a b/jap/node6.html 

  1
  
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 3.0//EN">





  
  

  2
  
<!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds -->





  
  

  3
  
<HTML>





  
  

  4
  
<HEAD>





  
  

  5
  
<TITLE>Stride Time Dynamics</TITLE>





  
  

  6
  
<META NAME="description" CONTENT="Stride Time Dynamics">





  
  

  7
  
<META NAME="keywords" CONTENT="gait-reprint">





  
  

  8
  
<META NAME="resource-type" CONTENT="document">





  
  

  9
  
<META NAME="distribution" CONTENT="global">





  
  

  10
  
<LINK REL=STYLESHEET HREF="gait-reprint.css">





  
  

  11
  
</HEAD>





  
  

  12
  
<BODY LANG="EN" bgcolor="white">





  
  

  13
  
 <A NAME="tex2html62" HREF="node7.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="/icons/latex2html/next_motif.png"></A> <A NAME="tex2html60" HREF="node3.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="/icons/latex2html/up_motif.png"></A> <A NAME="tex2html54" HREF="node5.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="/icons/latex2html/previous_motif.png"></A>   <BR>





  
  

  14
  
<B> Next:</B> <A NAME="tex2html63" HREF="node7.html">Statistical Methods</A>





  
  

  15
  
<B>Up:</B> <A NAME="tex2html61" HREF="node3.html">Methods</A>





  
  

  16
  
<B> Previous:</B> <A NAME="tex2html55" HREF="node5.html">Protocol</A>





  
  

  17
  
<BR> <P>





  
  

  18
  
<H3><A NAME="SECTION00030300000000000000">Stride Time Dynamics</A></H3>





  
  

  19
  
<P>





  
  

  20
  
To study the intrinsic stride-to-stride dynamics and its changes with age, some





  
  

  21
  
 preprocessing was performed on each time series.  The first





  
  

  22
  
sixty seconds and the last five seconds of each time





  
  

  23
  
series were not included  to eliminate any





  
  

  24
  
start-up or ending effects and 





  
  

  25
  
to allow the subject to become familiar





  
  

  26
  
with the walking track. The time series were also processed to





  
  

  27
  
remove any pauses (stride time &gt; 2 seconds and the 5 seconds before and





  
  

  28
  
after any pauses) as well as any large spikes or outliers.  These





  
  

  29
  
outliers, which occurred infrequently, were removed so that the





  
  

  30
  
intrinsic dynamics of each time series could be more readily





  
  

  31
  
analyzed. This  was accomplished using





  
  

  32
  
previously established methods  (8,10) by: i) determining the mean and standard deviation of the





  
  

  33
  
stride time while excluding the 5% of the data with the lowest and





  
  

  34
  
highest values, and then ii) removing from the original time series





  
  

  35
  
all data that fell more than 4.0 standard deviations away from this





  
  

  36
  
mean value. The number of pauses (typically 0) and the number of





  
  

  37
  
strides excluded (typically 2 %) were similar in all three 





  
  

  38
  
age groups.





  
  

  39
  
<P>





  
  

  40
  
As shown in Table 1 and 





  
  

  41
  
summarized below, we applied several measures





  
  

  42
  
to analyze the variability and temporal structure of the stride time





  
  

  43
  
dynamics.





  
  

  44
  
<P>





  
  

  45
  
<P><P>





  
  

  46
  
<B>Stride-to-Stride Variability Measures</B>





  
  

  47
  
<P>





  
  

  48
  
To estimate the overall





  
  

  49
  
stride-to-stride variability, we calculated the standard deviation





  
  

  50
  
of each time series and 





  
  

  51
  
the coefficient of variation (CV) (100<IMG WIDTH=8 HEIGHT=20 ALIGN=MIDDLE ALT="tex2html_wrap_inline304" SRC="img7.png">standard deviation/mean), 





  
  

  52
  
an index of





  
  

  53
  
variability normalized to each subject's mean cycle duration.





