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.
References
1.
Salzman
, B.
, 2010
, “Gait and Balance Disorders in Older Adults
,” Am. Fam Physician
, 82
(1
), pp. 61
–68
.http://www.aafp.org/afp/2010/0701/p61.html2.
Hausdorff
, J. M.
, Rios
, D.
, and Edelberg
, H. K.
, 2001
, “Gait Variability and Fall Risk in Community-Living Older Adults: A 1-Year Prospective Study
,” Arch. Phys. Med. Rehabil.
, 82
(8
), pp. 1050
–1056
.3.
Riva
, F.
, Toebes
, M. J. P.
, Pijnappels
, M.
, Stagni
, R.
, and van Dieën
, J. H.
, 2013
, “Estimating Fall Risk With Inertial Sensors Using Gait Stability Measures That Do Not Require Step Detection
,” Gait Posture
, 38
(2
), pp. 170
–174
.4.
Ihlen
, E. A. F.
, Weiss
, A.
, Bourke
, A.
, Helbostad
, J. L.
, and Hausdorff
, J. M.
, 2016
, “The Complexity of Daily Life Walking in Older Adult Community-Dwelling Fallers and Non-Fallers
,” J. Biomech.
, 49
(9
), pp. 1420
–1428
.5.
Lamoth
, C. J.
, Van Deudekom
, F. J.
, Van Campen
, J. P.
, Appels
, B. A.
, De Vries
, O. J.
, and Pijnappels
, M.
, 2011
, “Gait Stability and Variability Measures Show Effects of Impaired Cognition and Dual Tasking in Frail People
,” J. Neuroeng. Rehabil.
, 8
(1
), p. 2
.6.
Leverick
, G.
, Szturm
, T.
, and Wu
, C. Q.
, 2014
, “Using Entropy Measures to Characterize Human Locomotion
,” ASME J. Biomech. Eng.
, 136
(12
), p. 121002
.7.
Bisi
, M. C.
, Riva
, F.
, and Stagni
, R.
, 2014
, “Measures of Gait Stability: Performance on Adults and Toddlers at the Beginning of Independent Walking
,” J. Neuroeng. Rehabil.
, 11
(1
), p. 131
.8.
Grassberger
, P.
, and Procaccia
, I.
, 1983
, “Estimation of the Kolmogorov Entropy From a Chaotic Signal
,” Phys. Rev. A.
, 28
(4
), pp. 2591
–2593
.9.
Pincus
, S.
, 1995
, “Approximate Entropy (ApEn) as a Complexity Measure
,” Chaos
, 5
(1
), pp. 110
–117
.10.
Richman
, J. S.
, and Moorman
, J. R.
, 2000
, “Physiological Time-Series Analysis Using Approximate Entropy and Sample Entropy
,” Am. J. Physiol. Heart Circ. Physiol.
, 278
(6
), pp. 2039
–2049
.http://ajpheart.physiology.org/content/278/6/H2039.long11.
Kinsner
, W.
, 2010
, “System Complexity and Its Measures: How Complex is Complex
,” Advances in Cognitive Informatics and Cognitive Computing
(Studies in Computational Intelligence), Vol. 323, Springer, Berlin, pp. 265
–295
.12.
Lipsitz
, L. A.
, and Goldberger
, A. L.
, 1992
, “Loss of ‘Complexity’ and Aging. Potential Applications of Fractals and Chaos Theory to Senescence
,” JAMA
, 267
(13
), pp. 1806
–1809
.13.
Vaillancourt
, D. E.
, and Newell
, K. M.
, 2002
, “Changing Complexity in Human Behavior and Physiology Through Aging and Disease
,” Neurobiol. Aging
, 23
(1
), pp. 1
–11
.14.
Costa
, M.
, Peng
, C.-K.
, Goldberger
, A. L.
, and Hausdorff
, J. M.
, 2003
, “Multiscale Entropy Analysis of Human Gait Dynamics
,” Physica A
, 330
(1–2
), pp. 53
–60
.15.
Bisi
, M. C.
, and Stagni
, R.
, 2016
, “Complexity of Human Gait Pattern at Different Ages Assessed Using Multiscale Entropy: From Development to Decline
,” Gait Posture
, 47
, pp. 37
–42
.16.
Lamoth
, C. J. C.
, Ainsworth
, E.
, Polomski
, W.
, and Houdijk
, H.
