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

Cerebral vasospasm is a typical complication occurring after Subarachnoid Hemorrhage, which may lead to delayed cerebral ischemia and death. The standard method to detect vasospasm is angiography, which is an invasive procedure. Monitoring of vasospasm is typically performed by measuring Cerebral Blood Flow Velocity (CBFV) in the major cerebral arteries and calculating the Lindegaard Index. State estimation techniques rely on mathematical models to estimate arterial radii based on available measurements. Mathematical models of cerebral hemodynamics have been proposed by Ursino and Di Giammarco in 1991, and vasospasm was modeled by Lodi and Ursino in 1999. We propose two new models. 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 states of Model 1, from which we readily obtain estimates of the arterial radii. Simulations show that Model 2 is capable of providing good estimates for the radius of the MCA, allowing the detection of the vasospasm.