Journal of Cranio-Maxillofacial Surgery (2008) 36, 443e449 Ó 2008 European Association for Cranio-Maxillofacial Surgery doi:10.1016/j.jcms.2008.04.003, available online at http://www.sciencedirect.com
Dimensional error in selective laser sintering and 3D-printing of models for craniomaxillary anatomy reconstruction* Daniela Nascimento SILVA, MSc, PhD1,*, Marı´lia GERHARDT DE OLIVEIRA, PhD1,*, Eduardo MEURER, PhD2,*, Maria Ineˆs MEURER, PhD3,*, Jorge Vicente LOPES DA SILVA, MSc4,*, ´ RBARA, MSc4,* Ailton SANTA-BA 1
Department of Surgery (Head: Prof. Dr. Helena Willhelm de Oliveira), Pontifı´cia Universidade Cato´lica do Rio Grande do Sul (PUCRS), Porto Alegre, RS, Brazil; 2 Dentistry School, Universidade do Sul de Santa Catarina (UNISUL), Tubar~ ao, SC, Brazil; 3 Department of Pathology (Head: Prof. Dr. Alcı´bia Helena de Azevedo Maria), Universidade Federal de Santa Catarina (UFSC), Floriano´polis, SC, Brazil; 4 Centro de Pesquisas Renato Archer (CenPRA), Campinas, SP, Brazil
SUMMARY. Background: Selective laser sintering (SLS) and three-dimensional printing (3DPÔ) are rapid prototyping (RP) techniques to fabricate prototypes from biomedical images. To be used in maxillofacial surgery, these models must accurately reproduce the craniofacial skeleton. Purpose: To analyze the capacity of SLS and 3DPÔ models to reproduce craniomaxillary anatomy and their dimensional error. Material: Dry skull, helical computed-tomography images, SLS and 3DPÔ prototypes, and electronic calliper. Methods: Tomographic images of a dry skull were manipulated with the InVesalius biomedical software. Prototypes were fabricated using SLS and 3DPÔ techniques. Ten linear measurements were made on the models and compared with corresponding dry skull measurements (criterion standard) carried out with an electronic calliper. Results: We observed a dimensional error of 2.10 and 2.67% for SLS and 3DPÔ models, respectively. The models satisfactorily reproduced anatomic details, except for thin bones, small foramina and acute bone projections. The SLS prototypes showed greater dimensional precision and reproduced craniomaxillary anatomy more accurately than the 3DPÔ models. Conclusion: Both SLS and 3DPÔ models provided acceptable precision and may be useful aids in most maxillofacial surgeries. Ó 2008 European Association for CranioMaxillofacial Surgery
Keywords: craniofacial, precision, rapid prototyping
the build tray moves down, and a new layer of powder is deposited and sintered. When the manufacturing process is complete, the prototype is removed from the tray, and the surrounding unsintered powder is dusted off. The prototype surface is finished by sandblasting. The SLS prototype is opaque, and its surface is abrasive and porous (Berry et al., 1997; Meurer et al., 2003). The 3DPÔ system uses print heads to selectively disperse a binder onto the powder layers. This technology has a lower cost than similar techniques. First, a thin layer of powder is spread over a tray using a roller similar to the one used in the SLS system. The print head scans over the powder tray and delivers continuous jets of a solution that binds the powder particles as it touches them. No support structures are required while the prototype is fabricated because the surrounding powder supports the unconnected parts. When the process is complete, the surrounding powder is aspirated. In the finishing process, the prototype surfaces are infiltrated with a cyanoacrylate-based material (Ashley, 1991; Sachs et al., 1992a). This study evaluated the dimensional error and the reproducibility of anatomical details in prototypes produced using the SLS and 3DPÔ technologies (powder-based addition systems) in comparison with a dry human skull
INTRODUCTION Biomedical prototypes or models have been largely used in maxillofacial surgery, as an aid to diagnosis and treatment planning. However, the quality and precision of different rapid prototyping (RP) systems have not been definitely established (Berry et al., 1997; Schneider et al., 2002; Meurer et al., 2003). New RP technologies, such as selective laser sintering (SLS) and three-dimensional printing (3DPÔ) have a lower cost and shorter manufacturing times than traditional stereolithography (SL). The SLS technique uses a CO2 laser beam to selectively fabricate models in consecutive layers. First, the laser beam scans over a thin layer of powder previously deposited on the build tray and levelled with a roller. The laser beam heats the powder particles and fuses them to form a solid layer, and then moves along the X and Y axes to design the structures according to Computer Aided Design (CAD) data. After the first layer fuses, * Financial support: Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq). * These authors contributed equally.
