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Dynamic stability of running: The effects of speed and leg amputations on the maximal Lyapunov exponent
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10.1063/1.4837095
/content/aip/journal/chaos/23/4/10.1063/1.4837095
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/4/10.1063/1.4837095
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Subject with a unilateral transtibial amputation running on a high-speed instrumented treadmill.

Image of FIG. 2.
FIG. 2.

Sagittal-plane knee angles for (left) a non-amputee runner and (right) a runner with a unilateral transtibial amputation, both running at 4 m/s. Blue and red correspond to the left and right leg, respectively, of the NA runner, and to the affected and unaffected leg, respectively, of the WA subject. 0° is full extension; negative angles correspond to flexion of the joint.

Image of FIG. 3.
FIG. 3.

Estimating embedding parameters for the data of Figure 2 : mutual information as a function of the delay τ, plotted in units of the sampling rate of a second, and % false near neighbors as a function of thedimension . The minima of the mutual information curves occur near (i.e., 173 ms) for both knees of the non-amputee (“NA”) runner and (i.e., 183 ms) for both knees of the runner with a unilateral transtibial amputation (the “WA” subject). All four false near neighbor curves drop to 10% at  = 3. Color code as in the previous figure: blue and red correspond to the left and right leg, respectively, of the NA runner, and to the affected and unaffected leg, respectively, of the WA subject.

Image of FIG. 4.
FIG. 4.

Delay-coordinate embeddings of the traces in Figure 2 with the τ and values suggested by the curves in Figure 3 . Again, time () is in units of , the inverse of the 300 Hz sampling rate of the time series.

Image of FIG. 5.
FIG. 5.

Lyapunov exponent calculations for the embedded data of Figure 3 . The slopes of the scaling regions of these curves—fit by the superimposed lines in the plots—represent estimates of the maximal Lyapunov exponent of the corresponding trajectories. As before, time is plotted in units of the sampling interval s. The stride intervals in these trials were 0.65 and 0.71 s for the NA and WA subjects—i.e., 196 and 211 sampling intervals, respectively.

Image of FIG. 6.
FIG. 6.

values for the embedded knee-joint dynamics of non-amputees and subjects with amputations. The values reported are in units of inverse , the sampling interval of the data; to convert them to inverse seconds, one multiplies by the 300 Hz sampling rate.

Image of FIG. 7.
FIG. 7.

values for the embedded hip-joint dynamics of non-amputees and subjects with amputations. The values reported are in units of inverse , the sampling interval of the data; to convert them to inverse seconds, one multiplies by the 300 Hz sampling rate.

Image of FIG. 8.
FIG. 8.

values for the embedded sacrum-position dynamics of non-amputees and subjects with amputations. The values reported are in units of inverse , the sampling interval of the data; to convert them to inverse seconds, one multiplies by the 300 Hz sampling rate.

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/content/aip/journal/chaos/23/4/10.1063/1.4837095
2013-12-10
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dynamic stability of running: The effects of speed and leg amputations on the maximal Lyapunov exponent
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/4/10.1063/1.4837095
10.1063/1.4837095
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