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Delineation of moving targets with slow MVCT scans: implications for adaptive non-gated lung tomotherapy

This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2007 Phys. Med. Biol. 52 1119 (http://iopscience.iop.org/0031-9155/52/4/017) View the table of contents for this issue, or go to the journal homepage for more

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INSTITUTE OF PHYSICS PUBLISHING Phys. Med. Biol. 52 (2007) 1119–1134

PHYSICS IN MEDICINE AND BIOLOGY

doi:10.1088/0031-9155/52/4/017

Delineation of moving targets with slow MVCT scans: implications for adaptive non-gated lung tomotherapy Christopher Smeenk1, Stewart Gaede1,2 and Jerry J Battista1,2 1

Radiation Oncology Program, London Regional Cancer Program, London, Ontario, Canada Department of Medical Biophysics and Department of Oncology, University of Western Ontario, London, Ontario, Canada 2

Received 23 August 2006, in final form 14 December 2006 Published 25 January 2007 Online at stacks.iop.org/PMB/52/1119 Abstract Accurate imaging is a prerequisite for adaptive radiation therapy of mobile tumours. We present an evaluation of the performance of slow computed tomography (CT) for mapping and delineating the excursion boundary of a moving object using a tumour phantom scanned with the helical MVCT scanner of a tomotherapy unit. A spherical test object driven by sinusoidal motion in both the lateral and cranial-caudal directions was used to determine how well MVCT images depict the true envelope of the motion. Such information is useful in interpreting the CT images relative to the static object case when radiotherapy gating is to be used or in determining the internal target volume (ITV) when beam gating is not possible. A computer simulation of the CT imaging process was developed which incorporates the third generation fan beam geometry and helical acquisition technique of the tomotherapy MVCT system. Motion artefacts are mainly characterized by the parameter α = Tgantry/Trespiration which is interpreted as the period of the gantry rotation (Tgantry) in units of the respiratory period (Trespiration). Experimental tests were performed using a fixed gantry period of 10 s per full rotation and respiratory period ranging from 4.0 (α = 2.5) to 1.0 (α = 10) s. These cases represent typical clinical imaging conditions on the tomotherapy unit, as well as an extreme test case where the gantry period is intentionally set to be much greater than the respiratory period (termed an ‘ultra-slow’ scan). The accuracy of target (ITV) delineation is evaluated by comparing volumes generated using isodensity contours on the MVCT images to the true motion envelope, known a priori in this phantom study. As expected, motion artefacts are present in clinical MVCT images and they are not averaged over the slow gantry period of rotation. Furthermore, artefacts are not significantly affected by scanning with different helical pitch values. Greater distortions from the true density distribution are observed for lateral motion compared to cranial-caudal motion. Volumes generated by iso-density contours yield better agreement with the motion envelope for scans performed under ultra-slow conditions (α = 10) compared to typical clinical imaging conditions (α = 2.5). If the MVCT 0031-9155/07/041119+16$30.00 © 2007 IOP Publishing Ltd Printed in the UK

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gantry cannot be rotated very quickly due to engineering constraints in order to achieve ultra-fast CT, we suggest an opposite approach as an interim measure for mapping the ITV. Adjusting MVCT scan conditions to a very slow acquisition (α = 10) may be a good compromise for determining the ITV for non-gated adaptive tomotherapy of moving lung tumours. (Some figures in this article are in colour only in the electronic version)

