COMPUTATIONAL TECHNIQUES FOR INVERSE PROBLEMS IN KIDNEY MODELING

In order to understand the concentrating mechanism of the mammalian ki dneys, 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: d etermine h from a given V. This problem is ill-posed. Therefore, the r egularization methods must be used to circumvent the ill-conditioning. We show how the Levenberg-Tikhonov-Marquard method with the Sobolev n orm can be used to handle the inverse problem.