A macro photogrametric method for precise

MACRO PHOTOGRAMETRY IN ORTHODONTICS Biological Mechanisms of Tooth Movement and Craniofacial Adaptation Edited by Z. Davidovitch and J. Mah, pages 149-158 © 2004 Harvard Society for the Advancement of Orthodontics, Boston, Massachusetts, USA

A macro photogrametric method for precise measurements of long term tooth movement during canine retraction with the Hybrid Retractor Martin Geiger, Christina Dorow, Gert Brauchle, Franz G. Sander Department of Orthodontics, University of Ulm, Germany Key words: Orthodontic Tooth Movement, Canine Retraction, Optical, Macro Photogrametry, In Vivo Measurement, Three-Dimensions, Translations, Rotations, Tooth Movement Rate, Computer-Aided Tomography

Summary

previously published. The small magnitudes of translation and rotation of the tooth were calculated and plotted as functions of time. The canines were distalized bodily, without tipping 4 mm and 8 mm, respectively, within 103 days. The rate of orthodontic tooth movement was found to be in the range of 0.5 mm and 2.5 mm per month. A maximum intra-individual ratio in the tooth movement rate of 4:1 after two months of treatment was evaluated. Further, the photogrametric coordinates allowed us to visualize the characteristics of the dentition and of the tooth movement in three-dimensions.

The aim of this clinical study is to measure in vivo the small three-dimensional translations and rotations the tooth executes under the action of orthodontic appliances. The three-dimensional data were used for the discussion of the long distance tooth movement in the case of canine retraction. We used the three-dimensional optical method of macro photogrametry. In clinical practice, a digital camera was used to take the photos of oral situations. With help of the identified landmarks, software then calculated from a number of the two-dimensional photos three-dimensional coordinates of object points and translations and rotations relative to the initial tooth position. Orthodontic tooth movements induced by the compound super elastic canine retraction spring Hybrid Retractor were recorded precisely and calculated in three dimensions. We measured the canine retraction of two upper canines. Due to the fixed distance of the durable landmarks on the brackets relative to the teeth, the accuracy was superior to the accuracy of other methods

Introduction

Modern orthodontics requires not only the qualitative evaluation of clinical treatment results, but also the exact quantitative measurement of the tooth movement. Small magnitudes of movement of the crown can result in large unwanted movements of the tooth root. These have to be quantified and in the case of significant unwanted side effects, the appliance needs correction for best treatment results. A well suited measurement method has to satisfy

Address Correspondence to: Dr. Martin Geiger, University of Ulm, Department of Orthodontics, D-89081 Ulm, Germany; Email: martin.geiger@ medizin.uni-ulm.de

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GEIGER, MARTIN; DOROW, CHRISTINA; BRAUCHLE, GERT; FRANZ G., SANDER

Fig. 1 Aligned Inside the frame, from left to right, are the marked molar tube attachments, the premolar bracket and the vertical slot bracket (Mini-Mono, Forestadent, Germany) for the canine. These macro photogrametric objects were modified for the macro photogrametry. The brackets are surrounded by the scaling frame (Geiger et al., 2000). The scaling frame is manufactured very precisely by CNC-milling machines and is made of stainless steel. The equidistant durable markers of the control points are CNC-laser marked. The dimensions of the frame in the image plane are 25 mm by 45 mm. The dimension in the depth of the image is achieved by the visible step of 0.5 mm along the outline. The frame is temporarily fixed to the ligated archwire in the patients jaw via specific removable brackets (Mobi-lock, Forestadent, Germany) which are connected to the frame with casted bars.