1. Introduction Much work has been done to understand motion artefacts in kilovoltage CT images (Chen et al 2004, Gagne and Robinson 2004, Lagerwaard et al 2001, Mori et al 2006). In radiation therapy, motion artefacts in images used for treatment planning can affect the accuracy of delineating the clinical target volume (CTV) and mapping the extent of its motion characterized as the internal target volume (ITV) (Chen et al 2004). Errors in overestimating the CTV and ITV can lead to increased dose to surrounding healthy tissue, while localized underestimates can lead to geographic miss and poor dose coverage of some tumour zones. Solutions to this problem include using time-resolved or four-dimensional (4D) scans to define the movement of the CTV and to then apply gated radiotherapy for a selected instantaneous position of the CTV (Mageras et al 2004). This form of gated radiotherapy is being developed for traditional treatment machines and for tomotherapy (Kim et al 2006). If beam gating is not appropriate or unavailable for a patient, treatment planning can proceed, based on the ITV derived from a fast CT scan data set or alternatively from a deliberately ‘slow’ CT scan (Lagerwaard et al 2001, Wurstbauer et al 2005). In ‘slow’ CT scanning, the CT image acquisition time is comparable to the respiratory period. It is commonly assumed that the tumour motion artefacts are sufficiently averaged out over the duration of slow image acquisition and that the therapy is delivered to the true ITV without beam gating. Currently, there is an interest in using frequent online CT imaging to modify the radiation treatment as the tumour position, shape and size change over the course of radiation therapy (Ramsey et al 2006). For this to be successful with moving tumours, it is first necessary to understand the accuracy and potential limitations in imaging small moving objects similar to tumours in lung when the imaging times are long or prolonged, as is the case with MVCT images acquired on the tomotherapy unit. The accuracy of slow CT scans in mapping tumour positions is the subject of some controversy. Clinical studies have repeatedly shown that slow CT scans yield larger and more reproducible tumour volumes than those obtained by rapid CT scans. In some cases this has been used to argue in favour of shrinking the motion margins when planning with slow CT scans (Wurstbauer et al 2005). Some investigators have found that planning with slow CT scans is inferior to planning on a pair of breath-hold scans taken at inspiration and expiration, respectively, to show maximum excursions of the tumour volume (Shih et al 2004). Others have shown that planning with multiple slow CT scans yields more complete knowledge of the true extent of tumour motion compared to a single slow CT scan (Lagerwaard et al 2001). Overall, studies of lung patients conclude with a recommendation that slow CT scanning gives a reasonable approximation to the motion envelope of a moving tumour. However, such conclusions are not based on a priori knowledge or the controlled movement of lung tumours in vivo. When phantom measurements are performed using slow CT scans under more controlled conditions, the conclusions differ considerably from those of clinical studies. Gagne and

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Robinson (2004) and Mori et al (2006) have found that motion artefacts are most severe when the gantry period is approximately equal to the motion period—as is the case in slow CT. MVCT images acquired on a tomotherapy system use a much slower gantry rotation period (10 s) than is available on diagnostic scanners (Tgantry ∼ = 0.5 s) and also slower than what has traditionally been referred to as slow CT scanning (Tgantry ∼ = 4 s). It is therefore of interest to investigate the image artefacts associated with slower gantry rotation periods used in tomotherapy. Will slow MVCT lead to improvements or degradation in visualizing the true motion envelope of a small moving object similar to a tumour? This type of study has implications for adaptive radiotherapy where the knowledge of the target location and shape is needed on a frequent basis to adjust a course of non-gated radiation treatment, such as present-day tomotherapy.

2. Materials and methods 2.1. Megavoltage CT imaging system The commercial on-line CT system (TomoTherapy Inc., Madison, WI) uses a 3.5 MV x-ray beam to scan a patient on the treatment couch. MVCT images are displayed as a 512 × 512 matrix with a 38.6 cm diameter field of view. The beam width measures 5 mm in the isocentre plane and the available helical pitch values (couch movement per rotation in units of the beam width) are 0.8, 1.6 and 2.4. Each pitch corresponds to a reconstructed image slice spacing of 2, 4 or 6 mm, respectively. The tomotherapy system is considered a third generation CT geometry with one subtle difference: the radius of curvature of the detector is 110 cm while the source-to-detector distance is 145 cm (Meeks et al 2005). This off-focus arrangement is used to improve the x-ray quantum detection efficiency and hence reduce the MVCT dose to the patient. 2.2. Tumour phantom description The tumour phantom used to evaluate the fidelity of the MVCT images is a lucite sphere (density = 1.1 g cm−3) measuring 25 mm in diameter. The sphere was supported by a block of styrofoam (density = 0.04 g cm−3) which was then coupled to a drive mechanism otherwise used on a moving lung phantom (Quasar, Modus Medical Devices, London, Ontario). The phantom is driven by sinusoidal motion in one dimension with a variable amplitude and period. In this work, we used a fixed amplitude of 10 mm for both lateral and cranial-caudal motions. The period used was set to either 4.0 ± 0.3 or 1.0 ± 0.1 s. The phantom motion was manually synchronized with the radiation beam using a trigger based on the ‘beam on’ signal at the tomotherapy unit’s operator console. The initial gantry angle was recorded based on the console display for use in the computer simulations. Rotating the phantom platform allowed independent testing of artefacts for motion both in the imaging plane (lateral direction) and orthogonal to the imaging plane (cranial-caudal direction). Gagne and Robinson (2004) have used a similar setup and shown that motion in the anterior-posterior direction produces qualitatively similar artefacts to motion in the lateral direction, albeit rotated by 90◦ in the reconstructed images. We expect, therefore, that our results for lateral motion will also hold for anterior-posterior motion. Motion artefacts have been shown (Gagne and Robinson 2004) to depend mainly on the ratio of the gantry rotation period to the respiratory period, which is described by the

