The Effects of Aging and Dual Tasking on Human Gait Complexity During Treadmill Walking: A Comparative Study Using Quantized Dynamical Entropy and Sample Entropy

Abstract

Quantized dynamical entropy (QDE) has recently been proposed as a new measure to quantify the complexity of dynamical systems with the purpose of offering a better computational efficiency. This paper further investigates the viability of this method using five different human gait signals. These signals are recorded while normal walking and while performing secondary tasks among two age groups (young and older age groups). The results are compared with the outcomes of previously established sample entropy (SampEn) measure for the same signals. We also study how analyzing segmented and spatially and temporally normalized signal differs from analyzing whole data. Our findings show that human gait signals become more complex as people age and while they are cognitively loaded. Center of pressure (COP) displacement in mediolateral direction is the best signal for showing the gait changes. Moreover, the results suggest that by segmenting data, more information about intrastride dynamical features are obtained. Most importantly, QDE is shown to be a reliable measure for human gait complexity analysis.

Sample Entropy of Human Gait Center of Pressure Displacement: A Systematic Methodological Analysis

“… [ 3 ] of a dataset of length is the negative natural logarithm of the conditional probability of two successive counts of similar pairs (Chebyshev distance less than a tolerance size of r ) of template size and without allowing self-matches. SampEn is calculated as follows [ 7 ]; consider a time series of length N given below: First, m value is chosen to construct series of pairs, size m as: Next, matching templates are found by comparing their chebyshev distance to a pre-determined r value while excluding self-comparison. Next, a variable called is built which is the number of pairs satisfying the aforementioned criteria: Next, is defined as: This process is repeated for and r to form : Lastly, SampEn is calculated based on and as …”

“…Larger entropy values indicate less regularity or predictability in a time series. These measures have been used in gait analysis, and have been shown to discriminate between fallers and non-fallers [ 6 ], older and younger adults [ 7 , 8 ] and walk only (WO) and dual-task (DT) walking condition [ 7 ]. Various entropy measures have been proposed based on Shannon’s entropy [ 9 ] and its successor method, Approximate Entropy [ 10 ].…”

“…It has also been shown that there may be temporal scales in changes that occur in spatio-temporal gait variables [ 12 ]. However, these signals lack intra-stride information, which represents important passive and active gait control process [ 7 ]. Recent gait studies have examined “whole” gait signals (entire time series as opposed to stride-to-stride gait variables), such as trunk linear acceleration [ 1 , 6 , 13 , 14 ], joint angular positions [ 15 ] and center of pressure of feet displacement [ 7 , 16 ].…”

“…Center of pressure displacement in the mediolateral direction (ML COP-D) has been extensively used to examine the balance performance during standing conditions (base of support stationary) [ 17 , 18 , 19 ]. However, its usage in gait analysis is limited to a few studies [ 1 , 7 , 16 , 20 ]. This might be due to the limitation of the facilities that collect data on a treadmill or during overground walking.…”

“…ML COP-D is capable of representing both single and double support phases of the gait cycle. It has also been shown that SampEn of ML COP-D better distinguishes between different treadmill walking conditions as compared to the SampEn of other commonly used signals (e.g., trunk linear acceleration) [ 7 ].…”