# Quantification of the Influence of Prosthetic Ankle Stiffness on Static Balance Using Lower Limb Prosthetic Simulators

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Stiffness Characterization

#### 2.2. Subjects and Protocol

#### 2.3. Data Processing

## 3. Results

#### 3.1. Ankle Stiffness

#### 3.2. Static Balance Depending on the Prosthetic Ankle Stiffness

#### 3.3. Joint Angles

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANOVA | Analyse Of Variance |

AP | Antero-Posterior |

CE | Closed Eyes |

CI | Confidence Intervals |

COM | Center Of Mass |

COP | Center Of Pressure |

ESAR | Energy Storage And Release |

ML | Medio-Lateral |

OE | Open Eyes |

ROM | Range Of Motion |

sd | standard deviation |

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**Figure 3.**The 95% confidence ellipse of the global COP for the subject 9 in the Ref configuration with OE.

**Figure 4.**Ankle stiffness normalized by the critical stiffness ${K}_{crit}={m}_{tot}g{h}_{COM}$ against the total mass of the subject (subject mass + prosthetic simulator mass).

**Figure 5.**AP range normalized by the COM height against the foot stiffness normalized by the critical stiffness ${K}_{crit}={m}_{tot}g{h}_{COM}$ in the OE (

**left**) and CE (

**right**) situation.

**Figure 6.**Linear regression of the joint angles ROM as a function of the normalized ankle stiffness in the OE (

**left**) and CE (

**right**) situation.

Subject | Age | Sex | Mass | COM Height | Tested Prostheses | ||
---|---|---|---|---|---|---|---|

[kg] | [mm] | M1 | M3 | M6 | |||

1 | 22 | F | $55.0$ | $902.1$ | ✓ | ✓ | |

2 | 25 | F | $55.3$ | $901.7$ | ✓ | ✓ | ✓ |

3 | 25 | F | $60.6$ | $854.3$ | ✓ | ✓ | ✓ |

4 | 28 | M | $61.5$ | $850.7$ | ✓ | ✓ | ✓ |

5 | 25 | M | $67.5$ | $868.4$ | ✓ | ✓ | ✓ |

6 | 24 | M | $70.2$ | $891.2$ | ✓ | ✓ | |

7 | 24 | M | $74.1$ | $930.1$ | ✓ | ✓ | |

8 | 24 | M | $76.4$ | $987.4$ | ✓ | ✓ | |

9 | 40 | M | $77.7$ | $970.4$ | ✓ | ✓ | ✓ |

10 | 30 | M | $77.7$ | $910.2$ | ✓ | ✓ | |

11 | 24 | M | $98.6$ | $906.0$ | ✓ | ✓ |

Stiffness (Nm/rad) | |||
---|---|---|---|

M1 | M3 | M6 | |

n cycles * | 7 | 7 | 10 |

mean | $203.15$ | $297.82$ | $417.16$ |

sd | $6.23$ | $7.52$ | $8.06$ |

**Table 3.**Mean (sd) of the COP AP range normalized by the COM height (AP range) and the joint angles ROM for each configuration and situation.

Configuration | Ref. | M6 | M3 | M1 | ||||
---|---|---|---|---|---|---|---|---|

Situation | OE | CE | OE | CE | OE | CE | OE | CE |

AP range | $1.7\phantom{\rule{3.33333pt}{0ex}}\left(0.3\right)$ | $2.0\phantom{\rule{3.33333pt}{0ex}}\left(0.5\right)$ | $1.9\phantom{\rule{3.33333pt}{0ex}}\left(0.3\right)$ | $3.0\phantom{\rule{3.33333pt}{0ex}}\left(1.2\right)$ | $2.3\phantom{\rule{3.33333pt}{0ex}}\left(0.3\right)$ | $4.3\phantom{\rule{3.33333pt}{0ex}}\left(1.9\right)$ | $2.6\phantom{\rule{3.33333pt}{0ex}}\left(0.3\right)$ | $5.0\phantom{\rule{3.33333pt}{0ex}}\left(1.8\right)$ |

(% COM height) | ||||||||

Ankle angle ROM | $1.1\phantom{\rule{3.33333pt}{0ex}}\left(0.3\right)$ | $1.1\phantom{\rule{3.33333pt}{0ex}}\left(0.3\right)$ | $1.3\phantom{\rule{3.33333pt}{0ex}}\left(0.5\right)$ | $1.7\phantom{\rule{3.33333pt}{0ex}}\left(0.8\right)$ | $2.2\phantom{\rule{3.33333pt}{0ex}}\left(0.7\right)$ | $3.1\phantom{\rule{3.33333pt}{0ex}}\left(1.8\right)$ | $2.3\phantom{\rule{3.33333pt}{0ex}}\left(0.7\right)$ | $4.6\phantom{\rule{3.33333pt}{0ex}}\left(2.6\right)$ |

(deg) | ||||||||

Knee angle ROM | $1.4\phantom{\rule{3.33333pt}{0ex}}\left(0.7\right)$ | $1.2\phantom{\rule{3.33333pt}{0ex}}\left(0.8\right)$ | $1.9\phantom{\rule{3.33333pt}{0ex}}\left(0.9\right)$ | $2.5\phantom{\rule{3.33333pt}{0ex}}\left(1.1\right)$ | $2.3\phantom{\rule{3.33333pt}{0ex}}\left(0.9\right)$ | $4.5\phantom{\rule{3.33333pt}{0ex}}\left(4.2\right)$ | $2.8\phantom{\rule{3.33333pt}{0ex}}\left(1.3\right)$ | $7.8\phantom{\rule{3.33333pt}{0ex}}\left(1.1\right)$ |

(deg) | ||||||||

Hip angle ROM | $1.7\phantom{\rule{3.33333pt}{0ex}}\left(1.1\right)$ | $1.5\phantom{\rule{3.33333pt}{0ex}}\left(1.0\right)$ | $2.0\phantom{\rule{3.33333pt}{0ex}}\left(1.0\right)$ | $2.8\phantom{\rule{3.33333pt}{0ex}}\left(1.8\right)$ | $2.4\phantom{\rule{3.33333pt}{0ex}}\left(0.7\right)$ | $3.9\phantom{\rule{3.33333pt}{0ex}}\left(2.8\right)$ | $2.6\phantom{\rule{3.33333pt}{0ex}}\left(0.8\right)$ | $6.4\phantom{\rule{3.33333pt}{0ex}}\left(6.4\right)$ |

(deg) |

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**MDPI and ACS Style**

Louessard, A.; Bonnet, X.; Catapano, A.; Pillet, H.
Quantification of the Influence of Prosthetic Ankle Stiffness on Static Balance Using Lower Limb Prosthetic Simulators. *Prosthesis* **2022**, *4*, 636-647.
https://doi.org/10.3390/prosthesis4040051

**AMA Style**

Louessard A, Bonnet X, Catapano A, Pillet H.
Quantification of the Influence of Prosthetic Ankle Stiffness on Static Balance Using Lower Limb Prosthetic Simulators. *Prosthesis*. 2022; 4(4):636-647.
https://doi.org/10.3390/prosthesis4040051

**Chicago/Turabian Style**

Louessard, Aude, Xavier Bonnet, Anita Catapano, and Helene Pillet.
2022. "Quantification of the Influence of Prosthetic Ankle Stiffness on Static Balance Using Lower Limb Prosthetic Simulators" *Prosthesis* 4, no. 4: 636-647.
https://doi.org/10.3390/prosthesis4040051