Introduction
Miniscrew-assisted rapid palatal expansion (MARPE) is a predictable option for nongrowing patients with maxillary transverse deficiency manifesting as posterior crossbite. However, recent evidence suggests a high frequency of asymmetrical expansion as a complication of MARPE.
Methods
Retrospective analysis of 9 patients (mean age: 21.7 years; 65% female; average Yonsei Transverse Index:–4.6 mm) included superimposition of pre (T1) and posttreatment (T2) cone-beam computed tomographies using a voxel-based technique on the anterior cranial base. T1 and T2 cone-beam computed tomographies were digitized in a common Cartesian plane, enabling linear and angular measurements using T1 landmarks as the reference to compare T2 landmarks. Geometric analyses included linear Euclidean left vs right and transverse distances, 3-dimensional (3D) angulation, and 3D matrix rotations to quantify asymmetry. Asymmetry thresholds were set at 2 mm or 2°. Stepwise regression was used to determine the association between potential explanatory variables and asymmetry.
Results
There was no statistically or clinically significant asymmetry of the ANS-PNS vector. Linear, angular, or zygomaticomaxillary roll of jugale, keyridge, or zygomaticofrontal suture around the ANS-PNS vector was found ( P >0.05). Statistically but not clinically significant linear asymmetry of keyridge (0.9 ± 0.9 mm; P = 0.02) and first molar furcation (0.7 ± 0.8 mm; P = 0.02) was found. Stepwise regression did not find any potential explanatory variables explaining the keyridge and the first molar furcation linear asymmetry.
Conclusions
Under the conditions of this study and 3D analyses, MARPE resulted in statistically significant linear asymmetry of the keyridge and the first molar furcation. Statistical significance does not equate clinical significance or relevance.
Highlights
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We produced a novel 3-D analysis of landmarks after CBCT voxel-based superimposition.
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MARPE results in statistically significant linear asymmetry for the keyridge and the first molar center of resistance.
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Most anatomic regions did not show clinically relevant asymmetry except in a minority of patients.
Maxillary transverse deficiency (MTD) in skeletally mature adolescents and adults is a common problem in orthodontic practices. Traditionally, surgical techniques were used to facilitate maxillary transverse expansion. With the recognition of the benefits of bone-borne anchorage followed the introduction of the miniscrew-assisted rapid palatal expansion (MARPE) in 1999, to overcome skeletal and sutural resistance to maxillary expansion.
Asymmetrical expansion ≥2 mm with MARPE treatment has been reported to occur in 27%-50% of patients, , whereas surgically-assisted rapid palatal expansion asymmetrical expansion has been found in 4%-8% of patients. , In the coronal plane or roll axis, MARPE follows a superior-inferior asymmetrical expansion pattern similar to surgically-assisted rapid palatal expansion. , MARPE often results in midpalatal and pterygomaxillary suture opening, nasomaxillary widening, the zygomaticomaxillary complex (ZMC) expands laterally, and the zygomatic bone rotates concomitantly with the maxilla around a center of rotation near the superior aspect of the zygomaticofrontal (ZF) suture. MARPE typically results in a parallel anteroposterior expansion pattern. ,,,, However, axial asymmetrical V-shaped expansion with greater anterior than posterior expansion is also reported. ,, Asymmetrical axial expansion has been attributed to anteroposterior positioning of the appliance. ,
Cone-beam computed tomography (CBCT) studies evaluating MARPE-produced asymmetry have relied on arbitrary reference planes to measure 2-dimensional (2D) distances and angles and 2D measurements made relative to a point of origin (0, 0, 0). Reference planes determined by the human anatomy or using a point of origin will invariably be inaccurate because of omnipresent multilevel facial asymmetry and curvature inherent to human anatomy. The inaccuracy of a point of origin and arbitrary reference planes will have a cascade of errors to all other measurements, especially the most distant. Fully automated superimposition of CBCTs using the anterior cranial base as a stable reference structure allows for assessment of displacements and remodeling of all skeletal and dental components within the field of view without the bias of observer-dependent techniques (ie, arbitrary reference planes, origin, etc.). ,,
To add to the knowledge base of MARPE-associated clinical outcomes, we sought to determine the following: in skeletally mature adolescents and adults, does MARPE result in clinically significant left vs right linear, angular, and roll asymmetries ≥2 mm or ≥2 o? We also sought to apply a novel 3D analysis of voxel-based superimposition of CBCTs for detecting and characterizing skeletal and dental asymmetry. The null hypotheses were as follows: no difference between left and right sides; no difference between T1 and T2; no difference between landmarks. Although there is no gold standard technique to measure asymmetry, our dual focus allows testing our novel method under specific conditions, while also generating clinically relevant insights into a narrowly defined population.
