Nonlinear dynamical model of human gait

Abstract

We present a nonlinear stochastic model of the human gait control system in a variety of gait regimes. The stride interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations become more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. The human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.

Size Effects on Correlation Measures

“…In particular, while the power spectrum of the artificially generated time series is a power law characterized by a correlation exponent β, the autocorrelation function of the time series we generate does not behave properly as a power law (and then there is no clear value of the exponent γ ) for small lengths of the time series (N < 2 12 ) and for low values of the correlation exponent β (β < 1/2). Thus, in our numerical simulations, we have considered lengths in the range 2 12 ≤ N ≤ 2 20 and values of β in the range 1/2 < β < 2. For any value of N and β, we have generated 2 25 /N correlated time series.…”

“…The deviations are larger for small (β around 0) and moderately large (β around 1) degree of correlations than for intermediate β values. Nevertheless, in general the values of Hurst's exponent H deviates substantially from the theoretically expected values, and could produce spurious results when analyzing time series: for example, for β = 0 (corresponding to purely random time series) Hurst's analysis provides, on average, H values of up to H = 0.63 for N = 2 8 or H = 0.58 for N = 2 12 . These results would lead to the conclusion that long-range correlations exist in the time series, when actually the time series is randomly generated.…”

“…Many examples can be mentioned: long-range correlations have been observed in DNA sequences [1,2], in cardiac dynamics (measuring interbeat time intervals) [3][4][5][6][7], in human electroencephalographic fluctuations [8,9], in human motor activity [10] and gait [11][12][13], in sensory receptors in neural systems [14], etc. Outside biophysical examples, long-range correlations are also present in meteorology [15][16][17][18][19], seismic signals [20], economics [21,22] and even in the properties of music [23].…”

Statistical quantifiers of memory for an analysis of human brain and neuro-system diseases

“…They studied the dynamical changes of human gait, connected with various diseases [13][14][15][16], the increasing instability of gait in elderly people [13,[16][17][18], presence of long-range correlations in stride interval fluctuations [19,20], stride-to-stride variability and its temporal organization in children [21]. Walking indeed constitutes a complex process which we only recently started to understand through the application of non-linear data processing techniques [12,[22][23][24][25][26][27].…”

Regular and stochastic behavior of Parkinsonian pathological tremor signals

“…A nonlinear dynamical model is used to analyze a variety of human gaits [24]. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations.…”