The purpose of this research was to compare mandibular growth rotation relative to the cranial base in different vertical facial patterns on the basis of multiple 2-dimensional (2D) and 3-dimensional (3D) superimposition methods.
Cone-beam computed tomography (CBCT) images taken at a mean interval of 54.8 ± 16.8 months were assessed from a sample of 70 growing patients. Three mandibular superimposition methods were compared against Björk’s structural method: (1) a 2D landmark method (2D-M1), (2) a voxel-based 3D method based on a previously reported method (3D-M1), and (3) a voxel-based 3D method incorporating symphyseal structures as references (3D-M2). After superimposition, the relative change in cranial base lines as depicted in sagittal views were measured for true mandibular rotation. Agreement between methods was assessed with Lin’s concordance correlation coefficient, Bland-Altman’s limits of agreement, and the Bradley-Blackwood test.
Lin’s concordance correlation coefficients ranged between 0.924 for the 2D-M1 method, 0.695 for the 3D-M1 method, and 0.965 for the 3D-M2 method. Bland-Altman limits of agreement were wide for all but the 3D-M2 method. Finally, the Bradley-Blackwood test of equality of means and variances was significant in all except the 3D-M2 method.
For time intervals between CBCT volume acquisitions >3 years, the use of the 2D-M1 and 3D-M1 methods is not recommended. There was a high concordance between the 3D-M2 method and Björk’s structural method when assessing mandibular growth rotation using relative changes in cranial base lines. The high concordance was displayed across all vertical facial types and for all time differences between first and second CBCT data acquisitions.
Björk’s seminal implant growth studies are considered the gold standard for evaluating craniofacial growth on serial cephalometric evaluations. Some of these studies culminated with the development of the so-called structural method . , However, it was not only implant-based studies that helped derive natural reference structures in the craniofacial region, but also histologic studies. Thus, evidence-based approaches to serial superimpositions were achieved at that time and remain unparalleled in the assessment of craniofacial growth.
Despite this noted accomplishment, the manner in which the implants were used in human subjects is today considered unethical for clinical or research purposes. Hence, direct replication of similar concepts using 3D imaging is not possible. One research and clinical area that has gained significant traction is the application of 3-dimensional (3D) superimposition on the cranial base of serial cone-bean computed tomography (CBCT) acquisitions. Although several 3D superimposition methods have an acceptable level of reliability, research is still required to make comparisons against a reference standard. However, specifically for mandibular superimposition, there is still much research required to assess 3D methods for use with serial superimposition on growing patients.
It is possible that mandibular 3D regional superimposition may support Björk’s implant work and permit the 3D implementation of the structural method. This approach would allow the orthodontist to evaluate growth over longer time intervals and assess changes that could otherwise have been undertaken using only 2-dimensional (2D), conventional methods. Thus, there exists the need to validate 3D methods of superimposition and registration against the 2D structural method to show that the methods are interchangeable and arrive at the same results with high accuracy and precision. Therefore, the aims of this study were 4-fold: (1) compare 2 rapid voxel-based 3D registration methods against Björk’s structural method, (2) compare a 2D method—using the mental reversal line described by Enlow and overlay of the mandibular canal—against the structural method to assess what value the mental reversal line landmark may provide, (3) account for vertical facial types, and (4) account for the time interval between T1 and T2 CBCT acquisitions. The primary outcome measure for each method is mandibular growth rotation relative to the cranial base.
Material and methods
Ethics approval was obtained from The University of Queensland School of Dentistry Research Ethics Committee (approval no. 1710).
On the basis of annual changes in true rotation measurements published by Wang et al, an appropriately powered sample size (power = 0.95) was determined using the method proposed by Lin. Setting α to 0.05, an acceptable loss of precision to 0.1 and assuming that under ideal conditions, the alternative methods have a precision of over 90% to the structural method (ie, random error of 10%), the suggested sample size for concordance correlation coefficients (CCC) based on these assumptions was 22 participants, and the least acceptable limit of agreement was a lower 95% confidence interval (CI) of 0.79. This minimum sample size was increased to 70 to investigate variation due to different vertical facial types and time between T1 and T2 CBCT acquisitions. In addition, a larger sample size would provide evidence of heterogeneity of variance in Bland-Altman plots.
