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Journal of Orthodontics, Vol. 32, No. 4, 282-293, December 2005 doi:10.1179/146531205225021285
© 2005 British Orthodontic Society

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Current Products and Practice

Three-dimensional cone beam computerized tomography in orthodontics

C. H. Kau and S. Richmond

Department of Dental Health and Biological Sciences, Wales College of Medicine, Biology Health and Life Sciences, Cardiff University, Cardiff, UK

J. M. Palomo and M. G. Hans

Department of Orthodontics, Case Western Reserve University, Cleveland Ohio, USA

Address for correspondence: J. M. Palomo, Department of Orthodontics, Case Western Reserve University, 10900 Euclid Ave. Cleveland, OH, 44106, USA. Email: palomo{at}case.edu


    Abstract
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
There has been an escalating interest in three-dimensional imaging devices over the last decade. Orthodontists are beginning to appreciate the advantages that the third dimension gives to clinical diagnosis, treatment planning and patient education. This article focuses on the cutting edge technology of cone beam CT, which utilizes conventional X-ray technology and computerized volumetric reconstruction to reproduce a three-dimensional image. A variety of applications and range of issues associated with this technology will be discussed.

Key words: Cone beam, tomography, imaging, orthodontics, three-dimensional


    Introduction
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
Cone beam computerized tomography (CBCT) was developed in the 1990s as an evolutionary process resulting from the demand for three-dimensional (3D) information obtained by conventional computerized tomography (CT) scans. Custom built cranio-maxillofacial CBCTs started to appear in the market over the last decade and a variety of applications to the facial and dental environments have been established. In recent times, there have been a number of pilot studies and reports of its clinical usages but experts believe that this technology is still in its infancy.1Go

This article hopes to give a brief introduction to CBCT technology and explore a number of issues regarding its usage in an orthodontic and clinical setting.


    Conventional computerized tomography (CT)
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
Computerized tomography was developed by Sir Godfrey Hounsfield in 1967 and since the first prototype, there has been a gradual evolution to five generations of such systems. The method of classification for each system is based on the organization of the individual parts of the device and the physical motion of the beam in capturing the data. First generation scanners consisted of a single radiation source and a single detector. The information was obtained slice by slice (Figure 1aGo). The second generation was introduced as an improvement and multiple detectors were incorporated within the plane of the scan. However, these detectors were not necessarily continuous nor did they span the diameter of the object. The third generation was made possible by the advancement in detector and data acquisition technology. These large detectors reduced the need for the beam to translate around the object to be measured and were often known as the ‘fan-beam’ CTs. Ring artefacts were often seen on the images captured distorting the three-dimensional image and obscuring certain anatomical landmarks. The fourth generation was developed to counter this problem. A moving radiation source and a fixed detector ring were introduced. This meant that modifications to the angle of the radiation source had to be taken into account and more scattered radiation was seen. Finally, the fifth and sixth generation scanners were introduced to reduce ‘motion’ or ‘scatter’ artefacts. As with the previous two generations, the detector is stationary and the electron beam is electronically swept along a semicircular tungsten strip anode. The radiation is produced at the point where the electron beam hits the anode and results in a source of X-rays that rotates about the patient with no translation components or moving parts. Projections of the X-rays are so rapid that even the heart beats of a person may be captured. This has led some clinicians to hail it as a 4D motion capture device.



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Figure 1 Diagrammatic representation of image capture technique of CT and CBCT devices (Courtesy of Mr Arun Singh, Imaging Sciences, Hatfield PA, USA)

 
Nevertheless, there are several limitations with these systems. They require a considerable physical space and are much more expensive than conventional radiographic machines. The images captured on the detector screens are made up of multiple slices, which are ‘stacked’ to obtain a final complete image making it time consuming and less cost efficient. In orthodontics, the radiation exposure to the patient was partially responsible in limiting the CT usage to complex craniofacial problems and specialized diagnostic information.


