口腔疾病防治, 2021, 29(9): 596-603 DOI: 10.12016/j.issn.2096-1456.2021.09.004

基础研究

不同洞缘角磨牙Ⅰ类洞复合树脂充填的应力分布

陈红星,, 刘思瑶, 黄雨亭, 潘爽,

哈尔滨医科大学附属第一医院牙体牙髓病科,哈尔滨医科大学口腔医学院牙体牙髓病科,黑龙江 哈尔滨(150001)

Stress distribution of composite resin filling in Class I cavity of molars with different cavosurface angle

CHEN Hongxing,, LIU Siyao, HUANG Yuting, PAN Shuang,

Department of Endodontics, the First Affiliated Hospital of Harbin Medical University, Department of Endodontics, School of Stomatology, Harbin Medical University, Harbin 150001, China

通讯作者: 潘爽,主任医师,博士后,Email:panshuang79@163.com,Tel:86-451-85553234

责任编辑: 张琳, 孙书昱

收稿日期: 2020-11-23   网络出版日期: 2021-06-18

Corresponding authors: PAN Shuang, Email:panshuang79@163.com, Tel: 86-451-85553234

Received: 2020-11-23   Online: 2021-06-18

作者简介 About authors

陈红星,医师,硕士研究生,Email:2224132694@qq.com

摘要

目的 利用三维有限元分析不同洞缘角对磨牙牙合面Ⅰ类洞复合树脂充填后应力分布的影响,为Ⅰ类洞形制备提供参考。方法 建立3个洞缘角角度(A组90°、B组120°、C组135°)的下颌第一磨牙牙合面Ⅰ类洞复合树脂充填的三维有限元模型,用热膨胀法模拟复合材料的聚合收缩,分析在聚合收缩和咬合载荷(600 N)的共同作用下,修复模型在应力和位移分布方面的力学行为。结果 窝洞尺寸相同的Ⅰ类洞,3种洞缘角度(其中B组、C组洞缘釉质斜面宽度为1 mm)的窝洞复合树脂修复后,A组修复模型总体及牙釉质的最大应力小于B组和C组修复模型总体及牙釉质的最大应力;3组牙本质和粘接剂的最大应力相近;C组复合树脂的最大应力最大,B组复合树脂的最大应力最小。从应力分布看,各修复模型中,最大应力主要集中在洞缘牙釉质、牙釉质-牙本质界面和修复材料边缘。结论 复合树脂充填磨牙牙合面Ⅰ类洞时,从减少剩余牙体组织应力的角度看,90°的洞缘角即无釉质斜面预备是一种较为理想的窝洞预备方式。

关键词: 下颌第一磨牙 ; 咬合面龋 ; Ⅰ类洞 ; 洞缘角 ; 三维有限元分析 ; 应力分布 ; 复合树脂 ; 釉质斜面

Abstract

Objective To analyze the effect of different cavosurface angles on the stress distribution of ClassⅠ cavity composite resin filling of molars through the three-dimensional finite element method and to provide references for the preparation of ClassⅠ cavities. Methods Three-dimensional finite element models of ClassⅠ composite resin filling of mandibular first molars with three different cavosurface angles (group A: 90°, group B: 120°, group C: 135°) were established. Polymerization shrinkage of composites was simulated with a thermal expansion approach. The mechanical behavior of the restored models in terms of stress and displacement distributions under the combined effects of polymerization shrinkage and occlusal load (600 N) was analyzed. Results For ClassⅠ cavities with the same cavity size, the total stress of the restoration model and the maximum stress of the enamel in group A were less than those in groups B and C after cavity composite resin restoration with three cavity cavosurface angles (in which the width of the enamel bevel was 1 mm in groups B and C). The maximum stress of the dentin and adhesive was similar in the three groups, the maximum stress of the composite in group C was the largest, and the maximum stress of the composite in group B was the smallest. In terms of stress distribution, the maximum stress in each restoration model was mainly concentrated in the enamel at the cavosurface, near the enamel-dentin interface and at the edge of the restoration material. Conclusion From the point of reducing the stress of residual tooth tissue, the preparation of 90° angle without enamel bevel is an ideal method for cavity preparation when composite resin is used to fill ClassⅠ cavities of molars.

