中国组织工程研究 ›› 2023, Vol. 27 ›› Issue (7): 992-997.doi: 10.12307/2023.076

• 组织工程骨材料 tissue-engineered bone • 上一篇    下一篇

基于三周期极小曲面骨小梁结构的设计及优化

刘佳辛1,2,贾  鹏3,门玉涛1,2,刘  璐4,王烨明3,叶金铎1,2   

  1. 天津理工大学,1天津市先进机电系统设计与智能控制重点实验室,2机电工程国家级实验教学示范中心,天津市  300384;3天津市天津医院,天津市  300350;4天津市骨植入物界面功能化与个性研究企业重点实验室,嘉思特华剑医疗器材(天津)有限公司,天津市  300190
  • 收稿日期:2021-11-27 接受日期:2022-02-12 出版日期:2023-03-08 发布日期:2022-07-16
  • 通讯作者: 门玉涛,博士,副教授,硕士生导师,天津理工大学,天津市先进机电系统设计与智能控制重点实验室,机电工程国家级实验教学示范中心,天津市 300384
  • 作者简介:刘佳辛,男,1994年生,河北省衡水市人,汉族,天津理工大学在读硕士,主要从事假体骨小梁结构设计及力学性能研究。 贾鹏,男,1979年生,天津市人,汉族,硕士,主治医师,主要从事创伤骨科研究。
  • 基金资助:
    天津市自然科学基金(18JCYBJC95200),项目负责人:门玉涛;天津市科技支撑重点项目(18YFZCS00890),项目负责人:刘璐;天津市科技计划项目生物医学工程科技重大专项(18ZXSGSY00010),项目参与人:刘璐;天津市重点实验室开放基金(SY-04-201902-003),项目参与人:贾鹏;天津市重点实验室开放基金(SY-04-201901-003),项目负责人:贾鹏

Design and optimization of bone trabecular structure with triply periodic minimal surfaces

Liu Jiaxin1, 2, Jia Peng3, Men Yutao1, 2, Liu Lu4, Wang Yeming3, Ye Jinduo1, 2   

  1. 1Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, 2National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China; 3Tianjin Hospital, Tianjin 300350, China; 4Tianjin Key Laboratory of Bone Implants Interface Functionalization and Personalization, Just Huajian Medical Device (Tianjin) Co., Ltd., Tianjin 300190, China
  • Received:2021-11-27 Accepted:2022-02-12 Online:2023-03-08 Published:2022-07-16
  • Contact: Men Yutao, MD, Associate professor, Master’s supervisor, Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, and National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China
  • About author:Liu Jiaxin, Master candidate, Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, and National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China Jia Peng, Master, Attending physician, Tianjin Hospital, Tianjin 300350, China Liu Jiaxin and Jia Peng contributed equally to this article.
  • Supported by:
    Natural Science Foundation of Tianjin, No. 18JCYBJC95200 (to MYT); Key Science and Technology Support Project of Tianjin, No. 18YFZCS00890 (to LL); Major Biomedical Engineering Science and Technology Project of Tianjin Science and Technology Program Project, No. 18ZXSGSY00010 (to LL); Tianjin Key Laboratory Open Fund, No. SY-04-201902-003 (to JP); Tianjin Key Laboratory Open Fund, No. SY-04-201901-003 (to JP)

摘要:

文题释义:
三周期极小曲面:在空间中3个方向呈周期性变化的平均曲率为零的曲面,具有高比表面积、全连通性和可控性等特点,是骨组织支架设计新选择。
骨小梁:作为皮质骨在松质骨内的延伸部分,表面覆有骨原细胞或成骨细胞。骨小梁的形状呈不规则空间网状结构,或为杆状结构,或为板状结构,具有支持造血组织作用。

