Related Experiment Video
Updated: Aug 29, 2026

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations
Published on: January 8, 2013
Stability and bifurcation in an integral-delay model of cardiac reentry including spatial coupling in repolarization
Philippe Comtois1, Alain Vinet
1Institute of Biomedical Engineering, Université de Montréal and Research Centre, Hôpital du Sacré-Coeur, 5400 Gouin W., Montréal (Québec), Canada H4J 1C5.
Abstract:
We present the bifurcation analysis of a revised version of the integral-delay model [Courtemanche et al., Siam J. Appl. Math. 56, 119 (1996)] of reentry in a one-dimensional ring that includes a spatial coupling in the calculation of the action potential duration. This coupling is meant to reproduce the modulation of repolarization by the diffusive current flowing through the intercellular resistance. We show that coupling modifies the criterion for the stability of the period-1 solution, which is no longer uniquely related to the action potential restitution curve, but depends also on the degree of coupling between cells and on the dispersion relation of the velocity. Coupling also changes the scenario from an infinite-dimension Hopf bifurcation to a finite sequence of Hopf bifurcations that take place at different ring lengths.
Related Concept Videos
Cardiac Action Potential
The cardiac action potential process involves a series of phases characterized by the movement of ions across the cardiac cell membranes, leading to the depolarization and repolarization of the cardiac myocytes.
Ionic Basis of Cardiac Action Potentials
Electrophysiology of Normal Cardiac Rhythm
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Propagation of Action Potentials
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
Mechanism of Cardiac Arrhythmias
Current Growth And Decay In RL Circuits
