纤维桩修复上颌第一磨牙牙体缺损的三维有限元力学分析

doi:10.3969/j.issn.1674-8115.2022.08.013

上海交通大学学报（医学版） ›› 2022, Vol. 42 ›› Issue (8): 1081-1094.doi: 10.3969/j.issn.1674-8115.2022.08.013

• 论著 · 临床研究 • 上一篇

纤维桩修复上颌第一磨牙牙体缺损的三维有限元力学分析

仲麒(), 黄雨捷, 张轶凡, 宋迎爽, 吴雅琴, 瞿方, 黄庆丰(), 胥春()

上海交通大学医学院附属第九人民医院口腔修复科，上海交通大学口腔医学院，国家口腔医学中心，国家口腔疾病临床医学研究中心，上海市口腔医学重点实验室，上海 200011

收稿日期:2022-03-17 接受日期:2022-06-17 出版日期:2022-08-12 发布日期:2022-08-12
通讯作者: 黄庆丰,胥春 E-mail:123281927@qq.com;hqfyy@163.com;imxuchun@163.com
作者简介:仲麒（1996—），男，住院医师，学士；电子信箱：123281927@qq.com。
基金资助:
国家自然科学基金面上项目(82071157);上海市卫生健康委员会卫生行业临床研究专项资助项目(201940009)

Three-dimensional finite element analysis on fiber-reinforced composite post-restored maxillary first molar with tooth defect

ZHONG Qi(), HUANG Yujie, ZHANG Yifan, SONG Yingshuang, WU Yaqin, QU Fang, HUANG Qingfeng(), XU Chun()

Department of Prosthodontics, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University School of Medicine; College of Stomatology, Shanghai Jiao Tong University; National Center for Stomatology; National Clinical Research Center for Oral Diseases; Shanghai Key Laboratory of Stomatology, Shanghai 200011, China

Received:2022-03-17 Accepted:2022-06-17 Online:2022-08-12 Published:2022-08-12
Contact: HUANG Qingfeng,XU Chun E-mail:123281927@qq.com;hqfyy@163.com;imxuchun@163.com
Supported by:
National Natural Science Foundation of China(82071157);Special Support Project for Clinical Research in Health Industry of Shanghai Municipal Health Commission(201940009)

摘要/Abstract

摘要：

目的·探究纤维桩修复上颌第一磨牙腭面（palatal-occlusal，PO）和远中邻面（distal-occlusal，DO）牙体缺损时适宜的修复策略。方法·建立上颌第一磨牙PO和DO 2种牙体缺损模型，每种缺损类型采用不放纤维桩（no post，NP）、腭根单纤维桩（palatal post，PP）、腭根及远颊根双纤维桩（palatal and distobuccal posts，PDP）、腭根及近颊根双纤维桩（palatal and mesiobuccal posts，PMP）以及三根管纤维桩（palatal， distobuccal and mesiobuccal posts，PDMP）5种不同策略进行全冠修复的有限元模型。若多桩组的纤维桩在树脂核内出现干扰，则将较细的桩于重叠处下方1 mm处水平截断。对各模型分别加载与牙体长轴平行的800 N垂直力和与牙体长轴呈45°角的225 N侧向力。通过有限元分析计算牙体组织和纤维桩内的等效应力及纤维桩-树脂水门汀、树脂水门汀-根管壁界面上的最大切应力。结果·对于牙体外表面的最大等效应力值，垂直载荷下PO缺损的PMP组和DO缺损的PDP组最小（分别为36.17 MPa、36.23 MPa），侧向载荷下PO缺损的PDMP组和DO缺损的PMP组最小（分别为40.47 MPa、42.05 MPa）。在2类牙体缺损中，置入纤维桩后根管内表面颈1/3的应力值普遍下降，中1/3的应力值普遍上升；腭根桩和近颊根桩中的最大等效应力值分别为垂直载荷和侧向载荷下的最高值（分别为60.75~71.29 MPa，45.91~51.82 MPa），相对应的纤维桩-树脂水门汀界面上最大切应力值也为相应载荷下的最高值（分别为11.26~12.93 MPa，12.38~13.03 MPa）。各组在垂直载荷下水门汀-根管壁界面上的最大切应力值相近（9.96~10.58 MPa），而在侧向载荷下PMP组和PDMP组水门汀-根管壁界面上的最大切应力值较高。结论·上颌第一磨牙应根据不同的牙体缺损类型采取不同的纤维桩修复策略：PO缺损宜采用腭根单纤维桩修复；DO缺损宜采用腭根加近颊根双纤维桩修复，同时控制垂直力。