    CBCT
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
Craniofacial CBCTs were designed to counter some of the limitations of the conventional CT scanning devices.2Go The object to be evaluated is captured as the radiation source falls onto a two-dimensional detector. This simple difference allows a single rotation of the radiation source to capture an entire region of interest, as compared to conventional CT devices where multiple slices are stacked to obtain a complete image (Figure 1Go).3Go The cone beam also produces a more focused beam and considerably less scatter radiation compared to the conventional fan-shaped CT devices.4Go This significantly increases the X-ray utilization and reduces the X-ray tube capacity required for volumetric scanning.5Go It has been reported that the total radiation is approximately 20% of conventional CTs and equivalent to a full mouth peri-apical radiographic exposure.6Go

These component innovations are significant and allow the CBCT to be less expensive and smaller. Furthermore, the exposure chamber (i.e. head), is custom built and reduces the amount of radiation. The images are comparable to the conventional CTs and may be displayed as a full head view, as a skull view or regional components.


    CBCT acquisition systems
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
There are currently four main system providers in the world market:

As clinical research in this technology escalates and as the cost reduces, there is no doubt that more providers will start to invest and promote this technology.

The available CBCT machines differ in size, possible settings, area of image capture (field of view), and clinical usage (Table 1Go).


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Table 1 Specification of the currently available cone beam CT machines approved for use in dentistry
 
NewTom 3G
The family of NewTom 3G (Quantitative Radiology, Verona, Italy) devices (Figure 2aGo) was introduced recently as part of an evolutionary process from its predecessor the NewTom 9000. The NewTom was the first device in the dental market to use CBCT technology.



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Figure 2 Currently available cone beam scanners approved for use in dental medicine: (a) NewTom 3G (courtesy of Aperio Services LLC – Sarasota – FL, USA). (b) IS i-CAT (courtesy of Imaging Sciences, Hatfield PA, USA). (c) Hitachi CB MercuRay (courtesy of Hitachi Medical System America Inc., Twinsburg, OH, USA). (d) J. Morita three-dimensional Accuitomo (courtesy of J. Morita USA, Irvine, CA, USA)

 
The system operates in a similar way to a conventional CT. The patient is imaged in a supine position, and scans of the head and neck are completed within 36 seconds. The system offers three possible fields of views. The manufacturers claim the system is able to produce a voxel resolution up to 0.125 mm when using the smaller field of view.

The voxel (volume pixel) represents a quantity of three-dimensional data, just as a pixel represents a point or cluster of points in two-dimensional data. The voxel resolution gives an indication of the ability to capture the finer details in a scan (e.g. the periodontal ligament is on average 0.5 mm wide and, therefore, in order to capture this detail a minimum of two voxels with a resolution of 0.25 mm is required).

Custom built software allows volumetric and surface area analysis of soft and hard tissues. These datasets may be exported into a standard Digital Imaging and Communications in Medicine (DICOM) 3-D format for image manipulation.

i-CAT
The i-CAT cone beam three-dimensional imaging system is developed by Imaging Sciences International (Imaging Sciences, Hatfield PA, USA) (Figure 2bGo). The three-dimensional image is captured with the patient sitting upright as in any standard OPT machine and the scan time varies from 20–40 seconds.

In the initial prototypes, only the maxillo-mandibular regions could be imaged, but with new improvements and modifications, the manufacturers now claim that a field of view of 20 x 25 cm may be obtained. This is sufficient to capture a standard facial image equivalent to that of a three-dimensional lateral cephalogram.

The manufacturers claim that the novel amorphous silicon flat panel detector provides no distortion, a 12-bit grayscale and a pixel size resolution of 0.125 mm. The flat panel provides good contrast and a long panel life, thus making better clinical images, while being cost effective.

One early criticism of the system was the distortion of the facial tissues produced by the chin rest when the patient was positioned in the device. This feedback has led the company to improve the patient posturing device and no such problems arise in the later versions of the system.

CB MercuRay
The CB MercuRay (Hitachi Medical Corporation, Tokyo, Japan) is the latest addition to the full view head and neck imaging CBCTs (Figure 2cGo).