Two anonymized CBCT volumes from each of 70 random patients and their records were obtained. Random selection was aided with the use of a random number generator ( random.org ). CBCTs were based on a mixed cohort of malocclusions in patients treated between 2006 and 2016 by a single orthodontist.
Data acquisitions up to 2009 were obtained using an i-Cat Classic, between 2009 and 2014 using the i-Cat Platinum, and from 2014 onwards using the i-Cat FLX (Imaging Sciences International, Hatfield, Pa). All 3 scanners were set at the same scanning parameters: 120 kVp; 8 mA; 0.3-mm voxel size; and scan time, 8.9 seconds; and a field of view of 16 × 22 cm. Images were reconstructed in Digital Imaging and Communications in Medicine files with a slice thickness of 0.3 mm.
The inclusion criteria for the study included randomly selected growing patients undergoing single-phase or 2-phase treatment, observation of growth, or interim treatment assessments. Patients with previous surgery, maxillofacial trauma, or major craniofacial anomalies were excluded. CBCTs with motion artifacts, orthodontic appliances, or a large number of metallic artifacts were excluded ( Table I ).
|Characteristic||n (%) or mean (SD, range)|
|Class I||16 (23)|
|Class II||42 (60)|
|Class III||12 (17)|
|Class I||32 (46)|
|Class II||34 (49)|
|Class III||4 (6)|
|Vertical facial type|
|T1, age, y||11.0 (2.0, 7 to 15)|
|T2, age, y||15.6 (1.9, 12 to 20)|
|Time between T1 and T2, mo||54.8 (16.8, 27 to 103)|
The volumes were imported into OnDemand3D (version 184.108.40.20610; CyberMed Inc, Seoul, South Korea) as shown in the study flowchart ( Fig 1 ). The T1-volume was opened in the fusion module and reoriented so that the lower border of the mandible was approximately parallel with the floor. In contrast, Koerich et al used a cropped volume using only the mandible; this study used the whole skull. These data were saved to the software’s database using the reslice tool and used for the 3D-M1 method. The lower border reorientation was not undertaken for other methods. The T2-volume was manually and approximately superimposed at the anterior cranial base of the T1-volume, followed by automatic voxel-based superimposition using the method outlined by Weissheimer et al. The resulting superimposition was inspected by qualitative visualization of the semitransparent cross-sectional, axial, and sagittal multiplanar reconstructions of all corresponding anatomic structures. This newly oriented T2-volume was then saved (reslice tool) to the software database. Next, both cranial base registered T1- and T2-volumes were opened in the software’s 3D Ceph module. Adapted from Melsen and Tollaro et al ( Fig 2 ), two 3D landmarks ( Table II ) were placed on the T1-volume: (1) Walker point (W-point) and, (2) a point located tangent to lamina cribrosa of the ethmoid lateral to prosphenion, approximating the sphenoethmoidal synchondrosis (SE-point). , , ,
|Nasion||N||Skeletal Class assessment; classification of vertical facial type||Midpoint of the frontonasal suture at the most anterior aspect||Swennen et al (2005)|
|Sella||Se||Skeletal Class assessment; classification of vertical facial type||Center of the hypophyseal fossa (sella turcica)||Swennen et al (2005)|
|Menton||Me||Classification of vertical facial type||Most inferior midpoint of the chin on the outline of the mandibular symphysis||Swennen et al (2005)|
|Right porion||R Po||Classification of vertical facial type; Cartesian coordinate system||Most superior point on the upper margin of the right cutaneous auditory meatus||Swennen et al (2005)|
|Right orbitale||R Or||Classification of vertical facial type; Cartesian coordinate system||Most inferior point of the right infraorbital rim||Swennen et al (2005)|