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C Smeenk et al Table 1. Values of motion and CT scanner parameters used for measurements. Direction of motion

Trespiration (s)

α

Pitch

Slice thickness (mm)

Lateral CC

4.0 4.0

2.5 2.5

0.8 0.8

2 2

Lateral CC

4.0 4.0

2.5 2.5

1.6 1.6

4 4

Lateral CC

4.0 4.0

2.5 2.5

2.4 2.4

6 6

Lateral CC

1.0 1.0

10 10

2.4 2.4

6 6

parameter α: α=

Tgantry Trespiration

.

Assuming a respiratory period around 4 s, α is approximately 2.5 under typical clinical imaging conditions for the tomotherapy MVCT system. For the purpose of comparison, CT scans were also performed with a respiratory period of 1.0 ± 0.1 s in which case α = 10. This period is not a realistic breathing rate for a human; however, it does replicate the artefacts that would occur if the respiratory period was 4.0 s and the gantry period was slowed to 40 s, for example. We refer to this condition as an ‘ultra-slow scan’. A complete list of scanning and motion parameters is given in table 1. 2.3. Computer simulation of CT data acquisition and image reconstruction To aid in the understanding and analysis of motion artefacts, a computer model of the MVCT system was developed (Matlab Version 6.5, Release 13, Mathworks Inc.). The simulation incorporates the divergent beam geometry and helical scan technique to simulate the acquisition of projections of x-rays through an object. Expressions for projections through an ellipsoid in the third generation CT geometry are given by Louis and Mass (1993). In this purely geometric model, line integrals through a homogeneous object of elliptical cross section are calculated for each ray in the CT system via the length of intersection of the ray with the ellipsoid surface. The computer model therefore does not account for beam hardening effects or differences in tissue contrast at different energies. As a result, all the artefacts we present are due to the interplay of CT gantry rotation and ray intersections through the moving phantom. The x-ray imaging beam profile of the MVCT system was incorporated into the simulation by using data measured with radiographic film. Each simulated projection is then simulated by a weighted average of infinitesimally thin projections over the measured beam profile. A helical weighting function is applied and interpolated projections are then filtered and back-projected along fan beam rays using well-known techniques (Hsieh 2003, Kak and Slaney 1988). Although the exact details of the commercial reconstruction algorithm are not known, a publication on the prototype MVCT system (Ruchala et al 1999) mentioned the use of the constant speed helical half-scan with interpolation (CSH-HH) algorithm originally published by Crawford and King (1990). This method has been assumed in our simulation studies. In this method, two sets of half-scan projections are interpolated to derive a single set of projections at each image plane. Rays are acquired and interpolated over approximately 360◦ as the object moves within the beam. We therefore continue to follow the convention of Gagne

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Figure 1. Diagram of the metrics used for characterizing volume conformity. The left diagram shows the excess volume (dots) and the right diagram shows the volume of intersection (vertical lines).

