上颌窦区种植修复的生物力学优化设计分析
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摘要
种植义齿具有活动义齿、固定义齿无法比拟的优势,被称为“人类的第三副牙齿”,现代种植早期,只有骨量充足的患者才可能进行种植修复。上、下颌骨前牙区由于其解剖特点被认为是进行种植修复的安全的区域,上颌后牙区骨质较疏松,同时由于上颌窦的存在,当牙槽嵴发生吸收,常导致牙槽嵴顶与上颌窦底距离过小,垂直骨量不足,在进行牙种植术时,种植体难以获得满意的初期稳定性或穿透上颌窦黏膜而导致种植的失败。在相当长的一段时间内,骨质较差骨量不足的患者被列入种植的禁忌证。随着骨缺损重建技术和正颌外科技术的进步,为骨量不足患者的种植修复提供了技术支持,上颌后牙区也成为种植治疗的常规位置。
一个成功的人工种植体应该和骨组织直接结合,将咀嚼力均匀合理地分布到周围骨组织,形成良好的生物力学相容性。种植体骨结合效果不佳或者应力分布不合理,都无益于种植体周围骨组织的重建,将可能导致种植修复的失败。各国学者在种植体生物力学相容性方面进行了大量的研究,目前公认影响种植修复生物力学特性的主要因素包括:种植体材料、种植体的宏观结构设计、种植体的表面处理、修复体设计、连接设计、颌骨的生物力学特性等。
以往针对上颌后牙区种植修复的生物力学分析,多为单因素、静态、离散观测,同时很多缺少纵向和横向的比较,不能准确、完整、有效的获取种植修复的生物力学信息。本课题拟利用结构光三维扫描技术、Pro/E机械设计软件和Ansys Workbench DesignXplorer优化设计模块,采用多因素、连续性、多目标优化分析,为不同情况下,上颌后牙区种植修复的临床设计选择和应用最佳的种植体提供理论依据,为保障上颌窦区种植修复的远期成功率奠定基础。
实验一:包含种植体的上颌窦区三维有限元模型的建立
应用结构光三维扫描技术、Pro/E与Ansys Workbench软件,借助自适应建模、双向参数传递功能,建立可随种植体参数变化的包含上颌骨骨块和种植体-基台复合体的三维有限元模型,力学加载后进行模型的准确性检测。该建模方法简化了有限元前处理过程,提高了建模的速度和精度,并且增加了模型的灵活性和扩展性,为后期进行上颌后牙区种植体的优化选择分析提供良好的模型支持。
实验二:窦嵴距充足时,种植体直径和长度的双变量优化分析
利用实验一建立的模型,设定窦嵴距为12mm,将种植体直径(D)和种植体长度(L)为优化变量,D变化范围为3-5mm,L为6-12 mm。应用皮质骨和松质骨的EQV应力峰值和种植体—基台复合体的位移峰值为评估指标。通过计算,结果提示:种植体直径的增大更有利于改善颊舌向力的力学分布,种植体长度的增大有利于改善垂直向力的力学分布;在临床上选择种植体时,只要骨量允许,种植体直径应不小于4.20mm,同时种植体长度应不小于9.50mm;相对于种植体长度而言应更重视直径的选择和设计。
实验三:窦嵴距高度变化时,颌骨的应力分析
本实验中设定窦嵴距高度(P)为优化目标,P变化范围为6-12mm。通过计算,评估指标同实验一,结果显示:窦嵴距的高度更易影响垂直向加载下皮质骨的应力大小;窦嵴距的高度发生变化时,对垂直向加载下松质骨的应力大小和种植体的稳定性影响较大;在上颌窦区进行种植修复时,理想的窦嵴距应不小于10.00mm。
实验四:窦嵴距等于8mm时,种植体长度的单变量优化分析
本实验中设定种植体长度(L)为优化目标,L变化范围为8-12mm。通过计算,结果显示:种植体的长度更易影响垂直加载下松质骨的应力大小;种植体的长度对侧向加载下皮质骨的应力大小和种植体的稳定性影响不大;从生物力学和临床角度考虑,种植体末端不宜进入上颌窦过长,刚刚穿透上颌窦底即可。
实验五:窦嵴距等于8mm时,种植体直径的单变量优化分析
本实验中设定种植体直径(D)为优化目标,D变化范围为3.00mm-6.00mm。通过计算,结果显示:种植体的直径更易影响垂直向加载下松质骨的应力大小;种植体的直径对侧向加载下皮质骨的应力大小和种植体的稳定性影响较大。从生物力学角度考虑,当窦嵴距较小时,种植体的直径应不小于4.50mm。
实验六:上颌窦区种植体螺纹高度和宽度的优化分析
本实验中设定种植体螺纹高度(H)和宽度(W)同时设为优化目标,变量H变化范围为0.20-0.60mm,变量W变化范围为0.10-0.40mm。通过计算,结果显示:种植体的螺纹高度和宽度的增大更有利于改善垂直向力的力学分布,对于改善垂直和颊舌向加载时种植体的稳定性影响无显著差异;在临床上选择种植体时,从生物力学角度而言,螺纹高度大于0.40mm同时宽度大于0.26mm时为螺纹种植体的最优设计;相对于螺纹种植体的宽度而言应更重视高度的选择和设计。
实验七:上颌窦区植骨三维有限元模型的建立
本实验以实验一建立的三维有限元模型为基础,建立了包含上颌骨、植骨骨块和种植体-基台复合体的三维有限元模型,为进行上颌窦区植骨修复的优化设计分析奠定良好的技术平台和实验基础。
实验八:上颌窦区植骨高度和宽度的优化分析
本实验中设定植骨高度(T)和宽度(R)同时设为优化目标,变量T变化范围为1-6mm,变量R变化范围为5-10mm。通过计算,结果显示:在进行上颌窦区植骨术中,植骨骨块的高度和宽度的增大更有利于改善垂直向力的力学分布;在临床上进行上颌窦区植骨术时,从生物力学角度而言,植骨高度大于3.00mm和同时宽度不少于8.50mm时为植骨骨块的最优设计;相对于植骨骨块高度而言应更重视保障种植体周围植骨宽度,以保证充足骨量。
综上所述,从生物力学角度考虑,对上颌窦区进行种植修复时:当窦嵴距骨量充足时,种植体直径最好不小于4.20mm、长度不小于9.50mm;当窦嵴距骨量轻度不足,可考虑使用大直径种植体进行代偿,直径应不小于4.50mm,种植体末端不宜穿通上颌窦底过长,刚刚穿透上颌窦底即可,此时种植体的螺纹设计应保障螺纹高度大于0.40mm、宽度大于0.25mm;当窦嵴距严重不足时应植骨,植骨高度应不小于3.00mm、宽度不少于8.50mm。
