Vol. 103 No. 4 April 2007

ORAL AND MAXILLOFACIAL RADIOLOGY Editor: Allan G. Farman

Accuracy of measurements of mandibular anatomy in conebeam computed tomography imagesJohn B. Ludlow, DDS, MS,a William Stewart Laster, DDS, MS,b Meit See, RDH,c

L’Tanya J. Bailey, DDS, MS,d and H. Garland Hershey, DDS, MS,e Chapel Hill and Raleigh, NCUNIVERSITY OF NORTH CAROLINA

Objectives. Cone beam computed tomography (CBCT) images of ideally positioned and systematically mispositioneddry skulls were measured using two-dimensional and three-dimensional software measurement techniques. Imagemeasurements were compared with caliper measurements of the skulls.Study design. Cone beam computed tomography volumes of 28 skulls in ideal, shifted, and rotated positions wereassessed by measuring distances between anatomic points and reference wires by using panoramic reconstructions(two-dimensional) and direct measurements from axial slices (three-dimensional). Differences between calipermeasurements on skulls and software measurements in images were assessed with paired t tests and analysis ofvariance (ANOVA).Results. Accuracy of measurement was not significantly affected by alterations in skull position or measurementof right or left sides. For easily visualized orthodontic wires, measurement accuracy was expressed by averageerrors less than 1.2% for two-dimensional measurement techniques and less than 0.6% for three-dimensionalmeasurement techniques. Anatomic measurements were significantly more variable regardless of measurementtechnique.Conclusions. Both two-dimensional and three-dimensional techniques provide acceptably accurate measurement ofmandibular anatomy. Cone beam computed tomography measurement was not significantly influenced by variation in

skull orientation during image acquisition. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2007;103:534-42)

Diagnosis and treatment of facial asymmetry requiresaccurate measurement of a variety of osseous and softtissue landmarks. Measurement of mandibular anatomyis problematic when using panoramic radiography.1

Previous studies suggest that projection geometry, focal

This work was supported by NIH grant DE-05215 from the NationalInstitute of Dental Research (to C.P.).aProfessor, Department of Diagnostic Sciences and General Den-tistry, University of North Carolina.bBrunk and Laster Orthodontics (private practice), Raleigh, NC.cThird-Year DDS Student, University of North Carolina.dAssociate Professor, Department of Orthodontics, University ofNorth Carolina.eProfessor, Department of Orthodontics, University of North Caro-lina.Received for publication May 7, 2005; returned for revision Apr 3,2006; accepted for publication Apr 6, 2006.1079-2104/$ - see front matter© 2007 Mosby, Inc. All rights reserved.

doi:10.1016/j.tripleo.2006.04.008

534

plane shape, differential vertical and horizontal magni-fication factors, and operator error in patient position-ing affect the utility of panoramic images to provideaccurate measurements.1-9 Although medical computedtomography (CT) imaging provides higher accuracywith no significant difference between measurement ofactual landmarks or CT images,10-11 its relatively highx-ray dose and examination costs make medical CTundesirable for routine orthodontic diagnosis. The in-troduction of low-dose, low-cost cone beam CT for oraland maxillofacial imaging holds the promise of over-coming these obstacles while providing more accuratecraniometric and orthodontic diagnostic informationthan conventional radiographic techniques.12 Becauseconventional medical CT technology differs from conebeam computed tomography (CBCT) in the choice ofx-ray sources, detectors, and reconstruction algorithms,performance characteristics may differ.13 Few studies

have investigated the accuracy of CBCT for craniomet-

OOOOEVolume 103, Number 4 Ludlow et al. 535

ric measurement.14 This study uses multiple positionsof multiple dry skulls to assess the accuracy of planerand three-dimensional measurements of mandibularanatomy.

MATERIAL AND METHODSSkull preparation and landmark identification

While a number of anatomical landmarks may bechosen to evaluate image fidelity in the assessment ofmandibular symmetry, a combination of investigator-applied radiopaque markers and natural anatomic land-marks that could be employed in making caudal-cranialand anterior-posterior measurements were chosen forthis study. Superior condylar surface (condylion), go-nial angle (gonion), and mental foramen were selectedas anatomic landmarks. Condylion to gonion measure-ment (C-G) provides an assessment of the verticaldimension of the ramus and its contribution to posteriorfacial height. Gonion to mental foramen measurement(G-MF) permits horizontal assessment of mandibulardimension. These dimensions are commonly affectedby mandibular asymmetry. Fixed-length straight orth-odontic wires, affixed to the mandible in vertical andhorizontal orientations, provided external references forimage measurement accuracy.

