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Dentition planning for image-guided implantology
International Congress Series 1268 (2004) 1168 – 1173
www.ics-elsevier.com
Dentition planning for image-guided implantology Ferenc Pongra´cz a,*, Zolta´n Ba´rdosi a, La´szlo´ Szabo´ b a
Research Division, Computer and Automation Research Institute, Zerind Vezer ut 29 B, Budapest H-1029, Hungary b AlbaDent Kft., Kecskemet, Hungary
Abstract. An interactive software module has been developed which can be used for 3D alignment of a graphical model of upper and lower dental arches. Using this module, special tools have been implemented for functional planning of dentition which can be compared to the CT image sequence of patients to create personalized results. The alignment procedure is made under the condition of centric occlusion, i.e., after bringing occlusal surfaces of mandibular and opposing maxillary arches into identical 3D position. The occlusal surfaces are approximated by triangles and used to build up the dentition curves around them. The presented procedure for dentition planning together with the implant positioning may serve as a flexible tool for image-guided prosthesis design. The involvement of function-related principles in dentition planning adds new optimization strategies in computer-assisted insertion of implants. D 2004 CARS and Elsevier B.V. All rights reserved. Keywords: Dentition planning; Centric occlusion; Occlusal triangles; Implant optimization
1. Introduction A variety of computerized analyses of lateral cephalographs is used to predict treatment change in different facial planes during dental surgery (Dentofacial Plannerk, OPALk, Quick Cephk, TIOPSk, etc. [1– 3]). These softwares enable simulation of different surgical jaw movements and illustrates these changes in terms of quantitative values and a jaw/profile silhouette (based on estimated hard – soft tissue ratios). However, a common problem with these softwares is how to find a way to test their validity and to analyse soft tissue/profile prediction errors and surgical accuracy. This concerns the fact that the observed anatomical landmarks are based on 2D radiographs and are only indirectly related to the optimal 3D occlusal surface between the maxillary and mandibular anatomies. Consequently, the diagnosing, correcting, and preventing irregularities of the teeth and poor occlusion still evoke a need for new approaches. Our article presents a novel procedure based on the functional planning of dentition. This is performed with graphical models of maxilla and mandibula which are viewed together with the volumetric model of patient’s CT data. Different mathematical tools have been * Corresponding author. Tel./fax: +36-1-275-8615. E-mail address: [email protected] (F. Pongra´cz). 0531-5131/ D 2004 CARS and Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2004.03.040
F. Pongra´cz et al. / International Congress Series 1268 (2004) 1168–1173
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developed for maintaining the conditions of centric occlusion and synchronizing the global movement of occlusal triangles to the local changes of dentition curves and single tooth’s position/orientation. The first implementation of this procedure was tested as an optimization module in a CT-based, image-guided implant planning software (ARTMA Virtual Implant Systemk). 2. Methods 2.1. Data acquisition and display The patient data are read in from a CT sequence, stored on a 3D grid as a volumetric model, and viewed together with the dentition model. CT scan axial acquisition is made by GE Medical System CT in HiSpeed mode (1-mm-slice thickness and slice step, 0.44 pixel size, 150 mA, 1 s exposure, 512 512 matrix, FOV 15 cm) and Philips CT Secura (1 mm/
Fig. 1. (A) Occlusal triangle in the upper dental arch with the full sequence of teeth on left side. The vertices of the occlusal plane are aligned in 3D with the relevant anatomical locations on patient’s CT. The tomographic background was removed for easier understanding. (B) Same arrangement for the lower dental arch. Both views show the opposite teeth sequence after projecting with the 4 4 locking matrix and its inverse. (C and D) Upper contours show the alignment of axis of the first molar of the selected maxillary part in the tangent and normal planes of the dental curve, respectively. Lower contours represent the related views of the opposing tooth in mandibula.
