单颗窄直径种植体支持的双单元悬臂修复下颌前牙区连续缺牙的三维有限元分析

doi:10.3969/j.issn.1674-8115.2025.03.006

上海交通大学学报（医学版） ›› 2025, Vol. 45 ›› Issue (3): 301-309.doi: 10.3969/j.issn.1674-8115.2025.03.006

单颗窄直径种植体支持的双单元悬臂修复下颌前牙区连续缺牙的三维有限元分析

鲍仁强(), 吕成奇, 俞律峰, 陆家瑜, 邹德荣()

上海交通大学医学院附属第六人民医院口腔科，上海 200233

收稿日期:2024-05-09 接受日期:2024-11-11 出版日期:2025-03-28 发布日期:2025-03-28
通讯作者: 邹德荣，主任医师，博士；电子信箱：drzou@sjtu.edu.cn。
作者简介:鲍仁强（1996—），男，硕士生；电子信箱：1823478277@qq.com。
基金资助:
国家自然科学基金(82071160);上海交通大学医学院“双百人”项目(20191832)

Single narrow-diameter implant-supported dual-unit cantilever restorations for consecutive missing teeth in the anterior mandible: a 3D finite element analysis

BAO Renqiang(), LÜ Chengqi, YU Lüfeng, LU Jiayu, ZOU Derong()

Department of Stomatology, Shanghai Sixth People′s Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai 200233, China

Received:2024-05-09 Accepted:2024-11-11 Online:2025-03-28 Published:2025-03-28
Contact: ZOU Derong, E-mail: drzou@sjtu.edu.cn.
Supported by:
National Natural Science Foundation of China(82071160);“Two-hundred Talents” Program of Shanghai Jiao Tong University School of Medicine(20191832)

摘要/Abstract

摘要：

目的·探究单颗窄直径种植体支持的双单元悬臂修复在下颌前牙区连续缺失情况下的适用性。方法·构建简化的下颌前牙区颌骨模型与单颗窄直径种植体支持的双单元悬臂模型。下颌前牙区的骨块长度、宽度、高度分别设定为20、5、15 mm。采用的窄直径种植体为Axiom 2.8两段式窄直径种植体，型号为2.8 mm×10 mm，基台为高度2.5 mm的直角基台。通过计算，设定缺牙间隙的范围为5.8~11.6 mm，故建立牙冠近远中宽度分别为5.8、6.8、7.8、8.8、9.8、10.8、11.8 mm的7组牙冠模型。将种植体、牙冠与颌骨模型通过Siemens Nx 12.0软件整合装配，然后将数据导入Ansys Workbench 18.0软件中进行有限元分析。模拟施加100 N的垂直向加载及斜向30°加载，分析种植体Von-Mises应力值及种植体周围皮质骨最大压应力、皮质骨最大拉应力和松质骨最大拉应力，探讨悬臂长度变化时相关应力的变化情况。结果·种植体颈部为主要应力集中区域。随着悬臂长度的增加，种植体的Von-Mises应力峰值、皮质骨及松质骨的最大拉应力值、皮质骨的最大压应力绝对值均逐渐增大，但是所有应力值均在生理承受范围内。测算得到的种植体Von-Mises应力峰值范围介于141.52~707.17 MPa，均小于其极限抗拉强度930 Mpa；皮质骨的最大拉应力（最大值为11.8 mm组的60.82 MPa）均小于皮质骨的抗拉极限100~130 MPa，而皮质骨的最大压应力绝对值（绝对值最大值为11.8 mm组的129.39 MPa）则均小于皮质骨的抗压极限绝对值170~190 MPa；松质骨的最大拉应力范围介于0.84~4.70 MPa，均小于或接近其极限强度2~5 MPa。结论·单颗窄直径种植体支持的双单元悬臂修复可能是一种可行的针对下颌前牙区连续缺失的治疗方法。

关键词: 窄直径种植体, 前牙悬臂, 三维有限元分析

Abstract:

Objective ·To evaluate the applicability of dual-unit cantilever restorations supported by a single narrow-diameter implant for consecutive missing teeth in the anterior mandibular region. Methods ·A simplified mandibular anterior jaw model and a dual-unit cantilever model supported by a single narrow-diameter implant were constructed. The dimensions of the mandibular anterior bone block were set to 20 mm (length), 5 mm (width), and 15 mm (height). The narrow-diameter implant used was the Axiom 2.8 two-stage implant, 2.8 mm×10 mm, paired with a 2.5 mm straight abutment. Based on calculations, the edentulous gap ranged from 5.8 mm to 11.6 mm, leading to the creation of seven crown models with mesiodistal widths of 5.8, 6.8, 7.8, 8.8, 9.8, 10.8, and 11.8 mm. The implant, crowns, and jaw model were assembled using Siemens Nx 12.0 software, and the data were imported into Ansys Workbench 18.0 for finite element analysis. A vertical load of 100 N and a 30° oblique load were applied to simulate occlusal forces. The Von-Mises stress on the implants, as well as the maximum compressive and tensile stresses in the cortical bone and the maximum tensile stress in the cancellous bone, was analyzed to investigate stress distribution under varying cantilever lengths. Results ·The implant neck region exhibited the highest stress concentration. As the cantilever length increased, the peak Von-Mises stress on the implants, the maximum tensile stress in the cortical and cancellous bones, and the maximum compressive stress in the cortical bones all increased progressively. However, all stress values remained within physiological limits. The peak Von-Mises stress ranged from 141.52 MPa to 707.17 MPa, below the implant′s ultimate tensile strength of 930 MPa. The maximum tensile stress in the cortical bones (with a peak of 60.82 MPa in the 11.8 mm group) was below the cortical bone′s tensile strength limit of 100‒130 MPa. The maximum compressive stress in the cortical bone (with an absolute maximum value of 129.39 MPa in the 11.8 mm group) was below the cortical bone′s compressive strength limit of 170 to 190 MPa (absolute values). The maximum tensile stress in the cancellous bone ranged from 0.84 MPa to 4.70 MPa, which was below or close to its ultimate tensile strength of 2‒5 MPa. Conclusion ·Dual-unit cantilever restorations supported by a single narrow-diameter implant may represent a viable treatment option for consecutive missing teeth in the anterior mandibular region.

