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3D analysis and clinical applications of CBCT images
3D analysis and clinical applications of CBCT images Mohamed Bayome, Jae Hyun Park, YoonJi Kim, and Yoon-Ah Kook Cone-beam computed tomography (CBCT) images is an essential element in diagnosing and treatment planning patients in need of orthodontic and/or orthognathic surgery. An accurate evaluation of the dental, skeletal, and softtissue relationships through the normative values of three-dimensional (3D) cephalometric parameters, specifically palatal and alveolar bone thickness, mandibular body and maxillary basal curve length, and basal arch form have been demanded. The normative values of innovative 3D cephalometric parameters for palatal bone thickness in adolescents versus adults may be helpful for clinicians to enhance the success in application and use of temporary skeletal anchorage devices. Characteristics of alveolar bone thickness, basal arch form, and facial asymmetry of both normal occlusion and Class III malocclusion are also discussed with 3D CBCT images. In this article, the various 3D analyses and clinical applications including bone thickness, facial asymmetry, basal curve length, and basal arch form are addressed. (Semin Orthod 2015; ]:]]]–]]].) & 2015 Elsevier Inc. All rights reserved.
Introduction ephalometric analysis has been a vital component in the diagnosis and treatment planning in orthodontics and orthognathic surgery. Various cephalometric analyses have been reported throughout decades.1–4 Each analysis was based on identification of several specific landmarks to calculate the linear and angular relationships among them. All the analyses aimed to evaluate the deviations in the skeletal and dentoalveolar relationships by comparing these relationships to normative values. These values, in some analyses, have been derived from growth studies such as Bolton5 and Burlington6 growth studies. Meanwhile, in other analyses they were based
C
The Catholic University of Korea, Seoul, South Korea; Department of Postgraduate Studies, the Universidad Autonoma del Paraguay, Asuncion, Paraguay; Arizona School of Dentistry & Oral Health, A.T. Still University, Mesa, AZ; Graduate School of Dentistry, Kyung Hee University, Seoul, South Korea; Department of Orthodontics, Seoul St. Mary’s Hospital, The Catholic University of Korea, 505 Banpo-Dong, Seocho-Gu, Seoul 137-701, South Korea. Address correspondence to Yoon-Ah Kook, DDS, PhD, Department of Orthodontics, Seoul St. Mary’s Hospital, The Catholic University of Korea, 505 Banpo-Dong, Seocho-Gu, Seoul 137-701, South Korea. E-mail: [email protected] & 2015 Elsevier Inc. All rights reserved. 1073-8746/12/1801-$30.00/0 http://dx.doi.org/10.1053/j.sodo.2015.07.003
on evaluation of a limited sample of selected normal occlusion volunteers.7,8 However, several inherent drawbacks existed in all those analyses such as magnification, superimposition of anatomical structures and presentation of a two-dimensional (2D) projection of a three-dimensional (3D) object. These may have led to the main factor affecting the reliability of cephalometric analyses: error in identification of landmarks and their projection on 2D.9,10 Also, the implication of head orientation increased the inquiry about the reliability of these measurements.11,12 The introduction of cone-beam computed tomography (CBCT) has resulted in the improvement of the quality of radiographic data due to overcoming the disadvantages of the conventional 2D radiographic techniques. The precision, accuracy, and reliability of landmarks identification as well as linear and angular measurements on CBCT images had been comprehensively evaluated.13–16 High intra- and inter-observer reliability of measurements were reported.17,18 In addition, the image distortion and the spatial resolution of a CBCT machine were assessed.19 The analysis of CBCT images has been valuable in numerous applications such as: (1) diagnosis of impacted and supernumerary teeth, in which the 3D images were superior to the
Seminars in Orthodontics, Vol ], No ] (), 2015: pp ]]]–]]]
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conventional 2D images,20–22 (2) treatment planning for placement of skeletal anchorage devices, in which CBCT scans allowed for the evaluation of bone thickness and density in different areas in the mandible and maxilla,23–25 (3) 3D volumetric assessment of the upper airway,26 (4) 3D analysis for diagnosis and treatment planning of orthodontic and orthognathic patients.27,28 Several advantages of CBCT were reported, including ability to assess the image from the three planes, the real-size 3D images, and absence of distortion or overlapping structures.29 The fine adjustment of the head position is not essential during taking the image, because the points keep their spatial relationships in 3D coordinates unchanged.30 Therefore, the reorientation of the images, on the contrary to the lateral cephalometric radiograph, is possible. Moreover, the ease of landmark identification and high precision of superimposing images have been reported.31,32 Significant differences were reported between angular measurements performed on 2D posteroanterior (PA) cephalograms and those on radiographs constructed from CBCT scans.33,34 In addition, Gribel et al.35 showed significant differences between measurements taken on a lateral cephalogram and those taken from a CBCT scan. Therefore, they suggested a mathematical formula in an attempt to convert the 2D cephalometric measurements into a 3D CBCT measurement. Although the radiation dose of the CBCT is lower than the medical spiral CT, it is still higher than that of a 2D cephalogram. However, this depends on the CBCT scanner’s specifications, the time of scanning, and the field of view. Therefore, it is recommended to apply the 3D cephalometric analysis to the cases that require comprehensive treatment. Clinicians should always keep in mind that the radiation exposure to a human being should be kept As Low As Reasonably Achievable (ALARA). In addition, no well-established digitization techniques of the 3D images has been standardized either on the multi-planar reconstruction (MPR) slices or on the rendered view. The recently proposed analyses could be technique sensitive. Moreover, custom-made analysis by each user requires good knowledge of spatial geometry and experience in working with 3D models.