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0.25 mm slice step/pixel size, 100 mA, 2 s exposure, 512 512, FOV 12.8 cm). Depth interpolation along the z-axis of the volumetric model is included for better resolution in some cases during the read in of DICOM data. The crown contours and default positions of each tooth are stored in a text file and read in during initialization. A divided axial view is created which displays the original and mirrored volumetric models of patient’s data according to the permanent arch terminology [4]. 2.2. Forcing centric occlusion during data manipulation in 3D The key element of the procedure is the representation of the occlusal plane on the views of opposing maxillar and mandibular arches. The curved occlusal plane is approximated by a triangle connecting the median point between the central incisors with the middle surface points of first molars on the left/right sides. Different 3D reference systems are attached to the occlusal triangles set in the CT view of patient’s upper and lower dental arches. Reshaping and 3D alignment of occlusal triangles and the related coordinate systems can be done on the upper and lower arches in a locked (registered) mode of centric occlusion, i.e., by continuous update of the projection matrix between the
Fig. 2. (A) Setting occlusal vertex in the upper dental arch at the median point between the central incisors. The other two vertices are positioned similarly on the surface of the first molars. The same goes for the occlusal points of lower arch in opposing view. The program automatically projects in 3D all related dental elements to the reference space of the opposing occlusal plane. (B and C) Direct surface reconstruction of the jaw with occlusal triangle and the preselected virtual teeth data for upper and lower dental arches.
F. Pongra´cz et al. / International Congress Series 1268 (2004) 1168–1173
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maxilla and mandibula. This matrix is nonorthogonal and is calculated by a simple generalization of the known direct linear transformation (DLT) method originally developed for registration between 3D and 2D spaces [5– 7]. The method is also supported by a least-square matrix inversion procedure with known singular value decomposition (SVD) algorithm [8]. This approach assures stable computational results even if extreme localization of opposing occlusal planes is made on the patient’s CT (Fig. 1A,B). 2.3. Occlusal plane versus local changes in dental curves Positions of each tooth on left and right dentition curves are connected by 3D cubic splines [9]. Two control points on these splines are moved together with the related central and side vertices of the occlusal plane. These dentition splines (altogether 4) are reshaped by displacement of not only the vertices of occlusal triangles but single tooth as well. According to the spline mechanics, any local change modifies the overall shape of a spline. This approach guarantees (at least mathematically) that the 3D sequence of teeth was functionally related to any change in occlusal surface and local displacements as well. The local alignment in spline tangent was made visible on virtual teeths’ orientations. After locking occlusal triangles by projection matrix, teeth positions can be displayed together with the opposing maxillary or mandibular teeth contours.
Fig. 3. (A and B) Setting occlusal triangles and the virtual dentitions in the upper and lower dental arches, respectively. They are related to each other by the locking matrix. (C) Implant alignment visualized in relation to the maxillary model of dental arch. (D) Dentition model for the mandibula.
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Local alignment of each tooth is possible on separate panels for mesiodistal and faciolingual inclinations which are related to the actual tangent and normal planes of the dental spline curve (Fig. 1C,D). Simple graphical interface is used for adding/removing a given tooth to/from the dentition curve or creating specific grouping. OpenGl view, summarizing the results in a 3D scene, is added which contains the iso-surface model of patient’s jaw and the aligned dentition model. 2.4. Visualization The tomographic view consists of twinned views displaying original and mirrored volumetric models of patient’s data and the virtual dental curves (Fig. 2A). Center scrolling, slice advance, and zooming are synchronized for the twinned views. The results of 3D localization of occlusal triangle and the virtual dental sequence are displayed within a 3D scene containing the transparent view of the iso-surface of the jaw (Fig. 2B,C). 3. Results The proposed planning procedure of dentition has been used in a program for virtual implant positioning. The functionally optimized 3D location of crown sequence was made visible in panels for implant positioning. After the initial build up of the graphical model of dentition, the implant’s position/orientation was adjusted according to the best relationship to the crown location (Fig. 3). In special cases, the optimal 3D alignment of a virtual dental element was modified according to the anatomical limits of the possible position of implant. This was made possible by local offsetting/rotation of selected individual crown contours. The selection of any single element or groups of teeth was made easier by help of a simple graphical interface. 4. Conclusions The program automatically projects all related dental elements to the reference space of the opposing occlusal plane in 3D. This relationship is identical to the condition of centric occlusion which is hard to reach in vivo during malfunction of patient’s occlusal mechanism or other anatomical defects. The accurate planning of dentition is important in maintaining stable functional forces, minimizing the effects of occlusal wear, etc. The use of function-related principles in dentition planning adds new optimization strategies in computer-assisted insertion of implants. The procedure starts during initialization by reading in default positions of the occlusal vertices and teeth located on an idealized dental arch. These data are stored in a text file which can be easily modified according to specific needs. The occlusal surfaces are approximated by triangles and used to build up the dentition curves around them. The teeth sequence is controlled by spline curves which convert local changes into a change distributed smoothly on the whole dental curve. Adjustment of mesiodistal and faciolingual inclinations of a model of individual tooth is possible on separate enlarged views. The results are viewable in a 3D window displaying surface-rendered model of patient’s jaw and localized implants.
