Inflammation propagation modeled as a reaction-diffusion wave

Abstract

Inflammation is a physiological process aimed to protect the organism in various diseases and injuries. This work presents a generic inflammation model based on the reaction-diffusion equations for the concentrations of uninflamed cells, inflamed cells, immune cells and the inflammatory cytokines. The analysis of the model shows the existence of three different regimes of inflammation progression depending on the value of a parameter R called the inflammation number. If R>1, then inflammation propagates in cell culture or tissue as a reaction-diffusion wave due to diffusion of inflammatory cytokines produced by inflamed cells. If 0<R<1, then inflammation vanishes and the system converges to the stable inflammation-free equilibrium. Finally if R<0, inflammation also propagates as a reaction-diffusion wave, but the mechanism of propagation is different, it is determined by positive feedback between inflammation and immune response. From the biological point of view, these three regimes correspond to acute inflammation resolved due to the immune response, to the disappearance of inflammatory reaction, and to an auto-immune inflammatory reaction or cytokine storm. We focus on finding the wave speed and other characteristics of inflammation progression by analytical and numerical methods, in order to deduce a qualitative understanding of various inflammatory reactions.

Keywords: Cytokine storm; Inflammation; Inflammation propagation; Reaction–diffusion equations; Wave speed.