Comparison of measurements of mandible growth using cone beam computed tomography and its synthesized cephalograms
© Lin et al.; licensee BioMed Central Ltd. 2014
Received: 29 May 2014
Accepted: 30 August 2014
Published: 10 September 2014
The current study aimed to compare the measurements of the mandible morphology using 3D cone beam computed tomography (CBCT) images with those using 2D CBCT-synthesized cephalograms; to quantify errors in measurements based on 2D synthesized cephalograms; and to clarify the effects such errors have on the description of the mandibular growth.
Mandibles of six miniature pigs were scanned monthly using CBCT over 12 months and the data were used to reconstruct the 3D bone models. Five anatomical landmarks were identified on each bone model, and the inter-marker distances and monthly distance changes were calculated and taken as the gold standard. Synthetic 2D cephalograms were also generated for each bone model using a digitally reconstructed radiography (DRR)-generation method. Errors in cephalogram measurements were determined as the differences between the calculated variables in cephalograms and the gold standard. The variations between cephalograms and the gold standard were also compared using paired t-tests.
While the inter-marker distance increases varied among the marker pairs, all marker pairs increased their inter-marker distances gradually every month, reaching 50% of the total annual increases during the fourth and fifth months, and then slowing down in the subsequent months. The 2D measurements significantly underestimated most of the inter-marker distances throughout the monitoring period, in most of the monthly inter-marker distance changes during the first four months, and in the total growth (p < 0.05).
Significant errors exist in the measurements using 2D synthesized cephalogram, underestimating the mandibular dimensions and their monthly changes in the early stages of growth, as well as the total annual growth. These results should be considered in dental treatment planning at the beginning of the treatment in order to control more precisely the treatment process and outcome.
Dental treatments are often performed while the mandible bone is still growing. This is especially true during the process of orthodontic treatment planning or the assessment of the outcome of craniomandibular surgery. Since the data of the growth of the mandible are difficult to obtain via human experiments, physicians have to rely on current images to infer future growth of the mandible in planning treatments and assessing their efficacy. Studies on the influence of factors related to the mandibular growth on the treatment outcome are not yet available. Therefore, including growth-related factors in the treatment plan at the beginning of the treatment in order to control more precisely the treatment process and outcome will be helpful for improving the quality of treatment.
The use of cephalograms for long-term, in vivo measurement of human mandible growth would require multiple exposures to radiation over the monitoring period, which is not feasible for ethical reasons. A limited number of in vivo studies attempted to image mandible shape changes at limited time instances with unequal intervals but failed to describe long-term growth [1, 2]. Predictive mathematical models may be helpful for resolving the above-mentioned difficulties but, to the best knowledge of the authors, no such mathematical models have been reported. Their experimental validations before their clinical applications present another problem. However, long-term follow-up experiments on animal bone-growth can shed light on the growth of the mandible, and can also be useful in the construction and experimental validation of predictive mathematical models. Therefore, considering the medical ethics, animal experiments are indeed necessary. Many of the previous studies on the mandible have used pigs as animal models because their anatomy, physiology, circulatory system, mastication system and teeth germination are very similar to those of humans [3–5]. This is especially true for mini-pigs in which the size and shape of the jaw, occlusion and bone metabolism rate are similar to those of humans [6–9]. Compared to other pig breeds, mini-pigs are small in body size and relatively easy to manipulate in experiments, making them much more feasible for use as subjects in mandible studies.
The purposes of this study were to compare the measurements of mandible morphology using 3D CBCT data with those using CBCT-synthesized 2D images; to quantify the errors in measurements using CBCT-synthesized 2D images; and to clarify whether such errors would affect the description of the changes of mandibular growth.
Subjects and experimental procedure
Bone model reconstruction and morphological parameters
Anatomical landmarks on the mandible utilized in this study
LP: lateral pole of condyle
The most protruding point on the lateral side of the mandibular condyle
CP: Coronoid process
The most protruding point on the Coronoid
The most posterior and inferior point at the mandibular angle
AMF: Anterior mental foramen
The most anterior edge of the export of the mental nerve
PMF: Posterior mental foramen
The most posterior leading edge export of the mental nerve
Generation of and measurement on synthesized cephalograms
On each DRR-generated synthesized cephalogram, the same anatomical landmarks on the 3D volumetric bone model were also identified by the same experienced dentist (HSL) using a self-developed program (MATLAB, Mathwork Inc., USA). The repeatability of this procedure was determined from the same dentist’s repeated operation, giving a very good intra-rater reliability (ICC > 0.93) .
Definitions of the variables for the description of the mandibular growth
Distance between two bony landmarks measured from CBCT data
Inter-marker distance error
The differences between 3D and 2D inter-marker distance
Monthly distance change
The difference in the inter-marker distances between the current and the previous month
Monthly distance change error
The difference between the 3D and 2D monthly distance change
Apart from descriptive statistical analysis of the calculated variables, paired t-tests were also performed to compare 2D measurements with the 3D gold standard of each of the inter-marker distances, monthly distance changes and total annual increases using SPSS version 13.0 (SPSS Inc., Chicago, IL, USA). A significance level of 0.05 was selected. Considering the resolution of the CBCT (0.25 mm), errors less than 0.25 mm were considered clinically non-significant even if statistical significance (p < 0.05) was found.
