Elsevier

Automatica

Volume 33, Issue 5, May 1997, Pages 851-870
Automatica

Paper
Nonparametric input estimation in physiological systems: Problems, methods, and case studies

https://doi.org/10.1016/S0005-1098(96)00254-3Get rights and content

Abstract

Input estimation from output data is an important problem in the analysis of physiological systems, because many signals of interest are not directly accessible to measurement. When the system is time-invariant, this problem is often referred to as deconvolution. Three representative physiological problems, regarding hormone secretion, insulin dynamics, and hepatic glucose production, are used to illustrate the major challenges: ill-conditioning, confidence intervals assessment, infrequent and nonuniform sampling, nonnegativity constraints, and computational efficiency. The paper provides a critical overview of the existing techniques, focusing on regularization theory and Bayesian estimation. In order to overcome some inadequacies of the existing methods, some new results are derived. In particular, the connection between the maximum-likelihood estimate of the regularization parameter and the notion of equivalent degree of freedom is studied. Moreover, a fast SVD-based numerical algorithm is developed that includes the optimization of the regularization parameter, and the computation of confidence intervals. The proposed techniques are validated on a benchmark problem and are shown to provide effective solutions to the three physiological case studies.

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    The original (preliminary) version of this paper was presented at the 12th IFAC World Congress, which was held in Sydney, Australia, during July 1993. The Published Proceedings of this IFAC Meeting may be ordered from: Elsevier Science Limited, The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, U.K. This paper was recommended for publication in revised form by Associate Editor Arun Bagchi under the direction of Editor Torsten Söderström.

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