3D cephalometric analysis The 3D analysis might represent a key to overcome all the traditional cephalometric disadvantages. However, a well-established method to digitize and analyze 3D radiographic images is, yet, controversial. Kochel et al.36,37 developed a 3D soft-tissue analysis based on the data derived from 3D stereophotogrammetric images. However, all the measurements were taken from the projections of the digitized points. Moreover, they evaluated correlation of the 3D soft-tissue data to variables retrieved from 2D lateral cephalometric analysis. Also, Farronato et al.38 proposed a 10-point 3D analysis of CBCT images directly digitized on the rendered view. They reported the reliability and the reproducibility of their method and compared it to 2D data. However, norms of the variables were not reported in their study probably due to the small sample size and the wide age range. More recently, Cheung et al.28 reported 3D cephalometric norms based on CBCT scans of Chinese population. Bayome et al.27 proposed a new 3D cephalometric analysis and evaluated the relationships among skeletal and dentoalveolar variables. Their study has also provided the norms of the 3D variables of a Korean normal occlusion population.
Segmentation of CBCT images To achieve a sound method for 3D analysis of a CBCT image, volume segmentation and image reorientation should be considered prior to landmark identification. Volume segmentation is the allocation and separation of an anatomical structure or region of interest from the 3D volumes so that it can be viewed individually. The difficulty of segmentation is mainly due to the variability and complexity of the biological tissues. Besides, the large size of the datasets and the limitations of imaging techniques, such as low contrast, motion and noise, may result in indistinct boundaries of the adjacent structures. Thresholding approach is one of the simplest stochastic segmentation techniques in which one or more values “thresholds” are used to create partitions according to voxel intensities. For example, a threshold could be set to separate air from soft tissue and another threshold to separate soft tissue from bone while a third one can separate bone from teeth. However, it is highly
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sensitive to noise and dependent on the threshold values.
transverse line to guide the construction of the horizontal plane in 3D coordinate systems.
Reorientation of head position
3D analysis procedures
The reorientation process depends on placing the image of the head into a known repeatable position in the coordinate system through defining the origin point and the X, Y, and Z planes. These definitions should be based on landmarks that are least susceptible to asymmetry and least affected by treatment procedures to strengthen the reliability and validity of the required planes. Nasion (N) and anterior nasal spines (ANS) tend to fall on or very close to the midsagittal plane in 90% of the population.39 Therefore, Bayome et al.27 selected N as an origin of the 3D coordinate system. The horizontal plane (X) was defined through the right and left orbitales (Or) and the left porion (Po) while the midsagittal plane (Y) was defined as the perpendicular plane passing through N and ANS. The vertical plane (Z) was the perpendicular to both X and Y (Fig. 1). Swennen et al.40 proposed a reorientation method “the anatomic Cartesian 3D cephalometric reference system” with the origin at Sella (S). However, this system is complicated and time consuming. Kook and Kim41 proposed a clinical method to easily reorient head using frontal facial and intraoral photographs. Park et al.42 suggested the use of the right and left zygomatic suture points or the Or as a stable
Several software programs has been developed to view, digitize, measure, and analyze CBCT data. Ludlow et al.29 recommended the identification of landmarks on the MPR slices due to its high accuracy. Another study showed landmarks digitized on the rendered view due to its ease and shorter analysis time.27 Nguyen et al.43 found high correlation between measurements from each of the slice section and volume render views of Invivo software (Anatomage Inc., San Jose, CA) and the physical measurements. Also, several studies reported high accuracy of linear and angular measurements in 3D volume render CBCT images compared to physical measurements.44–46 With the advent of 3D cephalometric analysis, new landmarks, reference planes, and measurements were made possible. The ability to 3D visualize the head and the possibility of taking sections into the 3D volume allowed practitioners to place landmarks accurately on structures that were not available on the 2D cephalograms. In turn, the 3D Cartesian system facilitated the creation of new reference planes and the evaluation of curvatures, besides the linear and angular relationships. The following are examples of the newly proposed landmarks, planes, and measurements.
Figure 1. Reorientation of head and coordinate system. N, nasion; X, the horizontal plane; Y, the midsagittal plane; Z, the vertical plane.
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Figure 2. Mandibular body variables. Me, menton; MBC, mandibular body curve; Go, gonion; 1, menton angle; 2, mandibular body length; 3, anterior mandibular body length; 4, posterior mandibular body length; 5, MBC angle.