With the outstanding advantages of the implant denture, the implant denture has been regarded as“the third teeth of human beings”. At the beginning of the contemporary dental implant era, the patients with better bone quality and quantity have been listed as the indication. The anterior mandible was primary implant site because it demonstrated remarkably good results in long-term follow-up studies. Patients with poorer bone quality and less quantity of bone, especially in the posterior region of maxilla, have been excluded from implant treatment for a long time. Because implant treatment of the edentulous posterior maxilla occasionally meet with problems due to the lack of bone volume beneath the maxillary sinus cavity. Resorption of the alveolar process after loss of posterior teeth support can proceed either from the oral side or by expansion of the sinus cavity into the alveolar process. The stability of the implant can be reduced and if implant break through the mucosa, which can result to the failure of the implant. Different bone grafting techniques have been developed and orthognathic surgical procedures adapted to the special demands of implant surgery have meant that most bone problems can now be solved.
The success of the dental implant should represent osseointegration with the bone. The implant should behavior better biomechanics compatibility except biocompatibility for better distribution of the stress in jaw bones. Excessive load on the interface of implant and bone caused by stress centralizing can induce the absorption of the bone around implant even result the failure of the implant. Lots of researches have demonstrated that the factors influencing implant biomechanics transmission of occlusal forces include implant material, macrostructure, surface treatment, prosthetic restoration design, connection design, and biomechanics characteristic of jaw bone et.al.
Many of the studies about biomechanics characteristic of implant in posterior maxilla region were univariate, discrete and independent. And these findings were insufficient and inaccurate. The main aim of the present study, through the 3DSS structure light scanning techniques, Pro/E and Ansys Workbench DesignXplorer mechanical engineering optimum technology, to analysis the implant optimum selection in different situations systematically. And provided us the theoretical references for the clinical design and selection of dental implant in the sinus region.
