# Analysis of the distribution of mechanical load on the plate and lateral hinge of a valgus-producing open wedge high tibial osteotomy during weight-bearing by simulating consolidation. Finite element study

Samuel Berthe, Henri Favreau, Karl Boulos, Matthieu Ollivier, Nadia Bahlouli, Mekki Tamir, Matthieu Ehlinger

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## To cite this version:

Samuel Berthe, Henri Favreau, Karl Boulos, Matthieu Ollivier, Nadia Bahlouli, et al., Analysis of the distribution of mechanical load on the plate and lateral hinge of a valgus-producing open wedge high tibial osteotomy during weight-bearing by simulating consolidation. Finite element study. Orthopaedics & Traumatology: Surgery & Research, 2024, pp.104115. 10.1016/j.otsr.2024.104115. hal-05280654

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Original article

# Analysis of the distribution of mechanical load on the plate and lateral hinge of a valgus-producing open wedge high tibial osteotomy during weight-bearing by simulating consolidation. Finite element study

Samuel Berthe<sup>a</sup>, Henri Favreau<sup>b</sup>, Karl Boulos<sup>b</sup>, Matthieu Ollivier<sup>c</sup>, Nadia Bahlouli<sup>a</sup>, Mekki Tamir<sup>b</sup>, Matthieu Ehlinger<sup>a,b,*</sup>

ARTICLE INFO

Keywords:

Hinge

Tibial osteotomy

Finite elements

Simulation

ABSTRACT

**Introduction:** High tibial osteotomy (HTO) is indicated for managing isolated medial knee osteoarthritis in a young patient with a metaphyseal deformity of the proximal tibia. In a medial open-wedge HTO, maintaining the integrity of the hinge is crucial for consolidation and preservation of the correction. Based on a validated model and preliminary results, the objective of this work was to measure and monitor the distribution of mechanical load on a locking fixation plate and the lateral hinge of an HTO using a finite element (FE) model during different phases of consolidation evolution, simulating single leg weightbearing.

**Hypothesis:** The working hypothesis was that with increasing consolidation, the stresses significantly decrease on both the plate and the lateral hinge, but with greater magnitudes on the plate and approaching zero on the hinge.

**Materials and methods:** A validated numerical model of a high tibial osteotomy (HTO) fixed with a locking plate on a real proximal tibial geometry (using Autodesk Fusion 360 and Altair HyperWorks software) was used. An axial load equivalent to one body weight was applied. Five scenarios were considered, resulting in five different models by varying, in the FE model, the Young's modulus of the trabecular and cortical bone, which allows for simulating the evolution of consolidation. Consolidation scenarios were tested by varying the mechanical properties of the HTO gap filling: 25% of normal bone properties, then 50%, 75%, and finally 100%, which is hypothetically considered as remodeled bone. The primary outcome measure was the maximum stress value in the areas of interest (Von Mises stresses, in MPa), specifically at the plate and lateral hinge.

**Results:** The decrease (in %) is major as early as the simulation of 25% consolidation in both areas of interest: a reduction of 91% on the plate and 93% on the hinge. The reduction in absorbed stresses continues in both areas, but with a more pronounced decrease on the plate. It is noteworthy that from 50% consolidation, under these experimental conditions, stresses remain comparable on the hinge, especially between 75% and 100% consolidation.

**Discussion:** The hypothesis is confirmed with a more marked decrease on the plate and approaching zero on the hinge, which seems logical in a consolidation process. Comparison with the literature is challenging, as only one finite element study has analyzed the influence of consolidation on the stresses absorbed by an HTO plate, but with different consolidation thresholds and without studying the hinge. This study has limitations: the model construction conditions, it is a finite element computer study, and the weight-bearing simulation for this study was static, which does not address the distribution of stresses during walking, this model is defined for a given valgus HTO plate and a specific opening and does not allow for extrapolation to distal femur opening osteotomies nor in clinical practice.

**Conclusion:** The hypothesis is confirmed; however, further studies are needed to validate these numerical results: an experimental part on instrumented cadaveric bone and comparative studies of fixation plates are necessary.

