Transactions on Biomedicine and Health vol 1, 1993 WIT Press, ISSN

Transcription

1 2d and 3d modelling comparison for a human first premolar to determine an appropriate cavityfillingmaterial B. Ekici, E. Giingor, M. Akyiiz & S. Altintas Bogazigi University, Istanbul, Turkey ABSTRACT A finite element Technique is used to examine the stress distribution in a human first premolar with and without cavity preparetion by using 2- dimensional and 3-dimensional models. The effects of different materials as cavity fillers on stress distribution are investigated. The effects of spring support conditions and temperature are also considered in the study. The finite element method, an often used engineering technique, is well suited for application to the dental stress analysis. 2D and 3D stress distribution have been investigated for a specific cavity design and for an inclined load conditions. Cavity preparation to first premolar causes high principal stress concentration as expected. Opening a cavity 1 mm above cole causes higher maximum principal stresses with respect to the tooth without cavity for both 2D and 3D models. The results obtained from these two different models are almost same. Gold and porcelain are placed both on aqua cem and ketac cem but, these materials providing better interfaces in clinical applications do not show important differences in mechanical point of view. Gold as cavity filling material shows good mechanical characteristics. It reduces the stress concentration due to the cavity opening. Porcelain shows better mechanical compatibility than gold. Stresses obtained by using porcelain are lower and the distribution of stresses are more homogenous. A higher temperature (50 C) results in a very slight increase in the stresses in the nodes around the cavity due to the increase in stresses created by restrained joints. Therefore temperature increase up to 50 C does not show any considerable increase. By using spring support condition displacements in longitudinal and horizontal directions are slightly increased. Springs with the coefficients given provide the elastic media given by the soft tissue under tooth.

2 264 Computational Biomedicine INTRODUCTION Fracture of sound whole theeth is a relatively uncommon event. However, failure of restored teeth, the restorative material and the joining interfaces occur as a result of many interrelated design and material factors. A major contributory factor is the complex stress and strain pattern set up both within the prothesis and hard tissue and also at the joining surfaces. It is possible to investigate some of these interrelated parameters by recourse to in vitro physical testing. However, such methods necessarily involve expensive and sophisticated equipment together with much time and expenditure in the setting up of each individual experiment (Williams K.R., J.T., Rees J.S. 1987). A knowledge of the intensity and distribution of stress can be helpful in avoiding or minimizing the failure of dental restorations. The effects of dental restorations and upon teeth themselves has been a topic of some interest to dental researchers over the past twenty years (Selna L.G., Shillinburg H.T., Kerp P.A. 1975). There are many cavity filling materials used in clinical applications. In this study it is thought that their mechanical behaviours undet certain conditions for the same model could be compared. Therefore, the most appropriate one for a specific cavity design and a load condition is desired to be found. MATERIALS AND METHODS The finite element method is suited to analyze the biological structures because the modelling of complex geometric shapes and maerials is easy with this technique. Inhomogenities of these structures can also be considered quiete easily. The finite element technique models the actual continuous structure with a discrete element representation (Thresher R.W., Saito G.E. 1973). The concept of the finite element method involves the idealization of the actual continuum as an assemblage of a finite number of discrete structural elements interconnected at a finite number of nodal points. The finite element are formed by figuratively cutting the original continuum into a number of appropriately shaped sections and retaining in the elements the

3 Computational Biomedicine 265 properties of the original material. (Farah J.W., Craig R.G. 1973) The process consists of satisfying compatibility within each element and equilibrium conditions are satisfied in the overall sense only. Local violations of equilibrium conditions within each element and at its boundaries could arise ( Farah J.W. et all 1974). The finite element approach is, in a sense, equivalent to the minimization of the total potential energy of the system in terms of the prescribed displacement field. If the displacement field is defined in a suitable way then, convergence to the correct value will correct (Khera S.C., et. all 1991). The model for 2 and 3 dimensional investigations is based on the actual geometrical data for the tooth and cavity preparation derived from an human first premolar. This approach allows an understanding of the regional stress variations related to the design of cavity preparation. A description of the development of 2 and 3 dimensional finite element model of the normal tooth and cavity preparation follows. Two and three dimensional representations for the first premolar with cavity are shown in Figure 1 a and b, respectively. Force is 25 kg L OQDB DODQ" OODO DQDQ OQDQ BED TO DDQQ M DDDD MS QQOQ DDDD ray MDO QQD/7 /ZD7 SEQ oooo am HUMAN FIRST PREMOLAR SHRUKKEN WRE FRAME Figure l.a 2 dimensional modelling of humanfirstpremolar As seen from the figure the region restrained is not allowed to move in any direction. The restrained joints can not move or rotate in x,y and z

