There are many inconsistencies in the literature regarding how to estimate the Lyapunov Exponent (LyE) for gait. In the last decade, many papers have been published using Lyapunov Exponents to determine differences between young healthy and elderly adults and healthy and frail older adults. However, the differences in methodologies of data collection, input parameters, and algorithms used for the LyE calculation has led to conflicting numerical values for the literature to build upon. Without a unified methodology for calculating the LyE, researchers can only look at the trends found in studies. For instance, LyE is generally lower for young adults compared to elderly adults, but these values cannot be correlated across studies to create a classifier for individuals that are healthy or at-risk of falling. These issues could potentially be solved by standardizing the process of computing the LyE.

This dissertation examined several hurdles that must be overcome to create a standardized method of calculating the LyE for gait data when collected with an accelerometer. In each of the following investigations, both the Rosenstein et al. and Wolf et al. algorithms as well as three normalization methods were applied in order to understand the extent at which these factors affect the LyE. First, the a priori parameters of time delay and embedding dimension which are required for phase space reconstruction were investigated. This study found that the time delay can be standardized to a value of 10 and that an embedding dimension of 5 or 7 should be used for the Rosenstein and Wolf algorithm respectively. Next, the effect of data length on the LyE was examined using 30 to 1300 strides of gait data. This analysis found that comparisons across papers are only possible when similar amounts of data are used but comparing across normalization methods is not recommended. And finally, the reliability and minimum required number of strides for each of the 6 algorithm-normalization method combinations in both young healthy and elderly adults was evaluated. This research found that the Rosenstein algorithm was more reliable and required fewer strides for the calculation of the LyE for an accelerometer.

According to the CDC in 2010, there were 2.8 million emergency room visits costing $7.9 billion dollars for treatment of nonfatal falling injuries in emergency departments across the country. Falls are a recognized risk factor for unintentional injuries among older adults, accounting for a large proportion of fractures, emergency department visits, and urgent hospitalizations. The objective of this research was to identify and learn more about what factors affect balance using analysis techniques from nonlinear dynamics. Human balance and gait research traditionally uses linear or qualitative tests to assess and describe human motion; however, it is growing more apparent that human motion is neither a simple nor a linear task. In the 1990s Collins, first started applying stochastic processes to analyze human postural control system. Recently, Zakynthinaki et al. modeled human balance using the idea that humans will remain erect when perturbed until some boundary, or physical limit, is passed. This boundary is similar to the notion of basins of attraction in nonlinear dynamics and is referred to as the basin of stability. Human balance data was collected using dual force plates and Vicon marker position data for leans using only ankle movements and leans that were unrestricted. With this dataset, Zakynthinaki’s work was extended by comparing different algorithms used to create the critical curve (basin of stability boundary) that encloses the experimental data points as well as comparing the differences between the two leaning conditions.