New landmarks 47
Lee et al. suggested that the 2D definition of the mandibular body might not be able to represent it on 3D image. Therefore, they proposed the mandibular body curve (MBC) points, which lie on the most convex point on the curvature of the mandibular body midway between the inner and outer borders (Fig. 2). They reported a significant difference between the asymmetry and normal occlusion groups in the posterior mandibular body length (MBCGo), but this difference was not significant in the mandibular body length (Me–Go).
New planes Cheung et al.28 proposed a new reference plane, the supraorbital margin plane, to overcome the limitations of 2D analysis in assessment of paranasal and infraorbital areas. However, further research applying new reference planes or implementing alternative methods, such as volumetric analysis might be required to enhance the evaluation of the midfacial complex configuration.
New measurements The measurement of angles and distances in 3D is considerably different from that in 2D due to
the effect of the roll, yaw, and pitch on the measurements that is defined as follows: cos θ ¼
a:b ; jajjbj
ð1Þ
where a and b are the vectors of each line. For example, a change in the roll of one line may change the value of the angle between this line and another when measured on 3D. However, this change will not affect the readings if it is measured on 2D. This, subsequently, changes the interpretation of the line-to-line angle measurements in 3D. The same is true for measuring 3D line-to-plane or plane-to-plane angles as they are assessed through determination of the plane’s normal vector and then using Eq. (1). In addition, 3D cephalometric analysis allowed volumetric and curvature evaluations. Recently, Bayome et al.27 suggested measuring the length of the mandibular body through calculating the length of the curve passing through menton (Me), MBC, and gonion (Go) to achieve a more accurate representation of the mandibular body. The coordinates of these points were entered into MATLABs 7.5 (R2007b) (The MathWorks Inc., Natick, MA). The 4th degree polynomial equation f ðx Þ of the best fitting curve that pass through the five points was generated as an
3D analysis and clinical applications of CBCT images
approximation of mandibular body.
the
curvature
f ðx Þ¼ p1 x 4 þ p2 x 3 þp3 x 2 þ p4 x þ p5
of
the ð2Þ
It was found that polynomial of 4th order approximated the curvature of the mandibular body with tolerable, or even negligible, mean square error. Mathematically, the length of a path from point a to point b on a curve represented by the function f ðx Þ is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Z b df ðx Þ 2 1þ dx ð3Þ Length ¼ dx a Then, the equation was entered into Maple™ 11.0 (Waterloo Maple Inc., Waterloo, ON, Canada) to calculate the differentiation of the function f ðx Þ: df ðx Þ ¼ 4p1 x 3 þ3p2 x 2 þ 2p3 x þp4 dx
ð4Þ
Then, the length of the curve from Go to Me was found by solving the integration: Z b qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Length ¼ 1 þ 4p1 x 3 þ3p2 x 2 þ2p3 x þ p4 dx a
ð5Þ where a and b are the values of X coordinates of Me and Go, respectively (Fig. 3). The same procedures were followed to calculate the length of the curve of the basal arch of the maxilla by incorporating the A point, and right and left canine eminence, and tuberosity, where a and b in the equation are the values of X coordinates of A point and tuberosity, respectively (Fig. 4).
3D analysis and variable relationships Bayome et al.27 showed significant differences between males and females in several vertical and transverse measurements. Similarly, Thilander et al.48 reported that the linear craniofacial measurements on lateral cephalograms were larger in males than in females, while angular measurements showed no statistical differences. This might suggest that the dimensions of the face played a major role in the gender dimorphism. The total facial height was about 5 mm larger in the study of Bayome et al.27 than in that of Cheung et al.,28 although the latter’s
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measurement was from N to gnathion (Gn) while the former’s was to the pogonion (Pg). This suggested an even larger difference between the 2 different Asian populations. Even though the Southern Chinese sample had about 7 mm longer upper facial height than Koreans, this can be attributed to the extension of the Chinese measurement to the A point while the Korean was till ANS. Meanwhile, the Korean sample had about 2 mm longer lower facial height than Chinese although their measurement was from ANS to Me while ours was from ANS to Pg, which implies even longer lower facial height for Koreans. Therefore, the difference in total facial height might be attributed mainly to the lower facial third. Several studies have evaluated condylar variables.49–52 You et al.49 suggested that the condylar unit (condyle, condylar neck, and part of the ramus) plays a central role in the mandibular asymmetry. However, Huntjens et al.50 found condylar asymmetries did not correlate well with facial asymmetry. Also, Sanders et al.51 reported no significant asymmetries among condylar measurements in Class I or Class II subdivision groups. Nevertheless, it was assumed that the subclinical condylar and mandibular asymmetry could be natural in juvenile patients, but the extend of this asymmetry is still indistinct.52 Also, Bayome et al.27 reported correlation between the condylar and mandibular variables which might be attributed to the adaptive capacity of the condyle as suggested by Enlow and Hans53; for example, the negative correlation between the condylar anteroposterior inclination and the gonial angle tends to preserve a proportion between the height of the mandible and its sagittal position in normal occlusion population. Recently, the difference in ramus length between both sides was reported as a characteristic of both mandibular retrusion and prognathism groups.54 Bayome et al.27 reported that the ramus length demonstrated a significant moderate negative correlation with the gonial angle (r ¼ 0.62). This might suggest that the longer the ramus the smaller its angle with the mandibular body. This configuration can be a mechanism to prevent elongation of the facial height. Also, deviation from this relationship on one side may result in facial asymmetry.