443
444 Journal of Cranio-Maxillofacial Surgery
(criterion standard) using the same protocol for acquisition and manipulation of computed-tomography (CT) images. METHODS A human dry skull was positioned with the Frankfurt plane parallel to the scan plane of a helical CT unit (Somatom Plus 4, Siemens, Munich, Germany) at Hospital Sao Lucas, Pontifı´cia Universidade Cato´lica do Rio Grande do Sul (PUCRS), Porto Alegre, Brazil. CT images were acquired using the following parameters: 0 gantry tilt; axial slices (193 slices); 1 mm slice thickness; 1.5 pitch; field of view (FOV) ¼ 20.8 cm; matrix 512 512; 120 kVp; and 130 mA. Skull volume was reconstructed with a slice thickness of 0.5 mm. CT data were recorded in a Digital Imaging Communications in Medicine (DICOM) 3.0 CD-R. The InVesalius software (CenPRA, Campinas, Brazil) was used to segment images at a 400e3300 threshold; files were converted to Standart Template Library (STL) format and sent to the Renato Archer Research Centre (CenPRA, Campinas, Brazil) for the fabrication of prototypes. The unit used for SLS prototyping was a Sinteristation 2000 (DTM, USA), and the material was a thin polyamide powder (PA 2200, EOS, Munich, Germany). The prototypes were finished with sandblasting. Prototype fabrication time was 15 h, and approximate cost was $600. A ZPrinterÒ 310 System (MIT, MA, USA) unit was used for the production of the 3DPÔ prototypes, and the materials were plaster powder (zpÔ102, Z Corporation, Burlington, USA) and a water-based binder. The prototypes were finished by application of a cyanoacrylate-based infiltration material (Z-Bond100, Z Corporation, Burlington, USA) to their surfaces. Prototype fabrication time was 4 h, and approximate cost was $430. Fig. 1 shows the sequence of steps for prototype fabrication.
Linear measurements (Table 1 and Fig. 2) were made with a StarrettÒ electronic calliper (Starrett Ind. e Com. Ltda, Sao Paulo, Brazil). Data were analyzed using descriptive statistics, and comparisons were made with the Student t test for paired samples. For each linear measurement, dimensional error was calculated as the absolute difference (mm) between the values obtained from the prototypes and those from the dry skull. Relative differences (%) were calculated as the absolute difference divided by the dry skull value 100, in accordance with studies conducted by Choi et al. (2002) and Chang et al. (2003). Each measurement of prototypes and dry skull was repeated 20 times by the same observer, and results were used for the subsequent comparison of mean values. Mean absolute difference ðmmÞ ¼ prototype value dry skull value Mean relative difference ð%Þ ðprototype value dry skull valueÞ 100 ¼ dry skull value
RESULTS Fig. 3 shows that the external measurements of the prototypes were greater than those of the dry skull, except for length palatal (LP). Internal prototype measurement values were lower than dry skull values, except for the zygomaticofrontal (ZFeZF) and length of internal cranium (LIC) of the SLS prototype. All differences were statistically significant at p # 0.05. Figs. 4 and 5 show the mean differences in linear measurements of the prototypes and of the dry skull. These
Fig. 1 e General process of SLS and 3DPÔ model production.
Dimensional error in selective laser sintering and 3D-printing models 445
Table 1 e Landmarks and linear measurements Landmarks and measurements Landmarks AP e aperture piriformis Ba e basion FC e frontal crest IOC e internal occipital crest ANS e anterior nasal spine PNS e posterior nasal spine EF e external frontal LM e lateral foramen magnum FO e foramen ovale ZF
EO e external occipital Op e opisthion T e tuberosity Zy e zygion
External measurements LEC e length of external cranium LP e length of palatal FOeFO BW e bizygomatic width MW e maxillary width Internal measurements LFM e length of foramen magnum LIC e length of internal cranium ZFeZF APW e aperture piriformis width FMW e foramen magnum width
data were used to calculate the mean relative differences of all linear measurements. The SLS prototype had a mean dimensional error of 0.89 mm (2.10%), and the 3DPÔ prototype, of 1.07 mm (2.67%).
