Fenton-Karma model

Fenton-Karma model. Temporal dynamics

A simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others) was introdused in [1].

du/dt = -J_fi - J_so - J_si,
dv/dt = Θ(u_c - u)(1 - v)/τ_v^- - Θ(u - u_c)v/τ_v⁺
dw/dt = Θ(u_c - u)(1 - w)/τ_w^- - Θ(u - u_c)w/τ_w⁺
J_fi = -vΘ(u - u_c)(1 - u)(u - u_c)/τ_d ,
J_so = uΘ(u_c - u)/τ_o + Θ(u - u_c)/τ_r ,
J_si = -w(1 + tanh[k(u - u_c^si)])/2τ_si.

τ_d = 1/5.8
τ_r = 130
τ_si = 127
τ_o = 12.5
τ_v⁺ = 10
τ_v^- = 18.2

τ_w⁺ = 1020
τ_w^- = 80

u_c = 0.13
u_c^si = 0.85
k = 10

Below you can explore the model for different parameter values.

Uo Vo Wo Ymax dt it
u, v, w variables are black, blue and red curves. The script makes 1000 it time steps dt.

[1] Flavio Fenton and Alain Karma Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillationa Chaos 8, 20 (1998)

Heart rhythms updated 7 Dec 2011