# Influence of contractile capacities of the ankle plantarflexor muscles on sagittal angular momentum during walking

Florian Ethevea*, Jérémie Beguea, Ophélie Larivièrea, Julien Testa, Georges Dalleau, Mickaël Begonb, c, Nicolas Peyrotd, Teddy Caderbya

Received date: 05/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

Keywords: walking, balance, muscular capacities, ankle muscles

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Whole-body angular momentum (H), sum of segmental angular momenta about the center of mass (CoM), is an indicator of gait (in)stability (Herr & Popovic, 2008). Compared to young adults, older adults exhibit a greater H range in the sagittal plane during gait initiation (Begue et al., 2021), potentially challenging balance control.

The trunk's angular momentum has a major influence on the body's overall angular momentum, likely resulting from the distal-to-proximal redistribution of lower-limb joint kinetics observed with aging (DeVita & Hortobagyi, 2000). Older adults rely more on hip power generation while reducing ankle contribution, possibly compensating for plantarflexor (PF) weakness. This suggests that sagittal H alterations may be linked to decline in PF contractile capacities.

Smith et al. (2024) found no significant correlation between maximal isometric PF strength and sagittal H during perturbed walking. However, these authors did not examine this relationship during unperturbed walking, nor did they assess the PF' maximal torque production at low ($T_0$) and high velocities $\omega_0$ and maximal power $P_{max}$ obtained from the torque-velocity ($T-\omega$) and power-velocity ($P-\omega$) relationships. Therefore, this study investigates the relationship between PF contractile capacities ($T_0$, $\omega_0$, $P_{max}$) and sagittal H during walking.

## 2. Methods

### 2.1 Population and experimental procedures

Fourteen healthy young adults (mean age: 23.4 ± 3.1 years; 7 females) participated after providing informed consent. They were positioned prone on an isokinetic dynamometer (Physiomed, Con-trex MJ, Germany) with the dominant foot secured. Following warm-up, they performed three maximal concentric PF contractions at 60, 120, and 180°/s. Torque and angular velocity were recorded at 2000 Hz.

Then participants walked on an instrumented dual-belt treadmill (Bertec Corporation, USA) at randomized speeds (0.75, 1, and 1.25 m/s) for one minute per condition. Forty-nine retro-reflective markers were placed bilaterally, and an 8-camera motion capture system (Qualysis, Sweden) recorded kinematic data at 100 Hz.

### 2.2 Data processing and analysis

#### Whole-body angular momentum (H)

Kinematic data were filtered using a zero-lag, fourth-order Butterworth filter (10 Hz). The inverse kinematics problem was solved using Biorbd (Michaud & Begon, 2021) applied to a 19-segment full body biomechanical model (Begue et al., 2021). H was calculated at the whole-body COM as following:

$$H = \sum_{i}^{n} [r_{i} \times m_{i}v_{i} + I_{i}\omega_{i}]$$

<footnote>a IRISSE, Le Tampon, La Réunion</footnote>

<footnote>b S2M, Montréal, Canada</footnote>

<footnote>c Centre de recherche du CHU Sainte Justine, Canada</footnote>

<footnote>d MIP, Le Mans, France</footnote>

<footnote>* Corresponding author: florian.etheve@univ-reunion.fr</footnote>
where $r_i$ is the position vector of the CoM of segment i relative to the whole-body CoM, $v_i$ is the linear velocity vector of segment i relative to the velocity vector of the whole-body COM (the mass-weighted average of segmental CoM positions), $m_i$ and $I_i$ are the mass and inertia tensor of segment i, respectively, and $\omega_i$ is the angular velocity of segment i around its own CoM. $H$ was normalized by $h \cdot m \cdot \sqrt{g \cdot h}$, where $h$ and $m$ are the participant's height and mass, respectively, and $g = 9.81 \text{ m.s}^{-2}$. The sagittal-plane angular momentum was obtained by considering the component around the mediolateral axis. The peak-to-peak range of sagittal $H$ was calculated for each cycle and then averaged across 30 cycles.

<figure><img src="image_1.png" /><figcaption>Figure 1: Mean and SD value $H$ in sagittal plane at 0.75, 1 and 1.25 m/s.</figcaption></figure>

## PF contractile capacities

Torque and velocity were filtered (10 Hz low-pass Butterworth filter). Peak torque and power were extracted for each isokinetic contraction to determine torque-velocity and power-velocity relationships. $T_0$, $\omega_0$ and $P_{max}$ were extrapolated from linear and polynomial models.

## 2.3 Statistical analysis

ANOVA assessed walking speed effects on sagittal $H$ range. Pearson correlations were used to examine relationships between PF functional capacities ($T_0$, $\omega_0$ and $P_{max}$) and sagittal $H$ at each speed. Significance was set at $p < 0.05$.