Keywords: mandibular first molar ; occlusal caries ; ClassⅠ cavity ; cavosurface angle ; three-dimensional finite element ; stress distribution ; composite resin ; enamel bevel

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本文引用格式

陈红星, 刘思瑶, 黄雨亭, 潘爽. 不同洞缘角磨牙Ⅰ类洞复合树脂充填的应力分布. 口腔疾病防治[J], 2021, 29(9): 596-603 DOI:10.12016/j.issn.2096-1456.2021.09.004

CHEN Hongxing, LIU Siyao, HUANG Yuting, PAN Shuang. Stress distribution of composite resin filling in Class I cavity of molars with different cavosurface angle. Journal of Prevention and Treatment for Stomatological Diseases[J], 2021, 29(9): 596-603 DOI:10.12016/j.issn.2096-1456.2021.09.004

开放科学(资源服务)标识码(OSID)

咬合面是从牙齿萌出开始最有可能发生龋齿的部位,尤其是恒磨牙上的咬合面上含有易滞留食物残渣和细菌的窝沟更增加了龋病发生的风险[1-3]。临床上对咬合面龋坏进行治疗时常制备Ⅰ类洞型并行银汞或树脂材料充填。复合树脂材料由有机树脂基质和无机填料组成,能够模拟牙齿的自然颜色和解剖特征,是临床上龋齿充填的常用材料。然而这类材料的缺点是机械特性如热膨胀系数与牙齿结构不匹配,并且因材料的固有特性易发生聚合收缩[4-6],这会使复合材料在聚合过程中以及行使咀嚼功能过程中在牙齿修复材料界面产生应力,影响修复体的使用寿命,最终导致修复失败[7]。牙齿复杂的几何形状使对其进行应力分布研究,特别是修复后的应力分布研究变得异常困难,三维有限元分析是使问题可视化的有力工具,可对复杂的结构进行建模和仿真,并可在施加载荷和边界条件时分析它们的力学性能和行为[8],即后牙内的应力分布在三维有限元中是其形状、其三维刚度分布和载荷的函数。关于Ⅰ类洞中洞缘角的研究标准尚不统一且缺乏相应的力学依据,因此笔者以下颌第一恒磨牙为研究对象,采用三维有限元模拟修复材料的聚合收缩和咬合载荷,比较分析不同洞缘角的牙合面Ⅰ类洞在复合树脂充填后,各修复模型在位移和应力分布方面的力学行为,为临床中设计修复方案提供理论参考。

1 材料和方法

1.1 建模素材选择

选择一位身体健康的成年男性志愿者的右侧下颌第一磨牙(牙齿形态正常,牙体完整,无缺损及磨耗,无牙周疾患及牙槽骨吸收),采用锥形束CT(cone beam computed tomography,CBCT)(KaVo 3D eXam公司,美国)对该牙进行扫描,将获得的扫描数据以DICOM格式存储,得到该牙的三维形态数据。

1.2 建立分析模型

1.2.1 三维数字模型的重建 使用Mimics 20软件(Materialise公司,比利时)读取CBCT数据,进行阈值分析和调整处理及三维模型重建,计算生成右下颌第一磨牙的牙体组织点云模型后导入GeomagicStudio 2014软件(3D Systems公司,美国),使用Geomagic软件对生成的模型进行表面去噪,将其转化为高质量的NURBS曲面模型,并将原NURBS曲面模型转化成CAD模型,最后通过Unigraphics NX 10软件(Siemens公司,德国)中的曲面缝合功能将其实体化,生成健康的右下颌第一磨牙三维实体模型。

从健康的下颌第一磨牙三维实体模型出发,在Unigraphics NX 10软件里通过布尔运算建立三个不同洞缘角(A组90°、B组120°、C组135°)的下颌第一磨牙牙合面Ⅰ类洞修复模型(图1)。该模型由牙槽骨(皮质骨1.5 mm、松质骨)、牙周膜(0.25 mm)、牙髓、牙釉质、牙本质、树脂复合修复体(粘接剂、复合树脂)和食物团块组成。

图1

图1   3组洞缘角度的三维实体模型

Figure 1   Three-dimensional solid models of cavosurface angles in the three groups

a: food modeling on the occlusal surfaces, the green part is the food lump; b: the cavosurface angle is 90°; c: the cavosurface angle is 120°; d: the cavosurface angle is 135°


模型要求:以咬合面观颊舌向、近远中向的中线的交点为参考点,从参考点向近远中向和颊舌向各延伸2 mm作为窝洞的长度和宽度(即窝洞的长度和宽度各4 mm),咬合面最深点作为参考点[9],构建3 mm深的窝洞。生成的Ⅰ类洞线角及点角进行圆钝处理,模拟临床上圆钝的线角及点角[10]。其中B组和C组的洞缘斜面宽度为1 mm。在上述3种实体模型中用壳单元模拟复合树脂修复体周围的粘接剂层[11-13],壳单元厚度设置为0.01 mm模拟粘接剂层的厚度(图1)。

1.2.2 网格划分 将实验模型导入有限元分析软件Abaqus(Version6.14)中,并行网格划分(表1)。

表1   各模型网格类型及节点与元素数量

Table 1  Mesh types and the number of nodes and elements in each model

ItemNumber of
nodes
Number of
elements
Element type
Enamel20 37712 733C3D10
Dentin34 74022 037C3D10
Contical bone13 9577 927C3D10
Spongious bone41 84326 283C3D10
Periodontal ligament26 48913 180C3D10M
Food bolus22 13613 996C3D10
Group A resin10 4476 407C3D10
Group B resin9 7116 189C3D10
Group C resin20 39212 968C3D10

