A Method for Obtaining a Three-Dimensional Geometric Model of Dental Implants for Analysis via the Finite Element Method

Abstract

Purpose: 

The aim of the study was to present a methodology of development of a virtual 3-dimensional dental implant model for analyses via the finite element method.

Materials and Methods: 

A set, consisting of a dental implant and abutment, was embedded in acrylic resin for subsequent metallographic grinding and polishing. After the evidentiation of the internal geometry of the implant, the specimen was treated in a sputter for observation using scanning electron microscopy (SEM). The SEM image was transported to computer-aided design software by which all details of the implant were measured. With the measures obtained, the geometry was reproduced with 3-dimensional modeling software. Finally, the model was imported into finite element method analysis software with which it was discretized, generating a mesh.

Results: 

A model with the accurate geometry of the implant was developed. A mesh of 297,600 elements and 490,045 nodes was generated. An aleatory acceleration simulation was performed to test the mesh, and no errors were identified.

Conclusion: 

The developed methodology generated a precise dental implant model, which can be applied in different finite element method simulations.

Prosthetic rehabilitation using dental implants has been shown to be predictable over the long term¹; however, biological and mechanical failures can still occur.² Understanding the biomechanical phenomena present in bone implant prosthesis system is essential for the maintenance and stability of osseointegrated rehabilitation. Consequently, since the development of implant dentistry, based on the concepts of Brånemark,³ great attention has been given to the behavior of the loads and stresses that occur in an implant-supported prosthesis.^4,5 Thus, many experimental and computational biomechanical studies have analyzed a variety of situations involving rehabilitation with dental implants, with the finite element method being one of the most used tools.^6–15

The finite element method is a nonexperimental computer simulation technique, which assesses the levels of stress, strain, and displacement in virtual structures when subjected to external or internal loads.^16–18 For the analysis, a realistic computational representation of the object's geometry is required for study, as well as its mechanical properties. This digital representation, called a model, is discretized into finite elements connected by nodes, generating a mesh, which makes it able to simulate the structural responses with the imposition of loads. As this is a numerical method, it is neither invasive nor destructive.^16–18 This method has been widely used in implant dentistry biomechanics, such as in the evaluation of stresses in the implant-bone interface, between implants and prosthetic abutments, in different dispositions, and with varying numbers of implants, among other applications, with the results accepted in the literature.^6–8

A major difficulty in a study using the finite element method is the geometric virtual reproduction of the objects to be analyzed. In implant dentistry applications, models of bone, implants, abutments, screws, and teeth are often used. Obtaining an accurate model of the implants is challenging because most of them have a specific design, with numerous distinct peculiarities, such as connections, platforms, and threads. In some cases, manufacturers concede the original computer-aided design (CAD) drawings,^{6,8,9,12,19–21} but as this process is not always possible, researchers need methods that reproduce the geometry of the implants virtually. Apparently, direct measurement of the implant to be analyzed for further modeling seems to be the most common method. However, very often, the details necessary for the reproduction technique are not presented. In other studies, the modeling methods are not even described.^{10,11,13,14,22}

The aim of this study was to demonstrate a methodology that was developed to obtain a model of an internal connection implant. Metallographic methods, microscopic techniques, and 3-dimensional modeling were used for the accurate reproduction of the implant, which resulted in a model applicable in studies using the finite element method.

Materials and Methods

A set consisting of a temporary titanium abutment (Temporary Abutment Engaging; Nobel Biocare AB, Gothenburg, Sweden) screwed to a titanium tri-channel internal connection implant (Replace; Nobel Biocare AB) was mounted with special acrylic resin for a metallographic technique (ClaroFast; Struers A/S, Ballerup, Denmark),^23,24 using an automatic hot mounting press (ProntoPress-20; Struers A/S). Then, this set was grinded under intense cooling with 600 granulation discs, in an automatic polishing machine (Abramin; Struers A/S), until half of the implant in the coronal direction was observed. At that point, the entire geometry of the implant-abutment assembly could be visualized. This pattern of grinding resulted in a flat surface without deformation of the specimen. The thinning process was finalized with a polishing cloth with colloidal silica paste (OP-U; Struers A/S), which resulted in a flat, scratch-free, and clean surface. The set was then treated in a sputter (Coater S 150 B; Edwards, Crowley, United Kingdom) in which it was coated with a uniform ultrathin layer of gold, leaving the sample conductive and with better contrast, adapting it for scanning electron microscopy (SEM) analysis (Fig. 1). Finally, images magnified 5 and 15 times were obtained using a scanning electron microscope (XL-30; Philips Electron Optics BV, Eindhoven, The Netherlands) (Fig. 2).

