Stomatologija, Baltic Dental and Maxillofacial Journal, 10: 67-71, 2008

Isaac Newton Lima da Silva, Gustavo Frainer Barbosa, Rodrigo Borowski Grecco Soares, Maria
Cecilia Gomes Beltrao, Ana Maria Spohr, Eduardo Golcalves Mota, Hugo Mitsuo Silva Oshima,

Luiz Henrique Burnett Jr.

SUMMARY

The use of Finite Element Analysis (FEA) is becoming very frequent in Dentistry. However,
most of the three-dimensional models presented by the literature for teeth are limited in terms of
geometry. Discrepancy in shape and dimensions can cause wrong results to occur. Sharp cusps and
faceted contour can produce stress concentrations, which are incoherent with the reality.
Aim. The aim of this study was the processing of tomographic images in order to develop an
advanced three-dimensional reconstruction of the anatomy of a molar tooth and the integration of
the resulting solid with commercially available CAD/CAE software.
Methods. Computed tomographic images were obtained from 0.5 mm thick slices of mandibular
molar and transferred to commercial cad software. Once the point cloud data have been generated,
the work on these points started to get to the solid model of the tooth with Pro/Engineer software.
Results. The obtained tooth model showed very accurate shape and dimensions, as it was
obtained from real tooth data with error of 0.0 to -0.8 mm.
Conclusion. The methodology presented was efficient for creating a biomodel of a tooth from
tomographic images that realistically represented its anatomy.

Key words: computer aided design, reverse engineering, tooth model.

INTRODUCTION

In the material science, to develop new or any materials, tools are needed to help obtain the expected results. These instruments allow the approach of the ideal design with the best mechanical qualities of the material in development. Dentistry, like other sciences that need constant material improvement, is one that uses technology from material science to reach the excellence in the patient’s buccal health treatment. FEA is one of these tools that are constantly used to create or to analyze the odontological materials. This can be seen in works by Sevimay, et al. [1]; Alkan, et al. [2]; Eskitascioglu, et al. [3]; Himmlová, et al. [4]; Yokohama, et al. [5]; Dejak, et al. [6]; Hansson & Werke [7]; Lang, et al. [8]; Simon, et al. [9]; Watanabe, et al. [10]; Lin, et al. [11], among others. Bathe [12] gives an account of the finite element that is one of the most frequently used methods in stress analysis. And he also emphasizes that the re- sults of the FEA computation depend on many indi- vidual factors, such as material properties, boundary condition, interface definition, and also on the overall approach to the model. Geng [13] says that the prop- erties of the materialsinclude density, Young’s modulus and Poisson’s ratio. However, many 3-dimensional FEA studies do not reproduce the real anatomic de- sign of dental element, or consider all the dental com- ponents homogeneous, isotropic and linearly elastic. In these cases the results give us only an approxi- mate idea, not the real data. So it is important to see that some distortion or erroneous information in the mechanical models will be decisive in the success tax rates of odontological treatment. With real infor- mation we can develop better materials in all den- tistry areas, such as prostheses, endodontic, implant, like others too.

1School of Mechanical Engineering, PontificalCatholic University

(PUCRS), Porto Alegre, Brazil
2School of Dentistry, PUCRS, Porto Alegre, Brazil
Isaac Newton Lima da Silva1 – M.E., MS, PhD, assoc. prof.
Gustavo Frainer Barbosa2 – DDS, MS
Rodrigo Borowski Grecco Soares1 – M.E.
Maria Cecilia Gomes Beltrao2 – DDS, MS, PhD, assoc. prof.
Ana Maria Spohr2 – DDS, MS, PhD, assoc. prof.
Eduardo Golcalves Mota2 – DDS, MS, PhD, assoc. prof.
Hugo Mitsuo Silva Oshima2 – DDS, MS, PhD, assoc. prof.
Luiz Henrique Burnett Jr.2 – DDS, MS, PhD, professor
Address correspondence to Prof. Dr. Luiz Henrique Burnett Jr.,
Av. Ipiranga 6681, Faculdade de Odontologia, Porto Alegre, RS –
Brazil, Zip 90619-900.
E-mail: burnett@pucrs.br

