Kabus et al. 2024

Key: kabus2024fast

This data-driven model was trained on optical voltage mapping data of human conditionally immortalised atrial myocyte (hiAM) monolayers. It uses a simple polynomial, a standard-deviation-based approximation for the gradient, and an exponential moving average to predict the updated value of the signal. As it can work with much higher time steps, it is computationally cheaper than the reaction-diffusion based models.

References

  1. https://doi.org/10.1016/j.compbiomed.2024.107949

Variables

  1. u = 0.02

  2. a = 0.1

  3. g = 0.0

Parameters

  • umin = -0.5

  • umax = 1.25

  • alpha = 0.008

  • dist = 8

  • wagu = -0.413919278037366

  • wgu = 0.193407562922741

  • wau = 0.0263083048287399

  • wa = 0.00109492883763741

  • wag = -0.318420911707539

  • wg = 0.153524735108221

  • wu = -0.0141740647636319

  • w = -0.00448181394403335

Source code

OpenCL kernel
const Real f = wagu*a*g*u + wag*a*g + wau*a*u + wa*a + wgu*g*u + wg*g + wu*u + w;

*_new_u = u + dt * f;

if(*_new_u < umin) { *_new_u = umin; }
if(*_new_u > umax) { *_new_u = umax; }

const Real alpha_= alpha/dt;
*_new_a = alpha_*(*_new_u) + (1 - alpha_)*a;

const Int dist_ = dist + 0.5;
Size sum0 = 0;
Real sum1 = 0;
Real sum2 = 0;
for(Int iy=-dist_; iy<=dist_; iy++) {
  for(Int ix=-dist_; ix<=dist_; ix++) {
    if((iy*iy + ix*ix) <= dist*dist) {
      const Real u_ = _r(_x(ix, _y(iy, states_old)));
      if(isfinite(u_)) {
        sum0 += 1;
        sum1 += u_;
        sum2 += u_*u_;
      }
    }
  }
}
if(sum0 > 0) {
  const Real avg = sum1/sum0;
  const Real var = sum2/sum0 - avg*avg;
  *_new_g = sqrt(var > 0.0 ? var : 0.0);
} else {
  *_new_g = 0.0;
}

Additional metadata

keywords:
- excitable media
- electrophysiology
- heart
- data-driven
parameter sets:
  aliev1996simple:
    umin: 0.0
    umax: 1.0
    alpha: 0.03
    dist: 5
    wagu: -0.22407
    wag: -0.82589
    wau: 0.0054601
    wa: 0.021655
    wgu: 0.31082
    wg: 0.23077
    wu: -0.0081478
    w: -0.009711
  optical:
    umin: -0.5
    umax: 1.25
    alpha: 0.008
    dist: 8
    wagu: -0.413919278037366
    wgu: 0.193407562922741
    wau: 0.0263083048287399
    wa: 0.00109492883763741
    wag: -0.318420911707539
    wg: 0.153524735108221
    wu: -0.0141740647636319
    w: -0.00448181394403335