We developed a theory for regional blood flow in the beating heart and validated it with measurements of coronary arterial inflow and venous outflow in the open-chest anesthetized dog. The model used measured aortic, left ventricular, and coronary sinus pressures as input data under control conditions and during long diastoles induced by vagal stimulation. A nonlinear two-compartment lumped model for each transmural layer was obtained by spatial averaging a continuum description of the myocardial microcirculation based on morphometric measurements and appropriate fluid and vascular mechanics principles. The chief results and conclusions of the study are 1) an intramyocardial time constant on the order of 1 s is required to explain the phase opposition between inflow and outflow; 2) capillary and venous perfusion are in phase with arterial pressure, and arterial flow is out of phase with arterial pressure except in superficial intramural layers; 3) subendocardial retrograde systolic flow increases with increased contractility and time constants and decreased arterial pressure; and 4) endocardial capillary and venule volume change by 5.5 and 10%, respectively, during the control cardiac cycle.
A continuum description of substrate-free dissipative reconfigurable metamaterials