Fig. 2 Zoomed view of the marked vertical slot bracket (Mini-Mono, Forestadent, Germany) for the canine. On each of the bracket wings, the laser marked photogrametric landmarks can be seen. The intertick distance of the visible ruler is 0.5 mm.

the following requirements: optical high resolution in all dimensions separation of translation and rotation magnitudes minimum of recording time no negative effect on the patients oral health documentation of the treatment history in the frame of the regular appointments automation as far as possible. This study follows on from earlier studies quantifying the patients oral situation by means of X-ray 3-D photogrametry (Sander and Sitzmann, 1987). For an in vivo method presented earlier by Droschl et al. (1992), small metal segments with calibrated holes attached to the brackets or tubes were used. The distances between the segments and the reference teeth were measured by an electronic sliding caliper. The small orthodontic translations and rotations were calculated using custom software. Instead of using a sliding caliper, Fischer-Brandies

Fig. 3 Schematic view of the object points of the teeth in the upper left quadrant. Tooth 23 is the retracted canine, teeth 25 and 26 are used as reference and blocked for maximum anchorage. The schematic view is from the buccal, showing the orthodontic brackets and tubes, bonded to the teeth, with 4 durable markers on each as object points (b1, ..., b4 and r1, ..., r8). The points (101, ..., 410) surrounding the teeth are the control points on the scaling frame, their coordinates are known to the software with high accuracy. The directions of the x-, y-, and z-axes define the local coordinate system originated in the center of the bracket base of canine 23. The distal-mesial oriented x-axis describes the main direction of the retraction and the z-axis can describe an eventually performed intrusion or extrusion of the canine. The buccal-lingual movement is recorded by the y-axis. Further definde are the rotational- (around the z-axis), tipping- (around the y-axis) and torquing-movement (around the x-axis).

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et al. (1996) used small removable marked metal segments also temporarily attached to the brackets or tubes. They acquired digital intraoral images and identified the markers using custom software that also calculated the translations and rotations. This procedure is in use for the orthodontic wire bending robot Bending Art System for the calculation of the parameters for the bending of stainless steel archwires for fixed orthodontic appliances. The Orthodontic tooth movement was also measured in three dimensions with a three-axis measuring microscope and a series of dental casts by Iwasaki et al. (2000), to demonstrate the pattern of the lag phase of tooth movement, and determine its dependence on the characteristics of the retraction force. This current study presents a faster and more precise method of measuring canine retraction in orthodontics in vivo in three dimensions. It is based on the method of macro photogrametry which was first applied in orthodontics for the measurement of molar uprighting (Geiger et al., 2000). The three-dimensional evaluation of orthodontic tooth movement was used for the design of novel orthodontic devices. This concept has been published earlier in general (Schneider et al., 2001) and in detail, as related to the Hybrid Retractor (Sander, 2000).

manufacturer (Forestadent, Germany). To reconstruct 3-D objects from 2-D images the minimum number of necessary images is two. In our study we obtained more photos (approx. six) for a numerical adjustment of the bundles of light rays to reduce the error caused by the manual identification of the points. The rays virtually connect object point (3-D) and image point (2-D) on the CCD-chip of the camera. Each object point was reconstructed by triangulation of at least two rays from the image to the object point. In this study we intended not to move the molar and 2nd bicuspid which were used as reference teeth. Theese teeth were fixed with a Nance-appliance for maximum anchorage. To achieve the required accuracy, a 3-D scaling frame (Fig. 1), with a number of 3-D control points (Fig. 3) with coordinates known to the software, had to be inserted into the patients mouth, and connected with the archwire appliance for taking the photographs. This frame had to be fixed to the reference teeth for a photographic session. However, in subsequent clinical sessions, the frame was fixed relative to the reference teeth in another location. Fig. 3 explains the typical situation in which the canine to be moved was identified by the 4 points b1 - b4. The reference teeth were identified by the 8 points r1 - r8. The scaling frame was identified by the remaining 40 points named 101 - 410. The 2-D image coordinates of these points were all the information the software had available to calculate the photogrametric 3-D coordinates of one epoque. The origin of the x-,y- and z-axis of our coordinate system was depicted. All translations and rotations were calculated corresponding to this origin. We changed the coordinate system from an orientation according to the base of the bracket of the tooth to be moved (Geiger et al., 2001) to a new orientation parallel to the characteristics of the jaw median, the molar width and the occlusal plane (Fig. 4). The origin of each local coordinate system was located in the center of the vertical slot bracket basis. The x-axis (distal-mesial) was oriented parallel to the median, the y-axis (buccal-lingual) was oriented parallel to the connection line between the centers of the two first molar attachments, perpendicular to the x-axis. The z-axis (cervical-coronal) was perpendicular to the x-and y-axis, directed coronally. In translations, the torque was centred around the x-axis, the tip around the y-axis and the rotation of the canines around the z-axis. The distalisation magnitude was represented by a negative

