A global mathematical model for the simulation of stenoses and bypass placement in the human arterial system

Abstract

This paper is concerned with a global mathematical model for the human circulation; we describe its construction, its validation and its application to study the haemodynamical effect of stenoses and bypass placement in the arterial system. A geometric multiscale approach is adopted combining one-dimensional (1D) descriptions to represent 55 major arteries and zero-dimensional (0D) compartmental descriptions for the heart, lungs, the venous system and the microcirculation. Modern non-linear numerical methods are implemented for solving the 1D systems of hyperbolic partial differential equations and high-order Runge–Kutta methods are used to solve the systems of Ordinary Differential Equations resulting from the compartmental models. The complete global mathematical model is then validated for healthy and stenotic cases comparing numerical predictions from the model against in-vivo measurements. Results show overall satisfactory agreement. In addition, a sensitivity analysis is conducted in order to assess the influence of the most important parameters on some haemodynamical quantities of interest. We then apply the model to simulate the haemodynamics for healthy controls and subjects with arterial stenosis. We study the haemodynamical effect of bypass placement, considering different locations in the arterial system, different degrees of severity, for both single and multiple arterial stenoses. Haemodynamical quantities of interest in the study are local pressure and flow rate. We observe that large stenotic plaques near the heart cause abnormally strong pressure waves in the circulatory system and two adjacent occlusions worsen the phenomenon. We find that the mathematical model is capable of predicting the most convenient bypass location and graft dimensions, consistent with normal haemodynamics.