Romanian Biotechnological Letters Vol. 20, No. 4, Modelling and Finite Element Method in Dentistry

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1 Romanian Biotechnological Letters Vol. 20, No. 4, 2015 Copyright 2015 University of Bucharest Printed in Romania. All rights reserved ORIGINAL PAPER Modelling and Finite Element Method in Dentistry Abstract Received for publication, July 07, 2014 Accepted, May 16, 2015 ANDREEA ANGELA ŞTEŢIU 1, VALENTIN OLEKSIK 2, MIRCEA ŞTEŢIU 2, MIHAI BURLIBAŞA* 3, VICTOR TRĂISTARU 3, LUMINIŢA OANCEA 4, SERBAN BERTESTEANU 5,6, ILEANA IONESCU 1 Faculty of Medicine, Lucian Blaga University, Sibiu, Romania, 2 Faculty of Engineering, Lucian Blaga University, Sibiu, Romania, 3 Faculty of Midwifery and Nursing, University of Medicine and Pharmacy Carol Davila Bucharest, Romania, 4 Faculty of Dental Medicine, University of Medicine and Pharmacy Carol Davila Bucharest, Romania. 5 Head & Neck Surgery Clinic, Colţea Clinical Hospital, Bucharest, Romania; 6 University of Medicine and Pharmacy Carol Davila, Bucharest, Romania *Correspondence address: Bld. Mărășești nr. 2B, Sc. 2, et. 5, ap. 17, sector 4, Bucharest, Romania, Tel: ; mburlibasa@gmail.com Our aim is to provide to the researchers with a method for applying finite element analysis in dentistry. It is well known that dentistry has evolved and more prosthetic reconstructions are made using CAD-CAM technology. Thus, is necessary to investigate how the stress and deformations in this works are acting and if there are some possibilities to improve the shapes of the preparations. Starting point was 3D scanning of the dental casts and natural teeth as well. 3D modelling stage for teeth reconstruction is presented. As conclusion a finite element analyse of natural teeth is presented. The FEM provide us information about stress and strains, principal stress and principal strains, nodal displacements and safety factor. Keywords: finite element method, dentistry, teeth modelling. Introduction The finite element method (FEM) allows finding approximate solutions of partial differential equations and of integral equations as well. The solution approach is based either on eliminating the differential equation completely, or rendering the partial differential equations into an approximating system of ordinary differential equations, which are then numerically integrated [1, 2, 3, 4, 5]. In engineering this allows to search static analysis, dynamic or own values cases. For complicated cases one of them can be used to simplify the model and to solve differential equations on this simplified model, or on a real model obtained after scanning. In literature is shown that in around 99% cases the real model investigation is closer to reality than the solutions revealed from a simplified model analyse. Therefore the modelling process after scanning must be laborious and precise [1, 2, 3, 6, 7, 8]. Materials and Methods 2.1. Scanning process. The CAD-CAM technologies in dentistry are usually used in laboratory techniques of reconstruction for teeth or dental structures. It has developed when the use of zirconium became base material in all-ceramic fixed prosthetics parts. In order to be manufactured in laboratory, zirconium being a hard material, it became easier to use pre- Romanian Biotechnological Letters, Vol. 20, No. 4,

2 ANDREEA ANGELA ŞTEŢIU, VALENTIN OLEKSIK, MIRCEA ŞTEŢIU, MIHAI BURLIBAŞA, VICTOR TRĂISTARU, LUMINIŢA OANCEA, SERBAN BERTESTEANU, ILEANA IONESCU synthesized zirconium oxide, more machinable, and after machining to obtain a hard structure for crowns and multi-unit bridges in the anterior and posterior segments. For our goals it can be used the Next Engine 3D Scanner (fig. 1A) in order to capture objects in full colour with multi-laser precision and output 3D scan models to popular design software like Solid Works, Catia, ProEngineer, Solid Edge, Unigraphics. In figure 1 is presented a dental cast and a natural tooth being scan. The captured images are presented in order to be processed with design software and tools. Figure 1. Scanning process. A scanned model; B capture of the scanned model; C human teeth; D capture of a real teeth. For the same goal, scanning a dental cast one part of the CERCON system Cercon EYE [9] can be used to scan and obtain certain image of a model as shown in figure 2. In figure 2 is presented CERCON EYE scanning system of a cast and its captured image to be modelled and machined. Figure 2. Using CERCON [9] scanning system. A positining the model to be scanned; B model position in Cercon eye; C image captured; D Cercon eye laser beam scrolling the model Romanian Biotechnological Letters, Vol. 20, No. 4, 2015