关键词: 磨牙, 纤维桩, 桩核技术, 有限元分析, 应力

Abstract:

Objective ·To explore the appropriate strategy for restoring maxillary first molars with palatal-occlusal (PO) defect or distal-occlusal (DO) defect by using fiber-reinforced composite posts. Methods ·Two types of defects in maxillary first molars were established: PO defect and DO defect. For each type, 5 finite element models with different restoration strategies were created: no post (NP), palatal post (PP), palatal and distobuccal posts (PDP), palatal and mesiobuccal posts (PMP), and palatal, distobuccal and mesiobuccal posts (PDMP). In the multi-post groups, if 2 posts overlapped in the resin core, the thinner one was horizontally trimmed 1 mm below the intersection point. The models were loaded by a vertical force—an 800 N force parallel to the long axis of the tooth, and a lateral force—a 225 N force directed at 45° to the long axis of the tooth. The following parameters were calculated by using finite element analysis: equivalent stress in the tooth structure and the posts, and maximum shear stress on the post-cement and cement-canal interfaces. Results ·Under the vertical loading, the maximal equivalent stress on the external surfaces of the tooth with PO defect was the lowest in the PMP group (36.17 MPa), while it was the lowest in the PDP group with DO defect (36.23 MPa). Under the lateral loading, it was the lowest in the PDMP group with PO defect (40.47 MPa), while it was the lowest in the PMP group with DO defect (42.05 MPa). With either defect, the equivalent stress on the internal surfaces generally decreased at the cervical 1/3 of root canals and increased at the middle 1/3 after post inserting. Palatal canal post and mesiobuccal canal post respectively withstood the highest equivalent stress under vertical loading and lateral loading (60.75?71.29 MPa and 45.91?51.82 MPa, respectively), and the maximal shear stresses on these two post-cement interfaces were also the highest under the corresponding loading (11.26?12.93 MPa and 12.38?13.03 MPa, respectively). The maximum shear stresses on the cement-canal interfaces were similar among the groups under the vertical loading (9.96?10.58 MPa), while under the lateral loading they were higher in the PMP group and the PDMP group. Conclusion ·The appropriate strategy for fiber-reinforced composite post restoration on maxillary first molars should be determined according to the type of tooth defect. For PO defect, the strategy of one post restoring in palatal canal is recommended; for DO defect, the strategy of two posts restoring in palatal and mesiobuccal canals respectively with approaches to reduce vertical occlusal force is recommended.

Key words: molar, fiber-reinforced composite post, post and core technique, finite element analysis, stress

中图分类号:

R783.3

仲麒, 黄雨捷, 张轶凡, 宋迎爽, 吴雅琴, 瞿方, 黄庆丰, 胥春. 纤维桩修复上颌第一磨牙牙体缺损的三维有限元力学分析[J]. 上海交通大学学报（医学版）, 2022, 42(8): 1081-1094.

ZHONG Qi, HUANG Yujie, ZHANG Yifan, SONG Yingshuang, WU Yaqin, QU Fang, HUANG Qingfeng, XU Chun. Three-dimensional finite element analysis on fiber-reinforced composite post-restored maxillary first molar with tooth defect[J]. Journal of Shanghai Jiao Tong University (Medical Science), 2022, 42(8): 1081-1094.

图/表 12

图1 上颌第一磨牙2种牙体缺损树脂核充填修复后模型Note：A. PO defect. B. DO defect.