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Figure 3. Mandibular body curve length. Go, gonion; Me, menton; MBC, mandibular body curve.
Soft-tissue 3D analysis The facial appearance has a strong influence on the self-esteem and social acceptance.55,56 Therefore, it is imperative that special attention should be paid for the facial esthetics during orthodontic and orthognathic treatment planning, especially, since the perception of facial attractiveness is subjective, and dependent on ethnicity, age, gender, culture, and personality.57,58 In addition, lack of agreement on standards, and personal and cultural bias heightened the controversy between the idealization and individualization of treatment.
Several facial analyses have been suggested based on soft-tissue landmarks and parameters registered either on a tracing of a radiograph or photograph.59–67 However, besides the criticism of the reliability and creditability of several proposed variables, all these analyses suffered the same disadvantages related to the 2D representation of a 3D object. Moreover, the response of soft-tissue features to changes in skeletal and dentoalveolar relationships was overlooked. Several authors have endeavored to develop a 3D soft-tissue analysis based on various 3D recording techniques such as laser scanning, holography, and stereophotogrammetry.36,37,68–70
Figure 4. Maxillary basal curve length. Max. T, maxillary tuberosity; C E, canine eminence; A, A point.
3D analysis and clinical applications of CBCT images
Plooij et al.71 defined new bone-related soft-tissue landmarks on 3D stereophotogrammetric images and reported high reproducibility and reliability of identification. They suggested that a 3D softtissue analysis can be accurately produced without the need to obtain hard tissue records. Kochel et al.36,37 developed a 3D soft-tissue analysis on 3D stereophotogrammetric images, but all the measurements were taken from projections of the digitized points. A previous study on CBCT images of a normal occlusion population showed that males had a significantly greater intercanthal distance, nasal and mouth widths, and posterior facial width than females.72 Also, it demonstrated that there were no significant differences between the right and left sides.72 However, other studies reported asymmetry in normal occlusion population with pleasing facial features.70,73 This disagreement might be due to differences in the evaluation methods and errors in landmark identification. Nevertheless, up to date, no 3D cephalometric analysis has been widely used in clinical practice, and validated for practicality, reliability, reproducibility, and clinical relevance.
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third of the face, moderate to weak correlations were found between the lower facial height and nasal and mouth widths. In addition, the upper facial width had strong to moderate correlation with the maxillary height and length and mandibular body curve length.72
Conclusion 3D cephalometric analysis is becoming a vital tool to evaluate the relationships among skeletal and dentoalveolar cephalometric variables. New landmarks and variables were suggested to assess anatomical structures that were not recognizable on 2D radiographs especially in the transverse dimension and the midfacial area. The development of 3D hard- and soft-tissue cephalometric analyses may produce a new understanding of the relationships between soft-tissue, skeletal and dentoalveolar cephalometric variables. These analyses can be useful for accurate diagnosis and treatment planning and for evaluation of treatment outcomes of orthodontics or orthognathic surgery.
Relationships between hard and soft tissues
References
Several articles have evaluated the relationship between hard- and soft-tissue cephalometric variables. However, a consensus has not been reached. Ferrario and Sforza74 reported that the facial soft tissue was influenced by skeletal variables and McNamara et al.75 demonstrated a significant relationship between incisor position and the thickness of upper lip. Nonetheless, other authors found that correlations between hard- and soft-tissue parameters were not common.59,76 Recently, a 3D soft-tissue analysis showed weak to moderate correlations between the SNA and Tragus-N-subspinale angle, and between the SNB and Tragus-N-sublabiale angle, sagittally.36 Also, correlations were reported between the lower gonial angle and N-gonion (Go)–gnathion (Gn) angle and between the basal plane angle and the subnasale (Sn)–Pg–Go–Gn angle vertically.37 However, another study reported no significant correlations between hard- and soft-tissue variables except for the posterior facial width with the maxillary length and facial height.72 In the lower
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descriptors and traditional cephalometric methods. Am J Phys Anthropol. 2003;121:172–180. Bergman RT. Cephalometric soft tissue facial analysis. Am J Orthod Dentofacial Orthop. 1999;116:373–389. Legan HL, Burstone CJ. Soft tissue cephalometric analysis for orthognathic surgery. J Oral Surg. 1980;38:744–751. Holdaway RA. A soft-tissue cephalometric analysis and its use in orthodontic treatment planning. Part I. Am J Orthod. 1983;84:1–28. Holdaway RA. A soft-tissue cephalometric analysis and its use in orthodontic treatment planning. Part II. Am J Orthod. 1984;85:279–293. Peck H, Peck S. A concept of facial esthetics. Angle orthod. 1970;40:284–318. Ricketts RM. Esthetics, environment, and the law of lip relation. Am J Orthod. 1968;54:272–289. Powell N, Humphreys B. Proportions of the esthetic face. New York: Thieme–Stratton; 1984. Arnett GW, Jelic JS, Kim J, et al. Soft tissue cephalometric analysis: diagnosis and treatment planning of dentofacial deformity. Am J Orthod Dentofacial Orthop. 1999;116: 239–253. Ferrario VF, Sforza C, Poggio CE, et al. Distance from symmetry: a three-dimensional evaluation of facial asymmetry. J Oral Maxillofac Surg. 1994;52:1126–1132. Stauber I, Vairaktaris E, Holst A, et al. Three-dimensional analysis of facial symmetry in cleft lip and palate patients using optical surface data. J Orofac Orthop. 