A mathematical model of the action of stem cells for cardiac tissue

Stem cells have shown to have a high potential for the treatment of heart failure (infarct) through regeneration of cardiac tissue and restoration of cardiac contractility. In a previous paper a first, simplified, numerical model of the action of stem cells was proposed with the aim of studying the optimal protocol for the stem implant in the tissue in order to replace the necrotic area (localization of the implant, number of stem cells to be implanted in each injection, implant times and so on). The model described the cell growth, the nutrient transport and its consumption via reaction-diffusion equations. Since the stem tend to reconstruct the damaged tissue, substituting the necrotic cells, the shrinking of the ischemic area led to a moving boundary problem. The theoretical and numerical model assumed, for simplicity, a spherical symmetry of the necrotic area. The stem cells distribution and their proliferation near the ischemic area, as well as the transport of nutrients were studied and were correlated with several parameters, as the maximum reaction rate, the saturation coefficient, the cell death parameter, the stem cell and the nutrient diffusion coefficient, the nutrient flux, the radius of the necrotic area, the implantation factor, the stem cell decay rate. Several parameters were obtained from literature, while others were taken in physiologically reasonable ranges. The research group from IFT-CNR recently performed several experiments in order to relate pH, stem cells growth, metabolism and mortality to the temperature, the glucose concentration and nutrient volume. In this communication we test the previous model with the experimental data, in order to tune the parameters and give some preliminary, though still semiquantitative, predictions, also with a view to modify the geometry of the infarcted area.