Finite element analysis of stress distribution in intact and porcelain veneer restored teeth

The aim of this study was to investigate the stress distribution generated in a veneer restoration of an upper central incisor compared to intact teeth using the finite element analysis after applying a lingual buccal loading at the incisal edge. Methods: Two models were developed: one model contained enamel, dentine, cementum, periodontal ligament, cortical and trabecullar bones, and the other model was a veneer restoration; both models were developed using MSC/Nastran software (MacNeal-Schwendler Corporation, Los Angeles, CA, USA) as the pre- and post-processor. A 10-N load was applied at the incisal edge from the lingual to the buccal side to simulate oral conditions in this area (protrusion). Results: Von Mises stresses were then analysed for three different regions: A-B (enamel elements under the veneer or second enamel layer), A′-B′ (buccal enamel and/or veneer element layer) and C-D (lingual enamel elements layer). A higher stress mode was observed for both models at the lingual cervical region. Conclusions: The presence of a veneer restoration on the incisors is a good alternative to mimic the behaviour of enamel under protrusion loading conditions. The use of veneers to replace enamel during rehabilitations is recommended.     

Mechanics of the maxillary central incisor. Influence of the periodontal ligament represented by beam elements

This study aimed to evaluate the influence of loading on a maxillary central incisor with the periodontal ligament (PDL) represented by 2D elastic beam elements using a 2D finite element analysis. Two models (M) were built varying the PDL representation: Mh (homogeneous PDL) and Mht (heterogeneous PDL with beam3 elements). Stress and displacements were determined for three loading conditions (L): Ll, lingual face loading at 45° with the tooth long axis; Li, perpendicular to the incisal edge; and Lip, on the incisal edge, parallel to the tooth long axis. Evaluation was performed on ANSYS software. Lip provided lower stress variation on the tooth and support structures when compared to Ll and Li. PDL's influence on stress values was lower for Lip. Oblique loading showed stress and displacement not observed in parallel loading condition through PDL's heterogeneous representation and it is probably incompatible with the in vivo condition.     

Influence of resin cement thickness and temperature variation on mechanical behavior of dental ceramic fragment restoration

To evaluate the stress behavior of ceramic fragment restoration, varying the thickness of the cement layer and intraoral temperature variation. A solid model of a upper lateral incisor was obtained and a defect at enamel distal/incisal edge was restored with a ceramic fragment. Based on this initial model, 4 different models (M) were built: M1 – absence of cement layer (CL) (0?μm of thickness); M2 – CL with an uniform thickness of 50?μm; M3 – CL with 50?μm at the margin of ceramics and 100?μm in the inner area far from margins; M4 – CL with 50?μm at the margin of ceramics and 200?μm in the inner area far from margins. The environment temperature changed from 5?°C to 50?°C in 4 increments. The finite element analysis was performed. Increase the cement layer thickness generated higher stress levels on ceramic surface in all temperatures, as well as on cement interface. In general hot temperature was the worst scenario for ceramic fragments integrity, since tensile and compressive stress were more intense. The maximum principal stress on ceramic fragment was found 90?MPa for M4 at 50?°C, followed for M3 (87?Mpa). For CL, the peak of stress was found for M3 at 5?°C (47?MPa). Is it possible to conclude that thick resin cement layer contribute to higher stress concentration on ceramic fragment, and extremely hot temperatures increase the risk of structural failure, since both ceramic and \cl are exposed to higher compressive and tensile stresses.     