Material And Methods
Institutional review board approval (number: 23-0253) was granted by the University of North Carolina at Chapel Hill to perform this retrospective study.
Deidentified CBCT digital imaging and communications in medicine volumes from 26 consecutively treated patients (4 men and 5 women) were obtained from Yonsei University, Seoul, South Korea. The inclusion criteria were as follows: skeletally mature patients with pretreatment and posttreatment CBCT scans of diagnostic quality with the teeth apart, allowing for landmark placement on the occlusal surfaces, unilateral or bilateral posterior crossbite, MTD < Yonsei transverse index (YTI), first molar mesiobuccal (MB) cusp difference lower limit (–3.3 mm), and MTD < center of resistance difference lower limit (–6.2 mm). Exclusion criteria included previous orthodontic expansion, periodontal disease and untreated carious lesions, systemic diseases, medications that may affect bone metabolism, and dentofacial anomalies, such as cleft lip and palate and craniofacial asymmetry. Patients previously treated with expansion or presented with asymmetries were excluded because a study by Almaqrami suggested that prior expansion and the presence of pretreatment asymmetry resulted in more asymmetrical expansion with MARPE treatment. One of the goals of this study was to measure the development of asymmetry resulting from MARPE treatment.
Seventeen patients were excluded from the study as they did not meet our study’s criteria. Therefore, 9 patients were accepted for analysis and exceeded our needed sample size calculation, thus reducing the risk of committing a type II error. Patients had a mean age of 21.7 ± 3.2 years and were treated from 2017-2019. MTD was measured using Euclidean distances in the YTI method.
A study by Elkenawy et al reported a left-right asymmetry of 1.1 mm with a standard deviation of 1.1 mm. Given our strict inclusion criteria and small sample size, we used the Hedges g, a bias-corrected effect size, rather than the Cohen d , which can overestimate effects in small samples. To detect a clinically relevant asymmetry of 2 mm or 2° using a paired samples t test, assuming a standard deviation of 1.1 mm, the standardized effect size (Cohen d ) was 1.82, and the bias-corrected Hedges g was 1.64. Using the Hedges g value, the required sample size to achieve 80% power at α = 0.05 (2-sided) was 5 patients.
The appliance consisted of a standard linear jackscrew connected to arms soldered to bands on the maxillary first premolars (U4s) and maxillary first molars (U6s). Soldered to the jackscrew were 4 tubes for miniscrew placement. Four miniscrews were placed parasagitally in the anterior and posterior midpalate. Miniscrews were 1.5 mm in diameter and 8-10 mm in length. MARPE was activated with 1 turn per day (0.2 mm/turn). The expander was activated until the palatal cusps of the U6 contacted the buccal cusp tips of the mandibular first molar. Expanders were retained for 3 months after active expansion and then removed.
All CBCT images were taken using Pax Zenith 3D (Vatech, Seoul, South Korea). The exposure parameters were preadjusted for a 24 × 19 cm field of view, voxel size of 0.3 mm, 105 kVp, 5.4 mA, and exposure time of 24 seconds. CBCTs were taken with the patient’s teeth slightly apart. This allowed for accurate placement of landmarks, yet precluded cephalometric analysis.
