Spatio-Temporal Evolution of Cellular Automata based Single Nephron Rigid Tubular Model

Abstract

Partial differential equations play an important role in mathematical modeling of nephrons. The finite difference solution methods exhibit regular, period doubling and irregular oscillations. In this paper, a single nephron model with transport mechanism and autoregulatory mechanism has been developed using cellular automata framework for a rigid tubule. Cellular automata framework captures the emergent behavior of the system. The importance of cellular automata approach of studying a dynamical system emanates from its ability to capture new behavior not easily shown by numerical analysis. The governing equations of a single nephron model are converted to cellular automata local rules using ultradiscretization. The emergent properties from the local cellular automata rules have been compared with the reported experimental findings. It has been shown that cellular automata framework with ultradiscretization is a promising approach to model macrolevel behaviors of physiological systems.