, 2010
, “Variability and Stability Analysis of walking of Transfemoral Amputees
,” Med. Eng. Phys.
, 32
(9
), pp. 1009
–1014
.17.
Kavanagh
, J. J.
, 2009
, “Lower Trunk Motion and Speed-Dependence During Walking
,” J. Neuroeng. Rehabil.
, 6
(1
), p. 9
.18.
Rhea
, C. K.
, Silver
, T. A.
, Hong
, S. L.
, Ryu
, J. H.
, Studenka
, B. E.
, Hughes
, C. M.
, and Haddad
, J. M.
, 2011
, “Noise and Complexity in Human Postural Control: Interpreting the Different Estimations of Entropy
,” PLoS One
, 6
(3
), p. e17696
.19.
Kang
, H. G.
, Costa
, M. D.
, Priplata
, A. A.
, Starobinets
, O. V.
, Goldberger
, A. L.
, Peng
, C. K.
, Kiely
, D. K.
, Cupples
, L. A.
, and Lipsitz
, L. A.
, 2009
, “Frailty and the Degradation of Complex Balance Dynamics During a Dual-Task Protocol
,” J. Gerontol. A Biol. Sci. Med. Sci.
, 64A
(12
), pp. 1304
–1311
.20.
Fino
, P. C.
, Mojdehi
, A. R.
, Adjerid
, K.
, Habibi
, M.
, Lockhart
, T. E.
, and Ross
, S. D.
, 2016
, “Comparing Postural Stability Entropy Analyses to Differentiate Fallers and Non-Fallers
,” Ann. Biomed. Eng.
, 44
(5
), pp. 1636
–1645
.21.
Terrier
, P.
, and Dériaz
, O.
, 2013
, “Non-Linear Dynamics of Human Locomotion: Effects of Rhythmic Auditory Cueing on Local Dynamic Stability
,” Front Physiol.
, 4
, p. 230
.22.
Scafetta
, N.
, Marchi
, D.
, and West
, B. J.
, 2009
, “Understanding the Complexity of Human Gait Dynamics
,” Chaos
, 19
(2
), p. 026108
.23.
Hausdorff
, J. M.
, 2005
, “Gait Variability: Methods, Modeling and Meaning
,” J. Neuroeng. Rehabil.
, 2
(1
), p. 19
.24.
Wayne
, P. M.
, Gow
, B. J.
, Costa
, M. D.
, Peng
, C.-K.
, Lipsitz
, L. A.
, Hausdorff
, J. M.
, Davis
, R. B.
, Walsh
, J. N.
, Lough
, M.
, Novak
, V.
, Yeh
, G. Y.
, Ahn
, A. C.
, Macklin
, E. A.
, and Manor
, B.
, 2014
, “Complexity-Based Measures Inform Effects of Tai Chi Training on Standing Postural Control: Cross-Sectional and Randomized Trial Studies
,” PLoS ONE
, 9
(12
), p. e114731
.25.
Bizovska
, L.
, Svoboda
, Z.
, Vuillerme
, N.
, and Janura
, M.
, 2017
, “Multiscale and Shannon Entropies During Gait as Fall Risk Predictors—A Prospective Study
,” Gait Posture
, 52
, pp. 5
–10
.26.
Kinsner
, W.
, 2007
, “Single-Scale Measures for Randomness and Complexity
,” Sixth IEEE International Conference on Cognitive Informatics
(COGINF
), Lake Tahoo, CA, Aug. 6–8, pp. 554
–568
.27.
Van Emmerik
, R. E. A.
, Ducharme
, S. W.
, Amado
, A. C.
, and Hamill
, J.
, 2016
, “Comparing Dynamical Systems Concepts and Techniques for Biomechanical Analysis
,” J. Sports Health Sci.
, 5
(1
), pp. 3
–13
.28.
Beauchet
, O.
, Annweiler
, C.
, Montero-Odasso
, M.
, Fantino
, B.
, Herrmann
, F. R.
, and Allali
, G.
, 2012
, “Gait Control: A Specific Subdomain of Executive Function?
” J. Neuroeng. Rehabil.
, 9
(1
), p. 12
.29.
Al-Yahya
, E.
, Dawes
, H.
, Smith
, L.
, Dennis
, A.
, Howells
, K.
, and Cockburn
, J.
, 2011
, “Cognitive Motor Interference While Walking: A Systematic Review and Meta-Analysis
,” Neurosci. Biobehav. Rev.
