Discrete network models of interacting nephrons

The kidney is one of the major organs involved in whole-body homeostasis, and exhibits many of the properties of a complex system. The functional unit of the kidney is the nephron, a complex, segmented tube into which blood plasma is filtered and its composition adjusted. Although the behaviour of individual nephrons can fluctuate widely and even chaotically, the behaviour of the kidney remains stable.In this paper, we investigate how the filtration rate of a multi-nephron system is affected by interactions between nephrons. We introduce a discrete-time multi-nephron network model. The tubular mechanisms that have the greatest effect on filtration rate are the transport of sodium and water, consequently our model attempts to capture these mechanisms. Multi-nephron systems also incorporate two competing coupling mechanisms–vascular and hemodynamic–that enforce in-phase and anti-phase synchronisations respectively. Using a two-nephron model, we demonstrate how changing the strength of the hemodynamic coupling mechanism and changing the arterial blood pressure have equivalent effects on the system. The same two-nephron system is then used to demonstrate the interactions that arise between the two coupling mechanisms. We conclude by arguing that our approach is scalable to large numbers of nephrons, based on the performance characteristics of the model.