Cerebral autoregulation is one of the most critical control systems in the body, as a constant tissue perfusion is necessary for proper functioning of the brain. As a response to changes in blood pressure, this control system modulates cardiovascular parameters to maintain a constant cerebral blood flow. Transcranial Doppler ultrasound measurements are routinely used to measure blood flow velocity in the middle cerebral arteries, one of the largest suppliers of blood to the brain. These measurements are then used to estimate blood flow and assess efficacy of cerebral autoregulation. However, these measurements do not currently provide reliable indicators for early diagnosis of potential impairments in the cerebral arteries, as they lack the necessary accuracy. One problem from basing the estimates derived from measurements is the questionable assumption that regulation only influences the diameter of microvasculature, while the diameter of larger vessels, such as the middle cerebral artery, remains constant. It is now clear that the large arteries are compliant suggesting that the diameter of the middle cerebral artery can indeed change in response to variations in pulsatility. In addition, estimates derived from measurements do not account for topological variations in network of cerebral arteries, such as the main distribution system, the circle of Willis. These questions will be studied using a new one-dimensional fluid dynamic model of the circle of Willis. Geometric data for this model will be obtained from magnetic resonance angiographs. To solve these equations, new numerical methods will be used. Viscoelastic equations describing the compliance of the vascular wall will be introduced and the effects of including non-Newtonian flow will be studied. Additionally, the effects of curvature of the vessel topology will be estimated. In particular, the internal carotid artery, curves about 180 degrees from when it enters the scull to it is attached to the circle of Willis. To validate this model, computed results will be compared with measurements of cerebral blood flow and network topology. The model will be used to predict effects of changes in the topology as well as changes in outflow boundary conditions. For example, plan to study the effects on distribution of blood flow in response to changes in boundary conditions and compare this with changes in diameters of the proximal vessels. Furthermore, we plan to study changes between healthy subjects and in elderly DM patients. Mathematical models have long been used to study fluid dynamic properties of arteries, however no studies have used this approach to design patient specific models to predict CBF and cerebral autoregulation.
Cerebral autoregulation is a critical control system in the body, as constant tissue perfusion is necessary for proper functioning of the brain. In response to changes in blood pressure, this control system modulates cardiovascular parameters to maintain a constant cerebral blood flow. Impairments in cerebral autoregulation have been observed in patients with type II diabetes and are associated with an increased risk of stroke. Ultrasound measurements are routinely used to measure blood flow velocity in the cerebral arteries, the largest suppliers of blood to the brain. These measurements are then used to estimate cerebral blood flow and assess efficacy of cerebral autoregulation. One problem is the questionable assumption that regulation only influences the diameter of the microvasculature, while the diameter of larger vessels, such as the middle cerebral artery, remains constant. It is now clear that the large arteries are compliant suggesting that the diameter of middle cerebral artery can indeed change in response to variations in pulsatility. In addition, estimates derived from measurements do not account for topological variations in network of cerebral arteries, such as the main distribution system, the circle of Willis. These facts suggest that there is a need for development of more advanced methods to estimate cerebral blood flow. In this study we propose to combine physiological data analysis with mathematical fluid dynamic modeling to predict cerebral blood in healthy and diabetic patients. Mathematical models have long been used to study fluid dynamic properties of arteries, however no studies have used this approach to design patient specific models to predict cerebral blood flow. Modeling detailed hemodynamics allows us to develop hypotheses that can predict mechanisms that underlie regulatory failure. The proposed model and new numerical methods for fluid dynamics models with time dependent boundary conditions will be a considerable contribution to applied mathematics and biological sciences applications. Students, who will be doing research in this area, will have skills and knowledge in applied and computational mathematics, and physiology. Such professionals are in great demand.
