BCF model

Bueno-Orovio - Cherry - Fenton (BCF) model. Temporal dynamics

du/dt = -(J_fi + J_so + J_si) ,
dv/dt = [1 - H(u - V_v)](v_∞ - v)/τ_v^- - H(u - V_v)v/τ_v,
dw/dt = [1 - H(u - V_w)](w_∞ - w)/τ_w^- - H(u - V_w)w/τ_w,
ds/dt = ((1 + tanh[k_s(u - U_s)])/2 - s)/τ_s,
J_fi = -vH(u - V_v)(u - V_v)(U_u - u)/τ_fi,
J_so = (u - U_o)[1 - H(u - V_w)]/τ_o + H(u - V_w)/τ_so,
J_si = -H(u - V_w)ws/τ_si,
τ_v^- = [1 - H(u - V_v]τ_v1 + H(u - V_v)τ_v2,
τ_s = [1 - H(u - V_w]τ_s1 + H(u - V_w)τ_s2 ,
τ_o = [1 - H(u - V_o)]τ_o1 + H(u - V_o)τ_o2 ,
τ_w^- = τ_w1 + (τ_w2 - τ_w1) (1 + tanh[k_w(u - U_w)])/2,
τ_so = τ_so1 + (τ_so2 - τ_so1^-) (1 + tanh[k_so(u - U_so)])/2,
v_∞ = 1 - H(u - V_v) ,
w_∞ = [1 - H(u - V_o)](1 - u/τ_w∞) + H(u - V_o)w_∞^*,

V mV = 85.7u - 84 .

U_o = 0
U_u = 1.58
V_v = 0.3
V_w = 0.015
V_v^- = 0.015
V_o = 0.006
τ_v1 = 60
τ_v2 = 1150
τ_v = 1.4506
τ_w1 = 70
τ_w2 = 20
k_w = 65
U_w = 0.03
τ_w = 280

τ_fi = 0.11
τ_o1 = 6
τ_o2 = 6
τ_so1 = 43
τ_so2 = 0.2
k_so = 2
U_so = 0.65
τ_s1 = 2.7342
τ_s2 = 3
k_s = 2.0994
U_s = 0.9087
τ_si = 2.8723
τ_w∞ = 0.07
w_∞^* = 0.94

Time is mesured in msec. Below you can explore the model for different parameter values.

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

Heart rhythms updated 8 Dec 2011