and Robinson (2004) in using the total gantry period per full rotation (10 s) to characterize motion artefacts through the parameter α. 2.4. Measures of volume conformity The accuracy of the reconstructed MVCT images can be assessed by determining how well the volume of the moving object contoured on CT images conforms to the actual mechanical excursions of the moving tumour phantom. The true CT numbers within the region of interest in the scan depend on the sphere’s position as a function of time:
100 HU ((x − xc (t))2 + (y − yc (t))2 + (z − zc (t))2 )1/2
r CT number(x, y, z, t) = −1000 HU otherwise where r is the radius and (xc (t), yc (t), zc (t)) is the position of its centre of mass as a function of time3 . The coordinate system complies with that given by ICRU Report 62 (1999) where different axial planes are specified by the Y position. The actual occupancy of the phantom at each image plane is denoted by O(x, y, z) and it is the true average of the phantom’s position over the imaging time:  t0 +Timage 1 CT number(x, y, z, t) dt O(x, y, z) = Timage t0 where t0 is the time at the beginning of each image acquisition and Timage is the duration of time to acquire a single image. The true envelope of the motion is defined by voxels where the CT number is non-zero, that is, O(x, y, z) > −1000 HU. The motion envelope represents the true extent of the phantom’s motion over all respiratory phases. The object is delineated on the CT images using a range of iso-density threshold values. We have not included any expansion margin beyond the iso-density contours. The iso-density volumes are then compared with the motion envelope to evaluate how well the MVCT images correspond to the true occupancy volume. Two quantities are of interest (see figure 1): (a) The excess volume included in the iso-density volumes (figure 1, left). These are voxels that have a density greater than the threshold, but fall outside the true motion envelope. This phenomenon occurs because of motion artefacts. 3 The CT number of air on the MVCT system (TomoTherapy Inc.) appears as −1024 HU which is inconsistent with the traditional definition of CT number. In this paper, we follow the traditional definition wherein vacuum is defined as −1000 HU.

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Figure 2. Measurement, simulation and actual occupancy images at different axial planes (Y coordinate) for cranial-caudal motion. Pitch = 2.4, α = 2.5.

(b) The volume of intersection between the iso-density volumes and the motion envelope (figure 1, right). Both the volume of intersection and the excess volume are normalized to the size of the true motion envelope. These quantities give an indication of how well the delineated CT volume conforms to the true occupancy at each image plane. 3. Results 3.1. Motion artefacts in MVCT images Our results indicate that MVCT images contain the expected motion artefacts due to scanning with a slow gantry rotation period. All the images presented are for scans with pitch 2.4 and yielding 6 mm reconstructed slice spacing. This is the most commonly used clinical imaging setup since it delivers the lowest dose to the patient for frequent imaging during adaptive tomotherapy. The physicians and therapists at our clinic find this number of images sufficient for alignment purposes. There are some differences observed for cranial-caudal versus lateral motions. The results of scans for cranial-caudal motion are shown in figure 2. The first and second columns show the measured and simulated images at four different axial planes in the scan, denoted by different coordinate positions on the Y axis. The third column shows the true occupancy at the image slice. All images are displayed with a level at −450 HU and

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Figure 3. Measurement, simulation and actual occupancy images at different axial planes (Y coordinate) for lateral motion. Pitch = 2.4, α = 2.5.

window width of 1100 HU. If the motion were truly averaged out by slow CT scanning, there should be excellent agreement between the measured images and the occupancy images which represent the true average of the sphere’s density over the imaging time. For cranial-caudal motion, however, there are motion artefacts which appear as a blurring or ‘smudging’ of the density. This is more pronounced for axial slices farther from the centre of the motion. Even at the slice closest to the origin, the density distribution of the sphere is distorted from its actual occupancy. Artefacts for lateral motion are shown in figure 3. In this case, there is clear disagreement between the measured and occupancy images despite the use of a slow gantry rotation. The accuracy of the simulations can be more quantitatively evaluated by looking at pixel profiles through the measured and simulated images. These are presented in figure 4. The profiles are taken along the central row of pixels in the images shown in figure 3. Profiles for the occupancy images are also shown. In general, there is good agreement between simulation and measurement but with two clear exceptions. There is evidence of a beam hardening artefact located at the origin of the measured MVCT images. This is most apparent in the profiles in the upper left and lower right corners of figure 4. The artefact appears as a small region at the isocentre where the pixel values are elevated by approximately 160 HU over the surrounding region. We have observed this feature in all MVCT images and believe it to be associated with spectral effects which are accentuated in the central CT detectors (Hajdok 2004); it is not the result of phantom motion. The second difference is the prediction by the simulation

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Figure 4. Image profiles in the lateral direction for the images shown in figure 3 (lateral motion). Measured images—solid line; simulated images—dashed line; actual occupancy images—dasheddotted line.

