# A Comparison of Postural Stability during Upright Standing between Normal and Flatfooted Individuals, Based on COP-Based Measures

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Equipment

#### 2.3. COP-Based Measures

#### 2.3.1. Traditional COP Methods

#### 2.3.2. Entropy Methods

_{n}and different modes of oscillation (IMF

_{i}, i = 1,…,n). For this analysis, we assumed n = 7 (Figure 2). The detrended signal IMFs were used to derive the CI values of the entropy measures using the formulae above.

#### 2.4. Data Analysis

#### 2.5. Statistics

## 3. Results

#### 3.1. Traditional COP-Based Measures

#### 3.2. Entropy Measures

_{6}and IMF

_{7}(0.1–0.3 Hz; Table 3).

_{2,3}, IMF

_{3,4}, and IMF

_{2,3,4}) revealed no significant differences between the two groups, but the low-frequency combinations (IMF

_{5,6}, IMF

_{6,7}, and IMF

_{5,6,7}) revealed statistically significant differences in complexity between the groups (Table 6). The results were thus similar to those presented in Table 3: a significant difference in the lower-frequency IMFs.

## 4. Discussion

_{6}and IMF

_{7}signals (Table 3); (3) there were no significant differences in the MMSE (Table 5); and (4) reconstructed combinations of IMFs for the entropy-based measures, IMF

_{5,6}, IMF

_{6,7}, and IMF

_{5,6,7}revealed significant differences in stability in both directions for both EO and EC between the two groups (Table 6). Thus, the traditional raw-data-based measures only revealed significant differences under EO conditions, whereas the entropy-based measures revealed differences under both EO and EC conditions.

_{2,3}[37]. Similarly, Jiang et al. found significant differences in complexity for older adults before and after using vibratory insoles; however, they found no such differences for younger adults [20]. Further, Wei et al. revealed statistically significant differences in complexity between younger and older adults using reconstructed IMF

_{5}, IMF

_{4,5}, and IMF

_{3,4,5}signals via MSE, and before and after the use of vibratory insoles among older adults using reconstructed IMF

_{4}, IMF

_{2,4}, IMF

_{3,4}, and IMF

_{2,3,4}signals via MMSE [31]. Huang et al. compared different COP systems using entropy measures, and found that IMF

_{5,6}was more sensitive than IMF

_{2,3}in distinguishing among young adults [18]. These studies show that the postural stability of younger adults differs from that of older adults, and that in younger adults it is less likely that changes will be detected after interventions.

_{2,4,5}[20]. Previous studies applying entropy-based measures have observed significant differences in postural stability mainly in the higher-frequency signals (~1–30 Hz) [18,19,20,31,32]. One study [40] showed that the frequency range is <2 Hz in human-body COP signals, and another study [41] used COP signals to show that visual input affects the lower frequencies. Further experimentation using appropriate parameters and specific IMF signal frequency ranges is required to verify the analysis results for different groups of participants, to evaluate how human balance control functions.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The participant steps in chalk then takes a step on a sheet of paper. The arch index ratio (R) of the footprint is then calculated [2].

**Figure 2.**Center of pressure (COP) displacement trajectories of a participant standing on a force plate were retrieved for the anterior–posterior (AP) and medial–lateral (ML) directions. The time series signal was then detrended into intrinsic mode functions (IMFs) using the empirical mode decomposition (EMD) method.

**Figure 3.**The overall architecture of assessment procedure for postural stability from the COP displacement trajectory of a participant standing on a force plate in normal foot and flatfooted persons. EC: eyes closed; EO: eyes open; MSE: multiscale entropy; MMSE: multivariate multiscale entropy.