Definition Point at the lateral margin of the aperture piriformis (bilateral) The median point of the anterior margin of the foramen magnum Tip of the bony frontal crest The anterior-most point of the internal occipital crest Tip of the bony anterior nasal spine The median point on the dorsal limit of palate The anterior-most point of the frontal in the median plane Point at the lateral-most margin of the foramen magnum (bilateral) Point at the medial margin of the foramen ovale (bilateral) Point at the medial margin of the zygomaticofrontal suture (bilateral) The median point of the anterior margin of the occipital The median point of the posterior margin of the foramen magnum Point at the lateral margin of the maxillary tuberosity (bilateral) Point at the lateral-most border of the centre of the zygomatic arch (bilateral) Distance between EF and EO Distance between ANS and PNS Distance between left and right FO Distance between left and right Zy Distance between left and right T Distance between Ba and Op Distance between FC and IOC Distance between left and right ZF Distance between left and right AP Distance between left and right LFM
DISCUSSION Most systems used to fabricate biomedical models provide satisfactory accuracy. However, the shape, dimensions and anatomic details of prototypes may be affected by errors at any phase of the RP process, such as CT image acquisition, image manipulation with biomedical software, or fabrication and finishing (Barker et al., 1994; Choi et al., 2002; Schneider et al., 2002; Tang et al., 2003). Some parameters should be carefully analyzed to ensure accuracy when using the SLS technology: slice thickness when the CAD model is resliced, diameter and angle of the CO2 laser beam, type and size of powder particles, and direction of fabrication (Tang et al., 2003). In the 3DPÔ system, the printing mechanism, the type and quality of the materials used in the fabrication of the prototypes, and the absorption properties of the powder when in contact with the binder and infiltration material are parameters that should be controlled to obtain a reliable final product (Sachs et al., 1992a; Chang et al., 2003). The analysis of external measurements (Fig. 3) showed that the length of external cranium (LEC), bizygomatic width (BW), FOeFO and maxillary width (MW) values of the SLS and 3DPÔ prototypes were greater than those of the dry skull. Only the LP value was lower. This may have occurred because the reference points for this measurement (anterior nasal spine [ANS] and posterior nasal spine [PNS]) are in areas of acute bone projections, and are, thus, more susceptible to the partial volume effect, which attenuates projections and consequently reduces the LP dimension. Choi et al. (2002) reported similar results in their analysis of the SL technique. Conversely, all internal measurement values of the 3DPÔ prototype were lower than those of the dry skull (Fig. 3). The same was found for the SLS prototype, except for LIC and ZFeZF, whose anatomic landmarks are also located in areas of acute bone projections (frontal crest [FC] in the LIC dimension) or in bone sutures (zygomaticofrontal suture, in the ZFe ZF dimension), regions that are greatly affected by the partial volume effect (Choi et al., 2002). The inverse correlation between external and internal dimensions may be explained by the dumb-bell effect described by Choi et al. (2002), in which the increase in external dimensions and a simultaneous decrease in internal dimensions indicate that the prototypes have greater dimensions than the original skull, and that the selected threshold may have been too low. Therefore, accuracy is dependent primarily on the choice of a scanning protocol and on data segmentation, especially the determination of threshold. Table 2 summarizes relevant studies about the accuracy of 3D CT imaging and RP techniques in the reproduction of craniofacial anatomy.
446 Journal of Cranio-Maxillofacial Surgery
Fig. 2 e Linear measurements.
