A study on the predictive model of porous hyperelastic properties of human alveolar bone based on computed tomography imaging_Journal of Biomedical Engineering

Authors：

WU Bin ¹ , LI Mingna ¹ , YANG Fan ^2,3,4 , YUAN Le ¹ , LU Yi ¹ , JIANG Di ¹ , YI Yang ¹ ,  YAN Bin ^2,3,4

1. School of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, P. R. China;
2. Department of Orthodontics, The Affiliated Stomatological Hospital of Nanjing Medical University, Nanjing 210029, P. R. China;
3. State Key Laboratory Cultivation Base of Research, Prevention and Treatment for Oral Diseases, Nanjing 210029, P. R. China;
4. Jiangsu Province Engineering Research Center of Stomatological Translation Medicine, Nanjing 210029, P. R. China;

Corresponding author：

YAN Bin, Email: byan@njmu.edu.cn

Keywords：

Alveolar bone; Predictive model; Hyperelasticity; Bone mineral density; Finite element simulation

DOI：

10.7507/1001-5515.202408014

Video：

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Alveolar bone reconstruction simulation is an effective means for quantifying orthodontics, but currently, it is not possible to directly obtain human alveolar bone material models for simulation. This study introduces a prediction method for the equivalent shear modulus of three-dimensional random porous materials, integrating the first-order Ogden hyperelastic model to construct a computed tomography (CT) based porous hyperelastic Ogden model (CT-PHO) for human alveolar bone. Model parameters are derived by combining results from micro-CT, nanoindentation experiments, and uniaxial compression tests. Compared to previous predictive models, the CT-PHO model shows a lower root mean square error (RMSE) under all bone density conditions. Simulation results using the CT-PHO model parameters in uniaxial compression experiments demonstrate more accurate prediction of the mechanical behavior of alveolar bone under compression. Further prediction and validation with different individual human alveolar bone samples yield accurate results, confirming the generality of the CT-PHO model. The study suggests that the CT-PHO model proposed in this paper can estimate the material properties of human alveolar bone and may eventually be used for bone reconstruction simulations to guide clinical treatment.

