A mathematical model of the intracerebral steal phenomenon in regional and focal ischaemia.

The objective of the present work was to mathematically estimate the extent and dynamics of intracerebral steal which may occur in response to cerebral vasodilation in regional and focal cerebral ischaemia. To this end, a spatially distributed mathematical model of regional cerebral blood flow (rCBF) was developed. The model contained a parallel system of intracerebral vascular resistances which were connected in series to a lumped extracerebral artery resistance and, for the focal ischaemia model, also a lumped pial collateral resistance. The rCBF was measured at 30 min of ischaemia in the following models: (1) bilateral carotid occlusion in spontaneously hypertensive rats (SHR), and (2) occlusion of the middle cerebral artery (MCA) in normotensive rats. The measured 3-dimensional rCBF data were used to set up the initial values of intracerebral resistance components. Cerebral vasodilation induced by inhalation of CO2 was simulated in the model by decreasing the values of both intracerebral and collateral resistance. Vascular responsiveness was specified to decrease with the ischaemic rCBF. In addition, a long term change in rCBF and resistance distribution was introduced to account for: (1) gradual rise in intracerebral resistance due to ischaemic oedema, and (2) adaptive decrease in collateral resistance. The following were predicted by the mathematical model. (1) At 60% maximum intracerebral dilatation a small intracerebral steal (5-10%) occurs at flow levels below 30-50 ml/100 g/min in both ischaemic models. (2) In focal ischaemia, the steal can be compensated by the 5% to 20% decrease in the collateral vascular resistance. (3) The rate of collateral adaptation overcomes the rate of intracerebral resistance rise and, therefore, eliminates the intracerebral steal after an adequately long period of time (on the order of a few hours). (4) An inverse steal effect can be demonstrated at the end of vasodilatation, provided that the time constant of collateral adaptation selected is longer (about 5:1) than the time constant of the intracerebral resistance rise. We conclude that the prediction of rCBF response to vasodilatation in cerebral ischaemia requires a knowledge of resting rCBF and of the response characteristics of both intracerebral and pial arterial segments.