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Modeling the Heart and
the Circulatory System
Editor
(cid:33)(cid:76)(cid:70)(cid:73)(cid:79)(cid:200)(cid:49)(cid:85)(cid:65)(cid:82)(cid:84)(cid:69)(cid:82)(cid:79)(cid:78)(cid:73)(cid:200)
MS&A
Modeling, Simulation & Applications
ABC
MS&A
Volume 14
Editor-in-Chief
A.Quarteroni
SeriesEditors
T.Hou
C.LeBris
A.T.Patera
E.Zuazua
Moreinformationaboutthisseriesat
http://www.springer.com/series/8377
Alfio Quarteroni Editor
Modeling the Heart
and the Circulatory System
Editor
AlfioQuarteroni
ÉcolePolytechnique Fédéralede Lausanne(EPFL)
Lausanne, Switzerland
ISSN2037-5255 ISSN2037-5263(electronic)
MS&A–Modeling,Simulation&Applications
ISBN978-3-319-05229-8 ISBN978-3-319-05230-4(eBook)
DOI10.1007/978-3-319-05230-4
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2014954657
©SpringerInternationalPublishingSwitzerland2015
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Lee,AndrewCookson,RadomirChabiniok,SimoneRivolo,EoinHyde,MatthewSinclair,Christian
Michler,TahaSochiandNicolasSmith.FromChapter3–MultiscaleModellingofCardiacPerfusion,
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Preface
This book contains a selection of the contributions presented at MPF2013 in June
2013inChia Laguna(Sardinia),the fifthedition ofa series devoted tothe mathe-
maticalandnumericalmodelingofphysiologicalflows.
The focus of this fifth symposium was on data analysis, digital imaging, math-
ematical models, and numerical simulation of the human circulatory system as a
whole,andmorespecificallyoncardiacmechanicsandelectrophysiology,heartper-
fusion,ventricularfluiddynamics,fluid-vesselwallinteractions,multiscaleanalysis
of blood rheology in small vessels, and system integration. The contributions pre-
sentedinthisbookprovideaveryinterestingoverviewonthestateoftheartofsome
ofthesetopicsandcontainseveraloriginalcontributionstothefield.Whatfollows
isashortaccountofthemostrelevantcontentsofeachchapter.
Inthefirstchapter,writtenbyN.Trayanovaandcoauthors,itisexplainedhow
biophysically detailed simulations can clarify experimental observations and help
reveal how organ-scale arrhythmogenic phenomena emerge from pathological ef-
fects at the tissue, cell, and protein levels. This “virtual heart” approach seeks to
use experiments and simulation to quantitatively characterize the action potential
responseofcardiaccellstoelectricalstimuli.
The construction of multiscale models of the electrical functioning of the heart
aimsatrepresentingtheintegrativebehaviorfromthemoleculetotheentireorgan
andisanessentialmethodologicalsteptowardsclinicalapplicationsofcardiacorgan
modeling.Thischapterfocusesonbothachievementsinmechanisticunderstanding
ofheartfunctionanddysfunctionandonthetrendsinthecomputationalmedicine
aspectofbiophysicallydetailedcardiacmodelingapplications.
Keyinattainingpredictivecapabilitiesofmultiscalebiophysicallydetailedcar-
diac models at the level of the organ has been the use of geometrically realistic
(typicallyMRI-orCT-based)modelsoftheventriclesandtheapplicationofdiffu-
siontensorimagingtomeasuretheanatomy,fiber,andsheetstructureoftheheart
inexvivostudies.Modelsofcardiacfunctionhavebenefittedsignificantlyfromthis
revolutioninmedicalimaging.Cardiacmodelshavebeenusedtogaininsightsinto
mechanismsofarrhythmiainmanydiseasesettingsandtounderstandhowexternal
currentscanterminateventriculararrhythmias.