Thirty dry skulls were borrowed from the AnatomyDepartment at the University of North Carolina atChapel Hill. Radiopaque .018-inch straight orthodonticwires, trimmed to precise lengths of 40.0 mm and 20.0mm, were attached to the right and left sides of eachmandible. The 40-mm markers were oriented approxi-mately parallel to C-G and affixed to the lateral surfaceof the mandibular ramus by using clear adhesive tape.The 20-mm markers were oriented approximately par-allel to G-MF and similarly attached to the lateralsurface of the mandibular body.

Paper adhesive labels were placed on the anteriorskull and marked with lines to facilitate skull position-ing for radiographic images. These labels were placedon the anterior nasal spine, nasion, and anatomicalpogonion. The labels were also marked 7 mm to the leftof each of these anatomic points. Graph paper wasplaced over the area on the skull where the calvariumhad been removed. A line representing the midsagittalplane was drawn on the graph paper. A second line wasdrawn 7 mm to the left of midsagittal. A third line wasscribed that was at 10° to midsagittal as measured witha protractor by using a vertex located 7 cm posterior tothe most anterior point on the midsagittal line.

Skull measurementAccurate determination of gonion is challenging.

The problem is related to the curving transition between

the posterior ramus margin and the inferior mandibular

border. It is difficult to locate the most posterior andinferior point on this curved surface without the aid ofsurface tangents and angle bisectors. In an approachthat permitted the application of tangents and bisectors,an angle-forming tool (Angle Divider No. 19050, BigHorn Corporation, Littleton, Colo) was modified withthe addition of wood block extensions (Fig. 1). Eachside of the mandible was positioned in the angle divisorsuch that the extensions simultaneously contacted 2points on the posterior ramus edge and 2 points on theinferior border of the mandible. Using the tip of apencil, the bisector of this gonial angle was markedwhere it visually intersected the cortical border of themandible. Marking of gonion was facilitated by agroove in the center of the bisector arm through whichthe pencil point was inserted. If a continuously curvinglower mandibular border was encountered, a tangent tothis surface at the middle of the body of the mandiblewas used. A digital caliper (Absolute Digimatic No.500-172, Mitutoyo America Corporation, Aurora, Ill)was used to measure the distances between C-G andG-MF. Distances were recorded to the nearest 0.1 mm.

Cone beam computed tomography imagesCone beam computed tomography images were ac-

quired with a NewTom 9000 CBCT scanner (NIMS.r.l., Verona, Italy) using a 9-inch field of view. Tomaintain their dry condition while immersed in water,skulls were placed in plastic bags and oriented in asupine position in an acrylic immersion box (20 cm �20 cm � 20 cm) for image acquisition. The box designincorporated vertical lines marking the midsagittalplane of the box. The aforementioned skull labels wereused to orient the skull midsagittal plane relative to thebox midsagittal plane. The box midsagittal plane was

Fig. 1. Modified angle divisor tool with right mandible seatedand ready for marking of gonial angle. A pencil will be placedin the groove of the bisector arm to mark gonion.

then aligned with respect to the midsagittal-positioning

OOOOE536 Ludlow et al. April 2007

laser of th CBCT unit. A laterally placed anterior-posterior positioning laser on the unit was used toadjust the height of the patient table until the laser wascentered on the ramus. For ideal position, midsagittalplanes of the skull and box were centered in the mid-sagittal-positioning beam. For shifted position, skullorientation remained the same, but the box was shiftedto the right until the midsagittal positioning beamaligned with the marks on the skull labels correspond-ing to the 7-mm lateral shifted position. For rotatedposition, the skull was removed from the box andrepositioned in such a way that the rotated line on thegraph paper covering the cranial vault now corre-sponded to the midsagittal plane of the box. After theskull was secured in place using a combination of rigidfasteners and elastic bands, the box was filled withwater to simulate the attenuation of soft tissues thatwould be present in clinical imaging. Computed tomog-raphy data were imported into NewTom 3G softwarefor primary reconstruction of images. Primary recon-structions were made using the large window settingwith .5-mm axial slices. Axial slicing was orientedparallel to the Frankfort plane.

