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Investigation of uncertainties in image registration of cone beam CT to CT on an image-

guided radiotherapy system

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2009 Phys. Med. Biol. 54 7263

(http://iopscience.iop.org/0031-9155/54/24/002)

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IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 54 (2009) 7263–7283 doi:10.1088/0031-9155/54/24/002

Investigation of uncertainties in image registration ofcone beam CT to CT on an image-guidedradiotherapy system

J R Sykes1, D S Brettle2, D R Magee3 and D I Thwaites1

1 Medical Physics and Engineering, St James’s Hospital, Leeds Teaching Hospitals Trust, Leeds,LS9 7TF, UK2 Medical Physics and Engineering, Leeds General Infirmary, Leeds Teaching Hospitals Trust,Leeds, LS1 3EX, UK3 School of Computing, University of Leeds, Leeds, LS2 9JT, UK

E-mail: jonathan.sykes@leedsth.nhs.uk

Received 12 June 2009, in final form 26 October 2009Published 20 November 2009Online at stacks.iop.org/PMB/54/7263

AbstractMethods of measuring uncertainties in rigid body image registration of fan beamcomputed tomography (FBCT) to cone beam CT (CBCT) have been developedfor automatic image registration algorithms in a commercial image guidancesystem (Synergy, Elekta, UK). The relationships between image registrationuncertainty and both imaging dose and image resolution have been investigatedwith an anthropomorphic skull phantom and further measurements performedwith patient images of the head. A new metric of target registration erroris proposed. The metric calculates the mean distance traversed by a set ofequi-spaced points on the surface of a 5 cm sphere, centred at the isocentrewhen transformed by the residual error of registration. Studies aimed at givingpractical guidance on the use of the Synergy automated image registration,including choice of algorithm and use of the Clipbox are reported. Thechamfer-matching algorithm was found to be highly robust to the increasednoise induced by low-dose acquisitions. This would allow the imaging doseto be reduced from the current clinical norm of 2 mGy to 0.2 mGy without aclinically significant loss of accuracy. A study of the effect of FBCT slicethickness/spacing and CBCT voxel size showed that 2.5 mm and 1 mm,respectively, gave acceptable image registration performance. Registrationfailures were highly infrequent if the misalignment was typical of normalclinical set-up errors and these were easily identified. The standard deviationof translational registration errors, measured with patient images, was 0.5 mmon the surface of a 5 cm sphere centred on the treatment centre. The chamferalgorithm is suitable for routine clinical use with minimal need for closeinspection of image misalignment.

0031-9155/09/247263+21$30.00 © 2009 Institute of Physics and Engineering in Medicine Printed in the UK 7263

7264 J R Sykes et al

1. Introduction

Image-guided radiotherapy systems with integrated kilovoltage x-ray imaging systems andutilizing cone beam computed tomography (CBCT) reconstruction techniques have recentlybecome commercially available (Jaffray et al 1999, Letourneau et al 2005, McBain et al 2006).These systems rely on the ability to localize target tissues, or their surrogates, and compareagainst the reference fan beam CT (FBCT) and associated target and organ at risk delineationsbelonging to the treatment plan. Errors in the patient position can be corrected easily bya couch translation and on some systems couch rotation. This has the potential to reducethe treatment margin added to the clinical target volume (CTV) to create the planning targetvolume (PTV) (ICRU 1999). Consequently the irradiation of surrounding normal tissues willbe reduced with an implied reduction in complications and, if the dose is escalated, there ispotential to increase local control (Ghilezan et al 2005, Burridge et al 2006, Gao et al 2006).

While the uncertainties in delivering radiotherapy to the CTV can be reduced with thesesystems, it is important to understand the residual uncertainties arising from the IGRT process.These are (a) accuracy of the spatial coordinates of the image with respect to the megavoltage(MV) treatment beam, (b) the uncertainties in image registration and (c) the accuracy withwhich the patient can be re-positioned. The first and last of these, which depend on goodsystem engineering, can be measured and where possible minimized through careful systemcalibration and quality assurance (Bissonnette et al 2008, Cho et al 2005, Meyer et al 2007,Sharpe et al 2006, Sykes et al 2008). The second can be facilitated by automatic imageregistration but inevitably requires human judgement to assess and adjust the alignment, ifunacceptable.

Image registration (IR) is the process of establishing correspondence between two images(Hill et al 2001). For CBCT-based image-guided radiotherapy, the two images are typicallya reference FBCT image used to plan the patient’s treatment and a CBCT image acquiredimmediately before or during the treatment session. The ability to correct the patient positionis often restricted to translational shifts with the possible inclusion of small rotations (Meyeret al 2007). For this reason, the correspondence between the two images is normally establishedthrough a rigid body transformation. The aim of the process is to determine a set of translationsand rotations that, if necessary, can be applied to the patient position. The accuracy of theinitial alignment of the images is therefore critical and is normally achieved by aligning theposition of the machine isocentre in the CBCT image with the planned isocentre position inthe reference CT image (Bissonnette et al 2008, Sykes et al 2008). In commercial IGRTsystems, both manual and automated methods of IR are typically implemented. With manualIR, the two images are overlaid in a fused display, showing each of the transaxial, sagittal andcoronal planes, and an operator manually translates and rotates one image with respect to theother. The currently available commercial IGRT systems all have different implementationsof automated rigid body IR. The Synergy R© system (Elekta, Crawley, UK) employs twoalgorithms; one designed for registering only the bony anatomy, called ‘Bone’, which uses thechamfer-matching algorithm (van Herk and Kooy 1994) and the second ‘Grey Value’, designedfor matching bone and/or soft tissues which uses the correlation ratio voxel similarity metric(Roche et al 1998, Smitsmans et al 2005). Automated IR has the potential to greatly speedup the alignment of two images and remove any subjectivity incurred by a human observer(Smitsmans et al 2005). This is important in order to minimize the impact on a clinical serviceif daily image-guided radiotherapy with online correction is to be implemented in a busyradiotherapy department.

