Information Technology Reference
In-Depth Information
0.9
0.85
0.8
0.75
0.7
100
200
300
400
500
Stride Number
Figure 2.24.
The time interval between strides for the first 500 steps made by a typical walker in an
experiment [
98
], from [
100
]. Reproduced with permission.
Using an SRV time series of 15 minutes, from which the data depicted in Figure
2.24
were taken, we apply the allometric aggregation procedure to determine the relation
between the aggregated standard deviation and aggregated average of the time series
as shown in Figure
2.25
. In the latter figure, the line segment for the SRV data is, as
we did with the other data sets, contrasted with an uncorrelated random process (slope
0.5) and a regular deterministic process (slope 1.0). The slope of the data curve is 0.70,
midway between the two extremes of regularity and uncorrelated randomness. So, as in
the cases of HRV and BRV time series, we again find the erratic physiologic time series
to represent random fractal processes.
The question regarding the source of the second-moment scaling is again raised.
Is the scaling due to long-range correlations or is it due to non-standard statistics?
We again use histograms to construct the probability density and the associated dif-
fusion entropy for the SRV data. The entropy is plotted as a function of the logarithm
of time in Figure
2.26
, where we see the probability scaling index
δ
=
0
.
69 for the
original SRV data and the index drops to
46 for the shuffled data. This scal-
ing suggests that the walker does not smoothly adjust stride from step to step, but
instead there is a number of steps over which adjustments are made followed by a
number of steps over which the changes in stride are completely random. The num-
ber of steps in the adjustment process and the number of steps between adjustment
periods are not independent. The results of a substantial number of stride-interval exper-
iments support the universality of this interpretation, see, for example, West [
100
], for a
review.
Finally, it should be pointed out that people use essentially the same control net-
work, namely maintaining balance, when they are standing still as they do when they
are walking. This suggests that the body's slight movements around the center of mass
of the body in any simple model of locomotion would have the same statistical behavior
as the variability observed during walking. These movements are called postural sway
and have given rise to papers with such interesting titles as “Random walking during
δ
=
0
.
