Modeling of Coronary Capillary Flow

Abstract

The coronary capillary flow is analyzed theoretically based on the laws of continuum mechanics. The capillary is considered as a long, elastic and permeable vessel loaded externally by tissue pressure. It is subjected to periodic length changes, together with adjacent myocytes. Capillary flow is driven by arteriolar-venular pressure differences. Ultrafiltration due to transmural hydrostatic and osmotic pressure gradients is included in the model. Consideration of mass conservation leads to a nonlinear flow equation. The results show that under stable physiological conditions ultrafiltration is of minor importance. The analysis of untethered capillaries predicts regional differences in capillary flow. In all regions, but more so in the subendocardium, capillaries undergo significant periodic volume changes, giving rise to intramyocardial pumping. In the deeper layers, capillary wall elasticity is of major importance. In the subepicardium, the possible capillary length-changes with adjacent myocytes tend to enhance systolic/diastolic volume differences. The predicted patterns of the overall capillary flow in the left ventricular (LV) wall are in good qualitative agreement with measured coronary phasic flow, showing systolic retrograde arterial inflow, accelerated venal outflow, and diastolic rapid filling accompanied by venal retrograde flow. Analysis of the flow in tethered capillary shows significant effect of the collagen attachments between the surrounding myocytes and the capillary wall. The advantage of the continuum analysis is demonstrated in the present study by its ability to elucidate and evaluate the role of flow controlling mechanisms and their complex interactions.