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Ch04-I044963.fm Page 17 Tuesday, August 1, 2006 6:33 PM
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Tuesday, August
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Lyapunov Exponent Lateral Lyapunov Exponent Vertical Lyapunov Exponent Anteroposterior
0.141 1 0.14 J. 14
1 1 t
0.12 1 0.12 1 0.12
1 0.1 1 1
0.1 i I 0.1
0.08 1 0.08 1 1 0.08
0.06 0.06
0.06
1
0.04 1 0.04
0.04 1 J-
0.02 _1_
0.02 0.02 J -
Young Elderly Young Elderly Young Elderly
Figure 4: Comparison of Lyapunov exponents between young and all elder subjects. The lower
and upperlines of the box are 25th amd 75th percentiles.
Lyapunov Exponent Lateral Lyapunov Exponent Vertical Lyapunov Exponent Anteroposterior
T + t
0.12 1 0.12 -i-
1 0.1
0.1 1
i 1
0.08 1 0.08
0.06 0.06
1
0.04 0.04
1
0.02 - I - 1 0.02
_l_ -L
Pre. Post. Pre. Post. Pre. Post.
Figure 5: Comparison of Lyapunov exponents between the pre-intervention and the
post-intervention subject in the elderly.

box are the 25th and 75th percentiles. The line in the middle of the box is the median. The
wiskers shows the extent of the rest of the data. Elderly subjects generally exhibited higher value
indicating much instability in all direction, but no statistical significance was observed except in
the vertical direction (p <0.05). Figure 5 shows the average value of the estimated Lyapunov
exponent comparing with the pre-intervention and the post-intervention in elderly subjects. The
post-intervention illustrates significantly smaller value of the exponent in all direction (p <0.05).
The result suggested that the method feasibly reveals the effects of the interventions on the
improvement of walking stability in elderly.

In the experiment, a short walking distance was chosen to avoid effects of fatigue from elderly
persons' walking. It is important to mention that estimation of Lyapunov exponents is sensitive to
the data size and the observation time. Therefore, estimation accuracy of Lyapunov exponents was
rather low in this study. However, we quantified the exponential rate of divergence of trajectories,
which followed trends of Lyapunov exponents. The proposed method was adequate to quantify
the nature of the dynamic system while walking. A quantitative measure of the walking stability
may provides an essential tool for assessing personnel risk of falls, designing proper treatments,
and monitoring progress and efficacy of the intervention.

CONCLUSION

This study presented a technique for assessing dynamic stability of walking using nonlinear time-
series analysis with a portable instrument. This method is easily applicable and reliable in the
clinical field and daily situations. The experimental results suggested that the proposed method