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Modeling methodology for nonlinear physiological systems

V Z Marmarelis1

  • 1Department of Biomedical Engineering, University of Southern California, University Park, Los Angeles 90089-1451, USA.

Annals of Biomedical Engineering
|March 1, 1997
PubMed
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A new modeling approach using principal dynamic modes (PDMs) offers a practical solution for analyzing complex nonlinear physiological systems. This method effectively captures arbitrary orders of nonlinearity from stimulus-response data.

Area of Science:

  • Biomedical Engineering
  • Systems Biology
  • Nonlinear Dynamics

Background:

  • Modeling nonlinear physiological systems is challenging due to their complex, arbitrary orders of nonlinearity.
  • Existing methods often fall short in capturing the full complexity of these systems.
  • Principal Dynamic Modes (PDMs) offer a novel framework for system identification.

Purpose of the Study:

  • To present a general modeling approach for nonlinear systems using Principal Dynamic Modes (PDMs).
  • To introduce two novel methods for estimating PDMs and associated nonlinearities from stimulus-response data.
  • To demonstrate the efficacy of the proposed methods for modeling nonlinear physiological systems.

Main Methods:

  • Utilizes a filter bank of PDMs feeding into a multi-input static polynomial nonlinearity.

Related Experiment Videos

  • Method I: Eigendecomposition of a matrix derived from kernel estimates.
  • Method II: Application of feedforward artificial neural networks with polynomial activation functions.

    • Main Results:

    • The proposed approach provides a general model for Volterra systems, applicable to arbitrary orders of nonlinearity.
    • Computer simulations demonstrate the effectiveness of both estimation methods.
    • The relative performance of the two methods is discussed.

    Conclusions:

    • This PDM-based approach offers a practicable solution for modeling highly nonlinear physiological systems.
    • Reliable estimation of PDMs from experimental data is crucial for successful model application.
    • The methodology expands the scope of systems that can be modeled using stimulus-response data.