Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five considered entropy measures increase meaningfully with the increased probability of falling in a simple passive bipedal walker model. The same four entropy measures also experienced statistically significant increases in response to increasing age and gait impairment caused by cognitive interference in an experimental study. Of the considered entropy measures, the proposed quantized dynamical entropy (QDE) and quantization-based approximation of sample entropy (QASE) offered the best combination of sensitivity to changes in gait dynamics and computational efficiency. Based on these results, entropy appears to be a viable candidate for assessing the stability of human locomotion.

References

1.
Su
,
J. L.
, and
Dingwell
,
J. B.
,
2007
, “
Dynamic Stability of Passive Dynamic Walking on an Irregular Surface
,”
ASME J. Biomech. Eng.
,
129
(
6
), pp.
802
810
.10.1115/1.2800760
2.
Garcia
,
M.
,
Chatterjee
,
A.
,
Ruina
,
A.
, and
Coleman
,
M.
,
1998
, “
The Simplest Walking Model: Stability, Complexity, and Scaling
,”
ASME J. Biomech. Eng.
,
120
(
2
), pp.
281
288
.10.1115/1.2798313
3.
Bruijn
,
S. M.
,
Meijer
,
O. G.
,
Beek
,
P. J.
, and
van Dieen
,
J. H.
,
2013
, “
Assessing the Stability of Human Locomotion: A Review of Current Measures
,”
J. R. Soc. Interface
,
10
(
83
), pp.
1
23
.10.1098/rsif.2012.0999
4.
Leverick
,
G.
,
Szturm
,
T.
, and
Wu
,
C. Q.
,
2013
, “
Investigation of the Suitability of Utilizing Permutation Entropy to Characterize Gait Dynamics
,”
ASME
Paper No. DSCC2013-3895. 10.1115/DSCC2013-3895
5.
Dingwell
,
J.
,
Cusumano
,
J.
,
Sternad
,
D.
, and
Cavanagh
,
P.
,
2000
, “
Slower Speeds in Patients With Diabetic Neuropathy Lead to Improved Local Dynamic Stability of Continuous Overground Walking
,”
J. Biomech.
,
33
(
10
), pp.
1269
1277
.10.1016/S0021-9290(00)00092-0
6.
Szturm
,
T.
,
Maharjan
,
P.
,
Marotta
,
J.
,
Shay
,
B.
,
Shrestha
,
S.
, and
Sakhalkar
,
V.
,
2013
, “
The Interacting Effect of Cognitive and Motor Task Demands on Performance of Gait, Balance and Cognition in Young Adults
,”
Gait Posture
,
38
(
4
), pp.
596
602
.10.1016/j.gaitpost.2013.02.004
7.
Szturm
,
T.
,
Marotta
,
J.
,
Wu
,
C. Q.
, and
Nayak
,
A.
,
2013
, “
Technology-Assisted and Motivational Program for a Blended Approach to Prevent and Manage Balance, Gaze, Mobility and Cognitive Decline With Age
,”
OA Evidence-Based Med.
,
1
(
1
), pp.
1
7
.10.13172/2053-2636-1-1-513
8.
Owings
,
T.
, and
Grabiner
,
M.
,
2004
, “
Step Width Variability, but Not Step Length Variability or Step Time Variability, Discriminates Gait of Healthy Young and Older Adults During Treadmill Locomotion
,”
J. Biomech.
,
37
(
6
), pp.
935
938
.10.1016/j.jbiomech.2003.11.012
9.
Arif
,
M.
,
Ohtaki
,
Y.
,
Nagatomi
,
R.
,
Ishihara
,
T.
, and
Inooka
,
H.
,
2002
, “
Analysis of the Effect of Fatigue on Walking Gait Stability
,”
Proceedings of 2002 International Symposium on Micromechatronics and Human Science
, Nagoya, Japan, Oct. 20–23 , pp. 253–258.10.1109/MHS.2002.1058043
10.
Arif
,
M.
,
Ohtaki
,
Y.
,
Nagatomi
,
R.
, and
Inooka
,
H.
,
2004
, “
Estimation of the Effect of Cadence on Gait Stability in Young and Elderly People Using Approximate Entropy Technique
,”
Meas. Sci. Rev.
