下颌后牙固定桥支持骨组织应力的三维有限元法分析Ⅲ.不同类型固定桥桥体下皮质骨应力的分析比较
作者：唐亮 陈光谦
单位：唐亮(暨南大学医学院口腔系 510632)；陈光谦(中国科学院广州地球化学研究所)
关键词：皮质骨；不同类型桥体 ；三维有限元法；应力
华西口腔医学杂志000117 摘 要：目的:比较下颌后牙固定桥不同类型桥体下皮质骨的应力分布情况。方法:设计临床上常用的3种类型桥体:改良鞍式、改良盖嵴式和盖嵴式桥体,其与桥体下粘膜接触的面积比分别约为1∶2/3∶1/3。用三维有限元法计算出2种载荷的桥体下皮质骨单元的最大主应力(εmax)和最小主应力(εmin)值。结果:3种桥体下皮质骨的应力分布规律相似,但接触面积较大者其皮质骨应力较小,应力最大值分别相差约5%～7%。结论:不同组织接触面积的桥体,对桥体下骨组织应力的影响不大。
Three-dimensional Finite Element Stress Analysis of Supporting Bone of Mandibular Posterior Fixed Bridge Part Ⅲ. Comparative Analysis with Stress of the Cortical Bone Beneath Different Pontics of Fixed Bridge
, 百拇医药
Tang Liang
(Department of Stomatology, Medical College, Jinan University)
Chen Guangqian
(Guangzhou Institute of Geochemistry, Chinese Academy of Sciences)
Abstract：Objective：To analysis stress of the cortical bone beneath different pontics of mandibular posterior fixed bridge by using three-dimentional finite element method. Methods: According to the measured data, the characters of all components of fixed bridge and the supporting tissues, and the principals of finite element, the three-dimentional finite element model was developed on the basis of an adult mandible. The model consisted of 1363 nodes and 1134 elements after the fixed bridge was placed. Three different pontics were designed. Young's mudulus and Poisson's ratio were obtained from the literature for each type of tissue or materials in the model. The surfaces of pontic next to the mucosa beneath the pontic consisted of nine elements and the contact area were respectively reduced 1/3. It was assumed all materials in the model were homogeneous, isotropic and linearly elastic. One vertical load of 20 kg and one horizontal load of 20 kg were applied respectively on the occlusal surface of the abutments and the pontics of three different fixed bridge. Three-dimentional finite element stress analysis was used to calculate the εmax and the εmin of the cortical bone beneath pontics of fixed bridge. Results: Under the vertical loading, the cortical bone beneath the pontics appeared compressive stresses, the stress values of the cortical bone beneath the pontics were respectively -0.211～-0.119 (εmax, kg/mm2), -0.355～-0.201 (εmin), -0.224～-0.125 (εmax), -0.375～-0.215 (εmin), -0.239～-0.133 (εmax), -0.395～-0.228 (εmin).Under the horizontal loading, the cortical bone beneath the pontics exhibited tensile stresses and compressive stresses. The stress values of the cortical bone beneath the pontics were respectively -0.004～0.283 (εmax,kg/mm2), -0.249～-0.009 (εmin), -0.0042～0.301 (εmax), -0.264～-0.0095 (εmin),-0.0045～0.322 (εmax), -0.281～-0.0101 (εmin). The stress in the cortical bone beneath the pontics increased when the area of contact was reduced, the stress values changed in 5%～7%, but the rules of stress distribution of three different pontics were similar. Conclusion: Stress values in the cortical bone beneath three pontics are small, and the change of stress in the cortical bone beneath the different pontics of mandibular posterior fixed bridge is small too.