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1.3 实验条件假设和边界条件设定

由于分析是在考虑非破坏条件的情况下进行的,因此假设所有材料在整个变形过程中都被定义为弹性线性材料。边界条件设定为牙槽骨的颊舌面及底部完全固定。

考虑到咀嚼功能的变异性和复杂性,所有模型都在咀嚼周期的闭合阶段承受载荷。采用滑动型接触单元模拟咬合面与食物团块之间的相互作用。

使用热膨胀方法,通过指定温度下降1 ℃来模拟粘接剂层和复合材料的聚合收缩。此外,咬合静载荷设置为600 N。载荷垂直施加,均匀分布在表面, 与收缩效应同时施加[13-14]。线膨胀系数和实验相关材料参数[10,12,15-16]表2

表2   材料的力学性能

Table 2  Mechanical properties of materials

ItemYoung’s modulus (MPa)Poisson’s ratioLinear shrinkage (%)Linear thermal expansion coefficientThicknesses (mm)
Enamel80 0000.30
Dentin18 0000.23
Resin composite12 0000.2510.003 3
Adhesive bonding4 0000.3010.003 30.01
Food bolus3 4100.10
Pulp20.48
Spongious bone1 3700.30
Contical bone13 7000.30
Periodontal ligament68.90.45

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2 结果

采用Abaqus有限元软件对上述模型从应力和位移分布的角度分析聚合收缩和咬合载荷的联合影响。结果以等效应力云图的形式显现。所进行的分析涉及具有脆性的材料,因此采用的观察指标为Von Mises等效应力,其反映材料内部某一点在不同方向上的综合受力情况,可以作为评判材料的综合应力指标。

2.1 修复模型总体位移及等效应力分布云图

3组模型的最大位移都发生在复合树脂部分,位移量分别为0.050 mm,0.052 mm,0.062 mm。3组修复模型Von Mises等效应力分布相似,洞缘釉质处出现应力集中,范围较小,颈部牙釉质区域则出现第二应力集中部位且范围较大。A组修复模型最大Von Mises等效应力峰值47.09 MPa,较B组(67.74 MPa)、C组(58.58 MPa)小(图2)。

图2

图2   3组修复模型总体位移及等效应力分布

Figure 2   Overall displacement and equivalent stress distribution in the repair models of the three groups

a-c: overall displacement of equivalent stress, with the maximum displacement occurring in the composite resin part; d-f: overall distribution of equivalent stress, with the stress mainly concentrated in the enamel at the cavosurface and cervical enamel; g: maximum stress of the repair model; group A: the cavosurface angle is 90°; group B: the cavosurface angle is 120°; group C: the cavosurface angle is 135°


2.2 修复模型各部分应力等效应力分布云图(包括颊舌剖面)及最大应力区域

粘接剂的等效应力分布云图如图3所示,粘接剂层的最大应力在3组修复模型中均分布在窝洞洞底处,各组最大Von Mises等效应力峰值相近,分别为0.020 1 MPa、0.020 0 MPa、0.019 9 MPa。

图3

图3   3组粘接剂等效应力分布

Figure 3   Equivalent stress distribution of adhesives in the three groups

a-c: distribution of equivalent stress of adhesives; d-f: distribution of equivalent stress of adhesives in the buccolingual direction, with the maximum stress concentrated at the angle of the axial medullary line at the bottom of the cavity; g: maximum stress of the adhesive repair model; group A: the cavosurface angle is 90°; group B: the cavosurface angle is 120°; group C: the cavosurface angle is 135°


复合树脂的等效应力分布云图见图4,3组模型中复合树脂最大应力分布的部位均为复合树脂与牙面交界处即洞缘处,从表面向下逐渐减小。但A组的应力集中范围比B组和C组小,且B组和C组的应力集中区域几乎遍布于整个洞缘斜面。各组最大应力情况,C组的Von Mises等效应力峰值最大(5.28 MPa),A组次之(3.46 MPa),B组最小(2.16 MPa)。

图4

图4   3组复合树脂等效应力分布

Figure 4   Equivalent stress distribution of composite resin in the three groups

a-c: distribution of equivalent stress of composite resin, with the maximum stress in each restoration model mainly concentrated at the edge of the restoration material; d-f: distribution of equivalent stress of composite resin in the buccolingual direction; g: maximum stress of composite resin; group A: the cavosurface angle is 90°; group B: the cavosurface angle is 120°; group C: the cavosurface angle is 135°


