A particular exact solution to the central core model of the renal medulla

We calculate the exact solution to the eight coupled, nonlinear ordinary differential equations describing the central core model of the renal medulla for the case in which no exchange of water is allowed between Tubes 1 and 3 with Tube 4. The calculation is based on the use of a particular form for the pump function that describes the flux of solute metabolically pumped from Tube 2 into the core. The analysis is extended by calculating corrections to this particular exact solution by using a perturbation method in which the small parameter is related to the now assumed nonzero water permeabilities.