The study consisted of two consecutive CBCT (I-CAT system) scans of an adolescent male patient between 2008 and 2009 (the patient was aged 8-10). The scans used had been taken for use as regular orthodontic records and his parents consented to use his CBCT scans to study mandibular growth. Three dimensional visual models were created from CBCT images from each year using the software package MATERIALISE MIMICS (Version 14, Plymouth, U.S.A). No attempt at alignment or registration was completed due to post alignment techniques that were already implemented on these scans.

The CBCT images used are 12-bit (4096 grey values possible per pixel) pixel maps that illustrate the X-ray attenuation coefficient of the tissue [28]. Each mandible CBCT data set used in this study consisted of 440 slices spaced 0.3mm apart, with an in plane pixel size of 0.3mm – yielding a voxel (3-D “pixel” made by stretching a pixels over its associated parallel slice thickness) with a volume of 0.027mm. These measurements are well within tolerance values discussed by Togashi et al. [16]. The CBCT data sets were then imported into MIMICS for preliminary 3D geometry creation. The program MIMICS initially scales the images to the Hounsfield scale, which sets the attenuation of water to zero. Using the Hounsfield scale the minimum pixel value is -1024, representing the attenuation of air [28]. The estimated pixel values using Hounsfield units (HU) that represent trabecular and cortical bone are 150-250 HU and 251-2100 HU respectively. Threshold segmenting and connected-components algorithm was conducted similar to Meehan et al. [23]. To ensure scientific conformity, the same pixel threshold values of 226 HU to 2042 HU were used when threshold segmenting the data sets. This was possible on our scans due to similar attenuation characteristics throughout; however, if required, regional thresholds can be joined as demonstrated by Stratemann et al. [19]. Segmentation creates a highlighted region of interest called a mask (Fig. 1). The initial estimated mask volume of the 2008 scan is 34.7 cm³ while the estimated mask volume of the 2009 mask is 34.8 cm³. The mean values of the 2008 and 2009 masks were both 838 HU; while the respective standard deviations of the mean HU values were 459 HU and 435 HU. The two CBCT scans contained image artifacts surrounding a lower lingual arch (a dental appliance attached to the mandibular teeth). Artifacts of this nature are due to the photoelectric effect and the high relative atomic number of the appliance. This affects the apparent attenuation of the surrounding tissue, because most of the beam is removed by the photoelectric effect in the lower lingual arch. This creates missing information when the CBCT data is back projected causing gross anomalies. Thus in accordance with Bibb et al., the affected regions were removed to ascertain a better 3D representation [21].

Fig. (1). Sample of threshold segmentation highlighting the region of interest, using Materialise: MIMICS. This slice is the inferior portion of mandibular body (transverse plane).

Fig. (2). 3-D model of the mandible, using Grey Value Interpolation, with all Photoelectric artifacts removed.

Fig. (3). 3-D vector map, on the right condyle, illustrating deviations of the surface meshes from the 2008 to 2009 models. Red-yellow indicates a positive change between nodes on the surface mesh, blue-green indicates a negative change.

Fig. (4). Virtual model of the 3-D growth map. The colour map (legend to the left) indicates the magnitude of change (in mm) of the 3-D surface from the 2008 model to the 2009 model.

Fig. (5). Right: physical model of figure 4, allowing analysis in any orientation. Left: a comparison of our model with a similar model developed with MRI scan [18].

Fig. (6). Study growth map (right) shown to be in conformity to similar maps found in literature [4] (Left). The arrows contained in the literature sample indicate relative growth direction and magnitude using the relative size and direction of the arrows. The colour map of the growth map image is the same as in figures 4 and 5. As seen, our growth visualization shows inward growth near the symphysis (upper chin) with outward growth along bottom of chin, body and ramus. Additionally, in both visualizations, the proximal side of the ramus show resorption whilst the distal side shows deposition. An interesting detail poorly captured in literature is the resorption anterior to the condyle, making the process more pronounced. Reprinted with permission from D. Enlow, R. Moyers, and W. Merow, Handbook of Facial Growth., W.B. Saunders Company, 1982. Copyright Elsevier.

Fig. (7). Sagittal views of the ramus, the study model on the left and the literature [4] sample on the right for comparison. Bluegreen on the study model represents resorption, and yellow-red represents deposition, using the same numerical scale for the relative growth as Fig. (4 and 5). Reprinted with permission from D. Enlow, R. Moyers, and W. Merow, Handbook of Facial Growth., W.B. Saunders Company, 1982. Copyright Elsevier.

Fig. (8). Angles and dimensions used to compare growth as per the landmarks [29] presented in Table 2, superimposed on a sagittal slice.

