# Influence of cartilage constitutive models on finite element evaluation of periacetabular osteotomy outcomes

Ebrétchè Renaud V.I. Amoakon, Zeinab Awada, Boumediene Nedjar, Ariane

Lavoie-Hudon, Victor Grenier, Etienne L. Belzile, Philippe Corbeil

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

## To cite this version:

Ebrétchè Renaud V.I. Amoakon, Zeinab Awada, Boumediene Nedjar, Ariane Lavoie-Hudon, Victor Grenier, et al.. Influence of cartilage constitutive models on finite element evaluation of periacetabular osteotomy outcomes. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the., 10.46298/mbj.16156. hal-05191708v2

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# Influence of cartilage constitutive models on finite element evaluation of periacetabular osteotomy outcomes

Ebrétchè Renaud V.I. Amoakon<sup>a, b, c*</sup>, Zeinab Awada<sup>d</sup>, Boumediene Nedjar<sup>e</sup>, Ariane Lavoie-Hudon<sup>a, c</sup>, Victor Grenier<sup>b</sup>, Etienne L. Belzile<sup>b</sup>, Philippe Corbeil<sup>a, c</sup>

a Groupe de Recherche en Analyse du Mouvement et Ergonomie, Université Laval, Québec, Canada

b Centre de Recherche du CHU de Québec, Université Laval, Québec, Canada

c Centre interdisciplinaire de recherche en réadaptation et intégration sociale (CIRRIS), Québec, Canada

d Laboratoire de Biomécanique et Mécanique des Chocs (LBMC), Université Claude Bernard Lyon 1, Lyon, France

e Laboratoire de Mécanique et Energétique d'Evry, Université Evry Paris-Saclay, Paris, France

* Corresponding author: ebretche-renaud-vidal-i.amoakon.1@ulaval.ca

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** hip adysplasia, patient-specific simulation, constitutive modeling, joint contact mechanics

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Acetabular dysplasia is a developmental abnormality of the hip that leads to poor load distribution across the articular cartilage, promoting premature wear and the onset of osteoarthritis. Clinically, it manifests as pain and reduced mobility (Mavcic et al. 2008). Periacetabular osteotomy (PAO) aims to reorient the acetabulum to reduce joint stress on the joint stresses and improve its stability. However, clinical and radiographic evaluations fail in quantifying the biomechanical effects of the correction on joint loading. Numerical modeling offers a complementary approach to analyze these effects. Although several cartilage models have been developed, few studies have compared their influence on the interpretation of post-PAO outcomes. This study uses finite element modeling to investigate how different biomechanical cartilage models influence joint loading before and after PAO. This preliminary work paves the way for the future implementation of poromechanical models (B. Nedjar 2013). These models often assume simplified material behavior, which may not capture the full complexity of cartilage mechanics in dysplastic joints, especially under physiological loading.

## 2. Methods

To explore the biomechanical implications of cartilage modeling choices, a patient-specific finite element

workflow was developed and applied. A numerical model of a dysplastic hip was constructed using imaging and motion capture gait data obtained from a 27-year-old patient before and after PAO of the right hip. Three cartilage modeling approaches were compared: a linear elastic model (homogeneous material with proportional response), a neo-Hookean hyperelastic model (suitable for large deformations), and an anisotropic HGO model (accounting for collagen fiber orientation) (Holzapfel et al. 2006).

The construction of the numerical model involved several steps. To simulate the dynamic behaviour of the hip during walking, motion capture data and ground reaction force data were implemented in a musculoskeletal model (Opensim). Hip joint angles and forces from the gait cycle were used as input parameters in Abaqus.

Imaging data from the patient was used to create a detailed representation of the hip joint, including the geometry of the acetabulum, femoral head surrounding cartilage and location of the joint center. The patient-specific finite element model provided a realistic basis for evaluating the biomechanical effects of PAO on joint loading. Differences between models were assessed in terms of Von Mises equivalent stress and strain distribution. Peak stress and strain values obtained during gait cycle were compared between
cartilage models. Sensitivity analyses were also carried
out on the material parameters of the different models.

Preliminary tests were performed on cubic samples
of simulated cartilage subjected to compression in order
to calibrate and compare the mechanical response of
the constitutive models under controlled conditions
before applying them to the patient-specific geometry.
These preliminary simulations also served to refine
numerical parameters and verify the stability of each
model under load.

3. Results and discussion

Understanding these mechanical differences is essential
for interpreting surgical outcomes accurately. Following
the preliminary tests, the three constitutive models
were applied to patient-specific cartilage geometries,
using joint loading conditions derived from motion
capture data.

Contrary to common assumptions, the neo-Hookean
model yielded the highest von Mises stress values, par-
ticularly localized in the anterior and posterior regions
of the cartilage. This is attributed to its strain-stiffening
behavior under large deformations, which results in
elevated local stresses. The linear elastic model, while
simpler, produced lower stress magnitudes and a more
uniform distribution, potentially underestimating stress
concentrations. In contrast, the HGO model exhibited
a heterogeneous stress distribution that varied with fiber
orientation, reflecting the anisotropic architecture of
native cartilage.

These differences in stress distribution between mod-
els are illustrated in Figure 1. Although preliminary
simulations on idealized cubic geometries were initially
considered to explore the isolated effect of constitutive
behavior, the results presented here are limited to ana-
tomically accurate models.

<figure><img src="image_3.png" /><figcaption>Figure 1. (a) Linear elastic model; (b) Neo-Hookean model; (c) HGO model.</figcaption></figure>

Credit: E.R.V.I.A

4. Conclusions

The choice of biomechanical model can significantly
influence the assessment of joint stresses following
PAO. Advanced models may offer a more realistic rep-
resentation of cartilage behavior compared to the linear
model. Ultimately, the integration of biphasic models
could enhance the depiction of interstitial fluid contri-
butions, which are crucial to the mechanical response
(Hua et al. 2022). This could lead to simulations that
better replicate physiological conditions.

This approach has the potential to improve the out-
comes of PAO by providing surgeons with detailed bio-
mechanical insights, ultimately leading to more effective
interventions for patients with acetabular dysplasia.

Conflict of Interest Statement

The authors have no conflicts to declare.

Contributor Roles

E.R.V.I.A: Conceptualization, Methodology, Formal analysis, Writing – original draft; Z.A: Conceptualization, Methodology, Writing – review & editing; B.N.: Methodology, Software, Formal analysis, Writing – review & editing; A.L.H: Conceptualization, Methodology; V.G: Conceptualization, Methodology; E.L.B.: Resources, Investigation, Writing – review & editing; P. C.: Methodology, Validation, Supervision, Writing – review & editing.

References

Mavcic, B., Kralj-Iglic, V., & Iglic, A. (2008). Stress distribution in the hip joint: Analysis of the effect of dysplasia. *Clinical Biomechanics*, *23*, 751–758.

Holzapfel, G. A., Gasser, T. C., & Ogden, R. W. (2006). Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. *Journal of the Royal Society Interface*, *3*(6), 15–35. https://doi.org/10.1098/rsif.2005.0073

Hua, X., Li, J., De Pieri, E., & Ferguson, S. J. (2022). Multiscale biomechanics of the biphasic articular cartilage in the natural hip joint during routine activities. *Computer Methods and Programs in Biomedicine*, *215*, 106606. https://doi.org/10.1016/j.cmpb.2021.106606

Nedjar, B. (2013). Formulation of a nonlinear porosity law for fully saturated porous media at finite strains. *Journal of the Mechanics and Physics of Solids*, *61*(3), 537–556. https://doi.org/10.1016/j.jmps.2012.09.010