The Application of Detrended Fluctuation Analysis and Adaptive Fractal Analysis on Center of Pressure Time Series in Parkinson's Disease By Melanie Weilert Submitted to the graduate degree program in Bioengineering and the Graduate Faculty of the University of Kansas in partial fulfillment of the requirements for the degree of Master of Science. ________________________________ Chairperson Dr. Carl Luchies ________________________________ Dr. Huazhen Fang ________________________________ Dr. Suzanne Shontz Date Defended: March 15th, 2017 The Thesis Committee for Melanie Weilert certifies that this is the approved version of the following thesis: The Application of Detrended Fluctuation Analysis and Adaptive Fractal Analysis on Center of Pressure Time Series in Parkinson's Disease ________________________________ Chairperson Dr. Carl Luchies Date approved: March 15th, 2017 ii Abstract The long term goal of this thesis is to create quantitative, clinically significant measures that allow for early detection of Parkinson’s disease (PD) postural instability (PI), the progression of PI due to PD progression, and ultimately, fall risk in PD patients. Current clinical assessments in PD are not sufficiently sensitive to predict fall risk. Although biomechanical postural sway measures have provided quantitative characterization towards the progression of PI associated with PD progression, these methods are still not sufficiently sensitive to allow for early detection of PD and fall risk. Thus, a need arises for new quantitative methods to be established which can further describe PI progression in PD. This thesis had two overall goals: Evaluate the appropriate selection of input parameters of detrended fluctuation analysis (DFA) and adaptive fractal analysis (AFA) in simulated signals. Test the sensitivity of AFA, as compared to DFA, towards center of pressure velocity (COPv) time series towards characterization of postural instability (PI) progression in patients with Parkinson’s disease. Specific Aim 1 determined through iterative testing of input parameter combinations that both AFA and DFA are highly sensitive to input parameters when considering fractional Brownian motion (fBm) signals. Input parameter ranges for fBm-like signals in appropriately-large biological data should be examined at maximum window sizes (nmax) values between N/6 and N/10; minimum window sizes (nmin) values around 4 to 6 samples; and for fitted polynomial order (M) for AFA to remain first order. Specific Aim 2 showed that fractal analysis methods may be sensitive towards detecting the development and progression of PI in PD. AFA and DFA were tested on postural sway data collected in a previous study that used mild PD patients (Hoehn and Yahr stage (H&Y) 2, iii without postural deficits), moderate PD patients (H&Y 3, with postural deficits), and age- matched healthy controls (HC). AFA produced the most clinically significant measure, Hfast, which detected changes in COPv dynamics across smaller time scales than other parameters. These results suggest that components of fractal analysis on COPv time series could be used in concert with traditional quantitative and clinical measures to further enhance the sensitivity of clinical analysis, the understanding of PD PI dynamics and progression, and development of predictive computational simulations of motor and postural control in PD. iv Acknowledgments I am extraordinarily grateful to all of the people in my life who have helped me during my graduate career! Without their unconditional and unwavering support, I would not have succeeded in graduate school. I would like to thank a few people in particular for their help, guidance, and support: Dr. Carl Luchies, my advisor and committee chair. I could not have asked for a more encouraging, supportive, and knowledgeable advisor to help guide me through my graduate career. Your thoughtful approach to teaching, mentorship, and research has made me a better person, professionally and personally. I am heartened knowing that I will enter a new phase of my life having learned all I can from you. My committee members, Dr. Huazhen Fang and Dr. Suzanne Shontz. Their willingness to meet, discuss, and advise me was integral to my success in writing this thesis. My approach to this study and my research would not be the same without their expertise and advice. The Parkinson’s disease patients and community members in this study. Without their dedication and volunteerism, this research would not be possible. My labmates and coworkers: Camilo, Ember, Mukui, Ednah, and Bhargavi—to name a few. Your friendship, support, encouragement, and help was essential to my life as a graduate student. Without you, I would not be the same person I am today. I am so grateful for the chance to get to know all of you! Dr. Jarod Hart for donating his time and expertise to help me hit the ground running with my research! My parents, Doris and John Weilert. Words cannot express how your love and support for me in every step of my life has impacted me. I couldn’t have done this without you. My sister Martha Weilert. You’ve watched and protected me as I have stumbled through life, always knowing I could lean on you when I was down. Seeing myself through your eyes gave me the confidence to carry on in many situations. Finally, my fiancé Jarrett Kille. You are my best friend, my anchor, and my better half. You have been with me every step of the way, good or bad, and never wavered in unconditionally loving and supporting me, no matter the path I chose to take. Thank you for everything. I love you. v Table of Contents Abstract ........................................................................................................................................................ iii Acknowledgments ......................................................................................................................................... v Table of Contents ......................................................................................................................................... vi List of Figures ............................................................................................................................................ viii List of Tables ............................................................................................................................................. viii Chapter 1: Introduction ................................................................................................................................. 1 Background and Motivation...................................................................................................................... 2 Specific Aims ............................................................................................................................................ 4 Thesis Content .......................................................................................................................................... 5 References ................................................................................................................................................. 6 Chapter 2: Background ............................................................................................................................... 10 Parkinson’s Disease ................................................................................................................................ 11 Epidemiology ...................................................................................................................................... 11 Etiology and Neurophysiology ........................................................................................................... 11 Symptoms, Diagnosis, and Therapies of PD ....................................................................................... 12 Rating of PD Progression .................................................................................................................... 14 Postural Instability and Fall Risk in PD .............................................................................................. 16 Parkinson’s and Postural Sway Analysis ................................................................................................ 17 Center of Pressure ............................................................................................................................... 17 COP and Postural Control Systems .................................................................................................... 18 Non-Stationarity of COP ..................................................................................................................... 20 COP Velocity ...................................................................................................................................... 23 Fractal Analysis of Postural Instability Measures ................................................................................... 23 Detrended Fluctuation Analysis .......................................................................................................... 25 Adaptive Fractal Analysis ................................................................................................................... 26 Parameter Selection in Fractal Methods ............................................................................................. 27 Limitations to Fractal Methods ..........................................................................................................