Cone beam computed tomography measurementusing panoramic slice and two-dimensional tool

Secondary reconstruction and measurement of theCBCT images was accomplished using the NewTom3G software package. With operator-selected 15- or20-mm slice thicknesses, the panoramic tool was usedon a representative axial slice to reconstruct the CBCTdata in the form of a panoramic image. Initial mappingof the panoramic path was adjusted as needed to ensure

Fig. 2. Example of 15-mm panoramic image layer used for tmarks are projections from the axial slice at the center ofgonion-mental foramen distance, B � horizontal reference w� gonial angle, and F � gonial angle bisector.

that all anatomical points of interest could be easily

located within the slice. Once the reconstruction hadtaken place, axial views of the data were used to locatespecific anatomical points. Superior condyle and theposterior edge of the mental foramen on each side weremarked using the software marking tool. These markswere centered on each landmark and were extendedapproximately 2 cm mediolaterally. In the case of thecondyle, the mark extended parallel to the long axis ofthe condyle. In the case of the mental foramen, themark was extended perpendicular to the long axis of thebody of the mandible at this point. These marks wereautomatically displayed in the panoramic image at thepoint where each intersected the center of the imagelayer. Gonial angle was defined using the softwareangle tool. In a manner analogous to the physical de-termination of gonion on the skull, the arms of theangle were placed in contact with the surface of theposterior ramus border and inferior mandibular bodyborder. A second angle was placed at the vertex of thefirst angle to form a bisecting angle. The contact of thebisector with the cortical border was defined as gonion(Fig. 2).

Measurements were made using a computer mouseto position the two-dimensional measurement toolcursor at one and then the other end of the landmarksof interest. The distance between landmarks alongthe curved plane at the center of the panoramic imagelayer was automatically calculated and displayed.Lengths of the vertical and horizontal markers aswell as C-G and G-MF distances were measured foreach side. The image reconstruction software andmeasuring tools are calibrated by the manufacturer

ensional measures. Condylion, gonion, and mental foramenage layer location (see Fig. 3). Measurement values: A �

vertical reference wire, D � condylion-gonion distance, E

wo-dimthe imire, C �

for 1:1 measurement.

OOOOEVolume 103, Number 4 Ludlow et al. 537

Cone beam computed tomography measurementusing axial slices and three-dimensional tool

The NewTom CBCT software allows the user tomeasure linear distances in 3 dimensions by using 2different axial slices. Vertical and horizontal markerswere measured by mouse clicking the three-dimen-sional measurement tool on the marker in the first axialslice in which it appeared, as well as the last axial slicebefore it disappeared. Due to their radiopaque natureand finite size, the ends of the markers were easilyidentified in the axial slices. Condylion to gonion mea-surement and G-MF measurements were made afterfirst marking gonion in the axial slice by using themarker tool. Gonion location was determined itera-

Fig. 3. Axial slices and marked measuring points. Red linesto the landmark. Crosshairs represent measuring points placedin every axial slice between the actual measurement point lmeasurement of condylion-gonion distance. B, Marking ogonion-mental foramen measurements. Outer values depict ccortical surface of the posterior aspect of the right mental fodistances.

tively. By double-clicking the cursor location on the

gonion region in the lateral scout view, the axial sliceassociated with this area is displayed. In this axial slice,the marker tool was used to draw a short line tangent tothe posterior ramus surface and perpendicular to thelong axis of the ramus. The location of this mark waschecked in the panoramic image layer. If the mark wasnot coincident with the intersection point of the gonialangle bisector line with the ramus border, the mark waserased and a different axial slice was selected andmarked. After gonion was marked, the cursor of thethree-dimensional measuring tool was positioned onthe mark for 1 of the 2 desired landmarks. The operatorthen scrolled through the stack of axial slices until themark for the other landmark was located. After select-

aced perpendicular to the panoramic image path and tangente three-dimensional measuring tool. Crosshairs are displayeds. A, Marking of superior condylar surfaces bilaterally and

ramus cortex at gonion bilaterally. Inner values representn to gonion measurement distance. C, Marking of the inner

. Measurements are gonion to mental foramen measurement

are plby th

ocationf theondylioramen

ing this landmark, the linear distance between the

OOOOE538 Ludlow et al. April 2007

points was automatically calculated. Fig. 3 providesexamples of axial slices containing condylion, gonion,and mental foramen. Measured distance and pairs ofcrosshairs indicating the trajectory between points areautomatically recorded on the images.