vi Preface
Themostfrequentlyappliedapproachtomodelthemechanicsofcardiactissue
isbasedoncontinuummechanics. Thereis,however,anotherpossibilitybasedon
the use of discrete mechanical approaches. InChapter 2, written byA.V. Panfilov
and coauthors, discrete mechanical models are proposed for the simulation of the
mechanoelectricalfeedback(MEF)ontheprocessofspiralwaveformationincar-
diac tissue. The two principal ways of formulating discrete mechanical models of
cardiactissuearepresented.Theso-calledoff-latticemodels,whichdescribecellsas
notbeingrestrictedtoaregulargrid,allowthedescriptionofbiologicalphenomena
suchascelldivisionandgrowthwithoutcausingimmediatemechanicallong-range
effects.Lattice-basedmodelsareinsteadmoreappropriatefordescribingmechani-
callong-rangeinteractionssuchasthefiniteelasticdeformationsofthehearttissue.
MEFistheeffectofthedeformationofcardiactissueonitsexcitationprocesses.
This chapter shows that MEF substantially affects the process of spiral wave ini-
tiation and discusses several new mechanisms that are found using the proposed
discretemechanicalapproach.
Anotherstudy concernsthe effectofstructural changes incardiac tissue onthe
heart’smechanicalpropertiesand,further,howtheseeffectsmaycausecardiacar-
rhythmia.Theauthorsalsoproposeandinvestigatehowtocoupleadiscretemechan-
icalmodeltoareaction-diffusionmodelforcontinuouselectricalpulsepropagation.
InChapter3,N.Smithandco-authorsinvestigatethemechanismsgoverningcoro-
narybloodflowinhealthyanddiseasedcoronaries,withtheaimofunderstanding
therelationshipbetweenthestructureofthecoronaryvasculatureanditsfunction,
which exhibits distinct characteristics over multiple scales. More specifically, the
coupledfluid-structuremodelofcoronaryflowoutlinedinthischapteraimstobring
together the principal components of the system to establish an integrated frame-
workforinvestigatingand,later,predictingmyocardialperfusiononanindividual-
specificbasisinaphysiologicallyrelevantmanner.Tothisendamodelofflowin
macroscopicarteries[theleftanteriordescending(LAD),leftcircumflex(LCx),and
rightcoronary(RCA)arteries],amulticompartmentDarcymodelrepresentingmy-
ocardialperfusionoverarangeofvesselsizes,andaporoelasticmodelcapturingthe
flowphenomenainthebeatingheartareproposed.Waveintensityanalysisandtis-
suesignalinperfusionMRI,bothofwhichrepresentingthecurrentstateoftheartin
invasiveandnoninvasivecardiologicalexams,createabasisforclinicaltranslation
ofthepresentwork.
InChapter4,writtenbyF.Nicoudandcoauthors,thegeometryoftheheartcav-
ities and associated wall motion are extracted from 4D medical images while the
valvesoftheheartaresimulatedbyusinglow-ordergeometricalmodels.Equations
are solved using a fourth-order low-dissipative finite-volume scheme and a mixed
arbitraryLagrangian-Eulerian/immersedboundaryframework.
Recenttechnologicalinnovationsinimagingtechniqueshaveprovidedvaluable
opportunities for direct noninvasive in vivo assessment of hemodynamics. Blood
flow velocities can be measured in vivo using phase-contrast magnetic resonance.
Medicalimagesarethenusedtogenerateamovingpatient-specificdomain,inwhich
thebloodflowequationsaresolved.Heartgeometrymovementsaregeneratedfrom
a4Dsequence.Theauthorsdevotespecificattentiontothegenerationofhigh-quality
Preface vii
meshthatdeformsconsistentlywiththeheartmotion.Onsuchahigh-qualitygridthe
unsteadyturbulentflowissimulatedbyalargeeddysimulationtechniqueintheleft
heartdescribedbyECG-gated3DCTscan.Theresultsshowthatfluidinertiamakes
theflowdifferfromonecycletoanotherintheupperpartoftheleftatrium,where
thecollisionofthejetsissuingfromthepulmonaryveinsmakestheflowchaotic.In
theleftventricle,velocityfluctuationsarereportedmainlyduringlatediastole.
