脑脊液的数学压力-体积模型
Mathematical pressure volume models of the cerebrospinal fluid
AI总结：
本文回顾了脑脊液压力-体积数学模型，指出多数模型是单一微分方程的特例，并建议未来模型需纳入大脑力学特性。
摘要：
在过去的二十年里，医学文献中涌现出大量数学模型，试图描述中枢神经系统腔室的压力和体积动力学。这些模型已被用于研究该腔室在诸如脑积水、头部损伤和脑水肿等病理临床条件下的行为。众多不同的方法导致了在各类模型的有效性、准确性或适用性方面相当大的困惑。在本文中，我们以简化的方式回顾了这些模型的数学基础，将数学细节留待附录中阐述。我们表明，大多数先前的模型实际上是描述脑脊液压力（CSF）随时间演变的单一基本微分方程的特例。这一方法的核心是假设脑脊液体积相对于压力的变化率是脑组织顺应性的度量，这进而导致依赖于顺应性函数形式的特定模型。所有这些模型实际上基本上没有提供关于大脑本身行为的信息。更近期的模型（使用有限元方法进行数值求解）已开始解决这一问题，但由于缺乏关于大脑力学特性的信息而面临困难。我们提出了关于如何开发考虑这些力学特性的模型的建议。
英文摘要：
Numerous mathematical models have emerged in the medical literature over the past two decades attempting to characterize the pressure and volume dynamics the central nervous system compartment. These models have been used to study he behavior of this compartment under such pathological clinical conditions s hydrocephalus, head injury and brain edema. The number of different pproaches has led to considerable confusion regarding the validity, accuracy or appropriateness of the various models. In this paper we review the mathematical basis for these models in a mplified fashion, leaving the mathematical details to appendices. We show at most previous models are in fact particular cases of a single basic differential equation describing the evolution in time of the cerebrospinal fluid pressure (CFS). Central to this approach is the hypothsis that the rate change of CSF volume with respect to pressure is a measure of the compliance of the brain tissue which as a consequence leads to particular models epending on the form of the compliance funtion. All such models in fact give essentially no information on the behavior of the brain itself. More recent models (solved numerically using the Finite Element Method) have begun to address this issue but have difficulties due to the lack of information about the mechanical properties of the brain. Suggestions are made on how development of models which account for these chanical properties might be developed.
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