Experiment 1
A maxillary segment in the sinus region with an implant and a superstructure was modeled using Pro/E, Ansys Workbench and Three Dimensional Sensing System (3DSS). The implant-bone complexes were assembled based on implant parameters by self-adapting assembled programme of Pro/E. Then the models were imported to Ansys Workbench software by bidirectional parameters transmitting of the two softwares. Self-adapting assembled 3D finite element analysis models of dental implant-bone complexes were rebuild and the accuracy of the models was also evaluated. The self-adapting assembled models provide the technical platform for further implant optimum design and analysis.
Experiment 2
Implant-bone complex models in experiment 1 were applied in this experiment. The vertical height of bone in sinus region was set as 12.00 mm. Implant diameter (D) and implant length (L) were set as input variables. D ranged from 3.00 mm to 5.00 mm, and L ranged from 6.00 mm to 16.00 mm. The Max EQV stresses in jaw bone and Max displacements in implant-abutment complex were set as evaluation targets. The results showed that larger implant diameter can improve the buccal-lingual stress distribution while larger implant length can improve the vertical stress distribution. Implant diameter exceeding 4.20 mm and implant length exceeding 9.50 mm are optimal selection for a cylinder implant in clinic, given that there is sufficient bone quality. Implant diameter is more important than implant length in implant selection and design.
Experiment 3
In this experiment, vertical height of bone in sinus region (P) was set as input variable. P ranged from 6.00 mm to 12.00 mm. Evaluation targets setting was as same as experiment 2. The results showed that P was apt to affect the cortical bone stress and implant stability under AX load. P should exceed 10.00 mm in the sinus region.
Experiment 4
In this experiment, implant length (L) was set as input variable. L ranged from 8.00 mm to 12.00 mm. Evaluation targets setting was as same as experiment 2. The results showed that L plays an important part in cancellous bone stress under AX load and have little effect on cortical bone stress and implant stability under BL load. Implant should just penetrate sinus floor by biomechanical and clinical consideration.
Experiment 5
In this experiment, implant diameter (D) was set as input variable. D ranged from 3.00 mm to 6.00 mm. Evaluation targets setting was as same as experiment 2. The results showed that D favored cancellous bone stress under AX load, as well as cortical bone stress and implant stability under BL load. When there is insufficient bone height, implant diameter should exceed 4.50 mm by biomechanical consideration.
Experiment 6
In this experiment, implant thread height (H) and thread width (W) were set as input variables. H ranged from 0.20 mm to 0.60 mm, and W ranged from 0.10 mm to 0.40 mm. The results showed that with the increasing of H and W, better stress distribution under AX load could be achieved, while there were little changes in the implant stability under both AX and BL loads. Thread height exceeding 0.40 mm and thread width exceeding 0.26 mm are optimal selection for a screwed implant by biomechanical consideration. Thread height is more important than thread width in implant selection and design.
Experiment 7
In this experiment, 3D finite model including maxilla, grafted bone and implant-abutment complex was created based on the modes in experiment 1. This model provides the technical platform for the optimum design and analysis of bone grafting in the sinus region.
Experiment 8
In this experiment, grafted bone height (T) and width (R) were set as input variables. T ranged from 1.00 mm to 6.00 mm, and W ranged from 5.00 mm to 10.00 mm. The results showed that with the increasing of T and R, better stress distribution under AX load could be achieved in the bone grafting in the sinus region. T exceeding 3.00 mm and R exceeding 8.50 mm are optimal selection by biomechanical consideration. R is more important than T in bone grafting in the sinus region.
To sum up, when there is sufficient bone quality, implant diameter should exceed 4.20 mm and implant length should exceed 9.50 mm. Meanwhile, implant with diameter exceeding 4.50 mm is more suitable to the region with insufficient bone quality. In this condition, implant tip should just penetrate sinus floor. Implant thread height should exceed 0.40 mm and implant thread width should exceed 0.25 mm. In bone grafting, grafted bone height should exceed 3.00 mm and bone width should exceed 8.50 mm.
