Design of new gradient scaffolds based on triply periodic minimal surfaces and study on its mechanical, permeability and tissue differentiation characteristics_Journal of Biomedical Engineering

Authors：

LIU Zhiqiang ,  GONG He , GAO Jiazi , LIU Zhehao , ZOU Shanshan , TIAN Sujing

Department of Mechanics, College of Mechanical and Aerospace Engineering, Jilin University, Changchun 130000, P.R.China;

Corresponding author：

GONG He, Email: gonghe@jlu.edu.cn

Keywords：

gradient triply periodic minimal surfaces scaffold; structural strength; flow property; permeability; tissue differentiation

DOI：

10.7507/1001-5515.202102054

Video：

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In order to establish a bone scaffold with good biological properties, two kinds of new gradient triply periodic minimal surfaces (TPMS) scaffolds, i.e., two-way linear gradient G scaffolds (L-G) and D, G fusion scaffold (N-G) were designed based on the gyroid (G) and diamond (D)-type TPMS in this study. The structural mechanical parameters of the two kinds of scaffolds were obtained through the compressive simulation. The flow property parameters were also obtained through the computational fluid dynamics (CFD) simulation in this study, and the permeability of the two kinds of scaffolds were calculated by Darcy's law. The tissue differentiation areas of the two kinds of scaffolds were calculated based on the tissue differentiation theory. The results show that L-G scaffold has a better mechanical property than the N-G scaffold. However, N-G scaffold is better than the L-G scaffold in biological properties such as permeability and cartilage differentiation areas. The modeling processes of L-G and N-G scaffolds provide a new insight for the design of bone scaffold. The simulation in this study can also give reference for the prediction of osseointegration after the implantation of scaffold in the human body.

Citation： LIU Zhiqiang, GONG He, GAO Jiazi, LIU Zhehao, ZOU Shanshan, TIAN Sujing. Design of new gradient scaffolds based on triply periodic minimal surfaces and study on its mechanical, permeability and tissue differentiation characteristics. Journal of Biomedical Engineering, 2021, 38(5): 960-968. doi: 10.7507/1001-5515.202102054 Copy

