Spiral wave dynamics and ventricular arrhythmias

184 Pages·2004·15.14 MB·English

Spiral wave dynamics and ventricular
arrhythmias
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OMSLAG KirstentenTusscher
DRUK FebodrukBV,Enschede
ISBN 90-393-3828-0
Spiral wave dynamics and ventricular
arrhythmias
Spiraal golf dynamica en ventriculaire aritmiee¨n
(meteensamenvattinginhetNederlands)
Proefschrift
terverkrijgingvandegraadvandoctoraandeUniversiteitUtrecht
opgezagvandeRectorMagnificus,Prof.Dr.W.H.Gispen,
ingevolgehetbesluitvanhetCollegevoorPromoties
inhetopenbaarteverdedigenop
maandag29november2004desmiddagste14.30uur
door
KirstenHendrikaWilhelminaJohannatenTusscher
geborenop23februari1976
teEnschede.
Promotor:
Prof.Dr.P.Hogeweg
FaculteitBiologie
UniversiteitUtrecht.
Co-Promotor:
Dr.A.V.Panfilov
FaculteitBiologie
UniversiteitUtrecht.
ThestudiesdescribedinthisthesiswereperformedatthedepartmentofTheor-
eticalBiologyandBioinformaticsatUtrechtUniversity. Theinvestigationswere
financiallysupportedbythePriorityProgramNonlinearSystemsoftheNether-
landsOrganizationforScientificResearch(NWO).
Voormijnouders

