Abstract
Stem cell transplantation therapy may inhibit inflammation during stroke and increase the presence of healthy cells in the brain. The novelty of this work, is to introduce a new mathematical model of stem cells transplanted to treat stroke. This manuscript studies the stability of the mathematical model by using the current biological information on stem cell therapy as a possible treatment for inflammation from microglia during stroke. The model is proposed to represent the dynamics of various immune brain cells (resting microglia, pro-inflammation microglia, and anti-inflammation microglia), brain tissue damage and stem cells transplanted. This model is based on a set of five ordinary differential equations and explores the beneficial effects of stem cells transplanted at early stages of inflammation during stroke. The Runge-Kutta method is used to discuss the model analytically and solve it numerically. The results of our simulations are qualitatively consistent with those observed in experiments in vivo, suggesting that the transplanted stem cells could contribute to the increase in the rate of ant-inflammatory microglia and decrease the damage from pro-inflammatory microglia. It is found from the analysis and simulation results that stem cell transplantation can help stroke patients by modulation of the immune response during a stroke and decrease the damage on the brain. In conclusion, this approach may increase the contributions of stem cells transplanted during inflammation therapy in stroke and help to study various therapeutic strategies for stem cells to reduce stroke damage at the early stages.