Modeling Autoregulation and Blood Flow in the Cerebral Vasculature

大脑自动调节是人体最关键的控制系统之一，因为持续的组织灌流是大脑正常运作所必需的。作为对血压变化的反应，该控制系统调节心血管参数以维持恒定的脑血流量。经颅多普勒超声测量通常用于测量大脑中动脉的血流速度，大脑中动脉是大脑最大的血液供应者之一。然后，这些测量被用来估计血流量和评估脑自动调节的效果。然而，这些测量目前并不能为早期诊断脑动脉的潜在损害提供可靠的指标，因为它们缺乏必要的准确性。根据测量得出的估计值存在一个问题，即监管只影响微血管的直径，而大脑中动脉等较大血管的直径保持不变。现在很明显，大动脉是顺应性的，这表明大脑中动脉的直径确实可以随着脉动性的变化而改变。此外，根据测量得出的估计没有考虑大脑动脉网络的拓扑变化，如主要的分布系统，威利斯环。这些问题将用一种新的威利斯环的一维流体动力学模型来研究。这一模型的几何数据将从磁共振血管成像中获得。为了求解这些方程，将使用新的数值方法。将引入描述血管壁柔度的粘弹性方程，并研究考虑非牛顿流动的影响。此外，还将估计血管拓扑曲率的影响。尤其是颈内动脉，从它进入双桨时起弯曲约180度，与Willis环相连。为了验证该模型，计算结果将与脑血流和网络拓扑的测量结果进行比较。该模型将用于预测地形变化以及流出边界条件变化的影响。例如，计划研究边界条件变化对血流分布的影响，并将其与近端血管直径的变化进行比较。此外，我们计划研究健康受试者和老年糖尿病患者之间的变化。长期以来，数学模型一直被用来研究动脉的流体动力学特性，但还没有研究使用这种方法来设计特定于患者的模型来预测CBF和脑自动调节。大脑自动调节是体内的一个关键控制系统，因为持续的组织灌流是大脑正常运作所必需的。为了响应血压的变化，这个控制系统调整心血管参数，以保持恒定的脑血流量。在II型糖尿病患者中观察到大脑自动调节功能受损，并与中风风险增加有关。超声波测量通常被用来测量大脑动脉的血流速度，大脑动脉是大脑最大的血液供应者。然后，这些测量被用来估计脑血流量和评估脑自动调节的效果。一个问题是，认为调控只影响微血管的直径，而大脑中动脉等较大血管的直径保持不变的假设是有问题的。现在很明显，大动脉是顺应性的，这表明大脑中动脉的直径确实可以随着脉动性的变化而改变。此外，根据测量得出的估计没有考虑大脑动脉网络的拓扑变化，如主要的分布系统，威利斯环。这些事实表明，有必要开发更先进的方法来估计脑血流量。在这项研究中，我们建议结合生理数据分析和数学流体动力学模型来预测健康和糖尿病患者的脑血流。长期以来，数学模型一直被用来研究动脉的流体动力学特性，但还没有研究使用这种方法来设计特定于患者的模型来预测脑血流。通过建立详细的血流动力学模型，我们可以提出一些假说，来预测导致调节失灵的机制。所提出的含时变边界条件流体动力学模型和新的数值方法将为应用数学和生物科学的应用做出重大贡献。学生将在这一领域进行研究，他们将拥有应用数学和计算数学以及生理学方面的技能和知识。这样的专业人才需求量很大。

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.