InChapter5,G.KarniadakisandH.Leipresentacomprehensivecomputational
frameworkbasedonthemesoscaledissipativeparticledynamics(DPD)methodto
investigatethethreekeyhallmarks(heterogeneousmorphology,rheology,andvaso-
occlusion)ofthehematological disordersicklecellanemia(SCA).Themultiscale
nature ofthe DPDmodel allows theauthors toaddress thedifferent dynamic pro-
cessesoverawiderangeoflengthandtimescalesinvolvedinthisdisease.Acoarse-
grainedstochasticmodelisbuiltuptorepresentthedevelopmentoftheintracellular
aligned sickle hemoglobin polymer domain for sickle red blood cells (SS-RBC).
Usingonlytheexperimentallymeasuredbulkgrowthrateofthesicklehemoglobin
polymer astheinput, themodel successfully predicted the typical sickle cell mor-
phologies without introducing further ad hoc assumptions. The inferred cell mor-
phologiesenabledtheauthorstofurtherexploretherheologyofheterogeneousSS-
RBCs suspensions with accurate prediction of the shear viscosity for the different
cellrigidityandmorphologies.Inparticular,theirsimulationsofthehemodynamics
of SS-RBC suspensions suggested that the sickle/elongated SS-RBC suspension,
once in microcirculation, does not induce vaso-occlusion by itself. Moreover the
flowresistanceinducedbythiscellgroupcouldbeevenlowerthanthatinducedby
othercellgroups.Despitebeingcounterintuitive,thisresultisconsistentwithrecent
experimentalstudiesonvaso-occlusioncrisis.
InChapter6,writtenbyA.Gizziandcoauthors,themathematicalmodelformula-
tionofthemechanochemicalcouplinginsinglecardiomyocytesbasedonanactive
strain approach has been analyzed and extended to realistic three-dimensional ge-
ometries. Theproposed activation mechanism is consistent with a thermodynamic
frameworkentailinganonlinearcouplingamongcalciumdynamicsandlocalstret-
ches.Thecontinuumapproachadoptedisalongthelineofrecentbio-chemomechan-
icalmodelsofsinglecellsformulatedintermsofactive-strainhyperelasticity.The
model is capable of reproducing the propagation of calcium waves and the corre-
spondingspontaneouscontractionwithinthecell,aswellasthebendingbehavior,
peculiarfeaturesofathree-dimensionalstructure.Afiniteelementmethodisusedto
discretizethemodelequations;asetofnumericalexperimentscomparingtwo-and
three-dimensionalreconstructedcardiomyocytegeometriesprovideevidenceofthe
mainfeaturesofthemodelanditsabilitytopredictcalciumpropagationpatternsand
contractility,ingoodagreementwithexperimentalobservations.Differentboundary
conditionsareconsideredtoreproducephysiologicalconstraints.Thecorresponding
resultingstresspatternsarethenanalyzed.
Chapter7,writtenbyK.A.MardalandO.Evju,developsacriticalreviewonthe
assumptionoflaminarflowinphysiologicalflowapplications. Mostfluidflowsin
ourhumanbodyarebelievedtobelaminarinhealthyindividuals,anexceptionbeing
thebloodflowintheheartandaorta.Ontheotherhand,variouspathologies,such
viii Preface
asatherosclerosisandaneurysms,involveanatomicalalterationscausingdistributed
flowandpossiblyeventurbulentflow.Thismayleadtoanunhealthymechanotrans-
duction(theprocesswherebycellsconvertmechanicalstimulitochemicalactivity,
whichisvital intheremodeling thatoccursinvessels), causingremodeling ofthe
vasculature that again increases flow disturbances. Recent research has therefore
challengedtheassumptionoflaminarflowinsuchpathologiesandplacedthefocus
onthepossibleroleoftransitionalorturbulentflow.
While the laminar regime and in many applications the fully developed turbu-
lentregimearereasonablywellunderstoodfrombothamodelingandanumerical
point of view, the transitional regime with occasional turbulence poses additional
challenges.Modelingisdifficultinparticularbecauseitischallengingtoprecisely
predicttheonsetoftheturbulentspots.Insteadofmodelingtheturbulence,onemight
increasetheresolutioninspaceandtimeandresolveallscalesoftheturbulentflow
numerically,atechniquecalleddirectnumericalsimulation(DNS).