Fig. 1: Mounting consisting of an implant and an abutment after grinding, polishing and treatment in a sputter.

Fig. 2: SEM image of the coronal section of the implant and abutment (5× magnification).

The digital image generated by SEM was transported to CAD software (Solidworks 2010; Dassault Systèmes SolidWorks Corp., Concord, MA) with which the measurement process of all the internal and external geometry of the implant was conducted. To ensure correspondence between the digital file and the real object, a scaling factor was applied to the image, which was determined by the ratio of the indicated bar length of the SEM scale and by the bar length measured by the CAD software using the digital image. From that moment on, any measurement taken of the image would result in the actual size of the implant parts. In sequence, measurements of the external and internal geometry of the implant, including the length, external and internal threads, and thickness of the walls, were taken with the use of software dimensioning tools (Figs. 3 and 4). To obtain the exterior part of the connection design, an image of the implant platform generated by optical microscopy (BX-60; Olympus Corporation, Tokyo, Japan) was exported to CAD software with which the scale adjustment process was repeated by taking the real measure of the 4.3-mm-diameter platform as a reference. Once more, after applying the scale factor, dimension tools were used to acquire the measurements (Fig. 5).

Fig. 3: Measurements performed in the SEM image of the implant.

Fig. 4: Details of the measurements obtained at the apex of the implant (SEM, 15× magnification).

Fig. 5: Measurements of the implant platform obtained with the optical microscopy.

With all the measures taken, the process of 3-dimensional modeling of the implant was performed.^25,26 The external geometry of the implant was obtained by revolving the outer contours around the symmetrical axis of the implant (Fig. 6), whereas the cervical microthreads were obtained with a revolved cut of the thread profile, also around the symmetrical axis. The external and internal threads were created in 3 steps. First, the thread profile was defined. Then, the thread path was designed as a helix curve. In the third step, a cut tool was used, in which the predefined profile followed the curve determined in the second step, removing material along its route. Finally, the internal geometry of the implant was generated by a revolved cut.

Fig. 6: Outline of the external geometry of the implant in the 3-dimensional modeling software.

Results

A 3-dimensional model of the implant, which was suitable to be preprocessed and discretized into a finite element mesh, was obtained (Figs. 7 and 8). To test the applicability of the model, a mesh with 297,600 tetrahedral elements and 490,045 nodes was generated with CAE (computer-aided engineering) software (Ansys 11.0; Ansys, Inc., Canonsburg, PA). The mechanical properties for commercially pure titanium were set to 117 GPa for the elastic modulus and 0.30 for Poisson ratio.¹⁶ The implant was defined to be fully constrained and then an aleatory vertical acceleration of 30 mm/s² was applied to the platform to test the mesh. No errors were identified (Figs. 9–11).

Fig. 7: Three-dimensional model of the implant.

Fig. 8: Three-dimensional model of the implant: internal geometric view.

Fig. 9: Three-dimensional finite element mesh: external view.

Fig. 10: Three-dimensional finite element mesh: platform.

Fig. 11: Simulation of a vertical acceleration of 30 mm/s² applied to the implant platform: von Mises stresses.

