Stability and sustained oscillations in a ventricular cardiomyocyte model

  • Bogdan Amuzescu
  • Adelina Georgescu
  • Gheorghe Nistor
  • Marin Popescu
  • Istvan Svab
  • Maria-Luisa Flonta
  • Alexandru Dan Corlan
Article

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 (Ist), the corresponding projection of the static bifurcation diagram in the (Ist, 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 (gsi and gK), 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 gsi, EADs and sustained high amplitude oscillations due to an unstable resting state may occur simultaneously.

Key words

Luo-Rudy I model discontinuous dynamical systems static bifurcation diagram basins of attraction numerical methods for bifurcation 

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Copyright information

© International Association of Scientists in the Interdisciplinary Areas and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bogdan Amuzescu
    • 1
  • Adelina Georgescu
    • 2
  • Gheorghe Nistor
    • 3
  • Marin Popescu
    • 3
  • Istvan Svab
    • 1
  • Maria-Luisa Flonta
    • 1
  • Alexandru Dan Corlan
    • 4
  1. 1.Department of Biophysics and Physiology, Faculty of BiologyUniversity of BucharestBucharestRomania
  2. 2.Academy of Romanian ScientistsBucharestRomania
  3. 3.Department of Mathematics and Computing SciencesUniversity of PitestiPitestiRomania
  4. 4.Cardiology DepartmentBucharest University Emergency HospitalBucharestRomania

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