Modeling of Kidney Hemodynamics: Probability-Based Topology of an Arterial Network

Through regulation of the extracellular fluid volume, the kidneys provide important long-term regulation of blood pressure. At the level of the individual functional unit (the nephron), pressure and flow control involves two different mechanisms that both produce oscillations. The nephrons are arranged in a complex branching structure that delivers blood to each nephron and, at the same time, provides a basis for an interaction between adjacent nephrons.

The functional consequences of this interaction are not understood, and at present it is not possible to address this question experimentally. We provide experimental data and a new modeling approach to clarify this problem. To resolve details of microvascular structure, we collected 3D data from more than 150 afferent arterioles in an optically cleared rat kidney.

Using these results together with published micro-computed tomography (μCT) data we develop an algorithm for generating the renal arterial network. We then introduce a mathematical model describing blood flow dynamics and nephron to nephron interaction in the network. The model includes an implementation of electrical signal propagation along a vascular wall.

Simulation results show that the renal arterial architecture plays an important role in maintaining adequate pressure levels and the self-sustained dynamics of nephrons. By maintaining the volume and composition of the body fluids within narrow ranges, and by producing a set of hormones that affect the blood vessels, the kidneys provide important long-term regulation of blood pressure.

Disturbances of kidney function can cause hypertension, a prevalent disease in modern societies. The kidneys protect their own function against short-term variations in blood pressure at the level of the individual unit (the nephron). In recent years, it has become clear that there is an interaction between nephrons, and that this interaction is mediated through the arterial network of the kidney.

The renal vacular network has a complex topology, and at present there are no computational models of this topology, precluding a computational assessment of the consequences of nephron-nephron interactions for renal blood flow control. In this work we focus on understanding how kidney specific vascular structure affects blood flow patterns and nephron-to-nephron interaction in kidney.

The paper presents an approach to constructing realistic models of the renal vascular architecture. We developed a computational approach to reproduce the architecture and to examine its consequences for the operating regime of the nephrons.