Participants | Footprint Type (mean ± SD) | p-Value | |
---|---|---|---|

Flatfooted (n = 17) | Normal (n = 37) | ||

Males | 13 | 16 | |

Females | 4 | 21 | |

Arch index (R) | 1.26 ± 0.17 | 0.71 ± 0.09 | 0.000 |

Age (years) | 22.53 ± 1.42 | 23.62 ± 2.29 | 0.076 |

Height (cm) | 169.79 ± 7.93 | 165.76 ± 7.63 | 0.081 |

Weight (kg) | 68.44 ± 13.23 | 60.93 ± 10.35 | 0.051 |

BMI (kg/m^{2}) | 23.59 ± 3.06 | 22.06 ± 2.56 | 0.062 |

**Table 2.**Descriptive statistics (mean ± SD) for the commonly-used COP-based measures of postural stability with eyes open (EO) and eyes closed (EC) for two groups of participants (flatfooted and normal). MDIST: mean resultant distance; AP: anterior–posterior; ML: medial–lateral; RDIST: root mean square distance; TOTEX: total excursion; MVELO: mean displacement velocity; AREA_CC: 95% confidence circle area; AREA_CE: 95% confidence ellipse area.

Measures (Units) | EO | EC | ||||||
---|---|---|---|---|---|---|---|---|

Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | |

MDIST (mm) | 3.51 ± 1.23 | 2.77 ± 1.10 | 2.23 | 0.030 * | 3.83 ± 2.27 | 3.05 ± 1.19 | 1.66 | 0.102 |

MDIST_AP (mm) | 2.68 ± 1.01 | 2.18 ± 0.89 | 1.81 | 0.077 | 3.01 ± 1.77 | 2.41 ± 0.92 | 1.65 | 0.106 |

MDIST_ML (mm) | 1.73 ± 0.77 | 1.26 ± 0.63 | 2.38 | 0.021 * | 1.77 ± 1.22 | 1.39 ± 0.85 | 1.32 | 0.192 |

RDIST (mm) | 4.03 ± 1.40 | 3.20 ± 1.26 | 2.17 | 0.034 * | 4.44 ± 2.57 | 3.54 ± 1.37 | 1.67 | 0.100 |

RDIST_AP (mm) | 3.32 ± 1.23 | 2.73 ± 1.11 | 1.74 | 0.087 | 3.78 ± 2.19 | 3.02 ± 1.11 | 1.70 | 0.094 |

RDIST_ML (mm) | 2.17 ± 0.95 | 1.57 ± 0.77 | 2.47 | 0.017 * | 2.22 ± 1.51 | 1.73 ± 1.04 | 1.39 | 0.171 |

TOTEX (mm) | 523.8 ± 106.6 | 508.8 ± 81.9 | 0.57 | 0.572 | 602.2 ± 161.6 | 579.7 ± 103.2 | 0.62 | 0.540 |

TOTEX_AP (mm) | 376.6 ± 83.4 | 358.7 ± 52.3 | 0.96 | 0.339 | 442.5 ± 124.9 | 424.3 ± 76.6 | 0.66 | 0.512 |

TOTEX_ML (mm) | 282.6 ± 63.4 | 283.0 ± 57.2 | −0.02 | 0.985 | 312.2 ± 96.8 | 304.0 ± 69.9 | 0.36 | 0.723 |

MVELO (mm/s) | 8.73 ± 1.78 | 8.48 ± 1.37 | 0.57 | 0.572 | 10.04 ± 2.69 | 9.66 ± 1.72 | 0.62 | 0.540 |

MVELO_AP (mm/s) | 6.28 ± 1.39 | 5.98 ± 0.87 | 0.96 | 0.339 | 7.37 ± 2.08 | 7.07 ± 1.28 | 0.66 | 0.512 |

MVELO_ML (mm/s) | 4.71 ± 1.06 | 4.72 ± 0.95 | −0.02 | 0.985 | 5.20 ± 1.61 | 5.07 ± 1.16 | 0.36 | 0.723 |

AREA_CC (mm^{2}) | 160.8 ± 126.9 | 106.3 ± 89.6 | 1.82 | 0.075 | 231.6 ± 370.1 | 130.4 ± 126.3 | 1.50 | 0.141 |

AREA_SW (mm^{2}/s) | 9.84 ± 5.03 | 5.03 ± 7.45 | 1.78 | 0.081 | 12.62 ± 11.85 | 9.06 ± 5.46 | 1.52 | 0.135 |