**Level of evidence:** V; expert opinion, controlled laboratory study.

<footnote><sup>a</sup> Laboratoire ICube, Université de Strasbourg – CNRS, 4 rue de la Manufacture des Tabacs, 67000 Strasbourg, France</footnote>

<footnote><sup>b</sup> Service de Chirurgie Orthopédique et de Traumatologie, Hôpital de Haute-pierre II, 1 Avenue Molière, 67098 Strasbourg Cedex, France</footnote>

<footnote><sup>c</sup> Département de Chirurgie Orthopédique, Hôpital Sainte-Marguerite, Hôpital Universitaire de Marseille, 270 Boulevard Sainte Marguerite, 13009 Marseille, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: matthieu.ehlinger@chru-strasbourg.fr (M. Ehlinger).</footnote>
# 1. Introduction

To treat isolated medial femorotibial osteoarthritis in young patients with a metaphyseal deformity of the proximal tibia, valgus high tibial osteotomy (HTO) is useful [1,2]. For this procedure, it is important to preserve the lateral hinge (maintaining angular correction, ensuring primary stability, achieving consolidation within a reasonable timeframe (6–12 weeks) [3–7]). The lateral hinge should be considered the weak link of the assembly and can be protected [5–8]. The most used fixation method for HTOs today is the locking plate, regardless of the manufacturer [2,5–8].

In a previous finite element (FE) study, we confirmed that there is a distribution of stresses both on the plate and the hinge, emphasizing the importance of the plate and the absolute necessity of preserving the hinge [9]. The plate absorbs most of the load. This work validated an FE model using a 4 mm mesh across all model elements, except in high-stress areas (within the plate and the hinge), which were meshed with an element size of 0.7 mm.

Few FE studies have evaluated the stresses absorbed by a locking plate used to stabilize an HTO while simulating walking [10–13], and to our knowledge, only one has analyzed the influence of consolidation [14]. The authors studied the effect of gap filling in the HTO on the plate for two types of plates and on setups with varying lengths [14]. The stresses absorbed by the hinge were not studied, and their simulation did not extend to complete consolidation with remodeling.

Full weight-bearing is quite possible [15,16] when a locking plate was used. Therefore, the objective of this work was to measure the distribution of mechanical load on the medial plate but also on lateral hinge throughout the consolidation process of the HTO while simulating weight-bearing. The working hypothesis was to emphasize the relationship between consolidation levels and stress variations. Indeed that as consolidation increases, the stresses significantly decrease on the plate and the lateral hinge, but with greater amplitudes on the plate and approaching zero on the hinge.

# 2. Materials and methods

## 2.1. The model

The FE model used was validated in a previous study [9], replicating the bone geometry of a healthy left tibia reconstituted in 3D from DICOM images of a cadaveric tibia. It consists of a cortical area (5 mm thick) and a trabecular (spongy) area.

An anatomical plate for high tibial osteotomy from the Newclip® laboratory (Nantes, France), was modeled based on a real model (titanium plate, size 1, left side). An open medial wedge high tibial osteotomy was produced on the tibial model (10° correction, hinge of 1 cm) [9,17]. The locking screws of the plate were simplified due to technical calculation constraints (particularly the representation of the screw threading and the screw tips).

The computer-aided design (CAD) software Fusion 360 by Autodesk (Autodesk®, San Rafael, California, USA) was used. The meshing of the various models, as well as the implementation of properties and boundary conditions, was carried out using Altair® HyperWorks HyperMesh® (Troy, Michigan, USA). Finally, the Radioss solver from Altair® was used to calculate the deformation fields during loading.

Previous results obtained [9] from mesh convergence at the hinge and plate level allowed for the definition of the most suitable FE model: a mesh of 4 mm on all the elements of the model except in the high-stress zones within the plate and the hinge, which was meshed with an element size of 0.7 mm, providing better accuracy for the study. The mesh is continuous between the different components. Thus, there are no issues at the interfaces. This implies that there is no slipping between the plate and the bone, as well as between the screws and the bone. Two areas of interest were analysed for the visualization of deformations: plate and lateral hinge (Fig. 1).

Five scenarios were considered, resulting in five different models by varying, in the FE model, the Young's modulus of the trabecular and cortical bone, which allows for simulating the evolution of consolidation (Table 1):

- 1: Osteotomy with no filling, hence no signs of consolidation.

- 2: Osteotomy filled with bone exhibiting 25% of normal mechanical properties. By hypothesis and extrapolation, this simulates 25% consolidation.

- 3: Osteotomy filled with bone exhibiting 50% of normal mechanical properties. By hypothesis and extrapolation, this simulates 50% consolidation.

- 4: Osteotomy filled with bone exhibiting 75% of normal mechanical properties. By hypothesis and extrapolation, this simulates 75% consolidation.

- 5: Osteotomy filled with bone exhibiting 100% of normal mechanical properties. By hypothesis and extrapolation, this simulates 100% consolidation with a bone callus at the remodeling stage.

## 2.2. Mechanical properties

For this FE model, the proximal tibia is all considered to be homogeneous, isotropic, and exhibiting linear elastic behavior, particularly for the cortical bone [9,14,17,18].