,
4
(
2
), pp.
29
40
. Available at: http://www.measurement.sk/2004/S2/Arif.pdf
11.
McGregor
,
S.
, and
Bollt
,
E.
,
2012
, “
Control Entropy: What is It and What Does It Tell Us?
Clin. Kinesiol.
,
66
(
1
), pp.
7
12
. Available at: http://people.clarkson.edu/~ebollt/Papers/McGregor%26Bollt_66_1_7-12.pdf
12.
Sun
,
S.
,
2010
, “
Complexity Analysis of the Gait Time Series Using Fine-Grained Permutation Entropy
,”
Proceedings of the Sixth International Conference on Natural Computation
, Yantai, China, Aug. 10–12, pp. 3878–3879. 10.1109/ICNC.2010.5582745
13.
Costa
,
M.
,
Peng
,
C.
,
Goldberger
,
A.
, and
Hausdorff
,
J.
,
2003
, “
Multiscale Entropy Analysis of Human Gait Dynamics
,”
Physica A
,
330
(
1–2
), pp.
53
60
. 10.1016/j.physa.2003.08.022
14.
Cai
,
S.
,
Zhou
,
P.
,
Yang
,
H.
,
Zhou
,
T.
,
Wang
,
B.
, and
Zhao
,
F.
,
2007
, “
Diffusion Entropy Analysis on the Stride Interval Fluctuation of Human Gait
,”
Physica A
,
375
(
2
), pp.
687
692
.10.1016/j.physa.2006.10.027
15.
Karmakar
,
C.
,
Khandoker
,
A.
,
Begg
,
R.
,
Palaniswami
,
M.
, and
Taylor
,
S.
,
2007
, “
Understanding Ageing Effects by Approximate Entropy Analysis of Gait Variability
,”
Proceedings of the 29th Annual International Conference of the IEEE EMBS
, Lyon, France, Aug. 23–26, pp.
1965
1968
.10.1109/IEMBS.2007.4352703
16.
Khandoker
,
A.
,
Palaniswami
,
M.
, and
Begg
,
R.
,
2008
, “
A Comparative Study on Approximate Entropy Measure and Poincare Plot Indexes of Minimum Foot Clearance Variability in the Elderly During Walking
,”
J. Neuroeng. Rehabil.
,
5
, p.
4
.10.1186/1743-0003-5-4
17.
Bandt
,
C.
, and
Pompe
,
B.
,
2002
, “
Permutation Entropy: A Natural Complexity Measure for Time Series
,”
Phys. Rev. Lett.
,
88
(
17
), p.
174102
.10.1103/PhysRevLett.88.174102
18.
Leverick
,
G.
,
Wu
,
C. Q.
, and
Szturm
,
T.
, “
Coarse Quantization in Calculations of Entropy Measures for Experimental Time Series
,”
Nonlinear Dyn.
(in press).10.1007/s11071-014-1647-z
19.
Richman
,
J.
, and
Moorman
,
J.
,
2000
, “
Physiological Time-Series Analysis Using Approximate and Sample Entropy
,”
Am. J. Physiol.: Heart Circ. Physiol.
,
278
(
6
), pp.
2039
2049
. Available at: http://ajpheart.physiology.org/content/278/6/H2039.short
20.
Chen
,
W.
,
Zhuang
,
J.
,
Yu
,
W.
, and
Wang
,
Z.
,
2008
, “
Measuring Complexity Using Fuzzyen, Apen, and Sampen
,”
Med. Eng. Phys.
,
31
(
1
), pp.
61
68
. 10.1016/j.medengphy.2008.04.005
21.
Leverick
,
G.
,
2013
, “
Entropy Measures in Dynamical Systems and Their Viability in Characterizing Bipedal Walking Gait Dynamics
,” MSc thesis, University of Manitoba, Winnipeg, MB, Canada.
22.
Al-Yahya
,
E.
,
Dawes
,
H.
,
Smith
,
L.
,
Dennis
,
A.
,
Howells
,
K.
, and
Cockburn
,
J.
,
2010
, “
Cognitive Motor Interference While Walking: A Systematic Review and Meta-Analysis
,”
Neurosci. Biobehav. Rev.
,
35
(
3
), pp.
