2023, Vol. 27 ›› Issue (7): 992-997

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   

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