Means (standard deviations) of the total annual increase of the inter-marker distances †
This study aimed to compare the measurements of mandible morphology made on 3D CBCT data (gold standard) with those on CBCT-synthesized 2D cephalograms; to quantify the errors in measurements made on CBCT-synthesized cephalograms; and to clarify whether such errors would affect the description of the changes in mandibular growth. While the increases of the inter-marker distances varied among the marker pairs, all marker pairs increased their inter-marker distances gradually every month, reaching 50% of the total annual increases during the fourth and fifth months, and then slowed down in the subsequent months (Figure 6). The errors in 2D measurements caused significant underestimations in most of the inter-marker distances throughout the monitoring period (Figure 8), in most of the monthly inter-marker distance changes during the first four months (Figure 9), and in the total growth (Table 3). These results showed that significant errors were prevalent in the 2D measurements of the dimensions and their monthly changes in the early stage of growth, as well as in the total growth of the mandible.
The measurement errors using 2D imaging are related to the fundamental characteristics of the image formation which is based on the projection of X-rays from a point source through the mandible onto the image plane (Figure 1). With point X-ray projections, the centerline of the imaging source is perpendicular to the image plane. The magnification ratio is dependent upon the ratio of the distance between the source and the imaging plane, and the distance between the source and the object. Thus, reducing the distance between source and object will increase the magnification ratio, and vice versa. For a 3D solid object with a complicated geometry and thickness, the projection is the result of non-uniform magnification. These characteristics largely explained the observed 2D measurement errors.The errors in the 2D distance measurements appeared to be affected by the inter-marker distances, and the angles between the inter-marker segments and the image plane (projection angle). For example, since GO-CP and LP-GO were on the ramus that was close to a flat plate and nearly parallel with the projection plane, and since these segments were not the longest ones, they were found to have the smallest errors (<1.5 mm) among all the marker pairs (Figure 8). On the other hand, since LP-CP had the greatest projection angle (>30° for both sides), it had considerable errors (2.3-5.2 mm) even though it was the shortest segment (13–32 mm). Marker pairs with similar distances and projection angles had similar magnitudes of inter-marker distance errors (Figure 8).The large errors in measuring inter-marker segments located between the mental foramen and the outer edge of the ramus could also be explained by the distance and angle factors determined largely by the anatomy. Since the mandibular body resembles a “V”-shape in the transverse plane, each side of the body formed an angle with the image plane, contributing to the errors in the inter-marker segments on the mandibular body. Therefore, being the longest segments on the mandible (length 65–170 mm) with projection angles in the range of 15°-20°, LC-AMF and GO-AMF were found to have the largest measurement errors (3.6-7.1 mm). With similar projection angles, shorter segments on the mandible body in space would thus produce smaller errors, between 1.1 and 5.4 mm (Figure 8).
The error on the side of the mandible further away from the image source was mostly much greater than that on the side closer to the source. In the current study, 2D projection measurements were made on images calibrated back to the median plane. This caused a magnification effect for the side of the mandible closer to the image source but a shrinking effect for the side further away from the source. As indicated in the aforementioned information, the angle formed by the inter-marker segments and the projection plane often led the 2D measurement methods towards a trend of underestimating the true segment length as determined by the 3D methods. Therefore, considering the relative positions of the mandible, image source and image plane, it appears that the magnification effects would compensate for the errors in results for the side closer to the image source while further underestimation of the true length would be expected. It was also observed from the results of the current study that the error of LP-GO on the side of the mandible further away from the image source was greater than that on the side closer to the source, and the difference increased with time.
For many years, the 2D cephalogram has been used by orthodontists as the standard method for assessing the changes of facial bone morphology. Two-dimensional cephalogrametric measurements have also been used to describe the growth of the facial bones. However, the facial bones are three-dimensional objects. Therefore, many details cannot be measured accurately. The superposition of the images of the bones can also lead to measurement errors owing to human misinterpretation. It would be even more difficult to use 2D images for measuring patients who exhibit non-symmetrical or deformed facial morphology. The current study used low radiation CBCT so it was possible to obtain 3D anatomical measurements over the growth process.
The current study was the first in the literature to evaluate the errors associated with 2D measurements over the growth process. This is in contrast to previous studies on the differences in measurements between 2D and 3D image-based methods using a single object at a set growth point in time. While the current study showed that similar bone growth patterns could be obtained using 2D measurements, the measured amount and rate of change of the bone morphology over time were found to be affected by the errors associated with 2D measurements. Two-dimensional measurements caused significant and different underestimations of the inter-marker distances throughout the monitoring period, of the monthly inter-marker distance changes during the first four months and of the total growth. These errors are difficult to eliminate because of their non-homogeneous and non-linear nature. The measurement errors were proportional to the inter-marker distances and their projection angles that were non-homogeneous within the bone and also related to the non-linear growth of the mandible over time . The current results suggest that 2D measurements of the dimensions and their monthly changes during the early stage of growth, as well as the total growth of the mandible, should be interpreted cautiously.
In the current study the amount of growth recorded in the pigs was approximately equivalent to the growth in humans from birth to the age of nine years. The results suggest that the misinterpretation owing to 2D image errors must be taken into account for dental treatment or craniofacial surgery in a growing mandible. Although the current approach cannot be performed on humans due to ethical considerations, in the future, if radiation doses and costs could be reduced, a 3D image-based method could replace the 2D image-based method in providing more accurate measurement parameters. The viewpoint raised in the current study should be included in clinical considerations when drawing up plans for treatment, taking into consideration the effects of growth time-points in interpreting imaging results.
Significant errors exist in the measurements using 2D imaging methods, underestimating the mandibular dimensions and their monthly changes in the early stages of growth, as well as total annual growth of the mandible. These results should be considered in dental treatment planning at the beginning of the treatment in order to control more precisely the treatment process and outcome.
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