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Inferential framework for nonstationary dynamics. II, Application to a model of physiological signaling

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Duggento, Andrea, Luchinsky, Dmitri G., Smelyanskiy, Vadim N., Khovanov, I. A. and McClintock, P. V. E.. (2008) Inferential framework for nonstationary dynamics. II, Application to a model of physiological signaling. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol.77 (No.6). Article: 061106. ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.77.061106

Abstract

The problem of how to reconstruct the parameters of a stochastic nonlinear dynamical system when these are time-varying is considered in the context of online decoding of physiological information from neuron signaling activity. To model the spiking of neurons, a set of FitzHugh-Nagumo (FHN) oscillators is used. It is assumed that only a fast dynamical variable can be detected for each neuron, and that the monitored signals are mixed by an unknown measurement matrix. The Bayesian framework introduced in Paper I (Phys. Rev. E 77, 06110500 (2008)) is applied both for reconstruction of the model parameters and elements of the measurement matrix, and for inference of the time-varying parameters in the non-stationary system. It is shown that the proposed approach is able to reconstruct unmeasured (hidden) slow variables of the FHN oscillators, to learn to model each individual neuron, and to track continuous, random and step-wise variations of the control parameter for each neuron in real time.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)

Divisions:

Faculty of Science > Engineering

Library of Congress Subject Headings (LCSH):

Nonlinear theories, Stochastic systems, Neurons -- Mathematical models

Journal or Publication Title:

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

Publisher:

American Physical Society

ISSN:

1539-3755

Official Date:

4 June 2008

Dates:

Date	Event
4 June 2008	Published

Volume:

Vol.77

Number:

No.6

Number of Pages:

Page Range:

Article: 061106

Identification Number:

10.1103/PhysRevE.77.061106

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Funder:

Engineering and Physical Sciences Research Council (EPSRC), United States. National Aeronautics and Space Administration (NASA)

References:

[1] R. Mukkamala and R. J. Cohen, Am. J. Physiol.: Heart.
Circ. Physiol. 281, H2714 (2001).
[2] S. Lu and K. H. Chon, IEEE Trans. on Sig. Proc. 51,
3020 (2003).
[3] A. B. Schwartz, X. T. Cui, D. J. Weber, and D. W.
Moran, Neuron 52, 205 (2006).
[4] F. Lotte et al., Journal of Neural Engineering R1 (2007).
[5] S. Eyal and S. Akselrod, Meth. of Inform. in Medicine
39, 118 (2000).
[6] D. G. Luchinsky, V. N. Smelyanskiy, A. Duggento, and
P. V. E. McClintock, “Inferential framework for nonstationary
dynamics. Part I. Theory”, Phys. Rev. E 77,
061105 (2008).
[7] R. FitzHugh, Biophys. J. 1, 445 (1961).
[8] J. Nagumo, S. Animoto, and S. Yoshizawa, Proc. Inst.
Radio Engineers 50, 2061 (1962).
[9] A. T. Winfree, The Geometry of Biological Time
(Springer-Verlag, New York, 1980).
[10] J. Keener and J. Sneyd, Mathematical Physiology
(Springer-Verlag, New York, ADDRESS, 1998).
[11] E. N. Best, Biophys. J. 27, 87 (1979).
[12] J. Rogers and A. McCulloch, IEEE Trans. Biomed. Eng.
41, 743 (1994).
[13] R. R. Aliev and A. V. Panfilov, Journal of Theoretical
Biology 181, 33 (1996).
[14] P. Chen, SIAM J. Math. Anal. 23, 81 (1992).
[15] O. Berenfeld and S. Abboud, Med. Eng. and Phys. 18,
615 (1996).
[16] D. Bullock, P. Cisek, and S. Grossberg, Cereb. Cortex 8,
48 (1998).
[17] S. Rajasekar and M. Lakshmanan, J. Theor. Biol. 166,
275 (1994).
[18] R. Mannella, Intern. J. Mod. Phys. C 13, 1177 (2002).
[19] D. M. Bates and D. G. Watts, Nonlinear Regression and
Its Applications (Wiley, New York, 1988).
[20] D. G. Luchinsky et al., Phys. Rev. E 72, 021905 (2005).
[21] V. V. Osipov, D. G. Luchinsky, V. N. Smelyanskiy, and
D. A. Timucin, Proc. AIAA/ASME/SAE/ASEE Joint
Propulsion Conf. and Exhibit, AIAA Conference Proceedings
(AIAA, Cincinnati, OH, 2007), p. 5823.
[22] D. G. Luchinsky et al., Proc. AIAA
Infotech@Aerospace 2007 Conf. and Exhibit, AIAA
Conference Proceedings (AIAA, Robnert Park, CA,
2007), p. 2829.