The present study investigated the day-to-day reliability (quantified by the absolute and relative reliability) of nonlinear methods used to assess human locomotion dynamics. Twenty-four participants of whom twelve were diagnosed with knee osteoarthritis completed 5 min of treadmill walking at self-selected preferred speed on two separate days. Lower limb kinematics were recorded at 100 Hz and hip, knee, and ankle joint angles, three-dimensional (3D) sacrum marker displacement and stride time intervals were extracted for 170 consecutive strides. The largest Lyapunov exponent and correlation dimension were calculated for the joint angle and sacrum displacement data using three different state space reconstruction methods (group average, test-retest average, individual time delay and embedding dimension). Sample entropy and detrended fluctuation analysis (DFA) were applied to the stride time interval time series. Relative reliability was assessed using intraclass correlation coefficients and absolute reliability was determined using measurement error (ME). For both joint angles and sacrum displacement, there was a general pattern that the group average state space reconstruction method provided the highest relative reliability and lowest ME compared to the individual and test-retest average methods. The DFA exhibited good reliability, while the sample entropy showed poor reliability. The results comprise a reference material that can inspire and guide future studies of nonlinear gait dynamics.

References

References
1.
Hausdorff
,
J. M.
,
Peng
,
C. K.
,
Ladin
,
Z.
,
Wei
,
J. Y.
, and
Goldberger
,
A. L.
,
1995
, “
Is Walking a Random Walk? Evidence for Long-Range Correlations in Stride Interval of Human Gait
,”
J. Appl. Physiol.
,
78
(
1
), pp.
349
358
.
2.
Hausdorff
,
J. M.
,
2005
, “
Gait Variability: Methods, Modeling and Meaning
,”
J. Neuroeng. Rehabil.
,
2
, p.
19
.
3.
Alkjaer
,
T.
,
Raffalt
,
P. C.
,
Dalsgaard
,
H.
,
Simonsen
,
E. B.
,
Petersen
,
N. C.
,
Bliddal
,
H.
, and
Henriksen
,
M.
,
2015
, “
Gait Variability and Motor Control in People With Knee Osteoarthritis
,”
Gait Posture
,
42
(
4
), pp.
479
484
.
4.
Yentes
,
J. M.
,
Hunt
,
N.
,
Schmid
,
K. K.
,
Kaipust
,
J. P.
,
McGrath
,
D.
, and
Stergiou
,
N.
,
2013
, “
The Appropriate Use of Approximate Entropy and Sample Entropy With Short Data Sets
,”
Ann. Biomed. Eng.
,
41
(
2
), pp.
349
365
.
5.
Raffalt
,
P. C.
,
Vallabhajosula
,
S.
,
Renz
,
J. J.
,
Mukherjee
,
M.
, and
Stergiou
,
N.
,
2017
, “
Dynamics of Stride Interval Characteristics During Continuous Stairmill Climbing
,”
Front. Physiol.
,
8
, p.
609
.
6.
Yentes
,
J. M.
,
Denton
,
W.
,
McCamley
,
J.
,
Raffalt
,
P. C.
, and
Schmid
,
K. K.
,
2018
, “
Effect of Parameter Selection on Entropy Calculation for Long Walking Trials
,”
Gait Posture
,
60
, pp.
128
134
.
7.
Dingwell
,
J. B.
, and
Cusumano
,
J. P.
,
2000
, “
Nonlinear Time Series Analysis of Normal and Pathological Human Walking
,”
Chaos
,
10
(
4
), pp.
848
863
.
8.
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
.
9.
Dingwell
,
J. B.
, and
Marin
,
L. C.
,
2006
, “
Kinematic Variability and Local Dynamic Stability of Upper Body Motions When Walking at Different Speeds
,”
J. Biomech.
,
39
(
3
), pp.
444
452
.
10.
Buzzi
,
U. H.
,
Stergiou
,
N.
,
Kurz
,
M. J.
,
Hageman
,
P. A.
, and
Heidel
,
J.
,
2003
, “
Nonlinear Dynamics Indicates Aging Affects Variability During Gait
,”
Clin. Biomech.
,
18
(
5
), pp.
435
443
.
11.
Raffalt
,
P. C.
,
Guul
,
M. K.
,
Nielsen
,
A. N.
,
Puthusserypady
,
S.
, and
Alkjaer
,
T.
,
2017
, “
Economy, Movement Dynamics, and Muscle Activity of Human Walking at Different Speeds
,”
Sci. Rep.
,
7
(
1
), p.
43986
.
12.
van Schooten
,
K. S.
,
Rispens
,
S. M.
,
Pijnappels
,
M.
,
Daffertshofer
,
A.
, and
van Dieen
,
J. H.
,
2013
, “
Assessing Gait Stability: The Influence of State Space Reconstruction on Inter- and Intra-Day Reliability of Local Dynamic Stability During Over-Ground Walking
,”
J. Biomech.
,
46
(
1
), pp.
137
141
.
13.
Kang
,
H. G.
, and
Dingwell
,
J. B.
,
2006
, “
Intra-Session Reliability of Local Dynamic Stability of Walking
,”
Gait Posture
,
24
(
3
), pp.
386
390
.
14.
Henriksen
,
M.
,
Lund
,
H.
,
Moe-Nilssen
,
R.
,
Bliddal
,
H.
, and
Danneskiod-Samsoe
,
B.
,
2004
, “
Test-Retest Reliability of Trunk Accelerometric Gait Analysis
,”
Gait Posture
,
19
(
3
), pp.
288
297
.
15.
Stolze
,
H.
,
Kuhtz-Buschbeck
,
J. P.
,
Mondwurf
,
C.
,
Johnk
,
K.