Due to the nature of automated IR, there will be uncertainties in the process which willlead to small and sometimes, in the case of registration failure, very large errors. For this

Investigation of CBCT-CT image registration uncertainties in IGRT 7265

reason, automated IR is often used as a first approximation of alignment which is followedby visual assessment. Often a manual refinement by an experienced, well trained, operator isnecessary. Implementation of online correction of patient position on a daily basis is limitedboth by the time taken for an operator to perform IR and the availability of trained operators.A reliable IR algorithm could alleviate these difficulties if it is fast and can reliably matchtwo images with minimal uncertainty. The residual error needs to be considerably smallerthan the patient (or target) positioning error it is measuring and any catastrophic failure of thealgorithm needs to be immediately obvious by visual inspection.

Image registration errors have been studied by many investigators, often to demonstratethe benefits of an algorithm they have developed or implemented. There are many techniquesto assess image registration errors, often employed in combination. These include (a) visualinspection, (b) identification of corresponding point landmarks, (c) internal and externalfiducial markers, (d) comparison with previously validated methods, (e) use of virtual andphysical phantoms, (f) misalignment of images by artificial transformation of images eitherrandomly or systematically sampling the parameter space and (g) consistency using threeimages. References for many of these studies up until 2001 can be found in reviews by Hillet al (2001) and West et al (1997).

While the uncertainties in the chamfer-matching algorithm have been extensively reported(van Herk et al 1997, 1998, van Herk and Kooy 1994), these studies are specific to imageregistration between FBCT, MR and PET and measure the registration uncertainties in aresearch setting. In the current study, techniques similar to those employed in the van Herkstudies are utilized to investigate the uncertainties in image registration of FBCT and CBCTimages of the skull using the chamfer-matching algorithm as implemented in the Synergysystem.

Often the resolution of clinical images is limited for practical reasons. For example,CBCT of a head with a (0.5 mm)3 voxel size takes approximately 4 min to reconstruct the540 × 540 × 520 volume on the Synergy R© system and IR times also increase, whereasimages reconstructed at a (1 mm)3 voxel size are ready for IR within a few seconds of imageacquisition. A further limitation is the x-ray dose to the patient which, by UK law (IRMER2000, HMSO), should be minimized as far as possible without compromising the ability toperform the intended task, which in this case is the image registration component of IGRT.Understanding how these factors affect image registration will help optimize the acquisitionsettings for IGRT protocols.

This current investigation aimed to determine if the automatic IR algorithms providedin a commercial image-guided radiotherapy system are sufficiently reliable and accurate forroutine use in IGRT with minimal operator verification. This was achieved by measuring theresidual IR errors and failure rates and studying the effect of a number of clinical factors thatmay affect performance. These factors include image acquisition dose, FBCT slice width,CBCT voxel size, choice of algorithm, and selection of the image region to be registered. Thestudy concentrates on the use of the chamfer-matching algorithm for IR of the bony anatomyof the skull which acts as a surrogate for target position of intra-cranial target volumes.

2. Methods

The uncertainty in IR of the bony anatomy automatic IR algorithm implemented in theXVI(v3.5) software application (X-ray Volumetric Image (XVI)) of the Synergy system wasmeasured by misaligning the FBCT and CBCT scans with a randomly sampled rigid bodytransformation and executing an automatic IR. This was performed many times for eachFBCT–CBCT scan pair and the resultant rigid body transform parameters were compared with

7266 J R Sykes et al

those applied to determine the distribution of the residual errors. The effects of varying FBCTscan slice width and CBCT scan voxel size were investigated using a skull phantom as wellas the effect of reduced CBCT scan dose. The uncertainty in IR was also measured on21 CBCT scans taken during normal treatment of seven patients having intra-cranialradiotherapy. Additionally, the effect of registration of the ‘Clipbox’ position (describedlater), choice of the automatic IR algorithm and multiple execution of automatic IR on theresidual errors were investigated on the patient scans.

2.1. CT and cone beam CT scans

A 3M skull phantom consisting of a human skull embedded in plastic was scanned five times ina CT simulator (GE Lightspeed) on two separate occasions. Three surface markers were usedto indicate the position of the lateral and overhead lasers with a fourth placed superiorly on thesagittal laser line. The trans-axial plane resolution was kept constant for all five scans, whilethe slice widths were nominally 0.625 mm (FBCT2), 1.25 mm (FBCT3), 2.5 mm (FBCT1,FBCT4) and 5 mm (FBCT5). The slice separations were the same as the slice widths for allFBCT scans. As FBCT1 was performed on a separate occasion to the others, the phantomposition in the scanner would not have been reproduced exactly. A basic treatment plan wascreated on a treatment planning system for each scan with the isocentre set at the origin of thescan. Each plan was sent via DICOM to the Synergy system (Elekta, Crawley, UK).

The phantom was then positioned on the couch of the Synergy system and aligned to theroom lasers using the external markers that were applied at the time of the FBCT scan. EightCBCT images were acquired using the Synergy system with a wide range of exposure settings(table 1). All scans were collimated to a 25 cm diameter and 25 cm scan length field of view.They were performed without a bow-tie filter, as this did not become available until after thisstudy.

All exposures were performed at 120 kV, and the dose was varied by adjusting the tubecurrent and pulse length per projection image from the lowest possible (10 mA, 10 ms),which is the current clinical protocol for all intra-cranial IGRT, to a moderately high exposure(80 mA, 40 ms). This high exposure was sufficient to saturate the detector for x-ray paths notincident on the phantom which led to significant shading artefacts in the reconstructed image.To achieve a high dose without introducing shading artefacts, a scan was also performed withreduced gantry speed. At this reduced speed, 1285 projection images were acquired during asingle 360◦ rotation instead of the typical 630.

To explore IR uncertainties at very low doses, i.e. lower than that which could be seton the Synergy system, a series of 1 mm thick copper plates were added to the beam at thelevel of the collimators. The maximum thickness of copper attenuation used was 4 mm. Theaddition of 4 mm of copper attenuation reduced the tube output, measured in-air and scaled tothe isocentre, from 82 μGy mA−1 s−1 to 1.2 μGy mA−1 s−1.

To simulate a further dose reduction, reconstruction was repeated for scans D and Hhaving set some of the projection images to be inactive in the database of the XVI software.Reconstructions were performed with projection images at angular intervals of 2◦, 4◦ and 9◦.The normal angular interval between projection images is 0.5◦. This enabled the scan dose tobe reduced by a further factor of 15 (table 1). Sample trans-axial slices through each of thescans are shown in figure 1. Dose reductions of this level are probably not required in clinicalpractise; however, image registration with these low-dose scans was necessary to determinethe point at which the performance of the algorithm deteriorated.