4 266 Computational Biomedicine directions. The direction of the load is vertical as indicated in Figure 1 (a-b). The applied load is 250 N. UNOEFORMED SHAPE AU.JOWTS WIREFRAME Figure l.b 3 dimensional modelling of humanfirstpremolar The boundary conditions therefore are; 1 displacements u,v,w,=0 at the region restrained 2 shear stress t=0 at free surfaces empirical equation is valid in the domain where S=strain C=compliance cc=thermal expansion coefficient a=stress T=temperature FEM analysis of the first premolar is performed by using SAP90 structural application program (Wilson E.L. Habibullah A. 1984). For this program, the necessary modelling was created. The geometrical data necessary for these analysis are obtained by using a human first premolar. First of all geometrical data, i.e., x,y, and z coordinates are obtained. For 3D modelling, there are 1449 joints and 792 solid elements in the model whereas for 2D modelling there are 601 joints and 514 solid elements in the model. After that adaptive mesh generation is tried to be obtained. First 216 joints are restrained, these

5 Computational Biomedicine 267 joints form the roots of the first premolar. In the model, actual dimensions of soft tissue (nerves) are considered. The 3D model is divided in 36 section in circumferential direction. There are 16 sections in longitudinal direction of the tooth. Enamel layer has the actual dimensions. Cavity opened in the model has the dimension of 3.5 mm width, 2 mm height and 2 mm depth. The cavity, as can be seen from Figure la for 2D model and from Figure 2 for 3D model is placed 1 mm above the cole. The cavity is perpendicular to the longitudinal axis of the tooth. The cavity and corresponding joint numbers are also shown in Figure 2. Force is 25 kg Figure 2 Cavity location and its dimensions in 3 dimensional modelling An 45 inclined load of 250 N is applied on the occlusal surface as a concentrated load to simulate the compression and bending loads at the same time. 250 N load is almost one third of maximum biting force (Goel V.K, Khera S.C., Kanwerdip S. 1990).The effect of this load is investigated under the following conditions on a 3D first premolar for the following conditions: a- first premolar without cavity b- first premolar having a cavity, c- first premolar at 50 C temperature, d- first premolar having a cavity filled with gold placed on ketac cem e- first premolar having a cavity filled with gold placed on aqua cem f- first premolar having a cavity filled with

6 268 Computational Biomedicine porcelain placed on ketac cem g- first premolar having porcelain placed on aqua cem a cavity filled with h- first premolar restrained conditions in 3D and 2D by spring support i- first premolar having a cavity amalgam placed on zinc oxide eugenol filled with and then, compared with respect to maximum principal stresses created. In terms of the clinical implication, before filling the cavity with filling material an adhesive material is used to obtain better interface between filling material and dentine (Yettram A.L., et all 1976, Derand T. 1991) For the same reason ketac cem and aqua cem are used for filling the cavity with gold or porcelain. These materials provide better interfaces between dentine and cavity filling materials. The mechanical properties of all of the materials used in these analyses are given in Table 1. Some of the data are obtained from the manufacturers. The enamel and the dentine are ascribed the mechanical properties used by Yettram, and Wright for analyses of first premolar under nodal loads i.e., where these are effectively mean values within the range of published data for each material. E and m denote the modulus of elasticity and the value of Poisson^s ratio respectively. Isotropy and the anisotropy of the constituent materials, certainly the enamel, has been shown to have little effect on the stress distribution in the normal tooth under concentrated loading (Wright K.W.J., Yettram A.L. 1978) Thermal irritation applied to the tooth is one of the important causes of pulpitis and pulp death. The pulp undergoes thermal irritation during ingestion of hot and cold drinks (Takahashi N.1982). Therefore, the effect of temperature on the stress distribution is also investigated. Restrained joints at the roots of the first premolar are assumed to have spring support conditions. Necessary data for spring coefficients for horizontal and vertical directions are obtained from published data (Selna L.G., et all 1975). These values are;

7 Figure 3 dentine Transactions on Biomedicine and Health vol 1, 1993 WIT Press, ISSN i 35 I! X CO - 1,0 0,8-0,6 : 0,4-0,2-; -0,0- -0,2- -0,4- -0,6- -0,8- -1,0 376 Computational Biomedicine Q- GOLD -+ NORMAL O- TEMPERATURE -»- CAVTTY *" SPRING SUPPORT H> PORCELAIN -A- AMALGAM Stress distribution for the section just beneath the cavity for Figure 4 for dentine Q- GOLD NORMAL TEMPERATURE CAVITY SPRING SUPPORT PORCELAIN AMALGAM Stress distribution for the section at the center of the cavity Maximum Principal Stress Figure 5 dentine E 1 0,8-0,6-0,4-0,2- -0,0- -0,2- -0,4- -0,6- -0,8 -j /\ if**^ ^s3^ a ^j^*^^^^. * i i i i Q- -*- -D- 0" GOLD NORMAL TEMPERATURE CAVITY SPRING SUPPORT PORCELAIN AMALGAM Stress distribution for the section just above the cavity for

8 270 Computational Biomedicine im Principal Stress x I (S» E I -0,6- -0, Q- GOLD NORMAL *- TEMPERATURE -«- CAVITY *- SPRING SUPPORT 0- PORCELAIN * AMALGAM Figure 6 enamel Stress distribution for the section just beneath the cavity for CO 15a. X (0 I 0,4 0,2; 0,0 - -0,2- -0,4- -0,6- -0,8- -1, GOLD NORMAL TEMPERATURE CAVITY SPRING SUPPORT PORCELAIN AMALGAM Figure 7 for enamel Stress distribution for the section at the center of the cavity GOLD NORMAL TEMPERATURE CAVITY SPRING SUPPORT PORCELAIN AMALGAM Figure 8 Stress distribution for the section just above the cavity for enamel

