University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations Dissertations and Theses November 2017 QUANTIFYING GAIT ADAPTABILITY: FRACTALITY, COMPLEXITY, AND STABILITY DURING ASYMMETRIC WALKING Scott W. Ducharme University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_2 Part of the Biomechanics Commons, and the Motor Control Commons Recommended Citation Ducharme, Scott W., "QUANTIFYING GAIT ADAPTABILITY: FRACTALITY, COMPLEXITY, AND STABILITY DURING ASYMMETRIC WALKING" (2017). Doctoral Dissertations. 1075. https://doi.org/10.7275/10668508.0 https://scholarworks.umass.edu/dissertations_2/1075 This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. QUANTIFYING GAIT ADAPTABILITY: FRACTALITY, COMPLEXITY, AND STABILITY DURING ASYMMETRIC WALKING A Dissertation Presented By SCOTT W. DUCHARME Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY September 2017 Department of Kinesiology © Copyright by Scott W. Ducharme 2017 All Rights Reserved QUANTIFYING GAIT ADAPTABILITY: FRACTALITY, COMPLEXITY, AND STABILITY DURING ASYMMETRIC WALKING A Dissertation Presented By SCOTT W. DUCHARME Approved as to style and content by: ______________________________________________ Richard E. A. van Emmerik, Chair ______________________________________________ Jane A. Kent, Member ______________________________________________ Brian R. Umberger, Member ______________________________________________ John W. Staudenmayer, Member ___________________________________ Jane A. Kent, Department Chair Department of Kinesiology DEDICATION To my children, Adele and Max, who are my perpetual sources of inspiration, motivation, and distraction. I love you both more than the world. ACKNOWLEDGEMENTS It takes a village to raise a doctoral student, and I have been incredibly fortunate to have received such love and support over these past few years. This dissertation would not have been made possible if not for the support from family, friends, mentors, and colleagues. I first want to thank my wife, Ann, for your love, encouragement, insights, and everlasting patience over the better part of a decade. I truly could not have gotten to this point without you. I cannot thank you enough. I would also like to thank my entire family, especially my mom and dad, for always providing your unconditional love and support, for encouraging (requiring) me to go to college in the first place, and for raising me with a work ethic that has allowed me to get to where I am. I would like to thank my committee members, Jane Kent, Brian Umberger, and John Staudenmayer, for your guidance on this project and throughout my doctoral studies. Although I could name every faculty member, I also want to acknowledge Joe Hamill for his ‘unofficial’ but essential mentorship. In addition, I must give a huge thank you to the first study’s collaborators, Josh Liddy, Jeff Haddad, Mike Busa, and Laura Claxton. Many of the ideas and study designs presented herein are the result of numerous discussions with this group that were fueled by curiosity in an attempt to understand the ‘Practicality of Fracticality’, as Laura put it. I also would like to acknowledge the academic mentors that helped me prior to my time at UMass. I would like to thank my undergraduate advisor, Gary Sforzo, for his guidance in my undergraduate years, and well beyond. I also would like to thank my master’s advisor, Will Wu, who has continued to provide me with mentorship and friendship throughout my doctoral program. v I also could not have made it through this program without the incredible support from my Totman family. Being in an environment surrounded by people who are not only brilliant, but also helpful and fun, has made success that much easier to achieve. The numerous conversations I have had with many of you, both scientific and otherwise, have been critically important in helping me along the way. Many thanks are due to the participants who took part in these studies. Thank you to each person who took time and energy out of your day to support this research. Last, but not least, I would like to thank my advisor, Richard van Emmerik. I came to UMass expecting the world, and surprisingly I received just that. I could not have asked for a better mentor. I have learned such valuable information and lessons from you about science and life in general. I can say without a doubt that I would not be the person I am today without your influence. vi ABSTRACT QUANTIFYING GAIT ADAPTABILITY: FRACTALITY, COMPLEXITY, AND STABILITY DURING ASYMMETRIC WALKING SEPTEMBER 2017 SCOTT W. DUCHARME, B.S., ITHACA COLLEGE M.S., CALIFORNIA STATE UNIVERSITY, LONG BEACH Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Richard E. A. van Emmerik Successful walking necessitates modifying locomotor patterns when encountering organism, task, or environmental constraints. The structure of stride-to-stride variance (fractal dynamics) may represent the adaptive capacity of the locomotor system. To date, however, fractal dynamics have been assessed during unperturbed walking. Quantifying gait adaptability requires tasks that compel locomotor patterns to adapt. The purpose of this dissertation was to determine the potential relationship between fractal dynamics and gait adaptability. The studies presented herein represent a necessary endeavor to incorporate both an analysis of gait fractal dynamics and a task requiring adaptation of locomotor patterns. The adaptation task involved walking asymmetrically on a split-belt treadmill, whereby individuals adapted the relative phasing between legs. This experimental design provided a better understanding of the prospective relationship between fractal dynamics and adaptive capacity. Results from the first study indicated there was no association between unperturbed walking fractal dynamics and gait vii adaptability in young, healthy adults. However, there was an emergent relationship between asymmetric walking fractal dynamics and gait adaptability. Moreover, fractal dynamics increased during asymmetric walking. The second study investigated fractal dynamics and gait adaptability in healthy, active young and older adults. The findings from study 2 showed no differences between young and older adults regarding unperturbed or asymmetric walking fractal dynamics, or gait adaptability performance. The second study provided further evidence for the lack of association between unperturbed fractal dynamics and gait adaptability. Furthermore, study 2 delivered additional support that asymmetric walking not only yields increased fractal scaling values, but also associates with adaptive gait performance in older adults. Finally, while the first two studies explored stride time monofractality during various walking tasks, the third study aimed to understand the potential multifractality, i.e. temporal evolution of fractal dynamics, of unperturbed and asymmetric walking. The results suggest that unperturbed walking is monofractal in nature, while more challenging asymmetric walking reveals multifractal characteristics, and that multifractality does not associate with adaptive gait performance. This dissertation provides preliminary evidence for the lack of relationship between gait adaptability and unperturbed fractal dynamics, and the emergent association between adaptive gait and asymmetric walking fractality. viii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS .................................................................................................v ABSTRACT ...................................................................................................................... vii TABLE OF CONTENTS ................................................................................................... ix LIST OF TABLES ........................................................................................................... xvi LIST OF FIGURES ........................................................................................................ xvii GLOSSARY OF TERMS ..................................................................................................xx CHAPTER I. INTRODUCTION ...................................................................................................1 1.1 Gait Adaptability ................................................................................................2 1.1.1 Fractal Dynamics ................................................................................2 1.1.1.1 Monofractals ........................................................................3 1.1.1.2 Multifractals .........................................................................5 1.1.2 Complexity Analyses ..........................................................................6 1.1.3 Split-Belt Treadmill Paradigm ............................................................9 1.2 Gait Stability ....................................................................................................10 1.2.1 Global Stability .................................................................................10 1.2.2 Local Stability ...................................................................................13