（牙合）面厚度与肩台宽度连续变化的下颌第一磨牙全瓷冠三维有限元分析

Selection of optimal occlusal thickness and shoulder thickness in mandibular first molar all-ceramic crown： a three-dimensional finite element analysis

目的 探讨（牙合）面厚度和肩台宽度同时连续变化情况下下颌第一磨牙全瓷冠的优化设计,以期为全瓷冠的临床设计提供理论基础.方法 运用逆向工程及计算机辅助设计技术建立（牙合）面厚度和肩台宽度连续变化的下颌第一磨牙三维有限元模型,设定（牙合）面厚度变化范围为1～3 mm,肩台宽度变化范围为0.4～1.2 mm,并在全瓷冠颊尖垂直向（牙合）面加载225 N的力,观察验面厚度和肩台宽度同时变化对全瓷冠、粘接剂、基牙、牙周膜和牙槽骨等效应力峰值的影响,同时进行灵敏度分析.结果 随着（牙合）面厚度和肩台宽度的增加,除牙周膜和牙槽骨的等效应力峰值无明显变化外,全瓷冠、粘接剂和基牙的等效应力峰值均下降.当（牙合）面厚度≥1.87 mm、肩台宽度≥0.66 mm时,全瓷冠、粘接剂和基牙的应力响应曲线斜率均位于-1～1之间,即在此区间内等效应力峰值变化相对较小.灵敏度分析显示,肩台宽度对全瓷冠和基牙等效应力峰值的影响较大,（牙合）面厚度对粘接剂等效应力峰值的影响较大.结论 在本项研究所设定的参数范围内,下颌第一磨牙全瓷冠的（牙合）面厚度应不小于1.87 mm,肩台宽度应不小于0.66 mm.

Objective To investigate the effect of different occlusal thickness and shoulder finish line depth on stress distribution of all-ceramic crowns and to select optimal occlusal thickness and shoulder finish line depth using continuous variation of parameters. Methods This analysis was performed using mandibular first molar finite element modl. The range of occlusal thickness was set from 1 mm to 3 mm, and that of shoulder finish line depth was from 0. 4 mm to 1.2 mm. Load of 225 N was applied perpendicularly to the occlusal surface of the tooth at all buccal cusps to simulate functional occlusal force. The maximum equivalent stresses in crown, cement layer, abutment, periodontal ligament, alveolar bone were calculated, and the sensitivities of stresses to the variables were also evaluated. Results The maximum equivalent stresses in crown, cement layer and abutment decreased as occlusal thickness and shoulder finish line depth were increased, while no obvious change were found in maximum equivalent stresses in periodontal ligament and alveolar bone. When occlusal thickness exceeded 1.87 mm and shoulder finish line depth exceeded 0. 66 mm,the tangent slope rate of the maximum equivalent stress response curves ranged from - 1 to 1. Data indicated that occlusal thickness played a more important role in reducing maximum equivalent stress in cement layer than finish line depth did, and shoulder finish line depth was a more effective parameter in reducing maximum equivalent stress in crown and abutment than occlusal thickness was. Conclusions Occlusal thickness exceeding 1.87 mm and shoulder finish line depth exceeding 0. 66 mm are optimal design for ceramic crown on mandibular first molar from biomechanical point of view.