Vulnerability to Reentry during the Acute Phase of
Myocardial Ischemia: a Simulation Study
JM Ferrero (Jr), B TrØnor, F Montilla, J SÆiz, JM Alonso, G Molt
Centre for Research and Innovation in Bioengineering, Universidad PolitØcnica, Valencia, Spain
Abstract
The aim of this work was to analyze the vulnerability
to reentry in a two-dimensional sheet of regionally-
ischemic and anisotropic myocardial tissue at different
stages of acute myocardial ischemia. We used computer
modelling in order to elucidate the main factors
responsible for initiation and maintenance of reentry.
Simulations were carried out using a modified version
of the Luo-Rudy-II model. The simulated 2D tissue
included a central ischemic zone, a border zone and a
normal zone and was prematurely stimulated. The degree
of severity of the central zone was changed depending on
the stage of acute ischemia.
Our results offer a theoretical explanation of the
existence of a vulnerable phase for reentry between the
fifth and tenth minute of acute ischemia, and lead to the
conclusion that (a) strong hyperkalemia is needed to
sustain reentry and (b) severe degrees of hypoxia tend to
reduce myocardial vulnerability to reentry.
1. Introduction
Ventricular tachycardia and ventricular fibrillation are
potentially mortal arrhythmias caused by reentrant
electrical activity in the heart ventricles [1]. Although
they may occur in normal healthy myocardium under
certain circumstances, they are usually a consequence of
the electrophysiological changes caused by acute
myocardial ischemia [1,2]. If ischemia is regional, the
inhomogeneities developed in the myocardium seriously
predispose the substrate to reentry [1-5].
Experimental evidence has shown that several minutes
after coronary artery occlusion, reentrant activity
following premature stimulation may have the form of a
figure-of-eight, with two parallel reentrant circuits
circulating around an area of functional block [3-6]. This
pattern may be stable (ventricular tachycardia) or may
destabilize, leading to ventricular fibrillation [3,5]. Other
experimental works show that the incidence of these
types of arrhythmias is higher during the fifth and sixth
minute after the occlusion, ceasing after 10 minutes of
ischemia [7,8].
In this paper, we present a theoretical study of the
mechanisms of figure-of-eight reentry during the acute
phase of regional myocardial ischemia, focusing on the
influence of the degree of hypoxia (and, therefore, the
degree of activation of the ATP sensitive K
+
current,
I
K(ATP)
[9,10]), acidosis and hyperkalemia on the
vulnerability to reentry. Mathematical models were used
to simulate electrical activity of a virtual tissue which
imitated the conditions of regional acute ischemia. The
main results show that the likelihood of figure-of-eight
reentry increases with time after the coronary artery
occlusion, reaches a peak and finally decreases to zero
after 10-12 minutes of ischemia.
2. Methods
The dynamic Luo-Rudy (phase II) equations [11,12]
were chosen as the model to simulate the cardiac action
potentials and the underlying ionic currents due to its
comprehensiveness. To simulate acute ischemia, its three
main components were considered. Firstly, hypoxia was
modelled by partially activating the ATP-sensitive K
+
current (I
K(ATP)
), using the mathematical formulation of
Ferrero Jr et al [10]. Secondly, hyperkalemia was
simulated by elevating extracellular K
+
concentration
([K
+
]
o
). Finally, acidosis was modelled by its effect on
the Na
+
and Ca
2+
currents [13,14] as described below.
Although the myocardium is a three dimensional
structure, we used a 5.5 cm x 5.5 cm two-dimensional
tissue in our simulations. Figure 1 shows the structure of
the virtual tissue which, in order to properly simulate
regional acute ischemia, comprises three different zones.
A circular shaped central ischemic zone (CZ, 20 mm in
diameter [15]) is formed by cells directly affected by the
lack of blood flow. Inside this zone, the values of the
parameters affected by ischemia were chosen to
correspond to their experimental values measured at
different instants after the onset of ischemia. [K
+
]
o
was
set to a value in the range 5.4-12.5 mmol/L [9,15] to
simulate hyperkalemia; the fast inward Na
+
current (I
Na
)
and the Ca
2+
current through the L-type channels (I
Ca(L)
)
were scaled by a factor f
pH
in the range 1.0-0.7 to
simulate the main effects of intracellular and extracellular
acidosis [13,14]; and intracellular levels of ATP and ADP
0276-6547/03 $17.00 © 2003 IEEE 425 Computers in Cardiology 2003;30:425-428.