矫治力作用下牙颌正畸的弹粘塑性有限元分析
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摘要
口腔正畸治疗是正畸医生利用特定矫治装置,对患者的牙齿、颌骨等组织器官施加特定大小和方向的力,以达到在生理范围内定向移动牙齿、和/或影响颌骨生长之目的,从而矫正患者的牙颌面畸形的一种治疗方法。在正畸治疗中,正确地理解矫治力的传递,以及相应的牙、牙周膜、颌骨等组织受力后的生物力学效应,是正畸医师合理设计矫治力系统、进行有效正畸治疗的前提和基础,也是治疗成败的关键。正畸医师对患者的牙齿、颌骨等组织器官施加矫治力以达到治疗目的是利用各种专门装置来实现的。本文选取了两种正畸治疗系统进行研究,包括微螺钉种植体支抗(以下简称“微植体支抗”,Micro-Implant Anchorage,MIA)系统和Forsus矫治器系统。
微螺钉种植体支抗系统是将生物相容性良好的纯钛材料制成形状不同的螺钉,再根据需要植入颌骨的不同部位,以得到正畸治疗。而以Forsus为代表的固定式功能矫治器则以体积小、弹力持久均匀、矫治力易于控制、安装简便和整体疗程较短等优点,受到了正畸医师的广泛关注,代表了功能矫形治疗发展的趋势。
数值仿真分析是口腔生物力学研究的主要手段之一,已广泛应用于生物力学的研究。采用数值分析方法对微植体支抗系统和Forsus矫治器系统进行仿真分析,利于分析不同前导工况下的力学效应及矫治器的改良,并促进该矫治技术在临床的进一步使用。
论文在充分调研微植体支抗和forsus矫治技术运用的基础上,讨论了骨的弹粘塑性效应,采用UMAT编制弹粘塑性本构模型。紧密结合临床原型,利用CT扫描技术和有限元软件,建立了“微植体支抗-牙-上颌骨”和“Forsus-牙列-上下颌骨-颞下颌关节”三维模型。采用数值分析方法研究了微植体植入上颌骨后骨的动力学响应过程,揭示了在正畸力作用下上颌骨的应力场和变形场特别是塑性变形的时效过程,研究了Forsus对于下颌前导在不同工况下牙列、颌骨、颞下颌关节的应力场和应变场演化,以及Forsus反作用力推上颌第一磨牙向远中的力学效应,为微螺钉种植体支抗系统和Forsus矫治器系统的优化设计提供理论依据和指导。论文的主要工作和结论如下:
①回顾了正畸生物力学的研究现状,对有限元方法在口腔正畸数值模拟中的应用做了综述,重点考察了微植体支抗和Forsus矫治器技术在口腔正畸中的应用及研究。
②利用弹性元件、粘性元件和塑性元件的组合来构建骨的弹粘塑性本构关系。特别是在正畸矫治力作用下,骨具有时效特性的弹粘塑性本构模型。
③利用CT扫描技术、Mimics医学成像软件及ABAQUS软件,提出了计及上颌骨的弹粘塑性性质的建模方法,成功建立了逼真的微植体支抗-牙-上颌骨和三维整体模型,极大地提高了模型的几何相似性,探索了快速构建牙颌组织三维有限元模型的新方法。在充分考虑了微植体、牙、颌骨的时空变化特性的基础上,重点考察骨的时效特性,探讨微植体、牙、上颌骨随矫治时间变化的生物力学过程。
④基于各向同性、非线性、弹粘塑性的“Forsus-牙列-上下颌骨-颞下颌关节”模型,利用有限元方法研究Forsus导下颌向前不同工况下牙列、颌骨、颞下颌关节的力学分布状况,重点观察牙齿、颌骨和颞下颌关节的应力场和位移场的变化。在计及骨的粘性效应基础上,采用ABAQUS运动仿真技术动态分析Forsus反作用力推上颌第一磨牙向远中的力学效应。在此基础上给出了Forsus加载角度推荐范围、髁突生长改建范围和第一磨牙远中平移效果的方法。
The improvement of malocclusion is achieved by the mechanical force with a certain magnitude and direction through certain orthodontic appliance. Stress-strain distribution in the periodontal ligament and the surrounding alveolar bone which determines the mode of tooth movement help clinic orthodontist master the effective way of tooth movement. According to Newton’s third law, the force added to the orthodontic appliance will inevitably cause a force with the same magnitude and opposite direction. The counterforce must be resisted by a certain kind of organ or instrument such as headgear and TPA. Two orthodontic systems, Micro-implant anchorage (MIA) and Forsus appliance are selected.
Micro-implant anchorage (MIA) system is the special screw made of pure titanium material with good bio-compatibility. The screws were inserted into the alveolar ridge or upper and lower jaw bone of different site to get orthodontic treatment. In recent years, a great number of orthodontic doctors pay close attention to fixed appliance of Forsus, for such appliance is small in size, has more durable and homogeneous elastic force and easy to control too. What’s more, the installation is much easier and the course of treatment is shorter in general. In a word, fixed appliance suggests the new developmental trend of the orthopedic treatment appliance.
Numerical simulation analysis is one important means in oral biomechanical study, and it has been widely used in biomechanical study. By using the simulated analysis of the MIA system and the Forsus orthopedic force system, the different mechanical effects can be analyzed under different anterior guidance operating conditions, and the analysis improves the clinical application of the appliance as well.
In this dissertation, on the basis of the research on the application of MIA and the clinic treatment, elastic-viscoplasticity of bone is discussed. The UMAT program considering elastic-viscoplasticity constitutive relationship of material is written, combining with CT scan technique and FEM software, a numeral MIA-teeth-maxilla three-dimensional model was established. The dynamics response process of bone was investigated after the mini-screw inserted. A numerical analysis was presented for stress and strain transformation process in maxilla when under the orthodontic loadings. It provide an important scientific criterion for the optimize of MIA. The main work and conclusions in this dissertation are as follows:
①Advancement what have been made in recent years about orthodontic biomechanics was reviewed in this dissertation. Finite element method in orthodontic numerical simulation was summarized. The application and investigation of MIA in orthodontical treatment were reviewed as the focus.
②Use elastic, viscous and plastic parts to construct a elastic-viscoplastic constitutive relation of bone. Especially, under loading of orthodontic force, constitutive model of bone considering timing characteristics is given out.
③By CT scan technique, Mimics and ABAQUS, a new modeling method was presented. A reality MIA-tooth-maxilla three-dimensional model was established. The geometry comparability of model was improved in the extreme. And a new method to construct maxilla and teeth model quickly was explored. On the basis of full considering the change of time and space properties of MIA、teeth and maxilla, emphasis is on timing characteristics of bone, biomechanical progress of MIA、teeth and maxilla with orthodontic time increasing is discussed.
④A 3D model of Forsus-Dent-uperand lower jaw-TMJ with some visvelasto-plastic characters is built with isotropic,non-linearity and elastic- viscoplastic characteristics in the study. The mechanical behaviors of dentition, jaws and TMJ are studied by finite element method. The stress and displacement of dentition, jaws and TMJ are mainly researched in the study. Base on what is mentioned above, the paper recommend the load angle range of Forsus and scope of condylar reconstruction.
微螺钉种植体支抗系统是将生物相容性良好的纯钛材料制成形状不同的螺钉,再根据需要植入颌骨的不同部位,以得到正畸治疗。而以Forsus为代表的固定式功能矫治器则以体积小、弹力持久均匀、矫治力易于控制、安装简便和整体疗程较短等优点,受到了正畸医师的广泛关注,代表了功能矫形治疗发展的趋势。
数值仿真分析是口腔生物力学研究的主要手段之一,已广泛应用于生物力学的研究。采用数值分析方法对微植体支抗系统和Forsus矫治器系统进行仿真分析,利于分析不同前导工况下的力学效应及矫治器的改良,并促进该矫治技术在临床的进一步使用。
论文在充分调研微植体支抗和forsus矫治技术运用的基础上,讨论了骨的弹粘塑性效应,采用UMAT编制弹粘塑性本构模型。紧密结合临床原型,利用CT扫描技术和有限元软件,建立了“微植体支抗-牙-上颌骨”和“Forsus-牙列-上下颌骨-颞下颌关节”三维模型。采用数值分析方法研究了微植体植入上颌骨后骨的动力学响应过程,揭示了在正畸力作用下上颌骨的应力场和变形场特别是塑性变形的时效过程,研究了Forsus对于下颌前导在不同工况下牙列、颌骨、颞下颌关节的应力场和应变场演化,以及Forsus反作用力推上颌第一磨牙向远中的力学效应,为微螺钉种植体支抗系统和Forsus矫治器系统的优化设计提供理论依据和指导。论文的主要工作和结论如下:
①回顾了正畸生物力学的研究现状,对有限元方法在口腔正畸数值模拟中的应用做了综述,重点考察了微植体支抗和Forsus矫治器技术在口腔正畸中的应用及研究。
②利用弹性元件、粘性元件和塑性元件的组合来构建骨的弹粘塑性本构关系。特别是在正畸矫治力作用下,骨具有时效特性的弹粘塑性本构模型。
③利用CT扫描技术、Mimics医学成像软件及ABAQUS软件,提出了计及上颌骨的弹粘塑性性质的建模方法,成功建立了逼真的微植体支抗-牙-上颌骨和三维整体模型,极大地提高了模型的几何相似性,探索了快速构建牙颌组织三维有限元模型的新方法。在充分考虑了微植体、牙、颌骨的时空变化特性的基础上,重点考察骨的时效特性,探讨微植体、牙、上颌骨随矫治时间变化的生物力学过程。
④基于各向同性、非线性、弹粘塑性的“Forsus-牙列-上下颌骨-颞下颌关节”模型,利用有限元方法研究Forsus导下颌向前不同工况下牙列、颌骨、颞下颌关节的力学分布状况,重点观察牙齿、颌骨和颞下颌关节的应力场和位移场的变化。在计及骨的粘性效应基础上,采用ABAQUS运动仿真技术动态分析Forsus反作用力推上颌第一磨牙向远中的力学效应。在此基础上给出了Forsus加载角度推荐范围、髁突生长改建范围和第一磨牙远中平移效果的方法。
The improvement of malocclusion is achieved by the mechanical force with a certain magnitude and direction through certain orthodontic appliance. Stress-strain distribution in the periodontal ligament and the surrounding alveolar bone which determines the mode of tooth movement help clinic orthodontist master the effective way of tooth movement. According to Newton’s third law, the force added to the orthodontic appliance will inevitably cause a force with the same magnitude and opposite direction. The counterforce must be resisted by a certain kind of organ or instrument such as headgear and TPA. Two orthodontic systems, Micro-implant anchorage (MIA) and Forsus appliance are selected.
Micro-implant anchorage (MIA) system is the special screw made of pure titanium material with good bio-compatibility. The screws were inserted into the alveolar ridge or upper and lower jaw bone of different site to get orthodontic treatment. In recent years, a great number of orthodontic doctors pay close attention to fixed appliance of Forsus, for such appliance is small in size, has more durable and homogeneous elastic force and easy to control too. What’s more, the installation is much easier and the course of treatment is shorter in general. In a word, fixed appliance suggests the new developmental trend of the orthopedic treatment appliance.
Numerical simulation analysis is one important means in oral biomechanical study, and it has been widely used in biomechanical study. By using the simulated analysis of the MIA system and the Forsus orthopedic force system, the different mechanical effects can be analyzed under different anterior guidance operating conditions, and the analysis improves the clinical application of the appliance as well.
In this dissertation, on the basis of the research on the application of MIA and the clinic treatment, elastic-viscoplasticity of bone is discussed. The UMAT program considering elastic-viscoplasticity constitutive relationship of material is written, combining with CT scan technique and FEM software, a numeral MIA-teeth-maxilla three-dimensional model was established. The dynamics response process of bone was investigated after the mini-screw inserted. A numerical analysis was presented for stress and strain transformation process in maxilla when under the orthodontic loadings. It provide an important scientific criterion for the optimize of MIA. The main work and conclusions in this dissertation are as follows:
①Advancement what have been made in recent years about orthodontic biomechanics was reviewed in this dissertation. Finite element method in orthodontic numerical simulation was summarized. The application and investigation of MIA in orthodontical treatment were reviewed as the focus.
②Use elastic, viscous and plastic parts to construct a elastic-viscoplastic constitutive relation of bone. Especially, under loading of orthodontic force, constitutive model of bone considering timing characteristics is given out.
③By CT scan technique, Mimics and ABAQUS, a new modeling method was presented. A reality MIA-tooth-maxilla three-dimensional model was established. The geometry comparability of model was improved in the extreme. And a new method to construct maxilla and teeth model quickly was explored. On the basis of full considering the change of time and space properties of MIA、teeth and maxilla, emphasis is on timing characteristics of bone, biomechanical progress of MIA、teeth and maxilla with orthodontic time increasing is discussed.
④A 3D model of Forsus-Dent-uperand lower jaw-TMJ with some visvelasto-plastic characters is built with isotropic,non-linearity and elastic- viscoplastic characteristics in the study. The mechanical behaviors of dentition, jaws and TMJ are studied by finite element method. The stress and displacement of dentition, jaws and TMJ are mainly researched in the study. Base on what is mentioned above, the paper recommend the load angle range of Forsus and scope of condylar reconstruction.
引文
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