Measures | EO | EC | ||||||
---|---|---|---|---|---|---|---|---|

Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | |

CI_AP_IMF_{1} | 26.15 ± 4.51 | 27.64 ± 2.15 | −1.65 | 0.105 | 24.78 ± 4.93 | 26.71 ± 3.3 | −1.69 | 0.098 |

CI_AP_IMF_{2} | 15.75 ± 4.84 | 17.56 ± 4.07 | −1.43 | 0.16 | 15.69 ± 6.45 | 15.59 ± 5.65 | 0.06 | 0.954 |

CI_AP_IMF_{3} | 10.17 ± 3.34 | 11.03 ± 3.04 | −0.93 | 0.357 | 10.36 ± 3.08 | 10.17 ± 2.87 | 0.22 | 0.829 |

CI_AP_IMF_{4} | 11.21 ± 1.30 | 11.44 ± 1.83 | −0.45 | 0.655 | 11.26 ± 1.71 | 10.81 ± 1.71 | 0.91 | 0.368 |

CI_AP_IMF_{5} | 8.92 ± 0.53 | 9.00 ± 0.780 | −0.37 | 0.711 | 8.54 ± 0.89 | 8.70 ± 0.90 | −0.61 | 0.544 |

CI_AP_IMF_{6} | 6.47 ± 0.69 | 6.74 ± 0.826 | −1.18 | 0.245 | 6.22 ± 0.67 | 6.67 ± 0.73 | −2.15 | 0.036 * |

CI_AP_IMF_{7} | 3.46 ± 0.85 | 3.63 ± 1.02 | −0.60 | 0.549 | 3.13 ± 0.82 | 3.59 ± 0.68 | −2.16 | 0.036 * |

Measures | EO | EC | ||||||
---|---|---|---|---|---|---|---|---|

Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | |

CI_ML_IMF_{1} | 28.30 ± 1.35 | 28.44 ± 1.16 | −0.39 | 0.695 | 28.20 ± 1.16 | 28.516 ± 0.66 | −1.29 | 0.201 |

CI_ML_IMF_{2} | 21.00 ± 4.15 | 22.24 ± 4.03 | −0.98 | 0.332 | 18.34 ± 6.4 | 21.33 ± 5.36 | −1.78 | 0.081 |

CI_ML_IMF_{3} | 10.54 ± 4.76 | 11.26 ± 4.65 | −0.53 | 0.599 | 9.44 ± 4.41 | 10.24 ± 3.92 | −0.67 | 0.507 |

CI_ML_IMF_{4} | 9.37 ± 2.09 | 9.04 ± 2.59 | 0.46 | 0.65 | 9.39 ± 2.19 | 8.79 ± 2.11 | 0.95 | 0.346 |

CI_ML_IMF_{5} | 8.71 ± 1.19 | 8.85 ± 1.36 | −0.38 | 0.705 | 8.66 ± 1.32 | 8.80 ± 1.32 | −0.36 | 0.719 |

CI_ML_IMF_{6} | 7.05 ± 0.78 | 7.38 ± 0.86 | −1.33 | 0.188 | 6.75 ± 1.17 | 7.21 ± 0.80 | −1.70 | 0.095 |

CI_ML_IMF_{7} | 3.72 ± 0.98 | 4.16 ± 0.97 | −1.54 | 0.129 | 3.82 ± 0.82 | 4.07 ± 0.85 | −1.02 | 0.312 |

Measures | EO | EC | ||||||
---|---|---|---|---|---|---|---|---|

Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | |

CI_IMF_{1} | 5.80 ± 0.45 | 5.78 ± 0.41 | 0.13 | 0.894 | 5.74 ± 0.50 | 5.78 ± 0.52 | −0.27 | 0.787 |

CI_IMF_{2} | 7.94 ± 1.68 | 7.81 ± 1.07 | 0.33 | 0.74 | 7.48 ± 1.94 | 7.53 ± 1.37 | −0.12 | 0.905 |

CI_IMF_{3} | 7.30 ± 2.71 | 7.57 ± 2.19 | −0.40 | 0.693 | 7.08 ± 2.40 | 7.16 ± 1.84 | −0.13 | 0.895 |

CI_IMF_{4} | 9.86 ± 2.22 | 9.63 ± 2.51 | 0.33 | 0.741 | 10.37 ± 2.28 | 9.41 ± 1.96 | 1.58 | 0.119 |

CI_IMF_{5} | 12.53 ± 1.45 | 12.02 ± 1.78 | 1.04 | 0.303 | 12.49 ± 1.71 | 12.22 ± 1.85 | 0.50 | 0.619 |