of regions of unphysical negative density, i.e. regions where the pixel value drops below −1000 HU. Physically, this is not meaningful and it arises because of the misapplication of the filtered back-projection process for moving objects. We believe that the commercial software clips pixel values that would otherwise have density less than −1000 HU. If the phantom were scanned as it moves in a higher density medium (i.e. > −1000 HU), the misapplication of the filtered projections will result in artificially diminished density values in the background medium. An example of motion artefacts in an ‘ultra-slow’ scan is shown in figure 5 for lateral motion. Images are shown at the same slices as in figure 3, but the respiratory period has been changed to 1.0 ± 0.1 s in figure 5 (α = 10). Qualitatively, the CT and simulated images appear to much more closely resemble the actual occupancy. We also performed an ultra-slow scan for cranial-caudal motion (not shown). In this case as well, better correspondence with the actual occupancy was observed compared to the results for clinical scan conditions shown in figure 2. In order to confirm the generality and robustness of these predictions, additional simulations were performed (figures 6 and 7). The same phantom and imaging parameters as used for figure 2 were applied to the simulations unless otherwise noted. In figure 6, reconstructed CT images are shown for two different values of the breathing phase (φ = 0◦ and 135◦ ). It is apparent that changing the breathing phase results in a rotation of the artefact pattern in the reconstructed images but otherwise the artefact pattern is unchanged. The physical reason for the rotated artefact pattern is more apparent when comparing different scans in sinogram space.

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Figure 5. Measurement, simulation and actual occupancy images at different axial planes (Y coordinate) for lateral motion. Pitch = 2.4, α = 10.

Figure 7 shows simulated sinograms for scans of a moving phantom under several different gantry rotation speeds and for two different breathing phases. Simulated scans at diagnostic speeds (α = 0.1; figures 7(a) and (b)) show considerable differences depending on the breathing phase (Chen et al 2004). This is in contrast to scans under clinical tomotherapy imaging conditions (α = 2.5; figures 7(c) and (d)) where a different breathing phase corresponds to a simple shift of the original sinogram along the gantry position axis. This means that the artefact will appear rotated in reconstructed image space as is shown in figure 6. Figures 7(e) and (f) show the effect of different breathing phases under ultra-slow scan conditions (α = 10). In this case, the two sinograms are virtually identical. Consequently, the reconstructed images are less dependent on breathing phase. Figure 7 explains why artefacts in slower CT scans are less dependent on the breathing phase than artefacts in diagnostic scanners. Taken together, figures 6 and 7 indicate that the results of slow or ultra-slow CT scanning should be robust to a variety of breathing phases and respiratory periods (α values). 3.2. Volume conformity measures The CT images were contoured using a range of iso-density thresholds. A comparison of the iso-density contours with the true motion envelope is shown for cranial-caudal and lateral motions in figure 8. Typical clinical imaging conditions are presented in the two upper plots

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Figure 6. Simulated images in a CT scan for two breathing phases (φ) under tomotherapy scan conditions (pitch = 2.4, α = 2.5). Left column: φ = 0◦ , right column: φ = 135◦ .

for both cranial-caudal and lateral motions. Also shown in the lower plots are the iso-density contours and motion envelope for the ultra-slow scans (α = 10). The iso-density contours correspond to threshold densities of −890, −780, −670, −560, −450, −340, −230 HU. For lateral motion under typical clinically used imaging conditions (α = 2.5), it is clear that none of the iso-density contours correspond well with the true motion envelope. This is consistent with the work of Gagne et al (2005). For cranial-caudal motion, the contours more closely represent the motion envelope at the image shown. As one examines axial images farther from the centre of the motion envelope, the spreading of high CT numbers observed in figure 2 causes the iso-density contours to deviate more from the true motion envelope. These slices correspond to the object’s location at end inspiration and end expiration in patients. Isodensity contours in ultra-slow scans (α = 10) are shown in the lower plots in figure 8. These conform much better to the motion envelope when compared to the contours for standard clinical imaging conditions. The accuracy measures of the iso-density contours over the entire three-dimensional volume are presented in figure 9. We found little difference in either intersection volume or excess volume coverage using different helical pitch values or slice spacing. For ease of visualization, results are shown only for pitch = 2.4 and 6 mm slice spacing. The upper plot in figure 9 shows the intersection volume for cranial-caudal (solid lines) and lateral motions (dashed lines) under both clinical and ultra-slow conditions. The intersected volume represents the percentage of the motion envelope enclosed by the iso-density volume. The different motion directions and scan rates have roughly the same intersection volume at each