背景:近年来骨组织工程支架结构应用广泛,但其稳定性、可控性较差并易产生应力集中。三周期极小曲面具有多孔性、光滑性、连通性、多样性及可控性等诸多优点,为骨组织支架设计及应用提供了新思路。
目的:基于隐式曲面法构建骨小梁结构,应用有限元数值模拟方法及拓扑优化技术对其进行结构优化。
方法:①基于隐式曲面法参数化构建三周期极小曲面结构,构建三周期极小曲面S-P型、D型和G型骨小梁结构;②采用有限元数值模拟方法对构建的骨小梁结构进行压缩仿真;③利用变密度法和固体各向同性材料惩罚模型建立S-P骨小梁结构拓扑优化数学模型,进行结构优化。
结果与结论:①应力云图显示,3种骨小梁结构在单元结构相交处呈现较大应力值,S-P型出现在单元径向连接处,G型出现在轴向连接处,D型在轴向和径向连接处均有,S-P、G、D型骨小梁结构的等效应力分别为105.07,694.78,637.36 MPa;②位移云图显示,3种骨小梁结构接近施加位移面的部分位移最大,沿轴向递减,S-P型的总形变小于G、D型;③3种骨小梁结构的孔隙率均高于50%,其中S-P型孔隙率最高,达到90.7%,孔径为0.63 mm,骨长入性能优于G、D型;④经拓扑优化后,S-P型骨小梁结构的等效应力为149.11 MPa,质量减少13.9%,符合骨组织支架设计要求;⑤结果显示,基于三周期极小曲面参数化建模结合有限元数值模拟及拓扑优化方法对骨小梁结构进行设计优化,为骨植入物表面结构设计提供了新思路。

https://orcid.org/0000-0002-2573-6263(刘佳辛)

中国组织工程研究杂志出版内容重点:生物材料;骨生物材料口腔生物材料纳米材料缓释材料材料相容性组织工程

关键词: 参数化建模, 骨小梁, 三周期极小曲面, 拓扑优化, 力学性能仿真分析, 生物力学

Abstract: BACKGROUND: Bone tissue engineering scaffolds have been widely used in recent years, but their stability and controllability are poor, which may produce stress concentration easily. Triply periodic minimal surfaces have many advantages, such as porosity, smoothness, connectivity, diversity and controllability, which provide a new idea for the design and application of bone tissue scaffolds.
OBJECTIVE: To construct bone trabecular structure based on implicit surface method and optimize the structure by using finite element numerical simulation and topology optimization technology.
METHODS: (1) Based on the parameterization of implicit surface method and modeling S-P, D and G trabecular structures of triply periodic minimal surface were constructed. (2) Compression simulation of the constructed trabecular bone structure was carried out using finite element numerical simulation method. (3) The structure optimization of S-P bone trabecular structure was carried out by using variable density method and Solid Isotropic Material with Penalization interpolation model. 
RESULTS AND CONCLUSION: (1) The stress nephogram showed that the three trabecular structures exhibited larger stress values at the intersection of the unit structures. The S-P type appeared at the radial connection of the unit. The G type appeared at the axial connection. The D type appeared at the axial and radial connection. The equivalent stresses of S-P, G and D structures were 105.07, 694.78 and 637.36 MPa, respectively. (2) The displacement nephogram showed that the displacement of the three trabecular structures close to the displacement surface was the largest and decreased along the axial direction. The total deformation of the S-P type was smaller than that of the G and D types. (3) The porosity of the three trabecular bone structures was higher than 50%, with the highest porosity of the S-P type (90.7%) and an aperture of 0.63 mm. Bone ingrowth performance was better than G and D types. (4) After topology optimization, the equivalent stress of S-P structure was 149.11 MPa, the mass of which was reduced by 13.9%, which met the design requirements of bone tissue scaffold. (5) Therefore, the method of the design of bone trabecular structure that combines triply periodic minimal surface parametric modeling with finite element numerical simulation and topology optimization provides a new idea for the surface structure design of bone implants. 

Key words: parametric modeling, trabecular bone, triply periodic minimal surface, topology optimization, simulation analysis of mechanical properties, biomechanics

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