Model-based analysis of transmural vessel impedance and myocardial circulation dynamics

Abstract

The basic structure of a model of the coronary circulation has been developed to explain the relationship between transmural perfusion dynamics and intramyocardial mechanics. The model is in the form of a topologically isomorphic network representation and incorporates experimentally measured time-varying perfusion and intramyocardial pressure sources as driving inputs to the model. The intramyocardial vessels are treated as nonlinear impedance elements possessing regional external pressure-dependent resistance and capacitance. Three circuit branches, perfusing the epicardial, subepicardial, and subendocardial muscle layers, are mathematically modeled and are used to predict time-dependent flow within the left ventricular myocardium. The phasic coronary blood flow characteristics predicted by the model exhibit waveform patterns that correlate qualitatively with those patterns measured experimentally. In addition, the pressure-dependent vascular capacitance induces a sustained (out of phase with arterial inflow) venous systolic flow. The model also exhibits retrograde systolic subendocardial flow and stop-flow pressure, which are dependent on coronary resistive and capacitive properties and on the perfusion pressure decay time constant. Furthermore, the results predict an abrupt decrease in subendocardial flow with perturbation of either arteriolar or capillary bed compliance. The model describes time-dependent intramyocardial properties that have been confusing and controversial in the understanding of coronary circulation dynamics. Several steps are identified that are expected to improve and refine the model significantly.