### Abstract

Center of pressure is commonly used to evaluate standing balance. Even though it is incomplete, no better evaluation method has been presented. We designed our experiment with three standing postures: standing with feet together, standing with feet shoulder width apart, and standing with feet slightly wider than shoulder width. Our platform-based pressure system collected the instantaneous plantar pressure (standing footprint). A physical quantity of instantaneous standing footprint principal axis was defined, and it was used to construct an index to evaluate standing balance. Comparison between results from our newly established index and those from the center of pressure index to evaluate the stability of different standing postures revealed that the standing footprint principal axis index could better respond to the standing posture change than the existing one. Analysis indicated that the insensitive response to the relative position between feet and to the standing posture change from the center of pressure could be better detected by the standing footprint principal axis index. This predicts a wide application of standing footprint principal axis index when evaluating standing balance.

This project was funded by the National Natural Science Foundation of China under the Grant Numbers 10925208, 10972061, 11172073 and by Guangdong Natural Science Foundation under the Grant Number S2011010001829. The authors would like to acknowledge the support from the participants.

I. INTRODUCTION

II. MATERIALS AND METHODS

A. Test equipment

B. Test participants and requirements

C. COP and calculation of SFPA

III. RESULTS AND DISCUSSION

IV. AN APPLICATION

V. CONCLUSION

### Key Topics

- Pressure measurement
- 8.0
- Position sensitive detectors
- 6.0
- Tensor methods
- 5.0
- Computer software
- 3.0
- Surface patterning
- 2.0

## Figures

Distribution of COP and SFPA. (a) COP distribution when standing with feet together. (b) COP distribution when standing with feet shoulder width apart. (c) COP distribution when standing with feet slightly wider than shoulder width. (d) SFPA distribution when standing with feet together. (e) SFPA distribution when standing with feet shoulder width apart. (f) SFPA distribution when standing with feet slightly wider than shoulder width. In Figs. 1(a)–1(c) , the red circle stands for all participant's COP average radius at each instant. The values for three postures are 0.5391 cm, 0.287 cm, and 0.288 cm, respectively. In Figs. 1(d)–1(f) , the red line stands for each participant's SFPA value that is greater than zero at each instant, 8.455°, 0.469°, and 0.232°, respectively. The green line stands for each participant's SFPA value that is less than zero at each instant, −5.701°, −0.499°, and −0.235°, respectively.

Distribution of COP and SFPA. (a) COP distribution when standing with feet together. (b) COP distribution when standing with feet shoulder width apart. (c) COP distribution when standing with feet slightly wider than shoulder width. (d) SFPA distribution when standing with feet together. (e) SFPA distribution when standing with feet shoulder width apart. (f) SFPA distribution when standing with feet slightly wider than shoulder width. In Figs. 1(a)–1(c) , the red circle stands for all participant's COP average radius at each instant. The values for three postures are 0.5391 cm, 0.287 cm, and 0.288 cm, respectively. In Figs. 1(d)–1(f) , the red line stands for each participant's SFPA value that is greater than zero at each instant, 8.455°, 0.469°, and 0.232°, respectively. The green line stands for each participant's SFPA value that is less than zero at each instant, −5.701°, −0.499°, and −0.235°, respectively.

Distribution of ACOP and MCOP displacement. (a) Distribution of ACOP and MCOP when standing with feet together. (b) Distribution of ACOP and MCOP when standing with feet shoulder width apart. (c) Distribution of ACOP and MCOP when standing with feet slightly wider than shoulder. The calculation of the position value in the figures: first calculate the mean value of the position of ACOP and MCOP when standing, and then calculate the COP position of each instant relative to the mean value.

Distribution of ACOP and MCOP displacement. (a) Distribution of ACOP and MCOP when standing with feet together. (b) Distribution of ACOP and MCOP when standing with feet shoulder width apart. (c) Distribution of ACOP and MCOP when standing with feet slightly wider than shoulder. The calculation of the position value in the figures: first calculate the mean value of the position of ACOP and MCOP when standing, and then calculate the COP position of each instant relative to the mean value.

