Mathematical Modeling of the Heart

We are using mathematical models of cardiac tissue with various levels of complexity, ranging from generic to detailed physiological descriptions. The choice of the model depends on the specific problem at hand. Generic models play an important role for the understanding of fundamental principles of excitable media. For example, we have used generic models to explore the nonlinear dynamics underlying the interaction of rotating waves with heterogeneities. However, generic models do not permit to elucidate the molecular basis of cardiac function. The Fenton-Karma model has the minimal ionic complexity necessary to reproduce essential qualitatively characteristic dynamical properties of the system [1], while being computationally efficient. In contrast, physiological models aim at a detailed quantitative description of cellular physiology. However, model selection and the reliable estimation of model parameters from experimental data is utmost difficult. We focus on in silico modeling of different Na+ and Ca2+ transport dysfunction and their role in arrhythmia onset and perpetuation [2]. The numerical models are implemented using finite differences and parallelized using the message-passing interface (MPI). Irregular tissue boundaries are implemented using the phase field method, an elegant approach to satisfy no-flux boundary conditions on arbitrary geometries [3].

References

  1. F.H. Fenton and A. Karma, Chaos 8, 20-47 (1998).
  2. S. Petitprez et al., Circ. Research 108, 294-304 (2011)
  3. F.H. Fenton, E.M. Cherry, A. Karma, W.-J. Rappel, Chaos 15, 013502 (2005)