Download Computer Simulation of Bundle Branch re

February 1998, Melboume AUSTRALIA
2nd lntemational Conference on Bioelectromagnetism
Computer Simulation of Bundle Branch Re-entry in a 3D Cellular Automata Model of
the Heart
Paul H. Fleisch”, and Paul Wach
Department of Biophysics, Institute of Biomedical Engineering, Technical University Graz,
Inffeldgasse 18, A-8010 Graz, Austria
Abstract: A 3D cellular automata model of the entire
The Purkinje fibre network was represented by a sheet
heart was used for modelling the spread of excitation of conducting tissue on the endocardial surface of the
and repolarization in the heart. By modelling ventricle. Anisotropic conduction of the ventricular
ventricular pacing and premature stimuli the myocardium was modelled by different conduction
inducibility of bundle branch re-entry was investigated
velocities in direction of fibres and perpendicular to it.
Under normal conditions bundle branch re-entry of
His bundle
type A and B were induced. A reduction of conduction
velocity in the bundle branches resulted in multiple reentrant echo beats as well as a wider zone of re-entrant
lefi posterior
activation.
.
INTRODUCTION
Akhtar et id. [l] was the first to report
electrophysiologic findings in human studies that supported
the hypothesis of macro re-entry via the His-Purkinje
system. More complex pattern resulting in fascicular ree n q have recently been reported and show the importance
of the stimulus site: [2]. In diseased hearts, sustained bundle
branch reentrant tachycardia can occur when there is
sufficient delay in His-Purkinje conduction such that the reentrant impulse can continue to propagate around the
bundle branches. Serious hemodynamic consequences, such
as sudden cardiac death or syncope, are frequently the
initial clinical replesentation of this arrhyhma .
In the last deciide the increase of computational power
supported the devdopment of several 3D cellular automata
models [3-61 for calculating the spread of excitation and
the body surface electrocardiogram of the human heart.
The purpose of this study was to simulate the spread of
excitation in a 3D computer model of the entire heart and
to test the inducibility of bundle branch re-entry.
METHOD
The described 3D cellular automaton model is an
extended version of the previously published computer
model [5-61. In brief the heart anatomy was discretized in a
Cartesian co-ordinate system by a 2.5 10-3mgrid including
11 different carckiac tissues for the normal and 4 for
pathologic conditions. To each element of heart anatomy
an effective refractory period (ERP) value was assigned. A
conduction velocity was assigned for propagation inside as
well as between different cardiac tissues. In addition the
conduction velocity was assumed to increase linearly after
end of the ERP till the end of the relative refractory period.
The earliest regions to excite the ventricle were the
conjunction elements at the terminations of the bundle
branches where the excitation propagated to the Purkinje
fibre network and ventricular myocardium. The left bundle
is separated into three branches which excited the high
anterior paraseptal region, the midseptum and the posterior
paraseptal apical n:gion of the ventricle 0.153s, 0.155s and
0.165s after start of sinus node activation. In the right
ventricle a single lbundle excited the lower right apex and
the right ventricular free wall 0.004s and 0.01s after left
high anterior paraseptal activation. These locations were all
close to the sites mentioned in literature [7] as being
activated first.
155
/’. left midseptal branch
left anterior paraseptal branch
Figure 1: Schematic representation of the modeled bundle
branches.
The ERP dynamic depending on pacing cycle length
was taken into consideration by assuming ERP dependence
on the preceding time interval in the atrium whereas in the
ventricle the formula pubished by Gulrajani [SI was used
for all ventricular tissues by taking values from literature
[9-lo]. Figure 4 shows the ERP values of ventricular
myocardium and Purkinje fibre after a step increase of
pacing frequency. Similar measurements were first
reported by M.J. Janse in mongrel dogs [113.
10
100
1000
340 1
I340
320
320
300
I300
EFIBRE
280
8
k
260
240
220
200
180 1 ventricular myocardium
160 -
180
I
160
Figure 2: ERP dynamic of ventricular myocardium and
Purkinje fibre after a shortening of the basic cycle length
from 0.7s to 0.4s.
The algorithm for calculating the excitation process is
based on a modified version of Huygen’s principle for
constructing wavefronts. Each element of the heart
~
February 1998, Melboume AUSTRALIA
2nd International Conference on Bioelectromagnetism
left ventricular stimulation at least in the normal human
heart. This reversed re-entrant circuit was labelled type C
and involved retrograde propagation via the right bundle
branch and antegrade activation via the left bundle branch.
In our model type A and B were found.
A possible application of the model is to use it for
patient oriented simulation. By this way the computer
model can be used as an additional decision tool for
pharmacological antimhykuc therapy or ablation
procedure. Fuaher the model can be used for calculating
the magneto- and electrocar&ogram based on a known
pathologic substrate.
geometry can be in either of three states “excitable“,
“excited or “waiting“ during the computer simulation
process [SI.
Ventricular pacing at a basic cycle length of 0.7s in
combination with premature stimuli at different coupling
intervals and different anatomical locations was modelled
for testing the inducibility of bundle branch re-entry.
According to reference [2] the EW of the right bundle
branch was assumed to be longer compared to the left
bundle.
Results
In case of left and right apical ventricular premature
stimuli (S2) the preferred retrograde route of impulse
propagation was through the left bundle branches. In
addition the increment of S2H2 conduction time between
premature stimulus (Sa) and E s bundle (€I2) tended to have
a linear pattern in relationship to decreasing SIS2 coupling
intervals similar to the results described in literature [2].
In a next step ventricular stimuli were applied near the
terminations of the bundle branches for inducing re-entrant
activation. Single premature stimuli near the right
ventricular &ee wall resulted in single ventricular echo
beats. The premature beats were retrograde blocked at the
right bundle branch but sufficiently delayed to excite the
left sided His-Purkinje system in retrograde and the right
bundle branch in anterograde direction resultant in V3.
These excitation front was then finally blocked in the HisF’urkinje system.
In the left ventricle the high anterior paraseptal region
was selected for inducing re-entrant activation. This time
the premature stimulation resulted in fascicular re-entry.
The excitation travelled in retrograde direction along the
posterior bundle and excited the ventricle (V3)through the
anterior bundle. Then the excitation was finally blocked in
the His-Purkinje system.
A reduction of conduction velocity (as found under
pathologic conditions) in the bundle branches resulted in
multiple re-entrant echo beats as well as in a wider S1S2
time interval of re-entrant activation. In addition the
anatomical region where re-entrant activation occurred
increased.
DISCUSSION
Several limitations and simplifications of the
electrophysiologic process must be kept in mind. The
excitation process was modelled on a macroscopic level and
omitted electrotonic interactions between cardiac fibres. A
coarse 2.5.10-3m grid was used for simulating the
excitation process in the entire heart. These simplifications
seemed to be justified due to the scope of modelling macro
re-entrant activation. In addition the difference between
antegrade and retrograde conduction velocity and effective
refractory period was not taken into consideration.
According to reference [2] the re-entrant circuit of HisPurkinje system re-entry can be classified into three types.
Type A is the typical re-entry phenomenon seen with right
ventricular stimulation where retrograde conduction is via
the left bundle branch and anterograde conduction is via
the right bundle branch. Type B is typical seen with left
ventricular stimulation. Type B is a fascicular re-entry
where retrograde conduction occurs via a left sided fascicle
and anterograde conduction is via the other fascicle. The
reversal of re-entrant circuit of type A was rarely seen with
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Acknowledgement
This work was supported by the Austrian Science
Foundation (FWF) grant number P-9995MED
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