# Kinematic reconstruction of the spine with a regression model for load carriage study among soldiers

Aurélien Schuster, Charles Pontonnier, Georges Dumont

► To cite this version:

Aurélien Schuster, Charles Pontonnier, Georges Dumont. Kinematic reconstruction of the spine with a regression model for load carriage study among soldiers. Multidisciplinary Biomechanics Journal, 2025, 49th congress of the Société de Biomécanique, 10.46298/mbj.14469. hal-04737940v2

HAL Id: hal-04737940

https://hal.science/hal-04737940v2

Submitted on 31 Jan 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Kinematic reconstruction of the spine with a regression model for load carriage study among soldiers

Aurélien Schuster<sup>a, b*</sup>, Charles Pontonnier<sup>a</sup>, Georges Dumont<sup>a</sup>

<sup>a</sup> Univ Rennes, Inria, CNRS, IRISA, M2S, France

<sup>b</sup> Centre de Recherche des Ecoles de St-Cyr Coëtquidan (CREC), Guer, France

* Corresponding author: aurelien.schuster@ens-rennes.fr

Received date: 05/04/2024

Accepted date: 28/06/2024

Publication date: 31/01/2025

**Keywords:** spine motion, inverse kinematics, marker-based

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

## 1. Introduction

In a military context, knowledge of the mechanical behavior of the spine during soldiers' activities is essential to understanding the mechanism of load-carrying musculoskeletal disorders. To this end, it may be useful to consider an approach to the problem based on motion analysis, which requires numerical models capable of reproducing soldiers' movements. Various multi-body models of the spine have been developed to better understand the biomechanics of low back pain (Lerchl et al. 2023). However, the numerical fitting of these models requires spatial trajectories of reflective markers placed on the spine, which are occluded when the soldier is wearing a backpack. The aim of this study is to evaluate a multiple linear regression (MLR) approach used to reconstruct spine marker trajectories from visible markers that will not be occluded by wearing a backpack. The influence of using reconstructed markers on inverse kinematics results will be investigated.

## 2. Methods

### 2.1 Experiment

In a preliminary validity study, a motion capture experiment was carried out (Qualisys® system, 200Hz, 23 cameras). A volunteer participant (23-year-old male, h=1.90m, w=85kg) performed maximum spinal amplitude in each direction of motion: flexion-extension, lateral-bending and axial-rotation. This cycle was repeated 3 times at a slow pace and 3 times at a fast pace. The marker set used was a whole-body marker set comprising

49 markers placed according to ISB recommendations, and 9 additional markers were placed on the posterior processes of the vertebrae (C7, T1, T4, T5, T7, T8, T9, T12 and L1). A cluster of 6 markers was placed on the middle of the sternum to be used as an input of the reconstruction.

### 2.2 Human Models

The Twente spine model is an open-source, comprehensive and consistent subject-specific thoraco-lumbar model developed and validated by Bayoglu et al. (2019). It has been implemented in CusToM motion analysis library (Muller et al. 2019) and contains 17 vertebrae connected by ball joints (51 degrees of freedom). The implementation of kinematic constraints (Alemi et al. 2021) prevents unrealistic movements of the spine by allowing certain degrees of freedom (DoF) at intervertebral joints. The articular coordinates associated with these DoF, multiplied by a coefficient, are then associated with other intervertebral joints. This has led to the development of 7 models allowing from 3 to 9 degrees of freedom in the spine.

### 2.3 Multiple linear regression model

The coordinates of spinal markers that would be occluded were reconstructed from the visible markers: 4 head markers, 6 on the cluster, 1 on each acromioclavicular joint, 1 on the suprasternal notch, 1 on the xiphoid process and 1 on C7. Using a multiple linear regression (MLR) model (fitlm (X, Y) (MATLAB function), the coefficients of the MLR matrix A, its
intersection **B** and the residuals **R** associated to the spine markers coordinates for each acquisition have been computed (Eq. 1). Concerning the inputs of this function, **X** aggregates the visible marker coordinates and **Y** aggregates the marker coordinates of the spine to reconstruct.

$$Y = A X + B + R \quad (\text{Eq. 1})$$

Occluded spine markers coordinates were then recomputed and used for an inverse kinematics calculation.

## 2.4 Evaluation

Inverse kinematics was computed using experimental markers (EXPE) on the one hand and reconstructed markers (RECO) on the other hand, for the fast-paced trials. Firstly, root mean squared error (RMSE) of kinematic reconstruction for spine markers was computed for each direction of motion and for each model to assess whether the use of RECO or the number of DoF of the model has an impact on the kinematic reconstruction of the spine. Secondly, to assess whether the use of RECO has an impact on overall spine angle, RMSE has been computed between spine angle computed using EXPE and RECO.

