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Restoration of endodontically treated teeth with flared root canal and thin walls near the cervical part is frequently a challenge for dentists. It becomes especially complex when the involved teeth have previously undergone treatment for caries, fractures, endodontic-access preparation, canal instrument- ation, and other idiopathic causes. 1,2 These problems result in loss of tooth structure and consequent reduction in tooth resistance to myriad of intraoral forces. 3,4
A number of guidelines have been suggested for restoring endodontically treated teeth. 5,6 Post- retained crown is necessary to restore compromised teeth with flared canals. Some studies suggested that parallel posts provided greater retention and distributed occlusion forces more uniformly than tapered posts, thus reduced the risks of radicular fracture. 7 On the other hand, the development of new post materials and adhesive cements invoked a renewed investigation regarding the most effective way of restoring endodontically treated teeth. For example, the post system incorporated the use of adhesive materials and techniques for the intraradicular reinforcement of roots with thin walls, taking advantage of the advances in restorative technologies. 8 Some favorable clinical results with resin reinforcement and dowel and cores in structurally weakened teeth have been reported by some clinicians. 9 To avoid the extraction of weakened roots, filling of the radicular defects with restorative materials has been suggested. 10
The post core systems consisted of components of different rigidity, among which different elastic modulus existed between dentin, cement and post material. Therefore, many dentists have speculated that it might be a source of stress for the root structures. 11,12 However, no literature precedence was reported about the direct experimental measurement of the stress distribution at these locations. To date, it has been difficult to provide the valid index of stress distribution solely based experimental and clinical observation. On the other hand, finite element method (FEM) has recently become a powerful technique in dental biomechanics because its versatility to calculate stress distribution within complex structures, and it is most suitable for biological structures. Thus, we envision it as a good tool to evaluate the influence of model parameter variation once the basic model has been correctly defined.
Previously, some investigators 13,14 tried to used two-dimensional axisymmetric models to describe the post and core restorations mechanical behavior. Other investigators 15-17 reported that the materials of the post and core affected the stress distribution of endodontically treated teeth restored with post-and-core system using three-dimensional FEA. Meanwhile, limited information could be found in the literature about the comparison study of stress distribution in roots when cements with different modulus of elasticity were used. Some investigations showed that load transferred from post to root dentine structure differed due to the different cements used. These studies 18 confirmed the occurrence of stress redistribution through the entire root and its role in lightening specific regions from high stress concentrations, especially at post-dentin interface. To the best of our knowledge, there is no literature precedence about stress distribution in weakened roots using FEM.
The objective of this study was to analyze the stress distribution in weakened roots restored with different cements in combination with titanium alloy posts under one masticatory load, and to evaluate the results by comparing different cements by using three-dimensional (3D) FEA.
METHODS
Selection of cements and posts
The cements used in this study were Superbond C&B from Sun Medical CO., LTD of Japan, glass ionomer cement from Promedica of Germany, zinc polycarboxylate cement from SHOFU Inc. Kyoto of Japan, Panavia F from Kuraray of Japan, and zinc phosphate cement from Dental Materials Factory of Shanghai Medical Instruments Co., Ltd of China. The titanium alloy posts used in the study were from ParaPost System, Whaledent of America.
Sample selection and raw data acquisition for the model
A standard adult central maxillary incisor was selected in compliance with the standard criterion of Chinese human tooth. The sample was 23.0 mm long, with crown length of 11.2 mm, and root length of 11.8 mm, respectively. 19 Spiral CT scanned profiles of maxillary bone and teeth of the volunteer were obtained to generate two-dimensional images.
Establishment of 3D finite element model
Figs. 1, 2 show that root canal wall was 1.0 mm in thickness at the cervical 1/3 part of the root; the post was 8.0 mm in length and 1.5 mm in diameter. The thickness of the cement layer ranged from 0.04 mm to 1.4 mm in thickness. 10
CT images scanned with Micro Tek scanner were transferred into bitmap format first. Then the BMP bitmaps were imported into Photoshop7.0 and positioned precisely. The parts of research interest of the image were outlined and saved as grey-scale maps.
First, the image from the graphic file was fetched with Imread function in the Matlab6.5 software and expressed in 2D matrix. Data of matrix C (2Xn) in color-changed grey-scale map were found out by contour function (D,1); Then the data of blocked individual configuration were described with matrix. Finally, boundary data were smoothed and fitted with smooth function and saved as format that can be directly read by Ansys. Images were saved in *.dat or *.txt file format, and key points were saved as k, m, x, y, z. Parameters of image identification range, pixel spacing, and layer spacing were set up with this software, and different precision of model establishment could be read according to the need of the mechanics analysis method.