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(a)

(b)

(c)

(d)

(e)

(f)

Figure 7. Simulated sinograms for a phantom moving along the scanner Y axis (cranial-caudal motion) under different scanner conditions and two different breathing phases (φ = 0◦ , 135◦ ). (a), (b) α = 0.1 (diagnostic speed); (c), (d) α = 2.5 (clinically used tomotherapy speed); (e), (f) α = 10 (ultra-slow scan).

iso-density threshold. On average, the lowest iso-density contour threshold (−890 HU) covers 95% of the motion envelope and thus misses the remaining 5%. The difference in motion artefacts is manifested more clearly by studying the amount of excess volume included in iso-density contours, shown in the lower portion of figure 9. In this case, there is a clear distinction between the accuracy of CT scans with cranial-caudal versus lateral motions and scans in standard clinical conditions versus ultra-slow conditions. The artefacts for cranial-caudal motion were seen to be less severe than the artefacts for lateral motion in figures 2 and 3. This translates into less excess volume included in the iso-density contours for cranial-caudal motion, shown in the lower part of figure 9. Under both ultra-slow and clinical conditions the excess volume is greater for lateral motion (dashed lines) than it is for cranial-caudal motion (solid lines). In general, iso-density contours under ultra-slow conditions (α = 10) include significantly less excess volume. The density information is better averaged in the CT images obtained when α = 10 compared to the clinical conditions of the tomotherapy system. Consider the practical implications of figure 9 for the case of lateral motion. Using images acquired under clinical conditions (α = 2.5), contouring the phantom with a threshold of −890 HU will cover 90% of the true motion envelope and include an excess volume equivalent

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Figure 8. Iso-density contours (thin lines) compared to the true motion envelope (thick line) under different conditions. Upper left: cranial-caudal motion, α = 2.5. Upper right: lateral motion, α = 2.5. Lower left: cranial-caudal motion, α = 10. Lower right: lateral motion, α = 10. Iso-density contours shown correspond to −890, −780, −670, −560, −450, −340, −230 HU.

to 95% of the motion envelope. The amount of intersected and excess volume can be improved by scanning the phantom under ultra-slow conditions (α = 10) where 95% of the true envelope is covered and only 22% excess volume is included for the same iso-density contour. 4. Discussion The results here indicate that slow CT scans (α = 2.5) as used on the tomotherapy unit generally do not adequately average out the density of moving objects at each image slice. Motion artefacts in the CT images acquired under standard clinical imaging conditions represent severe distortions from the actual occupancy images. These results are consistent with other phantom studies (Chen et al 2004, Gagne and Robinson 2004, Gagne et al 2005, Mori et al 2006) of different rates of motion and CT gantry rotation speed. These studies have generally shown scans with gantry periods in the range 0.5–4.0 s all contain motion artefacts when objects move with typical respiratory periods. Patient studies on tumour motion and CT scan techniques (Lagerwaard et al 2001, Shih et al 2004, Wurstbauer et al 2005), however, have generally found slow CT scans (α approximately equal to 1) to yield reproducible (although

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Figure 9. Intersection and excess volume as a function of iso-density threshold. Upper plot: intersection volume; Lower plot: excess volume. Values are shown for: lateral motion α = 2.5 (dashed line, circles), lateral motion α = 10 (dashed line, triangles), cranial-caudal motion α = 2.5 (solid line, circles) and cranial-caudal motion α = 10 (solid line, triangles)

