Downloads: 1
Diff of
/jap/node6.html
[000000]
..
[7b91a9]
Switch to side-by-side view
--- a +++ b/jap/node6.html @@ -0,0 +1,163 @@ +<!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>Stride Time Dynamics</TITLE> +<META NAME="description" CONTENT="Stride Time Dynamics"> +<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="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> +<B> Next:</B> <A NAME="tex2html63" HREF="node7.html">Statistical Methods</A> +<B>Up:</B> <A NAME="tex2html61" HREF="node3.html">Methods</A> +<B> Previous:</B> <A NAME="tex2html55" HREF="node5.html">Protocol</A> +<BR> <P> +<H3><A NAME="SECTION00030300000000000000">Stride Time Dynamics</A></H3> +<P> +To study the intrinsic stride-to-stride dynamics and its changes with age, some + preprocessing was performed on each time series. The first +sixty seconds and the last five seconds of each time +series were not included to eliminate any +start-up or ending effects and +to allow the subject to become familiar +with the walking track. The time series were also processed to +remove any pauses (stride time > 2 seconds and the 5 seconds before and +after any pauses) as well as any large spikes or outliers. These +outliers, which occurred infrequently, were removed so that the +intrinsic dynamics of each time series could be more readily +analyzed. This was accomplished using +previously established methods (8,10) by: i) determining the mean and standard deviation of the +stride time while excluding the 5% of the data with the lowest and +highest values, and then ii) removing from the original time series +all data that fell more than 4.0 standard deviations away from this +mean value. The number of pauses (typically 0) and the number of +strides excluded (typically 2 %) were similar in all three +age groups. +<P> +As shown in Table 1 and +summarized below, we applied several measures +to analyze the variability and temporal structure of the stride time +dynamics. +<P> +<P><P> +<B>Stride-to-Stride Variability Measures</B> +<P> +To estimate the overall +stride-to-stride variability, we calculated the standard deviation +of each time series and +the coefficient of variation (CV) (100<IMG WIDTH=8 HEIGHT=20 ALIGN=MIDDLE ALT="tex2html_wrap_inline304" SRC="img7.png">standard deviation/mean), +an index of +variability normalized to each subject's mean cycle duration. +Both the standard deviation and the CV provide a measure of overall variations +in gait timing during the entire walk, i.e., the amplitude of the +fluctuations in the time series with respect to the mean. However, +these measures may be influenced by trends in the data (e.g., due +to a change in speed) and cannot distinguish between a walk with large changes +from one stride to the next and one in which stride-to-stride +variations are small and more long-term, global changes (e.g., a change in +average value) result in a large standard deviation. Therefore, +to estimate variability independent of +local changes in the mean, we quantified +successive stride-to-stride changes (i.e., the difference between the +stride time of one stride and the previous stride) by determining the first difference of +each time series. The first difference, a discrete analog +of the first derivative, is one standard method for removing slow varying trends and is calculated by subtracting the previous value in the +time series from the current value. The standard deviation of the first +difference time series provides +a measure of variability after detrending. +<P> +<P><P> +<B>Temporal Structure Measures</B> +<P> +To study the temporal organization, we applied three methods to analyze +different aspects of the dynamical structure of the +time series of the stride time. +<P> +<B>Spectral Analysis: </B> Fourier spectral analysis is a standard method for +examining the dynamics of a time series. To +insure that these dynamical measures were independent of the average +stride time or the stride time variability, we studied the first 256 +points of each subject's time series (after the 60 second ``start-up'' period) by first subtracting the mean and +dividing by the standard deviation. This produces a time series +centered at zero with a standard deviation of 1.0. Subsequently, +standard Fourier analysis using a rectangular window was performed on each time +series. To quantify any differences in the spectra, we calculated the +percent of power in the high frequency band (0.25--0.50 +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">) +to high frequency power. +This ratio excludes the power in the lowest frequencies and +thus is independent of very large scale changes in the stride time. +By computing the ratio of the fluctuations over relatively long time scales +(i.e., low frequencies) +to short time scales (i.e., high frequencies), an index of the +frequency ``balance'' of the +spectra is obtained. A large low/high +ratio is indicative of nonstationarity. +Therefore, to the extent that the gait of the younger children is more +nonstationary, one would expect this spectral +ratio to decrease with maturation. +<P> +<B>Autocorrelation Decay: </B> As a complementary method for analyzing +the temporal structure of gait dynamics, we examined the autocorrelation properties of +the stride time series. The autocorrelation function estimates how a +time series is correlated with itself over different time lags and +provides a measure of the ``memory'' in the system, i.e., for up to +how many strides is the present value of the stride time correlated +with past values. After direct calculation of the +autocorrelation function in the time domain (20), +we calculated two +indices of autocorrelation decay: <IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline310" SRC="img9.png"> and +<IMG WIDTH=31 HEIGHT=18 ALIGN=MIDDLE ALT="tex2html_wrap_inline312" SRC="img10.png">, the number of strides for the autocorrelation to decay +to 37 % (1/e) or 63 % (1-1/e) of its initial value, +respectively. To minimize any effects of data length, mean or +variance, we applied this analysis to the first 256 strides and +normalized each time series with respect to its mean and standard +deviation. This autocorrelation measure emphasizes the correlation +properties over a very short time scale, where the correlation decays +most rapidly. +If the ``memory'' of the system increases with maturity, one would +expect to see longer decay times in older children. +<P> +<B>Stride Time Correlations: </B> To further study the temporal +structure of the stride time dynamics (independent of the overall +variance), we also applied detrended fluctuation analysis +(DFA) (11,18) to each subject's stride time time series. DFA is a +modified random walk analysis that can be used to quantify the +long-range, fractal properties of a relatively long time series or, in +the case of shorter time series, (i.e., the present study), it can be +used to measure how correlation properties change over different time +scales or observation windows (10,18). Methodologic details have +been provided elsewhere (10-12,18). Briefly, the root-mean +square fluctuation of the integrated and detrended time series is +calculated at different time scales and the slope of the relationship +between the fluctuation magnitude and the time scale determines a fractal +scaling index, <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">. To determine +the degree and nature of stride time correlations, we used previously +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 +observation). This region was chosen as it provides a statistically +robust estimate of stride time correlation properties that are most +independent of finite size effects (length of data) (17) and because +it has been shown to be sensitive to the effects of neurological +disease and aging in older adults (10). Like the autocorrelation method, +the DFA method quantifies correlation properties. However, the DFA method +assumes that within the scale of interest the correlation decays in a power-law +manner and, therefore, a single exponent (<IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png">) can quantify the scaling. +Whereas the autocorrelation method was applied to examine the dynamics over very short time scales, +the DFA method as applied here examines scaling over relatively +longer time periods. +If the stride-to-stride fluctuations are more random (less correlated) in younger children, +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) +in this group. In contrast, +an <IMG WIDTH=10 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline314" SRC="img11.png"> value closer to 1.5 would indicate fluctutations +with a brown noise quality, indicatinig +the dominance of slow moving (18). +<P> +<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> +<B> Next:</B> <A NAME="tex2html63" HREF="node7.html">Statistical Methods</A> +<B>Up:</B> <A NAME="tex2html61" HREF="node3.html">Methods</A> +<B> Previous:</B> <A NAME="tex2html55" HREF="node5.html">Protocol</A> +</BODY> +</HTML>