Studies in Renal Hemodynamics

肾的主要功能单位是肾单位，肾单位是与肾小管相连的毛细血管。人类肾脏中大约有100万个肾单位，其中很大一部分可能通过微血管系统紧密结合在一起。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，以及如何将建模范例中的不确定性和建模中固有参数的不确定性纳入肾血流的计算模拟中。耦合在体内产生，并且必须包括在模型中。模型参数的不确定性是我们对正在研究的系统了解有限的公认结果；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结果。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。由于肾单位在过滤血液方面的作用，人们经常认为，无论是明确的还是含蓄的，在单个肾单位观察到的行为代表了整个肾脏的功能。事实证明，这一假设在许多情况下都是有效和有用的。然而，已知的是，两个单独的肾单位的耦合可以诱导出个体中不存在的这对肾单位的动态。肾单位的大规模耦合被认为发生在肾脏，很可能会引发系统的集体行为，而这是事先无法猜到的。同样，理想化的模型建模和模型参数的规范可能不能准确地反映体内肾单位存在的环境。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的作用。

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.