The Effects of Cerebral Vasospasm on Cerebral Blood Flow and the Effects of Induced Hypertension: A Mathematical Modelling Study

Abstract

Background: Induced hypertension has been used to promote cerebral blood flow under vasospastic conditions although there is no randomised clinical trial to support its use. We sought to mathematically model the effects of vasospasm on the cerebral blood flow and the effects of induced hypertension.

Methods: The Anatomically Detailed Arterial Network (ADAN) model is employed as the anatomical substrate in which the cerebral blood flow is simulated as part of the simulation of the whole body arterial circulation. The pressure drop across the spastic vessel is modelled by inserting a specific constriction model within the corresponding vessel in the ADAN model. We altered the degree of vasospasm, the length of the vasospastic segment, the location of the vasospasm, the pressure (baseline mean arterial pressure [MAP] 90 mm Hg, hypertension MAP 120 mm Hg, hypotension), and the presence of collateral supply.

Results: Larger decreases in cerebral flow were seen for diffuse spasm and more severe vasospasm. The presence of collateral supply could maintain cerebral blood flow, but only if the vasospasm did not occur distal to the collateral. Induced hypertension caused an increase in blood flow in all scenarios, but did not normalise blood flow even in the presence of moderate vasospasm (30%). Hypertension in the presence of a complete circle of Willis had a marginally greater effect on the blood flow, but did not normalise flow.

Conclusion: Under vasospastic condition, cerebral blood flow varies considerably. Hypertension can raise the blood flow, but it is unable to restore cerebral blood flow to baseline.

Keywords: Cerebral vasospasm; Induced hypertension; Modelling; Subarachnoid haemorrhage.

Fig. 1

Diffuse vasospasm of the MCA results in greater decreases in blood flow even if the degree of vasospasm is the same. The results were the same with a complete CoW. CoW, circle of Willis; d, distributed spasm; f, focal spasm; MCA, middle cerebral artery.

Fig. 2

Flow in the MCA is reduced as the severity of the ICA vasospasm increases; however, the effects are minimised by the presence of a complete CoW. Hypertension increases blood flow, but does not restore flow to 100% of baseline. CoW, circle of Willis; d, distributed spasm; f, focal spasm; Hype, hypertension; ICA, internal carotid artery; L, left vessel; MCA, middle cerebral artery.

Fig. 3

Blood flow in the MCA is only marginally affected by the presence of a complete CoW when the vasospasm affects the MCA itself. In this scenario the blood flow is related to the severity of the vasospasm and the length of the affected segment. CoW, circle of Willis; d, distributed spasm; f, focal spasm; Hype, hypertension; L, left vessel; MCA, middle cerebral artery.

Fig. 4

In the presence of diffuse vasospasm affecting both the ICA and MCA, there are decreases in the blood flow in the MCA, and hypertension, whilst causing a slight increase in the flow supply, is unable to restore it to normal. The largest flow reduction is observed in cases involving long segment disease of the worst severity and in the case of an incomplete CoW. In the presence of a complete CoW, the flow is related principally to the vasospasm within the MCA, being less sensitive to the vasospasm occurring in the ICA. CoW, circle of Willis; d, distributed spasm; Hype, hypertension; ICA, internal carotid artery; L, left vessel; MCA, middle cerebral artery.

Fig. 6

Flow in the ACA is dependent upon the presence of a complete CoW as well as the degree of vasospasm in the proximal ICA and the MCA. Much larger drops in blood flow are seen in the ACA when the CoW is incomplete. ACA, anterior cerebral artery; CoW, circle of Willis; d, distributed spasm; f, focal spasm; Hype, hypertension; ICA, internal carotid artery; L, left vessel; MCA, middle cerebral artery.

Fig. 5

Blood flow in the ACA increased in the presence of MCA stenosis as a result of shunting. ACA, anterior cerebral artery; CoW, circle of Willis; d, distributed spasm; f, focal spasm; Hype, hypertension; L, left vessel; MCA, middle cerebral artery.