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IFAC-PapersOnLine 49-26 (2016) 026–031ScienceDirectAvailable 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.2016.12.098© 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1
ClemensZeile
EberhardScholz
SebastianSager
Clemens Zeile et al. / IFAC-PapersOnLine 49-26 (2016) 026–031 27ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1ASimplified2DHeartModeloftheWolff-Parkinson-WhiteSyndromeClemensZeile∗EberhardScholz∗∗SebastianSager∗∗MathematicsDepartment,UniversityofMagdeburg,39106Germany(e-mail:clemens.zeile@ovgu.de;sager@ovgu.de).∗∗CardiologyDepartment,UniversityHospitalHeidelberg,69120Germany,(e-mail:eberhard.scholz@med.uni-heidelberg.de)Abstract:Theenormousprogressmadeincomputationalcardiacelectrophysiologyduringthepastdecadeshasresultedinadiverserangeofmodelsandnumericalmethods.Ingeneral,researchershaveelaboratedhighlycomplexanddetailedsimulatorsonthecellandtissuelevel.Incontrast,therehasbeenalackofsimplifiedwhole-heartmodelsthatstudyspecificheartarrhythmias.Inthisstudy,weapproximatetheelectrophysiologyofWolff-Parkinson-WhiteSyndromewithsuchamodel.Inordertoreproducethecardiacanomaly,weapplytheso-calledbidomainapproachinvolvingpartialdifferentialequations.Resultsshowthatthesimulationsarerealistic,bothinECGgenerationandelectricactivationsequence.Ourassessmentofthemodelimplementationtakesintoaccountparameterandgeometryvariation,whichsupportsarealisticviewofmedicalaspects.OurinsilicoanalysisthushelpsprovideclearinsightsintothemechanismsofarrhythmiasandassociatedECGchanges.Keywords:Medicalsystems,heart,electricalsignalpropagation,cardiacarrhythmias,electrocardiogram,Wolff-Parkinson-Whitesyndrome1.INTRODUCTIONCardiovasculardisease(CVD)accountedfor17.3milliondeathsin2013,makingitapparentlytheleadingcauseofdeathglobally(Naghavietal.(2014)).Withagrowingnumberofsufferer,itisestimatedthat90%ofCVDispreventable(McGilletal.(2008)).Cardiacarrhythmiasconstituteamajorfactorforsuddencardiacdeath(SCD).Oneofthesearrhythmias,atrio-ventricularreciprocat-ingtachycardia(AVRT),isassociatedwiththeWolff-Parkinson-White(WPW)syndrome.Here,syndromein-volvesanaccessoryelectricalconductionpathway(AP)betweenatriumandventricleleadingtoprematurelystim-ulated,andthuscontracted,ventricles.SymptomsofWPWincludepalpitationsandsyncope.Onlyinrarecases(lessthan0.6%,Naghavietal.(2014))isWPWfatal,forexample,whenaccompaniedbyatrialfibrillation.Acommonmeansofdetectingthediseaseisaslurredupstrokeintheelectrocardiogram,referredtoasa”deltawave”.ForfurtherdetailsonWPW,wereferthereadertoPageetal.(2015).TheopensourceframeworkChaste(GaryRMirams(2013))isanexcellenttoolformultiscaleandcomplexsimulations,andonethatcanhandleverydetailedcardiacelectrophysiologycomputations.Ittakesintoaccountavarietyofanatomicalandphysiologicalfeaturessuchasfiberorientation,cellheterogeneities,anisotropy,aswellasrestitutionproperties.ThesimulatorsacCELLerate(Seemannetal.(2010)),CARP(Vigmond(2003)),andOpenCMISS(Christie(2009))aresimilar,highlydetailedpackages.However,theseveryrealisticapproachesrequireexten-sivecomputationpower,andoccasionallyeventheuseofsupercomputers.Forinstance,CARPneeds6.4hina64-processormachinetosimulatejust200msofcardiacactivity(Mitchell(2010)).Toreducecomputationaleffort,Balakrishnanetal.re-centlyintroduceda2Dwhole-heartmodelinMatlabthatfocusesonthesimulationofcardiacarrhythmias(Balakr-ishnanetal.(2015)).Themodelusesaphenomenologicalapproachtocomputeelectricalsignalpropagation,i.e.,cellsindiscreteformlinearlyexchangecurrentwitheightneighboringcells.Soviljetal.(2014)describesa2Dsim-plified(intermsofanatomy)approachthatalsocoversthesurroundingtorsotocomputerealisticECGgenera-tion,albeitapplyingthenumericallydemandingbidomainequations.WeadoptedthismodelforacomprehensiveWPWstudyimplementation,sinceitrepresentsagoodcompromisebetweenrealisticsimulation,computationalloadandflexibility.WerefertoTrayanova(2011),Claytonetal.(2011),andHenriquez(2014)forreviewsonwhole-heartmodeling.DuetoWPW’sinnocuousnesscomparedtootherar-rhythmias(e.g.,ventricularfibrillation),thereareonlyfewWPWsimulationapproaches,andtheseusemainlycellularautomata(Zhuetal.(2007),Fleischmannetal.