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6.	Bittens M, Nackenhorst U. A fully implicit and thermodynamically consistent finite element framework for bone remodeling simulations. Computational Mechanics, 2023, 71(5): 853-866.
7.	Helgason B, Perilli E, Schileo E, et al. Mathematical relationships between bone density and mechanical properties: a literature review. Clinical biomechanics (Bristol, Avon), 2008, 23(2): 135-146.
8.	Quinn C, Kopp A, Vaughan T J. A coupled computational framework for bone fracture healing and long-term remodelling: investigating the role of internal fixation on bone fractures. International Journal for Numerical Methods in Biomedical Engineering, 2022, 38(7): e3609.
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14.	朱兴华,宫赫,白雪飞,等. 弹性模量与表观密度的分段函数关系用于股骨近端的结构模拟. 中国生物医学工程学报, 2003, 22(3): 250-257.
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16.	Parsa A, Ibrahim N, Hassan B, et al. Bone quality evaluation at dental implant site using multislice CT, micro-CT, and cone beam CT. Clin Oral Implants Res, 2015, 26(1): e1-e7.
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18.	Khaniki H B, Ghayesh M H, Chin R, et al. Hyperelastic structures: a review on the mechanics and biomechanics. International Journal of Non-Linear Mechanics, 2023, 148: 104275.
19.	Ogden R W, Hill R. Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London A Mathematical and Physical Sciences, 1997, 326(1567): 565-584.
20.	Oftadeh R, Perez-Viloria M, Villa-Camacho J C, et al. Biomechanics and mechanobiology of trabecular bone: a review. Journal of Biomechanical Engineering, 2015, 137(1): 0108021-01080215.
21.	Yang P, Hu N, Guo X, et al. An ultra-simple universal model for the effective elastic properties of isotropic 3D closed-cell porous materials. Composite Structures, 2020, 249: 112531.
22.	Schaffler M B, Burr D B. Stiffness of compact bone: effects of porosity and density. Journal of Biomechanics, 1988, 21(1): 13-16.
23.	Rothweiler R, Gross C, Bortel E, et al. Comparison of the 3D-microstructure between alveolar and iliac bone for enhanced bioinspired bone graft substitutes. Frontiers in Bioengineering and Biotechnology, 2022, 10: 862395.
24.	Pharr G M, Oliver W C, Brotzen F R. On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. Journal of Materials Research, 1992, 7(3): 613-617.
25.	Park S, Park J, Kang I, et al. Effects of assessing the bone remodeling process in biomechanical finite element stability evaluations of dental implants. Computer Methods and Programs in Biomedicine, 2022, 221: 106852.
26.	仵健磊, 刘云峰, 李伯休, 等. 不同牙槽骨有限元模型对牙周膜生物力学响应的影响. 生物医学工程学杂志, 2021, 38(2): 295-302.
27.	Ikebuchi K, Matsuda Y, Takeda M, et al. Relationship between masticatory function and bone mineral density in community-dwelling elderly: a cross-sectional study. Healthcare, 2021, 9(7): 845.
28.	Mohammed A O, Kaklamanos E G. Effect of ovariectomy-induced osteoporosis on the amount of orthodontic tooth movement: a systematic review of animal studies. European Journal of Orthodontics, 2021, 43(6): 672-681.
29.	Chen H, Zhou X, Shoumura S, et al. Age-and gender-dependent changes in three-dimensional microstructure of cortical and trabecular bone at the human femoral neck. Osteoporos Int, 2010, 21(4): 627-636.
30.	Luo Y. Bone mineral density averaged over a region of interest on femur is affected by age-related change of bone geometry. Osteoporos Int, 2018, 29(6): 1419-1425.

