On the choice of multiscale entropy algorithm for quantification of complexity in gait data

The present study aimed at identifying a suitable multiscale entropy (MSE) algorithm for assessment of complexity in a stride-to-stride time interval time series. Five different algorithms were included (the original MSE, refine composite multiscale entropy (RCMSE), multiscale fuzzy entropy, generalized multiscale entropy and intrinsic mode entropy) and applied to twenty iterations of white noise, pink noise, or a sine wave with added white noise. Based on their ability to differentiate the level of complexity in the three different generated signal types, and their sensitivity and parameter consistency, MSE and RCMSE were deemed most appropriate. These two algorithms were applied to stride-to-stride time interval time series recorded from fourteen healthy subjects during one hour of overground and treadmill walking. In general, acceptable sensitivity and good parameter consistency were observed for both algorithms; however, they were not able to differentiate the complexity of the stride-to-stride time interval time series between the two walking conditions. Thus, the present study recommends the use of either MSE or RCMSE for quantification of complexity in stride-to-stride time interval time series.

[1]  John McCamley,et al.  Effect of parameter selection on entropy calculation for long walking trials. , 2018, Gait & posture.

[2]  N. Vuillerme,et al.  The differences between overground and treadmill walking in nonlinear, entropy-based and frequency variables derived from accelerometers in young and older women - preliminary report. , 2018, Acta of bioengineering and biomechanics.

[3]  N. Stergiou,et al.  A Novel Approach to Measure Variability in the Anterior Cruciate Ligament Deficient Knee During Walking: The Use of the Approximate Entropy in Orthopaedics , 2006, Journal of Clinical Monitoring and Computing.

[4]  Rita Stagni,et al.  Are gait variability and stability measures influenced by directional changes? , 2014, Biomedical engineering online.

[5]  N. Stergiou,et al.  Human movement variability, nonlinear dynamics, and pathology: is there a connection? , 2011, Human movement science.

[6]  M. C. Bisi,et al.  Complexity of human gait pattern at different ages assessed using multiscale entropy: From development to decline. , 2016, Gait & posture.

[7]  Weizhong Guo,et al.  A comparative study on ApEn, SampEn and their fuzzy counterparts in a multiscale framework for feature extraction , 2010 .

[8]  Nicolas Caesar Petersen,et al.  Movement Behavior of High-Heeled Walking: How Does the Nervous System Control the Ankle Joint during an Unstable Walking Condition? , 2012, PloS one.

[9]  David J. Hewson,et al.  Intrinsic Mode Entropy for Nonlinear Discriminant Analysis , 2007, IEEE Signal Processing Letters.

[10]  D. T. Kaplan,et al.  Aging and the complexity of cardiovascular dynamics. , 1991, Biophysical journal.

[11]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Erik B. Simonsen,et al.  Gait variability and motor control in people with knee osteoarthritis. , 2015, Gait & posture.

[13]  Jacob Cohen.  Statistical Power Analysis , 1992 .

[14]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[15]  A L Goldberger,et al.  Physiological time-series analysis: what does regularity quantify? , 1994, The American journal of physiology.

[16]  Madalena Costa,et al.  Multiscale entropy analysis of complex physiologic time series. , 2002, Physical review letters.

[17]  Jeffrey M. Hausdorff,et al.  Effects of Cognitive Challenge on Gait Variability in Patients with Parkinson’s Disease , 2003, Journal of geriatric psychiatry and neurology.

[18]  Jeffrey M. Hausdorff,et al.  Multiscale entropy analysis of human gait dynamics. , 2003, Physica A.

[19]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[20]  Jeffrey M. Hausdorff,et al.  Increased gait unsteadiness in community-dwelling elderly fallers. , 1997, Archives of physical medicine and rehabilitation.

[21]  C. Peng,et al.  Multiscale entropy to distinguish physiologic and synthetic RR time series , 2002, Computers in Cardiology.

[22]  N. Stergiou,et al.  Gait variability measures reveal differences between multiple sclerosis patients and healthy controls. , 2012, Motor control.

[23]  Weiting Chen,et al.  Measuring complexity using FuzzyEn, ApEn, and SampEn. , 2009, Medical engineering & physics.

[24]  Nathaniel H. Hunt,et al.  The Appropriate Use of Approximate Entropy and Sample Entropy with Short Data Sets , 2012, Annals of Biomedical Engineering.

[25]  Ary L. Goldberger,et al.  Generalized Multiscale Entropy Analysis: Application to Quantifying the Complex Volatility of Human Heartbeat Time Series , 2015, Entropy.

[26]  L. Glass.  Synchronization and rhythmic processes in physiology , 2001, Nature.

[27]  A. Goldberger,et al.  Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence. , 1992, JAMA.

[28]  Madalena Costa,et al.  Multiscale entropy analysis of biological signals. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Jeffrey M. Hausdorff,et al.  Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease. , 1997, Journal of applied physiology.

[30]  A L Goldberger,et al.  Decreased neuroautonomic complexity in men during an acute major depressive episode: analysis of heart rate dynamics , 2011, Translational Psychiatry.

[31]  Jonathan B. Dingwell,et al.  Differential Changes with Age in Multiscale Entropy of Electromyography Signals from Leg Muscles during Treadmill Walking , 2016, PloS one.

[32]  Philippe Terrier,et al.  Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking , 2011, Journal of NeuroEngineering and Rehabilitation.

[33]  B. Ulrich,et al.  Dynamic stability of gait cycles as a function of speed and system constraints. , 2004, Motor control.

[34]  Jonathan B. Dingwell,et al.  Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking? , 2010, PLoS Comput. Biol..

[35]  Max J. Kurz,et al.  Levodopa influences the regularity of the ankle joint kinematics in individuals with Parkinson’s disease , 2010, Journal of Computational Neuroscience.

[36]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[37]  Anne Humeau-Heurtier,et al.  The Multiscale Entropy Algorithm and Its Variants: A Review , 2015, Entropy.

[38]  S. Pincus.  Approximate entropy (ApEn) as a complexity measure. , 1995, Chaos.

[39]  Wangxin Yu,et al.  Characterization of Surface EMG Signal Based on Fuzzy Entropy , 2007, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[40]  Arja Häkkinen,et al.  Heart Rate Dynamics after Combined Strength and Endurance Training in Middle-Aged Women: Heterogeneity of Responses , 2013, PloS one.

[41]  J. Zbilut.  Biosignatures of Health , 2009, Biological research for nursing.

[42]  P. Terrier,et al.  GPS analysis of human locomotion: further evidence for long-range correlations in stride-to-stride fluctuations of gait parameters. , 2005, Human movement science.

[43]  Stephen J. McGregor,et al.  Effect of Treadmill versus Overground Running on the Structure of Variability of Stride Timing , 2014, Perceptual and motor skills.

[44]  M. C. Bisi,et al.  Changes of human movement complexity during maturation: quantitative assessment using multiscale entropy , 2018, Computer methods in biomechanics and biomedical engineering.

[45]  M. C. Bisi,et al.  Measures of gait stability: performance on adults and toddlers at the beginning of independent walking , 2014, Journal of NeuroEngineering and Rehabilitation.

[46]  J. Yentes,et al.  Introducing Statistical Persistence Decay: A Quantification of Stride-to-Stride Time Interval Dependency in Human Gait , 2017, Annals of Biomedical Engineering.

[47]  Vivien Marmelat,et al.  Fractal fluctuations and complexity: current debates and future challenges. , 2012, Critical reviews in biomedical engineering.

[48]  C. Peng,et al.  Analysis of complex time series using refined composite multiscale entropy , 2014 .