Computer-assisted surgical simulation is being used increasingly in orthognathic surgery. However, occlusal definition is still undertaken using model surgery with subsequent digitization via surface scanning or cone beam computed tomography. A software tool has been developed and a workflow set up in order to achieve a virtual occlusal definition. The results of a validation study carried out on 60 models of normal occlusion are presented. Inter- and intra-user correlation tests were used to investigate the reproducibility of the manual setting point procedure. The errors between the virtually set positions (test) and the digitized manually set positions (gold standard) were compared. The consistency in virtual set positions performed by three individual users was investigated by one way analysis of variance test. Inter- and intra-observer correlation coefficients for manual setting points were all greater than 0.95. Overall, the median error between the test and the gold standard positions was 1.06 mm. Errors did not differ among teeth ( F = 0.371, P > 0.05). The errors were not significantly different from 1 mm ( P > 0.05). There were no significant differences in the errors made by the three independent users ( P > 0.05). In conclusion, this workflow for virtual occlusal definition was found to be reliable and accurate.
Virtual simulation, based on three-dimensional (3D) image planning systems, is used increasingly for preoperative planning of orthognathic surgery. Commercially available software packages provide convenient tools for 3D measurements, virtual osteotomy, bone segment repositioning, and soft tissue prediction. However, few of the currently available software packages provide tools for virtual occlusal definition.
In the current computer-assisted surgical simulation (CASS) workflow, the final occlusion is decided manually using model surgery with subsequent digitization via surface scanning procedures or cone beam computed tomography (CBCT). As well as being time-consuming and often inaccurate, the main drawback of this model surgery based-approach is that it cannot fully enable the surgeon to visualize how the final occlusion may change the morphology of the surrounding hard and soft tissues in 3D.
A software tool has been developed and a workflow set up in order to achieve a virtual occlusal definition within the present CASS protocol. A validation study was carried out to test its accuracy and reliability.
Materials and methods
This study was performed at a university school and hospital of stomatology in Beijing, China. The research protocol was approved by the institutional ethics committee.
Workflow of the virtual occlusal definition
The software tool was developed to realize a virtual occlusal definition based on visualization support and precise movements. A virtual workflow was set up accordingly.
First, the digital model data of the upper and lower jaws are imported into the virtual system. Thirty-seven pairs of corresponding marker points are then identified manually ( Fig. 1 ). Vectors are generated automatically between the upper points and the corresponding lower points, based on the principles of prosthodontics and orthodontics. For example, the mesiobuccal cusp point on the maxillary first molar is aligned with the buccal fissure point of the opposing mandibular first molar. The length and direction of vectors are determined by the distance and direction between theoretical corresponding points in the upper and lower jaws.
Second, with the lower dentition set as a fixed object, the position of the upper jaw is adjusted using an interactive adjustment tool, so as to align it with the lower jaw. Users are able to move the upper dentition either by typing in instructions in a dialog box ( Fig. 2 A) or by using a free-hand module ( Fig. 2 B). Rotation and transposition along a single axis makes movement easier to handle than with 3D adjustments. During the adjustment, two representative tools assist users to obtain information about the relationship between the cusp–fossa and tooth contact.
The collision heat map tool shows the vertical distance and contact between corresponding points using a colour scale. A collision detection algorithm calculates whether points on the upper and lower dentitions are in contact with, or overlap each other ( Fig. 2 C). Contact detection is only looked for in a small region, near the occlusal plane. This greatly reduces the calculations required, helping the software run smoothly.
The distance projection tool shows the directions of occlusal deviations. Vectors between corresponding points are projected onto the occlusal plane to determine sagittal and transverse deviations ( Fig. 2 D). In an ideal occlusion, bilateral vectors should be symmetrical in direction and length. Users can make adjustments by following these vectors.
Third, when the upper and lower jaws are near to final occlusion, adjustment tools in ‘adjustment hint grid view’ ( Fig. 2 E) are used to make automatic minor regulations. There are seven types of single-direction movement in the hint grid, including transverse transposition, rotation, sagittal transposition, and coronal rotation of the upper and lower jaws. The movements are calculated automatically, in real-time, according to parameters for a normal overjet, overbite, and better symmetry of bilateral vectors.
Every adjustment is aligned automatically and in real-time with every view on the interface. The user can revise the position of the upper jaw through an adjustment–gaining knowledge–further adjustment operation cycle until an optimal occlusion relationship is obtained. The workflow diagram is shown in Fig. 3 .