not necessarily accurate) depictions of moving tumours. This may have led to the belief that slow CT scanning averages out the density of moving objects more faithfully, but in these studies the true excursions of the motion are generally unknown and hence this conclusion is unfounded. There is some difference in the severity of the artefacts for different directions of motion. For lateral motion under standard clinical imaging conditions there is poor agreement between the occupancy and the CT images. None of the iso-density contours in the CT images correspond well with the true motion envelope. For cranial-caudal motion the correspondence is better, and this translates into less excess volume included in the iso-density contours. This may be somewhat reassuring, since the largest tumour motion tends to be in the cranial-caudal direction for patients (Steppenwoolde et al 2002). Additional simulations indicated that breathing phase does not significantly affect motion artefacts under clinical imaging conditions used in tomotherapy. This is in contrast to the work of Chen et al. (2004) applicable to diagnostic helical CT scanners. Our results differ because of the much slower gantry rotation used by the tomotherapy imaging system. At each image slice in diagnostic CT, the beam may or may not intersect the moving object depending on the initial breathing phase. In slow CT scanning, however, the beam is guaranteed to intersect the moving tumour at least once at every slice the tumour occupies. This was illustrated by the reproducibility of the tomotherapy sinograms for different values of the breathing phase shown in figures 7(c) and (d). Changing the breathing phase in a tomotherapy scan generates a translation of the sinogram. In the reconstructed CT images this results in a rotated artefact pattern. Otherwise, the artefacts are unchanged in appearance.

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We found that scanning under ultra-slow conditions (α = 10) can lead to better averaging of the density in the CT images and hence better correspondence of iso-contours with the true occupancy. This is because of more uniform sampling of x-rays passing through the entire motion envelope when the gantry rotation is further slowed down. When the rays are filtered and back-projected to reconstruct the CT images, this ensures more uniform constructive interference inside the motion envelope and destructive interference elsewhere. Artefacts observed under typical imaging conditions arise because of non-uniform sampling of the motion envelope. Simulations of ultra-slow scanning were found to be even more robust to variations in breathing phase than clinical tomotherapy scans. Another possible implementation of the ultra-slow scanning technique may be through interpolating projections over a larger gantry rotation. For example, reducing the pitch by a factor of 2 and interpolating over twice the number of projections effectively samples the same longitudinal distance (along the scanner Y axis) but takes twice as long due to a reduced couch velocity. As the gantry angular range in which to interpolate becomes larger, the sampling of the motion envelope will become more uniform and motion artefacts should be diluted and diminished. This approach could yield similar results to those obtained here for an ultra-slow scan but without changing the gantry rotation period. Our study used a high density phantom moving in air and only included simple harmonic motion patterns. However, it provides insight into the nature of motion artefacts generated by the slow MVCT scanner. If one wishes to adaptively modify a non-gated tomotherapy treatment plan for patients with moving tumours (Ramsey et al 2006), it may be prudent to slow down the gantry rotation further in order that the tumour density be better averaged and correct contours are seen. Implementing this clinically will require a reduction of the imaging dose rate (i.e. linac current mA) to maintain a low patient dose. The feasibility of this approach and implications of ultra-slow scanning on patient throughput in tomotherapy may restrict practical implementation. In addition, it will be of interest to study how the motion artefacts in MVCT images affect daily registration of the tumour volume (ITV) to the planning kVCT scan (or prior MVCT scans) taken under different temporal conditions. The results for ultra-slow scanning have implications for other forms of image-guided radiation therapy such as cone beam kVCT (Jaffray et al 2002). In cone beam CT, the gantry rotation speed of a linear accelerator means the scan time is much longer than one respiratory period (α ≈ 14). If the patient is able to breath reproducibly, ultra-slow scanning in cone beam CT may accurately reproduce the motion envelope (Sonke et al 2005). Our study has investigated the artefacts generated by a solid object moving in air. Since lung tissue has a greater density than air, one might question the relevance of these results to situations in real patients. This is a valid objection since figure 9 (upper) shows contouring CT images with an iso-density threshold of −780 HU covers only about 80% of the true motion envelope. Most lung tissue is more dense, so one may suspect that 80% coverage may not be achievable in patients imaged by MVCT. The situation is complicated by the misapplication of filtering the projections which was shown to result in artificially diminished density streaks in some regions around the moving object (see figure 4). For an object moving in a high density medium, we believe figure 9 will need adjustment according to the lower contrast. It should still be possible to achieve the same degree of coverage in a lung medium and a trend similar to figure 9 should be observed. In other words, the artefact geometry and intensity in a surrounding lung medium should be quite similar to those we have presented for scans in air. More studies are required to validate this work for clinical application to volumes that are crucial to successful radiotherapy. These refer to the ITV volume in ungated imaging and radiotherapy and the CTV in gated image-guided therapy.

