Tsallis statistics and neurodegenerative disorders

In this paper, we perform statistical analysis of time series deriving from four neurodegenerative disorders, namely epilepsy, amyotrophic lateral sclerosis (ALS), Parkinson’s disease (PD), Huntington’s disease (HD). The time series are concerned with electroencephalograms (EEGs) of healthy and epileptic states, as well as gait dynamics (in particular stride intervals) of the ALS, PD and HDs. We study data concerning one subject for each neurodegenerative disorder and one healthy control. The analysis is based on Tsallis non-extensive statistical mechanics and in particular on the estimation of Tsallis q-triplet, namely {qstat, qsen, qrel}. The deviation of Tsallis q-triplet from unity indicates non-Gaussian statistics and long-range dependencies for all time series considered. In addition, the results reveal the efficiency of Tsallis statistics in capturing differences in brain dynamics between healthy and epileptic states, as well as differences between ALS, PD, HDs from healthy control subjects. The results indicate that estimations of Tsallis q-indices could be used as possible biomarkers, along with others, for improving classification and prediction of epileptic seizures, as well as for studying the gait complex dynamics of various diseases providing new insights into severity, medications and fall risk, improving therapeutic interventions.