Eleven patients (five females, six males, age 19-23 yrs) with Class II, division 1 malocclusion (overjet 5-7mm) and asymptomatic TMJs was recruited for this study. Informed consent was obtained from the subjects, and the experimental protocols were approved by the Research Ethic Committee of Shandong university dental school (The qualifications and experience of the researchers meet the requirements of experiments; the research programs are in line with the scientific and ethical principles; The informed consent is obtained appropriately; Compared with the expected benefit of the research, the risk that the subjects may suffer is negligible.). The patients have understand and approved this consent procedure, and provided the permission for our research basing on her CBCT data.
The patients did not accepted extraoral headgear and miniscrew for additional anchorage, intermaxillary class II elastic was applied for subsequent anterior tooth retraction and normalizing the molar relationship. The patients were corrected from Class II occlusal relationship to a normal occlusion with extraction of the maxillary and mandibular first premolars and Class II elastics. The average treatment period and intermaxillary traction period was 2.2 years and 7.5 months.
Images were acquired using the CBCT scanner (KaVo Dental GmbH, Bismarckring, Germany) at a 0.30-voxel resolution with the scanning parameter of 120 kV, 5mA. The scan time was 8.9 seconds, and the slice thickness was 0.4mm. The CBCT datasets were exported in the DICOM (Digital Imaging and Communications in Medicine) format. The CBCT scans were taken at three time points: before (T1), after treatment (T2) and after retention(T3). And the CT iamges were imported in the MIMICS 20.01 for image processing. The procedure of 3D image acquisition and analysis for evaluation is the following.
1. Segmentation and reconstruction
Image segmentation of the anatomic structures of interest and the 3D graphic rendering were done by using the Mimics medical imaging density segmentation software. Various threshold values were selected that would produce as complete structures of the craniofacial complex as possible without too many holes or artifacts. All 3D models of T1,T2 and T3, such as maxillia, mandible, the cranical base and the mandibular chin were reconstructed respectively (Figure.1).
2. Sequential 3D superimposition
2.1 Regional superimposition of T1 and T2 mandibles
After 3D reconstruction, the 3D models of the T1 mandible and chin were exported as standard triangulated language (STL) points for superimposition to T2 mandible. Unlike the remodeling/modeling of condyle and alveolar process, the chin and symphysis regions are stable areas for 3-dimensional mandibular regional superimpositions [26,28].
Superimpositions of the mandibles were performed initially by manual point registration to approximate the surfaces as much as possible. The mandibular surface feature points which were easy to identify on the two mandibles were located for the initially superimposition (Figure.2 a-c). The T1 mandible and chin were registered to the T2 mandibular model grossly. Subsequently, superimposition was refined using the STL registration method. The transformation matrix of this method registered the stack of slices of the inferior chin STL models on the stack of slices of the mask of the T2 model sequentially (Fig.2 d). These transformations of the 3D models (mandible and chin) were synchronous. After the sequential rigid superimpositions (translation and rotation), the T1 mandible was aligned to T2 mandibular positions. The T1 mandible which was placed at the T2 positions were defined as reference mandible (T1r2). With the identical core position with T2 mandible and the same morphology with T1 mandible, the reference mandible can be used for separating the positional and morphological changes of mandible when they was exported back into T1 project file. After the regional superimposition of T1 and T2 mandibles, the morphological changes between T1 and T2 mandibles can be measured quantitatively. The growth volume at condyles can be separated and quantified after the 3D boolean operation of T1 and T2 mandibular models (subtraction).
The post-treatment 3D models such as cranial base, maxillary, mandible, chin, upper and lower teeth(T2) and the T1r2 reference mandible were exported as STL models for the subsequent registrations. The T2 mandible and chin, T1r2 reference mandible were imported into the T3 project file for mandibular regional superimpositions. The superimposition process was same as T1 and T2 mandibular registration (Fig.3 a-d). The T2 and T1r2 mandibles were aligned to the T3 position and acted as reference mandibles for calculating T3 mandibular position difference with T1 and T2 mandibles. The two mandibles were defined as T2r3 and T1r3 mandibles. After T3 mandibular regional superimposition, all the T3 models and T1r3/T2r3 mandibles were exported out as STL format for follow-up cranial base superimposition in T1 project file.
2.2 Global superimposition on cranial base
In the Mimics, the 3D models derived from T2 and T3 projects were imported into the T1 project file. The T2 models and T1r2 mandible were registered to the T1 structures by using the anterior cranial fossa as the reference (Fig.4 a-d). And the T3 models and T1r3/T2r3 mandibles were aligned to T1 structures with cranial superimposition too(Fig.5 a-d). The two superimposition processes were performed with point registration and STL registration independently. The endocranial surfaces of the cribriform plate region of the ethmoid bone and the frontal bone were chosen for location of reference points and STL registration. These regions were chosen because of their early completion of growth[28].
