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.
- Kidney models
- Numerical methods