The main functions of the kidney take place in the nephrons. For their proper operation, nephrons need to be supplied with a stable blood flow that remains constant despite fluctuations of arterial pressure. Such stability is provided by the afferent arterioles, which are unique vessels in the kidney capable of adjusting diameter. By doing so, afferent arterioles regulate blood delivery downstream, where the nephrons are located. The afferent arterioles respond to signals initiated by two mechanisms: the myogenic response which operates to absorb pressure perturbations within the vasculature, and tubuloglomerular feedback which operates to stabilize salt reabsorption.
In this thesis, a mathematical model of the renal nephrovasculature that represents both mechanisms in a dynamical context is developed. For this purpose, de- tailed representations of the myogenic mechanism of vascular smooth muscles and the tubular processes are developed and combined in a single comprehensive model. The resulting model is formulated with a large number of ordinary differential equations that represent the intracellular processes of arteriolar smooth muscles, coupled with a number of partial differential equations, mainly of the advection-diffusion-reaction type, that represent blood flow, glomerular filtration and the tubular processes. Due to its unique activation characteristics, the myogenic response is formulated with a set of delay differential equations.
The model is utilized to assess a verity of physiological phenomena: the conduction of vasomotor responses along the afferent arteriole, autoregulation under physiologic as well as pathophysiologic conditions, and renal oxygenation. A first attempt to model the impact of diabetes mellitus on renal hemodynamics is also made. Further, an application with clinical significance is presented. Namely, renal oxygenation is estimated under conditions that simulate those observed during cardiopulmonary surgery. Results indicate the development of renal hypoxia, which suggests an important pathway for the development of acute kidney injury.