## 2.3. Boundary conditions

A single-leg stance characterized by static loading is simulated. It is assumed that the high tibial osteotomy effectively restores load balance within the knee joint. The applied loading corresponds to approximately 1.1 times the body weight per tibial plateau [19] and is represented by a uniform pressure distributed over each plateau. This approach is consistent with previously described numerical models reproducing this physiological loading [9]. A fixed boundary condition is applied at the diaphysis. It is sufficiently distal from the region of interest to avoid any interference with measurements at the osteotomy site.

<figure><img src="image_4.png" /><figcaption>Fig. 1. Finite element model. The areas of interest are the plate and the hinge. The red zones correspond to the maximum absorbed stresses (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).</figcaption></figure>
<table><caption>**Table 1**
Mechanical characteristics at the level of the HTO of the different scenarios.</caption><thead><tr><th>Young's modulus (MPa)<br>Cortical - Trabecular</th><th>Corresponds to</th></tr></thead><tbody><tr><td>1 - 1</td><td>0% of consolidation</td></tr><tr><td>4750 - 19</td><td>25% of consolidation</td></tr><tr><td>9500 - 38</td><td>50% of consolidation</td></tr><tr><td>14250 - 56</td><td>75% of consolidation</td></tr><tr><td>19000 - 75</td><td>100% of consolidation</td></tr></tbody></table>

## 2.4. Judgment criteria

The loading at the osteotomy site is multiaxial. This means that the stress in the principal load direction alone does not represent the total mechanical load on the materials. The Von Mises stress criterion considers stress in all directions. Consequently, the judgment criterion is the maximum value of the stresses in the areas concerned (plate, lateral hinge) (Von Mises stresses, in MPa).

## 3. Results

The primary judgment criterion is the measurement of von Mises stresses (MPa) in the two areas of interest: the plate and the hinge. The stress measurements as a function of the consolidation are reported in Table 2. Fig. 2 highlights the reductions in stresses on the model.

The reduction (in %) is significant as early as the simulation of 25% consolidation in the two areas of interest: a reduction of 91% on the plate and 93% on the hinge.

The reduction in stresses in the two areas of interest continues, but with a much more pronounced decrease on the plate.

It should be noted that, starting from 50% consolidation, under these experimental conditions, the stresses remain comparable on the hinge, even more so between 75% and 100% consolidation.

## 4. Discussion

The working hypothesis was confirmed. The main result of this study is that the stresses absorbed by the plate and the hinge drastically decrease from the first phase of bone healing and continue more significantly compared to the stresses absorbed by the hinge. On the hinge, the stresses approach 0 at 75% simulated consolidation. This is consistent with a consolidation process that gradually relieves the initially stressed areas, with an increase in contact surface and an improvement in bone quality capable of absorbing these loads. However, there are still stresses in both areas of interest at the stage of 100% simulated consolidation, which can be explained by the existence of a "frame" at the proximal tibia level corresponding to "plate - epiphysis - hinge - metaphysis". This underscores the importance of preserving the hinge for the proper progression of the HTO [3-8]. The stresses present at the plate level even at the stage of "total consolidation" may explain

<table><caption>**Table 2**
Von Mises stresses at the level of the zones of interests.</caption><thead><tr><th>Scenarios</th><th>Von Mises<br>hinge (MPa)</th><th>Reduction<br>(%)</th><th>Von Mises<br>plate (MPa)</th><th>Reduction<br>(%)</th></tr></thead><tbody><tr><td>0% of<br>consolidation</td><td>25,0488</td><td>-</td><td>4,27566</td><td>-</td></tr><tr><td>25% of<br>consolidation</td><td>2,16399</td><td>91%</td><td>0,298601</td><td>93%</td></tr><tr><td>50% of<br>consolidation</td><td>1,49974</td><td>30.5%</td><td>0,2374</td><td>20.5%</td></tr><tr><td>75% of<br>consolidation</td><td>1,22672</td><td>18%</td><td>0,219334</td><td>7.5%</td></tr><tr><td>100% of<br>consolidation</td><td>1,07198</td><td>12.5%</td><td>0,212762</td><td>3%</td></tr></tbody></table>

the discomfort felt by the patient at the plate site and the need for removal.

Our knowledge, only one publication has examined the stresses absorbed during consolidation, but only on the plate [14]. Our work is original because it studied the stresses absorbed and the plate but also on the hinge. Indeed few recent studies in FE simulation addressing weight-bearing after valgus HTO have been conducted [9-14].

