Bueno-Orovio et al. 2008

Key: bueno2008minimal

This cardiac electrophysiology model by Bueno-Orovio, Cherry, and Fenton is a four-variable extension of the model by Fenton & Karma 1998. It was designed to reproduce action potential shapes and the restitution characteristics of their duration and of conduction velocity.

The model comes with parameter sets for the epi- (default) and endocardium of the human ventricule, as well as a midwall parameter sets. Additionally, the authors provide parameter sets emulating the models by Priebe & Beuckelmann 1998 (PB) and Ten Tusscher et al. 2004 (TNNP).

References

  1. https://doi.org/10.1016/j.jtbi.2008.03.029

  2. https://doi.org/10.1063/1.166311

  3. https://doi.org/10.1161/01.RES.82.11.1206

  4. https://doi.org/10.1152/ajpheart.00794.2003

Figure

Figure illustrating the Bueno-Orovio et al. 2008 model.

Variables

  1. u = 0.0

  2. v = 1.0

  3. w = 1.0

  4. s = 0.0

Parameters

  • diffusivity_u = 0.1171

  • u0 = 0

  • u_u = 1.55

  • theta_v = 0.3

  • theta_w = 0.13

  • theta_vm = 0.006

  • theta_0 = 0.006

  • tau_v1m = 60

  • tau_v2m = 1150

  • tau_vp = 1.4506

  • tau_w1m = 60

  • tau_w2m = 15

  • k_wm = 65

  • u_wm = 0.03

  • tau_wp = 200

  • tau_fi = 0.11

  • tau_o1 = 400

  • tau_o2 = 6

  • tau_so1 = 30.0181

  • tau_so2 = 0.9957

  • k_so = 2.0458

  • u_so = 0.65

  • tau_s1 = 2.7342

  • tau_s2 = 16

  • k_s = 2.0994

  • u_s = 0.9087

  • tau_si = 1.8875

  • tau_winf = 0.07

  • w_infstar = 0.94

Source code

OpenCL kernel
const Real Hthvm = (u - theta_vm > 0) ? 1 : 0;
const Real Hthw = (u - theta_w > 0) ? 1 : 0;
const Real Hth0 = (u - theta_0 > 0) ? 1 : 0;
const Real Hthv = (u - theta_v > 0) ? 1 : 0;

const Real Hkm = (1 + tanh(k_wm * (u-u_wm))) / 2;
const Real Hko = (1 + tanh(k_so * (u-u_so))) / 2;
const Real Hks = (1 + tanh(k_s * (u-u_s))) / 2;

const Real tau_vm = tau_v1m + Hthvm*(tau_v2m-tau_v1m);
const Real tau_wm = tau_w1m + (tau_w2m-tau_w1m)*Hkm;
const Real tau_so = tau_so1 + (tau_so2-tau_so1)*Hko;
const Real tau_s = tau_s1 + Hthw*(tau_s2-tau_s1);
const Real tau_o = tau_o1 + Hth0*(tau_o2-tau_o1);

const Real vinf = 1 - Hthvm;
const Real winf = (1-Hth0)*(1-u/tau_winf) + Hth0*w_infstar;

const Real Jfi = -v*Hthv*(u-theta_v)*(u_u-u)/tau_fi;
const Real Jso = (theta_w>u) ? (u-u0)/tau_o : 1.0/tau_so;
const Real Jsi = -Hthw*w*s/tau_si;

const Real U = -(Jfi + Jso + Jsi);
const Real V = (theta_v>u) ? (vinf-v)/tau_vm : - v/tau_vp;
const Real W = (theta_w>u) ? (winf-w)/tau_wm : - w/tau_wp;
const Real S = (Hks-s)/tau_s;

*_new_u = u + dt * (U + _diffuse_u);
*_new_v = v + dt * V;
*_new_w = w + dt * W;
*_new_s = s + dt * S;

