Real-time simulation of the transplanted tooth using model order reduction

Pierre Lahoud; Arif Badrou; Maxime Ducret; Jean-Christophe Farges; Reinhilde Jacobs; Aline Bel-Brunon; Mostafa EzEldeen; Nawfal Blal; Raphaël Richert

doi:10.3389/fbioe.2023.1201177

Real-time simulation of the transplanted tooth using model order reduction

Front Bioeng Biotechnol. 2023 Jun 29:11:1201177. doi: 10.3389/fbioe.2023.1201177. eCollection 2023.

Authors

Pierre Lahoud^{1

2

3}, Arif Badrou⁴, Maxime Ducret^{5

6

7}, Jean-Christophe Farges^{5

6

7}, Reinhilde Jacobs^{1

2

8}, Aline Bel-Brunon⁴, Mostafa EzEldeen^{1

2

9}, Nawfal Blal⁴, Raphaël Richert^{4

6

7}

Affiliations

¹ OMFS-IMPATH Research Group, Department of Imaging and Pathology, Faculty of Medicine, Leuven, Belgium.
² Department of Oral and Maxillofacial Surgery, University Hospitals Leuven, Leuven, Belgium.
³ Division of Periodontology and Oral Microbiology, Department of Oral Health Sciences, KU Leuven, Leuven, Belgium.
⁴ Laboratoire de Mécanique Des Contacts Et Structures, CNRS/INSA, Villeurbanne, France.
⁵ Laboratoire de Biologie Tissulaire Et Ingénierie Thérapeutique, UMR5305 CNRS/UCBL, Lyon, France.
⁶ Hospices Civils de Lyon, Lyon, France.
⁷ Faculty of Odontology, Lyon 1 University, Lyon, France.
⁸ Department of Dental Medicine, Karolinska Institute, Stockholm, Sweden.
⁹ Department of Oral Health Sciences, KU Leuven and Paediatric Dentistry and Special Dental Care, University Hospitals Leuven, Leuven, Belgium.

Abstract

The biomechanics of transplanted teeth remain poorly understood due to a lack of models. In this context, finite element (FE) analysis has been used to evaluate the influence of occlusal morphology and root form on the biomechanical behavior of the transplanted tooth, but the construction of a FE model is extremely time-consuming. Model order reduction (MOR) techniques have been used in the medical field to reduce computing time, and the present study aimed to develop a reduced model of a transplanted tooth using the higher-order proper generalized decomposition method. The FE model of a previous study was used to learn von Mises root stress, and axial and lateral forces were used to simulate different occlusions between 75 and 175N. The error of the reduced model varied between 0.1% and 5.9% according to the subdomain, and was the highest for the highest lateral forces. The time for the FE simulation varied between 2.3 and 7.2 h. In comparison, the reduced model was built in 17s and interpolation of new results took approximately 2.10^-2s. The use of MOR reduced the time for delivering the root stresses by a mean 5.9 h. The biomechanical behavior of a transplanted tooth simulated by FE models was accurately captured with a significant decrease of computing time. Future studies could include using jaw tracking devices for clinical use and the development of more realistic real-time simulations of tooth autotransplantation surgery.

Keywords: finite element analysis; machine learning; model order reduction (MOR); real-time simulation; tooth autotransplantation.