Orthognathic surgery involves correction of a dentofacial dysmorphology by repositioning the maxillary and mandibular bones into a pre-planned position with six degrees of freedom. This refers to the freedom of movement of a rigid body in three-dimensional (3D) space. The body is free to move anteriorly or posteriorly, superiorly or inferiorly, laterally or medially (translation in three perpendicular axes) combined with rotation about the three perpendicular axes, termed roll, yaw, and pitch, respectively. The potentially complex positional changes of the maxilla and mandible required during surgery are presently determined by a combination of preoperative model surgery planning, two-dimensional (2D) photocephalometric planning, or 3D planning.

Traditionally the assessment of 2D maxillary and mandibular changes has been determined by superimposing pre- and post-surgical lateral cephalograms on the anterior cranial base and calculating the changes in A-point and B-point, in the x and y directions. These single anterior points are often used to describe the movement of the entire maxillary and mandibular basal bone. However the points are dentoalveolar and are considered unreliable, as they are affected by surface remodelling and underlying tooth position. Postoperative skeletal position should rely on basal bone assessment, as any postoperative dental changes may camouflage the true basal bone position. Therefore clinical or 2D radiological assessment of tooth position may not accurately reflect basal bone changes.

Three-dimensional changes in the hard tissue position have been reported using 3D cephalometry, changes in volume, principal component analysis (PCA) and thin-plate spline analysis, and changes based on the surface model of the hard tissue. Measurements using 3D cephalometry are a natural progression from conventional 2D cephalometry and rely on landmark identification on a 3D surface model. Even though the assessment is relatively accessible using commercial software, the same problems with surface remodelling and changes due to underlying tooth position are present. There may be additional errors generating the 3D surface from the DICOM data and subsequent landmark identification. The previously reported method of volume changes does not adequately describe changes in basal bone position, whilst thin-plate spline analysis utilizes complex high-power statistical analysis. For instance a change in volume does not quantify directional or magnitude measurement.

A common method of assessing changes in 3D surfaces involves measuring the point-to-point distance of one mesh (the pre-intervention model) to the second mesh (post-intervention model) and generating a colour distance map. The main disadvantage with this technique is that the point-to-point measurement is the distance between two nearest points rather than the same corresponding points on the two surfaces. This has recently been explained in relation to quantifying changes in soft tissue. Given this problem, the question is raised as to whether the use of surface models to assess 3D skeletal changes is a valid method of assessment, especially given the complex morphology of the maxilla and mandible and the greater magnitude and variation in the direction of movement of the hard tissue compared to soft tissue changes.

Therefore the aim of this study was to determine the validity of using surface models as a method of assessing positional changes in the maxilla and the mandible as a result of simulated surgery.

Materials and methods

A Le Fort I osteotomy was performed on a plastic skull. Prior to the osteotomy, a locating plate was constructed from acrylic, which allowed the maxilla to be returned to its original position. The skull was mounted onto an adjustable universal joint that was secured to a 2-cm thick acrylic resin base. An adjustable stage was placed below the maxilla; between the stage and the maxillary occlusal plane there was a height adjustable platform. Once the maxilla was secured to the platform, this arrangement allowed only two degrees of freedom of movement of the maxilla, i.e., anteriorly or posteriorly and superiorly or inferiorly; any pitch, yaw, roll, and lateral or medial movements were restricted. Using a modified Denar Slidematic Facebow (Whip Mix, Louisville, KY, USA) with an attached spirit level, the skull was oriented and secured so that the Frankfort plane and inter-auricular plane were horizontal; the skull assembly was cone beam computed tomography (CBCT) scanned using 0.4 mm resolution and 22 cm extended field of view (i-CAT; Imaging Sciences International, Hatfield, PA, USA).

The maxilla was secured to the platform using sticky wax and released from the skull base. Using the adjustable stage, the maxilla was advanced in 3-mm increments and downgrafted in 2-mm increments. An approximate magnitude of movement was determined using a Vernier caliper positioned parallel to the path of movement of the maxilla ( Fig. 1 ). Following each maxillary movement, the skull was CBCT scanned using the protocol described previously. In total, 12 combined downgraft and advancement procedures were simulated for the maxilla.

Experimental set-up for the simulated surgical movements, allowing two degrees of freedom of movement, anteroposterior and vertical.

The data processing pipeline is shown in Fig. 2 . Following CBCT scanning, all of the DICOM scans were converted to surface mesh images using MeVisLab (MeVis Medical Solutions AG, Bremen, Germany) and saved in STL format. Using rigid registration and the iterative closest point (ICP) algorithm, the baseline scan and each of the maxillary movement scans were superimposed onto the skull base, maintaining the baseline image position using VRMesh (Seattle City, WA, USA), and saved in the new aligned 3D position. Since the skull was correctly oriented during the CBCT scan it was possible using Minimagics software (Materialise, Leuven, Belgium) to create a profile, passing through the sagittal plane, of the two superimposed images. Horizontal and vertical changes in the maxillary position were measured ( Fig. 3 ). To measure movement in only the sagittal plane, the CBCT scans were superimposed for each advancement whilst maintaining the same downgraft. For vertical movements, the advancements remained the same whilst the downgrafts were changed. In this way an additional 15 movements and measurements were generated.

Data processing pipeline (CBCT, cone beam computed tomography; AP, anteroposterior; ICP, iterative closest point).

Measuring the actual horizontal and vertical changes in maxillary position. (a) 3D surface models superimposed on the cranial base: baseline model (silver) and 9 mm advancement and 2 mm downgraft model (blue). (b) Horizontal and vertical changes in maxillary position based on a profile, passing through the sagittal plane of the two superimposed images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

A similar procedure was carried out for the mandible. Following each advancement, the mandible was secured to the maxillary dentition using sticky wax and CBCT scanned using the same scanning protocol. The same software pipeline was used to determine the horizontal changes in the mandible at each of the four advancement increments.

Analysis

The results of the error study showed that there was no systematic error ( P = 0.56) or random error ( r = 0.99), and the maximum error between readings was 0.2 mm.

Each pair of aligned baseline and simulated surgical 3D models were imported into VRMesh and both the skull images were deleted leaving only the maxilla or mandible ( Fig. 4 ). For each simulated surgical movement, three methods were used to analyse the distance between the two surface meshes: the mean absolute distance using 100% of the mesh points, the mean absolute distance based on the 90th percentile of the mesh points, and the root mean square (RMS) distance. The mean 90th percentile was determined by arranging the absolute distances between the two surface meshes for 100% of the mesh points in descending order and then calculating the mean of the lower 90th percentile. The RMS distance was calculated by squaring the absolute distances of 100% of the mesh points between the two surface meshes, averaging the squares, and then taking the square root.

Using VRMesh the skull images were deleted leaving only the maxilla, and the difference between the two surfaces was determined based on a colour distance map: (a) occlusal view, and (b) bucco-labial view. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)