# Is 3D load-balancing more relevant than 2D for estimating medial and lateral knee contact forces?

Elisa Jolas, Sacha Guitteny, Nolwenn Fougeron, Rachid Aissaoui, Charles

Pontonnier, Raphaël Dumas

► To cite this version:

Elisa Jolas, Sacha Guitteny, Nolwenn Fougeron, Rachid Aissaoui, Charles Pontonnier, et al. Is 3D load-balancing more relevant than 2D for estimating medial and lateral knee contact forces?. CMBBE 2025 - 20th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, Sep 2025, Barcelona, Spain. hal-05448716

HAL Id: hal-05448716

https://hal.science/hal-05448716v1

Submitted on 14 Jan 2026

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# IS 3D LOAD-BALANCING MORE RELEVANT THAN 2D FOR ESTIMATING MEDIAL AND LATERAL KNEE CONTACT FORCES?

Elisa Jolas (1), Sacha Guitteny (1), Nolwenn Fougeron (2), Rachid Aissaoui (3), Charles Pontonnier (2), Raphaël Dumas (1)

1. Univ. Gustave-Eiffel, LBMC UMR_T9406, Lyon, France; 2. Univ. Rennes, Inria, CNRS, IRISA - UMR 6074, Rennes, France; 3. ÉTS, LIO-TS, Montréal, Canada

## 1. Introduction

Accurate estimation of medial and lateral knee contact forces is crucial, as these forces are closely linked to osteoarthritis progression. A commonly used approach in musculoskeletal modelling is first to estimate musculotendon and joint reaction forces and then compute medial and lateral contact forces using a load-balancing approach in the frontal plane. This 2D approach does not account for all joint reaction components. This study proposes a 3D load-balancing approach to compute contact and ligament forces, and compares it to the 2D approach.

## 2. Materials and Methods

This study is based on a previously published dataset, with gait motion capture from healthy participants [1]. A uniformly scaled musculoskeletal model was built using the AnyBody Modeling System (AnyBody Technology, Denmark). Only the results from participant 2015004 will be presented and discussed here. The tibiofemoral hinge joint was modeled with a moving-axis, adapted from [2]. Contact point trajectories and ligament insertions on the femur and tibia were derived from [3]. Musculotendon forces were computed using static optimization. Medial and lateral contact forces were estimated using two approaches. In 2D, they were estimated based on the superior-inferior joint reaction force and abduction-adduction reaction moment. In 3D, contacts, anterior and posterior cruciate (ACL, PCL), medial and lateral collateral (MCL, LCL) ligament forces amplitudes ($g_l$), were estimated using the musculotendon forces ($f_j$), and the intersegmental forces and moments ($F_i$, $M_i$) taking into account the hinge moving-axis direction $e_k$. Their lines of action ($u_l$) and moment arms ($L_l$) were incorporated into a non-negative least-squares optimization (Eq. 1). This equation can be generalized to any joint $i$, with muscles $j$, axes $k$ and contacts/ligaments $l$:

$$ \min \left\| \begin{bmatrix} u_1 & \dots & u_6 \\ L_1 & \dots & L_6 \end{bmatrix}^{[g_1 \quad \dots \quad g_6]} - \begin{bmatrix} [F_i] \\ [M_i] - \begin{bmatrix} \sum f_j u_j \\ \Sigma(M_i \cdot e_k) e_k \end{bmatrix} \end{bmatrix} \right\|^2 \quad (1) $$
with $g_l > 0$

## 3. Results

The 3D approach showed higher medial forces throughout the stance phase, and could yield null lateral forces at heel strike (Fig. 1). ACL and PCL forces reached 450 N. LCL and MCL forces remained under 150 N or null.

<figure><img src="image_3.png" /><figcaption>Figure 1: Participant 2015004 (36y.o., 1.7m, 62kg): Contact and ligament force magnitude computed with both 2D and 3D load-balancing approaches.</figcaption></figure>

## 4. Discussion and Conclusions

The forces estimated using the 2D and 3D approaches showed differences. In some trials, unrealistic forces appeared during brief periods, possibly due to geometrical singularities or to joint reactions incompatible with $g_l > 0$. Considering such constraints during the static optimization [4] may overcome this issue. After further validation, the 3D load-balancing approach could prove promising, as it may more accurately reflect the articular mechanics relevant to the study of knee osteoarthritis.

## 5. References

1. Schreiber C, Moissenet. F. Sci Data; 6:111 (2019).

2. Dzialo CM et al., J Biomech; 72:71-80 (2018).

3. Dumas et al. Mechanism and Machine Theory Symposium, Guimaraes, Portugal (2024).

4. Moissenet F et al., J Biomech; 47(1):50-58 (2014).

## Acknowledgements:

We thank Michele Cononi and Nicola Sancisi from University of Bologna for providing knee joint data of the TLEM 2.0.