3 Modelling and Finite Element Method in Dentistry 2.2. Modelling process. For modelling it is necessary to import the acquired data, reducing data collection and number of points using a variety of predefined built-in filters of the scanner software. Multiple Scanning has direct influence on the processing phase of point s dispersion conducting to an approximately geometric model of the scanned object as shown in figure 1 B,D. Generating CAD models from point clouds depends on the real purpose of using the models. As an example, for studying the mechanical behaviour of the teeth or dental structures the main goal is to obtain an accurate geometric model. The results of this phase are geometric models in one of formats such as: IGES, VDA, STL, DXF, OBJ, VRML and the moats accurate CAD format for exporting a 3 D model ISO G Code, with images as in figure 3. Figure 3. CAD modells. A model generated from point clouds; B network model. Once a model is obtained it requires CAD editing in specialized software in order to have a geometrical shape and dimensions close to the reality as shown in figure 4. Therefore, is needed to erase the surfaces erroneously generated and replace them with correct desired surfaces and then assembling in a single surface, and generating the model volume based on existing surfaces. Figure 4. Editing a model. A acquired image with errors indicated by arrows; B network image of acquired shape; C initial shape; D final corrected shape. In integrated systems such as Cercon (9) is also necessary to manually or automatic correct the shapes in order to obtain an accurate CAD Model. In figure 5A is shown the model Romanian Biotechnological Letters, Vol. 20, No. 4,

4 ANDREEA ANGELA ŞTEŢIU, VALENTIN OLEKSIK, MIRCEA ŞTEŢIU, MIHAI BURLIBAŞA, VICTOR TRĂISTARU, LUMINIŢA OANCEA, SERBAN BERTESTEANU, ILEANA IONESCU of an abutment obtained after scanning with Cercon-Eye. Processing the margins of the preparations is shown in figure 5B and designing the bridge is shown in figure 5C. Figure 5. Processing an acquired image. A acquired image after scanning; B processing margins of the acquired image; C modelling the bridge crowns and connectors Finite element method analysis. As an analysing method adequate software such as ANSYS 11 [10, 11, 12] can be used. The software permits to analyse the strain and stress state based on the discrete principle and modal analysis using the finite element method. So we determine the strain and stress state when loading the model in static regime. To analyse the stress distribution, the equivalent tension von Mises ( ecv ) is used, and the ANSYS program calculates it as quadratic average of normal stress at the base, middle or top of the finite elements. For a better simulation of reality, the bite force to be introduced and simulated in finite element analysis with Ansys software is 400 N/teeth as it results from Waltimo s research, where the value of 847 N in the molar region is uniform distributed left/right and on the same side divided on 2 molars from which a greater surface has the first one [11, 12, 13, 14, 15]. In figure 6 is presented a molar to be studied when a tripod contact occurs modelled as a contact with a sphere which simulates the real teeth contact pattern. The results are obtained as graphs of stress and strain, displacements and safety factor charts. Analyse of these charts provides information about teeth, crowns or abutments comportment in vivo Romanian Biotechnological Letters, Vol. 20, No. 4, 2015

