Modeling methology for nonlinear physiological systems
Abstract
A general modeling approach for a broad class of nonlinear systems is presented that uses the concept of principal dynamic modes (PDMs). These PDMs constitute a filter bank whose outputs feed into a multi-input static nonlinearity of multinomial (polynomial) form to yield a general model for the broad class of Volterra systems. Because the practically obtainable models (from stimulus-response data) are of arbitrary order of nonlinearity, this approach is applicable to many nonlinear physiological systems heretofore beyond our methodological means. Two specific methods are proposed for the estimation of these PDMs and the associated nonlinearities from stimulus-response data. Method I uses eigendecomposition of a properly constructed matrix using the first two kernel estimates (obtained by existing methods). Method II uses a particular class of feedforward artificial neural networks with polynomial activation functions. The efficacy of these two methods is demonstrated with computer-simulated examples, and their relative performance is discussed. The advent of this approach promises a practicable solution to the vexing problem of modeling highly nonlinear physiological systems, provided that experimental data be available for reliable estimation of the requisite PDMs.
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- Authors
- Marmarelis, V. Z.
- Affiliations
- University of Southern California (US)
- Corresponding author
- Marmarelis, Vasilis Z.
- Venue
- Annals of Biomedical Engineering
- Published
- 1997-03
- Volume
- 25
- Issue
- 2
- Pages
- 239-251
- ISSN
- 0090-6964 (ISSN-L)
- 1573-9686
- OpenAlex
- W1227425701
- Cited by
- 94
- References
- 18
- Citations by year
- 2024: 1 · 2023: 3 · 2022: 1 · 2021: 1 · 2020: 2 · 2019: 2 · 2018: 4 · 2017: 7 · 2016: 7 · 2015: 2 · 2014: 4 · 2013: 8 · 2012: 6
- FWCI
- 7.59
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Annals of Biomedical Engineering (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Center for Research Resources (P41RR001861, RR01861)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Engineering › Computational Mechanics › Advanced Adaptive Filtering Techniques
- Keywords
- nonlinear system modeling, Volterra systems, filter banks, polynomial nonlinearity, kernel estimation, eigenvalue decomposition, feedforward neural networks, polynomial activation functions, physiological systems, nonlinear system identification
- MeSH terms
- Algorithms, Computer Simulation, Mathematics, Models, Theoretical, Physiology, Models, Statistical, Neural Networks, Computer, Nonlinear Dynamics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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