Materials and Methods:

For the three-dimensional evaluation of orthodontic tooth movement we used the optical method of macro photogrametry (Geiger et al., 2000; Geiger et al., 2001). Photographs were obtained during regular orthodontic appointments using a Kodak DCS460 digital camera. In this study we measured and calculated the successfully performed distalisation of canine teeth of a 13 year old boy. The superposition of CT-Data and macrophotogrametric coordinates for visualization was carried out for the distalisation of canine teeth of a 15 year old boy. In clinical practice, a digital SLR camera was used to obtain intra oral photogaphs. The chip in this camera of six mega pixels is capable of producing grey scale images for a smaller inter pixel distance compared to colour models. The brackets attached to the moved and to the reference teeth were marked in particular with durable points, called landmarks in classical photogrametry, for identification (Fig. 1 and Fig. 2). This marking was done during the production process at the 151 149-158.p65

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Fig. 4 Schematic diagram of the upper jaw to explain the origins and the orientation of the local coordinate systems used for the measurement of the translations and rotations of the retracted canines 13 and 23. The coordinate systems are the basis for the interpretation of the figures from 14 - 17 with the measurements. The typical in-out value of 20° shown for the retraction of canine 13, also applies to canine 23.

Fig. 5 The Hybrid Retractor spring (Sander, 2000) in situ. The stainless steel wire segment on the left side is inserted into a buccal tube attached to the molar and bent to stop sliding-out at the distal end. The step bending allows to adjust a small magnitude of intrusive force. Inside the cylinder on the right is a coil spring made of NiTialloy, which generates the retraction force. The green elastic prevents the release of this vertical segment.

Fig. 6 Detailed view of the torqued and bent vertical rectangular bar on the mesial side of the Hybrid Retractor which is also made of NiTi-alloy and produces counter-tip and counter-rotational moments. The distal rotation of this segment before the insertion into the vertical slot of the canine bracket is also shown. The small yellow polymer tube secures the length of this vertical bar.

orientation and location of the moved tooth. Further, it was now easy to compare our results with those of other methods (Iwasaki et al., 2000) which also use a global coordinate system as reference. From a number of 2-D photographs and with help of the identified image points, the computer software calculated first 3-D data of object points and second the data of translations and rotations of a tooth relative to its initial position. Clinical tooth movements using

x-coordinate, while extrusion was represented by a positive z-coordinate for both canines. For the right canine, a buccal movement was measured with a positive y-coordinate, and for the left canine, a buccal movement was measured with a negative y-coordinate. With this new orientation of the coordinate system, the interpretation of the translations and rotations of the tooth was independent of the pre-treatment 152 149-158.p65

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Fig. 7 The distalizing force of nearly constant 1 N produced by the Hybrid Retractor (in the configuration with a step-bending of 5mm (Fig. 5), i.e. no intrusive/extrusive force is generated) and measured along the retraction of the canine (Geiger et al., 2003). The retraction force had the largest magnitude and the unwanted transversal forces were negligible. Due to the super elastic property the magnitude of force is nearly constant over the main part of the distalisation.

Fig. 8 The moments produced by the Hybrid Retractor (in the same configuration as in Fig. 5) measured along the retraction of the canine (Geiger et al., 2003). The counter-tipping moment My is approx. 8 Nmm and the counter-rotation moment Mz is approx. 3 Nmm. The calculated ratios of My/Fx and of Mz/Fx are 8 mm and 3 mm. This ratio is well suited for a pure bodily translation of the canine.

Nmm and the counter rotation moment of 3 Nmm (Fig. 8) were generated by the bending and the torsion of this NiTi wire. Magnitudes of the counter moments depended on the configuration of the step bending (Sander, 2000) which was 5 mm in the presented case. The intended pure bodily movement of a canine implies low unwanted rotations and tippings of the moved tooth. Due to the retraction force and the high distance from the bracket to the centre of resistance of the root of the canine, the most critical component, is the tipping. Fig. 9 Panoramic radiograph of the dental and skeletal situation of the patient (a 13 year old boy) before the therapy. He had a skelettal class II malocclusion, with missing mandibular second bicuspids. The orthodontist decided to extract both maxillary first bicuspids, and to retract both maxillary canines using the Hybrid Retractor in a segmented archwire technique. Afterwards, the incisors were retracted.

