Introduction

Three dimensional (3D) computed tomography (CT) analysis has become widespread in various fields of dentistry and medical treatment. For example, 3D CT images of the mandible or maxilla bone provide important information for diagnosis of diseases and planning of implantations. If the clinical strategy of implantation is constructed on a two-dimensional X-ray, it is difficult for a clinician to visualize the geometry and density of the bone. Moreover, understanding and controlling the stress and strain induced by the masticatory system on the bone surrounding implants and superstructure is important for a longer period of time to ensure the success of the treatment. Therefore clinicians, and consequently patients, expect to have quick, accurate and reliable data for making a diagnosis with information regarding the optimal size and location of implants.

On the other hand, various restorative material alternatives are currently available for dental ceramic, hybrid composite for implant superstructure. Selection of the best alternative is dependent on the evaluation and satisfaction of several criteria. A dental ceramic, once only considered a treatment option for metal-free crown restorations, has been increasingly used in wider applications. As the mechanical properties and wear resistance of existing dental ceramic have improved, their use has expanded to include posterior intracoronal as well as extracoronal restorations including metal-free fixed prosthesis for implant superstructure.

There is a limited amount of dental research which is focused on the aforementioned aspects. In a finite element (FE) analysis, a large structure is divided into a number of small simple shaped elements, for which individual deformation (strain and stress) can be more easily calculated than for the whole undivided large structure. Using the traditional biophysical knowledge database in a rational validation process [1], the use of FE analysis in the dental field has been significantly refined during the last decade [2–9]. However, fixed prosthesis cannot be assimilated to a simplified geometric representation due to both their anatomical shape and layered structure. Sophisticated techniques have therefore been developed to refine geometry acquisition, such as the recreation and digitization of planar outlines. In general, a 3D FE modeling is a complicated process which is often the most time consuming for the scientists. In addition, this process is prone to errors and simplifications which may induce faulty predictions. Similar approaches can be used with a micro scale CT scanner for the simulation of small objects like teeth, dental implants and dental restorations [10]. However, micro scale CT scanner has a small space of radiography domain and too large a radiation exposure for living human patients to use. 3D modeling, which is constructed directly from CT, images the correct reliable data for making a diagnosis and clinical strategy of prosthetic dentistry. The aim of this present study is to evaluate the accuracy of dental ceramic object 3D FE model constructed directly from two different dental cone beam 3D CT systems.

Materials and methods

CT scan condition and definition of structures

CT scans were taken using a cone beam CT (CBCT) scanner by Asahi X-ray (Alphard-3030, Kyoto, Japan) and PLANMECA (ProMax 3D, Helsinki, Finland). Two different shapes of block were used in this study, and both blocks were scanned using CT. A 10.0 × 10.0 × 20.0 mm block was assumed as a simple structure. An 8.0 × 10.0 × 40.0 mm block of an 8-step wedge was assumed as a complex structure, and also step-wedge shape of block was widely used for X-ray contrast test for dental materials. The thickness of each step increased in increments of 1.0 mm. Each block was made of alumina (Nikkato Co., Tokyo, Japan). Figure 1 shows the geometry of the specimen. Table 1 shows the exposure conditions for both systems.

Fig. 1
figure 1

Specimens. a Standard block of alumina, b step-wedge block of alumina

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Table 1 Exposure conditions
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3D model constructed from CT images

A computer program (Mechanical Finder Version 5.2 Extended Edition, Research Center Of Computational Mechanics Inc., Tokyo, Japan) was used to derive the geometry or contours of the specimens from the CT scan images, and linear elements measuring 0.5 mm on the surface, and 0.1–0.5 mm on the inside were generated within each contour. The outline of the specimen on each CT slice was plotted, and the 3D solid model of each specimen was automatically generated from each of the CT scans. A 3D FE model was generated from a 3D solid model. Figures 2 and 3 show the 3D FE models generated by the software. CT scan (transfer to DICOM data) processing and FE model construction were performed on a PC Workstation (Precision Work Station 670, Dell Inc., Texas, USA) using the FE analysis software Mechanical Finder Version 5.2 Extended Edition.

