Mathematical Modeling of Cell Proliferation Using Stochastic Processes

Abstract

The human body is like a microsociety, in which its members are cells that reproduce by division and are organized in collaborative groups, called tissues. Each cell has a well-defined role: to send, to receive or to interpret and process extracellular signals. Another way of seeing the structure and the organization of a tissue is through random paths and actions that may occur between its cells. These random paths, similar to the Biological Brownian motion, have several possible directions. Mathematics models these possible directions with stochastic processes. Thus, tissue modeling can be done using branching processes, which can be approximated with diffusion processes, in order to apply Kolmogorov equations to compute the expected time value when a tissue reaches a certain size.