skull. Their results showed a mean absolute difference of 0.62 ^ 0.35 mm (0.56 ^ 0.39%). Chang et al. (2003) evaluated the accuracy of the 3DPÔ technique in RP of three types of bone defects: unilateral maxillectomy, maxillectomy, and orbitomaxillectomy in fresh cadaver skulls. The defects simulated resections of a tumour in the maxillary sinus. Their results showed that mean error was lower than 2 mm. According to Waitzman et al. (1992), the dimensional error of 3D
Results of this study showed a dimensional error of 2.10% for the SLS prototype in comparison with the dry skull, a value that is greater than that reported by Berry et al. (1997), who found a 0.64% variation. However, those authors compared the prototype with the 3D CT image, whose dimensions might have been different from those of the original skull, and did not adopt a criterion standard. Choi et al. (2002) investigated the accuracy of SL prototypes produced from CT data of a dry
200 180
Mean (mm)
160 140 120 100 80 60 40 20 0
LEC
BW
LP
FO-FO
MW
LIC
LFM
External
FMW
ZF-ZF
APW
Internal Linear measurements
Dry skull
SLS model
3DP™ model
Fig. 3 e Mean and standard deviation (SD) of the linear dimensions of dry skull, SLS and 3DPÔ models. Dry skull: LEC ¼ 184.43 (^0.26), BW ¼ 123.11 (^0.20), LP ¼ 52.04 (^0.27), FOeFO ¼ 48.41 (^0.69), MW ¼ 73.40 (^0.14), LIC ¼ 154.62 (^0.36), LFM ¼ 34.61 (^0.07), FMW ¼ 27.16 (^0.11), ZFeZF ¼ 99.36 (^0.22), APW ¼ 26.25 (^0.15). SLS model: LEC ¼ 187.37 (^0.19), BW ¼ 125.22 (^0.14), LP ¼ 51.46 (^0.21), FOeFO ¼ 50.32 (^0.13), MW ¼ 74.53 (^0.31), LIC ¼ 155.16 (^0.19), LFM ¼ 33.49 (^0.07), FMW ¼ 26.17 (^0.16), ZFe ZF ¼ 99.55 (^0.30), APW ¼ 25.26 (^0.14). 3DP model: LEC ¼ 186.76 (^0.14), BW ¼ 125.28 (^0.10), LP ¼ 51.66 (^0.12), FOeFO ¼ 50.51 (^0.16), MW ¼ 74.73 (^0.16), LIC ¼ 153.86 (^0.12), LFM ¼ 32.52 (^0.07), FMW ¼ 25.29 (^0.18), ZFeZF ¼ 98.60 (^0.48), APW ¼ 24.54 (^0.40).
Absolute differences Mean (mm)
Dimensional error in selective laser sintering and 3D-printing models 447 3,0 2,5 2,0 1,5 1,0 0,5 0,0 -0,5 -1,0 -1,5 -2,0 -2,5 LEC
BW
LP
FO-FO
MW
LIC
LFM
External
FMW
ZF-ZF
APW
Internal
Linear measurements SLS model - Dry skull
3DP™ model - Dry skull
Fig. 4 e Comparison of linear measurements of dry skull, SLS and 3DPÔ models: absolute differences’ means.
Relative differences Mean (%)
CT is about 0.9%, whereas Asaumi et al. (2001) found a variation of 2.16%. In this study, the 3DPÔ prototypes had a mean error of 2.67%, a value slightly lower than the one reported by Chang et al. (2003). It is important to point out that those authors used fresh cadaver skulls with soft tissues. Additional studies should evaluate the effect of these tissues on 3D CT imaging and biomedical prototypes. Our results demonstrated that SLS prototypes reproduced the craniomaxillary dimensions with a slightly greater accuracy than the 3DPÔ prototypes. One factor that may partly explain the smaller dimensions of the SLS prototypes is the superficial wear caused by sandblasting (Berry et al., 1997; Meurer et al., 2003). Additionally, the dimensions of 3DPÔ prototypes may have been greater because of cyanoacrylate infiltration (Sachs et al., 1992a). The unused powder that surrounds the prototype in the SLS system cannot be reused. Because of the high cost of the material, several parts are fabricated simultaneously. This may explain the long fabrication time for the SLS technique (16 h), very close to the time required for fabrication with the SL system (D’Urso et al., 1998; Choi and Samavedam, 2002; Sannomiya and Kishi, 2002; Mazzonetto et al., 2002). The powder remaining in the 3DPÔ system may be reused, and the parts may be fab-
ricated individually, which substantially reduces prototype fabrication time (4 h) (Sachs et al., 1992a,b; Mazzonetto et al., 2002). Therefore, the 3DPÔ technique has a lower final cost than the SLS technique, which, in turn, has a lower cost than the SL technique (Sachs et al., 1992a,b; Stoker et al., 1992; Mazzonetto et al., 2002; Meurer et al., 2003). The dimensional error of the SLS and 3DPÔ prototypes was within acceptable values. Asaumi et al. (2001) suggest that dimensional changes may not affect the success of surgical applications if such changes are within a 2% variation. However, it is necessary to identify the necessary level of RP accuracy for specific surgical procedures in maxillofacial surgery and to adapt the use of prototypes to each procedure. The dimensional accuracy found here may be satisfactory when the prototypes are used for communication with patients, diagnosis, or presurgical planning, particularly for more complex surgeries, such as correction of large bone displacement due to trauma and severe facial deformities (D’Urso et al., 1998; Santler et al., 1998). Chiarini et al. (2004) used RP to plan cranioplasties. For the same purpose, Rotaru et al. (2006) simulated the reconstruction of a large cranial defect using SLS prototypes. Recently, Paeng et al. (2007) demonstrated the effectiveness of the preoperative simulation of distraction
8 7 6 5 4 3 2 1 0
LEC
BW
LP
FO-FO
MW
LIC
LFM
External
FMW
ZF-ZF
APW
Internal
Linear measurements SLS model - Dry skull
3DP™ model - Dry skull
Fig. 5 e Comparison of linear measurements of dry skull, SLS and 3DPÔ models: relative differences’ means.
