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Nonlinear Dynamical Systems and Adaptive Filters in Biomedicine

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Abstract

In this paper we present the application of a method of adaptive estimation using an algebra–geometric approach, to the study of dynamic processes in the brain. It is assumed that the brain dynamic processes can be described by nonlinear or bilinear lattice models. Our research focuses on the development of an estimation algorithm for a signal process in the lattice models with background additive white noise, and with different assumptions regarding the characteristics of the signal process. We analyze the estimation algorithm and implement it as a stochastic differential equation under the assumption that the Lie algebra, associated with the signal process, can be reduced to a finite dimensional nilpotent algebra. A generalization is given for the case of lattice models, which belong to a class of causal lattices with certain restrictions on input and output signals. The application of adaptive filters for state estimation of the CA3 region of the hippocampus (a common location of the epileptic focus) is discussed. Our areas of application involve two problems: (1) an adaptive estimation of state variables of the hippocampal network, and (2) space identification of the coupled ordinary equation lattice model for the CA3 region.

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Authors and Affiliations

  1. Center for Applied Optimization, ISE Department, and Biomedical Engineering Program, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

  2. Departments of Neurology and Neuroscience, and Biomedical Engineering Program, Brain Institute and Gainesville V.A. Medical Center, University of Florida, Gainesville, FL, 3261-6595, USA

    J. Chris Sackellares

  3. Scientific Foundation of Researchers and Specialists on Molecular Cybernetics and Informatics, Kiev, Ukraine

    Vitaliy A. Yatsenko

  4. ISE Department, University of Florida, Gainesville, FL, 3261-6595, USA

    Sergiy I. Butenko

Authors
  1. Panos M. Pardalos
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  2. J. Chris Sackellares
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  3. Vitaliy A. Yatsenko
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  4. Sergiy I. Butenko
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Pardalos, P.M., Sackellares, J.C., Yatsenko, V.A. et al. Nonlinear Dynamical Systems and Adaptive Filters in Biomedicine. Annals of Operations Research 119, 119–142 (2003). https://doi.org/10.1023/A:1022930406116

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