  
  

  54
  
Both the standard deviation and the CV provide a measure of overall variations





  
  

  55
  
in gait timing during the entire walk, i.e., the amplitude of the





  
  

  56
  
fluctuations in the time series with respect to the mean.  However,





  
  

  57
  
these measures may be influenced by  trends in the data (e.g., due





  
  

  58
  
to a change in speed) and cannot distinguish between a walk with large changes





  
  

  59
  
from one stride to the next and one in which stride-to-stride





  
  

  60
  
variations are small and more long-term, global changes (e.g., a change in





  
  

  61
  
average value) result in a large standard deviation.  Therefore, 





  
  

  62
  
to estimate variability independent of 





  
  

  63
  
local changes in the mean, we quantified 





  
  

  64
  
successive stride-to-stride changes (i.e., the difference between the





  
  

  65
  
stride time of one stride and the previous stride) by determining the first difference of





  
  

  66
  
each time series.  The first difference, a discrete analog





  
  

  67
  
of the first derivative, is one standard method for removing slow varying trends and is calculated by subtracting the previous value in the 





  
  

  68
  
time series from the current value. The standard deviation of the first





  
  

  69
  
difference time series provides 





  
  

  70
  
a measure of variability after detrending.





  
  

  71
  
<P>





  
  

  72
  
<P><P>





  
  

  73
  
<B>Temporal Structure Measures</B>





  
  

  74
  
<P>





  
  

  75
  
To study the temporal organization, we applied three methods to analyze





  
  

  76
  
different aspects of the dynamical structure of the 





  
  

  77
  
time series of the stride time.





  
  

  78
  
<P>





  
  

  79
  
<B>Spectral Analysis:&nbsp;&nbsp;</B> Fourier spectral analysis is a standard method for





  
  

  80
  
examining the dynamics of a time series. To





  
  

  81
  
insure that these dynamical measures were independent of the average





  
  

  82
  
stride time or the stride time variability, we studied the first 256





  
  

  83
  
points of each subject's time series (after the 60 second ``start-up'' period) by first subtracting the mean and





  
  

  84
  
dividing by the standard deviation. This produces a time series





  
  

  85
  
centered at zero with a standard deviation of 1.0. Subsequently,





  
  

  86
  
standard Fourier analysis using a rectangular window was performed on each time





  
  

  87
  
series.  To quantify any differences in the spectra, we calculated the





  
  

  88
  
percent of power in the high frequency band (0.25--0.50





  
  

  89
  
strides<IMG WIDTH=15 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline306" SRC="img8.png">) and the ratio of the low (.05 -- 0.25 strides<IMG WIDTH=15 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline306" SRC="img8.png">)





  
  

  90
  
to high frequency power.





  
  

  91
  
This ratio excludes the power in the lowest frequencies and





  
  

  92
  
thus is independent of very large scale changes in the stride time.





  
  

  93
  
By computing the ratio of the fluctuations over relatively long time scales





  
  

  94
  
(i.e., low frequencies)





  
  

  95
  
to short time scales (i.e., high frequencies), an index of the 





  
  

  96
  
frequency ``balance'' of the 





  
  

  97
  
spectra  is obtained. A large low/high 





  
  

  98
  
ratio is indicative of nonstationarity.





  
  

  99
  
Therefore, to the extent that  the gait of the younger children is more





  
  

  100
  
nonstationary, one would expect this spectral





  
  

  101
  
ratio to decrease with maturation.





  
  

  102
  
<P>





  
  

  103
  
<B>Autocorrelation Decay:&nbsp;&nbsp;</B> As a complementary method for analyzing





  
  

  104
  
the temporal structure of gait dynamics, we examined the autocorrelation properties of





  
  

  105
  
the stride time series.  The autocorrelation function estimates how a





  
  

  106
  
time series is correlated with itself over different time lags and





  
  

  107
  
provides a measure of the ``memory'' in the system, i.e., for up to





  
  

  108
  
how many strides is the present value of the stride time correlated





  
  

  109
  
with past values.  After direct calculation of the





  
  

  110
  
autocorrelation function in the time domain  (20),  





  
  

  111
  
we calculated two 





  
  

  112
  
indices of autocorrelation decay: <IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline310" SRC="img9.png"> and





  
  

  113
  
<IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline312" SRC="img10.png">, the number of strides for the autocorrelation to decay





  
  

  114
  
to 37 % (1/e) or 63 % (1-1/e) of its initial value,





  
  

  115
  
respectively.  To minimize any effects of data length, mean or





  
  

  116
  
variance, we applied this analysis to the first 256 strides and





  
  

  117
  
normalized each time series with respect to its mean and standard





  
  

  118
  
deviation. This autocorrelation measure emphasizes the correlation





  
  

  119
  
properties over a very short time scale, where the correlation decays





  
  

  120
  
most rapidly. 