牙釉质的等效应力分布云图见图5,3组模型中显示出相似的应力趋势,应力集中部位在洞缘釉质处及颈部釉牙本质交界处。A组的最大Von Mises等效应力峰值最小(38.09 MPa),B组最大(67.74 MPa)。

图5

图5   3组牙釉质等效应力分布

Figure 5   Equivalent stress distribution of enamel in the three groups

a-c: distribution of equivalent stress of enamel, with the maximum stress in each restoration model mainly concentrated in the enamel at the cavosurface and the cervical enamel-dentin interface; d-f: distribution of equivalent stress of enamel in the buccolingual direction; g: maximum stress of enamel; group A: the cavosurface angle is 90°; group B: the cavosurface angle is 120°; group C: the cavosurface an-gle is 135°


牙本质的等效应力分布云图如图6所示,3组模型的应力分布类似,都在洞底髓室顶处和洞侧壁釉质牙本质交界处,并在交界处向下零星扩散。A组牙本质最大Von Mises等效应力峰值为47.09 MPa,B组为46.36 MPa,C组为46.65 MPa,3组最大Von Mises等效应力峰值相近。

图6

图6   3组牙本质等效应力分布

Figure 6   Equivalent stress distribution of dentin in the three groups

a-c: distribution of equivalent stress of dentin; d-f: distribution of equivalent stress of dentin in the buccolingual direction, with the maximum stress concentrated at the cavity bottom above the pulp chamber top and the enamel-dentin interface along the lateral wall of the cavity; g: maximum stress of dentin; group A: the cavosurface angle is 90°; group B: the cavosurface angle is 120°; group C: the cavosurface angle is 135°


3 讨论

下颌第一磨牙因其萌出最早,对建立正常咬合关系、承担咀嚼功能起着重要作用,但由于其牙合面窝沟点隙复杂且深,有利于细菌产生的酸累积且在口腔中行使功能时间长,常因患者口腔健康意识不佳而导致龋坏进行修复治疗[17],因此本实验选择下颌第一磨牙作为观察对象。

临床上对发生在牙合面的龋坏常制备Ⅰ类洞型后进行充填以恢复牙齿的原有形态和功能,随着粘接修复材料的发展,直接复合树脂材料在后牙修复中因具有较高的粘附性、良好的可操作性和令人满意的性能而被广泛应用[12]。然而复合树脂材料的显著缺点是聚合收缩和机械特性与牙齿结构不匹配,可在牙齿修复界面产生应力,导致界面缺陷,为术后微渗漏、继发龋、牙本质过敏的发生埋下隐患[18]。有研究人员提出改变洞缘角来改善以上问题,但是关于洞缘角的大小及其所形成的釉质斜面宽度尚无统一标准[19-21]。本研究在确保Ⅰ类洞中1 mm的釉质斜面宽度不变的情况下,改变不同的洞缘角大小,分析洞缘角度的单独作用。

传统口腔建模多在标准离体牙模型上采用切片、磨片法和人工测量标本等方法制备,存在样本收集困难、耗时长的问题,并且常因设备及操作误差,难以表达复杂组织结构及特性,导致实验结果偏差大。随着计算机技术的发展,通过逆向工程软件可将口腔模型转变为精确的三维数字化模型。应用逆向工程软件的有限元方法可以分析在一般情况下牙齿中产生的应力并且该分析允许在同一模型中多次重复评价不同因素、不同部位的应力变化,而不对原始样本造成破坏[22]。因此本研究采用临床上广泛应用的CBCT,扫描获得全面清晰且完整的下颌第一磨牙的二维信息,通过Mimics、Geomagic逆向工程软件建立下颌第一磨牙实体模型,通过Abaqus有限元软件按临床标准,制备精确的复合树脂修复的不同洞缘角的下颌第一磨牙Ⅰ类洞的研究模型,随后进行网格划分并研究应力分布。

3组模型中,最大位移值均位于复合树脂处,修复模型中的这种位移分布是由于复合材料(12 000 MPa)相对于牙釉质(80 000 MPa)的低弹性模量所致。3组修复模型的最大位移差异不显著,不同洞缘角并不改变树脂充填体的最大位移,这说明该最大位移是由复合树脂本身的材料特性决定的,与洞缘角无关。3组模型中最大应力都位于牙釉质上,分析原因可能由于牙釉质的弹性模量较高,并且在力的传导和分散中起着重要作用,是承担牙合力的主要组织,所以易形成应力集中区,因此在临床中应强调保留釉质的重要性。

