儿童乳磨牙非金属冠设计及关键参数的三维有限元分析

Design of non-metallic crown for primary molars and analyzation of stress distribution:a finite element study

目的通过有限元法探索乳磨牙非金属冠制作的关键参数,为乳磨牙非金属冠的临床应用提供参考。方法构建下颌第二乳磨牙三维模型;限定牙冠厚度为0.5 mm,设计无角肩台解剖式、无角肩台非解剖式、刃状边缘解剖式、刃状边缘非解剖式4种牙冠形态;对无角肩台非解剖式牙冠设计0.50、0.75、1.00、1.25、1.50 mm 5种牙冠厚度,对牙冠分别赋予聚醚酮酮(polyetherketoneketone,PEKK)(PEKK组)、聚甲基丙烯酸甲酯(polymethylmethacrylate,PMMA)树脂(PMMA组)和树脂浸润陶瓷(树脂浸润陶瓷组)3种不同材料,模拟垂直及倾斜加载,对模型各组件进行应力及疲劳分析;将上述0.50、0.75、1.00、1.25、1.50 mm 5种厚度的无角肩台非解剖式牙冠的材料赋予为PMMA树脂,模拟牙冠旋转脱位,对不同厚度的无角肩台非解剖式牙冠进行非轴向固位分析。结果构建下颌第二乳磨牙有限元模型后,静力及疲劳分析显示无角肩台非解剖式牙冠及粘接剂层的von Mises应力峰值最小,安全系数最高。对比不同材料,树脂浸润陶瓷组在牙冠颊侧边缘出现明显的应力集中,PEKK组粘接剂层出现应力集中。非轴向固位分析显示0.50、0.75、1.00、1.25、1.50 mm 5种厚度的牙冠在转动相同角度时需要的扭矩大小分别为4856.1、4038.1、3497.3、3256.3及3074.3 N⋅m,各组粘接剂断裂面积大小:0.50 mm组<0.75 mm组<1.00 mm组<1.25 mm组<1.50 mm组。结论乳磨牙非金属冠的设计中,冠的边缘设计建议为无角肩台,内冠形态为非解剖式,面最小预备量为1.00 mm,制作材料建议采用与牙本质及粘接剂弹性模量接近且各项测评性能较稳定的PMMA树脂材料。

Objectives To study the design of nonmetallic crowns for deciduous molars by means of computer aided design and to analyze the key parameters of the nonmetallic crowns of deciduous molars using finite element method.Methods The three-dimensional model of a mandibular second primary molar was constructed by using a micro-CT system.The thickness of the crown was limited to 0.5 mm and four different crown shapes(chamfer+anatomic,chamfer+non-anatomic,knife edge+anatomic and knife edge+non-anatomic)were designed.Then,the crown shape was limited as chamfer+non-anatomic and five different thicknesses of the crown(0.50,0.75,1.00,1.25,1.50 mm)were designed,and three different materials,including polyetherketoneketone(PEKK),polymethylmethacrylate(PMMA)resin and resin-infiltrated ceramic,were applied to make the crown.Stress distribution and fatigue of each component of the model under vertical and oblique loadings were analyzed by using finite element method.Non-axial retention analysis was performed on chamfer+non-anatomic crowns,made of PMMA resin,with thicknesses of 0.50,0.75,1.00,1.25 and 1.50 mm.Results Among the four crown shape designs,the chamfer+non-anatomic type crown showed the lowest von Mises stress and the highest safety factor.By comparing three different materials,the resin-infiltrated ceramic group showed obvious stress concentration on the buccal edge of the crown and the PEKK group showed stress concentration in the adhesive layer.Results of non-axial retention analysis showed that the torques required by the crowns with five thicknesses at the same rotation angle were as follows:4856.1,4038.1,3497.3,3256.3 and 3074.3 N⋅m,respectively.The comparison of areas of the adhesives fracture among groups were as follows:0.5 mm group<0.75 mm group<1.00 mm group<1.25 mm group<1.50 mm group.Conclusions In the design of nonmetallic crowns for primary molars,the edge of the crown should be designed as chamfer,the shape of the inner crown should be non-anatomical and the minimum preparation amount of the occlusal surface should be 1.00 mm.Among the three materials,PMMA resin,of which elastic modulus is similar to the dentin and the dental adhesive,might be the most suitable material for the crowns of primary molars.