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Regular and stochastic behavior of Parkinsonian pathological tremor signals

Author

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  • Yulmetyev, R.M.
  • Demin, S.A.
  • Panischev, O. Yu.
  • Hänggi, Peter
  • Timashev, S.F.
  • Vstovsky, G.V.

Abstract

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.

Suggested Citation

  • Yulmetyev, R.M. & Demin, S.A. & Panischev, O. Yu. & Hänggi, Peter & Timashev, S.F. & Vstovsky, G.V., 2006. "Regular and stochastic behavior of Parkinsonian pathological tremor signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 655-678.
    • Handle: RePEc:eee:phsmap:v:369:y:2006:i:2:p:655-678
    DOI: 10.1016/j.physa.2006.01.077
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    References listed on IDEAS

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    1. Yulmetyev, Renat M. & Emelyanova, Natalya A. & Demin, Sergey A. & Gafarov, Fail M. & Hänggi, Peter & Yulmetyeva, Dinara G., 2004. "Non-Markov stochastic dynamics of real epidemic process of respiratory infections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 300-318.
    2. Gonze, Didier & Halloy, José & Goldbeter, Albert, 2004. "Emergence of coherent oscillations in stochastic models for circadian rhythms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 221-233.
    3. Yulmetyev, Renat & Demin, Sergey & Emelyanova, Natalya & Gafarov, Fail & Hänggi, Peter, 2003. "Stratification of the phase clouds and statistical effects of the non-Markovity in chaotic time series of human gait for healthy people and Parkinson patients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 432-446.
    4. Yulmetyev, Renat M. & Mokshin, Anatolii V. & Hänggi, Peter, 2005. "Universal approach to overcoming nonstationarity, unsteadiness and non-Markovity of stochastic processes in complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 303-325.
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    Cited by:

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    3. Lahmiri, Salim, 2017. "Parkinson’s disease detection based on dysphonia measurements," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 98-105.
    4. De Gregorio, Juan & Sánchez, David & Toral, Raúl, 2022. "An improved estimator of Shannon entropy with applications to systems with memory," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. de Oliveira, M. Elias & Menegaldo, L.L. & Lucarelli, P. & Andrade, B.L.B. & Büchler, P., 2011. "On the use of information theory for detecting upper limb motor dysfunction: An application to Parkinson’s disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4451-4458.
    6. Mulligan, Robert F., 2014. "Multifractality of sectoral price indices: Hurst signature analysis of Cantillon effects in disequilibrium factor markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 252-264.

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