辽宁大连晚更新世马类牙齿釉质结构的研究

大连晚更新世的马类共包括三个种类:野驴(Equus hemionus)、小型的普氏野马中国马亚种(E. przewalskyi sinensis)、大型的大连马(E. dalianensis)。从它们颊齿的釉质层微观结构、釉柱大小及釉质层的厚度分析,晚更新世的野驴和现生的野驴是十分接近的,可以归于同一个种。大连马与现在的普氏野马也比较接近,可归于同一个大的类别。然而,普氏野马中国马亚种却与现生的普氏野马有着比较显著的区别:中国马颊齿釉质层的釉柱平均直径比现生的普氏野马大得多,而釉质层的厚度又比现生的普氏野马更薄,所以,原来的分类未必合适,中国马似不应归于普氏野马,它可能代表一个比较特殊的种类。     

Stress analysis of irradiated human tooth enamel using finite element methods

The objectives of this project were to use finite element methods to determine how changes in the elastic modulus due to oral cancer therapeutic radiation alter the distribution of mechanical stresses in teeth and to determine if observed failures in irradiated teeth correlate with changes in mechanical stresses. A thin slice section finite element (FE) model was constructed from micro CT sections of a molar tooth using MIMICS and 3-Matic software. This model divides the tooth into three enamel regions, the dentin-enamel junction (DEJ) and dentin. The enamel elastic modulus was determined in each region using nano indentation for three experimental groups namely – control (non-radiated), in vitro irradiated (simulated radiotherapy following tooth extraction) and in vivo irradiated (extracted subsequent to oral cancer patient radiotherapy) teeth. Physiological loads were applied to the tooth models at the buccal and lingual cusp regions for all three groups (control, in vitro and in vivo). The principal tensile stress and the maximum shear stress were used to compare the results from different groups since it has been observed in previous studies that delamination of enamel from the underlying dentin was one of the major reasons for the failure of teeth following therapeutic radiation. From the FE data, we observed an increase in the principal tensile stress within the inner enamel region of in vivo irradiated teeth (9.97 ± 1.32 MPa) as compared to control/non-irradiated teeth (8.44 ± 1.57 MPa). Our model predicts that failure occurs at the inner enamel/DEJ interface due to extremely high tensile and maximum shear stresses in in vivo irradiated teeth which could be a cause of enamel delamination due to radiotherapy.     

The Adaptive Significance of Enamel Loss in the Mandibular Incisors of Cercopithecine Primates (Mammalia: Cercopithecidae): A Finite Element Modelling Study

In several primate groups enamel is reduced or absent from the lingual (tongue) side of the mandibular incisor crowns akin to other placental and marsupial mammalian groups such as rodents, lagomorphs and wombats. Here we investigate the presumed adaptation of crowns with unilateral enamel to the incision of tough foods in cercopithecines, an Old World monkey subfamily, using a simulation approach. We developed and validated a finite element model of the lower central incisor of the rhesus macaque (Macaca mulatta) with labial enamel only to compute three-dimensional displacements and maximum principal stresses on the crown subjected to compressive loads varying in orientation. Moreover, we developed a model of a macaque incisor with enamel present on both labial and lingual aspects, thus resembling the ancestral condition found in the sister taxon, the leaf-eating colobines. The results showed that, concomitant with experimental results, the cercopithecine crown with unilateral enamel bends predominantly towards the inside of the mouth, while displacements decreased when both labial and lingual enamel are present. Importantly, the cercopithecine incisor crown experienced lower maximum principal stress on the lingual side compared to the incisor with enamel on the lingual and labial aspects under non-axial loads directed either towards the inside or outside of the mouth. These findings suggest that cercopithecine mandibular incisors are adapted to a wide range of ingestive behaviours compared to colobines. We conclude that the evolutionary loss of lingual enamel in cercopithecines has conferred a safeguard against crown failure under a loading regime assumed for the ingestion (peeling, scraping) of tough-skinned fruits.     

Distribution of enamel on the incisors of Old World monkeys

Longitudinal ground sections of 29 Old World monkey central lower incisors were studied histologically and metrically. Labiolingual incisor width tended to scale isometrically with body weight but with important deviations in relative incisor size, which appeared to be correlated with diet in accord with work by Hylander. Lower incisors of the predominantly folivorous colobine monkeys had a substantial layer of enamel on both lingual and labial aspects and consequently had blunt incisal edges. These teeth in both cercopithecins and papionins, which are omnivorous or frugivorous, had little or no enamel on the lingual aspect, resulting in sharp incisal edges. It is suggested that colobine incisors are used mainly in gripping and tearing leaves, whereas cercopithecine incisors are better adapted to cutting and scraping. Crown height showed a positive allometric relationship with overall incisor height, so that the tall incisors of papionins, especially Papio and Mandrillus, were more hypsodont than the shorter incisors of colobines and cercopithecins. This appears to be related to differences in the rates of incisor wear between the groups.     

