Int. J. Oral Maxillofac. Surg. 2015; 44: 1441–1450 http://dx.doi.org/10.1016/j.ijom.2015.06.007, available online at http://www.sciencedirect.com Invited Clinical Paper The William Bell Series 1,2,3 2,3,4 J. J. Xia , J. Gateno , 5 1 1 J. F. Teichgraeber , P. Yuan , J. Li , Algorithm for planning a double- 1,6 7 7 K.-C. Chen , A. Jajoo , M. Nicol , 2,3,4 D. M. Alfi 1 Surgical Planning Laboratory, Department of jaw orthognathic surgery using Oral and Maxillofacial Surgery, Houston Methodist Research Institute, Houston, TX, 2 USA; Oral and Maxillofacial Surgery, Institute a computer-aided surgical for Academic Medicine, Houston Methodist 3 Hospital, Houston, TX, USA; Oral and Maxillofacial Surgery, Weill Medical College, 4 Cornell University, NY, USA; Department of simulation (CASS) protocol. Oral and Maxillofacial Surgery, Houston Methodist Hospital, Houston, TX, USA; 5 Division of Pediatric Plastic Surgery, Part 2: three-dimensional Department of Pediatric Surgery, The University of Texas Health Science Center at 6 § Houston, TX, USA; Department of Oral and Maxillofacial Surgery, National Cheng-Kung cephalometry University Medical College and Hospital, 7 Tainan, Taiwan; Department of Mathematics, University of Houston, TX, USA J. J. Xia, J. Gateno, J. F. Teichgraeber, P. Yuan, J. Li, K. -C. Chen, A. Jajoo, M. Nicol, D. M. Alfi: Algorithm for planning a double-jaw orthognathic surgery using a computer-aided surgical simulation (CASS) protocol. Part 2: three-dimensional cephalometry. Int. J. Oral Maxillofac. Surg. 2015; 44: 1441–1450. # 2015 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved. Abstract. Three-dimensional (3D) cephalometry is not as simple as just adding a Key words: cephalometry; cephalometric ana- lysis; three-dimensional; two-dimensional; den- ‘third’ dimension to a traditional two-dimensional cephalometric analysis. There tofacial deformity; craniomaxillofacial are more complex issues in 3D analysis. These include how reference frames are deformity; computer-aided surgical simulation; created, how size, position, orientation and shape are measured, and how symmetry surgical planning; orthognathic surgery; plan- is assessed. The main purpose of this article is to present the geometric principles of ning sequence. 3D cephalometry. In addition, the Gateno–Xia cephalometric analysis is presented; this is the first 3D cephalometric analysis to observe these principles. Accepted for publication 8 June 2015 Introduction These measurements have been made on sagittal or coronal plane. There are two standardized plain radiographs called fundamental problems associated with tra- Since 1931, two-dimensional (2D) radio- 2–6 cephalograms. In these cephalograms, ditional 2D cephalometry. The first is graphic cephalometry has been used to which can be lateral or frontal, all the that many important parameters cannot be measure the shape, size, position, and 1 facial structures are projected onto a single measured. The second is that most 2D orientation of the different facial units. § To the authors’ knowledge, no currently available commercial software package is capable of performing such a 3D cephalometric analysis. The authors are developing a CASS planning software package, AnatomicAligner; this project is sponsored in part by the United States National Institutes of Health/National Institute of Dental and Craniofacial Research (NIH/NIDCR). It is designed specifically for orthognathic surgery. The software will be available freely to broader clinical and research communities in the near future (http://www.AnatomicAligner.com). 0901-5027/01201441 + 010 # 2015 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved. 1442 Xia et al. cephalometric measurements are distorted A simple way of envisioning the differ- The anatomical landmark method is 2,3 in the presence of facial asymmetry. ence between the global and local coordi- simple if the face has perfect symmetry. The recent introduction of cone beam nate system is to imagine a room with a The Frankfort horizontal is constructed computed tomography (CBCT) in an of- toppled chair. In this scenario, the refer- using both porions and both orbitales. fice setting has facilitated the acquisition ence frame of the room is the global The sagittal plane is constructed using of three-dimensional (3D) images with coordinate system. It is perfectly aligned any three midline landmarks, and the cor- lower amounts of radiation. 