5 Modelling and Finite Element Method in Dentistry Figure 6. ANSYS numerical analysis of a molar in tripod contact. A model with spherical tripod contact; B nods; C total equivalent stress (von Mises); D - deformation chart; E safety factor chart. Conclusions Using the analysing with finite element method provides information about stress and strains on xyz directions; principal stress and principal strains, and also equivalent (von Mises or Tresca) stress and strains; nodal displacements and total displacement at nodes; safety factor. For a better analysis it is necessary to obtain an accurate model of the studied part. This can be done using laser beam scanners and adequate software to correct the eventually scan errors. References 1. V. OLEKSIK, A. PASCU. Modern methods of study and research in mechanical engineering applied to medicine. Proceedings of 5th Balkan Region Conference on Engineering and Business Education & 2 nd International Conference on Engineering and Business Education, Sibiu, Romania Information on 3. Information on 4. L.J. van RUIJVEN, L. MULDER, T.M.G.J. van EIJDEN. Variations in mineralization affect the stress and strain distributions in cortical and trabecular bone. Journal of Biomechanics, 40(6): , (2007). 5. C. KOPLIN, R. JAEGER, P. HAHN. A material model for internal stress of dental composites caused by the curing process. Dental Materials, 25(3): , (2009). 6. MERDJI, R. MOOTANAH, B. A. B. BOUIADJRA, A. BENAISSA, L. AMINALLAH, EL B. O. CHIKH, S. MUKDADI. Stress analysis in single molar tooth. Materials Science and Engineering C 33: , (2013). 7. ELIOT J. CHIKOFSKY and JAMES H. CROSS II, Reverse Engineering and Design Recovery: A Taxonomy, IEEE Software, vol. 7, no. 1, pp , (1990). 8. MICHAEL L. NELSON. A Survey of Reverse Engineering and Program Comprehension, Technical Report arxiv cs/ , Old Dominion University Department of Computer Science, (1996). Romanian Biotechnological Letters, Vol. 20, No. 4,

6 ANDREEA ANGELA ŞTEŢIU, VALENTIN OLEKSIK, MIRCEA ŞTEŢIU, MIHAI BURLIBAŞA, VICTOR TRĂISTARU, LUMINIŢA OANCEA, SERBAN BERTESTEANU, ILEANA IONESCU 9. A.A. ŞTEŢIU, M. OLEKSIK, V. OLEKSIK, R. PETRUSE, M. ŞTEŢIU. The minimal burr dimensioning of teeth preparations to be restored with biomaterials. Romanian Biotechnological Letters, vol. 18, no. 3, pp , A.A. ŞTEŢIU, M. OLEKSIK, V. OLEKSIK, M. ŞTEŢIU, M. BURLIBAŞA. Mechanical behavior of composite materials for dental obturations. Romanian Biotechnological Letters,18, 4: , (2013). 11. M. ŞTEŢIU, A. ŞTEŢIU. Alternative analysis of masticatory forces. Proceedings of The 4th International Conference on Manufacturing Science and Education MSE Volume I, ISSN : , Editura Universităţii Lucian Blaga Sibiu, 2009: TAMAS VARADY, RALPH R. MARTIN, JORDAN COX. Reverse Engineering of Geometric Models - An Introduction. Computer Aided Design vol. 29, no. 4, pp , (1997). 13. MERDJI, R. MOOTANAH, B. A. B. BOUIADJRA, A. BENAISSA, L. AMINALLAH, EL B. O. CHIKH, S. MUKDADI. Stress analysis in single molar tooth. Materials Science and Engineering C 33: , (2013). 14. FRĂŢILĂ, V. OLEKSIK, C. BOITOR, A. PASCU, B. PIRVU. Numerical study about the strain analysis and the marginal design of dental indirect restorations. Romanian Biotechnological Letters,. 17, 4: , (2012). 15. M. FAGESA, P. SLANGENB, J. RAYNALA, S. CORNB, K. TURZOC, J. MARGERIT, F. J. CUISINIERA. Comparative mechanical behavior of dentin enamel and dentin ceramic junctions assessed by speckle interferometry (SI). Dental materials 28: e229 e238 (2012) Romanian Biotechnological Letters, Vol. 20, No. 4, 2015