# Including enthesis in a preliminary patellar tendinopathy finite element model

Audrey Berraz Ghiati, Mathias Blandeau, Jeremy Gonthier, Emilie Mathieu, et al..

Simoneau-Buessinger, Emilie Mathieu, Christophe Maréchal

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Audrey Berraz Ghiati, Mathias Blandeau, Jeremy Gonthier, Emilie Mathieu, et al. Including enthesis in a preliminary patellar tendinopathy finite element model. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the.., 10.46298/mbj.16239. hal-05191794v2

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# Including enthesis in a preliminary patellar tendinopathy finite element model

Audrey Berraz Ghiati*, Mathias Blandeau, Jeremy Gonthier, Emilie Simoneau-Buessinger, Emilie Mathieu, Christophe Maréchal

Univ. Polytechnique Hauts-de-France, LAMIH, CNRS UMR 8201, Valenciennes

* Corresponding author: audrey.berrazghiati@uphf.fr

Received date: 04/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** patellar tendinopathy, enthesis, finite element, motion capture

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

## 1. Introduction

Patellar tendinopathy is an injury occurring in sports that require repetitive jumps. Its prevalence in these elite sports can be up to 44.6% (Lian et al, 2005). Patellar tendinopathy is an insertion injury, also named enthesopathy, the enthesis being the insertion zone of a soft tissue to a bone. As bone and tendon have different mechanical properties, modelling a direct transition between the two would result in stress concentration at the interface. To avoid it, a functionally graded material connects tendon and bone. In the enthesis, gradation is assured by a linear increase of mineral proportion (Liu et al. 2010). Enthesis finite element (FE) modeling has been used to examine enthesis behavior but mostly for shoulder models (Liu et al. 2010) and with arbitrary boundary conditions applied to the tendon. However, subject-specific loading and material properties are known to have influence on FE simulations and are different for athlete and sedentary population. Moreover, enthesis is never included in complete joint models. Several FE models of patellar tendon have been used to predict injuries but enthesis was not modeled. The aim of this preliminary study is to evaluate the impact of modeling the enthesis on tendon fatigue-life with subject-specific loading and material properties of sedentary and athlete population.

## 2. Methods

### 2.1 Musculoskeletal model

Ten subjects (2 women and 8 men, 26±3 years, 71.6±13.7 kg, 174±6 cm) with no lower limb injury and

practicing moderate activity participated to this study. Following the IOR model, 32 markers were placed on the lower limb. Vicon motion capture camera system was used to capture the 3D motion of markers. Subjects were standing with each foot on a force platform and were asked to perform a maximal countermovement jump. Marker trajectories and ground reaction forces were filtered using low-pass 4^th^-order Butterworth filters with a cut-off frequency of respectively 18 Hz and 50 Hz. After scaling, knee angle and moment were calculated with inverse kinematics and inverse dynamics on Opensim. Patellar tendon force was calculated as knee moment divided by patellar moment arm which was set as 0.421 mm (O'Brien et al. 2010). Patellar tendon force was extracted during landing, defined as the time between time at which ground reaction force exceeded 10 N and time of maximal knee flexion.

### 2.2 Finite element model

A 3D tendon-bone model was developed in Abaqus (Fig. 1.) with simplified geometry. Tendon length, width and depth were set as 40.2 mm, 30.3 mm and 3.2 mm (Yoo et al, 2007). Femur and patella were modeled with the same section as tendon and a length of 20 mm. A 1 mm insertion was modeled between tendon and bones. The insertion was divided into nine zones to model gradation.

Tendon, bone and insertion mechanical properties were assumed to be hyperelastic isotropic. Neo-Hookean model was used with C₁₀ parameter set as 3846 MPa
for bone. Tendon's C₁₀ parameter was calculated from Young modulus and set to 85 MPa and 240 MPa to simulate sedentary and athlete population (O'Brien et al. 2010). Two different insertion models were created: one with full tendon properties representing the case without enthesis and one with graded properties. For graded properties, nine materials were created with properties resulting from interpolation on nine points from tendon to bone properties. The model was meshed with 103 668 quadratic hexahedral elements of size between 0.1 mm and 3 mm. Distal part of the tibia was fixed. Subject-specific patellar tendon force was divided by tendon cross sectional area (O'Brien et al. 2010) to obtain a surface traction which was applied to the top end of the tendon.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** (a) Patellar tendon model (b) Zoom on enthesis (c) Stress results at the enthesis.</figcaption></figure>

## 2.3 Data analysis

Nominal strain was obtained for each subject. Fatigue-life was calculated at the tendon (Firminger et al. 2022) at maximal patellar tendon force as:

Where $ε_n$ represents nominal strain on the tendon. Maximal nominal strain was taken at the enthesis.