Discussion

The process of transforming and transporting the details of a real system to a virtual format that a computer can recognize and work on is called computational modeling. The software does not identify and act on the object's shape but on the numbers that represent it on the space. Therefore, the way the researcher transfers the object's information to the computer during the modeling process is one of the most critical parts of the finite element method, especially when the object of study is an irregular continuous solid.¹⁶

When the finite element method is used in any field of knowledge, it is desirable to generate an exact, virtual geometric model of the structure to be studied to obtain results that can predict failures in real situations.^17,18 However, particularly in the medical field, there are limitations that require studies to apply assumptions to the models. Bone, for instance, being a complex living tissue, without a definite pattern and with characteristics that can vary from individual to individual, often appears in studies as a simplified model. In some situations, such as in comparative analyses or when the study objective is to determine stresses on prostheses, implants also appear as simple designs, usually as smooth cylinders.^7,10,27 In other cases, hardware limitations or the computational time required for processing extremely detailed models can lead to the simplification of these designs.¹⁶

However, as implants have reproducible geometry and defined mechanical properties, they should be modeled exactly according to the manufacturer's specifications, without simplifications. In simulations in which the purpose is the analysis of a new implant system or design, in stress studies of prosthetic components, in preload determinations, and in interactions between implants and periimplant bone tissue, an accurate model of the implant is desirable.^{6,9,12,14,15,18,20,21,28} It has been shown that the pattern of the threads and the external shape of the implant considerably influenced the stresses in periimplant bone.^8,9,29 The type of connection between the abutment and the implant also resulted in distinct patterns of strain.^11,21 Therefore, increasingly, implants have been represented in studies with their real standards. Obviously, the ideal would be to work with CAD models or engineering drawings provided by the manufacturers, which would ensure the accuracy of the design and provide substantial savings in time and resources. However, this provision does not often happen, possibly for industrial secrecy reasons. Nevertheless, researchers have already had the cooperation of companies.^{6,8,9,12,19–21,28} On the other hand, studies have claimed that they use implant models from some determined manufacturers,^{11,13,14,22,29–33} but without explaining in detail the methodology of how these models were obtained, leaving them irreproducible and violating one of the basic principles of the scientific method: the reproducibility. More recently, 3-dimensional laser scanners have been used to provide virtual models of biological macrostructures.^34,35 However, lasers are unable to scan the internal geometry of implants with the precision necessary to generate a viable CAD model.

In this study, to model a tri-channel internal connection implant, which could be an implant of any system, it was initially planned to obtain the measurements of all of the internal and external details, before designing with the CAD software. As it was not possible to obtain the precise measurements of the implant's internal parts with direct visualization or using metrology tools, the revelation of this geometry was achieved by the coronal cut of the implant using metallographic mounting and grinding. The advantage of this technique, compared, for example, with sectioning with a microtome,¹⁵ is that the mounted specimen does not suffer any deformation during grinding and thus preserves all of the details necessary for accurate measurement and subsequent modeling.^23,24 Images with the scale and the sufficient accuracy to view all of these details were achieved by means of microscopy. With these data, measurements of all parts of the implant were acquired using the basic dimensional tools in the CAD software. Then, 3-dimensional modeling could be initiated, when it was crucial select the appropriate software, with all of its functionality and technical resources determined by the researcher. This is the more time-consuming stage because it is a work of science and art.^25,26 Although this step seems to be simple drawing using software, in fact, it is model construction with the same geometry as the real object, which can be discretized without issues, being fully understood by the computer.²⁵ At this point, interaction between engineering and dentistry is essential for the development and functioning of a model that reaches the objectives proposed in the studies, with finite elements that will follow. The present implant model was exported and tested in a CAE software, and no errors were identified during an aleatory simulation. In the end, with the implant model correctly generated, further studies, such as preload analyses, periimplantar stress comparisons, and interactions between the implant and prosthetic abutment, among other simulations, may be developed.

Conclusions

With the finite element method, the creation of a precise geometric model by means of appropriate engineering software is essential for obtaining reliable and realistic solutions. The methodology that was presented demonstrated in detail the development of a reproducible and accurate 3-dimensional model of an internal connection implant, which can be used in 3-dimensional finite element studies.

Disclosure

The authors claim to have no financial interests in any of the products mentioned in this article.