CI_IMF_{6} | 12.24 ± 1.11 | 12.41 ± 1.26 | −0.48 | 0.633 | 11.88 ± 1.34 | 12.27 ± 1.47 | −0.93 | 0.357 |

CI_IMF_{7} | 10.64 ± 1.94 | 10.82 ± 1.23 | −0.42 | 0.679 | 10.36 ± 1.43 | 10.74 ± 1.16 | −1.06 | 0.296 |

**Table 6.**The optimization combination entropy based on MSE and MMSE analysis results for eyes open (EO) and eyes closed (EC).

Measures | EO | EC | ||||||
---|---|---|---|---|---|---|---|---|

Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | Flatfooted (n = 17) | Normal (n = 37) | t-Value | p-Value | |

CI_AP_IMF_{5,6} | 8.41 ± 0.72 | 8.65 ± 0.75 | −1.12 | 0.266 | 8.06 ± 0.92 | 8.35 ± 0.83 | −1.17 | 0.249 |

CI_ML_IMF_{5,6} | 8.93 ± 1.00 | 9.39 ± 1.19 | −1.37 | 0.176 | 8.67 ± 1.31 | 9.37 ± 0.86 | −2.35 | 0.023 * |

CI_IMF_{5,6} | 13.13 ± 1.36 | 13.52 ± 1.05 | −1.14 | 0.258 | 12.85 ± 1.23 | 13.41 ± 1.30 | −1.48 | 0.144 |

CI_AP_IMF_{6,7} | 5.06 ± 0.92 | 5.53 ± 0.67 | −2.09 | 0.042 * | 4.50 ± 0.94 | 5.51 ± 0.73 | −4.30 | 0.000 * |

CI_ML_IMF_{6,7} | 5.71 ± 0.82 | 6.22 ± 0.83 | −2.12 | 0.039 * | 5.76 ± 1.12 | 6.18 ± 0.83 | −1.53 | 0.133 |

CI_IMF_{6,7} | 11.36 ± 1.43 | 11.57 ± 1.20 | −0.58 | 0.564 | 11.04 ± 1.05 | 11.54 ± 1.09 | −1.59 | 0.118 |

CI_AP_IMF_{5,67} | 7.29 ± 1.04 | 7.69 ± 1.10 | −1.24 | 0.222 | 7.26 ± 0.82 | 7.71 ± 0.68 | −2.12 | 0.039 * |

CI_ML_IMF_{5,67} | 8.09 ± 1.13 | 8.82 ± 1.31 | −1.97 | 0.054 | 8.15 ± 1.49 | 8.92±0.96 | −2.31 | 0.025 * |

CI_IMF_{5,6,7} | 12.57 ± 1.04 | 12.82 ± 1.40 | −0.66 | 0.512 | 12.57 ± 0.97 | 13.19 ± 1.13 | −1.94 | 0.058 |

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**MDPI and ACS Style**

Chao, T.-C.; Jiang, B.C.
A Comparison of Postural Stability during Upright Standing between Normal and Flatfooted Individuals, Based on COP-Based Measures. *Entropy* **2017**, *19*, 76.
https://doi.org/10.3390/e19020076

**AMA Style**

Chao T-C, Jiang BC.
A Comparison of Postural Stability during Upright Standing between Normal and Flatfooted Individuals, Based on COP-Based Measures. *Entropy*. 2017; 19(2):76.
https://doi.org/10.3390/e19020076

**Chicago/Turabian Style**

Chao, Tsui-Chiao, and Bernard C. Jiang.
2017. "A Comparison of Postural Stability during Upright Standing between Normal and Flatfooted Individuals, Based on COP-Based Measures" *Entropy* 19, no. 2: 76.
https://doi.org/10.3390/e19020076