2008;69: 268–282. Hwang HS, Yuan D, Jeong KH, et al. Three-dimensional soft tissue analysis for the evaluation of facial asymmetry in normal occlusion individuals. Korean J Orthod. 2012;42:56–63. Plooij JM, Swennen GR, Rangel FA, et al. Evaluation of reproducibility and reliability of 3D soft tissue analysis using 3D stereophotogrammetry. Int J Oral Maxillofac Surg. 2009;38:267–273. Bayome M. Evaluation of Three-Dimensional Relationships Among Skeletal, Dentoalveolar, and Soft Tissue Variables in Normal Occlusion Sample. Seoul: The Catholic University of Korea; 2011, [Doctoral dissertation]. Shah SM, Joshi MR. An assessment of asymmetry in the normal craniofacial complex. Angle Orthod. 1978;48: 141–148. Ferrario VF, Sforza C. Size and shape of soft-tissue facial profile: effects of age, gender, and skeletal class. Cleft Palate Craniofac J. 1997;34:498–504. McNamara L, McNamara JA Jr, Ackerman MB, et al. Hard- and soft-tissue contributions to the esthetics of the posed smile in growing patients seeking orthodontic treatment. Am J Orthod Dentofacial Orthop. 2008;133: 491–499. Saxby PJ, Freer TJ. Dentoskeletal determinants of soft tissue morphology. Angle Orthod. 1985;55:147–154.
Introduction ephalometric analysis has been a vital component in the diagnosis and treatment planning in orthodontics and orthognathic surgery. Various cephalometric analyses have been reported throughout decades.1–4 Each analysis was based on identification of several specific landmarks to calculate the linear and angular relationships among them. All the analyses aimed to evaluate the deviations in the skeletal and dentoalveolar relationships by comparing these relationships to normative values. These values, in some analyses, have been derived from growth studies such as Bolton5 and Burlington6 growth studies. Meanwhile, in other analyses they were based
C
The Catholic University of Korea, Seoul, South Korea; Department of Postgraduate Studies, the Universidad Autonoma del Paraguay, Asuncion, Paraguay; Arizona School of Dentistry & Oral Health, A.T. Still University, Mesa, AZ; Graduate School of Dentistry, Kyung Hee University, Seoul, South Korea; Department of Orthodontics, Seoul St. Mary’s Hospital, The Catholic University of Korea, 505 Banpo-Dong, Seocho-Gu, Seoul 137-701, South Korea. Address correspondence to Yoon-Ah Kook, DDS, PhD, Department of Orthodontics, Seoul St. Mary’s Hospital, The Catholic University of Korea, 505 Banpo-Dong, Seocho-Gu, Seoul 137-701, South Korea. E-mail: [email protected] & 2015 Elsevier Inc. All rights reserved. 1073-8746/12/1801-$30.00/0 http://dx.doi.org/10.1053/j.sodo.2015.07.003
on evaluation of a limited sample of selected normal occlusion volunteers.7,8 However, several inherent drawbacks existed in all those analyses such as magnification, superimposition of anatomical structures and presentation of a two-dimensional (2D) projection of a three-dimensional (3D) object. These may have led to the main factor affecting the reliability of cephalometric analyses: error in identification of landmarks and their projection on 2D.9,10 Also, the implication of head orientation increased the inquiry about the reliability of these measurements.11,12 The introduction of cone-beam computed tomography (CBCT) has resulted in the improvement of the quality of radiographic data due to overcoming the disadvantages of the conventional 2D radiographic techniques. The precision, accuracy, and reliability of landmarks identification as well as linear and angular measurements on CBCT images had been comprehensively evaluated.13–16 High intra- and inter-observer reliability of measurements were reported.17,18 In addition, the image distortion and the spatial resolution of a CBCT machine were assessed.19 The analysis of CBCT images has been valuable in numerous applications such as: (1) diagnosis of impacted and supernumerary teeth, in which the 3D images were superior to the
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conventional 2D images,20–22 (2) treatment planning for placement of skeletal anchorage devices, in which CBCT scans allowed for the evaluation of bone thickness and density in different areas in the mandible and maxilla,23–25 (3) 3D volumetric assessment of the upper airway,26 (4) 3D analysis for diagnosis and treatment planning of orthodontic and orthognathic patients.27,28 Several advantages of CBCT were reported, including ability to assess the image from the three planes, the real-size 3D images, and absence of distortion or overlapping structures.29 The fine adjustment of the head position is not essential during taking the image, because the points keep their spatial relationships in 3D coordinates unchanged.30 Therefore, the reorientation of the images, on the contrary to the lateral cephalometric radiograph, is possible. Moreover, the ease of landmark identification and high precision of superimposing images have been reported.31,32 Significant differences were reported between angular measurements performed on 2D posteroanterior (PA) cephalograms and those on radiographs constructed from CBCT scans.33,34 In addition, Gribel et al.35 showed significant differences between measurements taken on a lateral cephalogram and those taken from a CBCT scan. Therefore, they suggested a mathematical formula in an attempt to convert the 2D cephalometric measurements into a 3D CBCT measurement. Although the radiation dose of the CBCT is lower than the medical spiral CT, it is still higher than that of a 2D cephalogram. However, this depends on the CBCT scanner’s specifications, the time of scanning, and the field of view. Therefore, it is recommended to apply the 3D cephalometric analysis to the cases that require comprehensive treatment. Clinicians should always keep in mind that the radiation exposure to a human being should be kept As Low As Reasonably Achievable (ALARA). In addition, no well-established digitization techniques of the 3D images has been standardized either on the multi-planar reconstruction (MPR) slices or on the rendered view. The recently proposed analyses could be technique sensitive. Moreover, custom-made analysis by each user requires good knowledge of spatial geometry and experience in working with 3D models.
