Design and mechanical performance of cell-gradient scaffolds based on three-period minimal surface

doi:10.12307/2025.430

Abstract

Abstract: BACKGROUND: The elastic modulus of bone-cartilage integration scaffolds differs significantly from that of natural bone-cartilage tissue, which can lead to a stress shield effect. As a result, the implants become loose and deformed, affecting the repair of osteochondral tissue. Cell gradient scaffolds made by axial direction three-period minimal surface have the same porosity and elasticity modulus as the human body, which provides a new idea for bone-cartilage scaffold design.
OBJECTIVE: To study the effect of cell type and pore size on the mechanical properties of cell gradient scaffolds.
METHODS: Three basic cells of Gyroid(G) type, Diamond(D) type, and Primitive(P) type were used. Through mathematical modeling of three-period minimal surface, different sizes and types of cells were used in the gradient region. A total of six kinds of cell gradient scaffolds (G-2P-4D, P-2D-4G, D-2P-4D, G-2D-4P, P-2G-4D, and D-2G-4P) were constructed and mechanical experiments and simulation experiments were conducted to evaluate the mechanical properties of the scaffolds. Flow performance parameters of the fluids in the scaffolds were obtained through computational fluid dynamics simulation.
RESULTS AND CONCLUSION: Finite element mechanical simulation and compression experiment showed that P-2G-4D and P-2D-4G with the highest elastic modulus (148.67 MPa and 152.1 MPa), bearing a higher body load, improved the stability of the scaffold. The stress distribution in D-2P-4G was even and effectively reduced stress concentration, so that the connection function area could effectively transfer stress and reduce stress shielding. Flow rate was changing the least in G-2D-4P (0.10-0.48 mm/s). Permeability was higher than other scaffolds so that body fluids were able to flow though the gradient scaffold after implantation. This design method provides a new idea for the design of osteochondral scaffolds, and the simulation analysis results also provide a reference for the prediction of bone integration after implantation of scaffolds.

Key words: three-period minimal surface, cell gradient, connection function, bone cartilage scaffold, mechanical property, flow performance

CLC Number:

Zhu Wenbo, Zhang Xujing, Xu Yan, Shi Xintong. Design and mechanical performance of cell-gradient scaffolds based on three-period minimal surface[J]. Chinese Journal of Tissue Engineering Research, 2025, 29(16): 3449-3457.

Figures/Tables 8

2.2 六种晶胞梯度三周期极小曲面支架的静力压缩实验结果 6种晶胞梯度三周期极小曲面支架在单轴1%压缩实验下的实验图和有限元模拟云图，如图8所示。在压缩实验过程中，梯晶胞度之间会逐层挤压。梯度三周期极小曲面支架在压缩过程中不同晶胞之间会出现连接区域应力集中问题，应力分布与晶胞选取有直接关系。D型晶胞整体受力均匀，没有明显的应力集中区域；P型晶胞应力主要集中在P型晶胞与其他晶胞的连接处；G型晶胞应力主要集中在晶胞内壁，变形以弯曲为主。D-2P-4G支架在连接函数的帮助下更容易将应力传递至支架其他区域，从而减少应力集中。G型晶胞在传递应力的过程中容易出现应力集中现象，G-2P-4D支架应力最大值在G型晶胞向2P型晶胞的过渡连接处，该区域存在很小的过渡截面，容易出现应力集中(图9A)；G-2D-4P支架应力最大值出现在G型晶胞向2D型晶胞转变的细小截面处(图9B)；D-2G-4P支架应力最大值在2G型向4P型的连接过程中(图9C)，横截面变小。随着G型晶胞单边尺寸变小，晶胞数量变多，应力传导过程中能快速将应力分布均匀，从而提高弹性模量。如D-2P-4G和P-2D-4G支架内部的最大应力均小于其他4个支架，2P和2D型晶胞过渡到4G型晶胞时单元横截面连接区域变多，横截面积变大。模拟实验结果显示D-2P-4G支架应力分布最为均匀，这是由于晶胞在梯度变化的过程中连接区域截面积变化较小，连接区域表面变化更为平滑，在压缩力学实验过程中能将应力均匀分布至下层结构，应力集中点少。根据公式(7)计算可得6种晶胞梯度三周期极小曲面支架的压缩力学实验和有限元分析的数据如表2、图10A所示。从数据结果分析来看，6种支架受压缩应力时，支架内部平均应力最小和最大值分别为13.064 MPa和16.143 MPa。得益于P型晶胞本身的受力好的特点，P-2G-4D和P-2D-4G支架有最高的弹性模量(148.67 MPa和152.1 MPa)。P型晶胞连接函数区域虽然会出现少量局部应力集中现象，但总体弹性模量均高于其他4组，使得支架能够承受更多的人体载荷，有助于提高支架长期稳定性。而G型晶胞本身应力传递过程中会出现壁面应力集中，从而导致支架整体弹性模量偏低(图9D)。在压缩力学实验过程进行到4%应变时，梯度三周期极小曲面支架内部出现一些裂纹。与均匀支架相比，晶胞梯度三周期极小曲面支架的失效形式发生变化，其失效形式沿轴向破坏，逐层破裂。选取弹性模量为77.75 MPa的D-2G-4P支架为例，如图10B所示，裂纹出现在中间G型晶胞以及向P型晶胞转变的轴向连接区域，与有限元模拟的应力较大的位置重合。6种晶胞梯度三周期极小曲面支架的有限元仿真模拟与压缩实验对比，见图10C。 "

