Breakdown of re-entry caused by transmural
APD dispersion and fibre orientation
Richard H Clayton, Arun V Holden.
School of Biomedical Sciences, University of Leeds, UK.
http://www.cbiol.leeds.ac.uk
1 - Introduction
3 – Biophysically detailed model
Ventricular fibrillation (VF) is a deadly cardiac arrhythmia, and one route to VF
is breakdown of a re-entrant wave. Several mechanisms underlying
breakdown have been proposed including steepness of the action potential
duration (APD) restitution curve and the effect of rotational anisotropy in the
ventricular wall.
In our second group of simulations we simulated re-entry in LV and RV wedges from the
Auckland canine ventricles, with and without rotational anisotropy, with no-flux
boundaries, and with excitability described by the Luo-Rudy phase 1 model [Circulation
1991;68:1501-1526].
We used both a simplified model of cellular cardiac electrophysiology in a slab
of tissue representing part of the LV free wall, and a biophysically detailed
model in anatomically detailed models of the LV and RV free walls.
2 – Simplified model
Transmural differences in the expression of
several ion channels contribute to differences in
the shape and duration of the action potential. We
approximated these differences by changing only
the K+ conductance gK of the LR1 model. APD
restitution curves for the endocardial layer (gK =
0.2 mS/cm2, blue) and epicardial layer (gK = 0.4
mS/cm2, red) are shown. The Ca2+ conductance
gCa was set to 0.03 mS/cm2 to give stable re-entry
for this range of gK.
250
200
APD (ms)
The ventricles are electrically heterogeneous, and endocardial tissue has a
longer APD than epicardial tissue. As a result, re-entry has a shorter period in
epicardial tissue, and the transmural difference in period could pull apart a
transmural re-entrant wave. The aim of this study was to use a computational
model to investigate the relative roles of rotational anisotropy and transmural
APD differences in destabilising re-entry.
150
100
50
0
0
250
500
750
1000
Diastolic Interval (ms)
The figures below show snapshots of activation and filaments 750 ms after initiation of reentry in the LV (left) and RV (right) for the uniform isotropic (top), uniform anisotropic
(middle), and nonuniform anisotropic (bottom) models.
In our first group of simulations we simulated action potential propagation in a 60 x 60 x
10 mm monodomain with and without 120º rotational anisotropy, with no-flux boundaries,
and with excitability described by the Fenton Karma (FK) model [Chaos 1998;8:20-47].
140
120
100
APD (ms)
We approximated transmural differences in APD
changing the parameter usic from 0.85 to 0.5 along
the short axis of the slab. APD restitution curves
for usic = 0.85 (red) and usic = 0.5 (blue) are shown
right. A linear change in usic resulted in a linear
change in APD with a total ∆APD of around 25%.
Re-entry in slabs with uniform usic of between 0.85
and 0.5 was stable, so we could use this model to
assess independently the effects of rotational
anisotropy and transmural APD differences on the
stability of re-entry with a transmural filament.
80
60
40
20
0
0
100
200
300
Diastolic Interval (ms)
The figure shows snapshots of activation on the top, middle and bottom surfaces of
isotropic (left) and anisotropic (right) simulations, 150 ms after initiation of re-entry.
8
8
7
7
6
6
Number of filaments
Number of filaments
The figure below shows filament behaviour in isotropic (left)and anisotropic (right)
simulations. In the isotropic simulations breakdown tended to be short-lived. Rotational
anisotropy produced longer and more persistent filaments.
The figures below show the number of filaments for the isotropic (blue), anisotropic
(orange), and nonuniform anisotropic (red) models. All six models showed breakdown,
but the number and persistence of filaments was greater for the RV simulations.
5
4
3
2
138
314
142
318
150
0
200
0.65
0.75
326
154
330
158
334
0.5
0.85
0.65
0.75
800
0
1000
200
400
600
800
1000
Time (ms)
3
3
2.5
2.5
2
1.5
1
0.5
0
2
1.5
1
0.5
0
anisotropic model
anisotropic with
APD differences
isotropic model
anisotropic model
anisotropic with
APD differences
0.85
3
Number of filaments
3
Number of filaments
0.55
600
Time (ms)
isotropic model
0.55
2
322
The figures below show the number of filaments for slabs with no (blue), modest (purple,
pink, and orange) and large (red) APD differences. The extent of breakdown depended
on the transmural difference in APD. In some of the isotropic simulations re-entry self
terminated, but in the anisotropic simulations breakdown was persistent.
0.5
400
Mean number of filaments
Time
(ms)
146
3
0
0
Mean number of filaments
Time
(ms)
310
4
1
1
134
5
2
1
0
4 – Conclusions
2
1
0
0
200
400
600
Time (ms)
800
1000
0
200
400
600
800
1000
Time (ms)
This work is supported by the UK EPSRC, UK MRC, and the British Heart Foundation
Transmural differences in APD are able to destabilise re-entry both in
simplified and in biophysically detailed models. Regional differences in APD
act synergistically with rotational anisotropy to break a single re-entrant wave
into multiple wavelet VF. This effect was more potent in the RV, where the
gradient of both APD and fibre rotation is higher than in the LV.
We are grateful to Professor Peter Hunter and his group in Auckland for making the
Auckland heart geometry available.