CBCTs were taken pretreatment (T1) and immediately postexpansion (T2). The CBCTs were oriented, and then anterior cranial base superimposition of T2 to T1 CBCTs was performed using a semiautomatic voxel-based registration method using ITK-SNAP version 4.0.1 ( www.itksnap.org ). , Therefore, T1 and T2 CBCTs shared a common 3D Cartesian plane. Superimpositions were verified for accuracy by an expert examiner (T.N.). Landmarks were chosen for reliability (description of landmarks are shown in Supplementary Table ). ,, Digitization of the T1 and T2 CBCTs with bilateral dental and skeletal landmarks was performed in 3-panel multiplanar gray scale windows and produced x, y, and z coordinate data for each landmark and left (L) and right (R) sides for bilateral landmarks (3D Slicer, slicer.org ; Supplementary Material ). In T1, hemimaxillae do not exist, and midline structures are single landmarks. Thus, anterior nasal spine (ANS) and posterior nasal spine (PNS) were digitized as single landmarks, and changes were measured to the bilateral ANS and PNS (ie, left and right) landmarks in T2.
To avoid confusion with the traditional cephalometric palatal plane (ANS-PNS), we will refer to the vector from ANS to PNS defined in 3D space (x, y, and z coordinates) as the ANS-PNS vector.
Afterward, the analysis of 3D coordinate data was conducted using Python version 3.12 ( python.org ) with the following packages: os, glob, json, numpy, pandas, xlsxwriter, polars, scipy.spatial.transform (for quaternion and Euler angle conversions), and collections.
To determine the left and right asymmetrical change of a landmark, the Euclidean distance from T1 to T2 of each landmark was measured (ie, the distance from T1 U4 palatal cusp to T2 U4 palatal cusp) ( Fig 1 ).
Skeletal and dental Euclidean distance T1-T2 ( purple , T1-T2 skeletal changes including ANS, PNS, ZF, Keyridge, and Jugale; brown, T1-T2 dental changes including U6 furcation, U6 MB cusp, U4 palatal apex, and U4 palatal apex).
The ANS-PNS vector, the long axes of U4s and U6s (U4 MB cusp to center of resistance, U6 palatal cusp to palatal apex, and contralateral right landmarks), and the alveolar bone (jugale to U6 ectomolare) were measured as vectors in T1 and T2 CBCTs. Each unit vector was rigidly transformed to a common origin. The Kabsch algorithm was applied to the transformed unit vectors to obtain a best-fit 3 × 3 rotation matrix. The rotation matrix was converted into a quaternion, from which the magnitude of the rotation vector equals the overall rotation angle (degrees). The quaternion was decomposed into Euler angles to allow for heuristic understanding of which plane predominantly contributes to the overall rotation. Although Euler angles do not mathematically sum to the quaternion-derived angle, the relative percentages provide an intuitive snapshot of directional asymmetrical rotation ( Fig 2 ).
Skeletal and dental angulation changes T1-T2 ( blue , T1 ANS-PNS vector and alveolar bone bending; pink , T2 ANS-PNS vector and alveolar bone bending; black , T1 U6 [MB cusp to furcation] and U4 [palatal cusp to palatal apex]; red , T2 U6 [MB cusp to furcation] and U4 [palatal cusp to palatal apex]).
Rotation of the ZMC was envisaged to roll like a cylinder in the coronal plane: the midpoint long axis of the cylinder is the ANS-PNS vector, and the radius of the cylinder is the jugale, keyridge, or ZF suture ( Fig 3 ).
ZMC envisioned as T2 left and right cylinders centered on the T2 ANS-PNS vector and radius determined by orthogonal projection vector to (A) Jugale, (B) Keyridge, and (C) ZF suture.
To quantify the angular roll of the ZMC, a rotation matrix was computed with the Rodrigues formula to align the normalized T2 ANS-PNS vector and the normalized T1 ANS-PNS vector, establishing a shared reference plane. A vector to jugale, keyridge, and ZF was first orthogonally projected to remove its component along the ANS-PNS vector. The T1 projected vector was then rigidly transformed using the rotation matrix. The angle between the projected T1 and T2 vectors was measured to quantify the magnitude of roll around the 3D palatal axis. This approach assumed the expansion of the ZMC, that is, left side counterclockwise and right-side rotation around the ANS-PNS vector axis.
