Pacemaker Created in Human Ventricle by Depressing Inward-Rectifier K⁺ Current: A Simulation Study

The Quantitative Relationship among the Number of the Pacing Cells Required, the Dimension, and the Diffusion Coefficient

The purpose of the paper is to derive a formula to describe the quantitative relationship among the number of the pacing cells required (NPR), the dimension i, and the diffusion coefficient D (electrical coupling or gap junction G). The relationship between NPR and G has been investigated in different dimensions, respectively. That is, for each fixed i, there is a formula to describe the relationship between NPR and G; and three formulas are required for the three dimensions. However, there is not a universal expression to describe the relationship among NPR, G, and i together. In the manuscript, surveying and investigating the basic law among the existed data, we speculate the preliminary formula of the relationship among the NPR, i, and G; and then, employing the cftool in MATLAB, the explicit formulas are derived for different cases. In addition, the goodness of fit (R ²) is computed to evaluate the fitting of the formulas. Moreover, the 1D and 2D ventricular tissue models containing biological pacemakers are developed to derive more data to validate the formula. The results suggest that the relationship among the NPR, i, and the G (D) could be described by a universal formula, where the NPR scales with the i (the dimension) power of the product of the square root of G (D) and a constant b which is dependent on the strength of the pacing cells and so on.

Biological pacemaker: from biological experiments to computational simulation

Pacemaking dysfunction has become a significant disease that may contribute to heart rhythm disorders, syncope, and even death. Up to now, the best way to treat it is to implant electronic pacemakers. However, these have many disadvantages such as limited battery life, infection, and fixed pacing rate. There is an urgent need for a biological pacemaker (bio-pacemaker). This is expected to replace electronic devices because of its low risk of complications and the ability to respond to emotion. Here we survey the contemporary development of the bio-pacemaker by both experimental and computational approaches. The former mainly includes gene therapy and cell therapy, whilst the latter involves the use of multi-scale computer models of the heart, ranging from the single cell to the tissue slice. Up to now, a bio-pacemaker has been successfully applied in big mammals, but it still has a long way from clinical uses for the treatment of human heart diseases. It is hoped that the use of the computational model of a bio-pacemaker may accelerate this process. Finally, we propose potential research directions for generating a bio-pacemaker based on cardiac computational modeling.

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.