Identification of Nonlinear Physiological Systems
David T Westwick and Robert E Kearney
(IEEE Press 2003 ISBN 0-471-27456-9)
This book has been produced as a successor to the classic text by Marmarelis and Marmarelis on the theme of Advanced Methods in
Physiological Modeling: the White Noise Approach, which was published in 1978. Since that time, much has occurred in relation
to the field of nonlinear identification particularly as a consequence of advances in computational methods.
Before commenting further, however, a caveat is needed in relation to the title of this work by Westwick and Kearney. The focus of
this new text, as was the case with that of Marmarelis and Marmarelis, is on signals which are to be interpreted in terms of black
box models, for instance those occurring in electrophysiology. It does not specifically address the problem of identifying systems
represented by physico-chemical models, for example metabolic, endocrine and physiological organ systems; models in which the
parameters correspond explicitly to physical or chemical properties of the dynamic processes being considered. There is a large
distinctive literature for this separate class of problem. Readers wishing to pursue this field would be well advised to consult
the writings of long-standing experts such Cobelli, DiStefano and Godfrey; leading-edge researchers of today, just as they were
thirty years ago.
Returning to this new work by Westwick and Kearney, the authors assume that the readership will have a basic grounding in linear
signals and systems. Background material beyond this level is summarised and there is an excellent set of references to further
reading. Each chapter includes both a number of simple problems as well as more extensive computational exercises, designed to
be tackled using MATLAB and the nonlinear system identification toolbox (NLID) developed by the authors. The style of writing
is very accessible with many illustrations drawn from physiological systems.
After some relevant background material, there are basic chapters on models of linear and nonlinear systems, with the latter
embracing Volterra and Wiener series, block structures, parallel cascades and the Wiener-Bose model. This is followed by a chapter
on the identification of linear systems. This is designed to lay the foundations for the more elaborate treatment of the nonlinear
identification problem, rather than to provide a comprehensive review of all available methods.
There then follows the final three substantive chapters which focus on issues and techniques relating to nonlinear identification.
The first of these deals with correlation methods. Although superior methods are now largely available, they still find widespread
adoption. Moreover, an appreciation of them is helpful as a precursor to the discussion of more recent approaches.
This is followed by a treatment of explicit least-squares methods. These include orthogonal algorithms, expansion bases and principal
dynamic modes. These methods are appropriate where model structures are linear in their parameters, such as Wiener or Volterra series,
and offer substantial improvements in model accuracy as compared to correlation methods. However, they are computationally expensive
and, of course, are limited to cases where linearity in the parameters exists.
These limitations provide a logical lead in to the final chapter which features iterative least-squares methods. These can be used
to tackle the real nonlinear problem, namely that where models have structures whose outputs are nonlinear functions of some or all
of their parameters. The chapter begins with treatments of the full range of gradient-based optimisation methods. This is followed
by consideration of the more recent parallel cascade methods. Full details of the mathematical treatments are presented in a lucid
manner and the chapter ends with a case study demonstrating the power of such methods when applied to a model of the visual processing
occurring in the light-adapted fly retina.
As one who many years ago reviewed that earlier text by Marmarelis and Marmarelis, I am happy to declare that this new work by
Westwick and Kearney is indeed a worthy successor. The authors communicate their ideas in a clear and logical manner, covering both
the underlying principles and the computational issues which need to be addressed in moving towards problem solution. It is a volume
that deserves to be on the bookshelf of all researchers involved in this increasingly important interface between signals and systems
theory on the one hand and physiology and medicine on the other.
Ewart Carson
February 2004
sd395@soi.city.ac.uk
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