Stability and sustained oscillations in a ventricular cardiomyocyte model.

Area of Science:

• Computational Biology
• Cardiac Electrophysiology
• Nonlinear Dynamics

Background:

• The Luo-Rudy I model simulates ventricular cardiomyocyte electrophysiology.
• It involves an 8-dimensional discontinuous dynamical system with complex nonlinearities and 15 parameters.

Purpose of the Study:

• To analyze the stationary problem of the Luo-Rudy I model.
• To investigate the bifurcation dynamics of cardiomyocyte electrophysiology under varying conditions.

Main Methods:

• Reduced the stationary problem to a nonlinear system in transmembrane potential (V) and intracellular calcium concentration ([Ca]i).
• Employed numerical approaches for bifurcation analysis.
• Utilized linear stability analysis and bifurcation theory.

Main Results:

• Identified complex static bifurcation diagrams with three solution branches and limit points.
• Observed damped oscillations, early after-depolarizations (EADs), and sustained oscillations.
• Discovered Hopf bifurcation points, limit points of cycles, and period doubling bifurcations.

Conclusions:

• Bifurcation theory accurately predicts complex electrophysiological behaviors.
• Specific parameter variations can induce EADs and sustained oscillations, mimicking cardiac arrhythmias.
• The study provides insights into the mechanisms underlying cardiac instabilities.