Computational techniques for inverse problems in kidney modeling

Abstract

In order to understand the concentrating mechanism of the mammalian kidneys, it is necessary to study the relationship between the parameter vector h (permeabilities of water and solutes) and the corresponding vector of concentration profiles V. We consider the inverse problem: determine h from a given V. This problem is ill-posed. Therefore, the regularization methods must be used to circumvent the ill-conditioning. We show how the Levenberg-Tikhonov-Marquard method with the Sobolev norm can be used to handle the inverse problem.