Emergent Pressure Dynamics In Coupled Nephron Compliance Tubular Model Using Cellular Automata Rules

Abstract

The dynamics of a coupled nephron model can be analyzed by studying the local and global properties. The governing equations of the model are solved using numerical methods to investigate the point-to-point spatiotemporal evolution. Bifurcation analysis has been used to study the global properties. The Cellular Automata (CA) framework was successfully used in the past to model emergent behavior of dynamical systems. The CA approach has not yet been investigated in the context of the coupled nephron model. In this paper, a CA approach has been proposed to study the global properties of the coupled nephron model for compliance tubule. Both tropical and Cole-Hopf transformation have been applied while arriving at the ultradiscretized equations. The CA rules have been derived from ultradiscretization for different transition cases. The global behavior of the derived CA rules has been compared with the class of dynamical systems, which has been observed in the experimental studies on nephrons. It is found that the CA approach captures the richness of the dynamical system behavior observed in the nephron experiments. This is promising and may lead to the development of CA models for analyzing the local behavior in future.

Keywords

• nephron
• pressure dynamics
• cellular automata
• ultradiscretization
• emergent properties