Studies in Renal Hemodynamics

肾脏的主要功能单位是肾元，一个连接肾小管的毛细血管丛。人体肾脏中约有100万个肾单位，其中很大一部分可能通过微血管紧密相连。通过计算和分析方法，将解决两个主要的研究问题：大量肾单位的耦合如何影响集体系统的动力学，以及如何将建模范式和建模固有参数中的不确定性纳入肾脏血流的计算模拟。耦合发生在体内，必须包含在模型中。模型参数的不确定性是我们对所研究系统的有限知识的公认结果；关于我们研究中使用的模型的局限性的不确定性可能会改变分析中确定的主要发现。回答这两个问题将为将模拟与实验联系起来提供重要的步骤。由于肾元在过滤血液中的作用，人们经常明确或含蓄地认为，在单个肾元中观察到的行为代表了整个肾脏的功能。这个假设在很多情况下都是有效和有用的。然而，已知两个个体肾单位的耦合会诱导个体中不存在的对动力学。肾单位的大量耦合，正如它被认为发生在肾脏中，可能会引起系统的集体行为，这是无法事先猜测的。同样，理想化的建模和模型参数的规范可能不能准确地反映肾元在体内存在的环境。该项目为肾脏血流调节这一复杂的生物系统的研究带来了新的数学思路，对人体健康起着重要作用。

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.