Study design

The study was reviewed and approved by the Research Ethics Board of School of Stomatology (protocol number 20200802). The sample size was calculated based on an α of 0.05 and a β of 0.2 to achieve the power of 80% and to detect the difference of 1.56 mm in condylar height measurements between groups, with a 1.65 mm estimated standard deviation [22]. The power analysis indicated a sample size of 11 was required. Fifteen patients who received MARPE treatment were retrospectively selected from the CBCT database. The inclusion criteria were as follows: (1) the distance between Menton and the median sagittal plane was greater than 2 mm; (2) mandibular body asymmetry due to the bodily shift of the mandible to the deviated side [3]; (3) ANB < 0º; (4) no history of oral and maxillofacial trauma, surgery or orthodontic treatment; (5) permanent dentition; (6) aged 18–30 years; (7) the palatal sutures were successfully separated after treatment. Patients with craniofacial syndrome, systemic disease, and temporomandibular joint disease were excluded.

The baseline of the fifteen patients was as follows: 6 males and 9 females, mean age 21.58 ± 3.12 years (minimum age 18, maximum age 26), BMI 21.17 ± 1.83 kg/m2; the maxillary transverse deficiency was 0.91 ± 1.16 mm diagnosed by Pennsylvania method [23]. The Mentons were 8.37 ± 3.61 mm deviated horizontally to the median sagittal plane.

Miniscrew-assisted rapid palatal expansion

Patients were treated by the maxillary skeletal expansion appliance type-II (BioMaterials, Korea) under the supervision of the same clinician, which expanded by 0.8 mm in 6 turns. (Fig. 1). The appliance consisted of bands to the permanent first molars and four holes for mini-implants. To fenestrate the palatal base and nasal base, the matching orthodontic mini-implants (BioMaterials, Korea) are 1.8 mm in diameter and 11 mm in length. After 24 h of bonding with glass ionomer, the expander was activated one sixth of a turn (0.13 mm) in the morning and evening, respectively, until the occlusal aspect of the palatal cusp of the maxillary first molars contacted the occlusal aspect of the buccal cusp of the mandibular first molars. The duration of expansion was 18 ± 4.65 days.

figure 1

Intraoral view of MARPE. a before expansion; b after expansion

CBCT imaging

The CBCT scans were taken before (T1) and after MARPE treatment immediately (T2). All CBCT scans were implemented with each patient awake in the position of the Frankfort horizontal plane parallel to the floor using the same CBCT scanner (NewTom 5G, QR srl, Verona, Italy.) by the same operator. Patients were guided to close their mouths with the maximum intercuspation and the upper and lower lips and tongue were relaxed. The scanning range is from the frontal to the lower margin of the fourth cervical spine (standard voxel size: 0.3 mm; scan time: 14 s; slice thickness: 0.3 mm, 110 kV, 5 mA,). Subsequently, the dataset was exported in digital imaging and communications in medicine (DICOM) file format.

Image registration

All the CBCT images were transferred into Materialse’s interactive medical image control system (MIMICS, version 21.0; Materialise, Leuven, Belgium). Primarily, the head position of CBCT data was adjusted. In the axial view, the head position is rotated so that the sagittal axis passes through both the anterior nasal spine (ANS) and bason (Ba). In the coronal view, the head position is rotated so that the horizontal reference line is tangent to the bilateral orbitals (Or). Use the “along plane” command to make the Frankfort horizontal plane (passing through bilateral Or and right porion) parallel to the true horizontal plane. Secondly, thresholding based on Hounsfield Units was used to create the original cranial base mask (401HU-2347HU), maxillary mask (401HU-2347HU), and mandibular mask (822HU-3071HU). Thirdly, 3D virtual models of cranial base, maxilla and mandible were reconstructed from their masks respectively. Then, the three-dimensional image models of T1 were exported as stereolithography (STL) and imported into T2 CBCT data. Finally, 3D cranial base and mandibular superimpositions of T1 and T2 data were done by point registration followed with STL registration. Point registration of the cranial base were done by placing several obvious landmark points on the cranial base, for example, the anterior clinoid process, midpoint of anterior margin of foramen magnum, and so on. Afterward, anterior cranial base area was selected for the STL registrations to improve accuracy, and the whole cranial moved with it. The minimal point distance filter was set as 0.10 mm [20]. Similarly, the registration of mandible is also completed by those two steps above (landmark points: bilateral mandibular foramina, mental trigone, and genial tubercle; STL registration area: mandibular symphysis) [24].

3D measurement

As shown in Fig. 2a, b, the following three reference planes were established: (1) Frankfort horizontal plane (FHP) (2) Median sagittal plane (MSP): perpendicular to the FHP through basion (Ba) and nasion (N). (3) Vertical reference plane (VRP): passing through Ba and perpendicular to FHP and MSP. The landmarks and variables of measurement are shown in Tables 1 and 2. The one side with chin deviation was defined as the deviated side, whereas the other side was defined as the non-deviated side.

figure 2

The deviated side of the mandible is on the patient’s own left side. Three reference planes in a front view, b side view; 3D reconstruction model, the red one represents T2 and the yellow one represents T1: c changes of mandibular position after cranial base registration, d morphological changes after mandibular registration

Table 1 Definition of landmarks
Table 2 Definition of measurement variables

Statistical analysis

Statistical analysis was performed by SPSS (version 20.0, IBM, New York, USA) software package. The intra-examiner reliability was determined by performing the measurements for each CBCT image on 2 separate occasions by one examiner at a 2-week interval. The intraclass correlation coefficients were calculated; then the mean of the 2 measurements was used in statistical analysis. The error of method was calculated using the Dahlberg formula:(ME = sqrt {{raise0.7exhbox{${Sigma (d)^{2} }$} !mathord{left/ {vphantom {{Sigma (d)^{2} } {2n}}}right.kern-nulldelimiterspace} !lower0.7exhbox{${2n}$}}}). For normal distribution data, paired t test was used to compare the difference between T1 and T2 for samples. In case of abnormal distribution, Wilcoxon signed rank test was used for comparison. P < 0.05 indicated that the difference was significant.

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