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Acknowledgements The first author thanks to Prof. R. Slavicek (Rudolfinerhaus, Vienna) for focusing our attention to the problem of 3D dentition planning and Dr. M. Truppe (MEDLIBRE, Mu¨nchen) for useful comments. References [1] R.R.J. Cousley, E. Grant, J.D. Kindelan, The validity of computerized orthognathic predictions, J. Orthod. 30 (2003) 149 – 154. [2] M. Harris, I.R. Reynolds, Cephalometric analysis, Fundamentals of Orthognathic Surgery, WB Saunders, London, 1991, pp. 38 – 48. [3] P.A. Aharon, S. Eisig, G.J. Cisneros, Surgical prediction reliability: a comparison of two computer software systems, Int. J. Adult. Orthod. Orthognath. Surg. 12 (1997) 65 – 78. [4] M. Massler, I. Schour, Atlas of the Mouth, American Dental Association, Chicago, 1958. [5] Y.I. Abdel-Aziz, H.M. Karara, Direct linear transformation from comparator coordinates into object – space coordinates, Proc. ASP/UI Symp. on Close-Range Photogrammetry, Urbana, IL, 1971, pp. 1 – 18. [6] M.E. Bowman, A.K. Forrest, Transformation calibration of a camera mounted on a robot, Image Vis. Comput. 5 (4) (1987) 261 – 266. [7] G.A. Wood, R.N. Marshall, The accuracy of DLT extrapolation in three-dimensional film analysis, J. Biomechanics 19 (9) (1986) 781 – 785. [8] W.H. Press, et al., Numerical Recipes in C. The Art of Scientific Computing, Cambridge Univ. Press, Cambridge, 1992. [9] D.F. Rogers, J.A. Adams, Mathematical Elements for Computer Graphics, Second edition, McGraw Hill, Boston, 1990.
www.ics-elsevier.com
Dentition planning for image-guided implantology Ferenc Pongra´cz a,*, Zolta´n Ba´rdosi a, La´szlo´ Szabo´ b a
Research Division, Computer and Automation Research Institute, Zerind Vezer ut 29 B, Budapest H-1029, Hungary b AlbaDent Kft., Kecskemet, Hungary
Abstract. An interactive software module has been developed which can be used for 3D alignment of a graphical model of upper and lower dental arches. Using this module, special tools have been implemented for functional planning of dentition which can be compared to the CT image sequence of patients to create personalized results. The alignment procedure is made under the condition of centric occlusion, i.e., after bringing occlusal surfaces of mandibular and opposing maxillary arches into identical 3D position. The occlusal surfaces are approximated by triangles and used to build up the dentition curves around them. The presented procedure for dentition planning together with the implant positioning may serve as a flexible tool for image-guided prosthesis design. The involvement of function-related principles in dentition planning adds new optimization strategies in computer-assisted insertion of implants. D 2004 CARS and Elsevier B.V. All rights reserved. Keywords: Dentition planning; Centric occlusion; Occlusal triangles; Implant optimization
1. Introduction A variety of computerized analyses of lateral cephalographs is used to predict treatment change in different facial planes during dental surgery (Dentofacial Plannerk, OPALk, Quick Cephk, TIOPSk, etc. [1– 3]). These softwares enable simulation of different surgical jaw movements and illustrates these changes in terms of quantitative values and a jaw/profile silhouette (based on estimated hard – soft tissue ratios). However, a common problem with these softwares is how to find a way to test their validity and to analyse soft tissue/profile prediction errors and surgical accuracy. This concerns the fact that the observed anatomical landmarks are based on 2D radiographs and are only indirectly related to the optimal 3D occlusal surface between the maxillary and mandibular anatomies. Consequently, the diagnosing, correcting, and preventing irregularities of the teeth and poor occlusion still evoke a need for new approaches. Our article presents a novel procedure based on the functional planning of dentition. This is performed with graphical models of maxilla and mandibula which are viewed together with the volumetric model of patient’s CT data. Different mathematical tools have been * Corresponding author. Tel./fax: +36-1-275-8615. E-mail address: [email protected] (F. Pongra´cz). 0531-5131/ D 2004 CARS and Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2004.03.040
F. Pongra´cz et al. / International Congress Series 1268 (2004) 1168–1173
1169
developed for maintaining the conditions of centric occlusion and synchronizing the global movement of occlusal triangles to the local changes of dentition curves and single tooth’s position/orientation. The first implementation of this procedure was tested as an optimization module in a CT-based, image-guided implant planning software (ARTMA Virtual Implant Systemk). 2. Methods 2.1. Data acquisition and display The patient data are read in from a CT sequence, stored on a 3D grid as a volumetric model, and viewed together with the dentition model. CT scan axial acquisition is made by GE Medical System CT in HiSpeed mode (1-mm-slice thickness and slice step, 0.44 pixel size, 150 mA, 1 s exposure, 512 512 matrix, FOV 15 cm) and Philips CT Secura (1 mm/