3D cephalometric analysis The 3D analysis might represent a key to overcome all the traditional cephalometric disadvantages. However, a well-established method to digitize and analyze 3D radiographic images is, yet, controversial. Kochel et al.36,37 developed a 3D soft-tissue analysis based on the data derived from 3D stereophotogrammetric images. However, all the measurements were taken from the projections of the digitized points. Moreover, they evaluated correlation of the 3D soft-tissue data to variables retrieved from 2D lateral cephalometric analysis. Also, Farronato et al.38 proposed a 10-point 3D analysis of CBCT images directly digitized on the rendered view. They reported the reliability and the reproducibility of their method and compared it to 2D data. However, norms of the variables were not reported in their study probably due to the small sample size and the wide age range. More recently, Cheung et al.28 reported 3D cephalometric norms based on CBCT scans of Chinese population. Bayome et al.27 proposed a new 3D cephalometric analysis and evaluated the relationships among skeletal and dentoalveolar variables. Their study has also provided the norms of the 3D variables of a Korean normal occlusion population.
Segmentation of CBCT images To achieve a sound method for 3D analysis of a CBCT image, volume segmentation and image reorientation should be considered prior to landmark identification. Volume segmentation is the allocation and separation of an anatomical structure or region of interest from the 3D volumes so that it can be viewed individually. The difficulty of segmentation is mainly due to the variability and complexity of the biological tissues. Besides, the large size of the datasets and the limitations of imaging techniques, such as low contrast, motion and noise, may result in indistinct boundaries of the adjacent structures. Thresholding approach is one of the simplest stochastic segmentation techniques in which one or more values “thresholds” are used to create partitions according to voxel intensities. For example, a threshold could be set to separate air from soft tissue and another threshold to separate soft tissue from bone while a third one can separate bone from teeth. However, it is highly
3D analysis and clinical applications of CBCT images
3
sensitive to noise and dependent on the threshold values.
transverse line to guide the construction of the horizontal plane in 3D coordinate systems.
Reorientation of head position
3D analysis procedures
The reorientation process depends on placing the image of the head into a known repeatable position in the coordinate system through defining the origin point and the X, Y, and Z planes. These definitions should be based on landmarks that are least susceptible to asymmetry and least affected by treatment procedures to strengthen the reliability and validity of the required planes. Nasion (N) and anterior nasal spines (ANS) tend to fall on or very close to the midsagittal plane in 90% of the population.39 Therefore, Bayome et al.27 selected N as an origin of the 3D coordinate system. The horizontal plane (X) was defined through the right and left orbitales (Or) and the left porion (Po) while the midsagittal plane (Y) was defined as the perpendicular plane passing through N and ANS. The vertical plane (Z) was the perpendicular to both X and Y (Fig. 1). Swennen et al.40 proposed a reorientation method “the anatomic Cartesian 3D cephalometric reference system” with the origin at Sella (S). However, this system is complicated and time consuming. Kook and Kim41 proposed a clinical method to easily reorient head using frontal facial and intraoral photographs. Park et al.42 suggested the use of the right and left zygomatic suture points or the Or as a stable
Several software programs has been developed to view, digitize, measure, and analyze CBCT data. Ludlow et al.29 recommended the identification of landmarks on the MPR slices due to its high accuracy. Another study showed landmarks digitized on the rendered view due to its ease and shorter analysis time.27 Nguyen et al.43 found high correlation between measurements from each of the slice section and volume render views of Invivo software (Anatomage Inc., San Jose, CA) and the physical measurements. Also, several studies reported high accuracy of linear and angular measurements in 3D volume render CBCT images compared to physical measurements.44–46 With the advent of 3D cephalometric analysis, new landmarks, reference planes, and measurements were made possible. The ability to 3D visualize the head and the possibility of taking sections into the 3D volume allowed practitioners to place landmarks accurately on structures that were not available on the 2D cephalograms. In turn, the 3D Cartesian system facilitated the creation of new reference planes and the evaluation of curvatures, besides the linear and angular relationships. The following are examples of the newly proposed landmarks, planes, and measurements.