448 Journal of Cranio-Maxillofacial Surgery Table 2 e Comparison with results of other studies on 3D CT or RP e skull differences
ACKNOWLEDGEMENTS
Authors
Comparison
Mean difference (%)
This study
SLSedry skull 3DPÔedry skull
2.10 2.67
Waitzman et al. (1992)
3D CTedry skull
0.9 (0.1e3.0)
Brazilian National Council for Scientific and Technological Development (Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico e CNPq); Renato Archer Research Center (Centro de Pesquisas Renato Archer e CenPRA).
Ono et al. (1994)
SLedry skull
3
Barker et al. (1994)
SLedry skull
0.6e3.6
Berry et al. (1997)
SLSe3D CT
0.64
Asaumi et al. (2001)
3D CTedry skull SLedry skull
2.16 0.63
Choi et al. (2002)
3D CTedry skull SLedry skull SLe3D CT
0.65 0.56 0.62
Chang et al. (2003)
3DPÔefresh skull
2.1e4.7
osteogenesis using biomedical prototypes in the surgical treatment of patients with hemifacial microsomia. Studies conducted by Mazzonetto et al. (2002) and Meurer et al. (2003) showed that prototypes are particularly useful in the surgical treatment of temporomandibular joint ankylosis because they make it possible to establish the depth of osteotomy in the drill used as a guide. However, due to the close anatomic relation of this joint with important anatomic structures, the dimensional error of prototypes should be taken into account when dimensions are transferred to the patient. Such procedure is important to prevent accidents, such as the rupture of the maxillary artery. In the determination of the anatomic margins of a tumour, the inaccurate representation of tumours in 3D CT and the dimensional error of prototypes (Santler et al., 1998) should be carefully considered. Further studies should be conducted to investigate whether the accuracy of prototypes is also satisfactory for other surgical procedures, such as dental implant placement (Poukens et al., 2002; Sarment et al., 2003). This study demonstrated that the accuracy of the RP systems should be evaluated for each of its fabrication stages. Technological advances have contributed significantly to the improvement of techniques that minimize prototype dimensional error. The development of new techniques, such as SLS and 3DPÔ, may contribute to a reduction of costs of the final product and benefit a greater number of patients.
CONCLUSIONS The SLS and 3DPÔ prototypes fabricated from CT images reproduce craniomaxillary dimensions with acceptable precision, and may be, therefore, useful in most maxillofacial operations. SLS prototypes have a greater dimensional precision and reproduce anatomical details of the craniomaxillary region more accurately than 3DPÔ prototypes.
