Computational techniques for inverse problems in kidney modeling

AbstractIn 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

The convergence of quasi-Gauss-Newton methods for nonlinear problems

AbstractQuasi-Gauss-Newton methods for nonlinear equations are investigated. A Quasi-Gauss-Newton method is proposed. In this method, the Jacobian is modified by a convex combination of Broyden's update and a weighted update. The convergence of the method described by Wang and Tewarson in [1] and the proposed method is proved. Computational evidence is given in support of the relative efficiency of the proposed method

Numerical solutions of differential equations for renal concentrating mechanism in inner medullary vasa recta models

AbstractTwo vasa recta models of the renal concentrating mechanism are presented. It is shown that by considering the effects of ascending vasa recta permeabilities, interstitial resistance, lateral small scale histotopography, and standard deviations in permeability values, these models lead to significant improvements in collecting duct urea and salt concentration ratios

A quasi-gauss-Newton method for solving non-linear algebraic equations

AbstractOne of the most popular algorithms for solving systems of nonlinear algebraic equations is the sequencing QR factorization implementation of the quasi-Newton method. We propose a significantly better algorithm and give computational results