Mathematical simulation of cerebral blood flow in focal ischemia.

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Abstract
A computer model was developed to describe regional cerebral blood flow and tissue oxygenation with autoregulation during focal ischemia produced by occlusion of th middle cerebral artery (MCA). This steady state model described the distribution of blood flow in the cerebral arterial system including the circle of Willis as well as the pial arterial anastomoses, and included a simplified form of autoregulation based on the local control of pressure and flow in the pial and intracerebral arteries, respectively. Preliminary simulation studies with the model yielded the following results. Less effective autoregulation was predicted by the model at low blood pressure in focal ischemia. Passive dilatation of the pial vasculature produced a leftward shift in the autoregulatory curve. Simulations with occlusion of the MCA revealed the ultimate importance of the pial anastomoses in providing adequate blood and oxygen supply in the ischemic territories including the specially vulnerable lenticulostriate area. The volume of the ischemic (pO2 less than 1 mmHg) brain tissue in the MCA-cortex estimated by using a concurrent Krogh cylinder model was 50% when the pial anastomoses were 80 micrometers in diameter and the ischemic area disappeared at 170 micrometers diameter. With relatively small anastomoses (less than 200 m) the model demonstrated intracerebral steal during intracerebral vasodilation. Passive dilation of the pial arteries including the pial anastomoses caused the steal to disappear and to reverse. These results suggest that both autoregulatory shift and steal reversal can be explained by passive dilatation of the pial vasculature.