Fig 1 Two models of restored maxillary first molar with tooth defect

图2 不同修复策略的上颌第一磨牙牙体缺损修复模型（以PO牙体缺损为例）Note：A. NP group. B. PP group. C. PDP group. D. PMP group. E. PDMP group. DB—distobuccal; MB—mesiobuccal; P—palatal.

Fig 2 Models of restored maxillary first molar with tooth defect by different restoration strategy (PO defect for example)

表1 材料及组织力学性能参数

Tab 1 Mechanical properties of materials and tooth tissues

Component	Elastic modulus/MPa	Poisson ratio
Cancellous bone^［20-21］	1 370	0.30
Cortical bone^［20-21］	13 700	0.30
Dentin^［20-21］	18 600	0.31
Gutta-percha^［22］	141.9	0.45
Periodontal ligament^［21］	68.9	0.45
Resin cement （crown） ^［23］	18 300	0.30
Resin composite （direct restoration） ^［23-24］	12 000	0.33
Resin core build-up/Resin cement （post） ^［22］	16 440	0.26
Zirconia ceramic crown ^{［20，24］}	200 000	0.33
Quartz fiber-reinforced composite post ^［25］	E_x =50 000， E_y =E_z =15 000	0.30

图3 加载位置及方向示意图Note：A. Vertical loading. The tooth was given an 800 N force parallel to the long axis (the direction of the 3D arrow) on the five points (red dots). B. Lateral loading. The tooth was given a 225 N force directed at 45° to the long axis (the direction of the 3D arrow) on the two points (red dots).

Fig 3 Schematics of the positions and directions of the loadings

图4 垂直载荷下牙体外表面的等效应力分布和最大等效应力值Note：A–F. PO defect. G–L: DO defect. A/G. NP group. B/H. PP group. C/I. PDP group. D/J. PMP group. E/K. PDMP group. F/L. The maximal equivalent stress (MES) in each group. The red arrows indicate the locations of maximum stress; the blue arrows indicate the locations of minimal stress; the yellow arrows indicate the stress concentration areas in furcation areas.

Fig 4 Equivalent stress distributions and MES on external surfaces of tooth tissues under vertical loading

图5 侧向载荷下牙体外表面的等效应力分布和最大等效应力值Note：A–F. PO defect. G–L: DO defect. A/G. NP group. B/H. PP group. C/I. PDP group. D/J. PMP group. E/K. PDMP group. F/L. The MES in each group. The red arrows indicate the locations of maximum stress; the blue arrows indicate the locations of minimal stress; the yellow arrows indicate the stress concentration areas in furcation areas.

Fig 5 Equivalent stress distributions and MES on external surfaces of tooth tissues under lateral loading

表2 纤维桩修复后各组根管内表面各区域最大等效应力值（MPa）

Tab 2 MES on internal surfaces of root canals after placing posts （MPa）

Group		PO defect						DO defect
		Vertical loading			Lateral loading			Vertical loading			Lateral loading
		P	DB	MB	P	DB	MB	P	DB	MB	P	DB	MB
NP
C		25.89	16.22	14.72	13.62	12.97	24.17	24.47	16.85	14.83	11.75	13.83	23.48
M		24.27	16.22	13.68	16.97	19.13	25.85	22.81	15.96	13.25	16.15	19.97	26.08
A		24.07	23.12	23.82	11.83	23.93	26.11	23.67	23.75	16.61	11.25	22.56	26.11
PP
C		18.62	16.11	14.90	11.15	12.90	24.95	18.35	15.98	14.96	11.51	12.67	23.76
M		35.04	16.11	13.76	19.53	19.54	26.94	36.52	15.98	12.73	19.19	19.11	24.89
A		26.66	24.17	17.32	11.22	24.84	17.51	23.73	20.75	31.70	10.84	20.37	33.79
PDP
	C	18.47	15.47	14.70	11.44	13.46	23.43	18.31	18.70	14.59	11.11	13.51	23.61
	M	36.84	27.37	13.48	20.51	19.60	24.94	35.39	26.77	13.01	19.19	20.41	25.85
	A	26.84	22.85	12.90	11.50	22.61	17.46	23.59	21.49	24.29	12.01	21.05	31.21
PMP
	C	18.58	15.87	15.13	10.82	12.82	20.57	18.46	15.80	14.59	11.43	12.37	22.23
	M	33.87	15.73	21.63	19.10	19.45	34.06	33.98	15.80	20.06	18.14	20.20	32.36
	A	31.43	18.36	26.53	14.27	21.01	27.90	27.72	20.44	31.63	11.97	20.37	37.53
PDMP
	C	18.25	15.23	13.22	11.15	13.50	21.49	18.48	14.59	15.20	11.39	13.46	20.86
	M	36.16	29.99	22.22	19.02	21.60	35.26	34.94	28.26	20.43	19.33	19.73	33.10
	A	23.90	23.81	30.73	10.98	20.02	35.45	23.72	22.31	15.32	11.63	22.73	20.00