The transferred *.dat or *.txt files were read from Ansys 8.1, then the points were changed into fitting curves, and the curves were transfered into plane and solid. Crown, post, core, and dentin models were made according to the experiment design. Obtained data were transferred into *.igs format which could be read with Pro/E. The transferred data were saved. The data were read in Pro/E and the curves that were prone to produce stress intensity were smoothed by Variable Section sweep method, and then the models were formed into packed multimer by fitting calculation. All these data were saved as *.igs or *.prt format. The data were imported into Ansys, and the solid was meshed with elements and nodes. Results were analyzed according to the material property, boundary condition, simulated load and distribution of stress.
Mesh division of 3D FE model
Mesh command in the Ansys software was used to perform a smart mesh division of the FE model. There were 30192 nodes and 10374 elements in the model.
Load type and boundary condition
In all cases, load of 100N was applied at the junction between upper 1/3 and middle 1/3 of the palatal surface of the crown at 45 ° angle with the tooth longitudinal axis. 20 Boundary condition of the model was fixed support on the bottom of the alveolar bone. 21
Hypothesis condition, main parameters and calculation of the model
All materials used in this study were assumed to be isotropic, homogenous, and elastic. Small deforma- tion was neglected during the loading. The elastic modulus and Poisson's ratio of materials could be seen in the attached Table 1. Maximum principle stress and Von Mises stress values in root dentin and cements could be obtained by introducing the model into FEA.
RESULTS
Peak values of maximum principal stress and Von Mises stress in root dentin
Table 2 shows Von Mises stress peak and maximum principal stress peak values in dentin and cement of root. Fig. 3 shows cloud atlas of Von Mises stress distribution in root restored with five different cements. As shown in Fig. 3, Von Mises stress peak concentrated at the labial and lingual dentin of external surface of the upper part of the root, which was independent to the cements used. Maximum principle stress peak was located at external surface of the lingual dentin at the upper part of the root.
From Table 2, when elastic modulus of the cement was increased from 1.8 GPa to 22.4 GPa, maximum principal stress and Von Mises stress peak values in dentin gradually decreased. When titanium alloy post was cemented with Superbond C&B (elastic modulus: 1.8 GPa), stress peak value in dentin reached its maximum (Von Mises: 24.51 MPa, maximum principle stress: 39.58 MPa). Comparatively, a small stress peak value in dentin was obtained when cemented with Panavia F(elastic modulus: 18.3 GPa) and zinc phosphate cement (elastic modulus: 22.4 GPa). No difference in stress peak value was observed when cemented with Panavia F or zinc phosphate cement.
Distribution pattern of Von Mises stress and maximum principal stress in root dentin
From Fig. 3, the high stress region of Von Mises stress was found to be located at labial and lingual dentin of mid-upper part of the root. High stress region of maximum principle stress was located at lingual dentin of mid-upper part of the root. By analyzing the stress cloud atlas of the cements, changes of the trend of the stress were observed. When the elastic modulus of the cement was increased, the maximum principle stress value and Von Mises stress value in high stress region were slightly decreased; when elastic modulus of the cement (Panavia F and zinc phosphate) was close to that of the dentin, the extension range of the maximum principle stress and Von Mises stress was small. In all experimental groups, high stress region extended along external surface of the root. The high stress extension range of Von Mises stress in external surface of lingual side of the root was greater than that of the labial side.
Maximum principal stress and Von Mises stress peak values in cement layer of roots
During stress loading, maximum principle stress and Von Mises stress in cements increased with the increase of elastic modulus of cements. Table 2 shows the peak values in all groups, among which Superbond C&B had the smallest stress value, while zinc phosphate had the largest stress value.
DISCUSSION
A three-dimensional finite element model of weakened root, restored with titanium alloy post in combination with different cements, was established for the first time in this study. Stress distribution pattern in dentin and cement layer of the root was analyzed. Five representative cements with elastic modulus ranging from 1.8 GPa to 22.4 GPa were selected for the study, among which, glass ionomer cement, zinc polycarboxylate cement, and zinc phosphate cement possessed weak bonding power 26 and Superbond C&B and Panavia F were from the category of resin cement which possessed strong bonding power to dental enamel, dentin and metal. 27-29 Paralleled post was selected in this study based on previous reports about its ability to distribute occlusal force more evenly and thus reduce fracture risk of the root. In this study, effect factor of cements was the only studied factor; other factors were considered to be constant because the focus of the study was on the effect of cements on stress distribution in restored weakened roots.