After the sequential registration, the T1, T2, T3 models and three reference mandibles (T1r2, T1r3, T2r3) were aligned in the same coordinate system (Fig.5 e-f). The mandibular gross changes which contain mandibular rotation, dentitional changes and condylar growth, mandibular displacement can be assessed by comparing the T1/T2/T3 mandibles. And to distinguish mandibular positional changes without interference of morphological changes, the comparison between virtual reference mandibles (T1r2, T1r3, T2r3) and their corresponding models were applied. There were six mandibles for assessment: T1 mandible, T2 mandible, T3 mandible, T1r2 mandible, T1r3 mandible and T2r3 mandible. And six pairing combinations of these mandibles were compared for evaluation of the morphological and positional changes respectively. The six pairwise combinations of these mandibles were showed as table 1.
Table 1 the Pairing combination for comparison for mandibular assessment
Pairing combination for comparison
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Purpose
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T1 mandible VS T1r2 mandible
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Positional changes between T1 and T2 mandibles
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T1 mandible VS T1r3 mandible
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Positional changes between T1 and T3 mandibles
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T2 mandible VS T2r3 mandible
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Positional changes between T2 and T3 mandibles
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T2 mandible VS T1r2 mandible
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Morphological changes between T1 and T2 mandibles
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T3 mandible VS T1r3 mandible
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Morphological changes between T1 and T3 mandibles
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T3 mandible VS T2r3 mandible
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Morphological changes between T2 and T3 mandibles
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3. 3D measurement
After registration, the T1,T2, T3 mandibles were aligned in the same coordinate system, the morphological and positional changes were measured independently with aid of the reference mandibles. Treatment, posttreatment, and overall changes were determined by the differences T2-T1, T3-T2, and T3-T1.
Morphological changes (T1r2 vs T2 , T2r3 vs T3, T1r3 vs T3)
To evaluate the mandibular morphological changes, the comparisons between pairwise mandibles (T1r2 vs T2 , T2r3 vs T3, T1r3 vs T3) were performed. The condyle, and alveolar process were our interested regions for assessment of mandibular growth. The condylar volume increment can be measured after 3D subtract boolen operation on pairwise condyles (Fig.6 d). The 3D growth drifts at condyle, mandibular ramus and 3D displacement of mandibular first molars (L6) were evaluated by measuring the Euclidean distances of paired landmarks. The 3D coordinate differences (Δx, Δy, Δz) of the paired landmarks can be calculated respectively for describing the 3D Euclidean distances in each direction (x-, y-, and z-axes) (Fig.6 b,c).
Positional changes: translation and rotation(T1r2 vs T1 and T1r3 vs T1,T2r3 vs T2)
After the cranial base superimposition, the reference (T1r2, T1r3, T2r3) and original mandibles (T1,T2) were aligned into the uniform coordinate system, and the reference mandibles can be compared with the original mandibles to evaluate the mandibular positional alterations without the interference of morphological alterations. The translation and rotation of the inertia coordinate systems of two geometry identical objects can be measured using the Calculate 3D Object Position Difference tool (Fig.6 a). An inertia coordinate system is fitted to the selected 3D object with the origin at the center of mass. The rotation angle can measured between the two respective axes of the coordinate systems. And the angles of three axes (X,Y,Z) were recorded as α, β, γ respectively. And the total translation can be described as three linear distances along the axes (Δx, Δy, Δz). The Euclidean distances of paired landmarks at condylion, mandibular first molars and pogonion on the surface of pairwise mandibles were measured to describe the mandibular 3D displacements. The 3D coordinate differences (Δx, Δy, Δz) of the paired landmarks were calculated in 3 directions: antero-posterior (y axis), vertical (z axis) and transverse (x axis). The 2D details of condylion remodeling and displacements were showed in Figure.7.
Statistical Analysis
All measurements were undertaken by a single operator and repeated after 2 weeks at the same console by same operator. The mean values of the 2 measurements were used for final analysis, as recommended by Baumrind and Frantz. Casual and systematic errors were calculated by comparing the values of the first and second measurements, with paired t tests and Dahlberg formula [49]. Descriptive statistics, including the means, standard deviations, minimums and maximums for all variables were calculated. Paired data t-test was used to evaluate differences at different periods (T1-T2, T2-T3, and T1-T3). And the differences 3D condylar growth and displacements (Δx,Δy,Δz ) were evaluated with paired t test.The level of significance was P<0.05. All statistical computations were carried out with a statistical software package for Windows, SPSS ver. 23.0 (IBM Corp., Armonk, NY, USA).