ObserversSkull dimensions were measured twice by observer

A and once by observer B. Wire segments were mea-sured twice in two-dimensional and three-dimensionalimages by observer C. Condylion to gonion measure-ment and G-MF distances were measured in CBCTimages once each by observers A and B. Observer Awas an experienced oral and maxillofacial radiologist.Observer B was a third-year dental student having littleprior experience with skull or image measurement tech-niques. Observer C was a third-year orthodontic resi-dent.

Statistical analysisInterobserver variation was determined by paired t

tests for skull, two-dimensional, and three-dimensionalmeasurements. Intraobserver measurement variationwas determined by paired t tests of first and secondmeasurements. To compensate for multiple compari-sons, significance was set at � � 0.01. Averages of the2 measurements of observer A were used for furthercomparisons of imaging method and anatomic feature.Paired t tests were used to determine statistical signif-icance between measurements of CT and photographicimages. Again, an alpha level of .01 was selected forstatistical significance. Analysis of variance (ANOVA)was performed on the subset of measurements commonto both two-dimensional and three-dimensional mea-surement techniques. The ANOVA model includedmain effects of two-dimensional versus three-dimen-sional measurements (2), skull orientation (3), skullside (2), and skull measurement feature (C-G, G-MF),as well as the interactions of these variables. Thethreshold for statistical significance was set at � � .05.

RESULTSTwo of the original 30 skulls had 1 or more image

volumes where a condyle was shifted or rotated out ofthe image volume, limiting the image data to 28 skulls.These skulls and images were excluded from the dataanalysis. Images from the 28 skulls were used to cal-culate interobserver measurement variation. In addi-tion, these skull images were used to determine mea-surement accuracy of horizontal and vertical referencewires. Following initial skull measurement, 3 of theskulls were unavailable for interobserver and intraob-server measurement. Therefore, complete data was

available for 25 skulls. Because an average of first and

second measurements of the skull features was used as“truth,” assessment of C-G and G-MF measurementaccuracy was constrained to the 25 skulls with com-plete data. Table I shows the reproducibility of repeatedmeasurement of skulls. Measurements were reproduc-ible for observer A with a mean difference of �0.08mm for C-G and 0.12 mm for G-MF between secondand first measurements. These differences were notstatistically significant. Interobserver variation wasgreater with a difference of �0.89 mm for C-G and0.87 mm for G-MF between observer A and observerB. These differences were statistically significant.

Repeated measurements of horizontal and verticallyoriented wires seen in Table II were not different fortwo-dimensional measurements and were on averagewithin 0.25 mm of each other. First and second three-dimensional measurements were also not statisticallydifferent and were on average within 0.07 mm withrepeated measurement. Interobserver variation in themeasurement of skeletal landmarks is seen in Table III.While significant differences in measurement were seenwith the 2 observers, the means of these differenceswere less than 0.9 mm.

Table IV shows ANOVA model factors and P valuesresulting from the assessment of difference and abso-lute value of difference between CT measurements anddirect skull measurements for observer A. Differenceand magnitude of difference (absolute value) measure-ments were not significant for measuring technique orskull position. The magnitude of difference in measur-ing right or left sides was significantly different; how-ever, on average, there was neither significant underes-timation nor overestimation due to skull side. Aninteraction of anatomic feature and skull side was sig-nificant for measurement difference, but not for mea-surement magnitude.

The sources of significant measurement differencesbetween CT and known wire dimensions or skull mea-surements can be seen in Tables V and VI. The data

Table I. Intraobserver and interobserver variation inmeasuring condylion-gonion and gonion-mental fora-men distances on 25 skulls

C-G G-MF

Intraobserverreading 2-1

Mean difference �0.08 0.12Standard error 0.17 0.13Probability of � |t| 0.6317 0.3627

InterobserverobserverA, B

Mean difference �0.89 0.87Standard error 0.25 0.26Probability of � |t| 0.0009 0.0018

C-G, condylion-gonion; G-MF, gonion-mental foramen; prob, authorqueried.

from wire measurements using either two-dimensional

bsolute

OOOOEVolume 103, Number 4 Ludlow et al. 539

or three-dimensional techniques demonstrate excellentaccuracy regardless of wire orientation, measurementside, or skull position. Average magnitude of differ-ences in wire measurements was less than 0.5 mm fortwo-dimensional CT, and less than 0.3 mm for three-dimensional CT. For the two-dimensional measurementtechnique, consistent undermeasurement of wires aver-aged approximately 1.2% of the actual distance, whilethe average magnitude of error was approximately2.0%. For three-dimensional measurement, horizontalwire length was slightly overestimated, whereas verti-cal wire length was underestimated. Average measure-ment error was approximately 0.7%, and the averagemagnitude of individual errors was approximately 1%.

