Some Numerical Results on Chemotactic Phenomena in Stem Cell Therapy for Cardiac Regeneration

Abstract

Biological models for cardiac regeneration and remodeling, along with the effects of cytokines or chemokines during the therapy with mesenchymal stem cells after a myocardial infarction, are of crucial importance for understanding the complex underlying mechanisms. This paper presents a mathematical model composed of three coupled partial differential equations that describes the dynamics of stem cells, nutrients and chemokines, highlighting the fundamental role of the chemokines during the myocardial tissue regeneration process. The system is solved numerically using mimetic difference operators and the MOLE library for MATLAB. The results show the tissue regeneration process in the necrotic part closest to the cell implantation area.

Keywords

• reaction–diffusion equations
• free boundary problem
• mimetic difference operators
• stem cell therapy
• chemokines
• chemotaxis