Mitchell & Schaeffer 2003

Key: mitchell2003two

A model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it useful in numerical simulations, especially in two or three spatial dimensions where numerical efficiency is so important. (2) It can be understood analytically without recourse to numerical simulations. This allows us to determine rather completely how the parameters in the model affect its behavior which in turn provides insight into the effects of the many parameters in more realistic models. (3) It naturally gives rise to a one-dimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenon–subcritical alternans–that does not occur for the commonly used exponential map.

References

  1. https://doi.org/10.1016/S0092-8240(03)00041-7

Figure

Figure illustrating the Mitchell & Schaeffer 2003 model.

Variables

  1. V = 0.0

  2. h = 0.9

Parameters

  • diffusivity_V = 1.0

  • V_gate = 0.13

  • tau_in = 0.3

  • tau_out = 6.0

  • tau_open = 120.0

  • tau_close = 150.0

Source code

OpenCL kernel
const Real J_in = h * (V*V * (1.0 - V)) / tau_in;
const Real J_out = -V / tau_out;
*_new_h = h + dt*(((V < V_gate) ? (1.0 - h) / tau_open : -h / tau_close));
*_new_V = V + dt*(J_in + J_out + _diffuse_V);

Additional metadata

keywords:
- excitable media
- electrophysiology
- heart
- phenomenological
example discretisation:
  dt: 0.23
  dx: 3.3
  stimulus: 0.087
units:
  t: ms
  x: mm
  u: 1