一个成功的人工种植体应该和骨组织直接结合,将咀嚼力均匀合理地分布到周围骨组织,形成良好的生物力学相容性。种植体骨结合效果不佳或者应力分布不合理,都无益于种植体周围骨组织的重建,将可能导致种植修复的失败。各国学者在种植体生物力学相容性方面进行了大量的研究,目前公认影响种植修复生物力学特性的主要因素包括:种植体材料、种植体的宏观结构设计、种植体的表面处理、修复体设计、连接设计、颌骨的生物力学特性等。
以往针对上颌后牙区种植修复的生物力学分析,多为单因素、静态、离散观测,同时很多缺少纵向和横向的比较,不能准确、完整、有效的获取种植修复的生物力学信息。本课题拟利用结构光三维扫描技术、Pro/E机械设计软件和Ansys Workbench DesignXplorer优化设计模块,采用多因素、连续性、多目标优化分析,为不同情况下,上颌后牙区种植修复的临床设计选择和应用最佳的种植体提供理论依据,为保障上颌窦区种植修复的远期成功率奠定基础。
实验一:包含种植体的上颌窦区三维有限元模型的建立
应用结构光三维扫描技术、Pro/E与Ansys Workbench软件,借助自适应建模、双向参数传递功能,建立可随种植体参数变化的包含上颌骨骨块和种植体-基台复合体的三维有限元模型,力学加载后进行模型的准确性检测。该建模方法简化了有限元前处理过程,提高了建模的速度和精度,并且增加了模型的灵活性和扩展性,为后期进行上颌后牙区种植体的优化选择分析提供良好的模型支持。
实验二:窦嵴距充足时,种植体直径和长度的双变量优化分析
利用实验一建立的模型,设定窦嵴距为12mm,将种植体直径(D)和种植体长度(L)为优化变量,D变化范围为3-5mm,L为6-12 mm。应用皮质骨和松质骨的EQV应力峰值和种植体—基台复合体的位移峰值为评估指标。通过计算,结果提示:种植体直径的增大更有利于改善颊舌向力的力学分布,种植体长度的增大有利于改善垂直向力的力学分布;在临床上选择种植体时,只要骨量允许,种植体直径应不小于4.20mm,同时种植体长度应不小于9.50mm;相对于种植体长度而言应更重视直径的选择和设计。
实验三:窦嵴距高度变化时,颌骨的应力分析
本实验中设定窦嵴距高度(P)为优化目标,P变化范围为6-12mm。通过计算,评估指标同实验一,结果显示:窦嵴距的高度更易影响垂直向加载下皮质骨的应力大小;窦嵴距的高度发生变化时,对垂直向加载下松质骨的应力大小和种植体的稳定性影响较大;在上颌窦区进行种植修复时,理想的窦嵴距应不小于10.00mm。
实验四:窦嵴距等于8mm时,种植体长度的单变量优化分析
本实验中设定种植体长度(L)为优化目标,L变化范围为8-12mm。通过计算,结果显示:种植体的长度更易影响垂直加载下松质骨的应力大小;种植体的长度对侧向加载下皮质骨的应力大小和种植体的稳定性影响不大;从生物力学和临床角度考虑,种植体末端不宜进入上颌窦过长,刚刚穿透上颌窦底即可。
实验五:窦嵴距等于8mm时,种植体直径的单变量优化分析
本实验中设定种植体直径(D)为优化目标,D变化范围为3.00mm-6.00mm。通过计算,结果显示:种植体的直径更易影响垂直向加载下松质骨的应力大小;种植体的直径对侧向加载下皮质骨的应力大小和种植体的稳定性影响较大。从生物力学角度考虑,当窦嵴距较小时,种植体的直径应不小于4.50mm。
实验六:上颌窦区种植体螺纹高度和宽度的优化分析
本实验中设定种植体螺纹高度(H)和宽度(W)同时设为优化目标,变量H变化范围为0.20-0.60mm,变量W变化范围为0.10-0.40mm。通过计算,结果显示:种植体的螺纹高度和宽度的增大更有利于改善垂直向力的力学分布,对于改善垂直和颊舌向加载时种植体的稳定性影响无显著差异;在临床上选择种植体时,从生物力学角度而言,螺纹高度大于0.40mm同时宽度大于0.26mm时为螺纹种植体的最优设计;相对于螺纹种植体的宽度而言应更重视高度的选择和设计。
实验七:上颌窦区植骨三维有限元模型的建立
本实验以实验一建立的三维有限元模型为基础,建立了包含上颌骨、植骨骨块和种植体-基台复合体的三维有限元模型,为进行上颌窦区植骨修复的优化设计分析奠定良好的技术平台和实验基础。
实验八:上颌窦区植骨高度和宽度的优化分析
本实验中设定植骨高度(T)和宽度(R)同时设为优化目标,变量T变化范围为1-6mm,变量R变化范围为5-10mm。通过计算,结果显示:在进行上颌窦区植骨术中,植骨骨块的高度和宽度的增大更有利于改善垂直向力的力学分布;在临床上进行上颌窦区植骨术时,从生物力学角度而言,植骨高度大于3.00mm和同时宽度不少于8.50mm时为植骨骨块的最优设计;相对于植骨骨块高度而言应更重视保障种植体周围植骨宽度,以保证充足骨量。
综上所述,从生物力学角度考虑,对上颌窦区进行种植修复时:当窦嵴距骨量充足时,种植体直径最好不小于4.20mm、长度不小于9.50mm;当窦嵴距骨量轻度不足,可考虑使用大直径种植体进行代偿,直径应不小于4.50mm,种植体末端不宜穿通上颌窦底过长,刚刚穿透上颌窦底即可,此时种植体的螺纹设计应保障螺纹高度大于0.40mm、宽度大于0.25mm;当窦嵴距严重不足时应植骨,植骨高度应不小于3.00mm、宽度不少于8.50mm。
With the outstanding advantages of the implant denture, the implant denture has been regarded as“the third teeth of human beings”. At the beginning of the contemporary dental implant era, the patients with better bone quality and quantity have been listed as the indication. The anterior mandible was primary implant site because it demonstrated remarkably good results in long-term follow-up studies. Patients with poorer bone quality and less quantity of bone, especially in the posterior region of maxilla, have been excluded from implant treatment for a long time. Because implant treatment of the edentulous posterior maxilla occasionally meet with problems due to the lack of bone volume beneath the maxillary sinus cavity. Resorption of the alveolar process after loss of posterior teeth support can proceed either from the oral side or by expansion of the sinus cavity into the alveolar process. The stability of the implant can be reduced and if implant break through the mucosa, which can result to the failure of the implant. Different bone grafting techniques have been developed and orthognathic surgical procedures adapted to the special demands of implant surgery have meant that most bone problems can now be solved.
