Modeling Autoregulation and Blood Flow in the Cerebral Vasculature

大脑自动调节是身体中最关键的控制系统之一，因为恒定的组织灌注对于大脑的正常功能是必要的。作为对血压变化的响应，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，这些测量值用于估计血流量并评估脑自动调节的功效。然而，这些测量目前并不能为脑动脉中潜在损伤的早期诊断提供可靠的指标，因为它们缺乏必要的准确性。基于从测量得出的估计的一个问题是有疑问的假设，即调节仅影响微血管的直径，而较大血管（诸如大脑中动脉）的直径保持恒定。现在很清楚，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的变化而变化。此外，从测量中得出的估计值不能解释脑动脉网络的拓扑变化，如主要分布系统，Willis环。 这些问题将研究使用一个新的一维流体动力学模型的循环威利斯。 该模型的几何数据将从磁共振血管造影中获得。为了求解这些方程，将使用新的数值方法。 将介绍描述血管壁顺应性的粘弹性方程，并研究包括非牛顿流的影响。 此外，还将估计血管拓扑结构曲率的影响。特别是颈内动脉，从它进入颅骨到它附着在Willis环上弯曲约180度。为了验证该模型，计算结果将与脑血流和网络拓扑结构的测量结果进行比较。该模型将用于预测拓扑结构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DM患者之间的变化。长期以来，数学模型一直被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CBF和脑自动调节。大脑自动调节是身体中的关键控制系统，因为恒定的组织灌注对于大脑的正常功能是必要的。为了响应血压的变化，该控制系统调节心血管参数以维持恒定的脑血流量。已在II型糖尿病患者中观察到脑自动调节受损，并与卒中风险增加相关。超声测量通常用于测量脑动脉中的血流速度，脑动脉是大脑最大的血液供应者。这些测量然后用于估计脑血流量和评估脑自动调节的功效。一个问题是有疑问的假设，即调节只影响微血管的直径，而较大血管（如大脑中动脉）的直径保持不变。现在清楚的是，大动脉是顺应性的，这表明大脑中动脉的直径确实可以响应脉动的变化而变化。此外，从测量中得出的估计值不能解释脑动脉网络的拓扑变化，如主要分布系统，Willis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，我们提出了联合收割机生理数据分析与数学流体动力学建模预测健康和糖尿病患者的脑血。长期以来，数学模型一直被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。模拟详细的血流动力学使我们能够发展的假设，可以预测的机制，监管失败的基础。所提出的模型和新的数值方法的流体动力学模型与时间相关的边界条件，将是一个相当大的贡献，应用数学和生物科学的应用。 学生，谁将在这一领域做研究，将在应用和计算数学和生理学的技能和知识。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.