, 百拇医药
Key words：cortical bone different pontics three-dimensional finite element stress▲
固定桥修复中,桥体组织面形态与接触面积的设计和制作是一个不可忽视的问题。许多学者[1～4]认为组织面高度光滑,在不影响美观、舌感和发音情况下接触面积越小越好。但小面积接触是否会使桥体下骨组织应力大幅度增加,目前尚未见有关报道。本文系通过三维有限元法分析,考察下颌后牙固定桥不同类型桥体下皮质骨的应力分布情况。
1 材料和方法
1.1 三维有限元模型的建立
模型建立、材料力学参数、实验假设,见参考文献[5]。
作者共设计3种不同组织面接触面积的桥体,以分别模拟改良鞍式、改良盖嵴式和盖嵴式桥体。3种桥体组织面接触面积比约为1∶2/3∶1/3,单元数不变,其接触面平面示意图见参考文献[6]。
, http://www.100md.com
1.2 加载条件
垂直向加载和舌颊水平向加载2种方式,各基牙及桥体载荷量分别为20 kg。
1.3 分析方法
用三维有限元法,计算出3种类型桥体下皮质骨单元的最大主应力(εmax)和最小主应力(εmin)值,单位kg/mm2。
2 结 果
2.1 改良鞍式桥体下皮质骨应力
改良鞍式桥体下皮质骨应力结果见参考文献[6]中表2。垂直向加载时,皮质骨均为压应力。εmax范围-0.211～-0.119 kg/mm2;εmin范围-0.355～-0.201 kg/mm2。水平向加载时,εmax大部分为拉应力,范围-0.004～0.283 kg/mm2;εmin均为压应力,范围-0.249～-0.009 kg/mm2。
, 百拇医药
2.2 改良盖嵴式桥体下皮质骨应力
改良盖嵴式桥体下皮质骨应力结果见表1。结果表明,垂直向加载时,皮质骨均为压应力。εmax范围-0.224～-0.125 kg/mm2;εmin范围-0.375～-0.215 kg/mm2。水平向加载时,εmax大部分为拉应力,范围-0.0042～0.301 kg/mm2;εmin均为压应力,范围-0.264～-0.0095 kg/mm2。
表1 改良盖嵴式桥体下皮质骨应力(kg/mm2) 单元号
垂直向加载
水平向加载
, 百拇医药 εmax
εmin
εmax
εmin
708
-0.224
-0.375
0.301
-0.038
709
-0.150
-0.239
, http://www.100md.com
0.072
-0.079
710
-0.125
-0.215
-0.0042
-0.163
711
-0.146
-0.243
-0.069
-0.239
712
, http://www.100md.com
-0.155
-0.254
0.031
-0.109
713
-0.161
-0.267
0.187
-0.0095
714
-0.153
-0.261
0.128
, http://www.100md.com
-0.033
715
-0.154
-0.256
0.0074
-0.119
716
-0.160
-0.263
-0.093
-0.264
2.3 盖嵴式桥体下皮质骨应力
, http://www.100md.com
盖嵴式桥体下皮质骨应力结果见表2。结果表明,垂直向加载时,皮质骨均为压应力。εmax范围-0.239～-0.133 kg/mm2;εmin范围-0.395～-0.228 kg/mm2。水平向加载时,εmax大部分为拉应力,范围-0.0045～0.322 kg/mm2;εmin均为压应力,范围-0.281～-0.0101 kg/mm2。表2 盖嵴式桥体下皮质骨应力(kg/mm2) 单元号
垂直向加载
水平向加载
εmax
εmin
, 百拇医药
εmax
εmin
708
-0.239
-0.395
0.322
-0.040
709
-0.159
-0.243
0.076
-0.084
, http://www.100md.com
710
-0.133
-0.228
-0.0045
-0.174
711
-0.154
-0.257
-0.073
-0.255
712
-0.164
-0.271
, 百拇医药
0.033
-0.115
713
-0.172
-0.284
0.198
-0.0101
714
-0.162
-0.277
0.136
-0.035
715
, 百拇医药
-0.164
-0.261
0.0079
-0.127
716
-0.169
-0.279
-0.099
-0.281
3 讨 论
本文设计了临床上后牙固定桥常采用的3种不同类型的桥体,其组织面与桥体下粘膜接触的面积比分别约为1∶2/3∶1/3。垂直向载荷下,桥体粘膜下皮质骨均表现为压应力;水平向载荷下,拉、压应力并存。3种桥体下皮质骨的应力分布规律相似,只是接触面积较大者其皮质骨应力较小,接触面积较小者,应力有所增加,但变化幅度不大,应力最大值分别相差约5%～7%。故作者初步认为,选择不同组织接触面积的桥体,对桥体下骨组织应力的影响不大。在固定桥桥体设计中,除了满足形态与咀嚼、发音等功能外,还应考虑微生物因素,提高桥体的自洁能力和利于患者的清洁,并注意美观、舒适等因素。■
