# Muscle coordination during load carrying at the ant scale: an OpenSim simulation based on Messor barbarus

Dmitry Sverkalov, Jordan Drapin, Santiago Arroyave-Tobon, Evan Economo, Pierre Moretto

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## To cite this version:

Dmitry Sverkalov, Jordan Drapin, Santiago Arroyave-Tobon, Evan Economo, Pierre Moretto. Muscle coordination during load carrying at the ant scale: an OpenSim simulation based on Messor barbarus. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the.., 10.46298/mbj.16248. hal-05191803v2

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Submitted on 23 Oct 2025

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# Muscle coordination during load carrying at the ant scale: an Opensim simulation based on *Messor barbarus*

Dmitry Sverkalov<sup>a</sup>, Jordan Drapin<sup>a</sup>, Santiago Arroyave-Tobon<sup>b</sup>, Evan Economo<sup>c</sup>, Pierre Moretto<sup>a*</sup>

<sup>a</sup> CRCA-CBI UMR 5169, Toulouse, France

<sup>b</sup> Bioinspired system lab - ISM, Marseille; France

<sup>c</sup> UMD Department of entomology, Baltimore, USA

* Corresponding author: pierre.moretto@univtlse3.fr

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** biolocomotion, load carrying, ant, simulation, Musculo-exoskeleton

© 2025 The Authors
Licence CC-BY 4.0
Published by Société de Biomécanique

## 1. Introduction

Insects exhibit remarkable biomechanical adaptations that enable efficient locomotion and load-bearing capabilities. However, their musculoskeletal systems are less studied than those of vertebrates, limiting our understanding of their mechanical efficiency and evolutionary adaptations. This research focuses on the musculoskeletal modeling of *Messor barbarus*, an ant species, to explore the relationship between its morphology, muscle function, and biomechanics. The primary aim is to develop a computational approach for estimating the mechanical properties of the ant's musculoskeletal system. This study intends to create a functional model of muscle coordination during locomotion and load transport. The research has applications in both biological understanding and robotics, particularly in designing bioinspired robotic systems that replicate the efficient movement strategies observed in ants.

## 2. Methods

### 2.1 Kinematic Model and Muscular System Integration

We integrated the muscular system into the existing kinematic model of *M. barbarus* (Arroyave-Tobon et al., 2022). The model consists of 39 segments connected by joints with 65 DOF. Initially designed to analyze free movement, it includes kinematic studies of positions, velocities, and accelerations.

### 2.2 Microtomographic Imaging and Muscle Segmentation

Microtomographic images were acquired at OIST (Japan) with a voxel size of 5.7 µm. The specimen (CASENT0790283) was segmented in 3D Slicer 5.2.2, focusing on the left thorax to optimize processing. The thorax contains 35 muscles, each leg 12 (Aibekova et al., 2022), but the study focused on nine thorax-head muscles involved in head articulation and load transport (fig. 1 A, B).

### 2.3 Muscle Modeling and Simulation

To simulate *Messor barbarus* muscle activity, we used OpenSim (v4.5) that allows musculoskeletal simulations for non-human organisms (Seth et al., 2018). Given the high rigidity of insect tendons compared to humans, we used the ‘RigidTendonMuscle’ model, which assumes tendons do not stretch. This simplification reduces the number of parameters while maintaining accuracy. The main parameters include optimal fiber length, tendon length at rest, pennation angle, maximal isometric force, and contraction velocity. These values were estimated based on micro-CT morphological data.

Fiber lengths were measured using 3D Slicer, taking the average of multiple fibers per muscle. To estimate fiber length under natural load conditions, videos of ants carrying objects were analyzed (Merienne et al. 2020), and the corresponding head positions were replicated in OpenSim to adjust muscle attachment distances.
To determine maximal isometric force, we relied on mandibular force measurements from previous studies (Püffel et al., 2023), using data on muscle volume, fiber length, and mechanical advantage. A constant specific tension value was assumed across all muscles to standardize force estimations.

## 2.5 Dynamic Analysis and Optimization

To analyze how the ant's muscles generate force during movement, an inverse dynamics approach was employed. This technique estimates muscle activation levels required to produce a given motion while minimizing energy expenditure. Additionally, static optimization methods were applied to predict the distribution of forces across muscles.

## 3. Results and discussion

Muscle fiber insertion points were extracted from 3D Slicer in JSON format and processed using Python. Muscle length was determined by the Euclidean distance between insertion points, and the pennation angle was calculated using the dot product between muscle fiber and tendon vectors. Muscle volume was calculated using voxel data in 3D Slicer, and PCSA was estimated by dividing muscle volume by muscle length from micro-CT images. Maximum isometric force per muscle was computed using a specific tension constant ($\sigma_{max} = 0.155$ N/mm²) derived from bite force measurements. OpenSim muscle modeling was done in OpenSim Creator using a 'RigidTendonMuscle' approach with the key parameters included in the table below.

