Volume 39, Issue 5 , Pages 457-462, May 2010
Virtual occlusion in planning orthognathic surgical procedures
Article Outline
- Abstract
- Materials and methods
- Results
- Discussion
- Funding
- Competing interests
- Ethical approval
- References
- Copyright
Abstract
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.
Keywords: virtual surgery, 3D planning, occlusion, orthognathic surgery
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[3], [15], [19], [20], [21], [22], [23] 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×0.2mm×0.2mm (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 threshold9 (Fig. 1).
Fig. 1.
To obtain digital dental models, plaster cast were separately CBCT scanned.
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.
Fig. 2.
(a) Initial setup in the 3D environment. (b) The dental model can be translated in any direction and (c) rotated round the X, Y and Z axes. (d) When the dental models collide, they are coloured red and penetration of the models is prevented. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
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. 3a), the tip of the vestibular cuspid of the first upper premolar and contact points between the first and second lower premolar (Fig. 3b), 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. 3c). 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).
Fig. 3.
(a–c) Corresponding points can be indicated manually on the upper and lower dentition models (d).
Fig. 4.
(a) After defining an initial position with the first tool, correspondences were indicated. (b) Simulation result. (c) To facilitate the dentition of a good occlusion, an occlusionogram is shown.
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 1mm (Fig. 4c).
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 0.2mm×0.2mm×0.2mm). 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. 5a, first row). The aligned casts, which were fixed in optimal occlusion, were digitized using a CBCT scanner (voxel resolution 0.2mm×0.2mm×0.2mm). 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 criterion10 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. 5a, third row); these sets were called P, Q and R.
Fig. 5.
(a) Manual procedure. First row: manually placed casts and fixed in final occlusion. Second row: digitized sets of casts. Third row: final co-aligned casts with separated and colour coded upper casts. (b) Virtual procedure. (c) Repetition of setup 1 for surgeon A after 3 weeks.
In a second setup, surgeon A was asked to define the desired occlusion for each data set with the presented software system (Fig. 5b). The relative initial position of the upper and lower dental models was randomized. This task resulted in a fourth set of aligned dentition models (set Y).
Finally, surgeon A repeated the first procedure, the manual definition of the desired occlusion for each patient data set (Fig. 5c). This task was performed 3 weeks after finishing the first validation procedure to prevent the surgeon from being biased. A fifth set of aligned dentition models (set Z) was obtained, after digitizing the aligned models and performing the alignment tasks.
The second phase of this study consisted of three steps. First, inter-observer reliability was defined by calculating the distance maps between sets P and Q and later on between P and R. In the second step, the same procedure was performed between sets P and Z to measure the intra-observer reliability. Third, the difference between a manually planned occlusion and an occlusion obtained with the software tool was revealed through the calculation of the distance maps between sets P and Y. For each distance map, the median distance and the 90% and 95% percentiles of the distance distribution were calculated. Since the differences close to the occlusal plane are of utmost importance, a region of interest was defined (Fig. 6a). The calculated distance maps are projected on top of the surface mesh by means of a colour code.
Fig. 6.
(a) Distances were only calculated in a small region around the occlusal plane. (b) The distances calculated between different sets can be projected on top of the dental surface mesh by means of a colour code. The colour bar ranges from −2
mm to 2mm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
The software tool was implemented in the Maxilim® 2.0 platform (Medicim NV, Mechelen, Belgium). All tests were performed on a standard personal computer (Pentium IV – 2.0GHz).
Results
The desired occlusion could be obtained easily with the presented software tools for all 11 data sets (Fig. 6b). Table 1 summarizes the results; each column lists the mean value of the specified statistic over all patient data sets. The median intra-observer variability measured 0.46mm. Even the 95 percentile statistic was less than 0.8mm, indicating that the defined occlusions were almost identical. The inter-observer variability was higher (average median value 0.72mm). The median difference between a manual obtained occlusion and an occlusion defined with the software tool was 0.60mm on average. It was concluded that the plaster-digital variability was slightly higher than the intra-observer variability, but was less than the inter-observer variability.