The success of the dental implant should represent osseointegration with the bone. The implant should behavior better biomechanics compatibility except biocompatibility for better distribution of the stress in jaw bones. Excessive load on the interface of implant and bone caused by stress centralizing can induce the absorption of the bone around implant even result the failure of the implant. Lots of researches have demonstrated that the factors influencing implant biomechanics transmission of occlusal forces include implant material, macrostructure, surface treatment, prosthetic restoration design, connection design, and biomechanics characteristic of jaw bone et.al.
Many of the studies about biomechanics characteristic of implant in posterior maxilla region were univariate, discrete and independent. And these findings were insufficient and inaccurate. The main aim of the present study, through the 3DSS structure light scanning techniques, Pro/E and Ansys Workbench DesignXplorer mechanical engineering optimum technology, to analysis the implant optimum selection in different situations systematically. And provided us the theoretical references for the clinical design and selection of dental implant in the sinus region.
Experiment 1
A maxillary segment in the sinus region with an implant and a superstructure was modeled using Pro/E, Ansys Workbench and Three Dimensional Sensing System (3DSS). The implant-bone complexes were assembled based on implant parameters by self-adapting assembled programme of Pro/E. Then the models were imported to Ansys Workbench software by bidirectional parameters transmitting of the two softwares. Self-adapting assembled 3D finite element analysis models of dental implant-bone complexes were rebuild and the accuracy of the models was also evaluated. The self-adapting assembled models provide the technical platform for further implant optimum design and analysis.
Experiment 2
Implant-bone complex models in experiment 1 were applied in this experiment. The vertical height of bone in sinus region was set as 12.00 mm. Implant diameter (D) and implant length (L) were set as input variables. D ranged from 3.00 mm to 5.00 mm, and L ranged from 6.00 mm to 16.00 mm. The Max EQV stresses in jaw bone and Max displacements in implant-abutment complex were set as evaluation targets. The results showed that larger implant diameter can improve the buccal-lingual stress distribution while larger implant length can improve the vertical stress distribution. Implant diameter exceeding 4.20 mm and implant length exceeding 9.50 mm are optimal selection for a cylinder implant in clinic, given that there is sufficient bone quality. Implant diameter is more important than implant length in implant selection and design.