Anatomical measurements were more variable re-gardless of measurement technique. Using two-dimen-sional measurement techniques, G-MF was overesti-

Table II. Repeated measurements accuracy. Differenc

Wireorientation

Skullside

2D measuremen

Mean Difference(Mean Abs Diff) SD

Horizontal Left 0.25 0.99(0.50) 0.39

Right �0.24 1.01(0.47) 0.34

Vertical Left 0.02 0.84(0.56) 0.39

Right 0.22 1.01(0.61) 0.47

2D, two dimensional; 3D, three-dimensional; mean abs diff, mean a

Table III. Interobserver variation in measuring go-nion-mental foramen and condylion-gonion distancesusing two-dimensional and three-dimensional measure-ment techniques on 28 skulls imaged in 3 positions:difference observers A and BLandmarks Side Measurement 2D 3D

G-MF Left Mean difference 0.17 �0.78Standard error 0.27 0.20Probability of � |t| 0.5185 0.0002

Right Mean difference 0.29 �0.75Standard error 0.20 0.19Probability of � |t| 0.1651 0.0002

C-G Left Mean difference �0.90 �0.62Standard error 0.19 0.19Probability of � |t| �.0001 0.0017

Right Mean difference �0.41 0.24Standard error 0.18 0.24Probability of � |t| 0.0314 0.2029

2D, two-dimensional; 3D, three dimensional; G-MF, gonion-mentalforamen; C-G, condylion-gonion; prob, author queried.

mated by 3.8%, whereas C-G was underestimated by

2.9%. Using three-dimensional techniques, G-MF andC-G were both overestimated by 2.5% and 3.1%, re-spectively. The average magnitude of error for all mea-surements was 2.8% for two-dimensional techniquesand 2.5% for three-dimensional techniques.

DISCUSSIONThere are a number of potential sources for measure-

ment error in this study. The CBCT unit actually rotateswith a slight wobble that is a potential source of imagedistortion. A correction algorithm is used to removethat distortion prior to reconstruction of images. Errorsin the algorithm or changes in the wobble pattern overtime may result in residual distortion. Precision ofmeasurement is limited by the resolution of the system.The reconstruction pixel size of 0.5 mm chosen for this

een first and second measurements for 28 skulls3D measurement

P valueMean Difference(Mean Abs Diff) SD P value

0.02 �0.02 0.56 0.71(0.34) 0.23

0.03 �0.05 0.42 0.24(0.19) 0.14

0.8 0.07 0.38 0.08(0.25) 0.19

0.04 0.03 0.36 0.46(0.37) 0.23

value of difference (measurement–truth).

Table IV. Assessment of difference and absolute valueof difference between image measurements and skullmeasurements: ANOVA model and resulting P values

Source Factors

DifferenceAbsolutedifference

Probability of� F

Probability of� F

Modality 2D, 3D 0.7107 0.0682Feature G-MF, C-G �.0001 �.0001Position Ideal, rotated,

shifted0.2510 0.5585

Side Right, left 0.1382 �.0001Modality*position 0.7772 0.9244Modality*feature 0.0338 0.6808Modality*side 0.5779 0.1942Position*feature 0.2633 0.1701Position*side 0.6556 0.6268Feature*side �.0001 0.3748

2D, two-dimensional; 3D, three-dimensional; G-MF, gonion-mentalforamen; C-G, condylion-gonion.*indicates interaction term.

e betwt

study limits accuracy of individual measurements to

h|.

.

OOOOE540 Ludlow et al. April 2007

�0.5 mm. In addition, partial volume averaging mayreduce the visibility of a structure within an imagelayer. This would tend to result in underestimation ofthe edges of structures such as cortical bone surfaces orthe orthodontic wire ends measured in this study. Al-though primary and secondary slice reconstructionthickness will also influence measurement, narrowerslices should result in better measurement accuracy.Measurement of wire markers in this study suggest thatthe NewTom 9000 performed well in providing vol-umes that are relatively free from distortion in vertical

Table V. Wire landmarks: comparison of differencesments of 20-mm horizontal wires and 40-mm vertical

Wireorientation

Skullside Measurement

Horizontal Left Mean error (mm)% errorSD

Right Mean error (mm)% errorSD

Vertical Left Mean error (mm)% errorSD

Right Mean error (mm)% errorSD

2D, two-dimensional; 3D, three-dimensional.*Average of 84 measurements (measurement in image�known leng†Average of 84 measurements |measurement in image�known lengt

Table VI. Skull landmarks: comparison of differencesments of gonion-mental foramen (G-MF) and condylio

LandmarksSkullside Measurement

G-MF Left Mean error (mm)% errorSD

Right Mean error (mm)% errorSD

C-G Left Mean error (mm)% errorSD

Right Mean error (mm)% errorSD

G-MF, gonion-mental foramen; C-G, condylion-gonion.*Average of 75 measurements (measurement in image�skull length†Average of 75 measurements |measurement in image�skull length|

and horizontal dimensions.