|Left orbitale||L Or||Classification of vertical facial type; Cartesian coordinate system||Most inferior point of the left infraorbital rim||Swennen et al (2005)|
|Right inferior gonion||R Inf Go||Classification of vertical facial type||First point on the most inferior tangential aspect of the mandibular right angle intercepted by the plane formed along the lower border of the mandible||Swennen et al (2005)|
|Right tangential gonion||R Go||Classification of vertical facial type||Point at the mandibular right angle that is determined by dropping a perpendicular line from the intersection point of the tangent lines to the posterior margin of the mandibular right vertical ramus and inferior margin of the mandibular right body or horizontal ramus||Ricketts (1979)|
|A-point||A-point||Skeletal Class assessment||Point of maximum concavity in the midline of the alveolar process of the anterior part of the maxilla||Swennen et al (2005)|
|B-point||B-point||Skeletal Class assessment; determination of mental reversal line on the anterior symphysis||Point of maximum concavity in the midline of the alveolar process of the mandible||Swennen et al (2005)|
|Walker point||W-point||2D and 3D methods in this study||The intersection of the junction between the lamina cribosa and sphenoid bone of the cranial surface of the anterior cranial fossa taken at the midline of the skull||Melsen (1974) ; Tollaro et al (1995)|
|Sphenoethmoidal point||SE-point||2D and 3D methods in this study||Any point between orbitosphenoid and posterior ethmoid bones||Madeline & Ester (1995) ; Calandrelli et al (2014)|
|Mental reversal line point||MRL-point||2D methods in this study||The mental reversal line is situated between the mental protuberance and the alveolar region anterior to the mandibular incisor roots||Duterloo & Planché (2011) ; Enlow (1968) ; Kurihara et al (1980)|
|Pogonion||Pog||Determination of mental reversal line on the anterior symphysis||Most anterior midpoint of the chin on the outline of the mandibular symphysis||Swennen et al (2005)|
|Gnathion||Gn||Classification of vertical facial type||The most anterior and inferior point on the contour of the mandibular symphysis||Swennen et al (2005)|
|Sella-nasion to A-point||SNA||Skeletal Class assessment||Angle of sella-nasion to A-point||Reidel (1952)|
|Sella-nasion to B-point||SNB||Skeletal Class assessment||Angle of sella-nasion to B-point||Reidel (1952)|
|Difference A- and B-points||ANB||Skeletal Class assessment||Difference between SNA and SNB||Reidel (1952)|
|Right FHMA||FHMA||Classification of vertical facial type||Frankfort Horizontal-mandibular plane angle||Tweed (1946), Downs (1948), Ricketts (1979)|
|Right SN-GoGn||SN-GoGn||Classification of vertical facial type||Sella-nasion to Gonion-Gnathion angle||Reidel (1952), Steiner (1953)|
|Right PFH:AFH||PFH:AFH||Classification of vertical facial type||Ratio of the posterior facial height to the anterior facial height||Siriwat & Jarabak (1985)|
|Reference line or plane||Coding||Usage|
|Na-Sella line||line([N], [Sella])||SN-GoGn angle|
|Me-Go line||line([Me], [R Inf Go])||FHMA|
|Gn-Tangential-Go line||line([Gn], [R Go])||SN-GoGn angle|
|Right Frankfort horizontal||line([R Or], [R Po])||FHMA|
|Cranial base line||line([W-Point], [SE-Point])||All 2D and 3D methods in this study|
|Sagittal division plane||plane([N], [Sella], [MRL-Point])||To divide right from left sides|
Using the software’s copy from function, we copied these 2 points from the T1-volume to the cranial base registered T2-volume allowing these landmarks to share the same x-, y-, and z-values on stable structures.
