On the mathematical modeling of inflammatory edema formation

Abstract

When pathogens enter into the body, the natural defense reaction is an immunological process triggered by the production of cytokines by macrophages. This reaction is called inflammation and it is an important and complex physiological response of living tissues to all harmful damages. As a consequence of the immune response, the most common symptoms are edema, redness, fever, and pain. All of these four symptoms are related to the physiological process of the immune defense system. For instance, edema may be caused by increased blood vessel wall permeability which leads to a swell at the infection site. So, edema is a consequence of interstitial fluid dynamics and its interactions with the immune system. In this present study, this physiological process is mathematically described by a nonlinear system of partial differential equations (PDE) based on a porous media approach. The model describes the interaction between the neutrophils and the pathogen, which in our case is non-specific bacteria. In addition, a poroelastic model is coupled with the inflammatory one resulting in an hydro-mechanical model for inflammatory edema. The new suggested model was able to reproduce key aspects of an inflammatory edema formation.