粘接剂层的最大应力在3组修复模型中都分布在窝洞洞底处,提示这些部位可能是最早出现粘接失败的地方。3组最大应力值相近(分别为A组0.020 1 MPa,B组0.020 0 MPa,C组0.019 9 MPa),这是由于粘接剂层的正常厚度为0.01 mm, 它的聚合收缩比复合树脂材料对产生应力的影响要小[10]。本研究中,3组复合树脂最大应力分布的部位都为洞缘复合树脂边缘处,C组应力峰值最大,A组次之,B组最小。为了最大限度减少复合材料在牙齿修复过程中产生的应力,Kowalczyk[23]提出了一种新型的复合材料的分层修复方法,即在窝洞表面覆盖一层细长的复合树脂薄层,这一层被称为“预层”,然后再进行水平分层充填。这种改良的Ⅰ类洞充填技术的有限元分析显示收缩应力降低75%。设置“预层”后,窝洞尺寸变小,“预层”的C因子接近1,得到了较好的结果。但是Rodrigues等[24]的研究表明在矩形Ⅰ类洞的有限元模型中,增加C因素不会增加应力峰值。本实验对3组修复模型的C因素进行计算,得出A组模型的C因素最大,为3.57,B组的C因素为2.52,C组的C因素最小,为2.27,同样发现C因素的增大没有导致模型整体最大应力的增大。显然,在后牙Ⅰ类洞型中,C因素不能作为评价聚合收缩应力的单一指标。最大等效应力是材料承受总体应力的情况,其所产生的应变即为等效应变,可作为判断材料是否出现磨损或破裂的可靠指征。3组模型中复合树脂的应力分布可以看到从窝洞表层向下应力峰值逐渐减小,这或许可以解释临床上修复体表层易出现磨损,少见修复体整体折裂的现象。而未经抛光的修复体表面会因粗糙度过大而产生应力集中点,增大折裂风险[25],提示复合树脂修复后可通过表面彻底的抛光进一步减少折裂风险。

从3组模型牙釉质层的应力分布云图可以看出牙釉质与复合树脂修复体的交界处可见应力集中,A组模型的应力峰值最小。虽然3组模型应力集中部位都在复合树脂材料和釉质的交界处,B组和C组应力集中范围较A组广泛,分析可能是由于B组和C组洞缘角造成的釉质斜面,使最大应力集中部位改变,这提示可以通过改变洞缘角改变应力集中部位,最大程度避开咬合接触点,但这可能会导致去除多余的牙釉质。

3组模型中牙本质的最大应力都分布在洞底靠近髓室顶附近和洞侧壁釉质牙本质交界处,大小差异不明显且均低于正常牙本质的抗拉强度。研究表明,牙本质的抗拉强度为40~50 MPa,抗压强度为245~343 MPa,所以本实验加载的情况下,3种修复模型均不会发生牙本质的损伤[26]

分析3组修复模型中复合树脂层和釉质层应力集中区可见,两者的应力集中区都在修复体和牙体界面的洞缘处,说明复合树脂修复的窝洞的失败可能最早出现在这里。如前所述牙釉质本身的弹性模量显著高于复合树脂的弹性模量,这可能是导致洞缘处牙釉质的最大应力大于复合树脂最大应力的原因,由此提示在选择复合树脂材料修复釉质层时,尽量选择弹性模量与牙釉质相匹配的复合树脂材料,较低弹性模量的复合树脂材料在功能性载荷下更易发生变形而产生位移,与粘接剂层分离,导致边缘密合差,产生继发龋。

本研究采用有限元方法检测不同洞缘角对磨牙牙合Ⅰ类洞复合树脂充填应力分布的影响,结果表明,复合树脂直接修复的磨牙牙合面Ⅰ类洞,90°的洞缘角能最大程度减小剩余牙体组织的应力。从保存牙体组织和临床可操作性角度看,临床上对后牙牙合面Ⅰ类洞制备90°的洞缘角可减少牙釉质的应力集中,从而减少釉质折裂。但是有限元的分析方法很难完全复制口腔内复杂的运动过程和生物环境,并且在建模过程中所假定的复合树脂和牙体硬组织之间的完美粘接在临床上几乎无法实现,且临床上对窝洞进行树脂充填不仅要考虑应力分布问题,还应综合考虑复合树脂性能及充填方式、酸蚀粘接系统、固化系统和固化方式、患者饮食习惯和咀嚼习惯等问题,因此仍需进一步的体内和体外研究来验证有限元数据结果。

【Author contributions】 Chen HX peformed the experiments, analyzed the data, and wrote the article. Liu SY, Huang YT revised the article. Pan S designed the study. All authors read and approved the final manuscript as submitted.

