Mathematical Models of Major Arterial Occlusion

Abstract

The occlusion of a major artery constitutes a serious health concern as it can restrict blood flow and oxygen transport to dependent tissue regions. Fortunately, the vasculature surrounding the occlusion has mechanisms by which it can adapt to try to restore and maintain adequate perfusion to these regions, though the details of these compensatory mechanisms are not well understood. The aim of the present study is to use mathematical modeling to investigate the effects of major arterial occlusion in multiple tissues and vascular geometries. A network representing the vasculature of the rat hindlimb is used to study peripheral arterial disease characterized by femoral artery occlusion. This work couples responses that occur on different time scales, namely vessel dilation and constriction on a short time scale and structural changes including arteriogenesis and angiogenesis on a long time scale. In the acute time frame, the responses that contribute most to changes in vascular tone are increases in flow and shear stress in collateral vessels and increases in metabolic signaling in distal arterioles. On the chronic scale, arteriogenesis is found to have a significantly larger effect on flow restoration than angiogenesis. A model of the major arteries and regions of the human brain is used to assess the impact of stroke caused by middle cerebral artery occlusion and the role of leptomeningeal collaterals in restoring flow downstream of the occlusion. The effects of incorporating pulsatile blood flow and arterial distensibility are also examined. The model demonstrates that the leptomeningeal collaterals are critical to restoring blood flow to the middle region, but the degree to which this is successful is highly dependent on conditions such as oxygen demand and arterial pressure. Overall, the results obtained from this study provide valuable insight into the vascular response mechanisms that contribute the most to flow compensation after occlusion and factors that may improve or worsen perfusion deficits. Insight from these models will inform the mechanisms and/or vessels to target in potential new treatments for peripheral arterial disease and stroke.