Table 1. The mean value over all patient data sets of the median, the 90% percentile and the 95% percentile of each distance distribution.
| Median (mm) | P 90% (mm) | P 95% (mm) | |||
|---|---|---|---|---|---|
| P–Q | 0.89 | 1.17 | 1.37 | ||
| Plaster–Plaster | Inter-variability | P–R | 0.55 | 0.79 | 0.91 |
| Plaster–Plaster | Intra-variability | P–Z | 0.46 | 0.65 | 0.76 |
| Plaster-Digital | P–Y | 0.60 | 0.81 | 0.91 | |
Discussion
Orthognathic surgery is a complex procedure, so accurate planning of the surgery is mandatory. Recently, 3D planning systems have been introduced. These systems start from 3D image data and enable the surgeon to perform 3D cephalometric analysis[16], [19], [23], to execute virtual osteotomies[1], [21], [23] while moving bone fragments in a 3D environment, and to simulate the patient's postoperative facial appearance[4], [11], [12], [21]. These systems offer the surgeon better surgical preparation, but none include virtual planning of dental occlusion. Defining a good occlusion is one of the most important steps in the surgical planning procedure, since it defines the relative position of the mandibular and maxillary bone fragments.
Until now, there have been few reports of how occlusal planning can be combined with a computer-aided planning system. Bettega et al.2 presented a complete computer-aided planning system. Their system allowed the surgeon to perform a 3D cephalometric analysis, split the skull into separate bone fragments, move the bone fragments in 3D and define the position of the mandibular bone fragment based on a defined occlusion. To find this occlusion, plaster casts were used. After manually positioning the lower and upper casts so that the desired occlusion was obtained, the relative movement of the lower cast was transferred to the virtual planning by means of a 3D optical localizer. Later, Chapuis et al. 5 used the same concept and presented some case results. They showed that an occlusion could easily be defined with this concept, but their approach and the Bettega system have limitations. First, plaster casts of the upper and lower dentition are still necessary because they are used to define the occlusion. Second, a 3D optical localizer is necessary to transfer the defined occlusion to the computer-aided planning system. These optical systems are expensive and not available in every clinical practice. Third, errors arise in their systems when transferring the manually defined occlusion to the computer-aided planning process.
Pongracz & Bardosi14 tried to omit the use of plaster casts and created a fully virtual occlusal planning tool. To define a good occlusion, they aligned upper and lower dental models based on corresponding points that were manually indicated. The accuracy of their method is hard to confirm since the contact behaviour between the upper and lower dentition is not modelled and the impenetrability of teeth is not guaranteed.
In this study a novel method that virtually defines the occlusion is presented. A rigid motion simulation engine ensures the impenetrability of the dental models. This engine enables the user to identify the desired occlusion semi-automatically. The motion engine allows almost real-time simulations.
The results of the validation study of 11 patient data sets showed that the plaster-digital reliability was slightly higher than the intra-observer reliability, but was less than the inter-observer reliability. It can be concluded that the presented system allows for the reliable determination of the desired occlusion. For less stable occlusions, where an occlusal adjustment in the form of teeth grinding could be necessary, a virtual grinding module was implemented, but not tested in this setup.
Despite these results, the authors acknowledge that virtual planning is not the same as manual planning. During manual planning, the surgeon ‘feels’ the models as he or she sets the real models in the desired occlusion; during virtual planning, the surgeon has to ‘see’ the occlusion. Although the presented system offers some solutions to facilitate this detection (e.g., with the occlusionogram), it is admitted that a learning curve is associated with this virtual occlusal planning system.
The system can run on any standard personal computer and no specialized expensive hardware is required. In this way, the presented method can be introduced easily into daily clinical practice. The system is completely virtual and no interactions with plaster casts are necessary. Based on the virtually defined occlusion, one can generate a virtual surgical splint[6], [8]. These surgical splints are used to transfer the planned occlusion to the operation theatre. Since the presented system is completely digital, it should be easy to generate splints in a fully automated process, as opposed to producing them by manufacturing. Recent efforts on realising skeletal virtual models including accurate dental surface information have been published[7], [13], [17]. The presented system enables the user to define the desired occlusion for these ‘augmented models’18. Once plaster casts are no longer required their generation and storage will no longer be necessary.
Having integrated the presented system into an orthognathic planning system (that allows 3D cephalometrics, the performance of osteotomies and the movement of bone fragments), the first complete orthognathic planning system is now a reality.
Funding
No funding.
Competing interests
No competing interests.
Ethical approval
No ethical approval necessary.
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PII: S0901-5027(10)00045-7
doi:10.1016/j.ijom.2010.02.002
© 2010 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Inc. All rights reserved.
Volume 39, Issue 5 , Pages 457-462, May 2010