Statistical analysis
Descriptive statistics of all the measurements at T1 and T2 were calculated, as well as T2-T1 changes. The Shapiro-Wilk test was used to assess the normality of data distribution. Independent samples and paired samples t tests and Wilcoxon signed rank tests were used for null hypothesis testing using a conventional P <0.05 significance threshold. The Cohen d effect size and 95% confidence intervals of the asymmetry were calculated.
Regression analysis was performed to explain statistically significant asymmetry. The potentially explanatory variables included age, sex, presence of posterior crossbite (ie, unilateral or bilateral crossbite), number of turns, extractions or nonextraction, degree of pterygomaxillary disjunction (ie, none, incomplete, or complete), number of cortices engaged by posterior miniscrews, time in treatment, CVM, palatal vault height, and baseline YTI MB cusp and furcation transverse discrepancy. Stepwise regression was used to select significant predictors.
To test the methodological reliability of our novel CBCT analysis, 7 of the 9 patients were randomly selected, and their T1 and T2 CBCTs were resuperimposed and redigitized again after 6 months. Reliability was measured using the interclass coefficient (2-way mixed effects), consistency, and single rater measurement. All Python parsing was verified with manual computations. Statistical analyses were carried out with R version 4.4.1 ( www.r-project.org ). The following R packages were used for statistical analysis and visualization: dplyr, reshape2, readxl, writexl, jsonlite, ggplot2, car, Matrix, lme4, vegan, knitr, and kableExtra. Regression analysis was performed with JMP Pro (version 17.2; SAS Institute Inc, Cary, NC).
Results
At T1, the average YTI MB cusp discrepancy was 4.4 ± 3.4 mm, and the average T1 YTI center of resistance discrepancy was–5.9 ± 1.3 mm. Null hypothesis testing revealed that our sample was statistically significantly deficient transversely at baseline for Class I thresholds ( P <0.01; data not shown).
At T2, the average YTI MB cusp discrepancy was 9.3 ± 2.4 mm, and the average YTI center of resistance discrepancy was–2.6 ± 2.1 mm. Null hypothesis testing revealed that MTD was corrected at T2 for YTI MB cusp discrepancy for Class I thresholds ( P >0.05). However, the YTI center of resistance discrepancy was not corrected to within Class I thresholds ( P <0.01; data not shown).
There was no clinically significant asymmetry of ANS, PNS, jugale, keyridge, or ZF (≥2 mm). Only keyridge was found to have statistically significant asymmetry ( P = 0.02) ( Table I ).
Table I
Euclidean distance changes T1-T2 and left vs right asymmetry
| Landmark | Mean left (mm) | Mean right (mm) | Asymmetry (mm) | P value | Effect size | 95% CI lower | 95% CI upper |
|---|---|---|---|---|---|---|---|
| ANS | 1.5 ± 0.8 | 1.9 ± 1.0 | 0.3 ± 0.8 | 0.23 | 0.4 | –1.0 | 0.3 |
| PNS | 1.5 ± 0.8 | 1.8 ± 1.2 | 0.3 ± 0.5 | 0.18 | 0.5 | –0.7 | 0.1 |
| ZF | 0.8 ± 0.3 | 0.6 ± 0.5 | 0.2 ± 0.5 | 0.43 | 0.3 | –0.3 | 0.6 |
| Keyridge | 0.7 ± 0.7 | 1.6 ± 0.9 | 0.9 ± 0.9 | 0.02 ∗ | 1.0 | –1.5 | –0.2 |
| Jugale | 1.5 ± 0.8 | 2.1 ± 1.1 | 0.6 ± 1.2 | 0.18 | 0.5 | –1.5 | 0.3 |
| First molar furcation | 1.6 ± 0.6 | 2.3 ± 1.0 | 0.7 ± 0.8 | 0.02 ∗ | 0.9 | –1.3 | 0.1 |
| First molar MB cusp | 3.5 ± 1.0 | 3.7 ± 1.3 | 0.2 ± 2.0 | 0.75 | 0.1 | –1.8 | 1.3 |
| First premolar apex | 2.2 ± 1.0 | 2.7 ± 1.4 | 0.6 ± 0.8 | 0.23 | 0.5 | –1.4 | 0.3 |
| First premolar P cusp | 3.0 ± 0.9 | 3.7 ± 1.0 | 0.7 ± 1.6 | 0.18 | 0.4 | –1.9 | 0.5 |
CI , confidence interval.