<table><caption>**Table 1.** Muscle parameters used for the simulation: optimal fiber length ($l_o$), tendon length ($l_T$), pennation angle ($\alpha$), and maximum isometric force ($F^{iso}$).</caption><thead><tr><th>Muscle</th><th><i>l</i><sub>o</sub><br>[mm]</th><th><i>l</i><sub>T</sub><br>[mm]</th><th><i>a</i><br>[deg]</th><th>Volume<br>[mm<sup>3</sup>]</th><th>PCSA<br>[mm<sup>2</sup>]</th><th><i>F</i><sup>iso</sup><br>[mN]</th></tr></thead><tbody><tr><td>Idlm1</td><td>0.54</td><td>0.46</td><td>0.00</td><td>0.0009</td><td>0.0017</td><td>0.27</td></tr><tr><td>Idvm9</td><td>0.50</td><td>0.29</td><td>8.75</td><td>0.0039</td><td>0.0078</td><td>1.22</td></tr><tr><td>Itpm1</td><td>0.41</td><td>0.21</td><td>11.9</td><td>0.0019</td><td>0.0048</td><td>0.74</td></tr><tr><td>Itpm2</td><td>0.38</td><td>0.36</td><td>18.4</td><td>0.0050</td><td>0.0134</td><td>2.09</td></tr><tr><td>Ivlm3</td><td>0.61</td><td>0.15</td><td>11.8</td><td>0.0129</td><td>0.0212</td><td>3.29</td></tr></tbody></table>

For OpenSim simulation, segment masses were determined, and net joint moments during walking cycles

<figure><img src="image_3.png" /><figcaption>**Figure 1.** 3D segmentation result with labeled thoracic muscles of Messor barbarus. (A) Reconstruction of the thoracic muscles. (B) OpenSim representation of the thoracic muscles (blue lines), showing the attachment points. (C) Activation level of the left-side muscles required to reproduce the joint moments derived from inverse kinematics.</figcaption></figure>

were computed. Static optimization estimated muscle activity, and residual joint torques ensured simulation feasibility. Artificial actuators controlled thorax translation and rotation. Finally, muscle activation levels for nine muscles involved in head movement during a free walk were obtained (fig. 1 C).

## 4. Conclusions

The purpose of this study was to build the musculoskeletal model of the *Messor barbarus* ant to understand the muscle coordination involved in load transport and the distribution of forces within the exoskeleton. The model requires validating parameters related to ant muscles and locomotion and could help compare transport capabilities across species and explore factors influencing task division in a colony. Understanding
these mechanisms is also key to developing mechatronic
systems or insect-inspired robots. Future studies will
focus on developing an exhaustive musculo-exoskel-
etal model of this ant including the allometry of the
different workers.

Conflict of Interest Statement

None.

Contributor Roles

DS: Data processing, Methodology, Writing original draft; JD: X-Ray image acquisition, data processing, SA-T: Methodology, Validation, Writing-review & editing; EC: Funding acquisition, Conceptualization, X-Ray image acquisition, PM: Project administration, Conceptualization, Funding acquisition, Supervision, Writing-review editing.

Data, software, code availability

Musculoskeletal model of the *Messor barbarus* ant.

References

Arroyave-Tobon, S., Drapin, J., Kaniewski, A., Linares,
J.-M., & Moretto, P. (2022). Kinematic modeling
at the ant scale: Propagation of model parameter
uncertainties. *Frontiers in Bioengineering and Biotechnology,*
*10*, 3. https://doi.org/10.3389/fbioe.2022.767914

Püffel, F., Johnston, R., & Labonte, D. (2023). A biomechanical model for the relation between bite force and mandibular opening angle in arthropods. *Royal Society Open Science, 10*(2). https://doi.org/10.1098/rsos.221066

Aibekova, L., Boudinot, B. E., Beutel, R. G., Richter, A., Keller, R. A., Hita-Garcia, F., & Economo, E. P. (2022). The skeletomuscular system of the mesosoma of formica rufa workers (hymenoptera : Formicidae). *Insect Systematics and Diversity, 6*(3). https://doi.org/10.1093/isd/ixac002

Seth, A., Hicks, J. L., Uchida, T. K., Habib, A., Dembia, C. L., Dunne, J. J., Ong, C. F., DeMers, M. S., Rajagopal, A., Millard, M., Hamner, S. R., Arnold, E. M., Yong, J. R., Lakshmikanth, S. K., Sherman, M. A., Ku, J. P., & Delp, S. L. (2018). Opensim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. *PLoS Computational Biology, 14*(7). https://doi.org/10.1371/journal.pcbi.1006223

Püffel, F., Johnston, R., & Labonte, D. (2023). A biomechanical model for the relation between bite force and mandibular opening angle in arthropods. *Royal Society Open Science, 10*(2). https://doi.org/10.1098/rsos.221066