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A Laplace transform approach to direct and inverse problems for multi-compartment models

Part of: Physiological, cellular and medical topics Integral transforms, operational calculus General theory in ordinary differential equations Algebraic combinatorics

Published online by Cambridge University Press:  16 March 2022

M. RODRIGO
M. RODRIGO*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia email: marianit@uow.edu.au
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Abstract

Multi-compartment models described by systems of linear ordinary differential equations are considered. Catenary models are a particular class where the compartments are arranged in a chain. A unified methodology based on the Laplace transform is utilised to solve direct and inverse problems for multi-compartment models. Explicit formulas for the parameters in a catenary model are obtained in terms of the roots of elementary symmetric polynomials. A method to estimate parameters for a general multi-compartment model is also provided. Results of numerical simulations are presented to illustrate the effectiveness of the approach.

Keywords

Compartment modelinverse problemLaplace transformpharmacokinetics

MSC classification

Primary: 92C42: Systems biology, networks 34A55: Inverse problems 44A10: Laplace transform
Secondary: 05E05: Symmetric functions and generalizations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 6 , December 2022 , pp. 1170 - 1184
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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