All scans were reconstructed at the standard clinical resolution with a (1 mm)3 voxelsize. A selection of scans were also reconstructed with a higher resolution of (0.5 mm)3 voxel

Investigation of CBCT-CT image registration uncertainties in IGRT 7267

Table 1. Acquisition parameters for CBCT scans of the skull phantom, tube output measuredin-air and CTDI dose. Scans marked with an asterisk (∗) were performed with a half scan, whilstthose with single (′), double (′′) and triple (′ ′ ′) quotes were performed with reduced numbers ofprojection images. See section 2.4 for details of the dose measurement method.

CBCTscanlabel

Nominaltubecurrent(mA)

Pulselength(ms)

Number ofprojectionimages

Thickness ofadded Cuattenuator (mm)

In-air dose(μGy mA−1 s−1

@ 100 cm)

CTDIdose(mGy)

A 40 10 1285 0 82 27B 80 40 631 0 82 107C 40 10 628 0 82 13D 10 10 623 0 82 3.3

D∗

10 10 350 0 82 1.9D′ 10 10 180 0 82 0.95D′′ 10 10 90 0 82 0.48D′ ′ ′ 10 10 41 0 82 0.21E 10 10 628 1 16 0.91F 10 10 628 2 6 0.38G 10 10 624 3 3 0.21H 10 10 628 4 1.2 0.12

H∗

10 10 350 4 1.2 0.066H′ 10 10 181 4 1.2 0.034H′′ 10 10 91 4 1.2 0.017H′ ′ ′ 10 10 41 4 0.023 0.008

size. The ‘Clipbox’, which allowed the selection of FBCT data within a cuboidal region forautomatic IR whilst excluding all data outside the region, was set according to the standardclinical protocol. This included the whole of the skull with a margin of approx. 1 cm andexcluded, as far as possible, the cervical spinal vertebrae and lower jaw.

2.2. Measurement of registration uncertainty

To assess the uncertainty in the IR process, CBCT scans were registered repeatedly withFBCT scans up to 200 times having first introduced a known misalignment by transformingthe CBCT image data. In an ideal world, the initial placement of the phantom on the couchwith the FBCT data, using the external reference marks and room lasers, would have beenperfect and IR would have exactly replicated the transform applied to the CBCT data. Inactuality, there was a small unknown initial placement error, and imperfections in the IR ledto imprecision in the IR transform parameters compared to those applied. In this study, a bestestimate of the initial placement was determined from the mean registration error and giventhe term ‘ground truth’. Residual error was defined as deviations of the image registrationerror from the mean.

For each repeat registration, the CBCT scan was first misaligned, by re-sampling witha rigid body transform chosen from a set of pre-prepared random transforms. Imagetransformation was performed using the Insight Image Toolkit (ITK v3.2, National Library ofMedicine, USA). For a single repetition, a copy of the original CBCT image was first loadedfrom the database, decompressed and then transformed with a rigid body transformation usingITK’s ‘VersorRigid3DTransform’ code. This was specified with three translation vectors

7268 J R Sykes et al

Figure 1. Trans-axial slices through the centre of the CBCT scans of the skull phantom showingthe effect of reducing the exposure, inserting copper attenuators and reconstructing with a reducednumber of projections. Table 1 lists the exposure and reconstruction settings for these scans. Allimages are displayed with CBCT data windowed to the same level and width.

corresponding to the x, y and z axes, while rotation about the same axis was specified usingITK versor notation (Yoo 2004). Trilinear interpolation was used to resample the transformedimage on to the original image’s voxel coordinates. The image was written back to the databasein compressed format overwriting the original image file. Automatic IR was initiated fromwithin the XVI software application. Once completed, the IR parameters were extracted fromthe CBCT system database and saved in a text file for subsequent analysis.

To make repeat IR with 200 random misalignments per FBCT–CBCT scan pair feasible,the XVI software application was operated automatically using a Windows scripting language(AutoIt v3, www.autoitscript.com). This script executed the code to transform the image andthen operated the user interface to perform a registration and finally executed the code toextract registration results from the XVI database and write them to a file ready for analysis.

The set of 200 random misalignments was created using the random number generator inMatlab (Moler 2004). The magnitude of the translation vector was sampled from a uniformdistribution between 0 and 20 mm, while the translation direction was randomly sampled over4π of solid angle. Rotations were also such that the rotation versor magnitude was sampled

Investigation of CBCT-CT image registration uncertainties in IGRT 7269

from a uniform distribution with angles between 0◦ and 20◦, while the versor axis of rotationwas randomly sampled over 4π of solid angle.

2.2.1. Study I: registration performance with imaging dose (skull phantom). Repeatregistrations of FBCT1 were performed with all CBCT scans (A-H′′′), reconstructed at a(1 mm)3 voxel size to determine the relationship between IR uncertainty with imaging dose.

2.2.2. Study II: registration performance with image resolution (skull phantom). Repeatregistrations were performed for CBCTA,D,H reconstructed with a (1 mm)3 voxel size againstFBCT2, FBCT3, FBCT4 and FBCT5. CBCTA,D,H were then reconstructed again at a(0.5 mm)3 voxel size and repeat registered with FBCT2–5. This enabled the effects of bothimage resolution and imaging dose on IR uncertainty to be studied.

2.2.3. Study III: registration performance with patient images. A total of 21 CBCT scans ofseven patient’s heads (three per patient) were repeat registered 200 times with their respectiveFBCT scans. The CBCT scans were chosen by sampling the first seven patients in the databaseand the first three scans in the list for each patient. Four of the seven patients were scannedwith a FBCT slice thickness of 5 mm, while the other three were scanned with a 2.5 mm slicethickness. All patient’s CBCT scans were acquired using the same voxel dimensions, tubevoltage and exposure settings as CBCTD. Image registration uncertainties were comparedwith the phantom measurements.

2.2.4. Study IV: registration uncertainty with the ‘Clipbox’ position (patient images). Thesensitivity of IR error to small variations of ‘Clipbox’ placement, normally adjusted by theoperator via the graphical user interface, was studied for FBCT–CBCT IR of one scan fromeach of the first three patients in study III. A set of 20 ‘Clipbox’ offsets were generated byassigning a randomly sampled offset to each of the left, right, anterior, posterior, superior andinferior borders. Each offset was sampled from a uniform distribution, with a ±2 cm width.The randomly generated ‘Clipbox’ offsets were added to the original values of the ‘Clipbox’using an SQL database query acting on the XVI database. A total of 100 repeat registrationswere performed for each ‘Clipbox’ setting and FBCT–CBCT image pair combination.