Stomatologija, Baltic Dental and Maxillofacial Journal, 2008, Vol. 10, No. 2

I. N. Lima daSilva et al. I. N. Lima daSilva et al.

Therefore, the purpose of this study was to cre- ate a computerized model of a human dental element with a realistic anatomy. The entire process for ob- taining the biomodel is presented here. The method- ology could be extended to other models other than a tooth.

MATERIALS AND METHODS

A new software was created (MSI2), which al- lowed the opening of tomographic images, their seg- mentation to extract the tooth contour, and the ex- portation of the relevant information to a format that could be opened by an engineering software. The resulting three-dimensionalsolid model can be applied to the development of finite element studies of dental implants. The software chosen for this study was the Pro/Engineer WildFire 2.0 (Parametric Technology Corporation (PTC), Needham, MA, USA). The re- lease of the software comes with 55 modules. The modules used in here were the Foundation, used to open the tooth geometric data converted by the de- veloped Medical Imaging Software – MiS2, and REX (Reverse Engineering Extension), which is a part- nership with another developer called Raindrop Geomagic (Geomagic Inc, North Carolina, USA), used to create the tooth external surface and, then, the solid.

So, the complete procedure involved the opening the medical images, in DICOM format, extract the I. N. Lima daSilva et al. SCIENTIFICARTICLES C points of the tooth boundary, export them to a format compatible with a CAD software, reopen the latter file, containing the point cloud, with the CAD soft- ware to then use its RE tools in order to obtain the solid.

Tomographic images are obtained by tomogra- phy (Somatom Plus 4 Volume Zoom, Siemens, Ger- many) in a certain way that a scanning head, moving in a helical trajectory around and over the length of the object being investigated, collects the data from the various slices with 0.5 mm thick of the object, each slice forming a 2d image with depth resolution equals to the pitch of the scanning head move. The equipment computer stores the data into a file in a non-compressed format.

In order to open the medical images, obtained with the tomographic equipment, the software devel- oped had to be able to retrieve each of the many slices’ JPEG images, stored in a sort of database file, called Dicom, which stands for Digital Imaging and Communications in Medicine. In such a file, a com- posite information object classes contains the patients and the images arrangement information. There, the many images are found and could be read by the soft- ware, as any other single JPEG image file would. Internally, the software treated each image as a z element in a xyz array. As the objective was the re- construction of a solid, out of a number of slice im- ages, the z increment was adjusted to the tomogra- phy resolution, and so were the x and y.

With the images stored in a 3d array, the pro- cessing was performed by manipulating the array el- ements. The software has a procedure that can de- termine whether a pixel on an image under query is an internal, external or a boundary point. It performs a connectivity test in each pixel, assigning a connec- tivity number to it. The larger this number, the more attached to other internal and boundary points it is. Internal and external point numbers are turned into minus one (-1). Figure 2 shows the result of the ap- plication of that routine to a slice image. By just look- ing at the pattern generated by the different connec-

tivity numbers the shape of the tooth contour can be inferred. The described sequence is repeated to each image in the array and the whole tooth boundary is found. The resulting point cloud was then stored in a file, which could be opened by the engineering soft- ware Pro/Engineer, see Figure 3. A point cloud is nothing more than a heap of x, y and z coordinate written in form of text.

Once the point cloud data have been generated, the work on these points could be started to get to the solid model of the tooth with Pro/Engineer. The process of transforming a physical part into a digital model is called Reverse Engineer (RE). A common application of the technique involves copying the real model contour by scanning the part, opening the points in a CAD software, generating a solid out of the scanned points, and making it manufacturable. In this article it was preferred to obtain the points from a tomography, therefore, making the method applicable to any part of a patient’s body, and not only a tooth. The part being modeled in that way does not have to be removed from the body in order to be scanned.