References

1] ZHAO D, ZHU T, LI J, et al. Ding Poly(lactic-co-glycolic acid)-based composite bone-substitute materials. Bioact Mater. 2020;6(2):346-360.
[2] SHUAI C, YANG W, FENG P, et al. Pan Accelerated degradation of HAP/PLLA bone scaffold by PGA blending facilitates bioactivity and osteo conductivity. Bioact Mater. 2020;6(2):490-502.
[3] HUANG X, LOU Y, DUAN Y, et al. Biomaterial scaffolds in maxillofacial bone tissue engineering: A review of recent advances. Bioact Mater. 2023;33:129-156.
[4] 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.
[5] QU HW, FU HY, HAN ZY, et al. Biomaterials for bone tissue engineering scaffolds: a review. Rsc Adv. 2019;9(45):26252-26262.
[6] BOSCHETTI F, PENNATI G, GERVASO F, et al. Biomechanical properties of human articular cartilage under compressive loads. Biorheology. 2004;41(3-4):159-166.
[7] 万李,王海蟒,蔡谞,等.骨软骨组织工程仿生梯度支架研究进展[J].材料工程,2022,50(2):38-49.
[8] ZHANG B, HUANG J, NARAYAN RJ. Gradient scaffolds for osteochondral tissue engineering and regeneration. J Mater Chem B. 2020;8(36): 8149-8170.
[9] KADKHODAPOUR J, MONTAZERIAN H, DARABI AC, et al. The relationships between deformation mechanisms and mechanical properties of additively manufactured porous biomaterials. J Mech Behav Biomed Mater. 2017;70:28-42.
[10] WEIßMANN V, BADER R, HANSMANN H, et al. Influence of the structural orientation on the mechanical properties of selective laser melted Ti6A14V open porous scaffolds. Mater Design. 2016;95: 188-197.
[11] GUO M, LI X. Development of porous Ti6A14V/chitosan sponge composite scaffold for orthopedic applications. Mater Sci Eng C Mater Biol Appl. 2016;58:1177-1181.
[12] 高芮宁,李祥.径向梯度多孔支架设计与力学性能分析[J].机械工程学报,2021,57(3):220-226.
[13] Salmani MM, Hashemian M, KHANDAN A. Therapeutic effect of magnetic nanoparticles on calcium silicate bioceramic in alternating field for biomedical application. Ceram Int.2020;46(17):27299-27307.
[14] 陈华伟,伍权.骨支架多孔结构建模综述[J].现代制造工程,2019(6): 147-153.
[15] WANG K, XIONG D. Construction of lubricant composite coating on Ti6A14 V alloy using micro-arc oxidation and grafting hydrophilic polymer. Mater Sci Eng C Mater Biol Appl. 2018;90:219-226.
[16] YANG N, TIAN YL, ZHANG DW. Novel real function based method to construct heterogeneous porous scaffolds and additive manufacturing for use in medical engineering. Med Eng Phys. 2015;37(11):1037-1046.
[17] MEYER U, BÜCHTER A, NAZER N, et al. Design and performance of a bioreactor system for mechanically promoted three-dimensional tissue engineering. Br J Oral Maxillofac Surg. 2006;44(2):134-140.
[18] HOLLISTER SJ. Porous scaffold design for tissue engineering. Nat Mater. 2005;4(7):518-524.
[19] 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.
[20] ZHANG XY, 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.
[21] CASTRO AG, PIRES T, SANTOS JE, et al. Permeability versus design in TPMS scaffolds. Materials. 2019;12(8):1313.
[22] 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.
[23] 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. Mater Design. 2017;126:98-114.
[24] YU GS, LI ZB, LI SJ, et al. The select of internal architecture for porous Ti alloy scaffold: a compromise between mechanical properties and permeability. Mater Design. 2020;192:08754.
[25] MONTAZERIAN H, MOHAMED MGA, MONTAZERI MM, et al. Permeability and mechanical properties of gradient porous PDMS scaffolds fabricated by 3D-printed sacrificial templates designed with minimal surfaces. Acta Biomater. 2019;96:149-160.
[26] HU C, LIN H. Heterogeneous porous scaffold generation using trivariate B-spline solids and triply periodic minimal surfaces. Graph Model. 2021;115:101105.
[27] 石志良,阮鹏成,高杰,等.钛合金变形Gyroid单元梯度多孔结构设计与分析[J].稀有金属材料与工程,2023,52(3):1155-1161.
[28] 丁佳伟.功能梯度TPMS支架的结构设计及性能研究[D].长春:吉林大学,2022.
[29] 张壮雅,赵珂,李跃松,等.基于体素和三周期极小曲面的骨支架多孔结构设计[J].计算机集成制造系统,2020,26(3):697-706.
[30] OLIVARES AL, MARSAL E, PLANELL JA, et al. Finite element study of scaffold architecture design and culture conditions for tissue engineering. Biomaterials. 2009;30(30):6142-6149.
[31] 刘志强,宫赫,高甲子,等.基于三周期极小曲面的新型梯度支架设计及其力学、渗透、组织分化特性研究[J].生物医学工程学杂志,2021,38(5):960-968.
[32] BIEMOND JE, AQUARIUS R, VERDONSCHOT N, et al. Frictional and bone ingrowth properties of engineered surface topographies produced by electron beam technology. Arch Orthop Trauma Surg. 2011;131(5): 711-718.
[33] 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.
[34] MA S, TANG Q, FENG QX, et al. Mechanical behaviours and mass transport properties of bone-mimicking scaffolds consisted of gyroid structures manufactured using selective laser melting Mech Behav Biomed Mater. 2019;93:158-169.

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