Large multiple-scale computer simulations of virtual hearts have been performed in many research laboratories (i) to understand the mechanism of heart diseases; and (ii) to utilize these cardiac models in drug development. In spite of the extensive studies, there are many fundamental dynamical features that are not clarified even in a simple ion-channel based cardiac model.

We have studied a state of ventricular fibrillation (VF) in a modified 2D Beerler-Reuter model (BR) from the viewpoint of nonlinear stochastic processes associated with the simple ion-channel model. The state of VF is characterized by the annihilation and creation of broken pieces of spiral waves. We firstly studied stochastic processes of the number of phase-singularity N(t) in the VF. It is found that N(t) can be identified by the Hyper-Gamma process under the influence of a multiplicative noise [1]. Then, we have examined the predator-prey variables [2] and construct a stochastic predator-prey model under the influence of multiplicative noises [3]. It is shown that the model can catch the dynamical features of the predator-prey variables in a VF state in the BR model.

 

References

[1] A. Suzuki and H. Konno, Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model, AIP Advances 1, 032103 (2011).

[2] N. F. Otani, et al., Characterization of multiple spiral wave dynamics as a stochastic predator-prey system, Phys. Rev. E78 021913 (2008) and references and models cited therein.

[3] H. Konno, A. Suzuki and Y. Uchiyama, (2012) preprint