Contents
1 GeneralIntroduction 1
1.1 TheElectricalConductionPathwayoftheMammalianHeart . . . . 1
1.2 EvolutionaryandEmbryologicalDevelopmentoftheMammalian
Heart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 CardiacArrhythmias . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 TypesofReentrantCardiacArrhythmias . . . . . . . . . . . 4
1.3.2 MechanismsofReentrantCardiacArrhythmias . . . . . . . 5
1.3.3 CausesofReentrantVentricularArrhythmias. . . . . . . . . 7
1.4 Modelingincardiacelectrophysiology . . . . . . . . . . . . . . . . . 11
1.4.1 Whyusemodelsincardiacelectrophysiology . . . . . . . . 11
1.4.2 Modelformalism . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.3 FitzHugh-Nagumoandionicmodels . . . . . . . . . . . . . 13
1.5 ThisThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
I Theinfluenceofheterogeneityonspiralwavedynamics 23
2 ReentryinheterogeneouscardiactissuedescribedbytheLuo-Rudyven-
tricularactionpotentialmodel 25
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 MaterialandMethods . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.1 Spiraldynamicsinhomogeneoustissue . . . . . . . . . . . . 28
2.3.2 Spiraldynamicsintissuewithagradientofheterogeneity . 29
2.3.3 Figure-eightreentryinagradientofheterogeneity . . . . . . 35
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3 Influence of randomly distributed obstacles on wave propagation and
spiralwavedynamicsinexcitablemedia 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Wavepropagationin2Dmedia . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 Planewavepropagationin2D . . . . . . . . . . . . . . . . . 43
3.3.2 Curvatureeffectsonwavespeedin2D . . . . . . . . . . . . 43
3.3.3 Vulnerabilityinthepresenceofobstaclesin2D . . . . . . . . 46
3.3.4 Effectofobstaclesonspiralwaverotationin2D . . . . . . . 47
3.3.5 Effectofobstaclesonspiralbreakupin2D . . . . . . . . . . 48
3.4 Wavepropagationin3Dmedia . . . . . . . . . . . . . . . . . . . . . 52
3.4.1 Vulnerabilityinthepresenceofobstaclesin3D . . . . . . . . 52
3.4.2 Effectofobstaclesonspiralbreakupin3D . . . . . . . . . . 54
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
vii
Contents
4 Eikonalformulationoftheminimalprincipleforscrollwavefilaments 61
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Reformulationoftheminimalprinciple . . . . . . . . . . . . . . . . 62
4.3 Shortestpathwavealgorithms . . . . . . . . . . . . . . . . . . . . . 64
4.4 Numericalresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
II Reentrantarrhythmiasinhumanventriculartissue 71
5 Amodelforhumanventriculartissue 73
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 MaterialsandMethods . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2.2 MembraneCurrents . . . . . . . . . . . . . . . . . . . . . . . 79
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3.1 SingleCell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3.2 DifferentCelltypes . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.3 1-Dpropagation . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3.4 Spiralwaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6 Dynamicsofreentrantarrhythmiasinthehumanventricles 109
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.3.1 MonomorphicandPolymorphicVentricularTachycardia . . 114
6.3.2 VentricularFibrillation . . . . . . . . . . . . . . . . . . . . . . 115
6.3.3 OrganizationofVentricularFibrillation . . . . . . . . . . . . 119
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
ColorPlates 131
7 SummarizingDiscussion 135
7.1 AReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.2 Modelcomplexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.3 Modellimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.4 FutureDirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Bibliography 147
Samenvatting 165
CurriculumVitæ 171
ListofPublications 173
Dankwoord 175
viii
1
General Introduction
Information transmission in the form of propagating waves of electrical excita-
tionisthefastestformoflong-rangeinternalcommunicationavailabletoanim-
als.Itisusedinboththenervoussystemandtheheart.Inthenervoussystemthe
electricalwavesencodesuchdiverseinformationasmovements,perceptionsand
emotions,whereasinthehearttheelectricalwavesinitiatecontractonofthecar-
diacmuscle. Abnormalpropagationoftheelectricalexcitationwavehasserious
medical consequences, in the brain it is believed to be associated with epilepsy,
whereasintheheartitleadstocardiacarrhythmias.
Among the most dangerous cardiac arrhythmias are the so-called reentrant
ventricular arrhythmias: ventricular tachycardia and fibrillation, during which
cardiaccontractionrateissubstantiallyincreased,and,inthelattercase,becomes
completely disorganized. Ventricular fibrillation leads to sudden cardiac death
andisthelargestcategoricalcauseofnaturaldeathintheindustrializedworld.
In this introduction we briefly discuss the important role of the specialized
electricalconductionsystemoftheheartincontrollingnormalheartrhythm,and
the evolutionary and embryological development of the cardiac anatomy and
conduction system of the mammalian heart. We than describe the two above
mentioned reentrant arrhythmias that are the subject of this thesis, and discuss
their possible mechanisms. Finally, we focus on the role of modeling studies in
gainingabetterunderstandingofcardiacarrhythmiasandthemodelformalisms
thatareused. Weendwithashortoutlineofthemodelingstudiesdescribedin
thisthesis.
1.1 The Electrical Conduction Pathway of the Mam-
malian Heart
Themammalianheartconsistsoffourchambers,theleftandrightatriumandthe
leftandrightventricle. Therightatriumandventriclefunctionasapumpforthe
pulmonarycirculation,whereastheleftatriumandventriclefunctionasapump
for the systemic circulation. For an effective pumping of this four-chambered
heart a number of processes are important. First, all cells in the left and right
atriashouldcontractsynchronouslytoensureafastandpowerfulatrialcontrac-
tionandanefficientpumpingofbloodfromtheatriatotheventricles. Timingof
1
1GeneralIntroduction
thecontractionofcardiacmusclecellsisregulatedviaanelectricalsignalcalled
action potential or excitation that serves as a trigger for contraction. Cardiac
muscle cells generate such an action potential and subsequently contract when
stimulatedwithanelectricalcurrentofacertainstrength. Sincecardiaccellsare
electricallycoupledviaso-calledgapjunctions,anactionpotentialgeneratedina
particularcellservesasacurrentsourceforaneighboringcell. Asaconsequence
this neighboring cell also generates an action potential and contracts. Because
of the strength of the electrical coupling between cardiac cells, fast propagating
wavesofelectricalactivity,calledexcitationwaves,leadtovirtuallysynchronous
contraction of the cardiac muscle cells. Under normal conditions the excitation
wave of the heart originates in the sino-atrial (SA) node, located in the upper
right atrium. The SA node consists of so-called pacemaker cells that are auto-
matically electrically active: they spontaneously generate action potentials with
a certain frequency. From the SA node the electrical wave travels outward and
excitesallatrialcells,leadingtoatrialcontraction.
As a next step, there should be a delay in cardiac activation and contraction
between the atria and ventricles. This delay is necessary, because the ventricles
should contract after being filled with blood supplied by the atria and hence
afteratrialcontraction. Thedelayisregulatedbytheatrio-ventricular(AV)node.
The atria and ventricles are electrically isolated except for the atrio-ventricular
node,wheretheelectricalsignalispassedonfromtheatriatotheventricleswith
very low velocity, resulting in the required delay. From the AV node the elec-
trical signal is passed on to the His bundle, the left and right bundle branches
and the Purkinje fibers, which end on the endocardial surface of the left and
rightventricularwallandseptum,causinganelectricalwavetospreadthrough
the ventricles that initiates ventricular contraction (Eckert et al., 1988; Berne &
Levy,1993).Thestrongelectricalcouplingbetweenthecardiacmusclecellsagain
ensures a fast propagation of the excitation wave. This leads to a synchron-
ized, powerful ventricular contraction and an efficient pumping of blood into
thebloodstream.
Finally, cardiac output should be adapted to the oxygen demands of the or-
ganism.Toachievethis,theautonomousnervoussystemregulatesheartrateand
contraction force, with sympathetic innervation increasing heart rate and force,
andparasympatheticinnervationhavingtheoppositeeffect. Heartrateisregu-
latedbychangingthefiringfrequencyoftheSAnodeandtherateoftransmission
oftheAVnode(Eckertetal.,1988;Berne&Levy,1993). Contractionforceisregu-
latedbyadaptingintracellularcalciumhandlingandtissuerestitutionproperties.
1.2 Evolutionary and Embryological Development of
the Mammalian Heart
In very small animals transport occurs through passive diffusion. In larger an-
imals, where distances are too long for passive diffusion, hearts and circulatory
systemsevolvedinparallelwithincreasingbodysizestoefficientlytransportres-
piratorygases,nutrients,wasteproducts,hormonesandheat.
2