A Patient Suffering From Neurodegenerative Disease May Have a Strengthened Fractal Gait Rhythm

Scale invariance in stride series, namely, the series shows similar patterns across multiple time scales, is used widely as a non-invasive identifier of health assessment. Detailed calculations in the literature with standard tools, such as de-trended fluctuation analysis and wavelet transform modulus maxima seem to lead a conclusion that patients suffering from neurodegenerative diseases have weakened fractal gait rhythm compared with healthy persons. These variance-based methods are dynamical mechanism dependent, namely, for some dynamical process the scale invariance cannot be detected qualitatively, while for some others the scale invariance can be detected correctly, but the estimated value of scaling exponent is not correct. Generally, we have limited knowledge on the dynamical mechanism. What is more, the stride series for the patients have a typical finite length of ~300, which may lead to unreasonable statistical fluctuations to the evaluation procedure. Hence, how a neurodegenerative disorder disease affects the scale invariance is still an open problem. In this paper the balanced estimation of diffusion entropy (cBEDE) is used to overcome the limitations. The volunteers include healthy individuals and patients with/without freezing of gait (FOG). It is found that scale invariance exists widely in the gait time series for all the individuals. The average of scaling exponents for patients suffering from FOG is similar with or larger than that for healthy individuals, and similar with that for patients without FOG. The patients not suffering from FOG have an average of scaling exponent significantly larger than that for healthy people. From the results estimated by cBEDE, we can conclude that a patient may have an increased scaling exponent, which is contradictory qualitatively with that in the literatures.