Fig. 1. (A) Occlusal triangle in the upper dental arch with the full sequence of teeth on left side. The vertices of the occlusal plane are aligned in 3D with the relevant anatomical locations on patient’s CT. The tomographic background was removed for easier understanding. (B) Same arrangement for the lower dental arch. Both views show the opposite teeth sequence after projecting with the 4 4 locking matrix and its inverse. (C and D) Upper contours show the alignment of axis of the first molar of the selected maxillary part in the tangent and normal planes of the dental curve, respectively. Lower contours represent the related views of the opposing tooth in mandibula.
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0.25 mm slice step/pixel size, 100 mA, 2 s exposure, 512 512, FOV 12.8 cm). Depth interpolation along the z-axis of the volumetric model is included for better resolution in some cases during the read in of DICOM data. The crown contours and default positions of each tooth are stored in a text file and read in during initialization. A divided axial view is created which displays the original and mirrored volumetric models of patient’s data according to the permanent arch terminology [4]. 2.2. Forcing centric occlusion during data manipulation in 3D The key element of the procedure is the representation of the occlusal plane on the views of opposing maxillar and mandibular arches. The curved occlusal plane is approximated by a triangle connecting the median point between the central incisors with the middle surface points of first molars on the left/right sides. Different 3D reference systems are attached to the occlusal triangles set in the CT view of patient’s upper and lower dental arches. Reshaping and 3D alignment of occlusal triangles and the related coordinate systems can be done on the upper and lower arches in a locked (registered) mode of centric occlusion, i.e., by continuous update of the projection matrix between the
Fig. 2. (A) Setting occlusal vertex in the upper dental arch at the median point between the central incisors. The other two vertices are positioned similarly on the surface of the first molars. The same goes for the occlusal points of lower arch in opposing view. The program automatically projects in 3D all related dental elements to the reference space of the opposing occlusal plane. (B and C) Direct surface reconstruction of the jaw with occlusal triangle and the preselected virtual teeth data for upper and lower dental arches.
F. Pongra´cz et al. / International Congress Series 1268 (2004) 1168–1173
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maxilla and mandibula. This matrix is nonorthogonal and is calculated by a simple generalization of the known direct linear transformation (DLT) method originally developed for registration between 3D and 2D spaces [5– 7]. The method is also supported by a least-square matrix inversion procedure with known singular value decomposition (SVD) algorithm [8]. This approach assures stable computational results even if extreme localization of opposing occlusal planes is made on the patient’s CT (Fig. 1A,B). 2.3. Occlusal plane versus local changes in dental curves Positions of each tooth on left and right dentition curves are connected by 3D cubic splines [9]. Two control points on these splines are moved together with the related central and side vertices of the occlusal plane. These dentition splines (altogether 4) are reshaped by displacement of not only the vertices of occlusal triangles but single tooth as well. According to the spline mechanics, any local change modifies the overall shape of a spline. This approach guarantees (at least mathematically) that the 3D sequence of teeth was functionally related to any change in occlusal surface and local displacements as well. The local alignment in spline tangent was made visible on virtual teeths’ orientations. After locking occlusal triangles by projection matrix, teeth positions can be displayed together with the opposing maxillary or mandibular teeth contours.
Fig. 3. (A and B) Setting occlusal triangles and the virtual dentitions in the upper and lower dental arches, respectively. They are related to each other by the locking matrix. (C) Implant alignment visualized in relation to the maxillary model of dental arch. (D) Dentition model for the mandibula.