Measuring features within a reconstructed imagelayer is analogous to making measurements on conven-tional transmission radiographs such as cephalometricor panoramic images. While predictable anatomic dis-tortions due to projection geometry and panoramic im-age layer formation characteristics are present, theireffect on actual anatomic structures is dependent on theshape and orientation of the structure. Because of this,true anatomical variation or asymmetry in a patient maybe difficult to distinguish from projective distortion inthe image. Cone beam computed tomography volumes

een two-dimensional and three-dimensional measure-for 28 skulls imaged in 3 positions

Difference*Absolute value of

difference†

2D 3D 2D 3D

�0.28 0.18 0.5 0.341.4% 0.9% 2.5% 1.7%

(0.58) (0.38) (0.39) (0.23)�0.20 0.03 0.47 0.19

1.0% 0.2% 2.4% 1.0%(0.56) (0.24) (0.34) (0.14)

�0.47 �0.23 0.56 0.251.2% 0.6% 1.4% 0.6%

(0.50) (0.23) (0.39) (0.19)�0.50 �0.36 0.61 0.37

1.3% 0.9% 1.5% 0.9%(0.60) (0.26) (0.47) (0.23)

een two-dimensional and three-dimensional measure-on (C-G) distances for 25 skulls imaged in 3 positions

Difference*Absolute value of

difference†

2D 3D 2D 3D

1.66 1.26 1.77 1.373.0% 2.3% 3.2% 2.5%

(1.78) (1.28) (1.68) (1.15)0.26 0.13 0.97 0.960.5% 0.2% 1.7% 1.7%

(1.34) (1.33) (0.95) (0.92)�2.1 �1.89 2.12 1.94�3.7% �3.4% 3.8% 3.5%

(1.24) (1.27) (1.21) (1.19)�1.13 �0.96 1.3 1.21�2.0% �1.7% 2.3% 2.2%

(1.05) (1.13) (0.83) (0.84)

betwwires

th).

betwn-goni

).

provide the radiologist with the flexibility of choosing

OOOOEVolume 103, Number 4 Ludlow et al. 541

the orientation of reconstructed image layer. The oper-ator has the advantage of constructing the image layerafter studying a volume of axial slices. In this way, theimage layer can be adapted to the anatomy of interest.

But the image layer may not fully conform to theanatomy in all directions. Panoramic image layers inthis study were mapped using representative axialslices. Generation of the reformatted panoramic imageextended the mapping perpendicular to the axial slicethrough the complete stack of axial slices. To be surethat relevant anatomy was contained in the panoramicview, a finite image layer of 15 or 20 mm was chosen.This means that anatomy anywhere within the imagelayer would be projected in the displayed panoramicimage on lines parallel to the axial slice plane andperpendicular to the mapping line. For a linear ana-tomic feature such as an orthodontic wire, oriented atan angle with respect to the reconstruction axis (the axisis perpendicular to the axial slice), and in a planeperpendicular to the panoramic mapping line, the imageof the feature will appear smaller than the feature’sactual size. This size reduction will be a function of thecosine of the angle formed by the feature with respectto the reconstruction axis. Angular deviations less than18° result in image size reductions less than 5%.

The situation in measuring gonion-mental foramen issomewhat different. The panoramic image layer ap-proximates the curve of the mandible between gonionand the mental foramen. However, the caliper measure-ment of gonion-mental foramen on the skull representsa straight line, which is a secant to the curve repre-sented by the panoramic image layer. Based on thepreceding theoretical arguments, it would be expectedthat two-dimensional measurements of a panoramicimage layer would overestimate gonion-mental fora-men distances and underestimate condylion-gonion dis-tances. This is supported by the data seen in Table VI.The measurement errors seen with two-dimensionaltechniques are reduced with three-dimensional mea-surement techniques. The small measurement errorsseen with two-dimensional measurement techniques inthis study suggest that the chosen anatomic points andreference wires had acceptably small deviations fromthe plane of the panoramic reconstruction.