# 3. Results and discussion

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Mean RMSE (degrees) between overall spine angles computed using EXPE and RECO.</figcaption></figure>

Kinematic reconstruction RMSE (Table 1) is systematically higher when RECO markers are used with an average increase of 36.3%. Furthermore, the reconstruction error tends to decrease with increasing number of DoF in the model, as in the study by Alemi et al. (2021), with a similar level of amplitude. Concerning the RMSE

for overall spine angle (Figure 1), the use of RECO induces a higher mean RMSE for flexion-extension and axial-rotation than for lateral-flexion direction of motion. Moreover, the number of DoF does not affect the mean RMSE of overall spine angle. But intervertebral joint kinematics should be investigated in detail to assess the impact of the number of DoF of the model with the use of RECO. In this study, only one subject and only fast-paced trials were considered, making it difficult to assess the accuracy of the MLR method.

<table><caption>**Table 1.** mean RMSE (mm) of kinematic reconstruction for spine markers using EXPE/RECO.</caption><thead><tr><th>Model</th><th>Flexion-Extension</th><th>Lateral-Bending</th><th>Axial-Rotation</th></tr></thead><tbody><tr><td>3 DoF</td><td>7.24 / 9.12</td><td>7.41 / 9.42</td><td>6.17 / 8.97</td></tr><tr><td>4 DoF</td><td>5.92 / 8.22</td><td>6.37 / 8.64</td><td>4.95 / 7.77</td></tr><tr><td>5 DoF</td><td>5.94 / 8.28</td><td>5.21 / 7.32</td><td>4.84 / 7.69</td></tr><tr><td>6 DoF</td><td>6.05 / 8.23</td><td>5.14 / 6.89</td><td>5.50 / 5.78</td></tr><tr><td>7 DoF</td><td>6.09 / 8.25</td><td>5.04 / 7.10</td><td>5.49 / 5.65</td></tr><tr><td>8 DoF</td><td>5.69 / 7.96</td><td>3.87 / 5.90</td><td>4.03 / 5.03</td></tr><tr><td>9 DoF</td><td>5.46 / 7.47</td><td>3.72 / 5.64</td><td>3.59 / 4.79</td></tr></tbody></table>

# 4. Conclusions

The aim of this study was to evaluate an MLR method for reconstructing the trajectories of spine markers, which would be occluded by a backpack. The results showed that the use of reconstructed markers for inverse kinematics induced an increase in kinematic reconstruction error and greater angular differences for flexion-extension and axial-rotation compared to lateral-bending. The results remain acceptable but could be improved by adding markers on the anatomical landmarks of the spine, as well as technical markers to improve the reconstruction.

## Acknowledgements

We would like to thank Riza Bayoglu for sharing anthropometrical database allowing the development of the Twente model into the CusToM's model library.

## Funding

The present study was partly funded by the chair of the enhanced soldier in the digital battlefield from the
St-Cyr Foundation and supported by French government funding managed by the National Research Agency under the Investments for the Future program (PIA) with the grant ANR-21-ESRE-0030 (CONTINUUM project).

**Conflict of Interest Statement**

The authors have no conflicting interests.

**References**

Lerchl, T., Nispel, K., Baum, T., Bodden, J., Senner, V., & Kirschke, J. S. (2023). Multibody Models of the Thoracolumbar Spine: A Review on Applications, Limitations, and Challenges. *Bioengineering*, 10(2), Article 2. https://doi.org/10.3390/bioengineering10020202

Bayoglu, R., Galibarov, P. E., Verdonschot, N., Koopman, B., & Homminga, J. (2019). Twente Spine Model: A thorough investigation of the spinal loads in a complete and coherent musculoskeletal model of the human spine. *Medical Engineering & Physics*, 68, 35-45. https://doi.org/10.1016/j.medengphy.2019.03.015

Muller, A., Pontonnier, C., Puchaud, P., & Dumont, G. (2019). CusToM: a Matlab toolbox for musculoskeletal simulation. *Journal of Open Source Software*, 4(33), 1-3. https://doi.org/10.21105/joss.00927

Alemi, M. M., Burkhart, K. A., Lynch, A. C., Allaire, B. T., Mousavi, S. J., Zhang, C., Bouxsein, M. L., & Anderson, D. E. (2021). The Influence of Kinematic Constraints on Model Performance During Inverse Kinematics Analysis of the Thoracolumbar Spine. *Frontiers in Bioengineering and Biotechnology*, 9, 688041. https://doi.org/10.3389/fbioe.2021.688041