Modelagem mecânica da formação de edemas

Abstract

Edema is one of the most common symptoms found in infectious diseases along with heat, redness, and pain. Often, edema may be a consequence of interstitial fluid dynamics and their interactions with the immune system. So, when a pathogen enters into the body, the natural consequence is an immunological reaction triggered by the production of cytokines by macrophages. This immunological response recruits other immune cells, e.g. the neutrophils, responsible for seeking and destroying these foreign invaders. This physiological process can be mathematically modeled by a nonlinear system of partial differential equations (PDE) based on porous media approach. In order to simplify the model, just the interaction between neutrophils and pathogens (an unspecified bacteria) is considered. The interstitial fluid dynamics can be influenced by the lymphatic system, blood capillaries, along with the inflammatory reaction. Initially, this work presents an approximation using constant porosity followed by a second approach using the poroelasticity theory proposed by Biot. The influence of the immune system is coupled by the Starling equation which models the flow in the capillary membranes. The simulations were presented, mostly, in a unidimensional domain, in order to make easier the comprehension of the results. Moreover, a two-dimensional study in the heart short axis is also presented to simulate a bacterial myocarditis. The numerical method used in unidimensional simulations is the finite volume method (FVM) and for the two-dimensional simulation is the finite element method (FEM). Finally, this study makes a qualitative validation of the in silico results with in vivo experimental data, in order to evaluate the proposed model.