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To study the influence of resin based and lithium disilicate materials on the stress and strain distributions in adhesive class II mesio-occlusal-distal (MOD) restorations using numerical finite element analysis (FEA). To investigate the materials combinations in the restored teeth during mastication and their ability to relieve stresses.One 3D model of a sound lower molar and three 3D class II MOD cavity models with 95° cavity-margin-angle shapes were modelled. Different material combinations were simulated: model A, with a 10μm thick resin bonding layer and a resin composite bulk filling material; model B, with a 70μm resin cement with an indirect CAD-CAM resin composite inlay; model C, with a 70μm thick resin cement with an indirect lithium disilicate machinable inlay. To simulate polymerization shrinkage effects in the adhesive layers and bulk fill composite, the thermal expansion approach was used. Shell elements were employed for representing the adhesive layers. 3D solid CTETRA elements with four grid points were employed for modelling the food bolus and tooth. Slide-type contact elements were used between the tooth surface and food. A vertical occlusal load of 600 N was applied, and nodal displacements on the bottom cutting surfaces were constrained in all directions. All the materials were assumed to be isotropic and elastic and a static linear analysis was performed.Displacements were different in models A, B and C. Polymerization shrinkage hardly affected model A and mastication only partially affected mechanical behavior. Shrinkage stress peaks were mainly located marginally along the enamel-restoration interface at occlusal and mesio-distal sites. However, at the internal dentinal walls, stress distributions were critical with the highest maximum stresses concentrated in the proximal boxes. In models B and C, shrinkage stress was only produced by the 70μm thick resin layer, but the magnitudes depended on the Young's modulus (E) of the inlay materials. Model B mastication behavior (with E=20GPa) was similar to the sound tooth stress relief pattern. Model B internally showed differences from the sound tooth model but reduced maximum stresses than model A and partially than model C. Model C (with E=70GPa) behaved similarly to model B with well redistributed stresses at the occlusal margins and the lateral sides with higher stress concentrations in the proximal boxes. Models B and C showed a more favorable performance than model A with elastic biomechanics similar to the sound tooth model.Bulk filling resin composite with 1% linear polymerization shrinkage negatively affected the mechanical behavior of class II MOD restored teeth. Class II MOD direct resin composite showed greater potential for damage because of higher internal and marginal stress evolution during resin polymerization shrinkage. With a large class II MOD cavity an indirect composite or a lithium disilicate inlay restoration may provide a mechanical response close to that of a sound tooth.Copyright © 2017 The Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

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To investigate the influence of different resin composite and glass ionomer cement material combinations in a "bi-layer" versus a "single-layer" adhesive technique for class I cavity restorations in molars using numerical finite element analysis (FEA).Three virtual restored lower molar models with class I cavities 4mm deep were created from a sound molar CAD model. A combination of an adhesive and flowable composite with bulk fill composite (model A), of a glass ionomer cement with bulk fill composite (model B) and of an adhesive with bulk fill composite (model C), were considered. Starting from CAD models, 3D-finite element (FE) models were created and analyzed. Solid food was modeled on the occlusal surface and slide-type contact elements were used between tooth surface and food. Polymerization shrinkage was simulated for the composite materials. Physiological masticatory loads were applied to these systems combined with shrinkage. Static linear analyses were carried out. The maximum normal stress criterion was adopted as a measure of potential damage.All models exhibited high stresses principally located along the tooth tissues-restoration interfaces. All models showed a similar stress trend along enamel-restoration interface, where stresses up to 22MPa and 19MPa was recorded in the enamel and restoration, respectively. A and C models showed a similar stress trend along the dentin-restoration interface with a lower stress level in model A, where stresses up to 11.5MPa and 7.5MPa were recorded in the dentin and restoration, respectively, whereas stresses of 17MPa and 9MPa were detected for model C. In contrast to A and C models, the model B showed a reduced stress level in dentin, in the lower restoration layer and no stress on the cavity floor.FE analysis supported the positive effect of a "bi-layer" restorative technique in a 4mm deep class I cavities in lower molars versus "single-layer" bulk fill composite technique.Copyright © 2019 The Academy of Dental Materials. Published by Elsevier Inc. All rights reserved.

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To study the influence of the resin bonding layer thickness and the bulk filling material stiffness in adhesive class II mesio-occlusal-distal (MOD) restorations using numerical finite element analysis (FEA).Four 3D-FE models of teeth restored with different filling material stiffness and resin bonding layer thickness were built-up and analyzed. The 3D model of a sound lower molar was also analyzed and compared with restored ones. The tooth tissues (enamel, dentin), dental restoration and bolus on the occlusal surface, was divided into 3D solid CTETRA elements with four grid points. The adhesive bonding around the dental restoration was modeled with shell elements. Polymerization shrinkage was simulated with a thermal expansion approach. Mechanical behavior of restored models in terms of stress and displacement distributions, under the combination effects of polymerization shrinkage and occlusal load (600 N), was analyzed. All the materials were assumed to behave as elastic materials throughout the entire deformation.Numerical results show that the mechanical response of the restored models was very different compared to the sound tooth ones, where the stress was uniformly distributed from enamel to dentin with no critical stress concentration. In the restored models, the highest stress values were detected in the enamel, near the enamel-dentin interface and in the bulk restorative material. Tooth preparations A and B showed lower gradient stresses than corresponding C and D. The value of the vertical displacement components in models A and B were higher than corresponding C and D. The maximum displacement values were mainly located around the groove and were higher by an order of magnitude than the sound models. The results showed better mechanical response with models A and B compared to C and D. It is also evident that resin bonding thickness slightly affected the stress level of the restored teeth.Class II MOD direct bulk resin composite restorations showed a high susceptibility to damage at the marginal and internal tissue interfaces depending on their own stiffness. The use of resin-based bulk filling materials is not recommended for large class II MOD adhesive restorations due to mechanical behavior failure risk.

