Entropy of balance--some recent results

Frank G Borg, Gerd Laxåback, Frank G Borg, Gerd Laxåback

Abstract

Background: Entropy when applied to biological signals is expected to reflect the state of the biological system. However the physiological interpretation of the entropy is not always straightforward. When should high entropy be interpreted as a healthy sign, and when as marker of deteriorating health? We address this question for the particular case of human standing balance and the Center of Pressure data.

Methods: We have measured and analyzed balance data of 136 participants (young, n = 45; elderly, n = 91) comprising in all 1085 trials, and calculated the Sample Entropy (SampEn) for medio-lateral (M/L) and anterior-posterior (A/P) Center of Pressure (COP) together with the Hurst self-similarity (ss) exponent alpha using Detrended Fluctuation Analysis (DFA). The COP was measured with a force plate in eight 30 seconds trials with eyes closed, eyes open, foam, self-perturbation and nudge conditions.

Results: 1) There is a significant difference in SampEn for the A/P-direction between the elderly and the younger groups Old > young. 2) For the elderly we have in general A/P > M/L. 3) For the younger group there was no significant A/P-M/L difference with the exception for the nudge trials where we had the reverse situation, A/P < M/L. 4) For the elderly we have, Eyes Closed > Eyes Open. 5) In case of the Hurst ss-exponent we have for the elderly, M/L > A/P.

Conclusions: These results seem to be require some modifications of the more or less established attention-constraint interpretation of entropy. This holds that higher entropy correlates with a more automatic and a less constrained mode of balance control, and that a higher entropy reflects, in this sense, a more efficient balancing.

Figures

Figure 1
Figure 1
Balance control system. A schematic view of the balance control system which describes a closed loop.
Figure 2
Figure 2
Entropy. Entropy for the X and Y direction for all the trials and the three subgroups: Elderly fallers (F), elderly non-fallers (NF), and young (Y). For each group the value is the group average.
Figure 3
Figure 3
Center of pressure (COP). Standard deviation of COP X and COP Y for all the trials and the three subgroups: Elderly fallers (F), elderly non-fallers (NF), and young (Y). For each group the value is the group average.
Figure 4
Figure 4
Hurst exponent. Hurst ss-exponent for X and Y direction for all the trials and the three subgroups: Elderly fallers (F), elderly non-fallers (NF), and young (Y). For each group the value is the group average.
Figure 5
Figure 5
Hurst exponent vs entropy. Hurst ss-exponent α(Y ) vs entropy S(Y ) for all the trials and the three subgroups. The lines show the local polynomial regression fit "loess" (W S Cleveland) which can be produced by the R-function panel.smooth.
Figure 6
Figure 6
Entropy vs COP. Entropy S(Y ) versus standard deviation σ(Y ) of COP Y for all the trials and the three subgroups. The lines show the local polynomial regression fit "loess".

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