Modeling bacterial clearance using stochastic-differential equations

Capillary - tissue fluid exchange is controlled by the blood pressure in the capillary and the osmotic pressure of blood (pressure of the tissue fluid outside the capillaries). In this paper, we develop a mathematical model to simulate the movement of bacteria into and within a capillary segment. The model is based on Fokker-Planck equation and Navier-Stocks equations that accounts for different boundary conditions. Also, we model the transportation through capillary walls by means of anisotropic diffusivity that depends on the pressure difference across the capillary walls. By solving the model with a numerical method, it was possible to predict the concentration of bacteria at points within the capillary. However, numerical analysis consumes computational time and resources. To efficiently simulate the bacterial clearance, we propose a segmentation model that is based on breaking the capillary network into smaller sections with pre-defined properties in order to reduce the overall computational time. The proposed model shows a great reduction in computational time and provides accurate results when compared to the numerical analysis.