Results

For a fundamental understanding of the case we used the conventional pre-treatment panoramic radiograph shown in Fig. 9. In addition to the calculated photogrametric coordinates, we were able to examine the grey scale oral photographs taken from the Kodak Digital Camera DCS460 in the ultra high resolution of six mega pixels. These phptographs served as the basis for the manual identification of the photogrametric landmarks and are shown in Fig. 10 (pre-) and in Fig. 11 (during-treatment) for the right canine, and in Fig. 12 (pre-) and in Fig. 13 (during-treatment) for the left canine. The time-dependency of the small magnitudes of translation and rotation of the tooth movement was reconstructed successfully and with high accuracy (Tab. 1). The magnitudes of the acting force system during

the super elastic NiTi canine retraction spring (the Hybrid Retractor [Sander, 2000; Sander et al., 2002) and (Fig. 5)] were acquired precisely and calculated in three dimensions. The construction of the Hybrid Retractor contains a super elastic coil spring in the small stainless steel cylinder and a super elastic vertical rectangular NiTi wire was attached to the cylinder (Fig. 6). The coil spring produced the retraction force of 1 N (Fig. 7). The counter tipping moment of 8 153 149-158.p65

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Fig. 10 Digital image showing the oral situation pre-treatment of the discussed case (maxillary right canine). The first bicuspid was extracted. The leveling archwire, which was ligated after the extraction is also visible. The photograph was taken immediately before the insertion of the Hybrid Retractor.

Fig. 11 Digital image recorded after 103 days of successful treatment of the maxillary right canine, using the ligated and activated Hybrid Retractor. The advantage of the segmented archwire technique is the control of the force system without any loss by friction. The distalising effect of the active Hybrid Retractor during the treatment is significant. The distance between the maxillary right canine and the lateral incisor has increased by 7.78 mm. The canine was distalized bodily and finished its retraction in the occlusal plane without any guidance by the archwire.

Fig. 12 This photographic image shows the upper left canine pre-treatment. The recording was taken at the same time as Fig. 8. The archwire, which is remaining from the leveling epoque, can be seen. Fig. 13 Image of the maxillary left canine, acquired after 103 days of treatment. A distalising effect of 4.73 mm bodily translation was measured for this canine. Only half of the distal movement of the maxillry right canine, shown in Fig. 9, was achieved. Due to the force system of the Hybrid Retractor (Figs. 5 and 6), no extrusion and no unwanted tipping occurred. The treatment for this tooth was not finished at this time, and was continued.

the distalisation are shown in Fig. 7 (distalizing force) and Fig. 8 (counter tipping- and counter rotation moments). They were acquired in the six-axes positioning and measuring system described by Geiger et al. (2003). Tooth movements of the distalized canines of the patient, measured in vivo, are plotted in Figs. 14 and 15 (translations of canine 13 and 23) and in Figs. 16 and 17 (rotations of canine 13 and 23). The measurements for the canine 13 recorded a bodily movement of -7.78 mm distalisation, accompanied by 6.12° of distal tipping and 11.02° of torque. The opposite canine, 23, showed a shorter bodily movement of -4.73 mm, together with negligible torque. The

tipping of the root was first mesially (-9.28° after 61 days) but later it was compensated to nearly zero degrees. The recordings were taken approx. every month for a maximum period of 103 days. We measured rotations of 29.26° for canine 13 (Fig. 16) and 20.50° for canine 23 (Fig. 17). From these rotations we had to subtract the immanent rotation 154

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Fig. 14 Magnitudes of translation of canine 13. The distalisation magnitude Tx increased nearly linearly over the treatment time, upto 7.78 mm. The smaller buccal movement Ty followed the shape of the mndibular dental arch. It increased up to 5.56 mm after 103 days of treatment. The canine nearly moved in the occlusal plane, which was recorded with the very small intrusion Tz of -0.36 mm.