  
  

  121
  
If the ``memory'' of the system increases with maturity, one would





  
  

  122
  
expect to see longer decay times in older children.





  
  

  123
  
<P>





  
  

  124
  
<B>Stride Time Correlations:&nbsp;&nbsp;</B> To further study the temporal





  
  

  125
  
structure of the stride time dynamics (independent of the overall





  
  

  126
  
variance), we also applied detrended fluctuation analysis





  
  

  127
  
(DFA)  (11,18) to each subject's stride time time series. DFA is a





  
  

  128
  
modified random walk analysis that can be used to quantify the





  
  

  129
  
long-range, fractal properties of a relatively long time series or, in





  
  

  130
  
the case of shorter time series, (i.e., the present study), it can be





  
  

  131
  
used to measure how correlation properties change over different time





  
  

  132
  
scales or observation windows  (10,18).  Methodologic details have





  
  

  133
  
been provided elsewhere  (10-12,18).  Briefly, the root-mean





  
  

  134
  
square fluctuation of the integrated and detrended time series is





  
  

  135
  
calculated at different time scales and the slope of the relationship





  
  

  136
  
between the fluctuation magnitude and the time scale determines a fractal





  
  

  137
  
scaling index, <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">. To determine





  
  

  138
  
the degree and nature of stride time correlations, we used previously





  
  

  139
  
validated methods  (10) and calculated <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png"> over the region <IMG WIDTH=100 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline318" SRC="img12.png"> (where n is the number of strides in the window of





  
  

  140
  
observation). This region was chosen as it provides a statistically





  
  

  141
  
robust estimate of stride time correlation properties that are most





  
  

  142
  
independent of finite size effects (length of data)  (17) and because





  
  

  143
  
it has been shown to be sensitive to the effects of neurological





  
  

  144
  
disease and aging in older adults  (10). Like the autocorrelation method,





  
  

  145
  
the DFA method quantifies correlation properties. However, the DFA method





  
  

  146
  
assumes that within the scale of interest the correlation decays in a power-law





  
  

  147
  
manner and, therefore, a single exponent (<IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">) can quantify the scaling. 





  
  

  148
  
Whereas the autocorrelation method was applied to examine the dynamics over very short time scales, 





  
  

  149
  
the DFA method as applied here examines scaling over relatively





  
  

  150
  
longer time periods.





  
  

  151
  
If the stride-to-stride fluctuations are more random (less correlated) in younger children,





  
  

  152
  
one would expect that <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png"> would be closer to 0.5 (white noise)





  
  

  153
  
in this group. In contrast, 





  
  

  154
  
an <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png"> value closer to 1.5 would indicate fluctutations





  
  

  155
  
with a  brown noise quality, indicatinig





  
  

  156
  
the dominance of  slow moving  (18).





  
  

  157
  
<P>





  
  

  158
  
<HR><A NAME="tex2html62" HREF="node7.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="/icons/latex2html/next_motif.png"></A> <A NAME="tex2html60" HREF="node3.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="/icons/latex2html/up_motif.png"></A> <A NAME="tex2html54" HREF="node5.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="/icons/latex2html/previous_motif.png"></A>   <BR>





  
  

  159
  
<B> Next:</B> <A NAME="tex2html63" HREF="node7.html">Statistical Methods</A>





  
  

  160
  
<B>Up:</B> <A NAME="tex2html61" HREF="node3.html">Methods</A>





  
  

  161
  
<B> Previous:</B> <A NAME="tex2html55" HREF="node5.html">Protocol</A>





  
  

  162
  
</BODY>





  
  

  163
  
</HTML>