Download IMRT verification by three-dimensional dose reconstruction

IMRT verification by three-dimensional dose reconstruction from portal
beam measurements
M. Partridge,a) M. Ebert,b) and B-M. Hesse
DKFZ Heidelberg, Im Neuenheimer Feld 280, D-69120 Heidelberg, Germany
共Received 16 October 2001; accepted for publication 22 May 2002; published 26 July 2002兲
A method of reconstructing three-dimensional, in vivo dose distributions delivered by intensitymodulated radiotherapy 共IMRT兲 is presented. A proof-of-principle experiment is described where an
inverse-planned IMRT treatment is delivered to an anthropomorphic phantom. The exact position of
the phantom at the time of treatment is measured by acquiring megavoltage CT data with the
treatment beam and a research prototype, flat-panel, electronic portal imaging device. Immediately
following CT imaging, the planned IMRT beams are delivered using the multiple-static field technique. The delivered fluence is sampled using the same detector as for the CT data. The signal
measured by the portal imaging device is converted to primary fluence using an iterative phantomscatter estimation technique. This primary fluence is back-projected through the previously acquired
megavoltage CT model of the phantom, with inverse attenuation correction, to yield an input
fluence map. The input fluence maps are used to calculate a ‘‘reconstructed’’ dose distribution using
the same convolution/superposition algorithm as for the original planning dose calculation. Both
relative and absolute dose reconstructions are shown. For the relative measurements, individual
beam weights are taken from measurements but the total dose is normalized at the reference point.
The absolute dose reconstructions do not use any dosimetric information from the original plan.
Planned and reconstructed dose distributions are compared, with the reconstructed relative dose
distribution also being compared to film measurements. © 2002 American Association of Physicists in Medicine. 关DOI: 10.1118/1.1494988兴
Key words: IMRT verification, electronic portal imaging, megavoltage CT
I. INTRODUCTION
The use of intensity modulation in radiation therapy 共IMRT兲
has been shown to enable the delivery of highly conformal
dose distributions.1 Escalation of the dose delivered to the
target, while maintaining an acceptable dose to surrounding
organs at risk, is only possible using IMRT in a significant
number of cases. The technology to plan and deliver such
treatments has received significant research interest in recent
years, and routine IMRT is now performed by a growing
number of groups around the world. Methods of delivery
include the use of multiple-static fields shaped with a multileaf collimator 共MLC兲; dynamically collimated fields using a
number of fixed gantry angles; dynamic, intensity-modulated
arc therapy, and tomotherapy.
With the routine introduction of such techniques, there is
significant current interest in verification. There are two reasons why verification is of particular interest in IMRT.
共i兲
Verification that the planned fluence distributions
have been successfully delivered. A particular concern
is that these new procedures may not be adequately
covered by standard verification protocols. Point dose
measurements frequently used as part of standard
verification procedures may be difficult to apply in
some IMRT cases, where the measurement point falls
on a steep dose gradient. Commissioning and quality
assurance of new types of planning and delivery techniques requires careful attention, including checking
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共ii兲
of small-field output factors in dose calculations and
the effects of MLC leaf position error on dose delivery.
Verification of patient positioning. Where high dose
gradients are used to spare organs at risk close to a
target volume, special attention should be given to
ensuring that the patient is correctly positioned. This
may include organ motion both between fractions and
during any given treatment fraction.
In a recent review, Essers et al. recommend that ‘‘portal
dose measurements 关should be made兴 during treatments with
a large dose inhomogeneity ... for instance in the thorax region or when using intensity-modulated beams.’’ 2
The first approach to verifying IMRT treatments was to
deliver the patient-optimized intensity-modulated beams to
an anthropomorphic or simple geometric phantom and measure the resultant dose distribution using film.3,4 The measured dose distribution is then compared to distributions for
the patient-optimized beams and recalculated using the particular phantom’s geometry. Burman et al. and Tsai et al.
both describe the integration of these pretreatment, filmbased measurements into comprehensive IMRT quality assurance procedures by combining the results in vivo point
dose measurements using TLDs.5,6
The use of electronic portal imaging devices 共EPIDs兲 is
also of interest for IMRT verification. Studies of the basic
dosimetric performance of EPIDs have been presented for
0094-2405Õ2002Õ29„8…Õ1847Õ12Õ$19.00
© 2002 Am. Assoc. Phys. Med.
