P2.25 Mathematical Modelling of the Systemic Circulation: Investigating Pressure and Flow Throughout the Microcirculation

Abstract

An early pathological process common to many vascular diseases is dysfunction of the small arteries. A variety of mechanisms are implicated including endothelial dysfunction. The final common pathway linking these functional pathologies to clinically significant disease is alteration of haemodynamic characteristics of the microcirculation, including the generation of small arteries at which the majority of the pre-capillary pressure drop occurs (resistance arteries).

We have extended a model of the systemic arterial system into the microcirculation. The model is divided into two parts: one comprising the larger arteries and one comprising the smaller arteries, coupled together through an outflow boundary condition at the terminals of the larger arteries. Blood flow and pressure in the larger arteries are predicted from a nonlinear 1D cross-sectional area-averaged model based on the Navier–Stokes equation. Inflow is ascending aortic flow measured using MRI. Small arteries in vascular beds are modelled as an asymmetric structured tree. Impedance is calculated throughout the asymmetric tree, allowing pressure and flow to be calculated at each vessel generation. Physical properties (dimensions, compliance etc) can be altered independently at each vascular generation of the microvasculature.

Using this model, we are able to simulate resistance artery pathologies identified as potential precursors of systemic disease. A detailed theoretical understanding of the haemodynamic impact of such resistance artery pathology on systemic blood flow and pressure has multiple potential uses. Current hypotheses concerning the pathophysiology of very early vascular disease eg ‘essential’ hypertension may be tested in silico and new hypotheses could potentially be generated.