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A simple model of filtration and macromolecule transport through microvascular walls

Multiple Sclerosis (MS) is a disorder that usually appears in adults in their thirties. It has a prevalence that ranges between 2 and 150 per 100 000. Epidemiological studies of MS have provided hints on possible causes for the disease ranging from genetic, environmental and infectious factors to other factors of vascular origin. Despite the tremendous effort spent in the last few years, none of the hypotheses formulated so far has gained wide acceptance and the causes of the disease remain unknown. From a clinical point of view, a high correlation has been recently observed between MS and Chronic Cerebro-Spinal Venous Insufficiency (CCSVI) in a statistically significant number of patients. In this pathological situation CCSVI may induce alterations of blood pressure in brain microvessels, thereby perturbing the exchange of small hydrophilic molecules between the blood and the external cells. In the presence of large pressure alterations it cannot be excluded also the leakage of macromolecules that otherwise would not cross the vessel wall. All these disorders may trigger immune defenses with the destruction of myelin as a side effect. In the present work we investigate the role of perturbed blood pressure in brain microvessels as driving force for an altered exchange of small hydrophilic solutes and leakage of macromolecules into the interstitial fluid. With a simplified, yet realistic, model we obtain closed-form steady-state solutions for fluid flow and solute transport across the microvessel wall. Finally, we use these results (i) to interpret experimental data available in the literature and (ii) to carry out a preliminary analysis of the disorder in the exchange processes triggered by an increase of blood pressure, thereby relating our preliminary results to the hypothesised vascular connection to MS.