2.2.5. Study V: registration performance after multiple image registrations (patient images).In discussions with other users, anecdotal evidence of improved IR results was alluded to ifthe ‘Bone’ IR was repeated twice and the results of the first IR were used as the starting pointof the second IR. To test this, double registrations were applied to three FBCT–CBCT imagepairs from patient 2. This patient was chosen as he/she exhibited the greatest registrationuncertainties and therefore the greatest potential for improvement.

2.2.6. Study VI: registration performance with the grey-level-matching algorithm (patientimages). Registration uncertainties were measured for the same three FBCT–CBCT imagepairs as study V by repeat registration using the ‘Grey value’ algorithm and compared to thecorresponding ‘Bone’ algorithm measurements in study III.

2.2.7. Study VII: the effect of image re-sampling (patient images). In the methods describedabove, each CBCT image was transformed with a rigid body transformation by interpolationand re-sampling using the functions in ITK. An alternative approach would have been to resetthe initial alignment of the images and therefore the starting point of the image registrationoptimizer with one of the random misalignments. In reality, there would be a physical

7270 J R Sykes et al

translation and rotation of the patient or phantom and the object would be sampled intothe voxels of the imaged volume through the reconstruction process. Interpolation and re-sampling provided a closer approximation to the real situation than the alternative approach.To demonstrate this, the three translation and three rotation parameters were adjusted byediting each parameter directly through the user interface of the XVI software application.The algorithm used these parameters as the starting point of the optimization required toperform image registration. An AutoIt script was written to automate this process and toemploy the same set of random misalignments used in the previous studies. For a successfulIR with the ‘Bone’ matching algorithm, the six transform parameters had values close to zero.The deviations from zero were analysed to determine the uncertainty in IR. This process wasperformed for the same three CBCT images pairs used in study V.

All studies were performed with 200 repeat registrations except study IV where 100 repeatregistrations were performed per ‘Clipbox’ to save time.

2.3. Image registration error analysis

In this study, the basic image registration error was calculated as the rigid body transformdifference between the applied and measured transforms. However, as previously discussed,there was an unavoidable error in the initial placement of the phantom on the Synergy systemscouch. This initial placement error, or ‘ground truth’, was estimated from the mean imageregistration error. In the case of the phantom measurements where multiple FBCT and CBCTscans were acquired without moving the phantom between scans for each modality, therewould have been a single ground truth for which the best estimate was found using the FBCTand CBCT image pair with the highest image quality. In the case of the patient scans, theground truth had to be estimated from each FBCT and CBCT scan pair. Details of the analysisare described in the following paragraphs.

The XVI software returned the six, rigid body, transform parameters resulting from IRusing the IEC 1217 (IEC 1996) coordinate system represented by three translations alongthe lateral, longitudinal and vertical axis passing through the machine isocentre, Tx, Ty andTz, respectively, and three rotations about the same axis, θx, θy and θ z. Meanwhile, the ITKVersorRigid3DTransform code used six parameters of which the first three, q1, q2 and q3,represented versor rotations about the lateral, vertical and longitudinal axis respectively andthe second three were translations, t1, t2 and t3, along the same axis.

The transform parameters measured by the XVI software mi (Tx, Ty, Tz, θ x, θ y, θz) forall N image registrations were first converted into the 4 × 4 rigid body transform matrixMi {i = 1, 2, 3, . . . , N}, representing a rotation followed by a translation. The correspondingapplied misalignments, given by the six ITK rigid body versor parameters ai (q1, q2, q3, t1, t2,t3), were also converted into a 4 × 4 igid body transform matrix Ai. The matrices Ei, whichrepresented the IR errors, and given by, Ei = MiA

−1i , were converted into the six parameter

ITK rigid body versor notation, ei (q1, q2, q3, t1, t2, t3).The distributions of each parameter of ei were approximately normally distributed. Hence,

the centre of these distributions could be considered to represent a best estimate of the ‘groundtruth’ of the initial placement error between the images of the phantom and patient on theCBCT and CT systems. The deviations from the centre of the registration were defined asresidual errors and were due to variability in the IR optimization algorithm when differentmisalignments were applied. Registration outliers were due to failure of the registrationoptimization to find the global minima.

In order to avoid the influence of outliers, the mean transform error, E, was calculatedfrom all registrations in which the parameters were within three standard deviations of their

Investigation of CBCT-CT image registration uncertainties in IGRT 7271

respective mean value (Humber et al 1996). The residual error �Ei was then given by�Ei = EiE

−1.To assist the interpretation of the residual errors, each of which had six parameters, a

single measure of target registration error was devised. A set of 643 equi-spaced pointswas constructed on the surface of a 5 cm radius sphere centred on the isocentre. The targetregistration error (TRE�Ei

) was defined as the mean displacement of all these points whentransformed by �Ei. A sphere of 5 cm radius centred on the isocentre was chosen, as thiswas likely to encompass a typical volume in which accurate IR might be required. It alsorepresented a parameter that produced a set of points that was, in some respects, similar to theset of points auto-segmented from the surface of the skull used in the study by van Herk andKooy to assess performance of the chamfer-matching algorithm (van Herk and Kooy 1994).

Since the distribution of TRE, for each FBCT–CBCT pair, followed a χ2 distribution withsix degrees of freedom, the median TRE was used as a measure of the random component ofthe registration error.

In the case of study I, the phantom was in the same position for all CBCT scans and,since CBCTA was judged to be of the highest quality, the mean transform error for imagepair FBCT1–CBCTA was chosen as a best estimate of the ‘ground truth’. This ground truthwas denoted by Eref . Calculations of residual errors �Ei and TRE�Ei

for IR of FBCT1 withCBCTB-H′ ′ ′ were performed relative to Eref .

Similarly, for study II, the phantom was in the same position for all FBCT scans and forall CBCT scans. FBCT5 had the smallest slice thickness and CBCTA(HR) had the smallestvoxel size and highest dose, and so the mean transform error for FBCT5–CBCTA(HR) was usedas a best estimate of the ‘ground truth’, Eref , for study II. �Ei and TRE�Ei

were calculatedrelative to Eref for IR of all other FBCT–CBCT pairs in the group.