Experiment 3
In this experiment, vertical height of bone in sinus region (P) was set as input variable. P ranged from 6.00 mm to 12.00 mm. Evaluation targets setting was as same as experiment 2. The results showed that P was apt to affect the cortical bone stress and implant stability under AX load. P should exceed 10.00 mm in the sinus region.
Experiment 4
In this experiment, implant length (L) was set as input variable. L ranged from 8.00 mm to 12.00 mm. Evaluation targets setting was as same as experiment 2. The results showed that L plays an important part in cancellous bone stress under AX load and have little effect on cortical bone stress and implant stability under BL load. Implant should just penetrate sinus floor by biomechanical and clinical consideration.
Experiment 5
In this experiment, implant diameter (D) was set as input variable. D ranged from 3.00 mm to 6.00 mm. Evaluation targets setting was as same as experiment 2. The results showed that D favored cancellous bone stress under AX load, as well as cortical bone stress and implant stability under BL load. When there is insufficient bone height, implant diameter should exceed 4.50 mm by biomechanical consideration.
Experiment 6
In this experiment, implant thread height (H) and thread width (W) were set as input variables. H ranged from 0.20 mm to 0.60 mm, and W ranged from 0.10 mm to 0.40 mm. The results showed that with the increasing of H and W, better stress distribution under AX load could be achieved, while there were little changes in the implant stability under both AX and BL loads. Thread height exceeding 0.40 mm and thread width exceeding 0.26 mm are optimal selection for a screwed implant by biomechanical consideration. Thread height is more important than thread width in implant selection and design.
Experiment 7
In this experiment, 3D finite model including maxilla, grafted bone and implant-abutment complex was created based on the modes in experiment 1. This model provides the technical platform for the optimum design and analysis of bone grafting in the sinus region.
Experiment 8
In this experiment, grafted bone height (T) and width (R) were set as input variables. T ranged from 1.00 mm to 6.00 mm, and W ranged from 5.00 mm to 10.00 mm. The results showed that with the increasing of T and R, better stress distribution under AX load could be achieved in the bone grafting in the sinus region. T exceeding 3.00 mm and R exceeding 8.50 mm are optimal selection by biomechanical consideration. R is more important than T in bone grafting in the sinus region.
To sum up, when there is sufficient bone quality, implant diameter should exceed 4.20 mm and implant length should exceed 9.50 mm. Meanwhile, implant with diameter exceeding 4.50 mm is more suitable to the region with insufficient bone quality. In this condition, implant tip should just penetrate sinus floor. Implant thread height should exceed 0.40 mm and implant thread width should exceed 0.25 mm. In bone grafting, grafted bone height should exceed 3.00 mm and bone width should exceed 8.50 mm.
引文
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3. Harris L J et al.Implant failures in orthopaedic surgery[J].Biomat Med Devorg,1979,7: 243-281.
4.熊亚茸,陈新,刘洪臣,等.种植体与天然牙在上颌骨复合体中应力的三维有限元分析[J].口腔颌面修复学杂志,2004,20(1):1-4.
5. Hanawa T. Titanium and its oxide film:A substrate for formation of apatite.In: Davies JE(ed) .Bone-Bimaterial Interface.Toronto: Univ of Toronto Press,1991,49.
6.关豪光,于秦曦.国际种植义齿的发展及现状.中华口腔医学杂志,1995,30:310.
7. Meijer GJ, Cune MS, Vandooren M, et al. Acomparative study of flexible (polyactive)versus rigid(hydroxyapatite permucosal dental implants. Clinical aspects.J Oral Rehabil,1997,24(2):85.
8. Skalak R.Biomechanical considerations in osseointegrated protheses. Journal of Prosthetic Dentistry,1983,49:843~848.
9. Lucie H,Tat’jana D,Alois K,Influence of implant length and diameter on stress distribution:Afiniteelement analysis.J Prosthet Dent,2004, 92 (2):139-44.
