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The heart is an organ with a limited capacity for regeneration and repair. In this paper, a new mathematical model is presented to study the left ventricular remodeling after myocardial infarction (MI) and followed stem cell therapeutic effort. The model represents the post-MI regeneration process of cardiomyocytes under stem cell therapy with oxygen restoration. The resulting system of nonlinear ordinary differential equations (ODE) is studied numerically in order to demonstrate the functionality and performance of the new model. The optimal time of stem cell injection for various oxygen restorations is determined. Moreover, the regeneration of cardiomyocytes is successfully correlated with improved left ventricle function observed in experiments. The proposed nonlinear ODE model is able to capture the complicated biological interactions in post-MI remodeling and can serve as a platform for in silico simulation and perturbation to optimize MI stem cell therapy. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the Mackey-Glass model with piecewise constant argument. Because the corresponding difference equation is the difference solution of the equation, the difference equation can clearly predict the dynamic behavior of the equation. So, we look at how the difference equation behaves.We study the asymptotic stability of the equilibrium point of the difference equation and it is obtained that this point is a repeller under some conditions. Also, it is shown that every oscillatory solution of the difference equation has semi-cycles of length at least two, and every oscillatory solution of the difference equation is attracted to the equilibrium point. Finally, some examples are presented to support the results. [ABSTRACT FROM AUTHOR]