HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text Full Text (PDF) Electronic Appendix Services Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via ISI Web of Science (7) Citing Articles via Google Scholar Google Scholar Articles by DeLong, R. Articles by Douglas, W.H. Search for Related Content PubMed PubMed Citation Articles by DeLong, R. Articles by Douglas, W.H.

Helical Axis Errors Affect Computer-generated Occlusal Contacts

¹ Minnesota Dental Research Center for Biomaterials and Biomechanics, Department of Oral Science, University of Minnesota School of Dentistry, Moos Health Science Tower, 515 Delaware Street, SE, Minneapolis, MN 55455; and
² Division of Biostatistics and Oral Health Clinical Research Center, Department of Preventive Sciences, University of Minnesota;

View larger version (32K): [in a new window]   Figure 1. Experimental vs. standard helical axis parameters. (A) Diagram of the experimental and standard helical parameters. Experimental helical axis parameters are calculated from the digital image of the mandible at two locations, A and B, defined by the centric and eccentric interocclusal record images (Spoor and Veldpaus, 1980). The unit vector E defines the orientation of the helical axis. The angle between the experimental and standard helical axis unit vectors, E, was calculated with the use of a second unit vector, ÉExp that points in the same direction as EExp and originates from PStd. The vector P, which points from the origin to a point on a line defined by E, defines the position of the helical axis. Differences in the experimental and standard position vectors, P, were calculated indirectly as the minimum distance, d, between the two lines defined by the helical axes (Zwillinger, 1996), because the 3D distance between PExp and PStd is not necessarily the minimum distance between the lines. Equations for the difference calculations are shown in (A). Mean differences between experimental and standard helical axis parameters are shown in (B) through (E) as a function of jaw movement expressed as a rotation about the helical axis (n = 5; error bars representing the standard deviations are smaller than the data symbols). Qualitatively, the angle (B) and the distance (C) between the experimental and standard helical axes are similar to the helical axis error model predictions represented by the "best fit" dashed line (Spoor, 1984; Woltring et al., 1985; de Lange et al., 1990b). The differences between the experimental and standard rotations about the helical axis (D) and translations along the helical axis (E) are nearly constant, as predicted by the helical axis error model, and are smaller than the 0.040 mm accuracy of the Comet 100 scanner.

View larger version (46K): [in a new window]   Figure 2. Experimental vs. standard contact parameters. (A) Diagram of the differences between the experimental and standard contact parameters. Contacts are defined by three parameters: Area, Centroid, and Normal. Area is the 3D surface area of the contact. We calculated differences in areas, A, by subtracting the experimental from the standard contact areas. The location of the contact is defined by the centroid, C, which is the center-of-mass of the points in the contact. The contact location error, C, was the 3D distance between the experimental and standard centroids. The normal, N, defines the orientation of the contact. It is a unit vector that originates at the contact centroid, points away from the contact, and is perpendicular to a plane that is tangent to the surface at the contact centroid. The angle between the experimental and standard contact Normals, N, was calculated by means of a second unit vector, N'Exp that points in the same direction as NExp and originates from CStd. Because it is possible to have non-identical contacts with identical centroids, areas, and normals, a fourth parameter, Overlap, was defined. Overlap was the average of the overlap of the two contact areas, O, divided by the two areas, expressed as a percentage. Equations for the differences in parameters and the overlap are shown in (A). See the Appendix for a more detailed description of the calculation of the contact parameters (www.dentalresearch.org). Mean differences between the experimental and standard contact parameters and the area overlap are shown in (B) through (E) as a function of the jaw movement used to calculate the helical axis parameters. The means represent the average over all contacts and 5 repeated measures (n = 5 times the number of contacts). The total number of contacts for the standard helical axis was 7. At 0.1°, 0.2°, 0.3°, and 0.4° jaw rotations, 1, 2, 6, and 8 contacts were averaged, respectively. The 7 "correct" contacts were averaged for the remaining jaw rotations. Error bars represent the standard deviations. All contacts were calculated for a mandibular rotation of 2.3° from maximum intercuspation based on the appropriate helical axis set. Contact parameter differences show a dependence on jaw position similar to that of the helical axis parameters (dashed line). Differences in the contact parameters with the use of helical axes calculated from jaw movements of 1.5° and larger were not significantly different (p > 0.05).

View larger version (85K): [in a new window]   Figure 3. Effects of helical axis parameters on contact shape. Occlusal contacts are shown for a 2.3° rotation of the mandible from maximum intercuspation based on the standard helical axis parameters and helical axis parameters calculated from 0.5°, 0.7°, 1.0° and 1.5° of jaw rotation. We calculated contacts by identifying the points on the aligned computer models of the maxillary and mandibular casts that were within 0.050 mm of each other. Contacts are shown as black regions on the occlusal surfaces of the teeth, and are identified by the black ovals on the full-arch standard image. Seven contacts were identified for the standard helical axis alignment of the casts. Visually, there is little difference between the contacts for the helical axis parameters calculated from 0.7° and larger jaw rotations.