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Stability and Oscillations in a Ventricular Cardiomyocyte Model Studied Using the Tools of Dynamic Systems Analysis and Bifurcation Theory
Marin Popescu,
Gheorghe Nistor,
Adelina Georgescu,
Alexandru Dan Corlan,
Bogdan Amuzescu,
C. Barbu,
Maria Luiza Flonta,
Biophysical Journal 96:664a-664a, 2009
ABSTRACT
Although ventricular fibers of the working myocardium in vivo or in
vitro do not feature pacemaker activity in normal conditions getting
depolarized and contracting only upon receiving current input from
the surroundings in certain pathological states they become prone to
generate sustained oscillations. These arrhythmogenic foci
(accelerated idioventricular rhythm) may quickly progress to
life-threatening arrhythmias. In order to get an insight into the
mechanisms underlying these rhythm disturbances we studied the
dynamics and bifurcation behavior of a simple mathematical model of
ventricular cardiomyocyte the Luo-Rudy I model using numerical and
analytical methods as described by Kurata et al. For different
configurations of parameters and initial conditions we found
equilibrium points (states where the field of variables vector
vanishes). These were further used to compute the eigenvalue vector
of the linearized system of differential equations at various values
of stimulus current (Istim) in the range of -5 to +5 uA/uF. Doubling
the time-dependent potassium conductance (gkt) resulted in sustained
self-oscillations in a narrow interval of Istim: (-0.7+0.3) uA/uF
for a reversal potential of the background current eb=0 mV and
(-3.0-2.1) uA/uF for the default value eb=-59.87 mV while for
normal gkt the system reached stable equilibrium over the entire
Istim range with either of the eb values tested.
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