Modelling tubuloglomerular feedback in coupled nephrons

Tubuloglomerular feedback (TGF) is a delayed negative feedback mechanism that stabilizes the glomerular filtration rate (renal blood flow) and salt concentration in a single nephron, the basic filtering unit of the kidney. Fluid flow through the nephron exhibits three distinct patterns. It may flow at a constant rate, or it may oscillate in one of two ways: regularly or chaotically. Earlier models indicate that the TGF mechanism plays a role in the mediation of both a constant flow rate and limit cycle oscillations. However, these models do not incorporate the influence of backleak (diffusion) in coupled nephrons (those that are linked anatomically by their vasculature). This dissertation examines the effects of backleak on coupled nephrons. The main result is that backleak stabilizes the system: coupled nephrons with backleak exhibit steady flow rates at higher feedback gains than do those without backleak. This same stabilizing effect was observed in a model of a single nephron with backleak. The model describing the TGF mechanism in two coupled nephrons is also extended in a model of three coupled nephrons. The results suggest that the addition of a nephron to the system may have a destabilizing effect: limit cycle oscillations are exacerbated when a third nephron is added to the system. Numerical methods are developed and implemented to study the predictions given by the bifurcation analysis