Hemodynamic analysis for the prevention and treatment of vascular diseases

In the present work, a theoretical and numerical analysis of the variable effect of distensibility and permeability in a rectangular microchannel representing a component of the vascular microcirculation was developed. For this purpose, a mass balance was performed to consider the capability of a blood vessel to expand and allow the migration of substances across the endothelium on response to increasing internal pressure. This analysis provided a partial differential equation for pressure as a function of longitudinal position and time. For this purpose, a mass balance was performed to consider the capability of a blood vessel to expand and allow the migration of substances across the endothelium on response to increasing internal pressure. This analysis provided a partial differential equation for pressure as a function of longitudinal position and time. Performing an order-of-magnitude analysis, this equation was dimensionless to identify the most relevant dimensionless parameters. This equation was solved analytically and numerically using asymptotic techniques and a finite difference scheme, respectively. Among the most relevant results the dimensionless parameters β and γ, which represent the effect of permeability and the increase in solute concentration across the endothelium, respectively, can be highlighted. This model replicated physiological and pathological situations, such as the formation of inflammatory edema in the microcirculation. It was observed that for increasing β value leads to a rise in pressure profiles along the microchannel, resulting in increased filtration flow through the endothelium. On the other hand, elevated γ values reflects an increase in intravascular pressure, associated with inflammatory conditions, leading to increased vascular wall distension. Each of these results affects the flow dynamics circulating through the vascular microchannel.