3D cephalom- to our surroundings: roof is up, floor is onal plane, which is made perpendicular to etry can correct the problems associated down, and walls are east, west, north, and the other planes, is aligned to both porions. with its 2D counterpart. However, 3D south. The toppled chair, lying in the Unfortunately, no human face is per- cephalometry is more complex than just middle of the room, has its local coordi- fectly symmetrical. In facial asymmetry, it 4 adding a third dimension to a 2D analysis. nate system aligned with the top, front, is complex to use landmarks to construct There are complex issues in 3D cephalom- and side of the chair. Only the chair’s the reference planes of the face. Let us first 2,3 etry. These include how reference sys- features define the local coordinate sys- consider the Frankfort horizontal. Four tems are created, how size, position, tem, which is independent of its spatial points define this plane: right orbitale, left orientation and shape are measured, and position or orientation. The global refer- orbitale, right porion, and left porion. how symmetry is assessed. Understanding ence frame and the chair’s local coordi- However, in facial asymmetry, these these basic principles is essential for the nate systems were aligned with each other points are not coplanar, which creates a correct use of 3D cephalometry. The main when the chair was standing upright and dilemma. A plane can be built using any purpose of this article is to present the turned south. However, in this example, three points. Which three of the four geometric principles of 3D cephalometry. when the chair is laid down on its side, the Frankfort points should be used? Each In addition, the Gateno–Xia cephalomet- global reference frame and local coordi- combination results in a different plane. ric analysis is presented; this is the first 3D nate system are not aligned. The details of To solve this problem, a best-fitting plane cephalometric analysis to observe these how global and local coordinate systems among the four points may be constructed. principles. are used in 3D cephalometry are described This is feasible when the head has minor below. asymmetries. However, in deformities like hemifacial microsomia, this best-fitting Basic principles of 3D cephalometry method will alter the axial plane by adding Global reference frame for the whole head Clinicians use cephalometry to determine a distorted landmark into the equation. the configuration of the face. An ideal The reference frame for the whole head is Now let us consider the sagittal plane. cephalometric analysis should measure composed of the axial, coronal, and sagit- This plane can be constructed using three the five geometric attributes of each facial tal planes. These planes are mutually per- midline landmarks, three pairs of bilateral unit. These include size, position, orienta- pendicular (Fig. 1). The sagittal plane landmarks, or even just one pair of bilat- tion, shape, and symmetry. Three of these divides the head into right and left halves. eral landmarks. In the first case, the mid- measurements – position, orientation, and The axial plane divides the head into upper line landmarks lie on the sagittal plane. In 2–4,7,8 symmetry – need a reference frame. and lower halves. The coronal plane the second case, the pairs of corresponding The reference frames and how the differ- divides the head into front and back bilateral landmarks are used to calculate ent geometric attributes should be mea- halves. Traditionally, two methods have three midpoints that lie on the sagittal sured are discussed below. been used to define the reference frame for plane. In the last case, a line is drawn the whole head: anatomical landmark and between the single pair of bilateral land- neutral head posture (NHP). marks and the sagittal plane is constructed Reference frames In 3D cephalometry, measuring position, orientation, and symmetry requires several different reference frames. The main ref- erence frame, ‘global’, encompasses the whole head (face and cranium). It can also be called the ‘global coordinate system’. Subordinate reference frames, ‘local’, be- long to each facial unit (e.g., maxilla, mandible, and chin). Both reference frames are coordinate systems made up of three mutually perpendicular planes. In cephalometry, there is only one ‘global reference frame’ and several ‘local coor- dinate systems’ – one for each facial unit. The local coordinate systems can also be called ‘local reference frames’. Although the terms ‘reference frame’ and ‘coordi- nate system’ can be used interchangeably, in order to avoid confusion for the reader, the term ‘reference frame’ referring to the whole head, and the term ‘coordinate sys- Fig. 1. Global reference frame (coordinate system) for the whole head. The reference frame for tem’ referring to each facial unit, are used the whole head includes three orthogonal planes: midsagittal (green), coronal (pink), and axial in the following text. (blue). Double-jaw orthognathic surgery