A hemodynamic model to predict regional cerebral blood flow and blood flow reserve in patients with carotid stenosis

Joseph P Archie Jr, PhD, MD Abstract Purpose. Patients with 50% or greater diameter stenosis are at risk for ischemic stroke due to embolization and/or reduced cerebral blood flow. The hemodynamics of progressive carotid stenosis on cerebral blood flow and blood flow reserve has not been adequately measured or predicted. This information is needed for stroke risk stratification in patients with carotid stenosis. The aim of this hemodynamic model study is to predict the contribution of carotid and collateral blood flows to regional cerebral blood flow and cerebral blood flow reserve in patients with moderate to severe carotid stenosis. Methods. A one-dimensional three-parameter fluid mechanics model for the carotid, collateral and brain vascular systems is used to predict regional cerebral blood flow and blood flow reserve as a function of percent diameter carotid stenosis. The model is based on the principal of conservation of energy as employed by Bernoulli to describe fluid flow on a streamline. When applied to the human cerebrovascular system there are three vascular resistance components; carotid, collateral and brain. Carotid artery vascular resistance is assumed to be a function of fractional percent carotid artery area stenosis. This is not a complex modern computational fluid mechanics study. The model blood flow algebraic equations have simple solutions, one of which gives patient specific collateral resistance values. The solutions are given as patient specific cerebral blood flows and flow reserve as a function of percent diameter stenosis. Established normal clinical values of regional cerebral blood flow, cerebral blood flow auto-regulation and the lower threshold of cerebral perfusion pressure for cerebral auto-regulation are used. Carotid vascular resistance is assumed to be proportional to percent area carotid stenosis. Theoretical solutions use mean systemic arterial pressure of 100mmHg and key clinical values of patient collateral vascular resistance. Clinical solutions use patient measured systemic arterial pressures and carotid stump pressures. The solutions are given as patient specific cerebral blood flow and reserve cerebral blood flow curves over the range of diameter carotid stenosis. Results. Normal regional cerebral blood flow of 50ml/min/100g is predicted to be maintained up to 65% diameter carotid stenosis as reserve blood flow is reduced. With further progression of carotid stenosis to occlusion approximately half of patients are predicted to develop some reduction in cerebral blood flow. However, only about 20% of patients have a decrease in cerebral blood flow below the 30ml/min/100g threshold for cerebral ischemic symptoms. Approximately 10% of patients are predicted to develop regional cerebral blood flow less than the 18ml/min/100g threshold for irreversible ischemic injury. The model predicts critical carotid artery stenosis to be between 65% and 71% diameter depending on mean systemic arterial pressure. With higher degrees of stenosis carotid artery blood flow cannot maintain normal cerebral flow without the contribution of collateral flow. The predicted magnitude of carotid energy dissipation between 60% and 90% stenosis is consistent with observed cervical bruit intensity. Predicted patient specific cerebral blood flow reserve is adequate to prevent significant cerebral ischemia in the majority of patients. Conclusions. Patient specific collateral vascular resistance blood flow curves predict regional cerebral blood flow and blood flow reserve as a function of the degree of diameter carotid artery stenosis. The carotid component of cerebral blood flow is predicted to maintain normal cerebral blood flow up to a critical carotid diameter stenosis of 65% to 71%. Collateral blood flow is necessary to maintain normal cerebral flow at higher degrees of carotid stenosis. The clinical model predicts that many patients do not have sufficient collateral flow to prevent a decrease in cerebral flow should carotid stenosis progress to high grade or occlusion. However, only about 10% of patients are predicted to develop irreversible regional cerebral ischemic injury. Estimated carotid stenosis energy dissipation magnitudes agree with observed cervical bruit intensity. Correlation of predicted cerebral reserve blood flow curves with clinically measured cerebrovascular reactivity/reserve has the potential to predict the probability of future cerebral ischemia in asymptomatic patients with 60% to 80% stenosis.