Three-dimensional finite element analysis of the maxillary central incisor in two different situations of traumatic impact

Dental trauma is one of the most common events in dental practice. However, few studies have investigated the biomechanical characteristics of these injuries. The objective of this study was to analyse the stress distribution in the dentoalveolar structures of a maxillary central incisor subjected to two situations of impact loading. The following loading forces were applied using a 3D finite element model: a force of 2000 N acting at an angle of 90°on the buccal surface of the crown and a vertical 2000 N force acting in the cleidocranial direction on the incisal surface of the tooth. Harmful stresses were observed in both situations, causing damage to both the tooth and adjacent tissue. However, the damage found in soft tissues such as periodontal ligament and dental pulp was negligible. In conclusion, injuries resulting from the traumatic situations were more damaging to the integrity of the tooth and its associated hard-tissue structures.     

Molar Microwear of Narrow-Headed Vole (<Emphasis Type="Italic">Microtus gregalis</Emphasis> Pall., 1779) Depending on the Feed Abrasiveness

In the narrow-headed vole, enamel microwear of the first mandibular molar (of the protoconid and entoconid anterior enamel wall) was studied under the laboratory conditions and at the fixed feed composition. The classic parameters and the area of the enamel prism lesion were taken into account. The enamel lesion patterns caused by the tooth–tooth and tooth–food interactions have been determined. Differences were found between the voles kept on feed with different abrasive properties, as well as between the lingual and buccal conids of the first mandibular molar. In the Microtus species, the ratio of micro-lesions (pits and scratches) did not depend on the abrasive properties of the feed consumed. The extent of preservation of the enamel contour anterior edge depended on the feed composition and could be used as an indicator for indirect evaluation of the Microtus species diet.     

Functional implications of enamel thickness in the lower molars of red colobus (Procolobus badius) and Japanese macaque (Macaca fuscata)

The purpose of this study is to determine whether teeth are likely to retain their functional efficiency throughout an individual's life time. This was done by comparing the enamel volume, the cross-sectional enamel area and the pattern of enamel distribution on unworn M(2)s of folivorous (Procolobus badius: red colobus; n=8) and frugivorous (Macaca fuscata: Japanese macaque; n=6) cercopithecids. The enamel volume of M. fuscata is significantly greater than that of P. badius. As the lower molars of colobines become worn, the dentine is exposed on the buccal cusps and narrow enamel rims are formed around the dentine exposures. The buccal enamel rims are especially well-developed and sharp, a pattern that has probably been selected for as being advantageous for shredding fibrous plant materials. The results of this study demonstrate that the enamel on the lingual side of the protoconid, where dentine exposure occurs first, is much thinner in P. badius than it is in M. fuscata. In addition, the dentine is exposed and thin enamel rims are formed faster in P. badius than in M. fuscata. Also, P. badius has significantly thinner and more uniform enamel distribution on the buccal wall of the crown and a higher protoconid. The buccal flare is well-developed in M. fuscata, but poorly developed in P. badius. It is tentatively suggested that the undeveloped flare and thinner enamel of P. badius combine to enable this species to maintain narrow rims, even after dental attrition, while the high cusps may be an adaptation for providing narrow enamel rims throughout life.     

