Adult skeletal malocclusion may require orthodontic surgery. Le Fort I maxillary osteotomy is one of the most commonly performed surgical procedures. This procedure is highly versatile and recommended for the correction of sagittal and vertical discrepancies.1 Osteotomies can be performed in single or multiple segments. When performed in multiple segments, the procedure is commonly executed on three distinct dentoskeletal pieces.2-5 This surgical approach facilitates the correction of transverse maxillary deficiency in patients with skeletal maturity. However, the benefits of maxillary segmentation extend beyond transverse correction, allowing for the correction of several other discrepancies.6

Segmental Le Fort I (three-piece surgery) allows correction of vertical, sagittal, and transverse discrepancies in a single surgical procedure, which is advantageous for patients.7 Other benefits include the possibility of improving the maxillary anterior segment, correction of inadequate inclination of the upper incisors,8 tooth size discrepancy,9 and pronounced curves of Spee and Curve of Wilson.9 Some clinical complications have been reported in the literature;10-13 however, these complications might be attributed to the lack of specific training in the technique. A previous study demonstrated low morbidity related to multi-segment maxillary osteotomies.14 This procedure has frequently been performed by surgeons in the United States.15 In addition, another study with a large sample (5,413 patients) and 10-year follow-up reported that the osteotomy type, including segmental Le Fort I osteotomies, did not impact the rates of morbidity, readmission, or reoperation for complications.16 Furthermore, several studies have confirmed that maxillary segmentation does not promote major skeletal or dental instability when appropriate bone grafting is performed. Therefore, the procedure should be considered when indicated.3,17-20

Despite the versatile design of the three-piece Le Fort I maxillary osteotomy,21 the stability of three-piece maxillary segmentation surgery remains controversial in the literature.2,6,22 Previous studies have reported relapse of incisor position changes achieved through segmentation surgical procedures in approximately 90% of the samples.6 Additionally, maxillary widening achieved with segmentation has been identified as an unpredictable procedure among various orthognathic surgical modalities.2,22 Proffit et al.23 demonstrated that the stability of Le Fort I multimaxillary segmentation for correcting transverse discrepancies ranks among the least reliable procedures commonly employed in various orthognathic surgical movements. Nevertheless, they could not assess skeletal changes independently from dental shifts. Additionally, their surgical protocol included segmentation between the canines and premolars, lack of palatal splints, and limited skeletal fixation systems. As a frequently employed surgical procedure in clinical practice, segmentation execution should be meticulously planned, and long-term stability must be considered. The lack of information and standardization regarding pre-surgical facial patterns, surgical techniques, location of the segmentations, post-surgical retainer protocols, and differentiation from skeletal and dental stability limit most studies published so far.4,22-24

Another limitation of previous studies is the utilization of two-dimensional methods3-6,20,23 to assess three-dimensional (3D) structures. The number of landmarks depends on the nature of the forms under study. In large structures, many landmarks can be used as homologous points.25 As the neurocranial structure is composed of relatively large, smooth bones with few sutural intersections, foramina, and bony prominences, the Euclidean distance matrix25 should be the selected analysis type. Collecting data from images of biological forms introduces challenges in landmark identification as the characteristics of the images can exert influence, potentially leading to a reduction in the number of landmarks or alterations in their types. Euclidean distances allow us to quantitatively compare the shapes of biological objects, offering advantages over other measurable components, including the maintenance of the relative position of all biological loci of interest or the geometric integrity of the form, as represented by landmarks.25 Considering the deficiencies in the literature, this study aimed to evaluate the skeletal stability of three-piece osteotomy surgery compared to one-piece maxillary osteotomy using Euclidean distances in a 3D cone-beam computed tomography (CBCT) methodology.