10. Atmaram, G.H., Mohammed, H. & Schoen, F.J.Stress analysis of single tooth implants. I. Effects of elastic parameters and geometry of implant. Biomaterials,Medical Devices and Artificial Organs, 7:99~104.
11. Breme J, Biehl V, Schulte W et al. Development and functionality of isoelastic dentalimplants of titanium alloys. Biomaterials, 1993, 14(12):887~892.
12. Meijer GJ, Dalmeijer RA, de Putter C, etal.A comparatine study of flexible(polyactive) versus rigid (hydroxyapatite)permucosal dental implants. II Histological aspects. J Oral Rehabil,1997,24(2):93.
13. Cullinane DM,Einhorn TA.Biomechanics of bone[M]∥Rodan BR.Principles of bone biology.San Diego:Academic Press,2002:17-32.
14. Hoshaw SJ,Brunski JB,Cochran GVB.Mechanical loading of Branemark implants affects interfacial bone modeling and remodeling[J].Int J Oral Maxillofac Implants,1994,9(3):345-360.
15. Iplikcioglu H,Akca K.Comparative evaluation of the effect of diameter, length and number of implants supporting three-unit fixed partial prostheses on stress distribution in the bone[J].J Dent,2002,30(1):41-46.
16. Lum LB. A biomechanical rationale for the use of short implants. J Oral Implantol. 1991,17(2):126-131.
17. Meijer HJA, Kuiper JH, Starmans FJM, Bosman F. Stress distribution around dental implant : influence of superstructure, length of implants and height of mandible. J Prosthetic Dent.1992, 68(1):92-102.
18. Mailath G, Stoiber B, Watzek G, Matejka M. Bone resorption at the entry of osseointegrated implants-a biomechanical phenomenon. Finite element study [in German]. Z Stomatol 1989, 86(4):207-216.
19. Matsushita Y, Kitoh M, Mizuta K, Ikeda H, Suetsugu T. Two-dimensional FEM analysis of hydroxyapatite implants: diameter effects on stress distribution. J Oral Implantol 1990, 16(1):6-11.
20. Tuncelli B,Poyrazoglu E,Koyluoglu AM,et al.Comparison of load transfer by implants abutment of various diameters. Eur J Prosthodont Res Dent,1997,5(2):79.
21. Winkler S,Morris HF,Ochi S.Ann Periodontol,2000,5(1):22-31.
22. Davarpanah M,Martinez H,Kebir M,et al.Int J Periodont Restor Dent,2001, 21(2):149-159.
23. Rieger MR , Mayberry M, Brose MO. Finite elementanalysis of six endosseous implants. J Prost het Dent ,1990 ,63 (6) :671.
24. Tsutsumi S,Fukuda,Tani Y. Biomechanical designingof implants. J Dent Research,1989,68:754~766.
25. Siegele DS,Soltsz U. Numerical investigations of the in-fluence of implant shape on stress distribution in the jawbone. Int J Oral Maxillofac Implants,1989,4:40~45.
26. Patra AK, Depaolo JM, Souza KS, Detolla D, etal.Guidelines for analysis and redesign of dental implants. Implant Dent,1998,7:68~75.
27. Mailth G,Stoiber B,Watzek G, et al. Bone resorptionat the entry of osseointegrated implants-a biomechanical phenomenon. Z Stomatol, 1989,86:162.
28. Holmgren EP,Seckinger RJ,Kilgren LMet al. Evaluating parameters of osseointegrated dental implants using finite element analysis-a two-dimensional comparative study examining the effects of implant diameter,implant shape and load direction. Oral Implantol, 1998, 24: 65~80.
29. Lozada J. Eight year clinical evaluation of HA-coated implants. J Dent Symp, 1993,1:67~69.
30. IvanoffCJ, GrondahlK, Sennerby L, et a.l Influence of variations in implantdiameters: a 3- to5-year retrospective clinical report [J]. Int JOralMaxillofac Implants, 1999, 14∶173-180.
31. Brunski JB. Biomechanical considerations in dental implant design [J]. Int JOral Implanto,l 1988, 5∶31-34.
32. Clelland NL,Lee JK,Gilat A. Use of an axisymmetric finite element method to compare maxillary bone variables for a loaded implant. J Prosthet Dent, 1993, 2(3):183~189.
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