, and
Friege
,
L.
,
1998
, “
Retest Reliability of Spatiotemporal Gait Parameters in Children and Adults
,”
Gait Posture
,
7
(
2
), pp.
125
130
.
16.
Wolf
,
A.
,
Swift
,
J. B.
,
Swinney
,
H. L.
, and
Vastano
,
J. A.
,
1985
, “
Determining Lyapunov Exponents From a Time-Series
,”
Physica D
,
16
(
3
), pp.
285
317
.
17.
Rosenstein
,
M. T.
,
Collins
,
J. J.
, and
De Luca
,
C. J.
,
1993
, “
A Practical Method for Calculating Largest Lyapunov Exponents From Small Data Sets
,”
Physica D
,
65
(
1–2
), pp.
117
134
.
18.
Kennel
,
M. B.
,
Brown
,
R.
, and
Abarbanel
,
H. D.
,
1992
, “
Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometrical Construction
,”
Phys. Rev. A
,
45
(
6
), pp.
3403
3411
.
19.
Sauer
,
T.
, and
Yorke
,
J. A.
,
1993
, “
How Many Delay Coordinates Do You Need?
,”
Int. J. Bifurcations Chaos
,
3
(
3
), pp.
737
744
.
20.
Sauer
,
T.
,
Yorke
,
J. A.
, and
Casdagli
,
M.
,
1991
, “
Embedology
,”
J. Stat. Phys.
,
65
(
3–4
), pp.
579
616
.
21.
Takens
,
F.
,
1981
, “
Detecting Strange Attractors in Turbulence
,”
Dynamical Systems and Turbulence, Warwick 1980
, Lecture Notes in Mathematics, Vol. 898, D. Rand, and L. S. Young, eds., Springer, Berlin, Germany, pp.
366
381
.
22.
Cignetti
,
F.
,
Decker
,
L. M.
, and
Stergiou
,
N.
,
2012
, “
Sensitivity of the Wolf's and Rosenstein's Algorithms to Evaluate Local Dynamic Stability From Small Gait Data Sets
,”
Ann. Biomed. Eng.
,
40
(
5
), pp.
1122
1130
.
23.
Bruijn
,
S. M.
,
Meijer
,
O. G.
,
Rispens
,
S. M.
,
Daffertshofer
,
A.
, and
van Dieen
,
J. H.
,
2012
, “
Letter to the Editor: "Sensitivity of the Wolf's and Rosenstein's Algorithms to Evaluate Local Dynamic Stability From Small Gait Data Sets
,”
Ann. Biomed. Eng.
,
40
(
12
), pp.
2505
2506
.
24.
Cignetti
,
F.
,
Decker
,
L. M.
, and
Stergiou
,
N.
,
2012
, “
Sensitivity of the Wolf's and Rosenstein's Algorithms to Evaluate Local Dynamic Stability From Small Gait Data Sets: Response to Commentaries by Bruijn
,”
Ann. Biomed. Eng.
,
40
(
5
), pp.
2507
2509
.
25.
England
,
S. A.
, and
Granata
,
K. P.
,
2007
, “
The Influence of Gait Speed on Local Dynamic Stability of Walking
,”
Gait Posture
,
25
(
2
), pp.
172
178
.
26.
Bruijn
,
S. M.
,
van Dieen
,
J. H.
,
Meijer
,
O. G.
, and
Beek
,
P. J.
,
2009
, “
Statistical Precision and Sensitivity of Measures of Dynamic Gait Stability
,”
J. Neurosci. Methods
,
178
(
2
), pp.
327
333
.
27.
Wurdeman
,
S. R.
,
Myers
,
S. A.
, and
Stergiou
,
N.
,
2014
, “
Amputation Effects on the Underlying Complexity Within Transtibial Amputee Ankle Motion
,”
Chaos
,
24
(
1
), p.
013140
.
28.
Grassberger
,
P.
, and
Procaccia
,
I.
,
1983
, “
Measuring the Strangeness of Strange Attractors
,”
Physica D
,
9
(
1–2
), pp.
189
208
.
29.
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.
H2039
H2049
.
30.
Peng
,
C. K.
,
Havlin
,
S.
,
Stanley
,
H. E.
, and
Goldberger
,
A. L.
,
1995
, “
Quantification of Scaling Exponents and Crossover Phenomena in Nonstationary Heartbeat Time Series
,”
Chaos
,
5
(
1
), pp.
82
87
.
31.
Hausdorff
,
J. M.
,
Mitchell
,
S. L.
,
Firtion
,
R.
,
Peng
,
C. K.
,
Cudkowicz
,
M. E.
,
Wei
,
J. Y.
, and
Goldberger
,
A. L.
,
1997
, “
Altered Fractal Dynamics of Gait: Reduced Stride-Interval Correlations With Aging and Huntington's Disease
,”
J. Appl. Physiol.
,
82
(
1
), pp.
262
269
.
32.
Fleiss
,
J. L.
,
1986
,
The Design and Analysis of Clinical Experiments
,
Wiley
,
New York
.
33.
Bruijn
,
S. M.
,
van Dieen
,
J. H.
,
Meijer
,
O. G.
, and
Beek
,
P. J.
,
2009
, “
Is Slow Walking More Stable?
,”
J. Biomech.
,
42
(
10
), pp.
1506
1512
.
34.
Kaipust
,
J. P.
,
McGrath
,
D.
,
Mukherjee
,
M.
, and
Stergiou
,
N.
,
2013
, “
Gait Variability Is Altered in Older Adults When Listening to Auditory Stimuli With Differing Temporal Structures
,”
Ann. Biomed. Eng.
,
41
(
8
), pp.
1595
1603
.
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