Mathematical models for sodium and water transportation in the kidney
Mathematical models of the entire renal tubule have been derived based on the continuity principle for mass and volume flow under the assumption that the primary driving force is the osmotic force. These models have been used to describe the variations of sodium concentration and volume flow rate along the total length of the tubule and the interstitium of a typical canine kidney under varied conditions. Models of this kind can be of help in predicting the behavior or result of the function of the kidney, in interpreting the experimental data, or even more, in understanding the abnormal function of the kidney. The system of simultaneous partial differential equations for the unsteady state of the tubule and interstitium function are multiple-point boundary-value problem which are very difficult to solve. However, the solutions of the steady state equations with permeability coefficients of each section of the tubule and some anatomical data acquired have been presented along with discussion of those results and conclusions that were drawn from them.