Mathematical modeling and simulation of molecular mass transfer across blood brain barrier in brain capillary

Abstract

The blood brain barrier (BBB) is a unique anatomical structure tightly regulated by the interplay of cellular and acellular components, thus providing maintenance of brain homeostasis, regulation of influx and efflux and protection from harm. In both health and disease, the BBB acts as a mediator between the peripheral and the central nervous system (CNS). Understanding the BBB is considered as a key for developing effective treatments for a wide range of CNS disorders. The main novelty of this study is to develop a 2-dimensional and 3-dimensional model of BBB mass transfer resistance to investigate effective diffusion and molecular mass transfer from inside the capillary to the extravascular space. In this study, the capillary and the tissue around it with non-uniform permeability are numerically simulated. The endothelial cells, basement membrane and astrocyte foot processes are modeled as a porous medium. Moreover, a correlation of mass transfer resistance between the capillaries and astrocytes was established to estimate an effective diffusion coefficient. Model validation is done according to the comparison of simulation results and experimental data for the nanodrug mass transfer resistance in a wide range of red blood cell distance in the capillary. This comparison corroborates an excellent agreement with an average deviation of 6%. It is well perceived that the internal diameter of capillaries and the distance between the outside of the capillary and astrocyte have significant effects on delivering materials to neurons. Moreover, blood flow velocity and the number of red blood cells dramatically deteriorate the nano-particles' concentration due to increasing the mass transfer resistance.