Unlike two-dimensional measurements within a re-constructed image layer, three-dimensional measure-ments are made between points within a volume andthus are not subject to projective distortion. The chal-lenge arises in defining and selecting the points to bemeasured. When CBCT images were measured withthe three-dimensional tool, it was not possible to locategonion in the axial slice without referencing the pan-oramic image layer where the gonial angle was calcu-

lated and bisected. This problem is an illustration of the

difficulty in using three-dimensional tools to measureanatomic points that have traditionally been definedusing two-dimensional image techniques and tools. Thethree-dimensional measurement tool in the NewTomsoftware was more accurate than the two-dimensionaltool for measuring distances where landmarks weredefined by visually unambiguous points such as theends of orthodontic wires. However, the absence of anangle measurement tool that could be used in a three-dimensional volume restricted the operator’s ability tofind an analogous point for gonion, which had beenreadily defined using lines and angles on the two-dimensional plane of a panoramic image. New measur-ing tools must be developed if clinicians are to take fulladvantage of the accuracy promised by three-dimen-sional measurements of CBCT volumes. At the sametime, orthodontists need to reassess the definition ofcephalometric landmarks that have been described interms of planar projections of sagittal and coronal anat-omy. These definitions may need to be modified formeasurement in three-dimensional volumes. New ana-tomic landmarks and reference planes may need to beadopted to take full advantage of the measurementaccuracy and diagnostic potential afforded by CBCTimaging.

The standard deviations for differences in repeatedskull measurements of 0.85 mm for posterior mandib-ular height and 0.6 mm gonion-mental foramen indicateless precision in measurement of skeletal dimensionsthan was seen with measurement of wire dimensionswith three-dimensional measurement techniques. Thisvariability is largely due to the difficulty in determininggonion. The modified angle-bisecting tool used in thisstudy was subject to parallax errors in positioning apencil within the bisector groove of the tool to markgonion (Fig. 1). It should be noted that systematicerrors in locating skull gonion related to the use of theangle-bisecting tool would have a detrimental impacton image measurements. The possibility of such anerror is suggested by the interobserver differences inskull measurement where posterior-mandibular heightwas overestimated and gonion-mental foramen was un-derestimated by an average of 0.9 mm by observer B.Experience in making measurements may also play arole in interobserver and intraobserver variability. Itmight be anticipated that the less-experienced observerB would have greater variability in measurements.

Wire measurement accuracy using the three-dimen-sional measuring tool is comparable to the accuracyreported by Marmulla and coauthors,15 who used anacrylic phantom. The mean absolute error of 0.13 mmand standard deviation of 0.09 mm in that study com-pares with mean absolute errors of 0.29 mm and stan-

dard deviation of 0.20 mm in this study. The use of a

OOOOE542 Ludlow et al. April 2007

computer algorithm to localize measurement pointswith pixel fractionalization in the former study versusobserver selection of measurement points by usingmouse manipulation of a cursor in this study may be theprinciple reason for the approximately twofold differ-ence in measurement accuracy.

Variations in skull positioning were incorporatedinto the design of this study because skull position hasbeen demonstrated to be a factor in measurement ac-curacy for conventional radiographic imaging and hasbeen cited as an important factor in false-positive andfalse-negative diagnosis of mandibular asymmetry inpanoramic imaging.1 Farman16 has argued that the bestof modern panoramic units may permit a posterioriadjustments to compensate both for patient position andfor differences in arch shape and tooth contact angula-tions in the maxilla and mandible. But this argumentignores the difficulty in distinguishing distortion result-ing from nonideal patient positioning from distortionresulting from skeletal asymmetry. It also overlooks thedifficulty in incorporating fiducial landmarks on thepatient so that images and measurements can be ad-justed after the fact when asymmetry is present. Theresults of the current study indicate that difficultiesassociated with patient positioning and uncertainties ofmeasurement accompanying patient asymmetry in pan-oramic images are not present in CBCT images.

