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，因为持续的组织灌注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供血源之一。然后用这些测量来估计血流量和评估大脑自动调节的有效性。然而，这些测量目前还不能为早期诊断脑动脉潜在损伤提供可靠的指标，因为它们缺乏必要的准确性。基于测量得出的估计值的一个问题是一个有问题的假设，即调节只影响微血管的直径，而大血管（如大脑中动脉）的直径保持不变。现在很清楚，大动脉是顺从的，这表明大脑中动脉的直径确实可以随着脉搏的变化而改变。此外，从测量中得出的估计并没有考虑到脑动脉网络的拓扑变化，如主要分布系统，威利斯圈。这些问题将使用一个新的一维威利斯环流体动力学模型来研究。该模型的几何数据将从磁共振血管造影中获得。为了解这些方程，将使用新的数值方法。将引入描述血管壁顺应性的粘弹性方程，并将研究包含非牛顿流的影响。此外，还将估计容器拓扑曲率的影响。特别是颈内动脉，从进入头骨到连接到威利斯肌圈弯曲了180度。为了验证该模型，计算结果将与脑血流量和网络拓扑的测量结果进行比较。该模型将用于预测拓扑变化的影响以及流出边界条件的变化。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。数学模型长期以来一直用于研究动脉的流体动力学特性，但没有研究使用这种方法设计患者特异性模型来预测CBF和大脑自动调节。大脑的自动调节是人体的一个关键控制系统，因为持续的组织灌注是大脑正常运作所必需的。为了应对血压的变化，该控制系统调节心血管参数以维持恒定的脑血流量。在II型糖尿病患者中观察到大脑自动调节功能受损，并与卒中风险增加有关。超声测量通常用于测量大脑动脉的血流速度，大脑动脉是大脑最大的供血源。然后用这些测量来估计脑血流量和评估脑自动调节的有效性。一个问题是有疑问的假设，即调节只影响微血管的直径，而大血管（如大脑中动脉）的直径保持不变。现在很清楚，大动脉是顺从的，这表明大脑中动脉的直径确实可以随着脉搏的变化而改变。此外，从测量中得出的估计并没有考虑到脑动脉网络的拓扑变化，如主要分布系统，威利斯圈。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，我们提出将生理数据分析与数学流体动力学建模相结合来预测健康和糖尿病患者的脑血。数学模型长期以来一直用于研究动脉的流体动力学特性，但是没有研究使用这种方法来设计患者特定的模型来预测脑血流量。建模详细的血流动力学使我们能够提出假设，可以预测潜在的调节失败的机制。所提出的具有时间依赖边界条件的流体动力学模型和新的数值方法将对应用数学和生物科学的应用作出重大贡献。在这一领域进行研究的学生将具备应用数学和计算数学以及生理学方面的技能和知识。这类专业人员需求量很大。

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.