MIMICS was then used to calculate a 3-D object, from the default menu, for the two associated masks using pre-defined high quality settings that preserve the integrity of the virtual models (see Fig. 2). A grey value interpolation scheme was used to account for partial volume effects in the voxels. This produces a surface that is generally more accurate versus a contour interpolation method. The contour method draws contours on the boundaries slice by slice, interpolating linearly between each slice, hence ignoring partial volume effects between the contours. The 3-D virtual models were then smoothed using a voxel based technique with an existing MIMICS algorithm to preserve calculated volumes. Preservation of 3-D volumes were verified by comparing before and after volumes. Implementation of the same algorithm on each of the scans ensured minimal subjectivity. In contrast to other literature on mandible segmentation [23,26], there was no manual segmentation implemented – as manual segmentation is time consuming and prone to errors. MIMICS is then used to export STL files of the two 3-D models.

The two STL files were imported into GEOMAGICS STUDIO/QUALIFY (Version 11, Research Triangle Park, U.S.A), a 3-D suite that was built for optimizing and comparing 3-D objects to a reference object. Within the STUDIO suite, the STL file was optimized by removing noise in the form of protruding vertices and localized holes (using the built in mesh-doctor feature). Typically, anomalies are formed due to a combination of noise in the CBCT image and the interpolation algorithm used to create the triangulated mesh. At this step any excessive deformations in the area of the teeth affected by the X-ray artifacts were removed manually. This was deemed acceptable as the teeth region would not be used for data analysis. Then, the mesh was rewrapped with new triangles using a built in algorithm, this ensured the triangles on both visual models were equal in size – important for comparing the models. The rewrapping tool in STUDIO calculates new vertices of each facet, in efforts to produce equivalent triangle sizes, based on the local curvature and Voronoi diagram indices.

After wrapping with similar triangles, the virtual models were imported into GEOMAGICS QUALIFY. In comparing the two mandible models, the 2008 model was set as the reference and the 2009 model was used as the comparison. The two virtual models were aligned using a built in algorithm for best fit. The algorithm sets the 2008 object as a fixed model, and works in two stages by floating the 2009 object. First stage fitting uses a small number of points (300) from similar locations on each object to simulate gross growth. The second stage uses a larger sample of points (1500) to make fine adjustments to best-fit the models, analogous to a least squares best fit algorithm. The reported average error from the alignment was inflated to 0.452mm due to anomalies in the teeth region. It was determined that increasing the sample size of the best-fit algorithm does not significantly improve the fit of the two objects (0.01mm improvement in error for every extra 1000 points). This post alignment method eliminates the need for CBCT alignment during scanning. Other methods include using a list of landmarks [7, 19, 29], or bypassing the alignment step altogether by quantifying a series of measurements to compare between virtual models [3].

The artifacts that affected the region of the teeth produce a small effect on the alignment of the two virtual models. However, the effect is limited due to the relatively small surface area covered by the teeth region (less than 4%). Following the alignment, the two objects were compared by an illustration of the 3-D deviation of the two virtual models, creating a growth model. A 3-D deviation map (Fig. 3) was computed, using built in features of QUALIFY, by measuring the orthogonal distance from the vertices of the reference object (2008 virtual model) to the float object (2009 virtual model). To ensure a realistic computational time, the maximum result point count was limited to 2 million data points. Table 1 illustrates the output parameters from the 3-D comparison. It should be noted that the maximum deviation of 4.34mm was inflated due to the teeth region, but is reported here for completeness. The 3-D comparison colour growth model is exported as a VRML file (Virtual Reality Modeling Language), as this format allows the embedment of colour within the 3-D mesh.

Several 2D parameters are used to describe the growth of the mandible by defining landmarks using planes and bisected angles [29]. These landmarks have been used in order to compare to literature, as well as to display some of the data possible with this kind of analysis. Table 2 presents the landmarks and succinct instructions on how to find them.

The growth study is followed up with the creation of a 3-D physical model, a novel and unique way to visualize the growth of the mandible. A growth map from the study was printed on a colour 3-D printer utilizing a rapid prototyping technique similar to Russett et al. [25], allowing a “graspable” physical model representing the growth of the mandible over a year. This was accomplished using the VRML file, which allows a 3-D printer to print the surface mesh with associated colours. The production of a physical model has great benefits for the use of explaining and conveying information.

The 3-D printing system used is a Spectrum Z™510 colour 3-D printing system manufactured by Z corportation (Burlington, U.S.A). The printer works in the same way most 3-D printers operate, in which a printer head selectively hardens thin layers of plaster duster with a sugar-water binding agent. The innovation of colour 3-D printing comes in the binding agent, where four separate print heads contain four binding agents: clear, cyan, magenta and yellow. Selective use of binding agents to harden regions of plaster allows the printing of 24 bit full colour models. Each layer of the model hardened by the binding agents is 0.1mm thick, with a maximum resolution of 600 x 540 dpi (www.zcrop.com).

