基于三周期极小曲面骨小梁结构的设计及优化  

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

作　　者：刘佳辛 贾鹏[3] 门玉涛[1,2] 刘璐 王烨明[3] 叶金铎[1,2] Liu Jiaxin;Jia Peng;Men Yutao;Liu Lu;Wang Yeming;Ye Jinduo(Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,School of Mechanical Engineering,Tianjin University of Technology,Tianjin 300384,China;National Demonstration Center for Experimental Mechanical and Electrical Engineering Education,Tianjin University of Technology,Tianjin 300384,China;Tianjin Hospital,Tianjin 300350,China;Tianjin Key Laboratory of Bone Implants Interface Functionalization and Personalization,Just Huajian Medical Device(Tianjin)Co.,Ltd.,Tianjin 300190,China)

机构地区：[1]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,天津市300384 [2]天津理工大学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

出　　处：《中国组织工程研究》2023年第7期992-997,共6页Chinese Journal of Tissue Engineering Research

基　　金：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。

摘　　要：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。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 w

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 

分 类 号：R459.9[医药卫生—治疗学] R318[医药卫生—临床医学] Q811[生物学—生物工程]