In both studies I and II, scans FBCT1 and FBCT4 respectively were performed withthe same acquisition parameters, but since they were performed on separate occasions theirrespective ‘ground truth’ registrations, or mean registration error, with CBCTA would havebeen different. Demonstrating that these two systematic errors were accurate would providesupport for the validity of the ‘ground truth’ estimates of studies I and II. This was achievedby transforming both FBCT1 and FBCT4 by their respective mean transform errors into thecoordinate space of CBCTA. Any misalignment between these two transformed FBCT scanswould have indicated inaccuracies in the estimates of the ‘ground truth’.

A systematic IR error, �E = E(Eref)−1, was defined as the residual between mean

transform error E, calculated for IR of each image pair in the study, and the ‘ground truth’ forthe study Eref . The TRE concept was also applied to the systematic IR error giving a systematictarget registration error, T RE�E . A systematic error calculation was not applicable to studiesIII, V, VI and VII, as no two FBCT–CBCT pairs were repeated with the patient in the sameposition.

Visual examination, using a purple–green colour fusion, of the results of imageregistrations, from study III, with TRE�Ei

between 4 mm and 7 mm, showed that registrationswith TRE�Ei

> 5 mm could be quickly identified as failures. For this reason, all registrationsexhibiting a TRE > 5 mm were classified as failures. The frequency of failures was calculatedas a percentage of the total number of registrations performed for a given FBCT–CBCT pair.

2.4. Measurement of dose

The in-air dose for an exposure with a static gantry angle was measured using a 15 cm3

parallel plate ion chamber (Inovision 96035B, Cleveland OH) placed at 75 cm from the focalspot. Measurements were made with and without the copper attenuators using exposures of

7272 J R Sykes et al

100 frames and totalling 10 mA s (table 1). CBCT dose was measured at the centre of theCTDI head phantom using the CTDI chamber (Shrimpton et al 1998) (PTW Freiburg GmbH)as described by Sykes et al (2005). Dose was measured for CBCT scans with acquisitionparameters corresponding to each of the CBCT scans of the skull phantom (table 1).

3. Results

For all pairs of FBCT–CBCT registrations, translation and rotation parameters were consistentwith the normal distribution. Most image pairs showed no inter-correlation of registrationerror, ei, parameters. For a few image pairs, significant (P < 0.05) but weak (C < 0.5)correlations (Pearson’s linear correlation coefficient) were observed. Further analysis wasperformed assuming a normal distribution of errors with independence of each of the sixtransform parameters. The distributions of TRE�Ei

values were found to be consistent withan underlying χ2 distribution with six degrees of freedom

(χ2

6

). Deviations from the χ2

distribution were observed in the upper tail.

3.1. Study I: registration performance with imaging dose

The distributions of TRE�Ei, relating to each image pair, were skewed, with an elongated

tail in the direction of increasing TRE�Ei(figure 2(a)). The median TRE�Ei

for each imagepair showed a low response to increasing dose. Inter-quartile and 90th percentile followeda similar trend. For IR with CBCTA-G, med

{TRE�Ei

}was between 0.5 mm and 0.6 mm,

with the exception of CBCTB. The med{TRE�Ei

}values for IR with CBCT scans having

dose lower than 0.44 mGy (CBCTE-H′ ′ ′) were between 0.7 mm and 0.9 mm. For CBCTD,acquired with acquisition settings typical of clinical use, 90% of all TRE�Ei

were within1 mm.

The reduction of dose by decreasing the number of projections acquired during CBCTD

had no significant effect. Similarly, no further degradation was observed between scansCBCTH′ and CBCTH′ ′ ′ reconstructed with reduced numbers of projection images. There wasa less than 5% failure rate for all the CBCT scans with the exception of CBCTD′ ′ ′ (figure 2(c)).The slight increase in the failure rate for CBCTD′ ′ ′ may be explained by the structural noisewhich is seen by the registration algorithm, while in CBCTH′ ′ ′, which had a lower failure rate,the structural noise was swamped by the stochastic noise and completely ignored.

Excluding IR with CBCTB, the systematic error, TRE�E , was less than 0.3 mm forCBCTB-E. Between CBCTF and CBCTH, TRE�E increased gradually and from CBCTH–CBCTH′ ′ ′, TRE�E remained stable at 0.5 mm (figure 2(b)).

Registrations with CBCTB showed elevated systematic and random error components(TRE�E = 0.7 mm, med

{TRE�Ei

} = 0.9 mm). This may have been due to the high exposureof the CBCTB scan which was sufficient to saturate the imager external to the phantom. Thiscaused a reduction in the grey level values and greater inhomogeneity for regions of thephantom that had uniform density.

3.2. Study II: registration performance with image resolution

Both systematic (TRE�E) and random (med{TRE�Ei

}) components of the registration errors

increased with increasing FBCT slice width (figures 3(a), (b)). The increase in registrationerrors were approximately linearly related to the FBCT slice width. There was no discernibleimprovement in the systematic component when using the high-resolution reconstruction andonly a small improvement in the random component. The relationship of IR error with FBCT

Investigation of CBCT-CT image registration uncertainties in IGRT 7273

(a)

(b)

(c)

Figure 2. Study I: (a) box and whisker plots for distributions of target registration error, TRE�Ei,

measured for repeat registrations of CBCTA-H′ ′ ′ with FBCT1, using the ‘Bone’ matching algorithmin Synergy. The imaging dose for these scans decrease from left to right and is indicated in theupper horizontal scale. The box gives the median, upper and lower quartiles with a notch indicatingthe confidence interval on the median. The whiskers extend from the 10th to 90th percentiles.(b) Plot of the systematic error, TRE�E , in the mean from the ‘ground truth’ estimate. (c) Barchart showing corresponding registration failure frequencies.

slice width held for both the high (CBCTA) and standard (CBCTD) dose scans but deterioratedfor the lowest dose scan (CBCTH).

Registration failures (figure 3(c)) were more frequent with registrations using CBCT scansacquired at the lowest dose and larger voxel size although the probability of failure was lessthan or equal to 1% for all image pairs.

3.3. Study III: patient registration performance

The random component of the IR error for the patient images (figure 4(a)) was generallygreater than for the phantom data. In particular, patient 2, who had a FBCT scan with a

7274 J R Sykes et al

(a)

(b)

(c)

Figure 3. Study II: (a) box and whisker plot for distributions of target registration error, TRE�Ei,

measured for repeat registrations of CBCTA,D,H, reconstructed at both ‘high’ and ‘standard’resolutions with FBCT2–5 using the ‘Bone’ matching algorithm in Synergy. The box gives themedian, upper and lower quartiles with a notch indicating the confidence interval on the median.The whiskers extend from the 10th to 90th percentiles. (b) Plot of the systematic error, TRE�E ,in the mean from the ‘ground truth’ estimate (FBCT2–CBCTA(High)). (c) Bar chart showingregistration failure frequencies for each FBCT–CBCT scan pair.

5 mm slice thickness, showed the largest random error with med{TRE�Ei

}in the range

2.0–2.2 mm. This was approximately twice that of study II where med{TRE�Ei

} =0.94 mm, (FBCT5-CBCTD(Standard)). Patient 6 exhibited the lowest random component of IR(med

{TRE�Ei

} = 0.7 mm). This was slightly greater than the 0.61 mm observed with thecorresponding phantom data with the same 2.5 mm CT slice width. The 90th percentile rangeswere 1.4 to 4.4 mm. The frequency of registration failures, TRE�Ei

> 5 mm, tended also to

Investigation of CBCT-CT image registration uncertainties in IGRT 7275

(a)

(b) (c)

Figure 4. Study III: (a) box and whisker plot for distributions of target registration error TRE�Ei

measured using seven patient head images. Each bar represents repeat registrations of one of threeCBCT scans with the respective patient’s FBCT scan using the ‘Bone’ IR algorithm in Synergy.The box gives the median, upper and lower quartiles with a notch indicating confidence intervalon the median. The whiskers extend from the 10th to 90th percentiles. (b) Bar chart showingcorresponding registration failure frequencies. (c) Plot of measured registration error, TRE�Ei

against applied misalignment, TREInitial for all patient data. The horizontal dotted line representsthe threshold value of TRE�Ei

above which registrations were classified as failures.

be greater for the patient image pairs than the phantom data (0–5.5%). The variations in therandom components between image pairs, of the same patient, were less than the variationbetween patients. This indicated that the morphology of the patient may have had a significanteffect on the uncertainty of the image registration.

7276 J R Sykes et al

The measured TRE�Eidata were plotted against the initial misalignment, expressed as

a target registration error using the method described previously, TREinitial, (figure 4(c)). Thisshowed that registration failures were more frequent and the spread of TRE�Ei

became largeras the initial misalignment increased.

A uniform distribution of initial misalignments with translations up to 40 mm and rotationsup to 20◦ was chosen to measure the performance of the IR algorithms well beyond the normalrange of clinical operation. Since typical initial misalignments are much less in clinicalpractise than tested in this study and the registration uncertainties appeared to be linearlyrelated to the magnitude of the initial misalignment, the registration uncertainties presentedhere will be an overestimate. To determine more clinically realistic estimates of registrationuncertainties, the data presented here were sub-sampled to reflect a distribution that wasmore typical of patient set-up errors found in clinical practise, i.e. independent translations,distributed normally (σ = 3 mm), and rotations about an axis of random orientation, alsodistributed normally (σ = 3◦). For the image registrations performed on the patient datain this study, 90% of all registrations had a TRE�Ei

less than 1.3 mm. When this error wasseparated into individual components along the patient’s cranial–caudal, anterior–posterior andlateral directions, the standard deviation of each component was found to be approximately0.5 mm. Whilst this error is small it should nevertheless be considered when designing CTV–PTV margins for IGRT protocols especially when the protocol involves online correction oneach fraction.

3.4. Study IV: registration uncertainty with the ‘Clipbox’ position

The random IR components showed a relatively low sensitivity to the ‘Clipbox’ position(figure 5). For the seven CBCT scans used in this study, the range of med

{TRE�Ei

}values

was no greater than 0.3 mm. Given an IR result using one of the Clipboxes, there was anequal probability of improving and degrading the registration with a minor adjustment of the‘Clipbox’.

3.5. Study V: registration performance after multiple image registrations

When IR was repeated using the result of the first IR as the starting point of the second,there was a small effect on the IR performance. A simple analysis would suggest that thedistribution of the random component was unchanged (figure 6(a)) and the number of failuresreduced slightly (figure 6(b)). A paired analysis (figure 6(c)) showed that 18 of the 28 failuresfor patient 2 in study III became successful with a repeat registration, while of the 22 failuresthat occurred when registration was performed again, only 6 had previously been successful.For those registrations that were successful on both first and second registrations there wasno benefit in having performed the second registration. No improvements were observed ifthe initial TRE�Ei

was greater than 25 mm. These results show that routine application ofa second multiple registration is not beneficial unless there is an obvious failure in the firstapplication.

3.6. Study VI: registration performance with the grey-level-matching algorithm

There was no discernible difference between the random component of IR errors performedwith the ‘Grey value’ IR algorithm when compared to the ‘Bone’ algorithm (figure 6(a)), butthe number of registration failures increased to between 6 and 9% (figure 6(b)). Two of thesefailures occurred with initial misalignments of 13 mm and 18 mm which were less than the

Investigation of CBCT-CT image registration uncertainties in IGRT 7277

(a)

(b)

Figure 5. Study IV: (a) box and whisker plot for distributions of target registration error TRE�Ei

measured for repeat registrations of CBCT scans for one fractions each of the first three patientsusing the ‘Bone’ IR algorithm in Synergy. Repeat registrations were executed 20 times for eachimage pair using 20 randomly sampled ‘Clipbox’ positions. The box gives the median, upperand lower quartiles with a notch indicating confidence interval on the median. The whiskersextend from the 10th to 90th percentiles. (b) Bar charts showing corresponding registration failurefrequencies.

smallest observed with the ‘Bone’ algorithm, 21. This might be indicative of a smaller capturerange for the Grey value algorithm. A paired analysis (figure 6(d)) showed that of the 28failures for patient 2 in study III, TRE�Ei

was reduced to less than 5 mm for 18 of them.Conversely, there were a greater number of failures, 48, with the ‘Grey value’ algorithm, and38 of these would have been successful with the ‘Bone’ algorithm. For registrations whichwere successful by both algorithms, the ‘Bone’ algorithm performed marginally better with amedian difference in TRE�Ei

of only 0.1 mm. The ‘Grey value’ registration algorithm alsotook typically 4 min to complete, while the ‘Bone’ algorithm took less than 5 s.