References Asaumi J, Kawai N, Honda Y, Shigehara H, Wakasa T, Kishi K: Comparison of three-dimensional computed tomography with rapid prototype models in the management of coronoid hyperplasia. Dentomaxillofac Radiol 30: 330e335, 2001 Ashley S: Rapid prototyping systems. Mech Eng 113: 34e43, 1991 Barker TM, Earwaker WJS, Lisle DA: Accuracy of stereolithographic models of human anatomy. Australas Radiol 38: 106e111, 1994 Berry E, Brown JM, Connell M, Craven CM, Efford ND, Radjenovic A, Smith MA: Preliminary experience with medical applications of rapid prototyping by selective laser sintering. Med Eng Phys 19: 90e96, 1997 Chang PS, Parker TH, Patrick Jr CW, Miller MJ: The accuracy of stereolithography in planning craniofacial bone replacement. J Craniofac Surg 14: 164e170, 2003 Chiarini L, Figurelli S, Pollastri G, Torcia E, Ferrari F, Albanese M, Nocini PF: Cranioplasty using acrylic material: a new technical procedure. J Craniomaxillofac Surg 32: 5e9, 2004 Choi JY, Choi JH, Kim NK, Kim Y, Lee JK, Kim MK, Lee JH, Kim MJ: Analysis of errors in medical rapid prototyping models. Int J Oral Maxillofac Surg 31: 23e32, 2002 Choi SH, Samavedam S: Modelling and optimisation of rapid prototyping. Compu Ind 47: 39e53, 2002 D’Urso PS, Atkinson RL, Lanigan MW, Earwaker WJ, Bruce IJ, Holmes A, Barker TM, Effeney DJ, Thompson RG: Stereolithographic (SL) biomodelling in craniofacial surgery. Br J Plast Surg 51: 522e530, 1998 Mazzonetto R, Moreira RW, Moraes M, Albergaria Barbosa JR, Passeri LA, Spagnoli DB: Uso de modelos estereolitogra´ficos em cirurgia bucomaxilofacial. Rev Assoc Paul Cir Dent 56: 115e118, 2002 Meurer E, Oliveira MG, Meurer MI, Silva JV, Ba´rbara AS, Heitz C: Biomodelos de prototipagem ra´pida em CTBMF. Rev Bras Cir Period 1: 172e180, 2003 Ono I, Gunji H, Suda K, Kaneko F: Method for preparing an exact-size model using helical volume scan computed tomography. Plast Reconstr Surg 93: 1363e1371, 1994 Paeng JY, Lee JH, Lee JH, Kim MJ: Condyle as the point of rotation for 3-D planning of distraction osteogenesis for hemifacial microsomia. J Craniomaxillofac Surg 35: 91e102, 2007 Poukens JM, Haex JK, Verdonck H, Riediger D: Study on the accuracy of stereolithographic surgical guides in dental implantology. Phidias Rapid Prototyp Med 8: 8e9, 2002 Rotaru H, Baciut M, Stan H, Bran S, Chezan H, Iosif A, Tomescu M, Kim SG, Rotaru A, Baciut G: Silicone rubber mould cast polyethylmethacrylateehydroxyapatite plate used for repairing a large skull defect. J Craniomaxillofac Surg 34: 242e246, 2006 Sachs E, Cima M, Bredt J, Curodeau A, Fan T: CAD-casting: direct fabrication of ceramic shells and cores by three dimensional printing. Manuf Rev 5: 117e126, 1992a Sachs E, Cima M, Williams P, Brancazio D, Cornie J: Three dimensional printing: rapid tooling and prototypes directly from a CAD model. J Eng Ind 114: 481e488, 1992b Sannomiya EK, Kishi K: Estereolitografia: aplicac¸~ao na odontologia: relato de dois casos clı´nicos. Rev Bras Odontol 59: 203e204, 2002 Santler G, Ka¨rcher H, Ruda C: Indications and limitations of threedimensional models in craniomaxillofacial surgery. J Oral Maxillofac Surg 26: 11e16, 1998 Sarment DP, Sukovic P, Clinthorne N: Accuracy of implant placement with a stereolithographic surgical guide. Int J Oral Maxillofac Implants 18: 571e577, 2003
Dimensional error in selective laser sintering and 3D-printing models 449 Schneider J, Decker R, Kalender WA: Accuracy in medical modelling. Phidias Rapid Prototyp Med 8: 5e14, 2002 Stoker GN, Mankovich NJ, Valentino D: Stereolithographic models for surgical planning. J Oral Maxillofac Surg 50: 466e471, 1992 Tang Y, Loh HT, Fuh JY, Wong YS, Lu L, Ning Y, Wang X: Accuracy analysis and improvement for direct laser sintering https://dspace. mit.edu/bitstream/1721.1/3898/2/IMST001.pdf; 2003, 2003 Available at: Waitzman AA, Posnick JC, Armstrong DC, Pron GE: Craniofacial skeletal measurements based on computed tomography: part I. Accuracy and reproducibility. Cleft Palate Craniofac J 29: 112e117, 1992
Dr. Daniela Nascimento SILVA, MSc, PhD School of Dentistry e PUCRS Av. Ipiranga 6681 Pre´dio 6, Sala 209 CEP 90619-900 Porto Alegre RS, Brazil Tel./Fax: +55 51 3320 3538 E-mail:
[email protected] Paper received 23 April 2007 Accepted 28 December 2007
