Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model

Abstract

The dynamics of ventricular fibrillation (VF) has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR) model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS) such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf) for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.

Superstatistics and System Identification for a Class of Generalized Cauchy Processes

“…The first order models I and II described in section 3 can be identified completely (i.e., the parameters of associated Langevin equations can be determined) by the procedure of inferring them (i.e., the estimation of (a, b) from the pdf and the direct estimation of the strength D m of noise) only from time series data, as is shown in [7]. The second order models III, IV and V in section 4 can be also identified completely by the procedure of inferring them only from time series data with the aid Proceedings of the 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications Okinawa, Nov. [1][2]2013 of the information on the correlation functions associated with them.…”

Computational models of ventricular arrhythmia mechanisms: recent developments and future prospects

“…Additional ideas from physics about the dynamical behaviour of nonlinear systems have contributed to our understanding of mechanisms that initiate and sustain re-entry [10][11][12][13]. Recent contributions include the dynamics of PS behaviour [14], the role of electrical coupling [15], and both diffuse [16] and focal [17] obstacles.…”

Stochastic process of pragmatic information for 2D spiral wave turbulence in globally and locally coupled Alief-Panfilov oscillators

“…It is also shown that how to estimate the parameters of distribution. Suzuki and Konno [13] simulated numerically temporal development of the number of phase singularities (NPS) for various states of spiral wave turbulence in the 2D space for the Beeler-Reuter model. Then, it is shown further that the distribution of the NPS can be described well by the HGD:…”

“…In the case of spiral wave turbulence (SWT) in 2D space, the temporal variation of the number of phase singularities (NPS) is subjected to the Gamma distribution for Aliev-Panfilov model [11] and the Hyper-Gamma distribution for Beeler-Reuter model [13]. In the case of the 2D SWT, the NPS does not exhibit the conformational change of the probability density function.…”