Mechanical vulnerability of lower second premolar utilising visco-elastic dynamic stress analysis

Stress analysis determines vulnerability of dental tissues to external loads. Stress values depend on loading conditions, mechanical properties and constrains of structural components. The critical stress levels lead to tissue damage. The aim of this study is to analyse dynamic stress distribution of lower second premolar due to physiological cyclic loading, and dependency of pulsatile stress characteristics to visco-elastic property of dental components by finite element modelling. Results show that visco-elastic property markedly influences stress determinants in major anatomical sites including dentin, cementum–enamel and dentin–enamel junctions. Reduction of visco-elastic parameter leads to mechanical vulnerability through elevation of stress pulse amplitude, maximum stress value; and reduction of stress phase shift as a determinant of stress wave propagation. The results may be applied in situations in which visco-elasticity is reduced such as root canal therapy and post and core restoration in which teeth are more vulnerable to fracture.     

Brief communication: comparing loading scenarios in lower first molar supporting bone structure using 3D finite element analysis

Finite element analysis (FEA) is a widespread technique to evaluate the stress/strain distributions in teeth or dental supporting tissues. However, in most studies occlusal forces are usually simplified using a single vector (i.e., point load) either parallel to the long tooth axis or oblique to this axis. In this pilot study we show how lower first molar occlusal information can be used to investigate the stress distribution with 3D FEA in the supporting bone structure. The LM₁ and the LP²‐LM¹ of a dried modern human skull were scanned by μCT in maximum intercuspation contact. A kinematic analysis of the surface contacts between LM₁ and LP²‐LM¹ during the power stroke was carried out in the occlusal fingerprint analyzer (OFA) software to visualize contact areas during maximum intercuspation contact. This information was used for setting the occlusal molar loading to evaluate the stress distribution in the supporting bone structure using FEA. The output was compared to that obtained when a point force parallel to the long axis of the tooth was loaded in the occlusal basin. For the point load case, our results indicate that the buccal and lingual cortical plates do not experience notable stresses. However, when the occlusal contact areas are considered, the disto‐lingual superior third of the mandible experiences high tensile stresses, while the medio‐lingual cortical bone is subjected to high compressive stresses. Developing a more realistic loading scenario leads to better models to understand the relationship between masticatory function and mandibular shape and structures. Am J Phys Anthropol, 2012. © 2011 Wiley Periodicals, Inc.     

3-D stress analysis in first maxillary premolar

The aim of this study was to investigate the stress distribution in a 3-D model of two-rooted tooth (first maxillary premolar) under two different occlusal force vectors by using finite element analysis. In the first model overall force of 200 N was divided into three vectors (cusp to fossa occlusion), and in the second model overall force was divided into 4 vectors (cusp to fossa and cusp to marginal ridge occlusion). The greatest compressive stress was found at the dentino- enamel junction in the cervical area of the both models (about -200 MPa). The greatest tensile stress was found at the vestibular aspect of buccal cusp in second model (about +3 MPa) and in the central fossa of the both models (about +28 MPa). Results indicate that in the both types of occlusal loadings the stress distribution was mainly compression and compressive forces were predominant over tensile stresses. In the second model with 4 vectors, stresses generated in the tooth structure were higher compared to the stresses generated in the first model with 3 vectors.     

Three-dimensional finite element analysis of the composite and compomer onlays in primary molars

Resin onlay restoration is an esthetic alternative technique used for restoring extensively damaged primary molars. Understanding the behavior of materials under repeated functional stress and how the stress is transmitted to the remaining tooth structure is important. The aim of this study was to compare stresses in primary molars restored with indirect composite and compomer onlay. 3D frame models of the right mandibular and maxillary primary molars and the alveolar bone were created using computerized tomography images of a six-year-old girl. The enamel and dentine layers above the cement layer were unified to generate onlay restoration, and composite and compomer were used as restorative materials. The vertical occlusal load (100?N) was applied to the teeth in the occlusal contact areas. The von Mises stress distributions and normal stress distributions of the y-axis (parallel to the long axis of tooth) were evaluated. The occlusal stress is transmitted to the cervical part of healthy teeth by spreading it through the enamel layer. The composite and compomer restorative materials exhibited similar stress distribution patterns. An indirect technique creates a structure similar to the original morphological form, and it allows restorations to distribute high occlusal stresses and to minimize possible breakages.     