1. Jeon H H, Teixeira H, Tsai A. Mechanistic insight into orthodontic tooth movement based on animal studies: a critical review. Journal of Clinical Medicine, 2021, 10(8): 1733.
2. Jin A, Xu H, Gao X, et al. ScRNA-Seq reveals a distinct osteogenic progenitor of alveolar bone. Journal of Dental Research, 2023, 102(6): 645-655.
3. Giorgio I, Dell'isola F, Andreaus U, et al. An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff's law. Biomechanics and Modeling in Mechanobiology, 2023, 22(6): 2135-2152.
4. Della Corte A, Giorgio I, Scerrato D. A review of recent developments in mathematical modeling of bone remodeling. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 2020, 234(3): 273-281.
5. Mirulla A I, Pinelli S, Zaffagnini S, et al. Numerical simulations on periprosthetic bone remodeling: a systematic review. Computer Methods and Programs in Biomedicine, 2021, 204: 106072.
6. Bittens M, Nackenhorst U. A fully implicit and thermodynamically consistent finite element framework for bone remodeling simulations. Computational Mechanics, 2023, 71(5): 853-866.
7. Helgason B, Perilli E, Schileo E, et al. Mathematical relationships between bone density and mechanical properties: a literature review. Clinical biomechanics (Bristol, Avon), 2008, 23(2): 135-146.
8. Quinn C, Kopp A, Vaughan T J. A coupled computational framework for bone fracture healing and long-term remodelling: investigating the role of internal fixation on bone fractures. International Journal for Numerical Methods in Biomedical Engineering, 2022, 38(7): e3609.
9. Currey J D. The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone. Journal of biomechanics, 1988, 21(2): 131-139.
10. Rice J C, Cowin S C, Bowman J A. On the dependence of the elasticity and strength of cancellous bone on apparent density. Journal of Biomechanics, 1988, 21(2): 155-168.
11. Kasra M, Grynpas M D. Static and dynamic finite element analyses of an idealized structural model of vertebral trabecular bone. Journal of Biomechanical Engineering, 1998, 120(2): 267-272.
12. Beaupre G S, Orr T E, Carter D R. An approach for time-dependent bone modeling and remodeling-application: a preliminary remodeling simulation. Journal of Orthopaedic Research, 1990, 8(5): 662-670.
13. Fischer K J, Jacobs C R, Levenston M E, et al. Observations of convergence and uniqueness of node-based bone remodeling simulations. Annals of Biomedical Engineering, 1997, 25(2): 261-268.
14. 朱兴华,宫赫,白雪飞,等. 弹性模量与表观密度的分段函数关系用于股骨近端的结构模拟. 中国生物医学工程学报, 2003, 22(3): 250-257.
15. Wu S, Luo S, Cen Z, et al. All-in-one porous membrane enables full protection in guided bone regeneration. Nature Communications, 2024, 15(1): 119.
16. Parsa A, Ibrahim N, Hassan B, et al. Bone quality evaluation at dental implant site using multislice CT, micro-CT, and cone beam CT. Clin Oral Implants Res, 2015, 26(1): e1-e7.
17. Wu B, Yuan L, Liu M, et al. Construction of a viscoelastic model of human cancellous bone in alveolar bone based on bone mineral density distribution. Materials, 2023, 16(23): 7427.
18. Khaniki H B, Ghayesh M H, Chin R, et al. Hyperelastic structures: a review on the mechanics and biomechanics. International Journal of Non-Linear Mechanics, 2023, 148: 104275.
19. Ogden R W, Hill R. Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London A Mathematical and Physical Sciences, 1997, 326(1567): 565-584.
20. Oftadeh R, Perez-Viloria M, Villa-Camacho J C, et al. Biomechanics and mechanobiology of trabecular bone: a review. Journal of Biomechanical Engineering, 2015, 137(1): 0108021-01080215.
21. Yang P, Hu N, Guo X, et al. An ultra-simple universal model for the effective elastic properties of isotropic 3D closed-cell porous materials. Composite Structures, 2020, 249: 112531.
22. Schaffler M B, Burr D B. Stiffness of compact bone: effects of porosity and density. Journal of Biomechanics, 1988, 21(1): 13-16.
23. Rothweiler R, Gross C, Bortel E, et al. Comparison of the 3D-microstructure between alveolar and iliac bone for enhanced bioinspired bone graft substitutes. Frontiers in Bioengineering and Biotechnology, 2022, 10: 862395.
24. Pharr G M, Oliver W C, Brotzen F R. On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. Journal of Materials Research, 1992, 7(3): 613-617.
25. Park S, Park J, Kang I, et al. Effects of assessing the bone remodeling process in biomechanical finite element stability evaluations of dental implants. Computer Methods and Programs in Biomedicine, 2022, 221: 106852.
26. 仵健磊, 刘云峰, 李伯休, 等. 不同牙槽骨有限元模型对牙周膜生物力学响应的影响. 生物医学工程学杂志, 2021, 38(2): 295-302.
27. Ikebuchi K, Matsuda Y, Takeda M, et al. Relationship between masticatory function and bone mineral density in community-dwelling elderly: a cross-sectional study. Healthcare, 2021, 9(7): 845.
28. Mohammed A O, Kaklamanos E G. Effect of ovariectomy-induced osteoporosis on the amount of orthodontic tooth movement: a systematic review of animal studies. European Journal of Orthodontics, 2021, 43(6): 672-681.
29. Chen H, Zhou X, Shoumura S, et al. Age-and gender-dependent changes in three-dimensional microstructure of cortical and trabecular bone at the human femoral neck. Osteoporos Int, 2010, 21(4): 627-636.
30. Luo Y. Bone mineral density averaged over a region of interest on femur is affected by age-related change of bone geometry. Osteoporos Int, 2018, 29(6): 1419-1425.

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