图6 纤维桩修复后各组根管内表面最大等效应力值相对直接冠修复时（NP组）的变化百分数Note：A. PO defect under vertical loading. B. PO defect under lateral loading. C. DO defect under vertical loading. D. DO defect under lateral loading.

Fig 6 Percentage of MES changes in each group compared to NP group on the internal surfaces of root canals after placing posts

表3 各组纤维桩内最大等效应力值（MPa）

Tab 3 MES in the posts in each group （MPa）

Post	Group	PO defect		DO defect
Post	Group	Vertical loading	Lateral loading	Vertical loading	Lateral loading
Palatal canal	PP	69.18	25.84	69.34	25.69
	PDP	60.75	25.49	66.95	25.63
	PMP	65.00	25.22	71.29	25.37
	PDMP	65.50	25.43	63.78	25.44
Distobuccal canal	PDP	42.50	26.29	39.73	27.50
	PDMP	44.65	28.16	39.85	27.06
Mesiobuccal canal	PMP	39.39	51.82	35.17	45.91
	PDMP	36.27	49.31	27.06	48.91

表4 纤维桩-树脂水门汀界面上最大切应力值（MPa）

Tab 4 Maximum shear stress on the post-cement interface （MPa）

Post	Group	PO defect		DO defect
Post	Group	Vertical loading	Lateral loading	Vertical loading	Lateral loading
Palatal canal	PP	11.75	7.30	12.93	7.41
	PDP	11.77	7.27	11.91	7.33
	PMP	11.39	7.49	11.26	7.33
	PDMP	11.50	7.27	12.92	7.40
Distobuccal canal	PDP	7.91	6.94	8.09	7.03
	PDMP	7.91	6.78	7.85	6.89
Mesiobuccal canal	PMP	7.40	12.38	7.48	12.84
	PDMP	7.73	13.00	7.57	13.03

图7 2种载荷下纤维桩-树脂水门汀界面上的切应力分布Note：A–D. PO defect under vertical loading. E–H. PO defect under lateral loading. I–L. DO defect under vertical loading. M–P. DO defect under lateral loading. A/E/I/M. PP group. B/F/J/N. PDP group. C/J/K/O. PMP group. D/H/L/P. PDMP group. The red arrows indicate the locations of maximum stress; the blue arrows indicate the locations of minimal stress.

Fig 7 Shear stress distributions on the post-cement interface under vertical and lateral loadings

表5 各组水门汀-根管壁界面上最大切应力值（MPa）

Tab 5 Maximum shear stress on the cement-canal interface in each group （MPa）

Group	PO defect		DO defect
Group	Vertical loading	Lateral loading	Vertical loading	Lateral loading
PP	9.96	6.72	10.35	6.67
PDP	10.14	7.06	10.28	7.00
PMP	10.35	11.45	10.26	11.37
PDMP	10.58	11.29	10.38	11.54

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纤维桩修复上颌第一磨牙牙体缺损的三维有限元力学分析

Three-dimensional finite element analysis on fiber-reinforced composite post-restored maxillary first molar with tooth defect

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