The X-ray source is made of a low energy fixed anode tube producing a cone-shaped X-ray beam that is captured on an image intensifier and a solid state CCD. The manufacturers claim a scan time of 10 seconds through a rotation of 360° that provides 288 views that can be seen either as 2-D or 3-D. The CB MercuRay offers three different fields of view and is the fastest CBCT machine currently available. This is an advantage in reducing patient movement during image capture.

3D Accuitomo
The 3D Accuitomo (J. Morita Mfg Corp, Kyoto, Japan) was developed as a collaboration between the School of Dentistry at Nihon University and J Morita MfG Corp (Figure 1dGo). The field of view of 30 x 40 mm focuses on more regional and specific anatomical investigations. The smaller field of view results in a reduced effective radiation of 7.4 µSv. This small and compact unit has the advantage of only requiring 1.6 times the space of a dental panoramic X-ray unit (1620 x 1200 mm).


    Clinical applications of orthodontic interest
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
With CBCT technology all possible radiographs can be taken in under 1 minute. The orthodontist now has the diagnostic quality of periapicals, panoramic, cephalograms and occlusal radiographs, and TMJ series at their disposal, along with views that cannot be produced by regular radiographic machines like axial views, and separate cephalograms for the right and left sides (Figure 3Go). A number of clinical applications have already been reported in the literature.5Go







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Figure 3 Images taken with a CBCT scanner (courtesy of Aperio Services LLC, Sarasota, FL, USA; and Hitachi Medical System America Inc., Twinsburg, OH, USA). (a) Soft tissue face. (b) Maxillofacial skeleton with fixed appliances in maxillary posterior dentition. (c) Soft tissue face and maxillofacial skeleton in the same view. (d) Image of patient with upper fixed appliances. (e) sagittal view of maxillofacial complex. (f) Coronal view of the posterior dentition. (g) Image equivalent to bite wing series. (h) Image equivalent to panoramic radiograph, using a 2 mm slice. (i,j) Image equivalent to traditional cephalograms, but with CBCT both left and right sides can be analysed and traced separately (an image equivalent to a traditional cephalogram can also be achieved by superimposing right and left structures into a single image). (k) A study series on a mandibular condyle. (l) TMJ area

 
Impacted teeth and oral abnormalities
The incidence of maxillary ectopic cuspids occurs in approximately 3% of the population. The distribution and location has been reported at 80% palatally and 20% buccally. The tube shift method (also known as the parallax technique) has been the traditional method of locating these cuspids and provides an arbitrary position and approximation of the level of difficulty for the management of the cuspid. This investigative technique uses two conventional radiographs and the location of the tooth identified by the movement of the objects respectively to the way in which the radiograph was taken. In addition, the extent of the pathology caused by the ectopic tooth and its surrounding structures has also been evaluated by these radiographs.7Go However, clinical reports using three-dimensional conventional CT scans have shown that the incidence of root resorption to the adjacent teeth has been larger than previously thought.8Go

A recent report found that the use of CBCT technology could add value to the management of patients with such anomalies.9Go The authors used the technology to precisely locate the ectopic cuspids and to design treatment strategies that allowed for minimally invasive surgery to be performed and helped to design effective orthodontic strategies.

Another interesting use of the CBCT is the location of incidental oral abnormalities in patients. Some centres in the USA have begun to adopt CBCT imaging into routine dental examination procedures. Initial reports have suggested that there were higher incidences of oral abnormalities than previously suspected (i.e. oral cysts, ectopic/buried teeth and supernumeraries).

The value of these findings must be taken with caution, as the number of elective treatments that may be carried out may be limited. This leads to the question of whether to intervene in every abnormality located on these three-dimensional images and the extent to which the patient needs to be informed. In the event that these abnormalities were to lead to pathological episodes, what responsibilities would the clinician and patient hold in the decision making process? This could lead to a host of future medico-legal problems on how clinicians and patients manage the information.

Airway analysis
The CBCT technology provides a major improvement in the airway analysis, allowing for its three-dimensional and volumetric analysis.

