Design and performance study of bone trabecular scaffolds based on triply periodic minimal surface method_Journal of Biomedical Engineering

Authors：

 MEN Yutao ^1,2 , TANG Shaocan ^1,2 , CHEN Wei ^1,2 , LIU Fulong ^1,2 , ZHANG Chunqiu ^1,2

1. Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, P. R. China;
2. National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, P. R. China;

Corresponding author：

MEN Yutao, Email: yutaomen@163.com

Keywords：

Triply periodic minimal surfaces; Porous scaffold; Topology optimization; Structural strength; Permeability

DOI：

10.7507/1001-5515.202310005

Video：

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Triply periodic minimal surface (TPMS) is widely used because it can be used to control the shape of porous scaffolds precisely by formula. In this paper, an I-wrapped package (I-WP) type porous scaffolds were constructed. The finite element method was used to study the relationship between the wall thickness and period, the morphology and mechanical properties of the scaffolds, as well as to study the compression and fluid properties. It was found that the porosity of I-WP type scaffolds with different wall thicknesses (0.1 ~ 0.2 mm) and periods (I-WP 1 ~ I-WP 5) ranged from 68.01% ~ 96.48%, and the equivalent elastic modulus ranged from 0.655 ~ 18.602 GPa; the stress distribution of the scaffolds tended to be uniform with the increase of periods and wall thicknesses; the equivalent elastic modulus of the I-WP type scaffolds was basically unchanged after the topology optimization, and the permeability was improved by 52.3%. In conclusion, for the I-WP type scaffolds, the period parameter can be adjusted first, then the wall thickness parameter can be controlled. Topology optimization can be combined to meet the design requirements. The I-WP scaffolds constructed in this paper have good mechanical properties and meet the requirements of repairing human bone tissue, which may provide a new choice for the design of artificial bone trabecular scaffolds.

Citation： MEN Yutao, TANG Shaocan, CHEN Wei, LIU Fulong, ZHANG Chunqiu. Design and performance study of bone trabecular scaffolds based on triply periodic minimal surface method. Journal of Biomedical Engineering, 2024, 41(3): 584-594. doi: 10.7507/1001-5515.202310005 Copy