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Partridge, Ebert, and Hesse: IMRT verification by 3D dose reconstruction
camera-based,7,8 liquid ionization chamber-based9–12 and
amorphous silicon flat-panel13,14 systems. Pretreatment verification of 2-D intensity-modulated beam portals has also
been demonstrated for both camera-based15,16 and liquid ionization chamber-based systems.17,18 In vivo dosimetric measurements were demonstrated using a camera-based EPID by
Kirby et al.,19 who reported multiple-static field verifications
showing the agreement between prescribed and measured
exit doses to within 3%, and McNutt et al.,20,21 who used a
convolution/superposition model, treating the EPID as part
of an ‘‘extended phantom’’ to create portal dose images,
showing agreement to within 4% 共2 SD兲. An iterative
method was then used to reconstructed dose distributions in
phantom, showing agreement to within 3% 共2 SD兲. Similar
in vivo measurements using the liquid ionization chamber
have been presented Boellaard et al.,22 showing a reconstructed midplane dose in clinical practice that agreed with
planned dose distributions to within 2% 共larynx兲 and 2.5%
共breast兲. Other in vivo dosimetric measurements have been
demonstrated by Chang et al.,23 who presented a phantom
study of 70 intensity-modulated prostate fields showing that
profiles matched to within 3.3% 1 SD and central-axis doses
to 1.8% 1 SD, Kroonwijk et al.,24 who showed in vivo dosimetry for prostate treatments and Partridge et al.,25 who
showed an in vivo breast dose measurement.
A number of the in vivo measurements describe dose to a
point outside of the patient 共e.g., the exit surface, or a portal
plane兲. To describe the dose distribution in three dimensions
inside the patient, some sort of transit dose calculation, or
back-projection of the measured beam portals is required.
Wong et al.26 described a comparison of a forward ray tracing calculation through the planning CT cube with exit dose
measurements made with film and TLD, but found matching
the geometry of the film and CT cubes a problem. Agreement
of 3% was seen after matching, but local differences of 5%–
10% were still apparent. A slightly different approach by
Aoki et al.27 was then extended by Hansen et al.,28 who
aligned EPID images with ‘‘beam’s eye view’’ DRRs and
back-projected the primary fluence from the EPID images
through the planning CT and calculated the deposited dose.
Phantom measurements showed agreement of TLD, film, and
transit dose measurements to within 2%.
A problem with transit dose calculations using the planning CT volume 共as pointed out by the above authors兲 is that
patient set-up errors or organ motion on the day of treatment
must be taken into account. Portal images and DRRs can
only be used to correct for rigid body motion, for nonrigid
transformations further 3-D anatomical information is required to avoid inaccurate and potentially misleading results.
A solution to this problem is to have a ‘‘treatment time’’ CT,
taken either using the megavoltage treatment beam 共MVCT兲,
a CT scanner close to the treatment machine 共i.e., inside the
treatment room兲 or additional kilovoltage CT hardware
added to the treatment machine.29
Nakagawa et al.30 presented verification images of a rotational arc therapy treatment, where measured fluence was
back-projected through a single-slice MVCT image, although full dosimetric calculations were not presented. The
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FIG. 1. Schematic overview of the adaptive radiotherapy treatment process.
If the patient geometry measured by the on-line CT is out of tolerance, a
decision must be made as to whether it is possible to simply reposition the
patient using a rigid body transformation and continue with treatment, or
replan.
single-slice approach has been further developed by the tomotherapy research group, showing first input fluence measurements, made by back-projecting measured exit fluence
through a treatment-time MVCT image,31 and then full dosimetric reconstructions.32,33 Results are shown that agree to
within 3 mm 共high dose gradients兲 or 3% 共low dose gradients兲.
Our aim in the work presented here is to demonstrate the
feasibility of three-dimensional dosimetric reconstruction of
IMRT distributions using a conventional LINAC. Treatmenttime volume images are obtained using megavoltage conebeam CT. An inverse-planned IMRT treatment is delivered to
an anthropomorphic phantom using the multiple-static field
delivery technique and the transmitted beams recorded using
an amorphous silicon flat-panel imager. The measured signal
is converted to primary fluence using a method similar to
that described by Hansen et al.,34 and back-projected through
the MVCT model of the phantom to yield the input fluence.
The dose is then calculated from the measured input fluence
maps and the MVCT model using the same planning system
dose calculation as for the original plan. Planned and reconstructed dose distributions 共both relative and absolute兲 are
presented and the applications and limitations of the technique are discussed.
II. METHOD
The concept investigated by the work described here is
summarized by Fig. 1. A phantom was CT scanned using a
stereotactic localization system and an inverse IMRT plan
generated. The phantom was set up for treatment on a linear
accelerator—using the same stereotactic system—and translated to the defined treatment position. A megavoltage CT
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FIG. 2. Transverse slices from planning the CT showing
the target and organ-at-risk outlines and the corresponding slice through the treatment-time megavoltage CT
cube.
scan was then acquired using an amorphous silicon flat-panel
imager before delivering the IMRT beams using the
multiple-static field technique. Beam delivery was recorded
using the flat-panel imager. The delivery was then repeated
with radiographic film inserted in the phantom. The IMRT
beams were also delivered to the flat-panel imager with the
phantom removed, to provide a measurement related to the
input fluence. The following sections describe each stage of
this process in detail and present the results of the dosimetric
measurements.
