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Introduction
Despite the decisive progress in the therapy of variouscardiac
diseases cardiac arrhythmia still represents amajor reason for
sudden death. Phenomena contri-buting to cardiac arrhythmia show a
very complexinterdependence and act on different structural
levelsof the myocardium. Automaticity and triggered activi-ty are
known to be arrhythmogenic mechanisms actingat the cellular level,
where the ion channels of the cellmembrane are involved. On the
other hand the interact-ion between cells, the spatial orientation
of musclefibers and the heterogeneous composition of the
myo-cardium also contribute to the generation of arrhythmia[1]. The
clinical experience showed that the macrosco-pic phenomenon of
reentry is the most commonmechanism of cardiac arrhythmia. Aiming
at the de-velopment of antiarrhythmic therapy algorithms
asystematic model based analysis of cardiac reentrymechanisms and
their determinants is an importantprerequisite.
Methods
Hypotheses concerning the mechanisms of EADswhich are based on
findings from electrophysiologicalinvestigations were tested and
validated using a com-puter model of the cardiac action potential.
The com-
plexity of the membrane model (based on the Beeler-Reuter [2]
and the Luo-Rudy models [7]), was strictlylimited to the main
components required by thesehypotheses for two reasons: first, to
avoid effects unre-lated to the EAD mechanism and second to
minimizethe computation expense required by the model ofaction
potential propagation.As demonstrated by electrophysiological
investigat-ions EADs show to be correlated to the presence of
ß-adrenergic agents like isoproterenol which acts com-parable to
the sympathetic transmitter agent in vivo.The properties of the
calcium L-type channel areaffected by isoproterenol resulting in a
shift of theactivating and inactivating characteristics [3]. In
addi-tion a deceleration of the channel inactivation wasobserved in
[5], which is considered in the model by anincrease of the
inactivation time constant τf (Vm) by 13%. However the main effect
of ß-adrenergic stimulat-ion on the calcium L-type channel is a
pronouncedincrease of the Ca channel conductivity.Beside the
impacts on the calcium L-type channel thedynamic potassium channel
is also affected by isopro-terenol. ß-adrenergic stimulation
enhances the conduc-tivity of the dynamic potassium channel (in the
modelthe conductivity was increased by 25 %) whereas thenon-dynamic
one is not affected [4][6].
Mechanisms of Afterdepolarization Induced Cardiac Arrhythmia
I. WEISS, A. URBASZEK, M. SCHALDACHDepartment of Biomedical
Engineering, University of Erlangen-Nuremberg, Germany
Summary
Since early afterdepolarizations (EADs) have shown to trigger
cardiac arrhythmia the purpose of this model studyis to investigate
the mechanisms of their generation process and furthermore to
elucidate the mechanisms of EAD-induced reentry circuits. EADs are
generated due to the reactivation of the calcium L-type channel
during the repo-larization phase of the action potential. The most
critical consequence of EADs is the pronounced prolongation ofthe
action potential duration, which increases the dispersion of
refractoriness. This may locally induce an unidi-rectional
transient block of excitation spreading which favors reentrant
circuits.
Key Words
Cardiac arrhythmia, early afterdepolarizations, cardiac reentry,
computer model
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membrane slices are computed based on a coupled dif-ferential
equation system (discrete cable equation):
To induce EADs in the model the activating and inac-tivating
characteristics of the calcium L-type channeland the dynamic
potassium channel were shifted asindicated in table 1.Due to the
functional changes induced by isoproterenolthe coordination of the
d, f and x gate is altered. Aninflection point appears in the
course of the transmem-brane potential after which the action
potential beco-mes flatter and the repolarization is nearby
completelystopped. A slight disturbance of the sensitive
currentequilibrium (Ca/K) towards a small net inward currentwill
trigger a new membrane depolarization. The dgating variable
continues to increase, opening a so-called ‘calcium window’ (figure
1). The resultinginward calcium current accelerates itself the
depola-rization process acting as a positive feedback. Therapidly
increasing transmembrane potential conditionsthat the f gate begins
to close again and stops theavalanche like opening of calcium
channels. A newrepolarization phase starts closing the calcium
window.To investigate the impacts of EADs on the
propagationphenomenon a model of one dimensional action poten-tial
propagation was designed (figure 2).The fiber is considered to be
build up of a chain ofcylindrical membrane slices each being
represented bya membrane model. These models are interconnectedby
resistors representing the intracellular (Ri) and theextracellular
(Re) space. Gap junctions were taken intoaccount which showed to
reduce the propagation velo-city if their resistance is increased.
A detail of the equi-valent electrical network to be analyzed is
depicted infigure 3. The transmembrane potentials for each of
the
Tab. 1. Impacts of isoproterenol on the gating variables.
Figure 1. The mechanism of EAD generation. Precondition-ing
phase and calcium window.
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In the model study it is assumed that the volume inclu-ding the
main part of the extracellular current flow iscomparable to the
intracellular volume, hence:
velocity of action potential propagation. The propaga-tion
velocity is modulated by the ratio:
Figure 2. Model of the cardiac muscle fiber. The double
out-lined rectangle represents the model of ionic channels. Rµ
isthe myoplasm resistance.
Figure 3. Network elements of the fiber model and defini-tion of
current flow directions.