The first 3D method (3D-M1), adapted from Koerich et al, used the following steps: (1) the T2 volume was manually moved over the T1 volume, (2) automated voxel-based registration with nonspecific boundaries, (3) a second automated registration confined to the mandible and teeth but not including the ascending ramus, and (4) a third automated registration with defined boundaries—sagittally from the internal symphysis to first molars including apical thirds of roots and entire lower mandibular border. For the second 3D method (3D-M2), again using the superimposition interface ( Figs 3 and 4 ), the T2-volume was translated and rotated, in all 3 dimensions, to achieve an initial best fit of natural reference structures according to Björk. An automated voxel-based registration was then undertaken, constrained by a region of interest overlay cube on the symphysis. The result was then first inspected for overlapping of Björk’s natural reference structures, , and secondly, for the permissible misalignment of nonstable areas. If the result was unsatisfactory (ie, lack of superimposition of stable reference structures), the region of interest cube was slightly resized smaller or larger in any or all of the 3 dimensions, and registration repeated. The third method (2D-M1) used the fully landmarked volumes saved in their cranial base superimposed positions ( Fig 5 ). Details on the steps required to apply those methods can be found in Supplementary Data 1 . The control method also used the full landmark volumes in their cranial base superimposed positions, with subsequent mandibular superimpositions only using Björk’s natural reference structures. Details on the above method’s steps are described in Supplementary Data 1 and the Supplemental Figure , as are further details relating to a Cartesian coordinate setup and tools used for angular measurements.
All deidentified data were recorded in an Excel spreadsheet (Microsoft Corporation, Redmond, Wash) in a blinded manner (using different files) to prevent viewing method outcomes. All methods undertaken in this study were completed by a single operator (C.S.F). Each method was performed separately and in bulk for that method across all patients before progressing onto a subsequent method. It was not possible to blind the timing difference between T1 and T2 as it would become obvious for a trained professional.
To identify vertical facial types, we used a composite of criteria ( Table III ). Initially, classification was adapted from Bishara and Jakobsen, using facial height ratio, and mandibular plane angle as used by Wong et al. This was followed by criteria from von Bremen and Pancherz if any disagreement occurred. Any further discordance was settled by assessing Björk’s 7 morphologic signs.
|Criteria source||Cephalometric indicators||Vertical facial pattern|
|Brachyfacial (hypodivergent)||Mesofacial (neutral growth pattern)||Dolichofacial (hyperdivergent)|
|Bishara & Jakobsen’s (1985) criteria|
|Siriwat & Jarabak (1985)||Facial height ratio (S-Go c /N-Me)||>0.63||0.59-0.63||<0.59|
|Wong et al (2016) based on Down’s (1948) modified FHMA||Mandibular plane angle to Frankfort Horizontal (FH-MeGo)||<22°||22°-29°||>29°|
|Additional criteria used in combination|
|von Bremen & Pancherz (2005) based on Riedel’s (1952) SN-GoGn||Mandibular plane angle to anterior cranial base (SN-GoGn)||<26°||26°-38°||>38°|
|Björk’s (1969) 7 morphologic signs||(1) Inclination of the condylar head||Upright condyle; forward condylar growth relative to posterior ramus border||Backward inclined condyle, usually slender with increased height|
|(2) Curvature of the mandibular canal||Reduced angle of curvature||May be increased angle of curvature|
|(3) Shape of the lower border of the mandible||Apposition of the lower part of the posterior ramus border, and resorption at the anterior border; resorption at the lower border of the gonial angle; bone apposition at the posterior symphysis||Apposition beneath the gonial angle and at the posterior ramus; resorption of the lower surface of the symphysis|
|(4) Inclination of the symphysis||Apposition of the ventral surface of the symphysis; increased in a backward direction||Toward a vertical direction|
|(5) Interincisal angle||Proclination of mandibular incisors||Usually retroclined mandibular incisors|
|(6) Interpremolar or intermolar angles||Increased||Reduced|
|(7) Anterior lower facial height||Reduced (short)||Increased (long)|
Random error was assessed by statistical analyses of double measurements taken 2 weeks apart for landmarks, angles, and facial height ratios ( Table IV ). Details of the error of method calculations can be found in Supplementary Data 2 .
