Mathematical modelling of transport across blood vessel walls

The last decade has seen an increasing interest in bio-mathematical modelling and scientific computing, resulting in new applications to relevant physiological phenomena and to a better understanding of the origin of various diseases. A topic of great interest to several degenerative diseases is filtration across microvessel walls. The role of the microvessel wall is to let oxygen and nutrients contained in the blood stream to reach the interstitium, and ultimately the surrounding cells, while blocking macromolecules. An understanding of these processes is important in preventing and curing neuro-degenerative diseases, as well as for exploring possible mechanisms to make drug delivery more efficient. This work presents a one-dimensional, time dependent mathematical model describing transport of blood plasma and macromolecules across blood vessel walls. The model takes into account the heterogeneous microvessel wall composition, in order to accurately describe trans-vascular flow. This results in a multi-layered domain, accounting for variable physical properties across the layers forming the micro-vascular wall. In particular, the glycocalyx and endothelium, accounted for in many biological studies, are represented in our model. This micro-structural, yet simplified description of the vascular wall, allows us to simulate the effect of glycocalyx damage and of other pathologies, such as hypertension, hemorrhage and hypovolemia, both in steady and time-dependent states. Due to the simplicity, and thus efficiency of the proposed model, simulations are fast and provide results which are in line with published experimental studies. Furthermore, the simulation tool may be useful for practical applications in physiological and medical studies, by evaluating the possible consequences of pathological conditions.