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Local alignment of each tooth is possible on separate panels for mesiodistal and faciolingual inclinations which are related to the actual tangent and normal planes of the dental spline curve (Fig. 1C,D). Simple graphical interface is used for adding/removing a given tooth to/from the dentition curve or creating specific grouping. OpenGl view, summarizing the results in a 3D scene, is added which contains the iso-surface model of patient’s jaw and the aligned dentition model. 2.4. Visualization The tomographic view consists of twinned views displaying original and mirrored volumetric models of patient’s data and the virtual dental curves (Fig. 2A). Center scrolling, slice advance, and zooming are synchronized for the twinned views. The results of 3D localization of occlusal triangle and the virtual dental sequence are displayed within a 3D scene containing the transparent view of the iso-surface of the jaw (Fig. 2B,C). 3. Results The proposed planning procedure of dentition has been used in a program for virtual implant positioning. The functionally optimized 3D location of crown sequence was made visible in panels for implant positioning. After the initial build up of the graphical model of dentition, the implant’s position/orientation was adjusted according to the best relationship to the crown location (Fig. 3). In special cases, the optimal 3D alignment of a virtual dental element was modified according to the anatomical limits of the possible position of implant. This was made possible by local offsetting/rotation of selected individual crown contours. The selection of any single element or groups of teeth was made easier by help of a simple graphical interface. 4. Conclusions The program automatically projects all related dental elements to the reference space of the opposing occlusal plane in 3D. This relationship is identical to the condition of centric occlusion which is hard to reach in vivo during malfunction of patient’s occlusal mechanism or other anatomical defects. The accurate planning of dentition is important in maintaining stable functional forces, minimizing the effects of occlusal wear, etc. The use of function-related principles in dentition planning adds new optimization strategies in computer-assisted insertion of implants. The procedure starts during initialization by reading in default positions of the occlusal vertices and teeth located on an idealized dental arch. These data are stored in a text file which can be easily modified according to specific needs. The occlusal surfaces are approximated by triangles and used to build up the dentition curves around them. The teeth sequence is controlled by spline curves which convert local changes into a change distributed smoothly on the whole dental curve. Adjustment of mesiodistal and faciolingual inclinations of a model of individual tooth is possible on separate enlarged views. The results are viewable in a 3D window displaying surface-rendered model of patient’s jaw and localized implants.
F. Pongra´cz et al. / International Congress Series 1268 (2004) 1168–1173
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Acknowledgements The first author thanks to Prof. R. Slavicek (Rudolfinerhaus, Vienna) for focusing our attention to the problem of 3D dentition planning and Dr. M. Truppe (MEDLIBRE, Mu¨nchen) for useful comments. References [1] R.R.J. Cousley, E. Grant, J.D. Kindelan, The validity of computerized orthognathic predictions, J. Orthod. 30 (2003) 149 – 154. [2] M. Harris, I.R. Reynolds, Cephalometric analysis, Fundamentals of Orthognathic Surgery, WB Saunders, London, 1991, pp. 38 – 48. [3] P.A. Aharon, S. Eisig, G.J. Cisneros, Surgical prediction reliability: a comparison of two computer software systems, Int. J. Adult. Orthod. Orthognath. Surg. 12 (1997) 65 – 78. [4] M. Massler, I. Schour, Atlas of the Mouth, American Dental Association, Chicago, 1958. [5] Y.I. Abdel-Aziz, H.M. Karara, Direct linear transformation from comparator coordinates into object – space coordinates, Proc. ASP/UI Symp. on Close-Range Photogrammetry, Urbana, IL, 1971, pp. 1 – 18. [6] M.E. Bowman, A.K. Forrest, Transformation calibration of a camera mounted on a robot, Image Vis. Comput. 5 (4) (1987) 261 – 266. [7] G.A. Wood, R.N. Marshall, The accuracy of DLT extrapolation in three-dimensional film analysis, J. Biomechanics 19 (9) (1986) 781 – 785. [8] W.H. Press, et al., Numerical Recipes in C. The Art of Scientific Computing, Cambridge Univ. Press, Cambridge, 1992. [9] D.F. Rogers, J.A. Adams, Mathematical Elements for Computer Graphics, Second edition, McGraw Hill, Boston, 1990.