Three distinct tasks had to be done in order to get a solid out of the points: the first one involved importing the point cloud file into Pro/Engineer, speci- fying the coordinate system for their placement and finally using the available tools of the menu “Points” to modify the point set. The second one was to wrap the point set to create a triangulated model and work on the model, if necessary, for removing unwanted triangles, for example. And the third part was the facet modeling. A facet model, also called Polygonal Mesh, is a native triangulated model of Pro/Engineer that is created by connecting the points of the data. It was in this last step that the model refinement oc- curred.

However, it happened that the software gener- ates the point cloud with a bit of noise. Noise, in this case, is a deviation of the points from its original place due to the limitations of the scanning devices or the routine in the MiS2 software that created the cloud. It causes points that do not belong to the data. In order to clean this noise and other undesirable geom- etry, Pro/Engineer supplies some useful tools.

The Sample Icon takes just a sample of the points. It is not necessary and not advisable to work with the whole points because the more points the model has, the more processing time is needed. The Reduce Noise tool uses statistical methods to place the points to its correct location. Based on this the level of noise reduction can be chosen and if the ge- ometry of the model is a Free-Form (reduces noise with respect to the surface curvature) or a Mechani- cal (keeps the sharp corners and edges) shape. Fi- nally, tools are available to delete some points, by just selecting them and simply deleting.

In the wrap the point set stage, the software uses all the points of the point set to create the wrap, which means that all the geometric information, including internal structures, is maintained. After enough work on the points has been done, there was no need to fix anything here, so it was ready now to create the facet geometry.

This third phase consists of creating a model that is native to Pro/Engineer. This is called a Facet model. Although the model already has mass properties, such as volume and density, it is not possible to run struc- tural and thermal analysis, which are future goals. So, there is the need to refine the facets as much as possible to make them good to be worked with fur- ther. For this purpose there are some other tools that change the coordinates of the existing points or add new points to the original set. The Refine icon im- proves the surface of the facet model by making the mesh denser, through subdivision of the existing fac- ets. This results in an increased number of facets in the model. Using this command results in a more de- tailed and smoother surface. The Relax tool smoothes the surface, by moving the coordinates of the facet vertices. The last command exploited was the Manifold.

A manifold representation of a model has all the triangles connected continuously by their edges except for boundary edges. If a point set represents a closed object, the Wrap command creates a closed object. However, noise in the scan data can result in a wrap model that is not closed or contains non-mani- fold edges, that is, some triangles in the model are not connected continuously by their edges. So there was the need to make the whole facet surface closed.

Now that a model with the extension of Pro/En- gineer part (prt) was created, it could be transformed in a solid model to, then, be able to do any type of 3d analysis. But, to do so, some curves and surfaces on the faceted model had to be created. That was done with a tool called Restyle. The Restyle module is the Reverse Engineer environment that enables the user to create a surface on top of the faceted feature for later solidification. The auto surface option was used. This tool creates paths along the entire surface of the triangulated data that would be used to build a surface to involve the whole model. Once a continu- ous surface was created, it could be solidified by just selecting the proper tool icon. This option adds mate- rial to the model, by using the surface feature geom- etry as the boundary, converting it into a solid geom- etry.

RESULTS AND DISCUSSION

Medical images provide very important informa- tion on the body structures and their related disor- ders. Because of that they are, for some pathologies, the only way of a precise diagnosis. These images can be obtained by a computer tomography (TC) or through a LASER scanner. Available in the Dicom format, the images of the various slices in JPEG for- mat, obtained by scanning the region of interest in the body, carry accurate geometric information of body organs, which can be used to generate three- dimensional models of those structures in a relatively easy way. Either in the TC or in the LASER scan- ning, the information obtained were a set of points that represents a spatial measurement (in the three coordinate system’s axes). These points are saved into a text file and then imported to a computational tool known as CAD (Computer Aided Design). Usually this file is called point cloud. Once that is opened it is possible to work on it using algorithms of refinement, sampling the points and creating curves and surfaces. As the model has been created, now it is ready to carry through any structural or thermal simulations and even to make a study of a particular surgical case where the surgeon dentist may need to understand and study the situation before starting the surgery. All these analyses can be made virtually with the great advantage of spending less time to get re- sults and not needing laboratories nor the physical teeth.