Fig. 15 Magnitudes of translation of canine 23. The distalisation magnitude Tx first increased only to 1.4 mm (after 61 days) and reached 4.73 mm after 103 days. The smaller buccal movement Ty reached a value of 3.78 mm. The canine showed a very small extrusion Tz of 0.15 mm after 103 days.

Fig. 17 Magnitudes of rotation of canine 23. The rotation around the vertical tooth axis was 9.95° after 61 days, then decreased to nearly zero and in the end we found 20.50° after 103 days. The most important component, the distal tipping (Ry), was below 10° after 61 days and decreased finally to zero°. The torque of the canine was slightly buccal (2.02°) after 61 days and changed later to 1.41° of lingual torque after 103 days in the end.

Fig. 16 Magnitudes of rotation of canine 13. The distal tipping (Ry) was 3.25° at day 61 and increased to a moderate 6.12° in the end. The lingual torque of the canine achieved a value of 11.02° after 103 days. The magnitude of rotation around the vertical tooth axis was first 13.24° after 61 days, and 29.26° at the end of treatment.

(Fig. 4) of the canine retraction of approx. 20° as the in-out value. That means we calculated distal rotations of only 9.26° (canine 13) and 0.50° (canine 23). These moderate rotations are also visible in the corresponding Fig. 18. The distal tooth movement rate in mm per month (30 days) is shown in Fig. 19. Due to the superelastic characteristic of the Hybrid Retractor, the retraction force was 1 N over the retraction period (plus the constant counter tipping and counter rotation moments). The tooth movement rate of canine 13 was compared with that of canine 23. During the distalisation of canine 13, the rate started at 2.01 mm/month for the first

25 days. Towards the end of the study (103 days) it increased to 2.54 mm/month. On the other hand, canine 23 moved a shorter distance and slower , starting at 0.92 mm/month for the first 25 days, then it decreased to 0.52 mm/month. However, it finally reached a rate of 2.38 mm/month, nearly the rate of the contralateral canine. The macro photogrametry and the resulting threedimensional data allowed us the so-called registration, a superposition of the coordinates of the photogrametric method with the surface data of computer tomography (CT). This superposition was based on the quasi155

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GEIGER, MARTIN; DOROW, CHRISTINA; BRAUCHLE, GERT; FRANZ G., SANDER Table 1 Accuracy of object points in macro photogrametry. Standard deviations of the calculated coordinates of a typical macro photogrametric epoque. The mean value of the standard deviation in the image plane is below 40 microns in the horizontal and below 20 microns in the vertical direction. In depth the mean value of the standard deviation is below 60 microns. The maximum deviation for every object point is below 100 microns.

standard deviation sx standard deviation sy standard deviation sz

mean value (mm) 0,038 0,014 0,064

automatic workflow of individual model generation for the segmented teeth using CT data and finite element software, which was published by Clement et al. (2004).

max. deviation (mm) at object point 0,070 310 0,015 408 0,100 310

of geometry and material properties. We measured rotations (Fig. 16 and Fig. 17) for both canines after the 103 days but Fig. 4 demonstrates that the canine has to follow the dental arch shape (determined by the mandibular or maxillary bone) during the retraction, and performs in the process an immanent rotation of about 20° against the second bicuspid and first molar. After the subtraction of this in-out value for the distal rotations, these canine rotations in our first patient were below 10° for canine 13 and nearly zero degrees for canine 23, suggesting that the unwanted distal rotations were very low. Due to the fixed position of the registration markers on the teeth, and the reduction of the error by the calculation of the three dimensional coordinates from about six images, the mean value of the accuracy is 0.06 mm in depth, or 0.04 mm in the image plane (Table 1). This degree of accuracy is superior to that of other methods for measuring tooth movement with small marked removable attachments inserted into the bracket slot. Droschl et al. (1992) reported a maximum error of 0.3 mm and a standard deviation of 0.08 mm. These attachments also have the risk of aspiration during the photographic session. Our higher accuracy is accompanied by faster processing during the check-up session, since we do not have to manufacture dental casts. It took a few minutes for the fixation of the 3-D scaling frame to the archwire appliance and the following recording of the photographic images per moved tooth. The manual identification of the landmarks in the grey scale images and the software supported calculation of the three-dimensional object points with commercially available software took approx. 60 minutes per epoque. The requirement for the reference teeth is a maximum anchorage. These should not be moved during orthodontic treatment. Depending on the case, the anchorage has to be reinforced by an additional fixed appliance, e.g. a

