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L. Treml, E. Bartocci, A. Gizzi:
"Modeling and Analysis of Cardiac Hybrid Cellular Automata via GPU-accelerated Monte Carlo Simulation";
Mathematics (MDPI), 9 (2021), 2.

The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and the large number of biological components involved make the modeling and the analysis of electrophysiological properties in cardiac tissue still an open challenge. We consider here a Hybrid Cellular Automata (HCA) approach modeling the cardiac cell-cell membrane resistance with a free variable. We show that the modeling approach can reproduce important and complex spatiotemporal properties paving the ground for promising future applications. We show how GPU-based technology can considerably accelerate the simulation and the analysis. Furthermore, we study the cardiac behavior within a unidimensional domain considering inhomogeneous resistance and we perform a Monte Carlo analysis to evaluate our approach.

http://dx.doi.org/10.3390/math9020164

https://www.mdpi.com/2227-7390/9/2/164