Modeling Dynamic Processes in the Intracranial System

9626391拉金研究员将生物数学建模、计算、缩放、渐近和微扰技术结合在一起，以更全面地了解与人类颅内系统动态过程相关的基本物理机制。一个一致的、完全依赖时间的、非线性的集中参数模型描述了颅内空间中压力、体积和血流之间的相互作用，该模型被改进、验证和扩展，以包括额外的生理学，如脑血管自动调节和与脊髓脑脊液空间的联系。利用标度和渐近技术辨识了一阶过程和相关的时间尺度。为了达到考虑震源事件所需的较高分辨率，探索了舱室内的动态建模和子模型与集中参数系统的其余部分的一致联系。提出了有效求解非线性模型方程的计算方法和策略。特别是，使用渐近-数值混合方法获得的结果在目前的情况下显示出很大的希望，因为这些过程发生在不同的时间尺度上。这个项目寻求开发一个现实而又易于处理的人脑压力和流体流动的数学模型。为此，目前的模型公式被扩展到包括额外的人类生理学，如脑血管自动调节，这是在面对波动的血压时保持大脑中足够的氧气转移所必需的血液流动的机制。开发了新的混合求解技术，以基于模型方程对压力和流动进行高效、准确的计算机模拟。改进的模型还通过将其数学预测与生理数据进行比较来验证。涉及正常生理和病理生理学的情况进行了研究。这项研究是应用数学家和神经外科医生共同参与的跨学科研究的一部分。尽管发展中的数学模型在涉及病理学的情况下似乎具有显著的临床实用价值，但临床方面在本研究中并未被考虑。重点完全放在增加我们对大脑中压力和流动的基本理解上。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量的关键因素。增强的数学模型包括一个血管调节方程，可以用来研究一氧化氮合酶(NOS)抑制剂对大脑的影响。一氧化氮合酶抑制剂的开发是美国生物技术公司目前非常感兴趣的一个主题。

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.