## 3. Results and discussion

Fatigue-life was averaged for the two models and the two material properties (Table 1). Results revealed a fatigue-life increase of respectively 15% and 12% for sedentary and athlete population between model without enthesis and graded insertion model. As a jump consists of take-off and landing, an athlete can perform 181 593 jumps before failure with graded model. A difference of 19 895 jumps is observed between the two models, which represents 40 weeks of volleyball practice (Firminger et al. 2022). Consequently, injury risk is overestimated when enthesis is not modelled. Also, fatigue-life varies between athlete and sedentary population which show the importance of subject-specific material properties. In this model, material parameters were taken from the literature. Tendon geometry was also simplified and knee moment was calculated from inverse dynamics.

<table><caption>**Table 1.** Number of cycles (mean±SD) before failure.</caption><thead><tr><th></th><th></th><th>Sedentary</th><th>Athlete</th></tr></thead><tbody><tr><td rowspan="2">Insertion properties</td><td>Full tendon</td><td>2 181<br>± 4 644</td><td>323 397<br>± 672 618</td></tr><tr><td>Gradation</td><td>2 506<br>± 5 368</td><td>363 187<br>± 756 317</td></tr></tbody></table>

## 4. Conclusion

An increase of fatigue-life is observed when enthesis is modeled in a FE model of patellar tendon. This result shows that tendon fatigue-life is overestimated when the enthesis is not modeled. Future work will include subject-specific material properties and knee moment calculation using muscular activation in this model.

## Acknowledgements

This work is supported by the French Ministry of Higher Education and Research and the National Center for Scientific Research (CNRS). The authors gratefully acknowledge the support of these institutions.

## Conflict of Interest Statement

The authors declare no conflict of interest.

## Contributor Roles

AB: Conceptualization, Software, Writing-original draft, Methodology; MB: Conceptualization, Supervision, Writing-review & editing, Methodology; JG: Data curation; ESB: Methodology; EM: Supervision, Writing-review & editing, Methodology; CM: Software, Supervision, Writing-review & editing.

## References

Lian, Ø. B., Engebretsen, L., & Bahr, R. (2005). Prevalence of jumper's knee among elite athletes from different sports: A cross-sectional study. *The American Journal of Sports Medicine*, 33(4), 561–567. https://doi.org/10.1177/0363546504270454.
Liu, Y., Birman, V., Chen, C., Thomopoulos, S., & Genin, Guy M. (2010). Mechanisms of bimaterial attachment at the interface of tendon to bone. *Journal of Engineering Materials and Technology* 133(011006). https://doi.org/10.1115/1.4002641

Yoo, J. H., Yi, S. R., & Kim, J. H. (2007). The geometry of patella and patellar tendon measured on knee MRI. *Surgical and Radiologic Anatomy*, 29(8), 623–628.
https://doi.org/10.1007/s00276-007-0261-x

O'Brien, T. D., Reeves, N. D., Baltzopoulos, V., Jones, D. A., & Maganaris, Constantinos N. (2010). Mechanical properties of the patellar tendon in adults and children. *Journal of Biomechanics, 43*(6), 1190–1195.
https://doi.org/10.1016/j.jbiomech.2009.11.028

Firminger, C. R., Haider, I. T., Bruce, O. L., Wannop, J. W., Stefanyshyn, Darren J., & Edwards, W. B. (2022). Are subject-specific models necessary to predict patellar tendon fatigue life? A finite element modelling study. *Computer Methods in Biomechanics and Biomedical Engineering, 25*(7), 729–739. https://doi.org/10.1080/10255842.2021.1975683