Key words: narrow diameter implant, anterior cantilever, 3D finite element analysis

中图分类号:

R783.6

鲍仁强, 吕成奇, 俞律峰, 陆家瑜, 邹德荣. 单颗窄直径种植体支持的双单元悬臂修复下颌前牙区连续缺牙的三维有限元分析[J]. 上海交通大学学报（医学版）, 2025, 45(3): 301-309.

BAO Renqiang, LÜ Chengqi, YU Lüfeng, LU Jiayu, ZOU Derong. Single narrow-diameter implant-supported dual-unit cantilever restorations for consecutive missing teeth in the anterior mandible: a 3D finite element analysis[J]. Journal of Shanghai Jiao Tong University (Medical Science), 2025, 45(3): 301-309.

图/表 9

图1 单颗种植体支持的牙冠模型Note： The mesiodistal widths of the crown were 5.8 mm (A), 6.8 mm (B), 7.8 mm (C), 8.8 mm (D), 9.8 mm (E), 10.8 mm (F), and 11.8 mm (G), respectively.

Fig 1 Crown models supported by a single implant

表1 整体模型各部分的参数

Tab 1 Elastic parameters of each part of the whole model

Material	Elasticity modulus/MPa	Poisson ratio
Implants and abutments (Ti Grade 5)	103 400	0.35
Cortical bone	13 700	0.30
Dense trabecular bone	1 370	0.30
Crowns (feldspathic porcelain)	82 800	0.35

图2 模型上力的加载点和加载方向Note： A. The loading mode of vertical force in the single crown. B. The loading mode of oblique 30° force in the single crown. C. The loading mode of vertical force in the connected crown. Red pentagons represent points of force loading; red arrows represent directions of force loading.

Fig 2 Loading points and directions of the forces on the modesl

图3 垂直加载条件下种植体上的Von-Mises应力峰值及位置Note：The implants of the 5.8 mm (A), 6.8 mm (B), 7.8 mm (C), 8.8 mm (D), 9.8 mm (E), 10.8 mm (F), and 11.8 mm (G) models. Different colors represent the magnitude of Von-Mises stress on the implants; the arrows indicate the locations of the stress peaks.

Fig 3 Von-Mises stress peak values and locations on the implants under vertical loading

图4 斜向30°加载条件下种植体上的Von-Mises应力峰值及位置Note： The implants of the 5.8 mm (A), 6.8 mm (B), 7.8 mm (C), 8.8 mm (D), 9.8 mm (E), 10.8 mm (F), and 11.8 mm (G) models. Different colors represent the magnitude of Von-Mises stress on the implants; the arrows indicate the locations of the stress peaks.

Fig 4 Von-Mises stress peak values and locations on the implants under oblique 30° loading

表2 垂直加载条件下种植体周围牙槽骨应力情况

Tab 2 Stress of alveolar bones around implants under vertical loading

Mesiodistal width of the crown /mm	Maximum tensile stress in the cortical bone/MPa	Maximum compressive stress in the cortical bone/MPa	Maximum tensile stress in the cancellous bone/MPa
5.8	10.68	-22.95	0.84
6.8	35.12	-61.69	1.95
7.8	38.58	-68.60	2.15
8.8	42.01	-75.26	2.36
9.8	42.14	-79.47	2.57
10.8	47.75	-86.20	2.73
11.8	50.04	-90.55	2.88

表3 斜向30°加载条件下种植体周围牙槽骨应力情况

Tab 3 Stress of alveolar bones around implants under oblique 30° loading

Mesiodistal width of the crown /mm	Maximum tensile stress in the cortical bone/MPa	Maximum compressive stress in the cortical bone/MPa	Maximum tensile stress in the cancellous bone/MPa
5.8	50.35	-91.10	3.85
6.8	46.10	-106.68	4.51
7.8	47.04	-110.50	4.56
8.8	50.81	-114.28	4.61
9.8	48.20	-119.18	4.64
10.8	57.78	-124.75	4.66
11.8	60.82	-129.39	4.70

图5 垂直加载条件下种植体周围皮质骨的最大压应力Note： The maximum compressive stress of cortical bones around the implants of the 5.8 mm (A), 6.8 mm (B), 7.8 mm (C), 8.8 mm (D), 9.8 mm (E), 10.8 mm (F), and 11.8 mm (G) models. Different colors represent the magnitude of compressive stress of cortical bones around the implants.

Fig 5 Maximum compressive stress of cortical bones around the implants under vertical loading

图6 斜向30°加载条件下种植体周围皮质骨的最大压应力Note： The maximum compressive stress of cortical bones around the implants of the 5.8 mm (A), 6.8 mm (B), 7.8 mm (C), 8.8 mm (D), 9.8 mm (E), 10.8 mm (F), and 11.8 mm (G) models. Different colors represent the magnitude of compressive stress of cortical bones around the implants.

Fig 6 Maximum compressive stress of cortical bones around the implants under oblique 30° loading

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单颗窄直径种植体支持的双单元悬臂修复下颌前牙区连续缺牙的三维有限元分析

Single narrow-diameter implant-supported dual-unit cantilever restorations for consecutive missing teeth in the anterior mandible: a 3D finite element analysis

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