The kidney model as an inverse problem

摘要

The mammalian kidney is modeled by a multipoint boundary-value problem for a system of nonlinear ordinary differential equations. A corresponding inverse problem is presented, which allows the rigorous judgement of the potential of the given modeling technique. For its numerical solution a discretization is proposed, which is tailor-made for kidney models. It leads to a nonlinear-programming problem with nonlinear equality and inequality constraints. The suggested methods are applied to current research problems in renal physiology.