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2.	Weißmann V, Bader R, Hansmann H, et al. Influence of the structural orientation on the mechanical properties of selective laser melted Ti6Al4V open-porous scaffolds. Materials & Design, 2016, 95: 188-197.
3.	Cuadrado A, Yánez A, Martel O, et al. Influence of load orientation and of types of loads on the mechanical properties of porous Ti6Al4V biomaterials. Materials & Design, 2017, 135: 309-318.
4.	Kadkhodapour J, Montazerian H, Darabi A, et al. Failure mechanisms of additively manufactured porous biomaterials: effects of porosity and type of unit cell. J Mech Behav Biomed Mater, 2015, 50: 180-191.
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8.	Li J, Chen D S, Fan Y B. Evaluation and prediction of mass transport properties for porous implant with different unit cells: a numerical study. Biomed Res Int, 2019: 3610785.
9.	Zhang L, Song B, Yang L, et al. Tailored mechanical response and mass transport characteristic of selective laser melted porous metallic biomaterials for bone scaffolds. Acta Biomater, 2020, 112: 298-315.
10.	Zhang X Y, Fang G, Leeflang S, et al. Topological design, permeability and mechanical behavior of additively manufactured functionally graded porous metallic biomaterials. Acta Biomater, 2019, 84: 437-452.
11.	Castro A G, Pires T, Santos J E, et al. Permeability versus design in TPMS scaffolds. Materials, 2019, 12(8): 1313.
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13.	Montazerian H, Mohamed M, Montazeri M M, et al. Permeability and mechanical properties of gradient porous PDMS scaffolds fabricated by 3D-printed sacrificial templates designed with minimal surfaces. Acta Biomater, 2019, 9: 149-160.
14.	Zhianmanesh M, Varmazyar M, Montazerian H. Fluid permeability of graded porosity scaffolds architectured with minimal surfaces. ACS Biomater Sci Eng, 2019, 5(3): 1228-1237.
15.	Ma S H, Song K L, Lan J, et al. Biological and mechanical property analysis for designed heterogeneous porous scaffolds based on the refined TPMS. J Mech Behav Biomed Mater, 2020, 107: 103727.
16.	Zhang L, Feih S, Daynes S, et al. Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading. Additive Manufacturing, 2018, 23: 505-515.
17.	Kadkhodapour J, Montazerian H, Raeisi S. Investigating internal architecture effect in plastic deformation and failure for TPMS-based scaffolds using simulation methods and experimental procedure. Mater Sci Eng C Mater Biol Appl, 2014, 43: 587-597.
18.	Montazerian H, Davoodi E, Asadi-eydivand M, et al. Porous scaffold internal architecture design based on minimal surfaces: a compromise between permeability and elastic properties. Materials & Design, 2017, 126: 98-114.
19.	Yu G S, Li Z B, Li S J, et al. The select of internal architecture for porous Ti alloy scaffold: a compromise between mechanical properties and permeability. Materials & Design, 2020, 192: 108754.
20.	Yang L, Yan C Z, Fan H Y, et al. Investigation on the orientation dependence of elastic response in Gyroid cellular structures. J Mech Behav Biomed Mater, 2019, 90: 73-85.
21.	Ma S, Tang Q, Feng Q X, et al. Mechanical behaviours and mass transport properties of bone-mimicking scaffolds consisted of gyroid structures manufactured using selective laser melting. J Mech Behav Biomed Mater, 2019, 93: 158-169.
22.	Ali D, Ozalp M, Blanquer S, et al. Permeability and fluid flow-induced wall shear stress in bone scaffolds with TPMS and lattice architectures: a CFD analysis. European Journal of Mechanics - B/Fluids, 2020, 79: 376-385.
23.	Melchels F P, Bertoldi K, Gabbrielli R, et al. Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials, 2010, 31(27): 6909-6916.
24.	Olivares A L, Marsal E, Planell J A, et al. Finite element study of scaffold architecture design and culture conditions for tissue engineering. Biomaterials, 2009, 30(30): 6142-6149.
25.	Zhang X B, Gong H. Simulation on tissue differentiations for different architecture designs in bone tissue engineering scaffold based on cellular structure model. J Mech Med Biol, 2015, 15(03): 1550028.
26.	LI Y, Jahr H, Pavanram P, et al. Additively manufactured functionally graded biodegradable porous iron. Acta Biomater, 2019, 96: 646-661.
27.	Yu S X, Sun J X, Bai J M. Investigation of functionally graded TPMS structures fabricated by additive manufacturing. Materials & design, 2019, 182: 108021.
28.	Zhou H L, Zhao M, Ma Z B, et al. Sheet and network based functionally graded lattice structures manufactured by selective laser melting: design, mechanical properties, and simulation. International Journal of Mechanical Sciences, 2020, 175: 105480.
29.	Melchels F P, Tonnarelli B, Olivares A L, et al. The influence of the scaffold design on the distribution of adhering cells after perfusion cell seeding. Biomaterials, 2011, 32(11): 2878-2884.
30.	Prendergast P J, Huiskes R, Soballes K. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech, 1997, 30(6): 539-548.
31.	徐高峰. 聚乳酸接骨板与钢板互锁治疗股骨远端粉碎性骨折的实验研究. 中国人民解放军第一军医大学, 2003.
32.	Liu F, Mao Z F, Zhang P, et al. Functionally graded Abbasi in multiple patterns: new design method, physical and mechanical properties. Materials & design, 2018, 160: 849-860.
33.	Beaudoin A J, Mihalko W M, Krause W R. Finite element modelling of polymethylmethacrylate flow through cancellous bone. J Biomech, 1991, 24(2): 127-136.
34.	Nauman E A, Fong K, Keaveny T M. Dependence of intertrabecular permeability on flow direction and anatomic site. Ann Biomed Eng, 1999, 27(4): 517-524.

