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

Abstract

In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes [31]- [34]. The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year oulds), young people (from 21 up to 29 year oulds), elderly persons (from 71to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused by Parkinson's disease. We have found out distinct differencies between the five submitted groups. On this basis we offer a new method of diagnostics and forecasting Parkinson's disease.

Spectral Analysis of Gait Variability of Stride Interval Time Series: Comparison of Young, Elderly and Parkinson's Disease Patients

“…We found that for patients with PD, the walking time series had a tendency to change suddenly, and this was not apparent in healthy young or elderly subjects. To confirm the long-term fluctuation of gait variability of Parkinson's disease patients, several researchers have reported gait fluctuations in two-to fiveminutes walk 13,26,27) . Hausdorff et al 13) reported gait variability of PD in a five-minute walk, but they reported no such sudden change as was seen in the present study.…”

“…Thus, this result newly reveals a periodicity in stride time of 20-100 seconds that is related to disease severity in individuals with PD. Yulmetyev et al 27) reported that the most trustworthy information can be obtained only from low power frequencies of gait in Parkinson's disease, but they did not report the relationship between the disease severity and the power spectrum.…”

Regular and stochastic behavior of Parkinsonian pathological tremor signals

“…The method is connected with the studies of statistical non-Markov effects, long-and short-range statistical memory effects, regularity and stochastic behavior effects, and dynamic alternation of relaxation modes in the patient in various dynamic states. The study of non-Markov effects in complex systems in biology [3,4,5,6], physics [6,7,8,9], seismology [10,11], and medicine [2,12,13,14] is of special interest for correlation analysis. The scale of time fluctuations, long-range effects, discreteness of various processes and states, and the effects of dynamic alternation in the initial time series are important role in this respect.…”

Age-related alterations of relaxation processes and non-Markov effects in stochastic dynamics of R–R intervals variability from human ECGs

“…In recent years universal methods of statistical physics have been more often used in medicine and biology. The methods of statistical physics which have been used to research real complex systems [20,21,22,23,24,25], in the field of cardiology reveal essentially new opportunities for the analysis, diagnostics and forecasting the processes of biological ageing and diseases of a human heart. They disclose dynamic features of HRV, latent for classical medical methods of research.…”

“…This theory has already found practical application in cardiology [21], neurophysiology [22,23], the study of locomotor and sensomotor activity [22], epidemiology [24] and seismology [25].…”