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5. Conclusion We have presented a phantom study for small moving objects on a helical MVCT scanner developed for adaptive tomotherapy. Averaging out of the density of a moving object is more representative when the gantry rotation period is at least ten times larger than the respiratory period. Since a rapid MVCT scanner may be impractical due to engineering constraints, the approach of ultra-slow CT may be a viable alternative for some lung patients treated by ungated tomotherapy, at the expense of patient throughput. Acknowledgments We acknowledge George DeWaele for constructing the phantom used in our experiment. We would like to thank Dr Isabelle Gagne and Dr Don Robinson for collaborating on providing the baseline CT simulation software. The code is based on a program originally found in Faridani (2003). The financial support of the Ontario Research and Development Challenge Fund (OCITS project) is gratefully acknowledged. References Chen G, Kung J and Beaudette K 2004 Artefacts in computed tomography scanning of moving objects Semin. Radiat. Oncol. 14 19–26 Crawford C and King K 1990 Computed tomography scanning with simultaneous patient translation Med. Phys. 17 967–82 Faridani A 2003 Introduction to the mathematics of computed tomography Inside Out: Inverse Problems and Applications vol 47 ed G Uhlmann (Cambridge: Cambridge University Press) pp 1–46 Gagne I and Robinson D 2004 The impact of tumour motion upon CT image integrity and target delineation Med. Phys. 31 3378–92 Gagne I, Robinson D, Halperin R and Roa W 2005 The use of phase sequence image sets to reconstruct the total volume occupied by a mobile lung tumour Med. Phys. 32 2211–21 George R, Vedam S, Chung T, Ramakrishnan V and Keall P 2005 The application of the sinusoidal model to lung cancer patient respiratory motion Med. Phys. 32 2850–61 Hajdok G 2004 A new artefact in CT: secondary effects of spectral beam hardening in the x-ray detector Proc. Imaging Network Ontario 3rd Annual Symp. (Toronto, Canada) Hsieh J 2003 Computed Tomography: Principles, Design, Artifacts and Recent Advances (Bellingham, WA: SPIE Optical Engineering Press) ICRU 1999 Prescribing, recording and reporting photon beam therapy (supplement to ICRU Report 50) ICRU Report 62 (Bethesda, MD: ICRU) Jaffray D, Siewerdsen J, Wong J and Martinez A 2002 Flat-panel cone-beam computed tomography for image-guided radiation therapy Int. J. Radiat. Oncol. Biol. Phys. 53 1337–49 Kak A and Slaney M 1988 Principles of Computerized Tomographic Imaging (Piscataway, NJ: IEEE) Kim B, Kron T, Chen J and Battista J 2006 Preliminary investigation of multi-pass respiratory gated helical tomotherapy Med. Phys. 33 2285 Lagerwaard F, van Sornsen de Koste J, Nijssen-Visser M, Schuchhard-Schipper R, Oei S, Munne A and Senan S 2001 Multiple ‘slow’ CT scans for incorporating lung tumour mobility in radiotherapy planning Int. J. Radiat. Oncol. Biol. Phys. 51 932–7 Louis A and Mass P 1993 Contour reconstruction in 3-D x-ray CT IEEE Trans. Med. Imaging 12 764–9 Mageras G et al 2004 Measurement of lung tumor motion using respiration-correlated CT Int. J. Radiat. Oncol. Biol. Phys. 60 933–41 Meeks S, Harmon J, Langen K, Willoughby T, Wagner T and Kupelian P 2005 Performance characterization of megavoltage computed tomography imaging on a helical tomotherapy unit Med. Phys. 32 2673–81 Mori S, Kanematsu N, Mizuno H, Sunaoka M and Endo M 2006 Physical evaluation of CT scan methods for radiation therapy planning: comparison of fast, slow and gating scan using the 256-detector row CT scanner Phys. Med. Biol. 51 587–600 Ramsey C, Langen K, Kupelian P, Scaperoth D, Meeks S, Mahan S and Seibert R 2006 A technique for adaptive image-guided helical tomotherapy for lung cancer Int. J. Radiat. Oncol. Biol. Phys. 64 1237–44

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