CONCLUSIONSA number of conclusions are suggested by the results

of this study. In contrast to current plane projection(cephalometric) and image layer (panoramic) tech-niques, measurements of anatomy in CBCT volumesexamined in this study were relatively uninfluenced byskull orientation. As is commonly reported for ad-vanced imaging and complex measurement tasks, op-erator experience has a positive effect on measurementaccuracy and reproducibility. For well-defined points,measurement accuracy was expressed by average errorsless than 1.2% for two-dimensional measurement tech-niques and less than 0.6% for three-dimensional mea-surement techniques. While the measured features andmeasurement techniques differed from previous stud-ies, average measurement errors from 0.2 mm to 2.1mm are in line with errors reported for both conven-tional and cone beam CT.14,17 With the appropriatechoice and definition of landmarks, and the availabilityof three-dimensional measuring tools, this accuracy hasthe potential of providing unambiguous information fordiagnosis of skeletal asymmetry, longitudinal monitor-ing of growth, and postsurgical assessment.

REFERENCES1. Laster WS, Ludlow JB, Bailey LJ, Hershey HG. Accuracy of

measurements of mandibular anatomy and prediction of asym-

metry in panoramic radiographic images. DentomaxillofacRadiol 2005;34:343-9.

2. Tronje G, Eliasson S, Julin P, Welander U. Image distortion inrotational panoramic radiography. II. Vertical distances. ActaRadiol Diagn (Stockh) 1981;22:449-55.

3. Habets LL, Bezuur JN, van Ooij CP, Hansson TL. The ortho-pantomogram, an aid in diagnosis of temporomandibular jointproblems. I. The factor of vertical magnification. J Oral Rehabil1987;14:475-80.

4. Kjellberg H, Ekestubbe A, Kiliaridis S, Thilander B. Condylarheight on panoramic radiographs. A methodologic study with aclinical application. Acta Odontol Scand 1994;52:43-50.

5. Turp JC, Vach W, Harbich K, Alt KW, Strub JR. Determiningmandibular condyle and ramus height with the help of anOrthopantomogram–a valid method? J Oral Rehabil 1996;23:395-400.

6. Xie Q, Soikkonen K, Wolf J, Mattila K, Gong M, Ainamo A.Effect of head positioning in panoramic radiography on verticalmeasurements: an in vitro study. Dentomaxillofac Radiol1996;25:61-6.

7. Catic A, Celebic A, Valentic-Peruzovic M, Catovic A, JerolimovV, Muretic I. Evaluation of the precision of dimensional mea-surements of the mandible on panoramic radiographs. Oral SurgOral Med Oral Pathol Oral Radiol Endod 1998;86:242-8.

8. Mckee IW, Glover KE, Williamson PC, Lam EW, Heo G, MajorPW. The effect of vertical and horizontal head positioning inpanoramic radiography on mesiodistal tooth angulations. AngleOrthod 2001;71:442-51.

9. Stramotas S, Geenty JP, Petocz P, Darendeliler MA. Accuracy oflinear and angular measurements on panoramic radiographstaken at various positions in vitro. Eur J Orthod 2002;24:43-52.

10. Cavalcanti MG, Haller JW, Vannier MW. Three-dimensionalcomputed tomography landmark measurement in craniofacialsurgical planning: experimental validation in vitro. J Oral Max-illofac Surg 1999;57:690-4.

11. Lo LJ, Lin WY, Wong HF, Lu KT, Chen YR. Quantitativemeasurement on three-dimensional computed tomography: anexperimental validation using phantom objects. Chang GungMed J 2000;23:354-9.

12. Maki K, Inou N, Takanishi A, Miller AJ. Computer-assistedsimulations in orthodontic diagnosis and the application of a newcone beam X-ray computed tomography. Orthod Craniofac Res2003;6(Suppl 1):95-101.

13. Vannier MW. Craniofacial computed tomography scanning:technology, applications and future trends. Orthod Craniofac Res2003;6(Suppl 1):23-30.

14. Lascala CA, Panella J, Marques MM. Analysis of the accuracy oflinear measurements obtained by cone beam computed tomography(CBCT-NewTom). Dentomaxillofac Radiol 2004;33:291-4.

15. Marmulla R, Wörtche R, Mühling J, Hassfeld S. Geometricaccuracy of the NewTom 9000 Cone Beam CT. DentomaxillofacRadiol 2005;34:28-31.

16. Farman AG. Panoramic radiographic images and the predictionof asymmetry Dentomaxillofac Radiol 2006;35:129.

17. Cavalcanti MG, Vannier MW. Quantitative analysis of spiralcomputed tomography for craniofacial clinical applications.Dentomaxillofac Radiol 1998;27:344-50.

Reprint requests:

John B. Ludlow, DDS, MS120 Dental Office Bldg.UNC School of DentistryChapel Hill, NC 27599-7450

jbl@email.unc.edu