7278 J R Sykes et al

(a)

(b)

(c) (d) (e)

Figure 6. Studies V, VI and VII: (a) box and whisker plot for distributions of target registrationerror TRE�Ei

measured for repeat registrations of CBCT scans with CT data for three fractionsof patient 2. The results for study III are compared with the alternative methods of studies V, VIand VII. In study V, the registration was run twice. Study VI used the ‘Grey value’ registrationalgorithm and study VII used an alternative method of applying an initial misalignment. Thebox gives the median, upper and lower quartiles with a notch indicating confidence interval onthe median. The whiskers extend from the 10th to 90th percentiles. (b) Bar chart showingcorresponding registration failure frequencies. (c)–(e) TRE�Ei

for each of the methods plottedagainst TRE�Ei

for study III. The inset for each of these plots has an expanded scale indicated bythe dashed box on the main plot.

3.7. Study VII: the effect of image re-sampling

The random components of the image registration errors were found to be much smallerwith fewer registration failures if the initial misalignment was created using the graphicaluser interface of the XVI application software (figures 6(a), (b)). This indicated that image

Investigation of CBCT-CT image registration uncertainties in IGRT 7279

re-sampling with tri-linear interpolation was an important component in the measurement ofimage registration errors.

3.8. Non-study-specific results

The alignment of scans FBCT1 and FBCT4 having both been transformed into the coordinatesspace of CBCTA using their respective mean transform errors were visualized using a green–purple fusion display similar to that employed in the Synergy system. The alignment of thetwo scans was excellent with only a few flashes of green, almost certainly due to interpolationeffects between trans-axial slices.

The majority of image registration errors were dominated by the translational component.The ratio of TRE calculated on the translational component alone to the TRE for both rotationand translation was greater than 90% for more than 60% of registrations. There was noconsistent bias towards translations along the longitudinal axis which might be suspected dueto the anisotropic size of the voxels in the FBCT scan.

4. Discussion

In a previous feasibility study (Sykes et al 2005), IR was shown to be highly accurate forFBCT-CBCT image pairs of a skull phantom and was robust to reduction of the imaging dose.The study used a voxel intensity-based IR algorithm using a global correlation cost functionin a treatment planning system and not the algorithms provided in the Elekta Synergy system.This study also relied on manually repeating IR which limited sample sizes and therefore theability to assess registration uncertainties. In the current follow-on study, the performance ofthe IR algorithm in a commercial IGRT system was assessed using 200 randomly sampledmisalignments with the aid of Windows scripting software. This enabled a much morecomprehensive analysis of IR uncertainties.

A further deficiency in the earlier study of Sykes et al (2005) was the use of the AldersonRando phantom (Phantom Laboratories, Salem, NY). The Rando phantom was not an idealchoice for an IR study, as it was made up of 3 cm thick slices each containing many cylindricalinserts to enable placement of small dosimeters. These would have been visible in both FBCTand CBCT images and could, therefore, have influenced the registration accuracy. In thecurrent study, a skull phantom was used which did not possess structures that could influencethe accuracy of IR.

The imaging dose was reduced as far as practically possible by using a combination ofcopper attenuators and reduced projection images in reconstruction. The ‘Bone’ algorithm wasfound to be very robust to a reduction in imaging dose by either method. This indicated thatimaging dose could be reduced from the current clinical norm of 2 mGy to 0.2 mGy withoutcompromising the performance of automatic image registration. Further dose reduction wouldalso be possible with only a small decrease in performance. These low doses were below thatavailable in normal operation of the equipment. This is a significant finding, particularlyfor paediatric patients in whom the concomitant imaging dose of repeat CBCT required foraccurate setup is of concern.

Over-exposure and saturation of the imager which increased the registration uncertaintyfor registrations with CBCTB could have been avoided with use of the bowtie filter, nowsupplied by the manufacturer. However, a bowtie filter is unnecessary for head and neckimaging where adequate image quality can be obtained without saturating the imager.

Chamfer matching relies on edge detection of the bony anatomy surface. The low-dosereconstructions of the head phantom using the copper attenuators had significantly increased

7280 J R Sykes et al

CT values for both the surrounding air and the phantom. The majority of this could havebeen avoided if the system had been re-calibrated for each thickness of copper used. Beamhardening would also have resulted in changes to the CT values for the phantom and air aswell as some slight cupping artefact, although the cupping artefact was not strongly evidentin these images. The algorithm performed well, despite the large changes to the CT valuesbecause it used a relative threshold value which was 15% greater than the voxel intensity ofwater, or plastic, in the case of the phantom, to segment the bony anatomy. The voxel intensityof water was determined from analysis of the image histogram (van Herk 2009). Therefore,the algorithm would adapt to the changes in the image grey scale.

It seemed remarkable that the image registration worked at all for the very low dose,high noise, reconstructions where the bone was barely visible. To confirm that the algorithmwas not mistakenly segmenting the stronger phantom-air surface a sample of the CBCT scansA–H′′′ were edited to deform the phantom-air surface. This was achieved by segmenting thephantom on CBCTA and expanding it with an asymmetric margin of 1 cm in the superior,anterior and left directions and 0 cm for all other directions. The volume between the originalphantom surface and the surface expanded asymmetrically was filled with simulated dataon a selection of the lower dose scans. The simulated data were randomly sampled froma Gaussian noise distribution with mean and standard deviation to closely match that ofthe plastic of the phantom in each of the low-dose scans. Repeat registrations gave similarsystematic and random error components to those measured with the original images verifyingthat the chamfer-matching algorithm was indeed extracting the correct surface.

While the increase in systematic and random uncertainties of IR with increasing FBCTslice width and CBCT voxel size was expected, the results show that there is little benefit inreducing FBCT slice width less than 2.5 mm or reconstructing the CBCT images at (0.5 mm)3

instead of (1 mm)3. Although not statistically significant, the patient data also suggest thatgood results can be obtained with 5 mm FBCT slice thickness but that 2.5 mm is more likelyto give better results. It would be expected that a deterioration in performance, similar to thatobserved with increasing FBCT slice width, would be observed for voxel sizes larger than1 mm or for asymmetric voxels with larger trans-axial slice widths. This was not studied, asthere was no time advantage to reconstructing larger voxel sizes.

