Accurate preoperative planning is mandatory for orthognathic surgery. One of the most important aims of this planning process is obtaining good postoperative dental occlusion. Recently, 3D image-based planning systems have been introduced that enable a surgeon to define different osteotomy planes preoperatively and to assess the result of moving different bone fragments in a 3D virtual environment, even for soft tissue simulation of the face. Although the use of these systems is becoming more accepted in orthognathic surgery, few solutions have been proposed for determining optimal occlusion in the 3D planning process. In this study, a 3D virtual occlusion tool is presented that calculates a realistic interaction between upper and lower dentitions. It enables the surgeon to obtain an optimal and physically possible occlusion easily. A validation study, including 11 patient data sets, demonstrates that the differences between manually and virtually defined occlusions are small, therefore the presented system can be used in clinical practice.
Virtual planning of orthognathic surgery is an extremely challenging area of research that combines medical imagery, computer graphics and mathematical modelling. Recently, three dimensional (3D) image based planning systems have become available that enable the surgeon to define necessary osteotomy planes preoperatively and to assess different surgical scenarios virtually. Using this technology means orthognathic surgery can be optimized and surgery time can be reduced.
Obtaining a good and stable dental occlusion is one of the key goals of orthognathic surgery. Traditionally, the final occlusion is defined with plaster casts of the upper and lower dental arches. The surgeon manually searches for a relative position for both casts, to obtain a good and stable occlusion. Based on the defined occlusion, a surgical splint is manufactured and used during surgery, transferring the virtual surgical planning into the operating theatre. This method is accepted as the global ‘gold standard’ of practice, but working with plaster casts has some drawbacks. First, the anatomical information from the complete skull is lost when looking at plaster casts. Second, although some information about the spatial orientation can be obtained from plaster casts mounted in an articulator, this simulation cannot fully enable a surgeon to visualise how the final occlusion may change the morphology of the surrounding hard and soft tissues in 3D. Third, storage of the plaster casts is problem. There is a need to make the manual procedure virtual. With the aim of bringing 3D imaging and computer-aided planning one step closer to practice, a new method to define the desired occlusion between the upper and lower dentition virtually was developed. An experimental study was performed to prove the validity of this new method.
Materials and methods
After making imprints (Alginoplast ® , Heraeus Kulzer GmbH, Hanau, Germany), dental plaster casts (Fujirock ® , GC, Japan) are manufactured. To obtain digital models of these casts, the upper and lower plaster casts are separately scanned using a Cone Beam CT (CBCT) scanner (i-CAT™ 3D Imaging System, Imaging Sciences International Inc., Hatfield, USA). The scanning resolution is set to 0.2 mm × 0.2 mm × 0.2 mm (voxel resolution). Based on the volumetric CBCT data, surface models of upper and lower dentitions are generated using the marching cubes algorithm with an appropriate threshold ( Fig. 1 ).
To allow the user to define a desired occlusion, contact behaviour between the dental models should be modelled. Since occlusion is defined as the relative position of the lower and upper dental arches, it is sufficient to move the upper dental arch towards the lower dental arch. In the presented system this movement can be realized by free-hand movements or by guided movements. A combination of both methods is thought to be sufficient to define the desired occlusion virtually. With the free-hand movement tool, the user can freely translate and rotate the upper dental model in a 3D environment ( Fig. 2 ). A rigid motion engine is used to calculate whether the upper and lower dental models collide. If collision occurs, the motion applied by the user is cancelled, resulting in temporary fixation of the upper dental model. To emphasize that collision has occurred, both models are coloured red. When the user moves the upper dental model to a non-colliding position, the red colour disappears. This framework prevents virtual penetration of the upper and lower dental models. This system enables the user to obtain a rough estimate of a good occlusal position. Owing to the irregular shape of the teeth, it is almost impossible and very time consuming to achieve perfect occlusion by manual alignment in the virtual software tool.
An additional guided movement tool was implemented which enables the user to define the final desired occlusion starting from a good initial position. The tool allows the user to indicate corresponding points on the upper and lower dental models manually. Typical correspondences are, for example, points on the midline between the upper and lower central incisors ( Fig. 3 a ), the tip of the vestibular cuspid of the first upper premolar and contact points between the first and second lower premolar ( Fig. 3 b), and the tip of the cuspid of the second upper premolar and the contact point between the second lower premolar and first lower molar ( Fig. 3 c). After the user has indicated at least three corresponding pairs of points, the system calculates a new position for the upper dental model. This new position is found by minimizing the distance between the indicated correspondences while respecting the impenetrability of the dental models. To assure these requirements, the rigid motion engine is used. To each corresponding pair of points, a ‘spring connection’ is assigned. The forces generated by these springs are applied to the upper dental model. Next, the rigid motion engine is used to calculate the resulting movement of the upper dental model for a short time step. This procedure is successively approximated (iteration); in each approximation step, the spring forces are updated and a new position for the upper dental model is calculated. After a few iterations, the model reaches a stable position, when the forces applied by the springs equal the contact reaction forces defined by the rigid motion engine. If a stable position is found, the result is presented to the user ( Fig. 4 ).
For this position, the system generates an occlusionogram of the upper and lower dentition. This occlusionogram is a distance map between the upper and lower dentition and gives the user a good idea where the teeth make contact. In the presented occlusionogram, a specific colour was assigned to all regions where the distance between both models measures less than 1 mm ( Fig. 4 c).
By combining the free-hand and guided movement tool, the user can iteratively define a good initial starting position and perform several motion simulation steps, finally obtaining good occlusion. To verify this statement, a validation study was performed ( Fig. 5 ). The dental casts of 11 orthognathic patients were collected. To allow comparison between the manual and virtual approach, only casts that did not require occlusal adjustments of the dentition were selected. For each patient, the upper and lower plaster casts were separately digitized using a CBCT scanner (voxel resolution 0.2 mm × 0.2 mm × 0.2 mm). Three maxillofacial surgeons (A, B and C) were asked to position the upper and lower plaster casts manually in a desired final occlusion and to fix the models together using sticky wax (Associated Dental Products Ltd., Purton Swindow, Wiltshire, UK) ( Fig. 5 a, first row). The aligned casts, which were fixed in optimal occlusion, were digitized using a CBCT scanner (voxel resolution 0.2 mm × 0.2 mm × 0.2 mm). These CBCT data sets of the plaster casts were superimposed on the CBCT volume of the corresponding lower dental cast. It was ensured that the lower dentitions of all corresponding data sets shared the same position. These aligned data sets were called the co-aligned volumes ( Fig. 5 a, second row). To obtain the superimposition, the maximisation of mutual information criterion was used. This criterion measures the information redundancy between the image intensities of corresponding voxels between the different CBCT scans. This information is aimed to be maximal when the images are geometrically aligned. To measure the differences in the spatial position of the upper casts in the three different data sets, the upper casts were separated from the lower casts and were colour coded. To obtain this separation a second alignment step was introduced. Each digitized upper plaster cast was aligned to the corresponding co-aligned volume. A set of dentition models in occlusion could be obtained for each surgeon and for each patient ( Fig. 5 a, third row); these sets were called P, Q and R.