Modeling Left Ventricle Perfusion in Healthy and Stenotic Conditions

Abstract

A theoretical fluid mechanical model is proposed for the investigation of myocardial perfusion in healthy and stenotic conditions. The model hinges on Terzaghi’s consolidation theory and reformulates the related unsteady flow equation for the simulation of the swelling–drainage alternation characterizing the diastolic–systolic phases. When compared with the outcome of experimental in vivo observations in terms of left ventricle transmural perfusion ratio (T.P.R.), the analytical solution provided by the present study for the time-dependent blood pressure and flow rate across the ventricle wall proves to consistently reproduce the basic mechanisms of both healthy and ischemic perfusion. Therefore, it could constitute a useful interpretative support to improve the comprehension of the basic hemodynamic mechanisms leading to the most common cardiac diseases. Additionally, it could represent the mathematical basis for the application of inverse methods aimed at estimating the characteristic parameters of ischemic perfusion (i.e., location and severity of coronary stenoses) via downstream ventricular measurements, possibly inspiring their assessment via non-invasive myocardial imaging techniques.