面向基于Voronoi结构的随机多孔骨植入材料的小孔结构参数化建模方法研究

Study on parametric modeling method of Voronoi random porous bone implant materials

目的探讨基于3D Voronoi结构的随机多孔骨植入材料建模参数与实际小孔结构参数之间的数学关系,并研究一种针对此类小孔结构的参数化建模方法,使其获得更准确的小孔结构。方法本文利用Rhinoceros三维建模软件配合Grasshopper插件进行了基于3D Voronoi结构的随机多孔骨植入材料的参数化建模研究,提出"等效体积球"方法拟合孔径,并通过析因实验获得了建模参数与实际小孔结构参数之间的数学关系,设计了一种控制模型平均孔径和孔隙率的参数化建模方法;为验证方法的有效性,使用上述建模软件设计了建模程序,并用选区激光熔化(SLM)工艺和316 L不锈钢粉末对其创建的多孔模型进行了制备,并测量了样件的实际孔径和孔隙率。结果本文设计的建模程序成功创建了一系列平均孔径为500~1 000 m,孔隙率为60%~80%的随机多孔模型;其中,小梁直径≥182 m的模型实现了SLM成形,成形样件呈现出较为明显的Voronoi随机孔隙结构,且其实际平均孔径与设计值的相对误差仅为8%,而实际孔隙率与设计值的绝对误差仅为±1.2%,与设计参数吻合度较高。结论本文设计的参数化建模方法有效地控制了随机多孔模型的小孔结构参数,为制备具有准确孔隙参数的随机多孔植入物提供了一种可行的方法。

Objective To facilitate the design of the random porous bone implant materials based on 3 D Voronoi structure and improve its structural accuracy, it is necessary to discuss the mathematical relationship between its modeling parameters and actual pore structure parameters, and develop a parametric modeling method for such pore structure.Methods 3 D modeling software Rhinoceros and its plugin program Grasshopper were utilized to study the parametric modeling methods for designing Voronoi random porous bone implant. After introducing the "Equivalent Volume Ball Method" for pore diameter fitting, a factorial experiment was inducted to obtain the mathematical relationship between the modeling parameters and the actual parameters. On the basis of works above, a method to control the mean pore diameter and porosity of the model is developed. As a verification for the effectiveness of this method, a modeling program was implemented using the softwares mentioned above, later a series of 316 L specimens was fabricated by SLM and their actual pore diameter and porosity was measured. Results The modeling program designed in this paper successfully created a series of random porous model with a mean pore diameter of 500-1 000 m and porosity of60%-80%. Among them, the model with trabecular diameter≥182 m was successfully fabricated with SLM, which also presented an obvious Voronoi random pore structure. The relative error of pore diameter is less than 8%, and the absolute error of porosity is less than ±1.2%, which can be consider as a close match to the designs. Conclusion The parametric modeling method proposed in this paper has realized the accurate control to the pore diameter and porosity of the Voronoi random porous model, thus providing a practical methodology to the accurate fabrication of random porous implant.