1. Kadkhodapour J, Montazerian H, Darabi A C, et al. The relationships between deformation mechanisms and mechanical properties of additively manufactured porous biomaterials. J Mech Behav Biomed Mater, 2017, 70: 28-42.
2. Weißmann V, Bader R, Hansmann H, et al. Influence of the structural orientation on the mechanical properties of selective laser melted Ti6Al4V open-porous scaffolds. Materials & Design, 2016, 95: 188-197.
3. Cuadrado A, Yánez A, Martel O, et al. Influence of load orientation and of types of loads on the mechanical properties of porous Ti6Al4V biomaterials. Materials & Design, 2017, 135: 309-318.
4. Kadkhodapour J, Montazerian H, Darabi A, et al. Failure mechanisms of additively manufactured porous biomaterials: effects of porosity and type of unit cell. J Mech Behav Biomed Mater, 2015, 50: 180-191.
5. 施建平. 面向骨植入体3D打印的多孔结构构建研究. 南京: 东南大学, 2018.
6. Wang Xiaojian, Xu Shanqing, Zhou Shiwei, et al. Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: a review. Biomaterials, 2016, 83: 127-141.
7. Li J, Chen D S, Luan H Q, et al. Numerical evaluation and prediction of porous implant design and flow performance. Biomed Res Int, 2018, 2018: 1215021.
8. Li J, Chen D S, Fan Y B. Evaluation and prediction of mass transport properties for porous implant with different unit cells: a numerical study. Biomed Res Int, 2019: 3610785.
9. Zhang L, Song B, Yang L, et al. Tailored mechanical response and mass transport characteristic of selective laser melted porous metallic biomaterials for bone scaffolds. Acta Biomater, 2020, 112: 298-315.
10. Zhang X Y, Fang G, Leeflang S, et al. Topological design, permeability and mechanical behavior of additively manufactured functionally graded porous metallic biomaterials. Acta Biomater, 2019, 84: 437-452.
11. Castro A G, Pires T, Santos J E, et al. Permeability versus design in TPMS scaffolds. Materials, 2019, 12(8): 1313.
12. Zhang X Y, Yan X C, Fang G, et al. Biomechanical influence of structural variation strategies on functionally graded scaffolds constructed with triply periodic minimal surface. Additive Manufacturing, 2020, 32: 101015.
13. Montazerian H, Mohamed M, Montazeri M M, et al. Permeability and mechanical properties of gradient porous PDMS scaffolds fabricated by 3D-printed sacrificial templates designed with minimal surfaces. Acta Biomater, 2019, 9: 149-160.
14. Zhianmanesh M, Varmazyar M, Montazerian H. Fluid permeability of graded porosity scaffolds architectured with minimal surfaces. ACS Biomater Sci Eng, 2019, 5(3): 1228-1237.
15. Ma S H, Song K L, Lan J, et al. Biological and mechanical property analysis for designed heterogeneous porous scaffolds based on the refined TPMS. J Mech Behav Biomed Mater, 2020, 107: 103727.
16. Zhang L, Feih S, Daynes S, et al. Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading. Additive Manufacturing, 2018, 23: 505-515.
17. Kadkhodapour J, Montazerian H, Raeisi S. Investigating internal architecture effect in plastic deformation and failure for TPMS-based scaffolds using simulation methods and experimental procedure. Mater Sci Eng C Mater Biol Appl, 2014, 43: 587-597.
18. Montazerian H, Davoodi E, Asadi-eydivand M, et al. Porous scaffold internal architecture design based on minimal surfaces: a compromise between permeability and elastic properties. Materials & Design, 2017, 126: 98-114.
19. Yu G S, Li Z B, Li S J, et al. The select of internal architecture for porous Ti alloy scaffold: a compromise between mechanical properties and permeability. Materials & Design, 2020, 192: 108754.
20. Yang L, Yan C Z, Fan H Y, et al. Investigation on the orientation dependence of elastic response in Gyroid cellular structures. J Mech Behav Biomed Mater, 2019, 90: 73-85.
21. Ma S, Tang Q, Feng Q X, et al. Mechanical behaviours and mass transport properties of bone-mimicking scaffolds consisted of gyroid structures manufactured using selective laser melting. J Mech Behav Biomed Mater, 2019, 93: 158-169.
22. Ali D, Ozalp M, Blanquer S, et al. Permeability and fluid flow-induced wall shear stress in bone scaffolds with TPMS and lattice architectures: a CFD analysis. European Journal of Mechanics - B/Fluids, 2020, 79: 376-385.
23. Melchels F P, Bertoldi K, Gabbrielli R, et al. Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials, 2010, 31(27): 6909-6916.
24. Olivares A L, Marsal E, Planell J A, et al. Finite element study of scaffold architecture design and culture conditions for tissue engineering. Biomaterials, 2009, 30(30): 6142-6149.
25. Zhang X B, Gong H. Simulation on tissue differentiations for different architecture designs in bone tissue engineering scaffold based on cellular structure model. J Mech Med Biol, 2015, 15(03): 1550028.
26. LI Y, Jahr H, Pavanram P, et al. Additively manufactured functionally graded biodegradable porous iron. Acta Biomater, 2019, 96: 646-661.
27. Yu S X, Sun J X, Bai J M. Investigation of functionally graded TPMS structures fabricated by additive manufacturing. Materials & design, 2019, 182: 108021.
28. Zhou H L, Zhao M, Ma Z B, et al. Sheet and network based functionally graded lattice structures manufactured by selective laser melting: design, mechanical properties, and simulation. International Journal of Mechanical Sciences, 2020, 175: 105480.
29. Melchels F P, Tonnarelli B, Olivares A L, et al. The influence of the scaffold design on the distribution of adhering cells after perfusion cell seeding. Biomaterials, 2011, 32(11): 2878-2884.
30. Prendergast P J, Huiskes R, Soballes K. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech, 1997, 30(6): 539-548.
31. 徐高峰. 聚乳酸接骨板与钢板互锁治疗股骨远端粉碎性骨折的实验研究. 中国人民解放军第一军医大学, 2003.
32. Liu F, Mao Z F, Zhang P, et al. Functionally graded Abbasi in multiple patterns: new design method, physical and mechanical properties. Materials & design, 2018, 160: 849-860.
33. Beaudoin A J, Mihalko W M, Krause W R. Finite element modelling of polymethylmethacrylate flow through cancellous bone. J Biomech, 1991, 24(2): 127-136.
34. Nauman E A, Fong K, Keaveny T M. Dependence of intertrabecular permeability on flow direction and anatomic site. Ann Biomed Eng, 1999, 27(4): 517-524.

Journal of Biomedical Engineering

Design of new gradient scaffolds based on triply periodic minimal surfaces and study on its mechanical, permeability and tissue differentiation characteristics

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