, 35
(3
), pp. 715
–728
.30.
Goldberger
, A. L.
, Peng
, C.-K.
, and Lipsitz
, L. A.
, 2002
, “What is Physiologic Complexity and How Does it Change With Aging and Disease?
,” Neurobiol. Aging
, 23
(1
), pp. 23
–26
.31.
McGregor
, S. J.
, Busa
, M. A.
, Skufca
, J.
, Yaggie
, J. A.
, and Bollt
, E. M.
, 2009
, “Control Entropy Identifies Differential Changes in Complexity of Walking and Running Gait Patterns With Increasing Speed in Highly Trained Runners
,” Chaos
, 19
(2
), p. 026109
.32.
Kurz
, M. J.
, and Hou
, J. G.
, 2010
, “Levodopa Influences the Regularity of the Ankle Joint Kinematics in Individuals With Parkinson's Disease
,” J. Comput. Neurosci.
, 28
(1
), pp. 131
–136
.33.
Szturm
, T.
, Marotta
, J.
, Wu
, C.
, and Nayak
, A.
, 2013
, “Technology-Assisted and Motivational Programme for a Blended Approach to Prevent and Manage Balance, Gaze, Mobility and Cognitive Decline With Age
,” OA Evidence Based Med.
, 1
(1
), p. 4
.34.
Szturm
, T.
, Sakhalkar
, V.
, Boreskie
, S.
, Marotta
, J. J.
, Wu
, C.
, and Kanitkar
, A.
, 2015
, “Integrated Testing of Standing Balance and Cognition: Test-Retest Reliability and Construct Validity
,” Gait Posture
, 41
(1
), pp. 146
–152
.35.
Szturm
, T.
, Sakhalkar
, V. S.
, Kanitkar
, A.
, and Nankar
, M.
, 2017
, “Computerized Dual-Task Testing of Gait and Visuospatial Cognitive Functions; Test-Retest Reliability and Validity
,” Front Hum. Neurosci.
, 11
, p. 105
.36.
Leverick
, G.
, Wu
, C.
, and Szturm
, T.
, 2015
, “Coarse Quantization in Calculations of Entropy Measures for Experimental Time Series
,” Nonlinear Dyn.
, 79
(1
), pp. 93
–100
.37.
Ihlen
, E. A. F.
, Sletvold
, O.
, Goihl
, T.
, Wik
, P. B.
, Vereijken
, B.
, and Helbostad
, J.
, 2012
, “Older Adults Have Unstable Gait Kinematics During Weight Transfer
,” J. Biomech.
, 45
(9
), pp. 1559
–1565
.38.
Cavanaugh
, J. T.
, Kochi
, N.
, and Stergiou
, N.
, 2010
, “Nonlinear Analysis of Ambulatory Activity Patterns in Community-Dwelling Older Adults
,” J. Gerontol. A Biol. Sci. Med. Sci.
, 65
(2
), pp. 197
–203
.39.
Bisi
, M. C.
, and Stagni
, R.
, 2016
, “Development of Gait Motor Control: What Happens After a Sudden Increase in Height During Adolescence?
,” Biomed. Eng. Online
, 15
, pp. 1
–12
.40.
McAndrew Young
, P. M.
, Wilken
, J. M.
, and Dingwell
, J. B.
, 2012
, “Dynamic Margins of Stability During Human Walking in Destabilizing Environments
,” J. Biomech.
, 45
(6
), pp. 1053
–1059
.41.
Rogers
, M. W.
, and Mille
, M. L.
, 2003
, “Lateral Stability and Falls in Older People
,” Exercise Sport Sci. Rev.
, 31
(4
), pp. 182
–187
.42.
Duysens
, J.
, Duysens
, J. P.
, Bastiaanse
, C. M.
, van Sprundel
, M.
, Schubert
, M.
, and Smits-Engelsman
, B. C.
, 2008
, “How Trunk Turns Affect Locomotion When You Are Not Looking Where You Go
,” Hum. Mov Sci.
, 27
(5
), pp. 759
–770
.43.
Dingwell
, J. B.
, Cusumano
, J. P.
, Cavanagh
, P. R.
, and Sternad
, D.
, 2001
, “Local Dynamic Stability Versus Kinematic Variability of Continuous Overground and Treadmill Walking
,” ASME J. Biomech. Eng.
, 123
(1
), pp. 27
–32
.Copyright © 2018 by ASME
You do not currently have access to this content.
