarabineinthetwocompartmentsofFigure2,andx3tox5thenumberofleukocytesinthethreecompartmentsofFigure1.Pharmacokinetics: ̇x1(t)=−k10·x1(t)−k12·x1(t)+k21·x2(t)+u(t)·BSAduration,(1) ̇x2(t)=k12·x1(t)−k21·x2(t),(2)Pharmacodynamics:E=slope·ln(1.0+x1(t)V·MMcyt),(3)LeukopeniaModel: ̇x3(t)=ktr·x3(t)·((Basex5(t))γ−1.0)−E·x3(t)(4) ̇x4(t)=ktr·(x3(t)−x4(t)),(5) ̇x5(t)=ktr·x4(t)−kcirc·x5(t).(6)Themodelparameters,constantsandcontrolswithinthemodelandtheirunitsarelistedinTable1.Table1.Modelparameters,constantsandcon-trolwithunitsParameterspUnitConstantsUnitktr1/dayk101/daykcirc1/dayk121/dayγ-k211/dayBase#·109/literVolumeliterslopeliter/molBodySurfaceArea(BSA)m2Controlu(t)UnitMolecularMass(MMcyt)g/molcytarabinedosemg/m2DurationdayForamoredetailedmodelanalysisanddiscussionseeRinkeetal.(2016).Forfurtherinvestigationsthesystemissum-marizedas ̇x(t)=f(x(t),u(t),p).3.PARAMETERESTIMATIONLetasetofone-dimensionalmeasurementsη1,...,ηmandknownvariancesσ2iattimepointst1,...,tmbegiven.Assumethatthemeasurementscanbedescribedbyanonlinearregressionηi=hi(x∗(ti),p∗)+εi(7)withthemodelresponsehicontainingthetruestatesx∗andtruebutunknownparametersp∗andtheinde-pendentandidenticallydistributedmeasurementerrorsεi∼N(0,σi/wi).Theadditionalvariableswi∈[0,1]are2016 IFAC FOSBEOctober 9-12, 2016. Magdeburg, Germany2

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