# Stress distribution in the edentulous maxilla during immediate loading using three rehabilitation models: a finite element analysis.

Sarah Latreche, Olina Rios, Franck Afota, Charles Savoldelli, Yannick Tillier

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Sarah Latreche, Olina Rios, Franck Afota, Charles Savoldelli, Yannick Tillier. Stress distribution in the edentulous maxilla during immediate loading using three rehabilitation models: a finite element analysis.. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the.., 10.46298/mbj.16182 .
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# Stress distribution in the edentulous maxilla during immediate loading using three rehabilitation models: A finite element analysis

Sarah Latreche<sup>a*</sup>, Olina Rios<sup>b</sup>, Franck Afota<sup>b</sup>, Charles Savoldelli<sup>b, c</sup>, Yannick Tillier<sup>c</sup>

a Oral and Dental Medicine Institute, 06300 Nice, France Oral and Dental Medicine Institute, 06300 Nice, France

b Head and Neck Institute, 06100 Nice, France

c Mines Paris, PSL University, Centre for Material Forming (CEMEF), UMR7635 CNRS, 06904 Sophia Antipolis, France

* Corresponding author: latreche.sarah@hotmail.fr

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** all-on-four, all-on-six, zygomatic implants, stress analysis, atrophic maxilla

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Rehabilitation of atrophic edentulous maxillae presents complex biomechanical challenges due to poor bone quality, limited volume, and anatomical constraints. Immediate loading protocols add further mechanical demands on implant-supported prostheses. This study aims to compare the stress distribution in the maxilla during immediate loading using three distinct implant-supported rehabilitation strategies: All-on-Four, All-on-Six, and Quad-Zygomatic. Finite element analysis (FEA Forge® software) was used to model and evaluate these configurations in a patient-specific context.

## 2. Methods

CBCT (cone beam computed tomography) imaging data were obtained from a 64-year-old female patient presenting with a severely atrophic maxilla, both prior to and following onlay bone grafting and bilateral sinus augmentation using allogenic bone. Three distinct FEA models were developed:

* Model 1: All-on-Four configuration with tilted distal implants,

* Model 2: All-on-Six configuration with vertical implants distributed along the full arch,

* Model 3: Quad-Zygomatic configuration with four zygomatic implants.

Each model included the maxillary bone (segmented into cortical and trabecular regions), implants, abutments, and a continuous prosthetic superstructure.

Material properties (Young's modulus, Poisson's ratio) were derived from the literature (Bhering et al., 2016; Guillaume Villatte et al., 2022; Türker et al., 2021), with grafted bone properties provided by the manufacturer. All materials were assumed to be linear, elastic, isotropic, and homogeneous.

Mesh convergence tests determined an optimal element size of 0.5 mm. The resulting tetrahedral meshes (P1+/P1 elements) consisted of 1.6M elements (Model 1), 3.1M elements (Model 2), and 1.7M elements (Model 3). A combined vertical and oblique force (45°) of 150 N was applied to simulate immediate occlusal loading.

## 3. Results and discussion

Stress analysis was conducted using von Mises and principal stress criteria (Table 1; Fig. 1). Across all three models, stress distributions were assessed in cortical and trabecular bone, implants, abutments, and prosthetic components.

In cortical bone, all configurations exhibited peak von Mises stresses concentrated in a circular area surrounding the neck region of the distal implants on the loading side, where the implants emerge from the bone. Among the models, Model 2 (All-on-Six) showed the most homogeneous von Mises stress distribution. Principal tensile stresses remained below levels generally considered detrimental to bone integrity (130 MPa and 5 MPa for cortical and trabecular bone respectively).
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Palatal view of von Mises stresses. 2. von Mises stresses in implants and abutments. 3. von Mises stresses in prosthesis.</figcaption></figure>