Fig. 2
figure 2

Plot of CT images in block (a Alphard-3030, b ProMax 3D) 1 ROI of CT images, 2 create mesh, 3 3D FE model

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Fig. 3
figure 3

Plot of CT images in step-wedge block (a Alphard-3030, b ProMax 3D) 1 ROI of CT images, 2 create mesh, 3 3D FE model

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Measurement of size accuracy

The specimens were constructed using 3D FE models on Mechanical Finder (MF). The external size of the block and step-wedge block was assumed to be ‘Actual Measurement Value’. Moreover, the specimens constructed by 3D FE model externals, using the distance measurement function between two points of MF, were measured. This value was assumed to be ‘CT Measurement Value’. Each block of the 3D FE model consisted of 48 pieces, making a total of 96 pieces, and three directions (X axis, Y axis, and Z axis) were measured for each piece. The experiments were performed in accordance with two-way analysis of variance (ANOVA) with the combination of factor A, axially (X axis, Y axis and Z axis) and factor B, X-ray CT device (Alphard-3030 and ProMax 3D), making a total of 6 combinations. Experiments were repeated 8 times, such that 48 experiments in all were carried out randomly.

Data analysis

After the difference between the actual measurement value and the CT measurement value was identified, mean value (X), standard deviation (SD), coefficient of variation (CV), and standard margin of error (SE) were calculated. Each mean value was analyzed using two-way analysis of variance (ANOVA) and multiple-comparison Tukey’s tests by Excel statistics (Excel statistics 2002 for Windows) for the statistical work. Tukey’s multiple comparison post hoc analysis was employed at a significance level of p < 0.05.

Results

Figures 2 and 3 show the results of 3D image of specimen. It was possible to construct a 3D FE model developed from both CT scanners. The accuracy of both CBCT scanners was assessed using block and step-wedge measurements.

Table 2 shows the result of the CBCT scans of the block and step-wedge block, using the Alphard-3030 and the ProMax 3D.

Table 2 Result of size accuracy of block and step-wedge block
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The length of block by Alphard-3030 was X = 10.20 ± 0.03 (X = Ave. ± SE), Y = 10.55 ± 0.03 (Y = Ave. ± SE), Z = 19.91 ± 0.14 (Z = Ave. ± SE). The CV was X = 0.88 %, Y = 0.76 %, Z = 0.40 %. The mean difference between the practical value and the measurements on the 3D CT images was 0.21, 0.56 and −0.09 mm, respectively.

The length of the block by ProMax 3D was X = 9.64 ± 0.04 (X = Ave. ± SE), Y = 9.88 ± 0.06 (Y = Ave. ± SE), Z = 17.38 ± 0.04 (Z = Ave. ± SE). The CV was X = 1.14 %, Y = 1.62 %, Z = 0.69 %. The mean difference between the practical value and measurements on the 3D CT images was −0.36, −0.12 and −2.61 mm, respectively.

The length of the step-wedge block by Alphard-3030 was X = 10.91 ± 0.03 (X = Ave. ± SE), Y = 7.85 ± 0.02 (Y = Ave. ± SE), Z = 39.46 ± 0.05 (Z = Ave. ± SE). The CV was X = 0.82 %, Y = 0.76 %, Z = 0.38 %. The mean difference between the practical value and measurements on the 3D CT images was 0.91, −0.15 and −0.54 mm, respectively.

The length of the step-wedge block by ProMax 3D was X = 9.81 ± 0.02 (X = Ave. ± SE), Y = 7.63 ± 0.05 (Y = Ave. ± SE), Z = 37.34 ± 0.05 (Z = Ave. ± SE). The CV was X = 0.51 %, Y = 1.70 %, Z = 0.37 %. The mean difference between the practical value and measurements on the 3D CT images was −0.19, −0.38 and −2.66 mm, respectively.

Analysis

The two-way ANOVA results for different factors and interactions were identified. The dual arrangement decentralization analysis was done from the mean value shown in Table 2. The difference of the size measurements in the block is shown in Fig. 4 and the step-wedge block is shown in Fig. 5. Small pictures were taken and compared of the block and the step-wedge block using ProMax 3D and Alphard-3030. Moreover, a tendency to take a picture which was smaller than the actual measurement value was noted in the ProMax 3D. In the result of the multiple comparison authorization of Tukey, no significant differences were found between Alphard-3030 on the Z axis and ProMax 3D on the Y axis of the block. In addition, there were also no significant differences observed between Alphard-3030 on the Y axis and ProMax 3D on the X axis compared with Alphard-3030 on the Z axis and ProMax 3D on the Y axis for the step wedge.