Among all properties of cement, elastic modulus was the most important factors that affecting stress redistribution of restorations. Stress was passed to root dentin by two ways: one was passed directly from tooth crown to root dentin; the other was from post and cement to root dentin. Stress distribution of weakened root restored with different cements was analyzed by FEM. Results showed that stress concentrated at upper part of the root. There were more possibilities of occurring fracture in upper part of the root when loading because root canal wall was thinner in upper part of the root. Therefore it is more important to reduce stress in upper part of the root. The key discoveries of this study were summarized below.
Relation between elastic modulus and stress in root dentin ： when tooth was loaded, occlusion force was passed to the root. The root dentin could bear the load together with the cement when elastic modulus of cement was closer to that of the dentin. This made stress in root distributed more evenly, high stress region extension was reduced, and maximum principle stress and Von Mises stress was also decreased. Thus the incidence of root fracture would be decreased. When cement with an elastic modulus close to the dentin was selected, optimal combination and mechanical compatibility of the cement and dentin could be achieved, thus enhanced the ability to resist external force together. Stress in dentin was reduced due to the cement sharing parts of the stress. Stress distribution in root could be improved and extension of high stress region could be prevented by selecting cements with elastic modulus close to that of the dentin, and thus further reduced root fracture incidence.
Load borne by cements changed with elastic modulus： when restorations cemented with cements with much less elastic modulus than that of the dentin, cements and adjacent root dentin could not deform at the same time. Under such conditions, the maximum principle stress and Von Mises stress in root dentin were greater because root dentin bore more load. When elastic modulus increased to 5.11 GPa, its deform-resistant ability increased accor- dingly. Under such conditions, the cement borne parts of the static load, so maximum principle stress and Von Mises stress in dentin were decreased. When elastic modulus was close to that of the dentin, root dentin and cement had similar deform- resistance ability, namely they could deform at the same time, bear static load by cement and root dentin, better the stress in root, evenly distribute the stress, and reduce extension range of high stress region. When elastic modulus was continuously exceeded to 18.6 GPa, deformation ability of cements was greater than that of the dentin, which made the cements bear more occlusion force, resulting in the fracture of cements first.
Results of this study further validate the principle that elastic modulus of the dental material used in restoration should be close to that of the dentin. Recently, the preference of dentists has been changed from very rigid materials to materials that closely resemble dentin to create a mechanically homogenous unit. 11,12 We successfully demonstrated FEM was effective in analyzing stress distribution in dentin and cement layer of the weakened root enforced with different cements. The stress analysis under our experimental conditions would provide some useful guidance for clinic practice. For examples, although Superbond C&B is currently used in clinic for its super adhesive ability, 27-29 it is not our recommendation to use it in the restoration of weakened root designed like the study. According to our analysis, deformation of cements was greater than that of the root dentin when occlusion force was passed to the root, which resulted in the majority of the force being borne by the root. For zinc phosphate, despite the fact that its elastic modulus was close to that of dentin and its stress concentration area was small, restoration with zinc phosphate still often failed because of its relatively great elastic modulus, fragility and low bonding power to dentin, enamel and metal. The finding of this study supported the work of Mendoza who claimed that those root systems restored with a dentin bonding cement were more resistant to failure than root systems that used zinc phosphate as the cementing medium. 10
It has been reported that the canal and the tooth contours as well as the dentine and cement thickness significantly affected the stress distribution in remained tissues, 30 while these indexes in weakened root were different with those of other experiment objects. Therefore, the stress distribution results of the study could not be compared with other investigations. However, the findings of our study confirmed the importance of the rigidity of the cement in the assessment of the ability of the material to redistribute the stresses in weakened root. These observations were in agreement with the experimental literature using external strain gauge measurements and the literature of FEA. 22,31
Although the stress distribution in weakened roots restored with different cements was successfully analyzed in this study, it also had limitations. Some of these limitations resulted from the assumptions made about the properties of the materials and tissues forming the finite element models, application of 100 N loading only, and the loading scenarios investigated lacking the complexity of loading, which occurs in function in the patient. However, as mentioned earlier, it was not the objective of this study to determine the numerical stress levels created within the restoration but to examine their distribution. The measure used in this study was not capable of testing the model to failure and therefore higher or lower loads would only change the magnitude of the stresses in the distribution pattern. Moreover, the numeric theoretical analysis was obtained in the study, and the findings should be validated in related clinical and in vitro experimental observations, which will further develop key principles in weakened radicular therapy.
In conclusion, by using 3 － D FEA, our study verified that elastic modulus was one of the important parameters to evaluate property of the cement and affect stress redistribution in restoration. Within the limitations of this study, the cement with elastic modulus similar to that of dentin could reinforce weakened root and reduce the stress in dentin. Thus, it may be a better choice for the restoration of weakened roots.
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