The results of our pilot study include a three dimensional virtual model of the 3-D deviation of the jaw between 2008 and 2009 (Fig. 4). In addition to the virtual model, a 3-D physical model was printed (Fig. 5). The physical model illustrates the same growth map as the virtual model and allows for easy viewing and in depth analysis. Additionally seen in Fig. (5), is our visualized growth model compared with Cevidanes et al. virtual model [18].

Fig. (6) shows a comparison of our growth map with predicted growth from literature [4]. Literature data is taken from cadaveric specimens of different ages at death thus showing an average relative geometry change [4]. Recorded growth from literature has shown by a series of arrows displaying the relative shape movement of the mandible as it grows, the size of the arrows representing the magnitude of growth over time. In our in vitro growth study, the growth is illustrated by a quantitative colour map. Fig. (7) shows a comparison of the 2008-2009 cross sectional growth from the study, compared with literature cross sectional growth data. From Fig. (7), we can see general conformity with the models and of the literature values [4, 10].

Maximum recorded growth (ignoring the areas affected by the artifacts) between the 2008 and 2009 virtual models is 1.67 mm on the condyle, while the maximum resorption is 1.0 mm adjacent to the symphysis (most anterior part of the mandible). The overall width of the mandible, measured from the medial side of the condyle, increased by 0.49mm - an increase of 2.8% over the year. Table 3 is data obtained by comparing the indices defined by aforementioned landmarks [29]. In addition to the data presented in Table 3, there is another angle formed between the corpus and the symphysis plane that remained constant at approximately 85 degrees. Fig. (8) illustrates various 2D parameters superimposed on a sagittal view of the 2008 mandible model, showing the landmarks used to extract the data [29].

The growth discussed in our study is the 3-D orthogonal difference obtained from two CBCT scans aligned using a best-fit algorithm, and thus the growth map does not take into account the drift effects from secondary displacements. Therefore, our model represents the overall shape change of the mandible, and is not a representation of how the mandible grows in its anatomical position. This is evident in examining the condyle region of our printed mandible, in which you can see significant relative growth. The actual growth pattern is expected to be as such: the ramus grows lengthwise forcing the downward growth of the body of the mandible. When comparing to the literature, this is an important distinction, as the common source of relative growth information of the mandible is based on averaged cadaver studies. These cadaver studies are conducted with multiple specimens of different individuals, illustrating the shape change of the mandible removed from anatomical context – thus making it easy to compare with our study. The studies also included vector information (Fig. 6), which can be easily obtained by a longitudinal study that tracks the displacements of chosen landmarks. However, this vector growth information represents the relative displacements of points and faces the issue of choosing homologous points in 3D space, which is something our proposed method aims to circumvent. Furthermore, our study compares the entire surface of the mandible, not the relative movement of landmarks, and thus can make use of an easily implemented best fit alignment algorithm. According to Stratemann et al., the transition from landmarks to our method, utilizing superimposition of entire surface-rendered 3D images, will enable objective comparisons [26].

Overall mandibular growth is relatively small compared to literature [15], but this is likely due to the decelerated growth in our studied jaw after the first growth spurt (age 9-10). Our study showed that the condyles grew outwards laterally (2.8%) over the course of the year. The outward growth of the condyles is expected due to the addition of material to the symphysis allowing the mandible to open progressively in a 'V' shape. It is thought that the outward condylar growth is due to pressure induced by the lateral growth of the maxilla [4].

The increased depth of the mandibular notch can be argued to be due to the gradual increase of forces on each side of the notch by the growing temporaral and lateral pterygoid muscles [4]. The coronoid process is pulled upwards as a result of the forces of the temporalis muscle, causing a general elongation of the process. The condyle is loaded through the TMJ joint, and as such its growth is thought to be a response to this significant induced stress. The general understanding is that the forces of mastication have a large impact on the shape of the mandible, and are thoroughly discussed in the literature [3, 4, 10].

The gonial angle (mandible angle) remained constant at 128 degrees throughout the course of this study (1 year). The expected result is that the gonial angle will decrease as time progresses [4, 10], at the average rate of less than a degree a year [29]. It is likely that our study did not span over a long enough time to track a change in mandibular angle of that magnitude. A gonial angle of 128 degrees reflects an average angle, as a typical gonial angle varies from 140 degrees at birth to 120 degrees at maturity [10].

The corpus length increased by 0.3mm, a change of 0.5%, while the ramus height increased by 0.5mm, a change of 1.1% over the course of the study (1 year). No known values at this age have been found for these measurements, although a reported trend is that these values tend to increase [4, 29]. The overall length defined earlier increased by 0.6mm over the year. This is expected as it is the hypotenuse of the corpus length and ramus height, both of which increased in dimension.

The importance of using graspable objects instead of virtual reality objects on a computer screen is summarized in literature [20, 30, 31]. The embedment of colour on our 3-D model illustrating the growth between the two models is, to our best knowledge, the first time an accurate physical representation of mandible growth has been accomplished. A physical model is ideal for determining general growth, while the virtual model allows numerous measurements and accessible visualization.