Abstract
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.