715
728
.10.1016/j.neubiorev.2010.08.008
23.
Chinn
,
S.
,
1991
, “
Repeatability and Method Comparison
,”
Thorax
,
46
(
6
), pp.
454
456
.10.1136/thx.46.6.454
24.
Young
,
L.
,
2003
,
Entropy
,
Princeton University Press
,
Princeton, NJ
, pp.
313
328
.
25.
Sun
,
Y.
, and
Wu
,
C.
,
2012
, “
Stability Analysis Via the Concept of Lyapunov Exponents: A Case Study in Optimal Controlled Biped Standing
,”
Int. J. Control
,
85
(
12
), pp.
1952
1966
.10.1080/00207179.2012.713985
26.
van Schooten
,
K.
,
Sloot
,
L.
,
Bruijn
,
S.
,
Kingma
,
H.
,
Meijer
,
O.
,
Pijnappels
,
M.
, and
van Dieen
,
J.
,
2011
, “
Sensitivity of Trunk Variability and Stability Measures to Balance Impairments Induced by Galvanic Vestibular Stimulation During Gait
,”
Gait Posture
,
33
(
4
), pp.
656
660
.10.1016/j.gaitpost.2011.02.017
27.
Strang
,
A.
,
Haworth
,
J.
,
Hieronymus
,
M.
,
Walsh
,
M.
, and
Smart
,
L.
,
2011
, “
Structural Changes in Postural Sway Lend Insight Into Effects of Balance Training, Vision, and Support Surface on Postural Control in a Healthy Population
,”
Eur. J. Appl. Physiol.
,
111
(
7
), pp.
1485
1495
.10.1007/s00421-010-1770-6
28.
Rigoldi
,
C.
,
Cimolin
,
V.
,
Camerota
,
F.
,
Celletti
,
C.
,
Albertini
,
G.
,
Mainardi
,
L.
, and
Galli
,
M.
,
2013
, “
Measuring Regularity of Human Postural Sway Using Approximate Entropy and Sample Entropy in Patients With Ehlers-Danlos Syndrome Hypermobility Type
,”
Res. Dev. Disabil.
,
34
(
2
), pp.
840
846
.10.1016/j.ridd.2012.11.007
29.
Callisaya
,
M.
,
Blizzard
,
L.
,
Schmidt
,
M.
,
Martin
,
K.
,
McGinley
,
J.
,
Sanders
,
L.
, and
Srikanth
,
V.
,
2011
, “
Gait, Gait Variability and the Risk of Multiple Incident Falls in Older People: A Population-Based Study
,”
Age Ageing
,
40
(
4
), pp.
481
487
.10.1093/ageing/afr055
30.
Lamoth
,
C.
,
van Deudekom
,
F.
,
van Campen
,
J.
,
Appels
,
B.
,
de Vries
,
O.
, and
Pijnappels
,
M.
,
2011
, “
Gait Stability and Variability Measures Show Effects of Impaired Cognition and Dual Tasking in Frail People
,”
J. Neuroeng. Rehabil.
,
8
, p.
2
.10.1186/1743-0003-8-2
31.
Rafiq
,
M.
,
McGovern
,
A.
,
Jones
,
S.
,
Harris
,
K.
,
Tomson
,
C.
,
Gallagher
,
H.
, and
de Lusignan
,
S.
,
2014
, “
Falls in the Elderly Were Predicted Opportunistically Using a Decision Tree and Systematically Using a Database-Driven Screening Tool
,”
J. Clin. Epidemiol.
,
67
(
8
), pp.
877
886
.10.1016/j.jclinepi.2014.03.008
32.
Muir
,
S. W.
,
Gopaul
,
K.
, and
Montero Odasso
,
M. M.
,
2012
, “
The Role of Cognitive Impairment in Fall Risk Among Older Adults: A Systematic Review and Meta-Analysis
,”
Age Ageing
,
41
(
3
), pp.
299
308
.10.1093/ageing/afs012
33.
Owings
,
T. M.
, and
Grabiner
,
M. D.
,
2003
, “
Measuring Step Kinematic Variability on an Instrumented Treadmill: How Many Steps are Enough?
J. Biomech.
,
36
(
8
), pp.
1215
1218
.10.1016/S0021-9290(03)00108-8
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