Computational techniques for inverse problems in kidney modeling

S. Kim; R. P. Tewarson

doi:10.1016/0893-9659(96)00036-5

Computational techniques for inverse problems in kidney modeling

S. Kim, R. P. Tewarson

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	77-81
Number of pages	5
Journal	Applied Mathematics Letters
Volume	9
Issue number	3
DOIs	https://doi.org/10.1016/0893-9659(96)00036-5
State	Published - May 1996

Bibliographical note

Funding Information:
by Korean Ministry of Education, BSRI-95-1430 and Ewha Women’s University, 1994-3. by NSF Grant DMS921664 and NIH Grant DK1759314. Author to whom all correspondence

Keywords

Ill-conditioning
Kidney models
Numerical methods
Regularization

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10.1016/0893-9659(96)00036-5

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title = "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.",

keywords = "Ill-conditioning, Kidney models, Numerical methods, Regularization",

author = "S. Kim and Tewarson, \{R. P.\}",

note = "Funding Information: by Korean Ministry of Education, BSRI-95-1430 and Ewha Women{\textquoteright}s University, 1994-3. by NSF Grant DMS921664 and NIH Grant DK1759314. Author to whom all correspondence",

year = "1996",

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AU - Tewarson, R. P.

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N2 - 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.

AB - 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.

KW - Ill-conditioning

KW - Kidney models

KW - Numerical methods

KW - Regularization

UR - https://www.scopus.com/pages/publications/0037888352

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DO - 10.1016/0893-9659(96)00036-5

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SN - 0893-9659

VL - 9

SP - 77

EP - 81

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 3

ER -

Computational techniques for inverse problems in kidney modeling

Abstract

Bibliographical note

Keywords

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