, 百拇医药
基金项目：本课题为广东省卫生厅资助项目(编号 D42400)
参考文献：
[1]Howard WW. Standards of pontic desighs. J Prosthet Dent, 1982,47(5):493～495
[2]Crispin BJ. Tissue respone to posterior denture base-type pontics. J Prosthet Dent, 1979,42(3):257～261
[3]Smith BGN. Dental Crowns and Bridge:Design and Preparation. 2nd ed. Chicago: Year Book Med Pub, 1990:189～253
, http://www.100md.com
[4]Murray HV, Sluder TB. Fixed Restorative Techniques. Rev. ed. Chapel Hill NC Vniv. of North Carolina Press, 1989:96～107
[5]唐亮,陈光谦.下颌后牙固定桥支持骨组织应力的三维有限元法分析.Ⅰ.固定桥基牙周围牙槽骨的表面应力分析.华西口腔医学杂志,1999,17(4):371～373
[6]唐亮,陈光谦.下颌后牙固定桥支持骨组织应力的三维有限元分析.Ⅱ.固定桥桥体下皮质骨的应力分布.华西口腔医学杂志,1999,17(4):374～376
收稿日期：1999-01-18, 百拇医药
单位：唐亮(暨南大学医学院口腔系 510632)；陈光谦(中国科学院广州地球化学研究所)
关键词：皮质骨；不同类型桥体 ；三维有限元法；应力
华西口腔医学杂志000117 摘 要：目的:比较下颌后牙固定桥不同类型桥体下皮质骨的应力分布情况。方法:设计临床上常用的3种类型桥体:改良鞍式、改良盖嵴式和盖嵴式桥体,其与桥体下粘膜接触的面积比分别约为1∶2/3∶1/3。用三维有限元法计算出2种载荷的桥体下皮质骨单元的最大主应力(εmax)和最小主应力(εmin)值。结果:3种桥体下皮质骨的应力分布规律相似,但接触面积较大者其皮质骨应力较小,应力最大值分别相差约5%～7%。结论:不同组织接触面积的桥体,对桥体下骨组织应力的影响不大。
Three-dimensional Finite Element Stress Analysis of Supporting Bone of Mandibular Posterior Fixed Bridge Part Ⅲ. Comparative Analysis with Stress of the Cortical Bone Beneath Different Pontics of Fixed Bridge
, 百拇医药
Tang Liang
(Department of Stomatology, Medical College, Jinan University)
Chen Guangqian
(Guangzhou Institute of Geochemistry, Chinese Academy of Sciences)
Abstract：Objective：To analysis stress of the cortical bone beneath different pontics of mandibular posterior fixed bridge by using three-dimentional finite element method. Methods: According to the measured data, the characters of all components of fixed bridge and the supporting tissues, and the principals of finite element, the three-dimentional finite element model was developed on the basis of an adult mandible. The model consisted of 1363 nodes and 1134 elements after the fixed bridge was placed. Three different pontics were designed. Young's mudulus and Poisson's ratio were obtained from the literature for each type of tissue or materials in the model. The surfaces of pontic next to the mucosa beneath the pontic consisted of nine elements and the contact area were respectively reduced 1/3. It