The geometrical cell dimensions are l = 10-2 cm,r0 = 10-3 cm
whereas the electrical characteristics areg = 6.7 mS/cm for the
electrolyte conductivity andcm = 1 µF/cm2 for the specific membrane
capacitance.Except of diseased regions the muscle fiber is
con-sidered to be homogeneous.The propagation phenomenon was
investigated forboth, a model of a linear and a ring shaped
musclefiber. It is assumed that only a fraction of the
totalmembrane area is effectively contributes to the mem-brane
capacitance. To reduce the computation expenseone excitable element
of the model was considered torepresent 5 cells. To adjust the
normal propagationvelocity under these border conditions to 1 m/s
thefraction of active membrane was chosen to be 85 %(cm,eff = 0.85
µF/cm2). A number of N=160 excitableelements corresponding to 800
was considered. Fornormal spread of excitation (propagation
velocity 1m/s) gap junctions were considered to be fully
opened(Rgap = 0 Ohm). In diseased tissue like ischemic regi-ons gap
junctions are known to close disconnecting thecells electrically.
It could be shown in the model thatan increase of the gap junction
resistance reduces the
Frequently reentry-based arrhythmia is observed whenregions of
the myocardium are temporary or persistentunexcitable. For example
an infarcted zone or an ope-ration scar is considered (figure
4).The excitation wave has to pass around the damagedtissue
following a ring shaped pathway. Based on thisobservation the
reentry phenomenon is investigated ina model of a ring shaped
muscle fiber (figure 5).EADs were induced within a small segment of
the ringmodel by modifying the model parameters of some ofthe
membrane slices. The resulting very pronounceddispersion of
refractoriness favors the start-up of areentry circuit which could
be initiated by two conse-cutive stimuli (S1,S2).
Results
The model study showed that EADs are generated dueto the
appearance of a so-called calcium windowduring the repolarization
phase of the action potential.The calcium window results because of
an alteration ofthe calcium L-type channel properties caused by
ß-adr-energic stimulation of cardiac tissue. In the reentrymodel
EADs were generated by assuming that the ß-adrenergic stimulation
increased the Ca channel con-
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rence of the ring fiber. It is called the recovery wave-length
because it is associated to the time required bythe sodium channel
to recover from inactivation. In themodel the ring diameter was
considered to be 2.55 cm(8 cm circumference) and the propagation
velocity wasreduced to 0.24 m/s by setting the gap junction
resi-stance to Rgap=8*Rµ. The action potential wave
lengthcorresponding to the APD90 parameter resulted to be4.6 cm.
The coupling interval S2-S1 was 380 ms resul-ting in a stable
reentry tachyarrhythmia correspondingto a cycle length of 329 ms
(182.4 min-1).
Discussion
In what concerns the EAD generation mechanism itcould be
concluded that the sarcoplasmic reticulumand the calcium
overload-induced release from the jun-ctional sarcoplasmic
reticulum are not necessarilyinvolved in this process. A critical
consequence ofEADs is the pronounced prolongation of the
actionpotential duration which contributes to the generationof a
local functional block of excitation spreadingfavoring reentrant
circuits. The initiation of the reen-trant circuit depends on the
relationship between thepropagation velocity, the longest way
between the sti-mulus location and the EAD zone and the
couplinginterval S2-S1. Whether the reentry wave
circulatesclockwise or counterclockwise depends on the locationof
the EAD zone. The counterclockwise direction ofrotation is achieved
if the EAD zone is placed in theleft branch as shown in the
discussed example. If theEAD zone is placed exactly diametrically
opposite to
ductivity 3.33-fold. The figure 5 indicates where EADsare
induced. The activating and inactivating characte-ristics of the
calcium L-type channel and the dynamicpotassium channel were
shifted as indicated in table 1.The fiber is stimulated as shown in
figure 6a (stimulusS1 at t = 0 ms). In the case of normal
propagation theexcitation spread takes place symmetrically in
bothbranches of the ring model. The wavefronts meet at
thediametrically opposite point of the stimulus locationand efface
each other. Afterwards both the left and theright branch repolarize
symmetrically (figure 6a).In the case of diseased tissue a region
of the ring fiberremains depolarized due to the occurrence of
EADs.The stimulus S2 is elicited 380 ms after S1 and propa-gates
normally until the EAD region is reached (figure6b). As a
consequence of the significantly prolongedaction potential duration
the excitation wave originat-ing from the S2-stimulus is blocked in
the branch ofthe ring fiber where EADs appeared (figure 6c).
Theexcitation propagates normally in the other branch buthas a
longer way to cover and arrives at the oppositeside of the cells
affected by EADs. Meanwhile thesecells have got fully or almost
fully repolarized (seearrow in figure 6d indicating the rise in the
baseline)and therefore the excitation wave can pass through
thisdomain reentering into the region where it
initiallystarted.However, stable reentry is possible only if the
wave-length corresponding to the refractory period of thepropagated
action potential is less than the circumfe-
Figure 4. Potential anatomic and functional reentry
path-ways.
Figure 5. Design of the ring model. EADs are induced with-in a
small segment of the ring-shaped fiber.
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136 June 1998
Progress in Biomedical Research
the stimulus location no reentry will occur. Stable re-entry,
however, is achieved only if the recovery wave-length is less than
the circumference of the ring.Out of this also the main finding
results giving eviden-ce that if reentry persists an excitable gap
exists whichallows the reentry to be suppressed by precisely
timedantitachycardia stimulation.
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Figure 6. Simulation results of cardiac reentry.