The validation tests were designed to address three points: (1) Whether the manual procedure of identifying marker points has good inter- and intra-observer reproducibility. (2) Whether the present workflow is accurate. (3) Whether the result of virtual occlusal definition by different users is consistent.
Therefore, three tests were performed: a reproducibility test for the manual procedure for marking points (test 1), an accuracy test (test 2), and a reproducibility test (test 3) for virtual occlusal definition.
According to the sample size calculation, assuming a desired power of 0.95, type I error rate ( α ) of 0.05, and an effect size of 0.5, 60 volunteers (30 female and 30 male) were required for this study. The inclusion criteria were the following: (1) northern Han Chinese ethnicity; (2) age between 18 and 27 years; (3) class I incisor relationship with overjet and overbite between 1 and 4 mm; and (4) Angle class I molar relationship. The exclusion criteria were as follows: (1) previous tooth loss or restorations; (2) obvious tooth torsion and uneven tooth length; (3) a history of orthodontic treatment; (4) severe caries with complete destruction of the occlusal surface; (5) obvious dental crowding; and (5) periodontal problems, such as gingival recession or periodontitis.
Impressions of the upper and lower jaws were recorded using silicon impression materials (Silagum-Putty Light; DMG, Hamburg, Germany) and were subsequently poured with super hard plaster (Labstone; Heraeus, Hanau, Germany) to fabricate dental casts. Digital dental models of the upper and lower dentitions were obtained using a 3D photo-optical scanner (Smart Optics/Activity 102; Model-Tray GmbH, Hamburg, Germany) with a resolution of 0.1 mm. Data were saved in stereolithography (STL) format.
The relationship between the upper and lower plaster casts was identified manually by one prosthodontist, fixed using silicone resin (O-Bite; DMG), and then digitized using a double scanning protocol with the same 3D scanner. The position of the upper dentition was set as the gold standard. Thirty-seven pairs of corresponding marker points were identified manually by users on each tooth and all the co-ordinate parameters were saved for reference ( Fig. 4 , upper row). The relationship between the upper and lower dentitions was then disturbed ( Fig. 4 , middle row) for purposes of the validation test. Users adjusted the upper jaw to achieve an optimized occlusion by following the virtual workflow ( Fig. 4 , lower row). When a user established an optimal occlusion, the position of the upper dentition was set as the test position. All the feature points were aligned with the upper jaw during the adjustment, so the difference between the gold standard and the test positions could be analyzed by the movement of feature points.
Errors were defined as the three-dimensional distance between the same feature point on the gold standard upper jaw ( x 1 ) and the user-adjusted upper jaw ( x 2 ). This was measured as the distance between the original co-ordinate parameters ( x 1 , y 1 , z 1 ) and the final co-ordinate parameters ( x 2 , y 2 , z 2 ) of the same marker point. No superimposition was necessary. The distance between x 1 and x 2 was calculated using the equation: <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='D=(x1−x2)2+(y1−y2)2+(z1−z2)2′>D=(x1−x2)2+(y1−y2)2+(z1−z2)2−−−−−−−−−−−−−−−−−−−−−−−−−−−√D=(x1−x2)2+(y1−y2)2+(z1−z2)2
D = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 + ( z 1 − z 2 ) 2
. Given that there were multiple points on each tooth, the average error for each tooth was calculated as: <SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='Δ=∑1nD/n’>Δ=∑n1D/nΔ=∑1nD/n
Δ = ∑ 1 n D / n
Test 1: Reproducibility test for the procedure of manually identifying marker points
Thirty of the 60 models were selected randomly for reproducibility testing. One investigator identified the marker points three times each on all 30 models, with a minimum interval of 24 h between markings. In addition, three individual investigators identified the marker points once on all 30 models. Inter- and intra-observer correlation coefficient tests were performed to check the reliability of the procedure.
Test 2: Accuracy test for the virtual occlusal definition
A single researcher established virtual occlusion in all 60 models. Descriptive statistics were used to investigate the error between the test and the gold standard positions. One-way analysis of variance (ANOVA) was performed to examine if the error was different between different teeth. An error of up to 1 mm was considered as the limit of tolerance for final occlusion. Errors above 1 mm were compared with t -tests.
Test 3: Reproducibility test for virtual occlusal definition by different users
Thirty of the 60 models were selected randomly for reproducibility testing. Three researchers independently established virtual occlusions in the 30 models. One-way ANOVA was performed to determine whether the positions set by different users were significantly different from each other.
For all the comparisons, P < 0.05 was considered statistically significant.