was assumed all materials in the model were homogeneous, isotropic and linearly elastic. One vertical load of 20 kg and one horizontal load of 20 kg were applied respectively on the occlusal surface of the abutments and the pontics of three different fixed bridge. Three-dimentional finite element stress analysis was used to calculate the εmax and the εmin of the cortical bone beneath pontics of fixed bridge. Results: Under the vertical loading, the cortical bone beneath the pontics appeared compressive stresses, the stress values of the cortical bone beneath the pontics were respectively -0.211～-0.119 (εmax, kg/mm2), -0.355～-0.201 (εmin), -0.224～-0.125 (εmax), -0.375～-0.215 (εmin), -0.239～-0.133 (εmax), -0.395～-0.228 (εmin).Under the horizontal loading, the cortical bone beneath the pontics exhibited tensile stresses and compressive stresses. The stress values of the cortical bone beneath the pontics were respectively -0.004～0.283 (εmax,kg/mm2), -0.249～-0.009 (εmin), -0.0042～0.301 (εmax), -0.264～-0.0095 (εmin),-0.0045～0.322 (εmax), -0.281～-0.0101 (εmin). The stress in the cortical bone beneath the pontics increased when the area of contact was reduced, the stress values changed in 5%～7%, but the rules of stress distribution of three different pontics were similar. Conclusion: Stress values in the cortical bone beneath three pontics are small, and the change of stress in the cortical bone beneath the different pontics of mandibular posterior fixed bridge is small too.
, 百拇医药
Key words：cortical bone different pontics three-dimensional finite element stress▲
固定桥修复中,桥体组织面形态与接触面积的设计和制作是一个不可忽视的问题。许多学者[1～4]认为组织面高度光滑,在不影响美观、舌感和发音情况下接触面积越小越好。但小面积接触是否会使桥体下骨组织应力大幅度增加,目前尚未见有关报道。本文系通过三维有限元法分析,考察下颌后牙固定桥不同类型桥体下皮质骨的应力分布情况。
1 材料和方法
1.1 三维有限元模型的建立
模型建立、材料力学参数、实验假设,见参考文献[5]。
作者共设计3种不同组织面接触面积的桥体,以分别模拟改良鞍式、改良盖嵴式和盖嵴式桥体。3种桥体组织面接触面积比约为1∶2/3∶1/3,单元数不变,其接触面平面示意图见参考文献[6]。
, http://www.100md.com
1.2 加载条件
垂直向加载和舌颊水平向加载2种方式,各基牙及桥体载荷量分别为20 kg。
1.3 分析方法
用三维有限元法,计算出3种类型桥体下皮质骨单元的最大主应力(εmax)和最小主应力(εmin)值,单位kg/mm2。
2 结 果
2.1 改良鞍式桥体下皮质骨应力
改良鞍式桥体下皮质骨应力结果见参考文献[6]中表2。垂直向加载时,皮质骨均为压应力。εmax范围-0.211～-0.119 kg/mm2;εmin范围-0.355～-0.201 kg/mm2。水平向加载时,εmax大部分为拉应力,范围-0.004～0.283 kg/mm2;εmin均为压应力,范围-0.249～-0.009 kg/mm2。
