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Annals of Biomedical Engineering

, Volume 37, Issue 5, pp 1028–1042 | Cite as

Parameter Estimation for Linear Compartmental Models—A Sensitivity Analysis Approach

  • Barbara Juillet
  • Cécile Bos
  • Claire Gaudichon
  • Daniel Tomé
  • Hélène Fouillet
Article
First Online:
Received:
Accepted:

Abstract

Linear compartmental models are useful, explanatory tools, that have been widely used to represent the dynamic behavior of complex biological systems. This paper addresses the problem of the numerical identification of such models, i.e., the estimation of the parameter values that will generate predictions closest to experimental observations. Traditional local optimization techniques find it difficult to arrive at satisfactory solutions to such a parameter estimation problem, especially when the number of parameters is large and/or few data are available from experiments. We present herewith a method based on a prior sensitivity analysis, which enables division of a large optimization problem into several smaller and simpler subproblems, on which only sensitive parameters are estimated, before the whole optimization problem is tackled from starting points that are already close to the optimum values. This method has been applied successfully to a linear 13-compartment, 21-parameter model describing the postprandial metabolism of dietary nitrogen in humans. The effectiveness of the method has been demonstrated using simulated and real data obtained in the intestine, blood and urine of healthy humans after the ingestion of a [15N]-labeled protein meal.

Keywords

Biological system modeling Inverse problem Parameter estimation Optimization methods Sensitivity Algorithms Compartmental models Nitrogen metabolism Dietary proteins Tissue distribution 

Abbreviations

BU

body urea

CV

coefficient of variation

d0

noise-free data

d1

low homogeneous noise data

d2

high homogeneous noise data

d3

high heterogeneous noise data

E

ileal effluents

G

gastric content

IL1

proximal intestinal lumen

IL2

distal intestinal lumen

LLF

log of the likelihood function

N

nitrogen

ODE

ordinary differential equations

PAA

peripheral free amino acids

PP

peripheral proteins

SA

sensitivity analysis

SAA

splanchnic free amino acids

SCP

splanchnic constitutive proteins

SEP

splanchnic exported proteins

UU

urinary urea

UA

urinary ammonia

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Notes

Acknowledgments

The authors would like to thank M. P. Saccomani from the University of Padova (Padova, Italy) for having checked the a priori identifiability of the studied model, and for helpful and constructive discussions on the global a priori identifiability of compartmental models. The authors also thank E. Cancès from the École Nationale des Ponts et Chaussées (Paris, France) and P. Michel from the École Nationale Supérieure (Paris, France) for helpful and stimulating discussions.

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Copyright information

© Biomedical Engineering Society 2009

Authors and Affiliations

  • Barbara Juillet
    • 1
  • Cécile Bos
    • 1
  • Claire Gaudichon
    • 1
  • Daniel Tomé
    • 1
  • Hélène Fouillet
    • 1
  1. 1.UMR914 Nutrition Physiology and Ingestive BehaviorINRA, AgroParisTechParisFrance

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