Additional metadata

keywords:
- excitable media
- electrophysiology
- heart
- generic
parameter sets:
  EPI:
    u0: 0
    u_u: 1.55
    theta_v: 0.3
    theta_w: 0.13
    theta_vm: 0.006
    theta_0: 0.006
    tau_v1m: 60
    tau_v2m: 1150
    tau_vp: 1.4506
    tau_w1m: 60
    tau_w2m: 15
    k_wm: 65
    u_wm: 0.03
    tau_wp: 200
    tau_fi: 0.11
    tau_o1: 400
    tau_o2: 6
    tau_so1: 30.0181
    tau_so2: 0.9957
    k_so: 2.0458
    u_so: 0.65
    tau_s1: 2.7342
    tau_s2: 16
    k_s: 2.0994
    u_s: 0.9087
    tau_si: 1.8875
    tau_winf: 0.07
    w_infstar: 0.94
  ENDO:
    u0: 0
    u_u: 1.56
    theta_v: 0.3
    theta_w: 0.13
    theta_vm: 0.2
    theta_0: 0.006
    tau_v1m: 75
    tau_v2m: 10
    tau_vp: 1.4506
    tau_w1m: 6
    tau_w2m: 140
    k_wm: 200
    u_wm: 0.016
    tau_wp: 280
    tau_fi: 0.1
    tau_o1: 470
    tau_o2: 6
    tau_so1: 40
    tau_so2: 1.2
    k_so: 2
    u_so: 0.65
    tau_s1: 2.7342
    tau_s2: 2
    k_s: 2.0994
    u_s: 0.9087
    tau_si: 2.9013
    tau_winf: 0.0273
    w_infstar: 0.78
  Midwall:
    u0: 0
    u_u: 1.61
    theta_v: 0.3
    theta_w: 0.13
    theta_vm: 0.1
    theta_0: 0.005
    tau_v1m: 80
    tau_v2m: 1.4506
    tau_vp: 1.4506
    tau_w1m: 70
    tau_w2m: 8
    k_wm: 200
    u_wm: 0.016
    tau_wp: 280
    tau_fi: 0.078
    tau_o1: 410
    tau_o2: 7
    tau_so1: 91
    tau_so2: 0.8
    k_so: 2.1
    u_so: 0.6
    tau_s1: 2.7342
    tau_s2: 4
    k_s: 2.0994
    u_s: 0.9087
    tau_si: 3.3849
    tau_winf: 0.01
    w_infstar: 0.5
  PB:
    u0: 0
    u_u: 1.45
    theta_v: 0.35
    theta_w: 0.13
    theta_vm: 0.175
    theta_0: 0.006
    tau_v1m: 10
    tau_v2m: 1150
    tau_vp: 1.4506
    tau_w1m: 140
    tau_w2m: 6.25
    k_wm: 65
    u_wm: 0.015
    tau_wp: 326
    tau_fi: 0.105
    tau_o1: 400
    tau_o2: 6
    tau_so1: 30.0181
    tau_so2: 0.9957
    k_so: 2.0458
    u_so: 0.65
    tau_s1: 2.7342
    tau_s2: 16
    k_s: 2.0994
    u_s: 0.9087
    tau_si: 1.8875
    tau_winf: 0.175
    w_infstar: 0.9
  TNNP:
    u0: 0
    u_u: 1.58
    theta_v: 0.3
    theta_w: 0.015
    theta_vm: 0.015
    theta_0: 0.006
    tau_v1m: 60
    tau_v2m: 1150
    tau_vp: 1.4506
    tau_w1m: 70
    tau_w2m: 20
    k_wm: 65
    u_wm: 0.03
    tau_wp: 280
    tau_fi: 0.11
    tau_o1: 6
    tau_o2: 6
    tau_so1: 43
    tau_so2: 0.2
    k_so: 2
    u_so: 0.65
    tau_s1: 2.7342
    tau_s2: 3
    k_s: 2.0994
    u_s: 0.9087
    tau_si: 2.8723
    tau_winf: 0.07
    w_infstar: 0.94
example discretisation:
  dt: 0.025
  dx: 0.26
  stimulus: 0.41
units:
  t: ms
  x: mm
  u: 1