, 百拇医药
2.2 改良盖嵴式桥体下皮质骨应力
改良盖嵴式桥体下皮质骨应力结果见表1。结果表明,垂直向加载时,皮质骨均为压应力。εmax范围-0.224～-0.125 kg/mm2;εmin范围-0.375～-0.215 kg/mm2。水平向加载时,εmax大部分为拉应力,范围-0.0042～0.301 kg/mm2;εmin均为压应力,范围-0.264～-0.0095 kg/mm2。
表1 改良盖嵴式桥体下皮质骨应力(kg/mm2) 单元号
垂直向加载
水平向加载
, 百拇医药 εmax
εmin
εmax
εmin
708
-0.224
-0.375
0.301
-0.038
709
-0.150
-0.239
, http://www.100md.com
0.072
-0.079
710
-0.125
-0.215
-0.0042
-0.163
711
-0.146
-0.243
-0.069
-0.239
712
, http://www.100md.com
-0.155
-0.254
0.031
-0.109
713
-0.161
-0.267
0.187
-0.0095
714
-0.153
-0.261
0.128
, http://www.100md.com
-0.033
715
-0.154
-0.256
0.0074
-0.119
716
-0.160
-0.263
-0.093
-0.264
2.3 盖嵴式桥体下皮质骨应力
, http://www.100md.com
盖嵴式桥体下皮质骨应力结果见表2。结果表明,垂直向加载时,皮质骨均为压应力。εmax范围-0.239～-0.133 kg/mm2;εmin范围-0.395～-0.228 kg/mm2。水平向加载时,εmax大部分为拉应力,范围-0.0045～0.322 kg/mm2;εmin均为压应力,范围-0.281～-0.0101 kg/mm2。表2 盖嵴式桥体下皮质骨应力(kg/mm2) 单元号
垂直向加载
水平向加载
εmax
εmin
, 百拇医药
εmax
εmin
708
-0.239
-0.395
0.322
-0.040
709
-0.159
-0.243
0.076
-0.084
, http://www.100md.com
710
-0.133
-0.228
-0.0045
-0.174
711
-0.154
-0.257
-0.073
-0.255
712
-0.164
-0.271
, 百拇医药
0.033
-0.115
713
-0.172
-0.284
0.198
-0.0101
714
-0.162
-0.277
0.136
-0.035
715
, 百拇医药
-0.164
-0.261
0.0079
-0.127
716
-0.169
-0.279
-0.099
-0.281
3 讨 论
本文设计了临床上后牙固定桥常采用的3种不同类型的桥体,其组织面与桥体下粘膜接触的面积比分别约为1∶2/3∶1/3。垂直向载荷下,桥体粘膜下皮质骨均表现为压应力;水平向载荷下,拉、压应力并存。3种桥体下皮质骨的应力分布规律相似,只是接触面积较大者其皮质骨应力较小,接触面积较小者,应力有所增加,但变化幅度不大,应力最大值分别相差约5%～7%。故作者初步认为,选择不同组织接触面积的桥体,对桥体下骨组织应力的影响不大。在固定桥桥体设计中,除了满足形态与咀嚼、发音等功能外,还应考虑微生物因素,提高桥体的自洁能力和利于患者的清洁,并注意美观、舒适等因素。■
, 百拇医药
基金项目：本课题为广东省卫生厅资助项目(编号 D42400)
参考文献：
[1]Howard WW. Standards of pontic desighs. J Prosthet Dent, 1982,47(5):493～495
[2]Crispin BJ. Tissue respone to posterior denture base-type pontics. J Prosthet Dent, 1979,42(3):257～261
[3]Smith BGN. Dental Crowns and Bridge:Design and Preparation. 2nd ed. Chicago: Year Book Med Pub, 1990:189～253
, http://www.100md.com
[4]Murray HV, Sluder TB. Fixed Restorative Techniques. Rev. ed. Chapel Hill NC Vniv. of North Carolina Press, 1989:96～107
[5]唐亮,陈光谦.下颌后牙固定桥支持骨组织应力的三维有限元法分析.Ⅰ.固定桥基牙周围牙槽骨的表面应力分析.华西口腔医学杂志,1999,17(4):371～373
[6]唐亮,陈光谦.下颌后牙固定桥支持骨组织应力的三维有限元分析.Ⅱ.固定桥桥体下皮质骨的应力分布.华西口腔医学杂志,1999,17(4):374～376
收稿日期：1999-01-18, 百拇医药