A transient model of the renal medulla.

The kidney is one of the most important organs in the body, responsible for regulating the volume and composition of the extracellular fluid; excreting metabolic waste (as urine) and foreign substances; and also producing some hormones. Through its functional unit, the nephron, blood is filtered and along the course of the different segments reabsorption and secretion takes place until the final product leaves the collecting duct as urine. This thesis focuses on the urine concentrating mechanism, presenting a transient shunt model of the renal medulla where a population of nephrons is merged into a common structure. The model, consisting of a coupled system of PDEs-ODEs describing concentrations and volume flows through the loop of Henle, collecting duct, and vasa recta, is solved by the numerical Method of Lines. For the first time in the case of a shunt model, the prebend transition occurring at a fixed distance before the turn at the tip of the descending loop of Henle is included. The hypothesis considering glycolysis as a source of external osmoles is presented in a model of the vasa recta, where a new numerical approach based on the software package Chebfun is considered. Later, this process is included in a full model of the renal medulla. Several results from the transient analysis are also presented, such as the time that it takes to wash out the gradient if an increase of blood flow occurs and the time that the gradient takes to build up for the different solutes.