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CAD-FE modeling and analysis of class Ⅱ restorations incorporating resin-composite, glass ionomer and glass ceramic materials

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To investigate the influence of specific resin-composite, glass ceramic and glass ionomer cement (GIC) material combinations in a "multi-layer" technique to replace enamel and dentin in class II mesio-occlusal-distal (MOD) dental restorations using 3D-Finite Element Analysis (FEA).Four 3D-FE models (A-D) of teeth, adhesively restored with different filling materials, were created and analyzed in comparison with a 3D model (E) of a sound lower molar. Models A, B & C had "multilayer" constructions, consisting of three layers: adhesive, dentin replacement and enamel replacement. Model A: had a low modulus (8GPa) composite replacing dentin and a higher modulus (12GPa) composite replacing enamel. Model B: had a GI cement replacing dentin and a higher modulus (12GPa) composite replacing enamel. Model C: had a low modulus (8GPa) composite replacing dentin and a very high modulus (70GPa) inlay replacing enamel. Model D: had a lithium disilicate inlay replacing both dentin and enamel with a luting cement base-layer. Polymerization shrinkage effects were simulated and a load of 600N was applied. All the materials were assumed to behave elastically throughout the entire deformation.Model A showed the highest stress distribution along all the adhesive interfaces of the shrinking resin-based materials with a critical condition and failure risk marginally and internally. Model D, by contrast, showed a more favorable performance than either of the multilayer groups (A-C). Stress and displacement plots showed an elastic response similar to that obtained for the sound tooth model. Model B and Model C performed according to their bilayer material properties. The use of a non-shrink dentin component simulating a GIC clearly affected the shrinkage stress at the basis of the Model B; while the bulk resin composite having a 12GPa Young's modulus and linear polymerization shrinkage of 1% strongly influenced the biomechanical response in the bucco-lingual direction.Direct resin-based composite materials applied in multilayer techniques to large class II cavities, with or without shrinking dentin layers, produced adverse FEA stress distributions and displacements. An indirect lithium disilicate inlay used to replace lost dentin and enamel in posterior restored teeth generated lower stress levels, within the limits of the elastic FEA model.Crown Copyright © 2017. Published by Elsevier Ltd. All rights reserved.

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Rodrigues MP, Soares P, Gomes M, et al.

Direct resin composite restoration of endodontically-treated permanent molars in adolescents: bite force and patient-specific finite element analysis

[J]. J Appl Oral Sci, 2020, 28:e20190544. doi: 10.1590/1678-7757-2019-0544.

DOI      URL     [本文引用: 1]

Veloso SR, Lemos CA, De Moraes SL, et al.

Clinical performance of bulk-fill and conventional resin composite restorations in posterior teeth: a systematic review and meta-analysis

[J]. Clin Oral Investig, 2019, 23(1):221-233. doi: 10.1007/s00784-018-2429-7.

DOI      URL     [本文引用: 1]

Смеянов ЮВ, Лахтин ЮВ.

The influence of stress-strain processes in tooth enamel on the marginal permeability of classⅠrestorations with a different design of the edge of the carious cavity

[J]. Wiad Lek, 2018, 71(1pt2):135-139.

[本文引用: 1]

Correia AO, Pereira VM, Bresciani E, et al.

Influence of cavosurface angle on the stress concentration and gaps formation in class V resin composite restorations

[J]. J Mech Behav Biomed Mater, 2019, 97:272-277. doi: 10.1016/j.jmbbm.2019.05.034.

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Meurer JC, Rizzante F, Maenossono RM, et al.

Effect of cavosurface angle beveling on the exposure angle of enamel prisms in different cavity sizes

[J]. Microsc Res Tech, 2020, 83(3):304-309. doi: 10.1002/jemt.23415.

DOI      URL     [本文引用: 1]

Soares PV, Machado AC, Zeola LF, et al.

Loading and composite restoration assessment of various non-carious cervical lesions morphologies--3D finite element analysis

[J]. Aust Dent J, 2015, 60(3):309-316. doi: 10.1111/adj.12233.

