Time-dependent coronary blood flow distribution in left ventricular wall.

A mathematical model of the coronary circulation in the left ventricular (LV) wall, which describes the time-dependent local blood perfusion throughout the myocardium and the coronary flow in the epicardial vessels, is presented. The myocardial perfusion is essentially controlled by the intramyocardial resistance and the coronary pressure driving force, whereas the epicardial arterial flow is dominated by the epicardial and intramyocardial arterial capacitance and the local transmural pressure on the vessels. The temporal and spatial intramural pressure [P im(y,t)], calculated based on a nested-shell spheroidal model of the LV, is used to evaluate the local intramural resistance to flow and the corresponding zero flow pressure. The calculation of the instantaneous flow in each layer is based on a local, time-dependent modification of the back-pressure concept. A function representing the local tonus of the small blood vessels [T wf(y)] is used to adjust the average coronary flow rate to the metabolic demand of each layer. The calculated results are compared with experimental data, and the assumptions of the model are examined against a variety of experimental conditions. The model provides a qualitative tool for comprehending the distributed flow phenomenon within the myocardium and its relation to cardiac mechanics and autoregulation.