Airway analysis has conventionally been carried out by using lateral cephalograms. A recent study carried on 11 subjects, using lateral cephalograms and CBCT imaging found that there was moderate variability in the measurements of upper airway area and volume.10Go

Three-dimensional airway analysis will no doubt be useful in understanding the reasons why clinical conditions like sleep apnoea and enlarged adenoids affect the way clinicians manage these complex conditions.

Assessment of alveolar bone heights and volume
Implantologists have long appreciated the third dimension in their clinical work. Conventional CT scans are used routinely to assess bone dimensions, bone quality and alveolar height, especially when multiple units are proposed. This has improved the clinical success of these prostheses, and led to more accurate and aesthetic outcomes in oral rehabilitation.

The introduction of CBCT technology means that both the cost and effective radiation dose can be reduced, suggesting that its frequency of use may increase. The CBCT has already been in use in implant therapy11Go and may be exploited in orthodontics for the clinical assessment of bone graft quality following alveolar surgery in patients with cleft lip and palate.12Go The images produced resulted in greater precision in the evaluation of bone sites and, therefore, gave the clinician a better chance of restoring the site with implants and also influenced the decision-making process of whether to move teeth orthodontically into the repaired alveolus.

Temporomandibular joint (TMJ) morphology
Condylar resorption occurs in 5–10% of patients who undergo orthognathic surgery. Recent three-dimensional studies have tried to understand how the condyle remodels and preliminary data suggests that much of the condylar rotation resulting in remodelling is a direct result of the surgical procedures alone.13Go TMJ changes following distraction osteogenesis treatment and dentofacial orthopaedics still need further study.

The quality of the images of the TMJ with CBCT machines is comparable to conventional CTs, but the image taking is faster, less expensive, and provide less radiation exposure. This has opened a new avenue for imaging the TMJ.14Go


    Radiation exposure
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
Even though the cone beam technology is able to provide three-dimensional volumetric images with up to four times less radiation than a conventional CT,15Go the resulting effective radiation is dependent on the settings used (kVp and mA). The use of lower mAs and/or collimation are some of the ways to reduce the amount of radiation the patient receives, but at the same time can produce a lower image quality than by using higher settings. Patient effective exposure dose from a CBCT machine has been reported to be as low as 45 µSv to as high as 650 µSv. As a reference, published exposure for an analogue full mouth series has been reported as 150 µSv;16Go for an analogue panoramic radiograph as 54 µSv17Go and a round trip from Paris to Tokyo adds 139 µSv of effective dose to each passenger.18Go,19Go

In 2001, an article associating the use of conventional CT in children to radiation-induced fatal cancer20Go raised some controversial concepts. As a result, CTs were adjusted to have a decrease in effective dose from 6000 to 2600 µSv.21Go Even at the highest settings and best image quality possible, none of the CBCT machines come close to those values.

The British Orthodontic Society Guidelines suggests that: ‘Radiographs should only be justified when the management of patient is dependent on the information obtained’.22Go The ADA Council on Scientific Affairs recommends the use of techniques that would reduce the amount of radiation received during dental radiography. Known as the ‘As Low As Reasonably Achievable’, or ALARA, principle, this includes taking radiographs based on the patient’s needs (as determined by an examination), using the fastest film compatible with the diagnostic task, collimating the beam to a size as close to that of the film as feasible and using leaded aprons and thyroid shields.

An accepted ratio between exposure and image quality needs to be reached in order to use the ALARA principle. Depending on the objective and desired outcome, alternative technologies should be explored since they may offer a less invasive three-dimensional technology.23Go27Go Figure 4Go demonstrates soft tissue scans of a growing patient analysed every 6 months and is produced using two Minolta VI 900 laser scanners and RapidFormTM Imaging Software.