|Landmarks (n = 10)||Absolute difference test-retest||SD||SEM||Median||Minimum||Maximum||Range||Wilcoxon signed rank test||Reliability|
|P value ∗||Cronbach’s α||ICC (95% CI) †|
|x-point||Mean Euclidean distance|
|Right porion||0.840||0.720||0.229||0.665||0.050||2.430||2.380||0.139||0.986||0.970 (0.891-0.992)|
|Right orbitale||0.740||0.620||0.197||0.470||0.100||1.850||1.750||0.646||0.946||0.904 (0.666-0.975)|
|Left orbitale||0.810||0.790||0.248||0.560||0.100||2.640||2.540||0.509||0.949||0.911 (0.681-0.977)|
|Right inferior gonion||0.420||0.330||0.104||0.335||0.010||0.880||0.870||0.168||0.989||0.974 (0.897-0.993)|
|Right gonion||0.490||0.410||0.128||0.355||0.030||1.180||1.150||0.384||0.981||0.962 (0.865-0.990)|
|Right porion||1.230||1.200||0.381||0.830||0.110||4.360||4.250||0.139||0.992||0.982 (0.928-0.995)|
|Right orbitale||0.640||0.600||0.189||0.465||0.030||2.010||1.980||0.168||0.994||0.986 (0.943-0.996)|
|Left orbitale||0.610||0.690||0.217||0.460||0.040||2.440||2.400||0.242||0.994||0.989 (0.958-0.997)|
|Right inferior gonion||1.710||1.810||0.574||1.000||0.090||6.020||5.930||0.509||0.994||0.989 (0.959-0.997)|
|Right gonion||1.390||1.700||0.538||0.705||0.040||5.260||5.220||0.332||0.995||0.991 (0.964-0.998)|
|Right porion||0.930||1.540||0.489||0.340||0.000||5.080||5.080||0.575||0.995||0.991 (0.966-0.998)|
|Right orbitale||0.250||0.270||0.085||0.150||0.000||0.920||0.920||0.384||0.997||0.995 (0.978-0.999)|
|Left orbitale||0.230||0.250||0.078||0.165||0.000||0.810||0.810||0.575||0.998||0.995 (0.983-0.999)|
|Right inferior gonion||0.930||1.340||0.422||0.405||0.070||4.520||4.450||0.332||0.991||0.983 (0.936-0.996)|
|Right gonion||0.950||0.980||0.309||0.745||0.080||3.330||3.250||0.610||0.995||0.990 (0.961-0.997)|
|x-, y-, z-point|
|Right porion||1.980||1.850||0.584||1.405||0.426||6.727||6.301||0.122||1.000||1.000 (0.999-1.000)|
|Right orbitale||1.120||0.750||0.237||0.970||0.355||2.649||2.294||0.325||1.000||0.999 (0.999-1.000)|
|Left orbitale||1.100||1.000||0.316||0.817||0.123||3.685||3.562||0.304||1.000||0.999 (0.999-1.000)|
|Right inferior gonion||2.120||2.150||0.679||1.142||0.436||7.568||7.133||0.096||1.000||1.000 (0.999-1.000)|
|Right gonion||1.920||1.830||0.580||1.298||0.336||6.283||5.947||0.185||1.000||1.000 (0.999-1.000)|
|Angles (n = 10)||Mean angle|
|Right FHMA||0.880||1.023||0.323||0.500||0.100||3.100||3.000||0.478||0.987||0.976 (0.908-0.994)|
|Right SN-GoGn||0.940||0.803||0.254||0.650||0.100||2.100||2.000||0.412||0.991||0.983 (0.934-0.996)|