Reconstructed in that way, the models are very useful for a realistic analysis produced by a CAE soft- ware, when designing new implants or surgical pro- cedures. Pileicikiene et al. [14] described a very de- tailed and similar methodology to create 3D models from mandible, temporomandibular joints and teeth using tomography slices. However, the authors did not describe the solid geometry that is an important step to prototyping. The possibility of developing rapid prototyping parts would aid the implant designers with the verification of accuracy and adjustment of the prosthetic components, for instance.

With the advances in the latest generation of computers, graphical hardware and software, and CAD/CAE software, the use of the finite element analysis became very attractive to many fields, in- cluding medical and dentistry purposes.

There are many commercially available CAE softwares that can simulate realistic loads and con- straints to produce close to exact results. Those softwares are, in the majority of the cases, integrated with a CAD module, which can be used to enter 3d parts to the simulation. The latest software comes with a variety of designing tools that are quite pow- erful to model well-behaved shapes, like the ones en- countered in the mechanical industry. However, body structures are quite complex in shape and the devel- opment of such models with the available software tools can be a very time-consuming and laborious task, not to say almost impossible job. But three-dimen- sional models are necessary for a realistic finite ele- ment analysis, and a way of directly interfacing medi- cal imaging data to a CAE software environment can considerably improve the analysis of dental implants, for instance, by providing very accurate geometric information.

This paper presents a methodology that allows the interface between medical imaging equipment (computer tomography – CT) data and engineering software. This method showed two kind of errors that were present through the whole process of ob- taining the solid, the error inherent to the tomographic equipment and the error resulting from the point cloud manipulation by the RE software. Here only the later one could be measured and was taken into account as a means of quantify the inaccuracy of the pro- cess. This error was directly measured on the model, using the available tool Measure>Distance, consid- ering the model surfaces and the closest points to them in the cloud. That error was found to lie between 0 and -0.8 mm, therefore shortening the model in relation to the real tooth geometry. The reason for that was that the filtering and smoothening routines tend to eliminate the cusps and sharp edges of the wrapped feature. The inaccuracy of the tomography can vary from equipment to equipment and is statis- tically independent from the software errors. Although these kinds of errors were present through the whole process of obtaining the solid, the magnitude of these errors can be reduced by the decrease of the dis- tance from the slices in JPEG format from the com- puter tomography.

The advantage of this method, when compared with the LASER scanner method, is the possibility on obtain data from the internal parts of the dental structure; witch is impossible by a LASER scanner method, that only obtains superficial structural de- tails. So it is possible identify the pulp and it respec- tively canals. It will help us to develop better me- chanical tests and, consequently, better materials, because we are being able to define the regions that form the dental complex with its real physical char- acteristics.

CONCLUSIONS

From the encouraging results obtained in this work, three conclusions could be drawn:

1) The methodology presented was efficient for creating a biomodel of a tooth from tomographic im- ages that realistically represented its anatomy.

2) The model could be utilized for FEA of den- tal implant designs that would not result in feature- based solid, therefore eliminating the problems of some very common in literature models, which have very sharp cusps and edges, resulting in non realistic stress concentrations.

3) The model errors could be measured, show- ing a reduction in its dimensions when compared to the real tooth tomographic data. Further evaluation of that effect in the FEA model has to be carried out.

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Received: 04 09 2007
Accepted for publishing: 21 06 2008