牙体预备对高嵌体修复下颌第一磨牙力学影响的初步研究

目的：通过有限元法,探讨高嵌体修复根管治疗后的下颌第一磨牙后,牙体预备形式对牙体组织受力的影响,为临床提供力学理论依据。方法：模拟右侧下颌第一磨牙的三维有限元模型,磨牙存在合面I类洞缺损,根管治疗后采用高嵌体修复,分别设计三种牙体预备形式,即覆盖全部牙尖、覆盖全部功能尖和覆盖部分功能尖的高嵌体修复,对模型进行加载,观察牙体组织的应力大小及分布。结果：覆盖全部牙尖高嵌体修复时牙釉质出现一个应力集中区,其他两种设计出现两个应力集中区。垂直载荷下,釉质的最大主应力在全部牙尖组分别低于其他两组92．29％和89．76％;舌颊向载荷下比其他两组分别降低80．91％和76．53％。三组牙本质的应力集中区趋于一致。垂直载荷下,牙本质的最大主应力在全部牙尖组分别高出其他两组12．92％和14．73％;舌颊向载荷下较其他两组高1．26％和5．08％。结论：从生物力学角度,覆盖全部牙尖的高嵌体更有利于牙体硬组织的受力,可以更好的对牙釉质起到保护作用。     

Effect of prism orientation and loading direction on contact stresses in prismatic enamel of primates: implications for interpreting wear patterns

The ability of prisms to effectively dissipate contact stress at the surface will influence wear rates in teeth. The aim of this investigation was to begin to quantify the effect of prism orientation on surface stresses. Seven finite element models of enamel microstructure were created, each model differing in the angulation of prism orientation with regard to the wear surface. For validation purposes, the mechanical behavior of the model was compared with published experimental data. In order to test the enamel under lateral loads, a compressed food particle was dragged across the surface from the dentino-enamel junction (DEJ) towards the outer enamel surface (OES). Under these conditions, tensile stresses in the enamel model increased with increases in the coefficient of friction. More importantly, stresses were found to be lowest in models in which the prisms approach the surface at lower angles (i.e., more obliquely cut prisms), and highest when the prisms approached the surface at 60 degrees (i.e., less obliquely cut). Finally, the direction of travel of the simulated food particle was reversed, allowing comparison of the difference in behavior between trailing and leading edge enamels (i.e., when the food particle was dragged either towards or away from the DEJ). Stresses at the trailing edge were usually lower than stresses at the leading edge. Taken together with what is known about prism orientation in primate teeth, such findings imply greater wear resistance at the intercuspal region and less wear resistance at the lateral enamel at midcrown. Such findings appear to be supported by archeological evidence.     