Fig. 4
figure 4

Difference of length of the block in different axis. Group means identified by the same lower case letter indicate no significant difference (p > 0.05). n = 8 for each group

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Fig. 5
figure 5

Difference of length of the step-wedge block in different axis. Group means identified by the same lower case letter indicate no significant difference (p > 0.05). n = 8 for each group

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Discussion

For medical CT, by means of the development of spiral/helical CT in the early 1990s, volume data could be acquired without misintegration of anatomical details [11]. Since the year 2000, cone beam CT scanners have come into use. Kalender [12] wrote that the transition from scanning one or only a few slices to data acquisition for an entire field means the transition from fan beam to cone beam geometry.

Cone beam CT systems for dental use have been developed by several manufacturers and are now providing important diagnostic information on the bone-impacted teeth, temporomandibular joints, bone fractures and pre-operative assessment for dental implants.

In this study, two different shaped blocks on two different cone beam CT images were measured, and both the reproducibility and accuracy of the size were evaluated.

Exposure conditions during cone beam CT used in this research were selected so that they were similar to those used in general clinical use. In principle, original high-quality CT images are needed to take a highly accurate 3D FE model. Up to now, to obtain high-quality CT images, the reduction of slice intervals, which increases the exposure time and X-ray tube voltage, needs to be considered. However, in medical imaging, radiation exposure has to be kept to a minimum. Because of this factor, the exposure conditions of this study were close to those used clinically.

The CT scan data were transferred to the FE model program which can use DICOM data. The DICOM data were taken into the integrated program of the CT image data processing and 3D FE model program called MF. MF is software that evaluates bone strength by gathering the entire 3D structure of bone, and then the data are applied to the structure analysis using the FE model. It was noted that a 3D FE model was able to transfer, add and extract data freely to the program. This could be utilized in clinical work as well. In addition, it is possible to evaluate bone strength from the 3D XCT image. Another important finding of this study was that a predetermined area of the objects could be automatically extracted according to the CT value.

The test objects were made of alumina. Because this material is commonly used in dentistry, its use provided additional rationale, and the alumina block had few defects making it suitable for this study. Measurement of length was possible using the MF software.

A 3D FE model for measurement was macroscopically determined using the computer mouse, and measurement points were macroscopically established on the image. However, there may be differences in such macroscopic determinations which may cause variations in the measurements.

The accuracy of the ProMax 3D and the Alphard-3030 CBCT scanners was assessed by comparing CV measurements. The accuracy of the Alphard-3030 was better than that of the ProMax 3D when measuring dimensions of the block. ProMax 3D’s accuracy was high in the direction of X in step-wedge measurements. However, the Alphard-3030 was better in the direction of Y. A difference was not observed between the objects in the direction of Z. The size of the 3D XCT image of the alumina block was reproduced in the 3D FE model with high accuracy.

It can be said that the accuracy of the model is high with regard to size because the observed differences were small, although these were considered significant as a result of the statistical work. Moreover, a significant difference between X-ray CT devices was found. As for ProMax 3D, −2.61 to −2.66 mm was measured Z axially, which was maximum value regardless of the kind of block. Though the Alphard-3030 reached a value almost identical to the actual measurement value, in the Z axis of step-wedge block, −0.54 mm was measured. This was considered to be small. This Z axis measurement was observed to be small in X-ray CT device. The difference in measurements from each X-ray CT device was attributed to inconsistent exposure conditions for each device. However, due to both a small margin of error and coefficient of variance, no difference between X-ray CT devices was observed for practical usage in terms of size accuracy. It was thought that the PC workstation and the efficiency of the software when making 3D FE models had the largest influence on the accuracy. Therefore, an increase in workstation memory is one possible way of minimizing inaccuracies, resulting in a more accurate 3D FE model based on data from X-ray CT devices. However, the quality of this constructed 3D FE model is also strongly influenced by the accuracy of the original CT images and the operator’s expertise.

Clinical significance

A finite element (FE) analysis has become widespread in various fields of dentistry. If FE analysis will be able to apply easily for understanding the physical phenomenon and stress concentrations, it is very useful for a clinician to construct the clinical strategy of dental diagnosis. Moreover, understanding and controlling the stress induced by the mastication force on the dental restoration is important for a longer period of time to ensure the success of the treatment. Therefore, dentist and patients need quick, accurate and reliable data for making a clinical strategy for dental diagnosis.

Conculusion

The following conclusions were made:

(1) 3D FE model constructed from CT images of a test object showed good precision in all dimensions.

(2) The results suggest that measurement of dimensions of cone beam CT images could be useful in applications where good reproducibility and accuracy of FE models are required.