A. kVCT data acquisition treatment planning
Three slices from the neck section of an Alderson-Rando
phantom were placed in a stereotactic head localization
frame and CT scanned with a Siemens Somatom scanner
共slice thickness 3 mm, slice resolution 0.6 mm⫻0.6 mm兲.
The slices were mounted on a 15° shallow wedge such that
the chin of the phantom was raised. This makes the axis of
the phantom neck parallel to the rotation axis of the scanner,
thus reducing the field of view required to acquire complete
CT data 共this was important due to the small field of view of
the flat-panel imager, as discussed below兲. An IMRT plan
was then generated using the Virtuos/KonRad inverse planning system 共DKFZ Heidelberg/MRC Systems, Heidelberg,
Germany兲. For the purposes of this study, a single cylindrical
‘‘organ at risk’’ 共OAR兲 running vertically through the phantom was defined. A ‘‘horseshoe’’-shaped target was then defined that partially wraps around the OAR. The plan was
generated with five equispaced beams 共36°, 108°, 180°, 252°,
and 324°兲, each divided in to a maximum of five intensity
levels. A transverse slice through the treatment isocenter of
the planning CT cube, showing the target and organ-at-risk
outlines, is shown in Fig. 2. All dose calculations described
here were performed using an in-house convolution/
superposition algorithm in preference to the planing system’s
standard pencil-beam model. The algorithm employs kernels
constructed by the weighted summation of monoenergetic
dose spread arrays, following the method of Mackie et al.35
Medical Physics, Vol. 29, No. 8, August 2002
B. Detector optimization and calibration
The detector used for all imaging measurements described
here was an amorphous silicon 共a-Si兲 flat-panel device comprised of a matrix of 256⫻256 pixels with a pitch of 800 ␮m
共RID256L, Perkin Elmer Optoelectronics, Germany兲. Each
pixel consists of an a-Si:H photodiode switched by a thinfilm transistor. This array is placed in contact with 134
mg/cm2 Gd2 S2 O:Tb phosphor screen 共Lanex fast, Kodak,
USA兲. The detector as-supplied was fitted with a 0.6 mm
aluminum cover plate.
Photoelectric interaction of lower-energy scattered radiation has been shown to produce an over-response in the assupplied detector when compared to a water-equivalent detector. Monte Carlo studies using the GEANT detector
simulation tool36 have shown that replacing the 0.6 mm aluminum plate with 3.0 mm copper provides an optimum improvement in spectral response—by preferential absorption
of the low-energy scattered radiation—with negligible degradation in spatial resolution.37 The total energy deposited in
the amorphous silicon layer of the detector was scored for a
series of monoenergetic pencil beams with energies from 200
keV to 6 MeV in steps of 200 keV and the optimum copper
build-up plate thickness determined. This Monte Carlo derived energy response function is particularly important
when correcting for scattered radiation; see Sec. II C. This
method implicitly assumes that the signal given by the amorphous silicon detector is directly proportional to the dose
deposited in the detection layer, and is independent of energy. This assumption is not strictly true, since both the phosphor screen and—to a lesser extent—the amorphous silicon
layer can be expected to exhibit an energy-dependent response. In this case, however, the effect of energy dependence is kept small due to the beam filtration provided by the
3.0 mm copper plate.37,38 A full Monte Carlo simulation of
the detector including optical effects in the phosphor screen
would be interesting, but is beyond the scope of this work.
Available integration times on the imager ranged from
80– 6400 ms per frame. The detector reads out using an ana-
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log to digital converter in a half-row interleaved raster scan,
with two charge amplifier ASICs working simultaneously.
For example, the incoming data stream for a frame arrives at
the acquisition computer in the following order: 共1,1兲 共129,1兲
共2,1兲 共130,1兲 ¯ 共128,1兲 共256,1兲 共1,2兲 共129,2兲, and so on,
where 共u,␯兲 is the column and row number of each pixel. The
signal charge transfer time 共effective dead time兲 for each
pixel is 2.4 ␮s, with the pixel integrating continually for the
rest of the frame.
The small size of the detector (20 cm⫻20 cm) limits this
study to small phantoms and a small target volume, although
the method described is readily applicable to larger detectors.