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8.	Kapfer S C, Hyde S T, Mecke K, et al. Minimal surface scaffold designs for tissue engineering. Biomaterials, 2011, 32(29): 6875-6882.
9.	Feng J, Liu B, Lin Z, et al. Isotropic porous structure design methods based on triply periodic minimal surfaces. Materials & Design, 2021, 210: 110050.
10.	Vijayavenkataraman S, Kuan L Y, Lu W F. 3D-printed ceramic triply periodic minimal surface structures for design of functionally graded bone implants. Materials & Design, 2020, 191: 108602.
11.	Wang Y. Periodic surface modeling for computer aided nano design. Computer-Aided Design, 2007, 39(3): 179-189.
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14.	邓珍波, 周长春, 樊渝江, 等. 多孔钛骨组织工程支架设计及孔结构表征. 稀有金属材料与工程, 2016, 45(9): 2287-2292.
15.	Yang N, Zhou K. Effective method for multi-scale gradient porous scaffold design and fabrication. Mater Sci Eng C Mater Biol Appl, 2014, 43: 502-505.
16.	Yang N, Quan Z, Zhang D, et al. Multi-morphology transition hybridization CAD design of minimal surface porous structures for use in tissue engineering. Computer-Aided Design, 2014, 56: 11-21.
17.	Yang N, Tian Y, Zhang D. Novel real function based method to construct heterogeneous porous scaffolds and additive manufacturing for use in medical engineering. Medical Engineering & Physics, 2015, 37(11): 1037-1046.
18.	刘佳辛, 贾鹏, 门玉涛, 等. 基于三周期极小曲面骨小梁结构的设计及优化. 中国组织工程研究, 2023, 27(7): 992-997.
19.	Liu B, Liu M, Cheng H, et al. A new stress-driven composite porous structure design method based on triply periodic minimal surfaces. Thin-Walled Structures, 2022, 181: 1-19.
20.	Yoo D. Computer-aided porous scaffold design for tissue engineering using triply periodic minimal surfaces. International Journal of Precision Engineering and Manufacturing, 2011, 12(1): 61-71.
21.	Zhou M, Pagaldipti N, Thomas H L, et al. An integrated approach to topology, sizing, and shape optimization. Structural and Multidisciplinary Optimization, 2004, 26(5): 308-317.
22.	Zhou M, Rozvany G I N. The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1): 309-336.
23.	Singh S P, Shukla M, Srivastava R K. Lattice modeling and CFD simulation for prediction of permeability in porous scaffolds. Materials Today: Proceedings, 2018, 5(9): 18879-18886.
24.	Chen H, Liu Y, Wang C, et al. Design and properties of biomimetic irregular scaffolds for bone tissue engineering. Computers in Biology and Medicine, 2021, 130: 104241.
25.	Sevilla P, Aparicio C, Planell J A, et al. Comparison of the mechanical properties between tantalum and nickel-titanium foams implant materials for bone ingrowth applications. Journal of Alloys and Compounds, 2007, 439(1-2): 67-73.
26.	Morgan E F, Bayraktar H H, Keaveny T M. Trabecular bone modulus-density relationships depend on anatomic site. Journal of Biomechanics, 2003, 36(7): 897-904.
27.	Li H, Wen J, Liu Y, et al. Progress in research on biodegradable magnesium alloys: a review. Advanced Engineering Materials, 2020, 22(7): 2000213.
28.	Arjunan A, Demetriou M, Baroutaji A, et al. Mechanical performance of highly permeable laser melted Ti6Al4V bone scaffolds. Journal of the Mechanical Behavior of Biomedical Materials, 2020, 102: 103517.
29.	屈华伟, 韩振宇, 卓越, 等. 骨组织工程多孔生物支架设计研究进展. 机械工程学报, 2019, 55(15): 71-80.
30.	Chua C K, Leong K F, Cheah C M, et al. Development of a tissue engineering scaffold structure library for rapid prototyping. Part 1: investigation and classification. International Journal of Advanced Manufacturing Technology, 2003, 21(4): 291-301.
31.	Chua C K, Leong K F, Cheah C M, et al. Development of a tissue engineering scaffold structure library for rapid prototyping. Part 2: parametric library and assembly program. International Journal of Advanced Manufacturing Technology, 2003, 21(4): 302-312.
32.	Hollister S J. Porous scaffold design for tissue engineering. Nature Materials, 2005, 4(7): 518-524.
33.	Deering J, Dowling K I, Dicecco L A, et al. Selective Voronoi tessellation as a method to design anisotropic and biomimetic implants. Journal of the Mechanical Behavior of Biomedical Materials, 2021, 116: 104361.
34.	Roh H, Jung S, Kook M, et al. In vitro study of 3D PLGA/n-HAp/β-TCP composite scaffolds with etched oxygen plasma surface modification in bone tissue engineering. Applied Surface Science, 2016, 388: 321-330.
35.	Hollister S J, Levy R A, Chu T, et al. An image-based approach for designing and manufacturing craniofacial scaffolds. International Journal of Oral and Maxillofacial Surgery, 2000, 29(1): 67-71.