Discussion

The presented method, with its time-dependent visualization of all magnitudes of movement, allows for the more detailed and more precise verification of the results of our clinical studies in orthodontics in all the components of translations and rotations. These results suggest that macro photogrametric measurements should be the input for an adjustment of the Hybrid Retractor during routine clinical check-up sessions. The group of Iwasaki (Iwasaki et al., 2000) measured an average tooth movement rate of 1.27 mm/28 days under an average load of 0.60 N. This value is in the lower range (due to the lower distalizing force they used), compared with our measurements between 0.52 and 2.54 mm/month in the same patient. We calculated a maximum intra-individual ratio of the tooth movement rates of 4:1 after 61 days for the same subject. The inter-individual tooth movement rate in the study of Iwasaki et al. (2000) varied as much as 3:1 even with equivalent loading conditions. Bourauel et al. (1999) simulated the orthodontic tooth movement for 5 patients using the finite element method with a schematic model of the canines and linear elastic material properties. One result was approx. 5 % deviation between the simulation, which was based on the same schematic geometry model for all the patients, and the clinical measurements of the individuals. Our results of the high clinical measured intra-individual variation of the tooth movement rate of 4 to 1 and the results of Iwasaki et al. (2000) with an inter-individual variation of 3 to 1 suggest that these simulations have to be performed with more realistic individual models 156 149-158.p65

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Fig. 19 Tooth movement rate illustrated by the change of the main distalisation component Tx of the tooth movement over time. The graph shows a comparison of the tooth movement rate of canine 13 to canine 23. We found a rate of 2.01 mm/month (for canine 13) after one month of action of the Hybrid Retractor. The rate increased a little up to 2.54 mm/month. Canine 23 showed a significantly lower rate (0.92 mm/month) in the beginning, decreasing to 0.53 mm/month. After 103 days, however, we recorded 2.38 mm/month, which is nearly the same rate as the movement rate of canine 13.

Fig. 18 Perspective view of the 3D reconstruction with photogrametric object points of the entire maxilla. It was realized by the numerical superposition of two separately calculated sets of 3D object points of each side of the jaw. This allowed the proper orientation of the coordinate system according to the characteristics of the individual jaw (median and molar width). The numbers denote the notation of the teeth. The origins of the two coordinate systems of the teeth 13 and 23 are located in the pre-treatment position (transparent teeth 13 and 23), they moved distally towards the posttreatment position (solid teeth 13 and 23) in 4 monthly intervals.

long-term tooth movement, including the lag phase (Iwasaki et al., 2000), a new clinical study should start with a one day interval between the photographic sessions during the first 10 days of treatment, and with intervals between check-up appointments shorter than a month. This scheme will, however, require a high level of cooperation by the patients. The finite element software ANSYS(r), used in this experiment, allowed us the visualization not only of the crowns, but also the location and orientation of the roots of individual human teeth. The finite element simulations of bone remodeling in our department can also be verified by means of the acquired reliable photogrametric position parameters. As mentioned earlier, the identification of the photogrametric landmarks in the images is performed manually. The contrast of the first series of marked brackets and of the scaling frame (Figs. 1 and 2) is not suitable for the automatic image processing feature built into the software. For this reason we developed opaque white coated brackets and scaling frames with a significant improvement in the contrast around the black landmarks (Fig. 20).