Theauthorsaddressbloodflowincerebralaneurysms,discussingtheconsequen-
ces of the assumption of laminar flow, and validate the use of stabilization tech-
niquesandtimediscretizationsonnumericaldissipation.Theyalsoreviewclinical
andbiomechanicalfindingssuggestingthattransitionalflowiscommonoratleast
notunusualinseveralpathologies.Finallytheydiscusscerebralaneurysmsindepth
and show that for some aneurysms transition may occur at a Reynolds number as
lowas300.
In Chapter 8, P. Zunino and coauthors investigate the effects of poroelasticity
on fluid-structure interaction in arteries. Blood flow is modeled as an incompress-
ibleNewtonianfluidconfinedbyaporoelasticwall.Atwo-layermodelisusedfor
theartery,wheretheinnerlayers(theendotheliumandtheintima)behaveasathin
membranemodeledasalinearlyelasticKoitershell,whiletheouterpartoftheartery
(themediaandadventitia)isdescribedbytheBiotmodel.Theassumptionsaremade
thatthemembranecantransducedisplacementsandstressestothearteryandthatit
ispermeabletoflow.Becauseofporoelasticity,theinteractionofthefluidandthe
structure at the interface is more complicated than in the case of a standard fluid-
structureinteractionproblem.Theweakenforcementofinterfaceconditionsbased
on Nitsche’s type mortaring techniques guarantees stability. In particular, the au-
thors are interested in qualitatively characterizing how the presence of intramural
flowcoupledtothearterialwalldeformationaffectsthedisplacementfieldaswell
asthepropagationofpressurewaves.Theirresultssuggestthataccountingforthein-
tramuralplasmafiltrationsignificantlyaffectsthearterialwalldisplacementaswell
as the propagation of pressure waves. However, it is observed that resorting to a
poroelasticmaterialmodelisnotessentialtocapturetheseeffects.Asimplermodel
basedonDarcyequationscombinedwithapproximatekinematicconditionsmaybe
adequatetocapturesimilareffects.
Chapter9,writtenbyY.Vassilevskiandcoauthors,addressestheprocessofgen-
eratinganatomicalmeshesoftheentirehumanbody.Accordingtotheauthors,the
idealapproachforconstructionofananatomicallycorrect3Dgeometricmodelisto
produce3Dgeometryfromindividualmedicalimages(CT,MRI,orotherslice-like
data). This requires strong involvement of human expertise. Moreover, such data
Preface ix
can be unavailable or may feature low quality due to several factors. The authors
proposeanalternativeapproachthatconsistsinfittingareferenceanatomicallycor-
rectmodelbasedoneitherindividualdataordetailedpost-mortemexaminationor
aconventionaldatabase.
Forpatient-specificbodymeshingtheauthorsadoptafour-stagealgorithmwhich
reliesontheassumption thatthepatient hasthesamestructuralbodycomposition
as the reference VHP (the Visible Human Project) model, i.e., the same set of tis-
suesandorgans.First,theyapplythesemiautomaticsegmentationofthereference
VHP images. Second, they perform the anthropometric mapping of the reference
modeltothepatientdimensions.Third,forselectedcross-sectionplanestheygen-
erate a piecewise affine transformation to map the reference segmentation to the
patientsegmentationonthebasisofuser-definedcontrolpointsonbothreferences
andpatientimages.
For patient-specific vascular network reconstruction the open source library
VMTKisadoptedtoproducevascularcenterlinesonthebasisofCT/MRIdatafol-
lowedbytheautomated“skeletonization”algorithm.Theproducedvasculargraph
possessesallthenecessarygeometricdataforhemodynamicsimulation.Theauthors
demonstratetheapplicabilityoftheirapproachtopredictivepersonalizedpostsurgi-
calbloodflowsimulations.
Lausanne,October2014 AlfioQuarteroni