DOI      URL     PMID      [本文引用: 1]

The present study analysed the effects of different occlusal loading on premolars displaying various non-carious cervical lesions morphologies, restored (or not) with composites, by 3D finite element analysis.A three-dimensional digital model of a maxillary premolar was generated using CAD software. Three non-carious cervical lesions morphological types were simulated: wedged-shaped, saucer and mixed. All virtual models underwent three loading types (100 N): vertical, buccal and palatal loading. The simulated non-carious cervical lesions morphologies were analysed with and without restorations to consider specific regions, such as the occlusal and gingival walls as well as the depth of the lesions. Data summarizing the stress distribution were obtained in MPa using Maximum Principal Stress.Palatal loads were responsible for providing the highest values of accumulated tensile stress on the buccal wall; 27.66 MPa and 25.76 MPa for mixed and wedged-shaped morphologies, respectively. The highest tensile values found on non-carious cervical lesions morphologies restored with composite resin were 5.9 MPa in the mixed morphology, similar to those found on sound models despite their morphologies and occlusal loading.The various non-carious cervical lesions morphologies had little effect on stress distribution patterns, whereas the loading type and presence of composite restorations influenced the biomechanical behaviour of the maxillary premolars.© 2015 Australian Dental Association.

Kowalczyk P.

Influence of the shape of the layers in photo-cured dental restorations on the shrinkage stress peaks-FEM study

[J]. Dent Mater, 2009, 25(12): e83-e91. doi: 10.1016/j.dental.2009.07.014.

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Rodrigues FP, Silikas N, Watts DC, et al.

Finite element analysis of bonded model Class I ′restorations′ after shrinkage

[J]. Dent Mater, 2012, 28(2):123-132. doi: 10.1016/j.dental.2011.10.001.

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The C-Factor has been used widely to rationalize the changes in shrinkage stress occurring at the tooth/resin-composite interfaces. Experimentally, such stresses have been measured in a uniaxial direction between opposed parallel walls. The situation of adjoining cavity walls has been neglected. The aim was to investigate the hypothesis that: within stylized model rectangular cavities of constant volume and wall thickness, the interfacial shrinkage-stress at the adjoining cavity walls increases steadily as the C-Factor increases.Eight 3D-FEM restored Class I 'rectangular cavity' models were created by MSC.PATRAN/MSC.Marc, r2-2005 and subjected to 1% of shrinkage, while maintaining constant both the volume (20 mm(3)) and the wall thickness (2 mm), but varying the C-Factor (1.9-13.5). An adhesive contact between the composite and the teeth was incorporated. Polymerization shrinkage was simulated by analogy with thermal contraction. Principal stresses and strains were calculated. Peak values of maximum principal (MP) and maximum shear (MS) stresses from the different walls were displayed graphically as a function of C-Factor. The stress-peak association with C-Factor was evaluated by the Pearson correlation between the stress peak and the C-Factor.The hypothesis was rejected: there was no clear increase of stress-peaks with C-Factor. The stress-peaks particularly expressed as MP and MS varied only slightly with increasing C-Factor. Lower stress-peaks were present at the pulpal floor in comparison to the stress at the axial walls. In general, MP and MS were similar when the axial wall dimensions were similar. The Pearson coefficient only expressed associations for the maximum principal stress at the ZX wall and the Z axis.Increase of the C-Factor did not lead to increase of the calculated stress-peaks in model rectangular Class I cavity walls.Copyright © 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Cornacchia TP, Las CE, Cimini CJ, et al.

3D finite element analysis on esthetic indirect dental restorations under thermal and mechanical loading

[J]. Med Biol Eng Comput, 2010, 48(11):1107-1113. doi: 10.1007/s11517-010-0661-7.

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Thermo-mechanical finite element analyses in 3-D models are described for determination of the stress levels due to thermal and mechanical loads in a healthy and restored tooth. Transient thermo-mechanical analysis simulating the ingestion of cold and hot drinks was performed to determine the temperature distribution in the models of the teeth, followed by linear elastic stress analyses. The thermal loads were applied on the occlusal and lingual surfaces. Subsequently, coupled variation of the temperature and mastication loading was considered. The vertical loading was distributed at occlusal points, adding up to 180 N. Maximum stresses were verified in resin restoration under thermal loads. When studying coupled effect of mechanical loading with that arising from thermal effects, higher tensile stress values occurred in porcelain restorations, especially at the restoration-dentin interface. Regions of high tensile stress were detected and their possible clinical significance with respect to restoration damage and microleakage were discussed.

Dejak B, Mlotkowski A.

Three-dimensional finite element analysis of strength and adhesion of composite resin versus ceramic inlays in molars

[J]. Prosthet Dent, 2008, 99(2):131-140. doi: 10.1016/S0022-3913(08)60029-3.

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