(1996)).Tofillthisresearchgap,weexaminetheWPWsyndromeusinganaccuratebidomainmodel,simplifyingitonlyenoughtoachievereasonablecomputationaltimes.WeextendtheSovilj-Modelbymeansof:•geometricadoptionwithanaccessorypathway(socalledbundleofKent),6th IFAC Conference onFoundations of Systems Biology in EngineeringOctober 9-12, 2016. Magdeburg, GermanyCopyright © 2016 IFAC1•variationinposition,sizeandconductionvelocityparametersofthebundleofKent,•computationofintracardiacelectrograms,•inductionofextrasystoletosimulateAVRT.Fromsimulations,wecandetectrealisticECGbehavior,specifically,thecharacteristicslurredupstrokeoftheQRScomplexcalleddeltawave.ToourknowledgethisisthefirstWPWevaluationwithbothextensiveandsimplifiedbidomainapproachesincludingtorsomodeling.Thesimu-lationssupportaholisticviewontheconnectionsbetweenthemedicalanomalyanditsECGmorphology.2.METHODSInthissection,wedescribethemainfeaturesoftheSoviljmodelandreferthereadertoSoviljetal.(2014)forfurtherdetails.Wealsodescribeourmodelextensions.2.1AnatomicalmodelingThemodelcomprisestorso,lungs,heartandbloodintheheartchamber.Theheartitselfisrepresentedbyindivid-ualareasforthesinoatrialnode,atria,atrio-ventricular(AV)node,ventricles,bundleofHis,bundlebranchesandPurkinjefibers,compareFigure1.Ourcardiacgeometryhasarangeof11.5cminlengthand9cminwidth.WemodifiedthemodelwithanAPbetweenatriaandventricles,whichisvariedinsizeandposition.Fig.1.Anatomicalmodeling:leftlateralaccessorypath-wayinblue(1),sinoatrialnode(2),atria(3),AVnode(4),bundleofHis(5),bundlebranches(6),Purkinjefibers(7),ventricles(8),andpartsoflungs(9).2.2GoverningequationsThebidomainmodeliscrucialfortheelectricalpropaga-tionmodelingoftissue.Itdistinguishesintracellularfromextracellularspaceregardingconductivitespropertiesandanisotropy.Initsparabolic-ellipticformtransmembranevoltageVandextracellularvoltageφearegivenby∇·((σi+σe)∇φe+σi∇V)=I(vol)total,(1)χ(Cm∂V∂t+Iion(u,V)−∇·(σi∇(V+φe)))=I(vol)i,(2)whereV=φi−φeandφidenotestheintracellularvoltage(comparePathmanathanetal.(2010)).Theparametersinthissystemaretheintracellularconductivitytensorσi,theextracellularconductivitytensorσe,themembranecapacitanceperunitareaCm,andthethesurface-area-to-volumeratioχ.udenotesasetofcell-levelvariables,whichinfluenceIion(u,V),theioniccurrentperunitsurfacearea.ThesourcetermI(vol)ireflectstheintracellularstimulusperunitvolumeandI(vol)total=I(vol)i+I(vol)eisthesumofbothintracellularandextracellularstimuli.LetHdenotetheregionoccupiedbythecardiactissue.ThevariablesI(vol)total,I(vol)i,I(vol)e,andIionarealldefinedonHanddependontime.WestressthattheexistenceofastimuliterminthemodelisanextensioncomparedtotheSovijlmodel.ItisnecessarytomodelextrasystolesandthereforetosimulateAVRT.Theseequationsareappliedonlyonthemyocardiumarea.Onthecelllevel,themodifiedFitzHughNagumo(FHN)equationsareused∂u∂t=ke(V−BA−du−b),(3)Iion=kc1(V−B)[a−V−BA][1−V−BA]+kc2u,(4)wherea,b,c1,c2,d,e,k,A,B,areparameters.FortheAP,weappliedthephysiologicalparametersfromBaarsetal.(2011)(seeTable1).WevarytheconductionparametersTable1.APparametersabc1c2dekABσiσe0.1302.6110.01140-851032-802-80torepresenthigherandlowervelocitiesthaninthenormalventricularconductionsystem,whichissetto8mS/m.AsindicatedinTable1,σiandσerangesthenbetween2and80mS/m.Theextracellularvoltageφeinthetorso,lungs,andblood,i.e.,thepassivevolumeconductordomains,isgivenby∇·(−σp∇φe)=0,(5)whereσpdenotesthedomainspecificelectricalconductiv-ity.Fortheboundaryconditionsofthetorsoandheart,weassumezero-fluxforφiandthattheoutwardfluxequalstheinwardfluxforφe.2.3IntracardiacElectrogramsInordertomatchsimulationswithclinicalpractice,wecalculatetheusualintracardiacelectrogramsresultingfromcatheters.Forthis,welocateelectrodesinthemodelatthehighrightatrium(HRA),rightventricularapex(RVA),bundleofHis(HIS),andcoronarysinus(CS).Theelectrodesarebipolar,i.e.,HRA=HRA1−HRA2,andsoon.Hence,ineachregion,thereisapairofelectrodes(seeFig.3)thatisgroundedbythereferenceelectrodeattherightleg.Sincethecoronarysinusisnotcoveredanatomicallyinthemodel,weplacedthecorrespondingelectrodesbetweenthebloodchambersoftheleftatriumandventricle.2016 IFAC FOSBEOctober 9-12, 2016. Magdeburg, Germany2
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