Studies in Renal Hemodynamics

肾的主要功能单位是肾单位，一种连接到肾小管的毛细血管。人类肾脏中约有一百万个肾单位，其中很大一部分可能通过微血管系统紧密偶联。通过计算和分析的方法，两个主要的研究问题将得到解决：如何耦合大量的肾单位影响集体系统的动态，以及如何可以不确定性，在建模范式和建模中固有的参数，被纳入计算模拟肾血流。偶联发生在体内，必须包括在模型中。模型参数的不确定性是一个公认的后果，我们有限的知识所研究的系统;不确定性的限制，我们的研究中使用的模型可能会改变分析中确定的主要结果。解决这两个问题将为模拟与实验的联系提供重要步骤。 由于肾单位在过滤血液中的作用，人们经常明确或含蓄地认为，在单个肾单位中观察到的行为代表了整个肾功能。 这一假设在许多情况下都被证明是有效和有用的。 然而，已知两个单独的肾单位的耦合会引起个体中不存在的对的动力学。肾单位的大量偶联，因为它被认为发生在肾脏中，将可能引起系统的集体行为，这是无法预先猜测的。同样地，模型参数的理想化建模和规范可能不能准确地反映肾单位在体内存在的环境。该项目为肾血流调节的研究带来了新的数学思想，肾血流调节是一个复杂的生物系统，对人类健康起着重要作用。

The principal functional unit of the kidney is the nephron, a capillary tuft connected to a renal tubule. There are about 1 million nephrons in the human kidney, and a significant fraction of these may be closely coupled through the microvasculature. Through computational and analytical methods, two major research questions will be addressed: how does coupling of a large number of nephrons affect the dynamics of the collective system, and how can uncertainty, in modeling paradigms and in the parameters inherent in modeling, be incorporated into computational simulations of renal blood flow. Coupling arises in vivo, and must be included in models. Uncertainty in model parameters is a recognized consequence of our limited knowledge of the systems under study; uncertainty regarding the limitations of the very models used in our studies may alter major findings identified in the analysis. Answering these two questions will provide important steps in linking simulations with experiment. Because of the nephron's role in filtering blood, it is frequently assumed, either explicitly or implicitly, that the behavior observed in a single nephron is representative of whole kidney function. This assumption has proven valid and useful in many contexts. However, the coupling of two individual nephrons is known to induce dynamics of the pair that is not present in the individual. Massive coupling of nephrons, as it is thought to occur in the kidney, will likely elicit collective behavior from the system that cannot be guessed beforehand. Likewise, idealized modeling and specification of model parameters may not accurately reflect the environment in which the nephron exists in vivo. This project brings new mathematical ideas to the study of renal blood flow regulation, a complex biological system that plays an important role in human health.