[primary] [ecg] [articles] [all entries]

# Stability and sustained oscillations in a ventricular cardiomyocyte model.

### Bogdan Amuzescu,
Adelina Georgescu,
Gheorghe Nistor,
Marin Popescu,
Istvan Svab,
Maria Luiza Flonta,
Alexandru Dan Corlan,

### Interdiscip Sci. 4(1):1-18, 2012

## ABSTRACT

The Luo-Rudy I model, describing the electrophysiology of a
ventricular cardiomyocyte, is associated with an 8-dimensional
discontinuous dynamical system with logarithmic and exponential
non-linearities depending on 15 parameters. The associated stationary
problem was reduced to a nonlinear system in only two unknowns, the
transmembrane potential V and the intracellular calcium concentration
[Ca]( i ). By numerical approaches appropriate to bifurcation
problems, sections in the static bifurcation diagram were
determined. For a variable steady depolarizing or hyperpolarizing
current (I (st)), the corresponding projection of the static
bifurcation diagram in the (I (st), V) plane is complex, featuring
three branches of stationary solutions joined by two limit points. On
the upper branch oscillations can occur, being either damped at a
stable focus or diverted to the lower branch of stable stationary
solutions when reaching the unstable manifold of a homoclinic saddle,
thus resulting in early after-depolarizations (EADs). The middle
branch of solutions is a series of unstable saddle points, while the
lower one a series of stable nodes. For variable slow inward and K(+)
current maximal conductances (g (si) and g (K)), in a range between 0
and 4-fold normal values, the dynamics is even more complex, and in
certain instances sustained oscillations tending to a limit cycle
appear. All these types of behavior were correctly predicted by linear
stability analysis and bifurcation theory methods, leading to
identification of Hopf bifurcation points, limit points of cycles and
period doubling bifurcations. In particular settings,
e.g. one-fifth-of-normal g (si), EADs and sustained high amplitude
oscillations due to an unstable resting state may occur
simultaneously.
[Medline]