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Figure 4 Use of three-dimensional non-invasive soft tissue imaging devices to study longitudinal growth changes in children

 

    Other matters
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
The CBCT is excellent for imaging hard tissues structures and most soft tissue components. However, it does not have the ability to map out exactly the muscle structures and their attachments. These intricate structures would have to be imaged using conventional magnetic resonance imaging (MRI) technology, which (incidentally) does not predispose the patient to radiation exposure.

The CBCT soft tissue images do not capture the true colour texture of the skin. Therefore, in order to obtain photographic quality resolution, manipulation of the images is still required. Successful attempts to map tissue texture maps onto conventional CTs have been reported and may be similarly applied to this new technology.28Go When they become available, perhaps they can successfully replace the photographs also taken during records. Another criticism made is the long capture time for a full view of a subject (scan time of 30–40 seconds), during which involuntary muscle movements (nostrils and breathing) will lead to inaccuracies to soft tissue capture. These limitations mean that the three-dimensional devices like stereo-photogrammetry and laser scanning are still the state of the art in soft tissue texture capture.

As with all new clinical equipment, cost is often a deciding factor. This is more significant to small and private specialized dental practices. All the four companies sell the CBCT devices as a standard base package and additional peripherals can increase the cost. These peripherals are often important to increase the field of view of the image capture or to improve the detector quality. There is also a substantial post-purchase maintenance that goes into each system. These are essential to the effective operation and optimal functioning of the system. Some companies may charge a premium in their maintenance packages and recover their costs in such a manner. So be sure to discuss this with the sales representative and add it on to the budget planning requirements. Finally, as no regulations have been implemented for the usage of these equipment, a budget may need to be set aside for the employment of a specially trained person to take these images.


    Conclusion
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
The long awaited incorporation of the third dimension to our radiographic records is now a reality. There is still room for improvement, however the CBCT technology appears to be here to stay.

The future in orthodontic imaging seems exciting as we discover new frontiers, and as the paradigm in orthodontics shifts from landmarks, lines, distances and angles to surfaces, areas and volumes.


    Acknowledgments
 
This is a collaborative effort between the Departments of Orthodontics of the Wales College of Medicine, Cardiff University and Case Western Reserve University.


    References
 Top
 Abstract
 Introduction
 Conventional computerized...
 CBCT
 CBCT acquisition systems
 Clinical applications of...
 Radiation exposure
 Other matters
 Conclusion
 References
 
1 Danforth RA, Peck J, Hall P. Cone beam volume tomography: an imaging option for diagnosis of complex mandibular third molar anatomical relationships. J Calif Dent Assoc 2003; 31: 847–52.

2 Halazonetis DJ. From 2-dimensional cephalograms to 3-dimensional computed tomography scans. Am J Orthod Dentofac Orthop 2005; 127: 627–37.[Medline]

3 Sukovic P, Brooks S, Perez L, Clinthorne NH. DentoCATTM—a novel design of a cone-beam CT scanner for dentomaxillofacial imaging: introduction and preliminary results. CARS 2001; 700–5.

4 Mah J, Hatcher D. Current status and future needs in craniofacial imaging. Orthod Craniofac Res 2003; 6 Suppl 1: 10–6; discussion 179–82.

5 Sukovic P. Cone beam computed tomography in craniofacial imaging. Orthod Craniofac Res 2003; 6 Suppl 1: 31–6; discussion 179–82.

6 Mah JK, Danforth RA, Bumann A, Hatcher D. Radiation absorbed in maxillofacial imaging with a new dental computed tomography device. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2003; 96: 508–13.[Medline]

7 Chaushu S, Chaushu G, Becker A. The role of digital volume tomography in the imaging of impacted teeth. World J Orthod 2004; 5: 120–32.[Medline]

8 Ericson S, Kurol PJ. Resorption of incisors after ectopic eruption of maxillary canines: a CT study. Angle Orthod 2000; 70: 415–23.[Medline]

9 Mah J, Enciso R, Jorgensen M. Management of impacted cuspids using 3-D volumetric imaging. J Calif Dent Assoc 2003; 31: 835–41.