## 3. Results and discussion

ANOVA showed no significant effect of speed on sagittal $H$ range ($p = 0.42$; Fig. 1.). These findings contrast with those of Gomez et al. (2024), who reported a significant increase in $H$ with speed during overground walking. This discrepancy may be due to differences in walking conditions between studies. Unlike overground walking, the use of a dual-belt treadmill likely increased step width, which could have limited speed-related variations in $H$.

Regarding the relationship between PF contractile capacities ($T_0$, $\omega_0$, $P_{max}$) and sagittal $H$ range, negative correlations were observed between $T_0$ and $H$ at all walking speeds (Table 1). This suggests that individuals with higher $T_0$ values exhibited a smaller $H$ range in the sagittal plane, which may place lower demands on balance control.

These results contrast with those of Smith et al. (2024), who found no correlation between isometric PF

torque and sagittal $H$. One possible explanation is that the perturbed walking condition in their study induced compensatory mechanisms that altered the relationship between PF torque and angular momentum.

<table><caption>Table 1: Correlation between ankle muscle capacity and $H$ range in the sagittal plane at different walking speeds.</caption><thead><tr><th rowspan="2"></th><th colspan="2">T<sub>0</sub></th><th colspan="2">ω<sub>0</sub></th><th colspan="2">P<sub>max</sub></th></tr><tr><th>r</th><th>p</th><th>r</th><th>p</th><th>r</th><th>p</th></tr></thead><tbody><tr><td>Sagittal H range at 0.75 m/s</td><td>-0.557</td><td>0.039*</td><td>0.140</td><td>0.551</td><td>-0.304</td><td>0.291</td></tr><tr><td>Sagittal H range at 1 m/s</td><td>-0.711</td><td>0.004**</td><td>0.297</td><td>0.302</td><td>-0.330</td><td>0.249</td></tr><tr><td>Sagittal H range at 1.25 m/s</td><td>-0.715</td><td>0.004**</td><td>0.205</td><td>0.483</td><td>-0.395</td><td>0.162</td></tr></tbody></table>

$T_0$ and $P_{max}$ were normalized by body mass.

* $p < .05$, ** $p < .01$, *** $p < .001$.

## 4. Conclusions

Our results reveal the existence of a relationship between PF contractile capacity and sagittal $H$ in young adults, with a higher $T_0$ associated with smaller sagittal $H$ range. These results encourage further investigation of this relationship in older adults, a population in which muscle contractile capacity typically declines and gait stability is more compromised.
## Acknowledgements

The author declares that no acknowledgements are made.

## Conflict of Interest Statement

The authors report no conflict of interest.

## Contributor Roles

FE: Conceptualization, Methodology, Investigation, Data curation, Formal analysis, Software, Writing original draft; JB: Conceptualization, Methodology, Writing- review & editing; OL: Conceptualization, Investigation, Software, Writing- review & editing; JT: Conceptualization, Methodology, Investigation; GD: Methodology, Formal analysis, Writing- review & editing; MB: Conceptualization, Methodology, Writing- review & editing; NP: Conceptualization, Methodology, Formal analysis, Writing- review & editing; TC: Methodology, Conceptualization, Funding acquisition, Supervision, Writing- review & editing.

## Funding

Our work was supported by a Regional Research Grant from the Réunion Region (grant #301410) and the European Regional Development Fund. Additionally, this research is part of the e-WALKING project (ANR-22-CE19-0009), which is funded by the French National Research Agency.

## Data, software, code availability

The author declares that no open-source data, software, or code is available for this study.

## References

Begue, J., Peyrot, N., Lesport, A., Turpin, N. A., Watier, B., Dalleau, G., & Caderby, T. (2021). Segmental contribution to whole-body angular momentum during stepping in healthy young and old adults. *Scientific Reports*, *11*(1), 19969. https://doi.org/10.1038/s41598-021-99519-y

DeVita, P., & Hortobagyi, T. (2000). Age causes a redistribution of joint torques and powers during gait. *Journal of Applied Physiology, 88*(5), 1804–1811. https://doi.org/10.1152/jappl.2000.88.5.1804

Herr, H., & Popovic, M. (2008). Angular momentum in human walking. *Journal of Experimental Biology*, *211*(4), 467–481. https://doi.org/10.1242/jeb.008573

Michaud, B., & Begon, M. (2021). biorbd: A C++, Python and MATLAB library to analyze and simulate the human body biomechanics. *Journal of Open Source Software*, *6*(57), 2562. https://doi.org/10.21105/joss.02562