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.

Manual marking of the marker points. A total of 37 pairs of corresponding marker points are identified manually using a feature point-marking interface. These are the cusp and fossa points on each tooth.

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.

Software tool for virtual occlusal definition. (A) Motivation dialog box: the user can adjust the position of the upper dentition by typing parameters into the box. (B) Free-hand engine: the user can move or rotate the upper dentition along a single direction by dragging the axis or circles freely using the mouse. (C) Collision heat map: the vertical distances between the upper and the lower dentitions are shown on a colour map. (D) Distance projection view: vectors between corresponding points are projected onto the occlusal plane to demonstrate sagittal and transverse deviations. (E) Adjustment hint grid view: this includes seven single-direction automatic minor revision tools that are applied when the upper and lower dentitions are close to each other. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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 .

Workflow for virtual occlusion definition.

Validation tests

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.

Validation test for the accuracy of virtual occlusal definition. Upper row: Original relationship between the upper and lower dentitions. The colour heat map shows good contact and the vector projection view shows a symmetric corresponding relationship between the feature points. Middle row: The original relationship between the upper and lower dentitions is disturbed by moving the upper dentition. The visualization window shows an inappropriate correlation. The collision heat map is blue, indicating an increased vertical distance. The distance projection view shows markedly asymmetric vector distribution, indicating that the upper jaw is to the left of the lower jaw. Lower row: Virtual occlusal definition. The visualization window shows a normal relationship between each cusp and fossa. The collision heat map is green, indicating that the marker points are in contact with each other without colliding. The distance projection view shows bilateral symmetry in the length and direction of vectors. All illustrations for the virtual occlusal definition (lower row) are similar to those of the upper row. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Statistical analysis

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.