10 Aboudara CA, Hatcher D, Nielsen IL, Miller A. A three-dimensional evaluation of the upper airway in adolescents. Orthod Craniofac Res 2003; 6 Suppl 1: 173–5.

11 Hatcher DC, Dial C, Mayorga C. Cone beam CT for pre-surgical assessment of implant sites. J Calif Dent Assoc 2003; 31: 825–33.

12 Hamada Y, Kondoh T, Noguchi K, et al. Application of limited cone beam computed tomography to clinical assessment of alveolar bone grafting: a preliminary report. Cleft Palate Craniofac J 2005; 42: 128–37.[Medline]

13 Bailey LJ, Cevidanes LH, Proffit WR. Stability and predictability of orthognathic surgery. Am J Orthod Dentofac Orthop 2004; 126: 273–7.[CrossRef][Medline]

14 Tsiklakis K, Syriopoulos K, Stamatakis HC. Radiographic examination of the temporomandibular joint using cone beam computed tomography. Dentomaxillofac Radiol 2004; 33: 196–201.[Abstract/Free Full Text]

15 Schulze D, Heiland M, Thurmann H, Adam G. Radiation exposure during midfacial imaging using 4- and 16-slice computed tomography, cone beam computed tomography systems and conventional radiography. Dentomaxillofac Radiol 2004; 33: 83–6.[Abstract/Free Full Text]

16 Frederiksen NL. X rays: what is the risk? Tex Dent J 1995; 112: 68–72.

17 Kiefer H, Lambrecht JT, Roth J. [Dose exposure from analog and digital full mouth radiography and panoramic radiography]. Schweiz Monatsschr Zahnmed 2004; 114: 687–93.

18 Bottollier-Depois JF, Trompier F, Clairand I, et al. Exposure of aircraft crew to cosmic radiation: on-board intercomparison of various dosemeters. Radiat Prot Dosimetry 2004; 110: 411–15.[Abstract/Free Full Text]

19 Bottollier-Depois JF, Chau Q, Bouisset P, et al. Assessing exposure to cosmic radiation on board aircraft. Adv Space Res 2003; 32: 59–66.[CrossRef][Medline]

20 Brenner D, Elliston C, Hall E, Berdon W. Estimated risks of radiation-induced fatal cancer from pediatric CT. Am J Roentgenol 2001; 176: 289–96.[Abstract/Free Full Text]

21 Rogers LF. Radiation exposure in CT: why so high? Am J Roentgenol 2001; 177: 277.[Free Full Text]

22 Isaacson KG, Thom AR, Eds. Guidelines for the Use of Radiographs in Clinical Orthodontics, 2nd edn. London: British Orthodontic Society, 2001.

23 Kau CH, Zhurov AI, Scheer R, Bouwman S, Richmond S. The feasibility of measuring three-dimensional facial morphology in children. Orthod Craniofac Res 2004; 7: 198–204.[Medline]

24 Kau CH, Cronin AC, Durning P, Zhurov AI, Richmond S. A new method for the 3D measurement of post-operative swelling following orthognathic surgery. Orthod Craniofac Res 2006; Forthcoming February.

25 Kau CH, Richmond S, Zhurov AI, et al. Reliability of measuring facial morphology using a 3-dimensional laser scanning system. Am J Orthod Dentofac Orthop 2005; 128: 424–30.[Medline]

26 Palomo JM, Subramanyan K, Hans MG. Creation of three dimensional data from bi-plane head x-rays for maxillo-facial studies. Int Congr Ser 2004; 1268C: 1253–1254.[CrossRef]

27 Palomo JM, Hunt DW, Jr, Hans MG, Broadbent BH, Jr. A longitudinal 3-dimensional size and shape comparison of untreated Class I and Class II subjects. Am J Orthod Dentofac Orthop 2005; 127: 584–91.[Medline]

28 Khambay B, Nebel JC, Bowman J, et al. 3D stereophotogrammetric image superimposition onto 3D CT scan images: the future of orthognathic surgery. A pilot study. Int J Adult Orthod Orthognath Surg 2002; 17: 331–41.




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