Figure 1. Reorientation of head and coordinate system. N, nasion; X, the horizontal plane; Y, the midsagittal plane; Z, the vertical plane.
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Figure 2. Mandibular body variables. Me, menton; MBC, mandibular body curve; Go, gonion; 1, menton angle; 2, mandibular body length; 3, anterior mandibular body length; 4, posterior mandibular body length; 5, MBC angle.
New landmarks 47
Lee et al. suggested that the 2D definition of the mandibular body might not be able to represent it on 3D image. Therefore, they proposed the mandibular body curve (MBC) points, which lie on the most convex point on the curvature of the mandibular body midway between the inner and outer borders (Fig. 2). They reported a significant difference between the asymmetry and normal occlusion groups in the posterior mandibular body length (MBCGo), but this difference was not significant in the mandibular body length (Me–Go).
New planes Cheung et al.28 proposed a new reference plane, the supraorbital margin plane, to overcome the limitations of 2D analysis in assessment of paranasal and infraorbital areas. However, further research applying new reference planes or implementing alternative methods, such as volumetric analysis might be required to enhance the evaluation of the midfacial complex configuration.
New measurements The measurement of angles and distances in 3D is considerably different from that in 2D due to
the effect of the roll, yaw, and pitch on the measurements that is defined as follows: cos θ ¼
a:b ; jajjbj
ð1Þ
where a and b are the vectors of each line. For example, a change in the roll of one line may change the value of the angle between this line and another when measured on 3D. However, this change will not affect the readings if it is measured on 2D. This, subsequently, changes the interpretation of the line-to-line angle measurements in 3D. The same is true for measuring 3D line-to-plane or plane-to-plane angles as they are assessed through determination of the plane’s normal vector and then using Eq. (1). In addition, 3D cephalometric analysis allowed volumetric and curvature evaluations. Recently, Bayome et al.27 suggested measuring the length of the mandibular body through calculating the length of the curve passing through menton (Me), MBC, and gonion (Go) to achieve a more accurate representation of the mandibular body. The coordinates of these points were entered into MATLABs 7.5 (R2007b) (The MathWorks Inc., Natick, MA). The 4th degree polynomial equation f ðx Þ of the best fitting curve that pass through the five points was generated as an
3D analysis and clinical applications of CBCT images
approximation of mandibular body.
the
curvature
f ðx Þ¼ p1 x 4 þ p2 x 3 þp3 x 2 þ p4 x þ p5
of
the ð2Þ
It was found that polynomial of 4th order approximated the curvature of the mandibular body with tolerable, or even negligible, mean square error. Mathematically, the length of a path from point a to point b on a curve represented by the function f ðx Þ is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Z b df ðx Þ 2 1þ dx ð3Þ Length ¼ dx a Then, the equation was entered into Maple™ 11.0 (Waterloo Maple Inc., Waterloo, ON, Canada) to calculate the differentiation of the function f ðx Þ: df ðx Þ ¼ 4p1 x 3 þ3p2 x 2 þ 2p3 x þp4 dx
ð4Þ
Then, the length of the curve from Go to Me was found by solving the integration: Z b qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Length ¼ 1 þ 4p1 x 3 þ3p2 x 2 þ2p3 x þ p4 dx a
ð5Þ where a and b are the values of X coordinates of Me and Go, respectively (Fig. 3). The same procedures were followed to calculate the length of the curve of the basal arch of the maxilla by incorporating the A point, and right and left canine eminence, and tuberosity, where a and b in the equation are the values of X coordinates of A point and tuberosity, respectively (Fig. 4).
