Modeling Dynamic Processes in the Intracranial System

研究者结合了生物数学建模、计算、缩放、渐近和摄动技术，以获得与人类颅内系统动态过程相关的基本物理机制的更完整的理解。一个一致的、完全依赖于时间的非线性集总参数模型描述了颅内空间的压力、体积和流量之间的相互作用，该模型得到了改进、验证，并扩展到包括额外的生理学，如脑血管自动调节和与脊髓脑脊液空间的联系。一阶过程和相关的时间尺度被确定使用标度和渐近技术。为了获得考虑焦点事件所需的更高分辨率，研究了隔室内的动态建模以及子模型与集总参数系统其余部分的一致链接。提出了非线性模型方程有效数值解的计算方法和策略。特别是，使用混合渐近数值方法获得的结果在目前的背景下显示出很大的希望，其中过程发生在不同的时间尺度上。该项目旨在为人脑中的压力和流体流动建立一个现实而易于处理的数学模型。为此，目前的模型公式被扩展到包括额外的人体生理学，如脑血管自动调节，这是在血压波动时维持大脑血液流动所需的足够氧气转移的机制。为了在模型方程的基础上对压力和流量进行高效、精确的计算机模拟，开发了新的混合求解技术。通过将数学预测结果与生理数据进行比较，验证了模型的有效性。涉及正常和病理生理的情况进行了研究。这项研究是跨学科努力的一部分，涉及应用数学家和神经外科医生。尽管发展中的数学模型在涉及病理的情况下似乎具有重要的临床效用，但目前的研究并未考虑临床方面。其重点完全在于增加我们对大脑压力和血流的基本理解。一旦开发和验证，增强的数学模型将对研究与生物技术相关的应用的研究人员有用。例如，大脑中血管系统的调节在创伤和中风等疾病中起着至关重要的作用。目前，一氧化氮正在成为调节脑血流的关键因素。增强的数学模型包括一个血管调节方程，可用于研究一氧化氮合酶（NOS）抑制剂对大脑的影响。NOS抑制剂的开发是当前美国生物技术公司非常感兴趣的课题。

9626391 Lakin The investigator combines biomathematical modeling, computation, scaling, asymptotics and perturbation techniques to obtain a more complete understanding of basic physical mechanisms associated with dynamic processes in the human intracranial system. A consistent, fully time-dependent, nonlinear lumped parameter model describing interactions between pressures, volumes, and flows in intracranial space is refined, validated, and expanded to include additional physiology, such as cerebrovascular autoregulation and links to the spinal cerebrospinal fluid space. First order processes and relevant time scales are identified using scaling and asymptotic techniques. To achieve the higher resolution necessary to consider focal events, dynamic modeling within compartments and consistent linkage of sub-models with the rest of the lumped parameter system is explored. Computational methods and strategies for efficient numerical solution of the nonlinear model equations are developed. In particular, results obtained using hybrid asymptotic-numerical methods show great promise in the present context where processes occur on disparate time scales. This project seeks to develop a realistic yet tractable mathematical model for pressures and fluid flows in the human brain. Toward this end, the current model formulation is extended to include additional human physiology, such as cerebrovascular autoregulation, the mechanism which maintains the blood flow in the brain necessary for adequate oxygen transfer in the face of fluctuating blood pressure. New hybrid solution techniques are developed to carry out efficient and accurate computer simulations of pressures and flows based on the model equations. The enhanced model is also validated by comparing its mathematical predictions with physiological data. Situations involving both normal and pathophysiology are studied. This research is part of an interdisciplinary effort involving both applied mathema ticians and neurosurgeons. Although the developing mathematical model appears to have significant clinical utility in situations involving pathology, clinical aspects are not considered in the present research. The focus is entirely on increasing our basic understanding of pressures and flows in the brain. Once developed and validated, the enhanced mathematical model will be useful to researchers studying applications associated with biotechnology. For example, regulation of the vascular system in the brain plays a crucial role in conditions such as trauma and stroke. Currently, nitric oxide is emerging as a key factor in adjusting brain blood flow. The enhanced mathematical model, which includes a vascular regulation equation, can be used to study the effect of nitric oxide synthase (NOS) inhibitors on the brain. The development of NOS inhibitors is a subject of great current interest to U.S. biotechnology companies.