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Abstract ObjectiveAn improved understanding of the role of the leptomeningeal collateral circulation in blood flow compensation following middle cerebral artery (MCA) occlusion can contribute to more effective treatment development for ischemic stroke. The present study introduces a model of the cerebral circulation to predict cerebral blood flow and tissue oxygenation following MCA occlusion. MethodsThe model incorporates flow regulation mechanisms based on changes in pressure, shear stress, and metabolic demand. Oxygen saturation in cerebral vessels and tissue is calculated using a Krogh cylinder model. The model is used to assess the effects of changes in oxygen demand and arterial pressure on cerebral blood flow and oxygenation after MCA occlusion. ResultsAn increase from five to 11 leptomeningeal collateral vessels was shown to increase the oxygen saturation in the region distal to the occlusion by nearly 100%. Post‐occlusion, the model also predicted a loss of autoregulation and a decrease in flow to the ischemic territory as oxygen demand was increased; these results were consistent with data from experiments that induced cerebral ischemia. ConclusionsThis study highlights the importance of leptomeningeal collaterals following MCA occlusion and reinforces the idea that lower oxygen demand and higher arterial pressure improve conditions of flow and oxygenation. 

Abstract ObjectiveTo incorporate chronic vascular adaptations into a mathematical model of the rat hindlimb to simulate flow restoration following total occlusion of the femoral artery. MethodsA vascular wall mechanics model is used to simulate acute and chronic vascular adaptations in the collateral arteries and collateral‐dependent arterioles of the rat hindlimb. On an acute timeframe, the vascular tone of collateral arteries and distal arterioles is determined by responses to pressure, shear stress, and metabolic demand. On a chronic timeframe, sustained dilation of arteries and arterioles induces outward vessel remodeling represented by increased passive vessel diameter (arteriogenesis), and low venous oxygen saturation levels induce the growth of new capillaries represented by increased capillary number (angiogenesis). ResultsThe model predicts that flow compensation to an occlusion is enhanced primarily by arteriogenesis of the collateral arteries on a chronic time frame. Blood flow autoregulation is predicted to be disrupted and to occur for higher pressure values following femoral arterial occlusion. ConclusionsStructural adaptation of the vasculature allows for increased blood flow to the collateral‐dependent region after occlusion. Although flow is still below pre‐occlusion levels, model predictions indicate that interventions which enhance collateral arteriogenesis would have the greatest potential for restoring flow.