1. Sing S L, An J, Yeong W Y, et al. Laser and electron-beam powder-bed additive manufacturing of metallic implants: a review on processes, materials and designs. Journal of Orthopaedic Research, 2016, 34(3): 369-385.
2. Murphy S V, Atala A. 3D bioprinting of tissues and organs. Nature Biotechnology, 2014, 32(8): 773-785.
3. Wang X, Xu S, Zhou S, et al. Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: a review. Biomaterials, 2016, 83: 127-141.
4. Karageorgiou V, Kaplan D. Porosity of 3D biomaterial scaffolds and osteogenesis. Biomaterials, 2005, 26(27): 5474-5491.
5. Liu Y, Wu G, de Groot K. Biomimetic coatings for bone tissue engineering of critical-sized defects. Journal of the Royal Society Interface, 2010, 7(Suppl 5): S631-S647.
6. Marin E, Fusi S, Pressacco M, et al. Characterization of cellular solids in Ti6Al4V for orthopaedic implant applications: trabecular titanium. Journal of the Mechanical Behavior of Biomedical Materials, 2010, 3(5): 373-381.
7. Martínez J, Song H, Dumas J, et al. Orthotropic k-nearest foams for additive manufacturing. ACM Transactions on Graphics, 2017, 36(4): 1-12.
8. Kapfer S C, Hyde S T, Mecke K, et al. Minimal surface scaffold designs for tissue engineering. Biomaterials, 2011, 32(29): 6875-6882.
9. Feng J, Liu B, Lin Z, et al. Isotropic porous structure design methods based on triply periodic minimal surfaces. Materials & Design, 2021, 210: 110050.
10. Vijayavenkataraman S, Kuan L Y, Lu W F. 3D-printed ceramic triply periodic minimal surface structures for design of functionally graded bone implants. Materials & Design, 2020, 191: 108602.
11. Wang Y. Periodic surface modeling for computer aided nano design. Computer-Aided Design, 2007, 39(3): 179-189.
12. Yoo D J. Porous scaffold design using the distance field and triply periodic minimal surface models. Biomaterials, 2011, 32(31): 7741-7754.
13. Melchels F P, Bertoldi K, Gabbrielli R, et al. Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials, 2010, 31(27): 6909-6916.
14. 邓珍波, 周长春, 樊渝江, 等. 多孔钛骨组织工程支架设计及孔结构表征. 稀有金属材料与工程, 2016, 45(9): 2287-2292.
15. Yang N, Zhou K. Effective method for multi-scale gradient porous scaffold design and fabrication. Mater Sci Eng C Mater Biol Appl, 2014, 43: 502-505.
16. Yang N, Quan Z, Zhang D, et al. Multi-morphology transition hybridization CAD design of minimal surface porous structures for use in tissue engineering. Computer-Aided Design, 2014, 56: 11-21.
17. Yang N, Tian Y, Zhang D. Novel real function based method to construct heterogeneous porous scaffolds and additive manufacturing for use in medical engineering. Medical Engineering & Physics, 2015, 37(11): 1037-1046.
18. 刘佳辛, 贾鹏, 门玉涛, 等. 基于三周期极小曲面骨小梁结构的设计及优化. 中国组织工程研究, 2023, 27(7): 992-997.
19. Liu B, Liu M, Cheng H, et al. A new stress-driven composite porous structure design method based on triply periodic minimal surfaces. Thin-Walled Structures, 2022, 181: 1-19.
20. Yoo D. Computer-aided porous scaffold design for tissue engineering using triply periodic minimal surfaces. International Journal of Precision Engineering and Manufacturing, 2011, 12(1): 61-71.
21. Zhou M, Pagaldipti N, Thomas H L, et al. An integrated approach to topology, sizing, and shape optimization. Structural and Multidisciplinary Optimization, 2004, 26(5): 308-317.
22. Zhou M, Rozvany G I N. The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1): 309-336.
23. Singh S P, Shukla M, Srivastava R K. Lattice modeling and CFD simulation for prediction of permeability in porous scaffolds. Materials Today: Proceedings, 2018, 5(9): 18879-18886.
24. Chen H, Liu Y, Wang C, et al. Design and properties of biomimetic irregular scaffolds for bone tissue engineering. Computers in Biology and Medicine, 2021, 130: 104241.
25. Sevilla P, Aparicio C, Planell J A, et al. Comparison of the mechanical properties between tantalum and nickel-titanium foams implant materials for bone ingrowth applications. Journal of Alloys and Compounds, 2007, 439(1-2): 67-73.
26. Morgan E F, Bayraktar H H, Keaveny T M. Trabecular bone modulus-density relationships depend on anatomic site. Journal of Biomechanics, 2003, 36(7): 897-904.
27. Li H, Wen J, Liu Y, et al. Progress in research on biodegradable magnesium alloys: a review. Advanced Engineering Materials, 2020, 22(7): 2000213.
28. Arjunan A, Demetriou M, Baroutaji A, et al. Mechanical performance of highly permeable laser melted Ti6Al4V bone scaffolds. Journal of the Mechanical Behavior of Biomedical Materials, 2020, 102: 103517.
29. 屈华伟, 韩振宇, 卓越, 等. 骨组织工程多孔生物支架设计研究进展. 机械工程学报, 2019, 55(15): 71-80.
30. Chua C K, Leong K F, Cheah C M, et al. Development of a tissue engineering scaffold structure library for rapid prototyping. Part 1: investigation and classification. International Journal of Advanced Manufacturing Technology, 2003, 21(4): 291-301.
31. Chua C K, Leong K F, Cheah C M, et al. Development of a tissue engineering scaffold structure library for rapid prototyping. Part 2: parametric library and assembly program. International Journal of Advanced Manufacturing Technology, 2003, 21(4): 302-312.
32. Hollister S J. Porous scaffold design for tissue engineering. Nature Materials, 2005, 4(7): 518-524.
33. Deering J, Dowling K I, Dicecco L A, et al. Selective Voronoi tessellation as a method to design anisotropic and biomimetic implants. Journal of the Mechanical Behavior of Biomedical Materials, 2021, 116: 104361.
34. Roh H, Jung S, Kook M, et al. In vitro study of 3D PLGA/n-HAp/β-TCP composite scaffolds with etched oxygen plasma surface modification in bone tissue engineering. Applied Surface Science, 2016, 388: 321-330.
35. Hollister S J, Levy R A, Chu T, et al. An image-based approach for designing and manufacturing craniofacial scaffolds. International Journal of Oral and Maxillofacial Surgery, 2000, 29(1): 67-71.

Journal of Biomedical Engineering

Design and performance study of bone trabecular scaffolds based on triply periodic minimal surface method

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