Title: On the fractal geometry of Gait dynamics in different neuro-degenerative diseases

Abstract

Neuro-degenerative diseases significantly influence the gait behavior and the ability to move. To explore theetiology of neuro-degenerative disease, it would be useful to characterize gait dynamics. The purpose of thisstudy is to classify different neurodegenerative diseases using fractal geometry. We use Gait Dynamics in NeuroDegenerative Disease Data Base including recordings from patients with Parkinson’s disease (n = 15), Huntington’s disease (n = 20), or amyotrophic lateral sclerosis (n = 13) and 16 healthy control subjects are alsoincluded (Hausdorff JM et al., 2000). The vibration analysis using power spectral densities (PSD) method hasbeen carried out to discover whether some type of power-law scaling exists for various statistical moments atdifferent scales of these databases. Using Discrete Wavelet Transform (DWT) and Wavelet Leader Multifractal(WLM) analysis, we explore the possibility that these recordings belong to the class of multifractal process forwhich a large number of scaling exponents are required to characterize their scaling structures. A non-linearanalysis called the Fractal Dimension (FD) using Higuchi algorithm has been performed to quantify the fractalcomplexity of recordings. According to our results, we noticed that neither the power spectral densities nor theHiguchi algorithm to find the fractal dimension alone were sufficient to separate different classes of patients andhealthy people. In addition, when multifractal analysis and scaling exponent were used as a classifier, the threeclasses could not be well separated. However, this study revealed that we have a wide range of exponents forsome of the gait recordings which indicates they have multifractal structure and they need to be indexed bydifferent exponents as we decompose them into different subsets. In other words, these multifractal subjectsrequire much more exponents to characterize their scaling properties compared to monofractal gait recordingswhich their spectrum displays a narrow width of scaling exponent. Another important outcome from our multifractal analysis is recognizing obvious changes in the shape of D(h) curves for some of the gait recordings whichis crucial in finding the best strategies to better controlling the gait mechanisms in different neurodegenerativediseases. Although the vibration analysis, fractal dimension and multifractal analysis may not be able to classifygait recordings, however, they can be used as comprehensive frameworks to further analysis, characterize andcompare the complexity and fractal behavior of gait recordings and data structures of different neurodegenerative diseases in clinical database. Likewise, beside the Higuchi algorithm to find the fractal dimension as a complexity measure for the gait recordings, it will require much more efforts and further clinicalanalysis to find a specific threshold which make the fractal dimension to be considered as a biomarker anddiagnosis tool for different neuro-degenerative diseases.