Direction distribution of SFPA. (a) Direction distribution of SFPA when standing with feet together. (b) Direction distribution of SFPA when standing with feet shoulder width apart. (c) Direction distribution of SFPA when standing with feet slightly wider than shoulder. The calculation of the direction value in the figures: first calculate the mean value of the direction of SFPA when standing, and then calculate the direction value of each instant relative to the mean value.

Direction distribution of SFPA. (a) Direction distribution of SFPA when standing with feet together. (b) Direction distribution of SFPA when standing with feet shoulder width apart. (c) Direction distribution of SFPA when standing with feet slightly wider than shoulder. The calculation of the direction value in the figures: first calculate the mean value of the direction of SFPA when standing, and then calculate the direction value of each instant relative to the mean value.

Relation between position, posture, plantar pressures and COP and SFPA. (a) Relation between anteroposterior position change of both feet and SFPA. (b) Relation between plantar pressure change of both feet and COP and SFPA. (c) Relation between the rotation of foot and SFPA. In Fig. 4(a) , left and right foot move anteroposterior symmetrically, i.e., when the left foot moves forward, the right foot moves backward. In Fig. 4(b) , when left foot plantar pressure remains unchanged, the right foot plantar pressure multiplies a coefficient (e.g., 1.1 or 0.9) so that the plantar pressures from left and right foot are inconsistent. In Fig. 4(c) , when left foot remains unchanged, the right foot rotates around its COP. One foot's instantaneous pressure is 323.26N and there are 115 sensors, indicating the standing footprint area is 115 cm^{2}. The foot's SFPA is ±16.52° (left foot is positive and left negative). Let the COP distance between the foot and the cloned one be 11.67 cm when standing with feet together. When standing with feet shoulder width apart, the distance is 28.67 cm and when standing with feet slightly wider than shoulder width, the distance is 51.67 cm.

Relation between position, posture, plantar pressures and COP and SFPA. (a) Relation between anteroposterior position change of both feet and SFPA. (b) Relation between plantar pressure change of both feet and COP and SFPA. (c) Relation between the rotation of foot and SFPA. In Fig. 4(a) , left and right foot move anteroposterior symmetrically, i.e., when the left foot moves forward, the right foot moves backward. In Fig. 4(b) , when left foot plantar pressure remains unchanged, the right foot plantar pressure multiplies a coefficient (e.g., 1.1 or 0.9) so that the plantar pressures from left and right foot are inconsistent. In Fig. 4(c) , when left foot remains unchanged, the right foot rotates around its COP. One foot's instantaneous pressure is 323.26N and there are 115 sensors, indicating the standing footprint area is 115 cm^{2}. The foot's SFPA is ±16.52° (left foot is positive and left negative). Let the COP distance between the foot and the cloned one be 11.67 cm when standing with feet together. When standing with feet shoulder width apart, the distance is 28.67 cm and when standing with feet slightly wider than shoulder width, the distance is 51.67 cm.

## Tables

ACOP, MCOP displacement, and direction of SFPA (Mean ± SD). The displacement unit is cm and the direction unit is degree. The calculation of the position value in the table: first calculate the mean value of the position of ACOP and MCOP when standing, and then calculate the COP position of each instant relative to the mean value. The calculation of the direction value in the table: first calculate the mean value of the direction of SFPA when standing, and then calculate the direction value of each instant relative to the mean value.

ACOP, MCOP displacement, and direction of SFPA (Mean ± SD). The displacement unit is cm and the direction unit is degree. The calculation of the position value in the table: first calculate the mean value of the position of ACOP and MCOP when standing, and then calculate the COP position of each instant relative to the mean value. The calculation of the direction value in the table: first calculate the mean value of the direction of SFPA when standing, and then calculate the direction value of each instant relative to the mean value.

Symmetry of standing posture (Mean ± SD). The displacement unit is cm and the direction unit is degree.

Symmetry of standing posture (Mean ± SD). The displacement unit is cm and the direction unit is degree.

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