3D analysis and variable relationships Bayome et al.27 showed significant differences between males and females in several vertical and transverse measurements. Similarly, Thilander et al.48 reported that the linear craniofacial measurements on lateral cephalograms were larger in males than in females, while angular measurements showed no statistical differences. This might suggest that the dimensions of the face played a major role in the gender dimorphism. The total facial height was about 5 mm larger in the study of Bayome et al.27 than in that of Cheung et al.,28 although the latter’s
5
measurement was from N to gnathion (Gn) while the former’s was to the pogonion (Pg). This suggested an even larger difference between the 2 different Asian populations. Even though the Southern Chinese sample had about 7 mm longer upper facial height than Koreans, this can be attributed to the extension of the Chinese measurement to the A point while the Korean was till ANS. Meanwhile, the Korean sample had about 2 mm longer lower facial height than Chinese although their measurement was from ANS to Me while ours was from ANS to Pg, which implies even longer lower facial height for Koreans. Therefore, the difference in total facial height might be attributed mainly to the lower facial third. Several studies have evaluated condylar variables.49–52 You et al.49 suggested that the condylar unit (condyle, condylar neck, and part of the ramus) plays a central role in the mandibular asymmetry. However, Huntjens et al.50 found condylar asymmetries did not correlate well with facial asymmetry. Also, Sanders et al.51 reported no significant asymmetries among condylar measurements in Class I or Class II subdivision groups. Nevertheless, it was assumed that the subclinical condylar and mandibular asymmetry could be natural in juvenile patients, but the extend of this asymmetry is still indistinct.52 Also, Bayome et al.27 reported correlation between the condylar and mandibular variables which might be attributed to the adaptive capacity of the condyle as suggested by Enlow and Hans53; for example, the negative correlation between the condylar anteroposterior inclination and the gonial angle tends to preserve a proportion between the height of the mandible and its sagittal position in normal occlusion population. Recently, the difference in ramus length between both sides was reported as a characteristic of both mandibular retrusion and prognathism groups.54 Bayome et al.27 reported that the ramus length demonstrated a significant moderate negative correlation with the gonial angle (r ¼ 0.62). This might suggest that the longer the ramus the smaller its angle with the mandibular body. This configuration can be a mechanism to prevent elongation of the facial height. Also, deviation from this relationship on one side may result in facial asymmetry.
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Figure 3. Mandibular body curve length. Go, gonion; Me, menton; MBC, mandibular body curve.
Soft-tissue 3D analysis The facial appearance has a strong influence on the self-esteem and social acceptance.55,56 Therefore, it is imperative that special attention should be paid for the facial esthetics during orthodontic and orthognathic treatment planning, especially, since the perception of facial attractiveness is subjective, and dependent on ethnicity, age, gender, culture, and personality.57,58 In addition, lack of agreement on standards, and personal and cultural bias heightened the controversy between the idealization and individualization of treatment.
Several facial analyses have been suggested based on soft-tissue landmarks and parameters registered either on a tracing of a radiograph or photograph.59–67 However, besides the criticism of the reliability and creditability of several proposed variables, all these analyses suffered the same disadvantages related to the 2D representation of a 3D object. Moreover, the response of soft-tissue features to changes in skeletal and dentoalveolar relationships was overlooked. Several authors have endeavored to develop a 3D soft-tissue analysis based on various 3D recording techniques such as laser scanning, holography, and stereophotogrammetry.36,37,68–70
Figure 4. Maxillary basal curve length. Max. T, maxillary tuberosity; C E, canine eminence; A, A point.
3D analysis and clinical applications of CBCT images
Plooij et al.71 defined new bone-related soft-tissue landmarks on 3D stereophotogrammetric images and reported high reproducibility and reliability of identification. They suggested that a 3D softtissue analysis can be accurately produced without the need to obtain hard tissue records. Kochel et al.36,37 developed a 3D soft-tissue analysis on 3D stereophotogrammetric images, but all the measurements were taken from projections of the digitized points. A previous study on CBCT images of a normal occlusion population showed that males had a significantly greater intercanthal distance, nasal and mouth widths, and posterior facial width than females.72 Also, it demonstrated that there were no significant differences between the right and left sides.72 However, other studies reported asymmetry in normal occlusion population with pleasing facial features.70,73 This disagreement might be due to differences in the evaluation methods and errors in landmark identification. Nevertheless, up to date, no 3D cephalometric analysis has been widely used in clinical practice, and validated for practicality, reliability, reproducibility, and clinical relevance.
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third of the face, moderate to weak correlations were found between the lower facial height and nasal and mouth widths. In addition, the upper facial width had strong to moderate correlation with the maxillary height and length and mandibular body curve length.72
Conclusion 3D cephalometric analysis is becoming a vital tool to evaluate the relationships among skeletal and dentoalveolar cephalometric variables. New landmarks and variables were suggested to assess anatomical structures that were not recognizable on 2D radiographs especially in the transverse dimension and the midfacial area. The development of 3D hard- and soft-tissue cephalometric analyses may produce a new understanding of the relationships between soft-tissue, skeletal and dentoalveolar cephalometric variables. These analyses can be useful for accurate diagnosis and treatment planning and for evaluation of treatment outcomes of orthodontics or orthognathic surgery.
Relationships between hard and soft tissues
References
Several articles have evaluated the relationship between hard- and soft-tissue cephalometric variables. However, a consensus has not been reached. Ferrario and Sforza74 reported that the facial soft tissue was influenced by skeletal variables and McNamara et al.75 demonstrated a significant relationship between incisor position and the thickness of upper lip. Nonetheless, other authors found that correlations between hard- and soft-tissue parameters were not common.59,76 Recently, a 3D soft-tissue analysis showed weak to moderate correlations between the SNA and Tragus-N-subspinale angle, and between the SNB and Tragus-N-sublabiale angle, sagittally.36 Also, correlations were reported between the lower gonial angle and N-gonion (Go)–gnathion (Gn) angle and between the basal plane angle and the subnasale (Sn)–Pg–Go–Gn angle vertically.37 However, another study reported no significant correlations between hard- and soft-tissue variables except for the posterior facial width with the maxillary length and facial height.72 In the lower
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