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<H3><A NAME="SECTION00040200000000000000">Temporal Structure Measures</A></H3>
<P>
<B>Spectral Analysis: </B>
The above results demonstrate that the <I>magnitude</I> of
stride-to-stride variability decreases with maturation in healthy
children. The question we next address is whether the <I>temporal
structure</I> of the stride time dynamics
is also age-dependent.
Figure 4 shows the results of spectral analysis for the time series shown in
Figure 1. As expected,
there appears to be a change in the frequency spectra with age.
The power in the higher frequency ranges appears to be slightly
larger in the oldest child and smaller in the two younger
children. Conversely, low frequency power appears to be reduced in the
11 year old child compared to the two younger children.
For the entire group in general, the percent of high frequency power was increased
and low frequency power was decreased in the oldest children compared to the other two groups
(Table 3). Although these trends were not significant,
there was a significant dependence of the low/high ratio on age group (p < .002).
This spectral ratio was significantly larger in the oldest children
compared to the 6 and 7 years olds (p < .02) and it also tended to be larger
in the 6 and 7 year olds compared with the youngest children (p=.06).
In other words, the ratio of the stride time fluctuations on relatively large time scales
to the fluctuations on shorter time scales decreased with age.
<P>
To confirm that this difference in spectral balance was not due to any
simple large-scale trends in the data, we performed spectral analysis of each
time series after detrending each time series (by taking the first
difference). The results were similar to those for the original time
series (Table 3), suggesting that there is a change in spectral
balance independent of large-scale trends in the data. Moreover,
we confirmed that this effect persisted even if we changed (somewhat
arbitrarily) the way in which the spectra were divided. For example, when the high
frequency band was re-defined as 0.3 to 0.4 stride<IMG WIDTH=15 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline306" SRC="img8.png"> and the low frequency band as
0.1 to 0.2 stride<IMG WIDTH=15 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline306" SRC="img8.png">, a similar effect of age on the balance of
spectral power was observed (Table 3 and Figure 5).
<P>
<B>Autocorrelation Measures: </B> As expected, measures of the decay of the autocorrelation function also varied with age. For the younger
children, <IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline358" SRC="img14.png"> decayed rapidly (after 2 or 3 strides), while
this decay time was generally larger in the two older groups. Specifically,
<IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline358" SRC="img14.png"> was 2.5 <IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 0.2 and 4.8 <IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 0.6 strides in the 3 and
4 year olds and the 6 and 7 year olds, respectively, (p < .0005). <IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline358" SRC="img14.png">
was slightly, but not significantly larger in the 11 to 14 year olds
(5.6 <IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 1.1 strides) compared to the 6 and 7 year olds. Similar
results were obtained for <IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline310" SRC="img9.png">. This measure of the decay of the
autocorrelation function was also lowest in the 3 and 4 year olds (5.8
<IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 1.0 strides), larger (p < .06) in the 6 and 7 year olds (11.4
<IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 3.3), and tended to be slightly larger in the 11 to 14 year
olds (19.0<IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 9.8; p < .01 compared to the youngest children).
<P>
<B>Stride Time Correlations: </B> The fractal scaling index, <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">,
was similar in the two youngest age groups and tended to decrease in the
oldest children (<IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png"> = 0.93 <IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 0.04, 0.93 <IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 0.03, 0.88 <IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 0.04, in the 3 and 4 years olds, 6 and 7 year olds, and 11 to 14 year olds,
respectively.)
When this analysis was performed on the first
difference of the time series (i.e., after removing any large trends),
the effect of age became more pronounced and statistically
significant (p < 0.01 and p < 0.05 comparing the 11 to 14 year olds to
the 6 and 7 year olds and the 3 and 4 years olds, respectively).
<P>
The DFA method automatically ``detrends'' the data by determining the
fluctuations about the least-squares, best fit straight line in each
window of observation. Nonstationarities (trends) that are not well
characterized by a straight line could possibly give rise to an
inaccurate scaling exponent. Therefore, to further examine the
dynamical properties, we also computed the scaling index <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">
using higher order DFA detrending. Specifically, we detrended each
window of box size <I>n</I> using 2nd order polynomials instead of the 1st
order, linear detrending (12).
<P>
With 2nd order detrending
of the time series, the age effect was apparent both before (see
Figure 6) and after taking the first difference of the time series. Among the younger
subjects (< 11 years old), ten subjects (about 25%) had scaling indices
greater than 1.0, while in the oldest subjects all of the scaling
exponents were less than 1.0. While the scaling properties were
similar in the 3 and 4 year olds and the 6 and 7 year olds, <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">
was significantly lower in the oldest children compared to the 6 and 7
year olds and compared to the 3 and 4 year olds (p < .05). The
mean <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png"> of the oldest children comes closest to the mean value
obtained in young adults
(Figure 6).
<P>
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