Elastic properties and masticatory bone stress in the macaque mandible

One important limitation of mechanical analyses with strain gages is the difficulty in directly estimating patterns of stress or loading in skeletal elements from strain measurements. Because of the inherent anisotropy in cortical bone, orientation of principal strains and stresses do not necessarily coincide, and it has been demonstrated theoretically that such differences may be as great as 45 degrees (Cowin and Hart, 1990). Likewise, relative proportions of stress and strain magnitudes may differ. This investigation measured the elastic properties of a region of cortical bone on both the buccal and lingual surfaces of the lower border of the macaque mandible. The elastic property data was then combined with macaque mandibular strain data from published and a new in vivo strain gage experiment to determine directions and magnitudes of maximum and minimum principal stresses. The goal was to compare the stresses and strains and assess the differences in orientation and relative magnitude between them. The main question was whether these differences might lead to different interpretations of mandibular function. Elastic and shear moduli, and Poisson's ratios were measured using an ultrasonic technique from buccal and lingual cortical surfaces in 12 macaque mandibles. Mandibular strain gage data were taken from a published set of experiments (Hylander, 1979), and from a new experiment in which rosette strain gauges were fixed to the buccal and lingual cortices of the mandibular corpus of an adult female Macaca fascicularis, after which bone strain was recorded during mastication. Averaged elastic properties were combined with strain data to calculate an estimate of stresses in the mandibular corpus. The elastic properties were similar to those of the human mandibular cortex. Near its lower border, the macaque mandible was most stiff in a longitudinal direction, less stiff in an inferosuperior direction, and least stiff in a direction normal to the bone's surface. The lingual aspect of the mandible was slightly stiffer than the buccal aspect. Magnitudes of stresses calculated from average strains ranged from a compressive stress of -16.00 GPa to a tensile stress of 8.84 GPa. The orientation of the principal stresses depended on whether the strain gage site was on the working or balancing side. On the balancing side of the mandibles, maximum principal stresses were oriented nearly perpendicular to the lower border of the mandible. On the working side of the mandibles, the orientation of the maximum principal stresses was more variable than on the balancing side, indicating a larger range of possible mechanisms of loading. Near the lower border of the mandible, differences between the orientation of stresses and strains were 12 degrees or less. Compared to ratios between maximum and minimum strains, ratios between maximum and minimum stresses were more divergent from a ratio of 1.0. Results did not provide any major reinterpretations of mandibular function in macaques, but rather confirmed and extended existing work. The differences between stresses and strains on the balancing side of the mandible generally supported the view that during the power stroke the mandible was bent and slightly twisted both during mastication and transducer biting. The calculated stresses served to de-emphasize the relative importance of torsion. On the working side, the greater range of variability in the stress analysis compared to the strain analysis suggested that a more detailed examination of loadings and stress patterns in each individual experiment would be useful to interpret the results. Torsion was evident on the working side; but in a number of experiments, further information was needed to interpret other superimposed regional loading patterns, which may have included parasagittal bending and reverse parasagittal bending.     

结合薄层CT技术建立下颌第一前磨牙三维有限元模型

目的结合薄层CT技术建立下颌第一前磨牙三维有限元模型。方法对正常人下颌第一前磨牙进行薄层CT扫描及图像处理,通过Matlab和ANSYS软件建立三维有限元模型,并加载验证模型力学分析的可行性。结果建立了包含髓腔的下颌第一前磨牙的三维有限元模型,得到101564个单元,144053个节点。载荷后的应力分布主要集中在颊尖部位和根尖部位,牙颈部受力较小。结论薄层CT技术与Matlab和ANSYS软件相结合,建立包含髓腔的下颌第一前磨牙的三维有限元模型,精度高、速度快,使用灵活,为后期的楔缺模型建立和分析奠定了基础。     

The primary enamel knot determines the position of the first buccal cusp in developing mice molars

The enamel knot (EK), which is located in the center of bud and cap stage tooth germs, is a transitory cluster of non-dividing epithelial cells. The EK acts as a signaling center that provides positional information for tooth morphogenesis and regulates the growth of tooth cusps by inducing secondary EKs. The morphological, cellular, and molecular events leading to the relationship between the primary and secondary EKs have not been described clearly. This study investigated the relationship between the primary and secondary EKs in the maxillary and mandibular first molars of mice. The location of the primary EK and secondary EKs was investigated by chasing Fgf4 expression patterns in tooth germ at some intervals of in vitro culture, and the relationship between the primary EK and secondary EK was examined by tracing the primary EK cells in the E13.5 tooth germs which were frontally half sliced to expose the primary EK. After 48 hr, the primary EK cells in the sliced tooth germs were located on the buccal secondary EKs, which correspond to the future paracone in maxilla and protoconid in mandible. The Bmp4 expression in buccal part of the dental mesenchyme might be related with the lower growth in buccal epithelium than in lingual epithelium, and the Msx2 expressing area in epithelium was overlapped with the enamel cord (or septum) and cell dense area. The enamel cord might connect the primary EK with enamel navel to fix the location of the primary EK in the buccal side during the cap to bell stages. Overall, these results suggest that primary EK cells strictly contribute to form the paracone or protoconid, which are the main cusps of the tooth in the maxilla or mandible.