Nance holding arch and a headgear or an orthodontic implant. This efficient measurement system provides a substantial contribution to the functional optimization of orthodontic devices. The advantage of the presented optical method compared to the previously used method of X-ray 3-D photogrametry (Sander and Sitzmann, 1987) is that the patient does not need to be exposed to x-rays. The X-ray 3-D photogrametry, however, allowed the operator to acquire coordinates of all rendered skeletal or dental points, whereas the optical macro photogrametry only allowed measurement of the location of objects marked with landmarks or durable points, but with very high accuracy. Assuming that we had recorded an adequate number of intra-oral photographs at the beginning of the treatment, and that we have identified the proper landmarks, we then can calculate a superposition of both sides of the jaw, to study the perspective view of the entire maxilla (Fig. 18) for diagnosis of the position of the teeth. Furthermore, this entire jaw model can serve as the basis for the orientation of the coordinate system (see also Fig. 4). To investigate the initial phase of the orthodontic

Acknowledgements

The study was funded by the German Research Foundation (contract number: SA 272/1-2). Their 157

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zur Gewinnung von Lageparametern für die FE-Rechnung. Die Methode der Finiten Elemente in der Biomechanik, Biomedizin und angrenzenden Gebieten, Universit ät Ulm, ISBN 3-9806183-3-1, 121-134. Geiger M., Schneider J., Sander F.G., (2001) Precise 3-dimensional in vivo measuring of orthodontic long-term tooth movement using digital photogrametry, Computer Methods in Biomechanics & Biomedical Engineering -4, Edited by J. Middleton, N. G. Shrive and M. L. Jones, Published by University of Wales College of Medicine. Geiger M., Schneider J., Sander F.G., (2003) Finite element calculation of bone remodeling on orthodontics by using forces and moments, Journal of Mechanics in Medicine and Biology, 3: 1-12. Iwasaki L.R., Haack J.E., Nickel J.C., Morton J., (2000) Human tooth movement in response to continuous stress of low magnitude, American Journal of Orthodontics and Dentofacial Orthopedics, 117: 175-183. Sander Ch., Geiger M., Sander F.G., (2002), Contactless Measurement of Canine Retraction by Digital Macrophotogrametry during Hybrid Retractor Application, J Orofac Orthop/Fortschr Kieferorthop, 63: 472-82. Sander, F. G., (2000) Biomechanical Investigation of the Hybrid Retraction Spring, J Orofac Orthop, 61: 341-351. Sander, F. G., Sitzmann, F., (1987) RÖntgenstereophotogrammetrie zur Diagnostik im Kiefer-Gesichtsschädel, Jahrbuch Fortschr. Kiefer-Gesichtschirurgie, Thieme Verlag Stuttgart, New-York, Bd. XXXII, 20-24. Schneider J., Geiger M., Clement R., Sander F.G., (2001) Konzept zur Entwicklung neuer individueller Behandlungselemente in der Kieferorthopädie mit Hilfe dreidimensionaler numerischer Simulation zum Knochenumbau, Biomed Tech, 46: 207-213.

Fig. 20 Another series of macro photogrametric objects, consisting of a smaller scaling frame and a bracket, which are coated opaque white to obtain optimum contrast in the digital images. The frame is temporarily fixed to the ligated archwire in the patients jaw by two brackets and stainless steel or elastic ligatures.

support is greatly appreciated. The authors would like to thank Mrs Gabriele Wachter for her help in the design of the illustrations.

References

Bourauel C., Freudenreich D., Vollmer D., Kobe D., Drescher D., Jäger A., (1999) Simulation of Orthodontic Tooth Movements, J Orofac Orthop/ Fortschr. Kieferorthop, 60: 136-151. Clement R., Schneider J., Brambs H.-J., Wunderlich A., Geiger M., Sander F.G., (2004) Quasiautomatic 3D finite element model generation for individual single-rooted teeth and periodontal ligament, Comp Meth Prog Bio, 73: 135-144. Droschl H., Bantleon H.P., Muchitsch A.P., Weiland F., (1992) Eine neue Methode zur quantitativen und qualitativen Messung von Zahnbewegungen, Fortschr Kieferorthop, 53: 11-15. Fischer-Brandies H., Orthuber W., Pohle L., Sellenrieck D., (1996) Bending and torquing accuracy of the bending art system (BAS), J Orofac Orthop, 57: 16-23. Geiger M., Schneider J., Sander F.G., (2000) Photogrammetrische Vermessung der kieferorthopädisch induzierten Zahnbewegung: Eine Methode

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