Credit: Sarah Latreche

<table><caption>**Table 1.** Maximum von Mises stress values calculated in each structure in MPa. Credit: Sarah Latreche</caption><thead><tr><th>Models</th><th>Cortical bone</th><th>Trabecular bone</th><th>Bone graft</th><th>Implants</th><th>Abutments</th><th>Prosthesis</th></tr></thead><tbody><tr><td>Model 1</td><td>25.59</td><td>7.40</td><td>-</td><td>75.47</td><td>190.27</td><td>148.50</td></tr><tr><td>Model 2</td><td>35.29</td><td>3.70</td><td>29.04</td><td>65.84</td><td>106.23</td><td>75.36</td></tr><tr><td>Model 3</td><td>50.95</td><td>6.67</td><td>-</td><td>46.88</td><td>56.80</td><td>100.48</td></tr></tbody></table>

At the implant level, stress concentrations were consistently observed at the implant-cortical bone interface, particularly at the neck region of distal implants. In Model 1 (All-on-Four), the highest stress was found at the neck of the tilted distal implant on the loading side. In Model 2 (All-on-Six) and 3 (Quad-Zygomatic), the stress peak occurred at the most distal implant on the loading side. For Model 3, stress was more evenly distributed between the four zygomatic implants.

In abutments, the highest stress values were model-dependent. Model 1 showed maximum von Mises stresses at the angled segment of the abutment.

In Model 2, stress concentrations localized at the abutment platform.

For the prosthetic superstructure, von Mises stress values were highest in Model 1. Notably, the maximum stress in Model 2 was 49.5% lower than in Model 1 and 25% lower than in Model 3. This substantial reduction in prosthetic stress in the All-on-Six configuration is attributable to the absence of cantilever extensions and the even distribution of occlusal forces across a larger number of implants.

In terms of bone displacement, all models exhibited values below the critical threshold that could compromise osseointegration. The All-on-Six model showed the lowest displacement values, further supporting its biomechanical advantage under immediate loading conditions.

This patient-specific simulation emphasizes the influence of implant distribution, angulation, and graft support on stress transfer during immediate loading. The presence of grafted bone in Model 2 enabled the use of six implants distributed along the arch. The findings support previous literature suggesting that
cantilever reduction and vertical posterior implants enhance mechanical performance. Zygomatic implants (Model 3), while useful in cases where grafting is contraindicated, showed higher stress values and less optimal load distribution.

## 4. Conclusions

Within the limitations of this in silico study, the All-on-Six configuration demonstrated the most favorable biomechanical performance under immediate loading conditions in an edentulous maxilla reconstructed with bone grafts. Digital twin modeling enabled precise assessment of stress behavior under realistic clinical conditions. When clinically feasible, combining vertical implant placement with full-arch grafting appears to be the optimal strategy in terms of mechanical safety and load distribution. Zygomatic implants remain a viable alternative when bone grafting is not possible.

## Acknowledgments

We are grateful to the manufacturers Megagen and SouthernImplant for their confidence in us and for providing us with their implants or CAD models of their implants.

## Conflict of Interest Statement

None.

## Contributor Roles

SL: Conceptualization, Methodology, Investigation, Data curation, Formal analysis Validation, Visualization, Writing-original draft; YT, CS: Conceptualization, Supervision; OR, FA: Methodology, Writing-review & editing

## References

* Bhering, C. L. et al. Comparison between all-on-four and all-on-six treatment concepts and framework material on stress distribution in atrophic maxilla: A prototyping guided 3D-FEA study. *Materials Science and Engineering: C*, 69, 715-725. https://doi.org/10.1016/j.msec.2016.07.059

* Villatte, G., Erivan, R., Cueff, R., Wittrant, Y., Boisgard, S., & Descamps, S. (2022). Evaluation of the biomechanical and structural properties of bone allografts treated with a new cleaning process. *World Journal of Advanced Research and Reviews*, 14(3), 608-616. https://doi.org/10.30574/wjarr.2022.14.3.0614

* Türker, N., Alkiş, H. T., Sadowsky, S. J., & Şebnem Büyükkaplan, U. (2021). Effects of occlusal scheme on all-on-four abutments, screws, and prostheses: A three-dimensional finite element study. *Journal of Oral Implantology*, 47(1), 18-24. https://doi.org/10.1563/aaid-joi-D-19-00334