Motivation. Blood flow provides nourishment and removes wastes from tissues. A crucial point to understand this basic function is to study the mass transfer across capillaries and arterial walls. This is a particularly challenging task because of the heterogeneity of the physical properties of the arterial wall.
Mechanics of trans-capillary exchange. The arterial wall is a complex structure made of several layers, namely the endothelium (the innermost layer with respect to the lumen), the intima, the internal elastic lamina, the media and finally the adventitia (the outermost one). In order to describe the transfer of chemicals through the walls, many phenomena must be taken into account. Precisely, molecules can diffuse into the wall, but are also transported by the filtration of plasma from the lumen to the outer wall. Moreover, the aforementioned tissues can be regarded as porous structures filled with plasma. Consequently, depending on the relative dimensions of the pores with respect to the considered molecules, selectivity effects and frictional phenomena should be suitably modelled.
Starting from the basic equations describing the physiological phenomena at hand, we set up a well-posed system of partial differential equations to describe the transfer of molecules through the arterial walls.
For the delicate question of characterizing the physical properties of the tissues constituting the walls, we apply an electric analogy for mass transport processes, aiming to reconstruct the physical parameters from available concentration measurements.
Clinical applications. Digital medical imagery systems and increasing computational power resources nowadays make possible the application of these complex mathematical models to realistic situations. More precisely, we take into account the following applications.