Double-wave reentry in excitable media

Modeling and Analysis of Cardiac Hybrid Cellular Automata via GPU-Accelerated Monte Carlo Simulation

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.

Universal mechanisms for self-termination of rapid cardiac rhythm

Excitable media sustain circulating waves. In the heart, sustained circulating waves can lead to serious impairment or even death. To investigate factors affecting the stability of such waves, we have used optogenetic techniques to stimulate a region at the apex of a mouse heart at a fixed delay after the detection of excitation at the base of the heart. For long delays, rapid circulating rhythms can be sustained, whereas for shorter delays, there are paroxysmal bursts of activity that start and stop spontaneously. By considering the dependence of the action potential and conduction velocity on the preceding recovery time using restitution curves, as well as the reduced excitability (fatigue) due to the rapid excitation, we model prominent features of the dynamics including alternation of the duration of the excited phases and conduction times, as well as termination of the bursts for short delays. We propose that this illustrates universal mechanisms that exist in biological systems for the self-termination of such activities.

Analysis of Circulating Waves in Tissue Rings derived from Human Induced Pluripotent Stem Cells

Developing more mature cardiomyocytes derived from human induced pluripotent stem cells is essential for cell transplantation and drug screening. In a previous study, we described a platform on which cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) formed three-dimensional self-organized tissue rings. Within these rings, traveling waves of action potentials spontaneously originate and propagate for a long time. In order to understand the dynamic behavior of these waves, we developed a mathematical model for the circulation of the electrical signal in such rings. By using the restitution curves of the action potential and the conduction velocity we demonstrated the mechanisms underlying the steady circulation and the features dependent on velocity. The analytic result agreed well with the experimental data in the origination, propagation, and long-term behavior of traveling waves within self-organized tissue rings. The theoretical analysis of traveling waves may also provide a reference to the analysis of reentrant rhythms in hearts.