The role of trigger waves in cancer angiogenesis

Abstract

This study includes mathematical modeling of biological observations and numer ical solutions of these models. Our study focused on different phenomenons, including; vessel formation, intracellular calcium ion concentration, traveling wave solutions, and cytosol elasticity. Understanding signaling in diseases is essential for a proper response. For this reason, understanding the secondary messenger signaling that mechanisms of ten prefer to use and their interaction with the mechanisms enables the system’s re sponse to be better understood. This study examined the interaction of angiogenesis, a mechanism that contributes to tumor growth, and cytosolic calcium ion, an intracel lular secondary messenger. Therefore, we simulated a mathematical model involving essential angiogenesis and calcium homeostasis elements using previously used models. In our simulations, we developed two and multiple cell scenarios and examined the results of our system in distributions of different angiogenic stimulus uptake. Since angiogenesis requires the cell to move in a specific direction, we simulated the cytosolic gelation- solution mechanism, inspired by another model used in the literature. We examined the condition under which the wave direction persists in the traveling wave configuration.