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<B> Next:</B> <A NAME="tex2html101" HREF="node11.html">Relationship of Stride Dynamics </A>





  
  

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<B>Up:</B> <A NAME="tex2html99" HREF="node8.html">Results</A>





  
  

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<B> Previous:</B> <A NAME="tex2html93" HREF="node9.html">Stride Time Variability Measures</A>





  
  

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<BR> <P>





  
  

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<H3><A NAME="SECTION00040200000000000000">Temporal Structure Measures</A></H3>





  
  

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<P>





  
  

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<B>Spectral Analysis:&nbsp;&nbsp;</B> 





  
  

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The above results demonstrate that the <I>magnitude</I> of 





  
  

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stride-to-stride variability decreases with maturation in healthy





  
  

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children. The question we next address is whether the <I>temporal





  
  

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structure</I> of the stride time dynamics 





  
  

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is also age-dependent.





  
  

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Figure 4 shows the results of spectral analysis for the time series shown in





  
  

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Figure 1. As expected, 





  
  

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there appears to be a change in the frequency spectra with age. 





  
  

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The power in the higher frequency ranges appears to be slightly





  
  

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larger in the oldest child and smaller in the two younger





  
  

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children. Conversely, low frequency power appears to be reduced in the





  
  

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11 year old child compared to the two younger children.  





  
  

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For the entire group in general, the percent of high frequency power was increased





  
  

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 and low frequency power was decreased in the oldest children compared to the other two groups





  
  

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(Table 3). Although these trends were not significant, 





  
  

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there was a significant dependence of the low/high ratio on age group (p &lt; .002).





  
  

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This spectral ratio was significantly larger in the oldest children





  
  

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compared to the 6 and 7 years olds (p &lt; .02) and it also tended to be larger





  
  

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in the 6 and 7 year olds compared with the youngest children (p=.06).





  
  

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In other words, the ratio of the stride time fluctuations on relatively large time scales





  
  

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to the fluctuations on shorter time scales decreased with age.





  
  

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<P>





  
  

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To confirm that this difference in spectral balance was not due to any





  
  

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simple large-scale trends in the data, we performed spectral analysis of each





  
  

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time series after detrending  each time series (by taking the first





  
  

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difference). The results were similar to those for the original time





  
  

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series (Table 3), suggesting that there is a change in spectral





  
  

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balance independent of large-scale trends in the data.  Moreover,





  
  

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we confirmed that this effect persisted even if we changed (somewhat





  
  

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arbitrarily) the way in which the spectra were divided. For example, when the  high





  
  

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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





  
  

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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





  
  

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spectral power was observed (Table 3 and Figure 5).





  
  

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<P>





  
  

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<B>Autocorrelation Measures:&nbsp;&nbsp;</B> As expected, measures of the decay of the autocorrelation function also varied  with age.  For the younger





  
  

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children, <IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline358" SRC="img14.png"> decayed rapidly (after 2 or 3 strides), while





  
  

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this decay time was generally larger in the two older groups. Specifically,





  
  

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<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





  
  

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4 year olds and the 6 and 7 year olds, respectively, (p &lt; .0005). <IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline358" SRC="img14.png">





  
  

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was slightly, but not significantly larger in the 11 to 14 year olds





  
  

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(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





  
  

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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





  
  

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autocorrelation function was also lowest in the 3 and 4 year olds (5.8





  
  

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<IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 1.0 strides), larger (p &lt; .06) in the 6 and 7 year olds (11.4





  
  

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<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





  
  

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olds (19.0<IMG WIDTH=12 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline288" SRC="img6.png"> 9.8; p &lt; .01 compared to the youngest children).





  
  

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<P>





  
  

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<B>Stride Time Correlations:&nbsp;&nbsp;</B> The fractal scaling index, <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">,





  
  

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was similar in the two youngest age groups and tended to decrease in the





  
  

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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, 





  
  

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respectively.)





  
  

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When this analysis was performed on the first





  
  

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difference of the time series (i.e., after removing any large trends),





  
  

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the effect of age became more pronounced and statistically





  
  

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significant (p &lt; 0.01 and p &lt; 0.05 comparing the 11 to 14 year olds to 





  
  

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the 6 and 7 year olds and the 3 and 4 years olds, respectively).





  
  

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<P>





  
  

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The DFA method automatically ``detrends'' the data by determining the





  
  

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fluctuations about the least-squares, best fit straight line in each





  
  

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window of observation. Nonstationarities (trends) that are not well





  
  

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characterized by a straight line could possibly give rise to an





  
  

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inaccurate scaling exponent. Therefore, to further examine the





  
  

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dynamical properties, we also computed the scaling index <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">





  
  

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using higher order DFA detrending. Specifically, we detrended each





  
  

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window of box size <I>n</I> using 2nd order polynomials instead of the 1st





  
  

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order, linear detrending  (12).





  
  

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<P>





  
  

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With 2nd order detrending





  
  

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of the time series, the age effect was apparent both before (see





  
  

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Figure 6) and after taking the first difference of the time series. Among the younger





  
  

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subjects (&lt; 11 years old), ten subjects (about 25%) had scaling indices





  
  

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greater than 1.0, while in the oldest subjects all of the scaling





  
  

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exponents were less than 1.0.  While the scaling properties were





  
  

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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">





  
  

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was significantly lower in the oldest children compared to the 6 and 7





  
  

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year olds and compared to the 3 and 4 year olds (p &lt; .05).  The





  
  

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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 





  
  

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obtained in young adults





  
  

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(Figure 6).





  
  

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<P>





  
  

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<B> Next:</B> <A NAME="tex2html101" HREF="node11.html">Relationship of Stride Dynamics </A>





  
  

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