This retrospective cohort study was approved by the Institutional Research Ethics Committee of School of Dentistry of Araraquara, São Paulo State University (IRB number: 01032912.2.0000.5416). Written informed consent was obtained from all participants. The sample consisted of CBCT scans of patients following the inclusion criteria: underwent Le Fort I with one-piece or three-piece maxillary segments and bilateral sagittal ramus osteotomies with counter-clockwise rotation of the maxillo-mandibular complex, performed by the same surgeon (LW), following the surgical protocol described by Wolford et al.,26 and Bennett and Wolford.27 Minimum age of 16 for women and 18 for men, along with adequate CBCT examinations were also considered a prerequisite. The exclusion criteria included the presence of syndromes, cleft lip and palate, history of facial trauma, and previous maxillo-mandibular surgeries. The sample size was calculated based on changes of at least 2 mm², a minimum intergroup difference of 2.0 mm, an alpha value of 5%, and a statistical power of 80%. The sample size of each group comprised of 17 participants.

From a database of 163 patients, 39 skeletal Class II patients met the inclusion criteria (26 women and 13 men) and were divided into two groups. Group 1 (n = 22) underwent three-piece Le Fort I maxillary segmentation and group 2 (n = 17) underwent one-piece Le Fort I maxillary osteotomy. The patients underwent counter-clockwise rotation of the maxilla-mandibular complex and mandibular advancement. The sample was selected considering the growth pattern (SN-GoMe ≥ 36º) and surgery was performed (maxillo-mandibular advancement with counter-clockwise rotation) for adequate comparisons between groups. Moreover, CBCT acquisition was performed with a resolution of 0.3 mm voxel during a 17.8-second scan and a field of view of 17 × 23 cm (I-Cat Platinum unit; Imaging Sciences, Hatfield, PA, USA). For each patient, CBCT examinations were performed at three different time points: T1, initial (1–5 days before surgery); T2, post-surgical (1–10 days after surgery); and T3, follow-up (minimum of 10 months after surgery). The mean time between T1 and T2 was 5.56 days and that between T2 and T3 was 476.14 days. The image size was computationally reduced to a 0.5 mm voxel size and the 3D voxel-based registration was conducted in the cranial base using the 3D Slicer and ITK-SNAP software (https://www.slicer.org and www.itksnap.org).28,29

Cephalometric values were obtained from the lateral radiographs to characterize the samples (Supplementary Table 1). Consequently, 3D skull surface models were constructed at T1, T2, and T3 using 3D Slicer 4.4.0.30,31 Landmarks were placed on the surface of the maxillary model using the “Q3DC” tool to assess the distances between the CBCT intervals and groups. Landmarks were placed at specific points on the 3D maxillary surface and in the cortical bone of the maxilla at the vertical level of the tooth apices (Table 1 and Figure 1). The 3D Euclidean distances25 were obtained using landmarks through two different methods: 1) between 3D models (Figure 2) to evaluate surgical changes (T2-T1 distance) and skeletal stability (T3-T2 distance), and 2) within the surface model (Figure 3) to evaluate surgical changes (T2-T1) and skeletal stability (T3-T2).

Figure 1. Landmark points marked on the three-dimensional maxillary surface.
PR, posterior right; CR, canine right; AR, anterior right; AL, anterior left; CL, canine left; PL, posterior left.

Figure 2. Example of the Euclidean three-dimensional (3D) distance using two landmarks on a 3D surface. PR measurements within groups. Example: PR T2-PR T1.
T1, pre-surgical; T2, post-surgical; PR, posterior right.

Figure 3. Euclidean three-dimensional distance obtained using two landmarks within the model. Example: posterior right to posterior left.

Table 1 . Landmarks, variable definitions, and localizations.

Abbreviation	Description	Localization
PR	Posterior right	Landmark at bone relative to the root apex of upper right second molar
PL	Posterior left	Landmark at bone relative to the root apex of upper left second molar
AR	Anterior right	Landmark at bone relative to the root apex of upper right central incisor
AL	Anterior left	Landmark at bone relative to the root apex of upper left central incisor
CR	Canine right	Landmark at bone relative to the root apex of upper right canine
CL	Canine left	Landmark at bone relative to the root apex of upper left canine
PR-PL	Posterior right to posterior left	Distance of the posterior right to posterior left landmarks
CR-CL	Canine right to canine left	Distance of the canine right to canine left landmarks

Reproducibility was assessed using the intraclass correlation coefficient (ICC) and normality was confirmed using the Kolmogorov–Smirnov test. The ICC values were above 0.90 for all measurements, except for the variables posterior left (PL) (T3-T2) and canine right to canine left (CR-CL) (T3) which were 0.80. Student’s t test evaluated the equality of means and tested the hypothesis that the skeletal change averages between times and groups were equal to zero. Supplementary Table 1 lists the cephalometric measurements of the samples. The two groups were initially similar at T1, and surgical changes (T2-T1) demonstrated no statistically significant differences. In addition, group 1 exhibited a significant difference for variables in T2–T1 (surgical changes), except for anterior inferior facial height (AIFH). Furthermore, group 2 also presented a significant difference for variables in T2-T1 except for SNA angle and AIFH. Descriptive statistics of the surgical changes and stability measures within the groups using 3D models are presented in Supplementary Tables 2 and 3. A comparison of T3-T2 also displayed no statistical difference between the groups (Table 2), indicating the same stability behavior. The descriptive statistics for each group (T1, T2, and T3) and the differences within groups (T2-T1 and T3-T2) for the CR-CL and posterior right-PL variables (within the surface model) are presented in Supplementary Table 3. All the aforementioned findings are consistent with the results displayed in Table 3. Statistically significant surgical changes (T2-T1) and similar stability (T3-T2) were also observed in the surface model.

Table 2 . Student’s t test for surgical changes (T2-T1) and stability (T3-T2) between group 1 and group 2 (between three-dimensional models).

Measurement (Group 1- Group 2)	Surgical change (T2-T1 distance)				Stability (T3-T2 distance)
	Mean (mm)	SE	P value		Mean (mm)	SE	P value
CR	0.73	0.64	0.258		0.21	0.24	0.398
CL	0.92	0.70	0.196		0.41	0.21	0.063
PR	1.39	0.99	0.169		0.10	0.31	0.746
PL	–0.12	1.07	0.908		0.42	0.27	0.128
AR	0.51	0.72	0.485		0.07	0.29	0.813
AL	0.66	0.75	0.389		0.23	0.28	0.426

Student’s t test with α = 5%..

T1, pre-surgical; T2, post-surgical; T3, follow-up; SE, standard error; CR, canine right; CL, canine left; PR, posterior right; PL, posterior left; AR, anterior right; AL, anterior left..

Table 3 . Differences between groups for T2-T1 and T3-T2 (within the surface model).

Measurement (Group 1-Group 2)	T2-T1				T3-T2
	Mean (mm)	SE	P value		Mean (mm)	SE	P value
CR-CL	3.06	0.57	< 0.001***		–0.39	0.65	0.555
PR-PL	3.44	0.54	< 0.001***		0.05	0.37	0.888

T1, pre-surgical; T2, post-surgical; T3, follow-up; SE, standard error; CR-CL, canine right to canine left; PR-PL, posterior right to posterior left..

***P < 0.001 is statistically significant..

The objective of this study was to compare the 3D stability of one-piece and three-piece Le Fort I maxillary osteotomies in a sample of hyperdivergent patients who were subjected to counter-clockwise rotation of the maxillo-mandibular complex and mandibular advancement. Considering a lack of literature, we aimed to homogenize the sample, which comprised patients with vertical pre-surgical facial pattern (SN-GoMe ≥ 36º: group 1, 41.00º ± 9.05º; group 2, 39.82º ± 7.58º), submitted to a surgical protocol preconized in the literature.26,27 All patients in group 1 underwent interdental segmentation between the lateral incisors and canines. Other studies have also segmented canines and first premolars, which can influence stability. This is because the right and left canines belong to the anterior segment and are susceptible to vertical and transversal relapse. A palatal splint was used as a stability tool.21 Considering that dental instability can be influenced by skeletal instability alone or by skeletal in addition to dentoalveolar instability, our objective was to assess skeletal component instability in overall relapse.

Maxillary multi-segmentation in the treatment of dental skeletal deformities represents an important surgical alternative and is considered a useful tool for the 3D surgical correction of maxillary malposition.11 A previous study10 evaluated the clinical outcomes and satisfaction of orthodontists who treated patients undergoing maxillary multi-segmentation. According to the orthodontists, 96% demonstrated improved occlusion after the surgical procedure. The present study did not incorporate orthodontist’s assessments of treatment outcomes. However, all patients from both groups in our study sample exhibited good occlusion at the longest follow-up, meeting the requirements of the American.32

Our results displayed similar stability when comparing one- and three-piece maxillary Le Fort I osteotomies (Tables 2 and 3). As landmarks are not influenced by tooth movement, this study focused on evaluating skeletal rather than dental stability. The average values for stability between 3D models (T3-T2 distance), within both groups, remained very close to each other, ranging from 1.26 to 1.69 mm for group 1 and 0.96 to 1.47 mm for group 2, with no significant difference observed between groups in any variable. The stability observed in both surgical techniques suggests that the clinical practice of maxillary segmentation does not increase the inherent instability of the Le Fort I osteotomy with counter-clockwise rotation and maxillo-mandibular advancement. Another factor that may have contributed to the positive stability results was that all patients in the sample were operated on by an experienced surgeon (LW). The skill of the surgeon is related to the etiology of relapse.

In patients who underwent maxillary multi-segmentation, a parasagittal incision was placed on the soft palate to prevent elastic movement contrary to the surgical change, causing an opposite effect.33 During the postoperative period, this group used a splint without occlusal coverage to eliminate the instability factor.21 This clinical practice can be considered a factor in stability improvement and perhaps could be one of the factors contributing to stability, aligning with findings from other studies.11,34,35 T2 scans were performed within a maximum of 19 days postoperatively to reduce the possibility of adaptive responses during this period. For the analysis within the surface model between groups, this statistical hypothesis was also accepted, indicating average values of –0.39 between canine regions (CR-CL) and 0.05 between posterior regions. These results demonstrate that neither surgical technique interfered with postoperative instability. Mandibular instability was not addressed in this study, however, we included only similar maxillo-mandibular movements to avoid the possible influence of mandibular post-surgical behavior (Supplementary Table 1).

In contrast, previous studies reported that instability rates for multi-segmental Le Fort I osteotomies vary from 23% to approximately 95%.2,4,6,36 However, these studies focused on the measurement of dentoalveolar surgical changes, either through radiographs or plaster models. After removal of the splint and completion of orthodontic treatment, these regions are subject to alterations and adaptations, generating dental and non-skeletal recurrences. In addition, no specific description was available of the surgical techniques employed or postoperative retention. Furthermore, in contrast to our study, simultaneous premolar extraction was performed during orthognathic surgery in one of the previous studies,6 which can result in additional surgical complications.

The main limitations of our study included the limited sample size, due to standardization requirements and the challenge of locating individuals with T2 CBCT scans, which are not commonly requested in clinical practice. However, the sample size was within an acceptable range considering the statistical power estimation for the variables studied. Nevertheless, the groups were selected considering the same growth patterns and surgical management for adequate comparisons. This is one of the few studies comparing the stability of one- and three-piece maxillary osteotomies using 3D Euclidean distances in a standardized sample. However, future studies with long longitudinal follow-ups and large samples should be conducted, especially because negative stability results have been reported in classic studies.2,4,6,36

One- and three-piece maxillary osteotomies demonstrated similar post-surgical skeletal stability.

FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for financial support (Processes 2013/05831-8 and 2014/09152-0).

Conceptualization: JRG, JI. Data curation: JI, PBM, JP. Formal analysis: RMK. Investigation: RMK, JRG, JI, PBM, JP. Methodology: JI. Project administration: JRG, JB. Resources: LW. Supervision: JRG, LW, JB. Validation: RMK. Visualization: RMK, JB. Writing–original draft: RMK, JI, PBM, JP. Writing–review & editing: RMK, JRG, LW, JB.

No potential conflict of interest relevant to this article was reported.

Supplementary data is available at https://doi.org/10.4041/kjod23.166.