Natural reference structures for three-dimensional maxillary regional superimposition in growing patients
Authors: Fan Yi , Han Bing , Zhang Yungeng , Guo Yixiao , Li Wei , Chen Huanhuan , Meng Chenda , Penington Anthony , Schneider Paul , Pei Yuru , Chen Gui , Xu Tianmin 
Published: September 2023

Abstract
Background
Assessment of growth-related or treatment-related changes in the maxilla requires a reliable method of superimposition. Such methods are well established for two-dimensional (2D) cephalometric images but not yet for three-dimensions (3D). The aims of this study were to identify natural reference structures (NRS) for the maxilla in growing patients in 3D, opportunistically using orthodontic mini-screws as reference; and to test the applicability of the proposed NRS for maxillary superimposition by assessing the concordance of this approach with Björk’s ‘stable reference structures’ in lateral projection.

Methods
The stability of the mini-screws was tested on longitudinal pairs of pre- and post-orthodontic cone-beam computed tomography (CBCT) images by measuring the distance changes between screws. After verifying the stability of the mini-screws, rigid registration was performed for aligning the stable mini-screws. Then, non-rigid registration was used to establish the dense voxel-correspondence among CBCT images and calculate the displacement of each voxel belonging to the maxilla relative to the mini-screws. The displacement vectors were transformed to a standardized maxillary template to categorize the stability of the internal structures statistically. Those voxels that displaced less relative to the mini-screws were considered as the natural reference structures (NRS) for the maxilla. Test samples included another dataset of longitudinal CBCT scans. They were used to evaluate the applicability of the proposed NRS for maxillary superimposition. We assessed whether aligning the maxilla with proposed NRS is in concordance with the maxillary internal reference structures superimposition in the traditional 2D lateral view as suggested by Björk. This was quantitively assessed by comparing the mean sagittal and vertical tooth movements for both superimposition methods.

Results
The stability of the mini-screws was tested on 10 pairs of pre- and post-orthodontic cone-beam computed tomography (CBCT) images (T1: 12.9 ± 0.8 yrs, T2: 14.8 ± 0.7 yrs). Both the loaded and the unloaded mini-screws were shown to be stable during orthodontic treatment, which indicates that they can be used as reference points. By analyzing the deformation map of the maxilla, we confirmed that the infraorbital rims, maxilla around the piriform foramen, the infrazygomatic crest and the hard palate (palatal vault more than 1 cm distal to incisor foramen except the palatal suture) were stable during growth. Another dataset of longitudinal CBCT scans (T1: 12.2 ± 0.63 yrs, T2: 15.2 ± 0.96 yrs) was used to assess the concordance of this approach with Björk’s ‘stable reference structures’. The movement of the maxillary first molar and central incisor showed no statistically significant difference when superimposing the test images with the proposed NRS or with the classic Björk maxillary superimposition in the lateral view.

Conclusions
The infraorbital rims, maxilla around the piriform foramen, the infrazygomatic crest and the hard palate (palatal vault more than 1 cm posterior to incisal foramen except the palatal suture) were identified as stable regions in the maxilla. These stable structures can be used for maxillary superimposition in 3D and generate comparable results to Björk superimposition in the lateral view.