The objective of the study analyzing both the stresses absorbed by the plate and the hinge was to compare three different setups to validate a new implant [12]. Their results showed a 23% decrease in the stresses absorbed by the lateral hinge for the new implant compared to the reference TomoFix® plate. Indirectly, this study provided insight into the stress distribution at the medial implant and the hinge. For the model with the TomoFix® plate, the medial plate supports approximately 200 MPa, and the hinge 34 MPa, nearly six times less. For the model using the new implant without the integrated metal wedge, the medial plate absorbs about 210 MPa, and the hinge about 26 MPa, nearly eight times less. Finally, for the model with the integrated wedge, the plate supports approximately 126 MPa, and the hinge 18 MPa, seven times less. The authors concluded that the integrated metal wedge on the plate was effective under their experimental conditions and would also help protect the hinge.

Only one study evaluated the influence of consolidation, but only on the plate and never on the hinge like our work [14]. The authors examined the filling effect of the HTO gap on the plate for two types of plates and setups where the length varied. The stresses absorbed by the hinge were not studied. Their simulation did not extend to full consolidation with remodeling, unlike our model. They defined three levels: 1/ appearance of connective tissue (= 1 week delay) (Young's Modulus at 1.4 MPa), 2/ fibrous tissue (= 2 weeks delay) (Young's Modulus at 28 MPa), 3/ callus considered immature (= 6 weeks delay) (Young's Modulus at 528 MPa). Their results showed a decrease in von Mises stresses (in MPa) on the plate throughout the stages of consolidation, regardless of the type of plate or the length of the setups. Comparing it our work remains delicate since the consolidation phases are different and the hinge was not analyzed in their study [14]. Nevertheless, the results are consistent with our findings. Indeed, there is a significant decrease in stresses on the plate in our study, although they remain high compared to the stresses absorbed by the hinge. This can be explained by our model's assumption that the entire osteotomy gap was filled, even as the mechanical properties of this tissue varied throughout the scenarios. Finally, the type of plate studied may also account for some of these differences, as it is shorter than their model and only has one row of proximal screws above the HTO (their plate has two screw levels, with one screw just above the osteotomy line [14]).

In the case of medial open-wedge HTO, it is crucial to preserve the lateral hinge, which allows for maintaining angular correction, ensuring primary stability, and achieving consolidation within a reasonable timeframe (6-12 weeks) [3-7]. The lateral hinge should be considered the weak link of the assembly and can be protected with a pin [5-8].

This study has limitations. The first concerns the model construction conditions, particularly the contact between the bone and the plate, which is difficult to replicate; here, the extrapolation made is a continuity of the model's meshes, with all elements considered as "glued" together. It is a finite element computer study, which cannot fully replicate reality, even if the parameters introduced into the model and the model itself are derived from real data. The weight-bearing simulation for this study was static, which does not address the distribution of stresses during walking. However, this type of study provides answers to questions that would be impossible to obtain through conventional experimental studies. In our model, by assumption, the entire osteotomy gap is filled, even though the mechanical properties of this filling evolve over time. This differs from clinical conditions where consolidation exhibits a centrifugal progression from the hinge [20]. Moreover, the locking screws of the plate were simplified due to technical calculation constraints, could be influenced the results. Finally, this model is defined
<figure><img src="image_5.png" /><figcaption>Fig. 2. Representation of the stress distribution in the areas of interest according to the 5 different scenarios.</figcaption></figure>

for a given valgus HTO plate and a specific opening and does not allow for extrapolation to distal femur opening osteotomies, nor in clinical practice. Further clinical studies are needed to confirm these results.

## 5. Conclusion

The hypothesis was confirmed. This study proves that it is crucial to preserve the lateral hinge, which allows for maintaining angular correction, ensuring primary stability, and achieving consolidation within a reasonable timeframe. The main result of this study is that the stresses absorbed by the plate and the hinge decrease significantly from the first phase of bone healing and continue more significantly on the former compared to the stresses absorbed by the hinge. Additional studies would be necessary to validate these numerical results: an experimental part on cadaveric bone as well as comparative clinical studies of fixation plates.

### CRediT authorship contribution statement

SB, ME, KB: writing.

HF, TM, MO: bibliography.

NB, MO, HF: proofreading.

SB, NB: data collection.

KB, TM: translation.

### Declaration of Generative AI and AI-assisted technologies in the writing process

No use of any generative AI or AI-assisted technologies to write this manuscript.

### Funding

None.

### Declaration of competing interest

None for this article. ME: consultant Lepine®, NewClip®, Ampli-tude®, Serf®, editor of the educational conference proceedings of the SOFCOT. HF, KB, TM: none. MO: educator consultant Arthrex®, New-clip®, Stryker®.

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