9 Computational Biomedicine 271 is for the section above the cavity. As stated above Figures 3 to 5 are for dentine region. Sections corresponding for Figures 6 to 8 are same as for Figures 3 to 5. The stress distribution around the cavity shows that maximum principal stresses around the cavity are higher than the other regions and also same region for the one without cavity. As seen from Figures 3 to 5 cavity opening causes high tensile stresses at the bottom and at the top of the cavity whereas it causes high compressive stresses in the center of the cavity. This is valid for dentine and enamel regions. The interface materials do not show considerable differences. The reason for this is related to their mechanical properties which are very close to each other. Gold as a cavity filler, reduces the high compressive stresses in the center of the cavity but, at the bottom and at the top of the cavity gold causes extra drop at the stress so that it causes a little bit higher compressive overall stresses. Although there is a slight increase in the maximum stresses at the top and at the bottom of the cavity the trend of the stress is almost homogeneous. It looks like the same as the trend of a first premolar without cavity (normal tooth). For the case of porcelain the effects are the same as the gold. Furthermore, porcelain has better stress distribution pattern than the one filled with gold. The effects of spring support foundation condition are negligible. This condition is for idealization of the real tooth modelling. Although, as seen from Figures 3-8 there is no considerable change for the maximum principal stresses for spring support foundation conditions, the corresponding displacements at the root of the first premolar are very different but, in a reasonable range. This shows that the model behaves same as real one in human mouth. Although in 2D and 3D modelling because of restrained joints region there is a slight increase in the stresses for the joints below the cavity, the effect of the temperature on stress distribution around the cavity is also negligible. As seen from the figures normal tooth, normal tooth with temperature and normal tooth with spring support conditions have almost same stress distribution

10 272 Computational Biomedicine around cavity. The differences occur when the displacements are concerned. ' The addition of temperature to the system increases the displacements. Of course these results are true only from the mechanical point of view. The microstructural and biological effects of the interface materials can not be considered in FE model yet. To appreciate realistically the stress distribution characteristic in a tooth under certain loading conditions, it is critical to use a three dimensional finite element model although in this study the results do not show too much differences (Khera S.C, et all 1988, Rubbin C., et all 1983). REFERENCES 1. Derand T. (1991) Stress Analysis of Cemented or Resin-bonded Loaded Porcelain Inlays Dental Materials 7: Farah J.W., Craig R.G. (1973) Finite Element Stress Analysis of a Restored Axisymmetric First Molar J. Dental Research July-August. 3. Farah J.W., Craig R.G., Skarskie D.L. (1974) Photoelastic and Finite Element Stress Analysis of a Restored Axisymmetric First Molar Journal of Biomechanics 6: Goel V.K, Khera S.C., Kanwerdip S. (1990) Clinical Implications of The response of Enamel and Dention to Masticatory Loads The journal of Prosthetic Dentistry 64: Khera S.C., Goel V.K., Chen R.C.S., Gurusami S.A ) Parameters of MOD Cavity Preparations: A 3-D FEM Study, Part II Operative Dentistry 16: Khera S.C, Goel V.K., Chen R.C.S., Gurusami S.A. (1988) A Three Dimensional Finite Element Model Operative Dentistry 13: Rubbin C., Krishnamurthy N., Capilouto E., Yi H. (1983) Stress Analysis of The Human Tooth Using a Three-Dimensional Finite Element Model J. Dent. Res Selna L.G., Shillinburg H.T., Kerp P.A. (1975) Finite Element Analysis of Dental Structures

11 Computational Biomedicine 273 Axisymmetric and Plane Stress Idealizations Journal of Biomedical Material Research, 9: Takahashi N. (1982) Thermal Conductive Analysis of Restored Teeth by Finite Element Method Journal of Oral Rehabilitation 9: Takahashi N., Kitagami T., Komori T. (1980) Behaviour of Theet Under Various Loading Conditions With Finite Element Method Journal of Oral Rehabilitation 7: Thresher R.W., Saito G.E. (1973) The Stress Analysis of Human Teeth Journal of Biomechanics 6: Williams K.R., J.T., Rees J.S. (1987) Finite Element Analysis of an Amalgam Restored Molar Tooth Dental Materials 3: Wilson E.L., Habibullah A. (1984) SapSO Structural Analysis Program Case Western University Berkeley California. 14.Wright K.W.J., Yettram A.L. (1978) Finite Element Stress Analysis of a Class I Amalgam Restoration Subjected to Setting and Thermal Expansion Journal of Dental Material Research Yettram A.L., Wright K.W.J., Pickard H.M. (1976) Finite Element Stress Analysis of The Crowns of Normal and Restored Teeth Journal of Dental Research Zhou S.M., Hu H.P., Wang Y.F. (1989) Analysis of Stresses and Breaking Loads for Class I Cavity Preparations in Mandibular First Molars Quintessence International 20: