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--- a +++ b/jap/node10.html @@ -0,0 +1,106 @@ +<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 3.0//EN"> +<!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --> +<HTML> +<HEAD> +<TITLE>Temporal Structure Measures</TITLE> +<META NAME="description" CONTENT="Temporal Structure Measures"> +<META NAME="keywords" CONTENT="gait-reprint"> +<META NAME="resource-type" CONTENT="document"> +<META NAME="distribution" CONTENT="global"> +<LINK REL=STYLESHEET HREF="gait-reprint.css"> +</HEAD> +<BODY LANG="EN" bgcolor="white"> + <A NAME="tex2html100" HREF="node11.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="/icons/latex2html/next_motif.png"></A> <A NAME="tex2html98" HREF="node8.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="/icons/latex2html/up_motif.png"></A> <A NAME="tex2html92" HREF="node9.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="/icons/latex2html/previous_motif.png"></A> <BR> +<B> Next:</B> <A NAME="tex2html101" HREF="node11.html">Relationship of Stride Dynamics </A> +<B>Up:</B> <A NAME="tex2html99" HREF="node8.html">Results</A> +<B> Previous:</B> <A NAME="tex2html93" HREF="node9.html">Stride Time Variability Measures</A> +<BR> <P> +<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> +<HR><A NAME="tex2html100" HREF="node11.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="/icons/latex2html/next_motif.png"></A> <A NAME="tex2html98" HREF="node8.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="/icons/latex2html/up_motif.png"></A> <A NAME="tex2html92" HREF="node9.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="/icons/latex2html/previous_motif.png"></A> <BR> +<B> Next:</B> <A NAME="tex2html101" HREF="node11.html">Relationship of Stride Dynamics </A> +<B>Up:</B> <A NAME="tex2html99" HREF="node8.html">Results</A> +<B> Previous:</B> <A NAME="tex2html93" HREF="node9.html">Stride Time Variability Measures</A> +</BODY> +</HTML>