The exact placement of the Clipbox boundaries and performing the IR a second timehad no appreciable effect on IR performance although for some registrations an improvementmay be observed. Performing the registration a second time, when the result of the first hasobviously failed, can, in some cases, lead to improved results. Theoretically, this result issurprising. Assuming that the registration failed because the optimizer had found a localoptimum, any deterministic gradient descent-type algorithm would remain in the local optimawhen re-optimized. This information provides practical guidance to operators of the XVIapplication regarding the relative merits of adjusting the Clipbox or repeating the automaticIR compared to manual adjustment of the registration.

In the first part of a study (Meyer et al 2007) investigating the positioning errors associatedwith CBCT, initial misalignments and hence the starting point for automatic IR were achievedby incrementing the coordinates of the treatment plan centre by 0.1 mm and 0.5 mm in thex, y and z directions. The Synergy system used the coordinates of the planned treatmentcentre in the FBCT frame of reference in order to provide an initial alignment of the CBCTscan with the FBCT scan. The ‘Grey value’ registration algorithm was able to exactly detectthe 0.1 mm displacements of the treatment centre, while the ‘Bone’ algorithm gave smallerrors, less than 0.3 mm and 0.4◦. This alternative method of assessing image registrationperformance did not require the re-sampling of image data, as would have been the case with aphysical shift and re-imaging of the phantom. As demonstrated in study VII, measurements to

Investigation of CBCT-CT image registration uncertainties in IGRT 7281

simulate phantom shifts, without re-sampling, may underestimate the uncertainties associatedwith image registration.

The re-sampling and sub-pixel interpolation of the CBCT image when transformed in thisstudy would not have exactly replicated a real shift of the phantom or patient. Structural noiseand image artefacts would also have been transformed and re-sampled along with the imagedata, whereas, in reality, they are more likely to have a fixed position in relation to the imageror to change characteristics according to the position and orientation of the subject. For thisreason, the results of this study may represent a lower bound for the performance of IR.

During the limited observer study, in which the 5 mm threshold for detection of imageregistration was determined, a range of TRE�Ei

values were identified for which there waspotential for misclassification. This range where TRE�Ei

was between 4 mm and 7 mmaccounted for only 0.5% of registrations and all these registrations were performed with initialmisalignments where TREinitial was greater than 20 mm. Given sufficient time and toolsto visualize and interact with the registered datasets, human observers may well be able todetermine registrations with TRE�Ei

less than 4 mm and this warrants further study. However,this study suggests that close inspection is unnecessary and that registration failure is bothinfrequent and is, for the most part, immediately obvious on inspection.

In this study, the TRE�Eiparameter of IR performance is proposed. The ‘Bone’

match algorithm utilized in the Synergy system is based on the chamfer-matching algorithmimplemented by van Herk and Kooy (1994). Analysis of IR errors in this and a later study(van Herk et al 1997) were performed in a similar manner to the methods used here. Theset of points used to define TRE in their study were those extracted from the surface of theskull in the CT image in order to perform the chamfer match. Since these points were notavailable for this study, TRE was calculated from the displacement of a set of points on thesurface of a sphere centred on the isocentre. This has the advantage of being independent ofthe algorithm. Furthermore, the sphere is centred on the isocentre which is typically the centreof the treatment volume and the centre of rotation of the moving image in the IR.

A number of authors have addressed the quality assurance of IR algorithms for bothradiotherapy treatment planning and image guidance. The methods employed are wide rangingand include use of phantoms and methods of visual assessment. As demonstrated in this studythe use of phantoms can underestimate the typical IR errors. Physical displacement of thephantoms is limited by both the time taken to perform each measurement and the precisionthat the phantom can be displaced (Moore et al 2004, Robar et al 2005). Visual assessmentis limited by both the subjective nature of the observer and the time taken to assess eachregistration. Identification of corresponding fiducial points on 3D images is also prone to error,as features that can be pinpointed in a 2D-sectional plane are rarely well defined perpendicularto the plane (Fitzpatrick et al 1998, West et al 2001). The number of corresponding points thatcan be readily defined is also a limiting factor. Many studies published on IR performancehave been performed by the developers of the algorithm and bench marked against otherestablished algorithms (West et al 1997, Viola and Wells 1997). Access to the source codemakes automation of the process relatively straightforward but does not test the commercialimplementation in the clinical setting.

This study was designed to address some of the deficiencies highlighted above. Phantomimages were used to explore parameters that could not be studied easily with patients suchas image dose and resolution. Patient data were used where possible but with the loss ofan absolute ground truth. The user interface was automated to allow many repeat IRs fromrandomly sampled misalignments. Even so many hours of computation time were required toproduce these results. These methods also required the ability to access the system databaseto extract and reinsert image data after transformation and to read the results of IR. This

7282 J R Sykes et al

highlights the difficulty in performing such measurements on a routine basis and poses apractical challenge to clinical medical physicists in their efforts to quality assure the IRcomponent of image-guided radiotherapy systems.

5. Conclusion

A method of measuring the uncertainties in IR of a commercial IGRT system has beendeveloped and used to study IR errors in both patient and phantom images for kV CBCT basedIGRT of intra-cranial tumours using the commercial ‘Bone’ chamfer-matching algorithm(Elekta, Crawley, UK). Results show that the chamfer-matching algorithm was reliable withnegligible random error at standard imaging doses and was resilient to the reduction ofimaging dose. This should allow imaging dose to be reduced from the standard 2 mGy usedcurrently in our clinic to 0.2 mGy or less, without impacting IR errors significantly. Imageregistration performance with FBCT slice widths of 2.5 mm and CBCT voxel size of (1 mm)3

was adequate, and further reduction of these parameters did not give clinically significantimprovements. The standard deviations of the lateral, cranial–caudal and anterior–posteriorrandom error components, measured using patient images, with initial misalignments typicalof clinical practise, were 0.5 mm.

Acknowledgments

This work was supported by the award of an IPEM Research Fellowship. The authors wouldlike to acknowledge Elekta for providing a standalone copy of their software which allowedmany hours of repeat registrations to be performed without impacting on the clinical service.

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