There was no statistically or clinically significant ANS-PNS vector angular asymmetry ( P >0.05). The greatest contribution to ANS-PNS vector angular asymmetry was in the yaw rotation (83%) and the least in the pitch rotation (4%). Roll rotation contributed to 13% of the ANS-PNS vector angular asymmetry ( Table II ).
Table II
Angulation changes T1-T2, left vs right asymmetry, and relative percentage of Euler angle composition of asymmetry
| Landmark | Mean left (°) | Mean right (°) | Asymmetry (°) | Asymmetry pitch (rel %) | Asymmetry yaw (rel %) | Asymmetry roll (rel %) | P value | Effect size | 95% CI lower | 95% CI upper |
|---|---|---|---|---|---|---|---|---|---|---|
| ANS-PNS | 0.81 ± 0.4 | 0.9 ± 0.6 | 0.1 ± 0.7 | 4% | 83% | 13% | 0.60 | 0.2 | –0.6 | 0.4 |
| Alveolar bone | 8.4 ± 7.2 | 13.2 ± 8.0 | 4.8 ± 6.4 | 90% | 7% | 2% | 0.06 | 0.8 | –9.7 | 0.08 |
| First molar MB cusp | 9.0 ± 4.6 | 5.9 ± 2.4 | 3.1 ± 5.0 | 76% | 19% | 5% | 0.10 | 0.6 | –0.7 | 7.0 |
| First molar P cusp | 7.9 ± 3.4 | 6.0 ± 3.0 | 1.9 ± 3.4 | 92% | 3% | 5% | 0.25 | 0.4 | –1.6 | 5.4 |
| First premolar | 3.3 ± 2.9 | 3.9 ± 2.9 | 0.6 ± 2.9 | 88% | 8% | 4% | 0.56 | 0.2 | –2.9 | 1.7 |
CI , confidence interval.
Overall asymmetry of alveolar bone bending was clinically significant and trended toward statistically significant asymmetry ( P = 0.06). The greatest contribution to alveolar bone bending angular asymmetry was in the pitch rotation (91%), and the least from the roll rotation (2%). Yaw rotation contributed 7% of the alveolar bond bending angular asymmetry ( Table II ).
ZMC roll at jugale, keyridge, and ZF around the ANS-PNS vector was not clinically or statistically asymmetrical ( P >0.05). Interestingly, the average magnitude of rotation was similar between jugale, keyridge, and ZF at 0.4° and trended toward statistical significance for keyridge and ZF ( P = 0.07) ( Table III ).
Table III
ZMC roll T1-T2 and left vs right asymmetry
| ZMC roll | Mean left (°) | Mean right (°) | Asymmetry (°) | P value | Effect size | 95% CI lower | 95% CI upper |
|---|---|---|---|---|---|---|---|
| @ Jugale | 1.4 ± 0.6 | 1.8 ± 0.8 | 0.4 ± 1.1 | 0.31 | 0.4 | –1.2 | 0.4 |
| @ Keyridge | 1.2 ± 0.4 | 1.6 ± 0.8 | 0.4 ± 0.5 | 0.07 | 0.7 | –0.7 | 0.03 |
| @ ZF | 1.3 ± 0.9 | 1.6 ± 0.7 | 0.4 ± 0.5 | 0.07 | 0.7 | –0.8 | 0.04 |
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