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Acta Neurochir Suppl. 2008;102:63-9.

Mathematical models of cerebral hemodynamics for detection of vasospasm in major cerebral arteries.

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Electrical Engineering Department, University of California Los Angeles, 44-123 Engineering IV Building, Los Angeles, CA 90095, USA.



Vasospasm is a common complication of aneurismal subarachnoid hemorrhage (SAH) that may lead to cerebral ischemia and death. The standard method for detection of vasospasm is conventional cerebral angiography, which is invasive and does not allow continuous monitoring of arterial radius. Monitoring of vasospasm is typically performed by measuring Cerebral Blood Flow Velocity (CBFV) in the major cerebral arteries and calculating the Lindegaard ratio. We describe an alternative approach to estimate intracranial arterial radius, which is based on modeling and state-estimation techniques. The objective is to obtain a better estimation than that offered by the Lindegaard ratio, that might allow for continuous monitoring and possibly vasospam prediction without the need for angiography.


We propose two new models of cerebral hemodynamics. Model 1 is a more general version of Ursino's 1991 model that includes the effects of vasospasm, and Model 2 is a simplified version of Model 1. We use Model 1 to generate Intracranial Pressure (ICP) and CBFV signals for different vasospasm conditions, where CBFV is measured at the middle cerebral artery (MCA). Then we use Model 2 to estimate the arterial radii from these signals.


Simulations show that Model 2 is capable of providing good estimates for the radius of the MCA, allowing the detection of the vasospasm. These changes in arterial radius are being estimated from measurements of CBFV, and CBF is never being measured directly. This is the main advantage of the model-based approach where several interrelations between CBFV, ABP and ICP are taken into account by the differential equations of the model.


Our results indicate that arterial radius may be estimated using measurements of ABP, ICP and CBFV, allowing the detection of vasospasm.

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