First-kind Fredholm integral equation of liver kinetics: numerical solutions by constrained least squares

Holt J.N. and Bracken A.J. (1980) First-kind Fredholm integral equation of liver kinetics: numerical solutions by constrained least squares. Mathematical Biosciences, 51 1-2: 11-24. doi:10.1016/0025-5564(80)90088-7


Author Holt J.N.
Bracken A.J.
Title First-kind Fredholm integral equation of liver kinetics: numerical solutions by constrained least squares
Journal name Mathematical Biosciences   Check publisher's open access policy
ISSN 0025-5564
Publication date 1980-01-01
Sub-type Article (original research)
DOI 10.1016/0025-5564(80)90088-7
Open Access Status Not yet assessed
Volume 51
Issue 1-2
Start page 11
End page 24
Total pages 14
Language eng
Subject 2613 Statistics and Probability
2700 Medicine
2611 Modelling and Simulation
2400 Immunology and Microbiology
1300 Biochemistry, Genetics and Molecular Biology
1100 Agricultural and Biological Sciences
2604 Applied Mathematics
Abstract A model for the enzymatic elimination of substrates from blood flowing through the liver has recently been developed, in which the liver is represented by an ensemble of elements acting in parallel. Taking into consideration statistical distributions of biochemical and hemodynamic properties of the elements, and the mixing of the outflows from the elements, it has been possible to formulate a first-kind Fredholm integral equation relating input and output concentrations of the substrate. The kernel of the integral equation is given as a solution of a transcendental equation. The present work treats the inverse problem of recovering information about the distributions of properties of the elements, given a set of input and output concentration data. Constrained least-squares techniques are used in conjunction with a quadratic spline approximation to the unknown distribution. Results of applying the method to synthetic data and prospects for the analysis of real data are discussed.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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