Since the entire object must be visible in every projection for
good quality CT reconstructions, the detector was mounted
at a fixed distance of 130 cm from the source using an inhouse constructed support frame, giving a field of view at the
isocenter of just 15.4 cm⫻15.4 cm. The resultant small
phantom-to-detector distances 共less than 25 cm兲 means that
the amount of scattered radiation incident on the detector
was high.
All images were filtered to remove the effect of defective
pixels, using a locally applied median window filter, and
dark-offset corrected during acquisition. The linearity of the
detector was measured by taking the signal recorded at the
center of a fixed-sized square field and varying the sourceto-detector distance. Two different detector calibration
schemes were then investigated. The first scheme records the
relative response ⌽Detected to an indecent beam ⌽Primary for
each pixel 共u,␯兲 in the image using the linear-quadratic
model described by Morton et al.,39
2
Scatter
⌽Detected⫽⌽Primary exp共 Bt u, ␯ ⫹Ct u,
共 t u, ␯ 兲 .
␯ 兲 ⫹⌽
共1兲
The matrices of coefficients B and C were fitted using a
series of images of known thicknesses t of water-equivalent
plastic acquired under reference conditions. The scatter correction ⌽Scatter is described in Sec. II C. This calibration
scheme is known to be useful for removing artefacts caused
by pixel-to-pixel variations in sensitivity in the detector and
off-axis changes in beam energy, giving high quality and
uniform images suitable for CT reconstruction. An absolute
calibration was also performed using the following method:
the imager was placed at 130 cm, symmetrically at the center
of a 10 cm⫻10 cm, 6 MV photon beam. The integration
time of the detector was set to 100 ms, averaging over 100
frames for one image. In the middle of the averaged frame
sequence, a 10 MU beam was delivered using a dose rate of
200 MU/min. The mean signal over a 16⫻16 pixel region of
interest 共12.8 mm⫻12.8 mm at the plane of the imager兲 at
the center of the image was then calculated. This method
relates the signal recorded by the imager to the absolute dose
delivered under reference conditions. This calibration does
not take into account the variations in responsivity of the
detector outside the averaged region of interest or off-axis
variation in beam energy. Given that the detector is not
water-equivalent, systematic errors in absolute dose are also
expected with field size. Dose reconstruction using both the
relative and absolute calibration methods are presented.
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C. Scattered radiation correction
With the detector placed close to the exit surface of the
phantom, a large amount of scattered radiation is incident on
the detector surface. The increased buildup plate thickness of
the modified detector helps to preferentially absorb lowerenergy multiply scattered radiation, but single Compton scatter must still be corrected for. The method used was based on
the iterative Monte Carlo kernel-based technique described
by Hansen et al.34 and later implemented by Spies et al.40
The raw image is first converted to effective radiological
water thickness, using the relative thickness calibration described in Eq. 共1兲. The scattered radiation present in the image is then estimated by convolution of the thickness map
with a thickness-dependent pencil beam scatter kernel. For
the work described here, the GEANT-calculated spectral response of the detector was incorporated into the precalculated pencil beam kernels. The procedure can be summarized
in the following form, where the scatter in a given iteration n
is given by
⌽Scatter共 n 兲 ⫽w
"␰ 共 t 共i,nj兲 ,r i j,kl 兲 ,
兺
兺 ⌽Primary
i, j
i, j k,l
共2兲
where r i j,kl is the distance from the scoring pixel i, j to the
presumed center of the scatter kernel ␰ at pixel k, l and w is
a scaling factor. The thickness map t(n) is calculated using
the scatter estimate from the previous iteration ⌽Scatter(n⫺1)
using the following equation:
0⫽C共 t共 n 兲 兲 2 ⫹Bt共 n 兲 ⫺ln
冉
⌽
⌽Primary
⫺⌽Scatter共 n⫺1 兲
Detected
冊
共3兲
共the scatter contribution is set to zero for the first iteration兲.
In practice, the iterative process is found to converge on an
acceptably accurate solution within three or four iterations.
D. The LINAC
All beams were delivered using the 6 MV photon beam of
a Siemens Primus LINAC 共Siemens Medical Systems, Concord, CA, USA兲 equipped with the standard 40 leaf-pair
MLC. Each leaf projects to 1 cm wide at the isocenter. The
IMRT beams were delivered automatically as a series of
multiple static fields using the Siemens Lantis control system. The control system of the LINAC limits the smallest dose
deliverable by each single beam to an integer number of
monitor units. For the IMRT beams, each beam segment is
simply rounded to the nearest integer number of MUs. For
the megavoltage CT data acquisition, the minimum dose deliverable for each projection was limited to 1 MU. The alignment of all phantoms was carried out using a stereotactic
localization system and the treatment room lasers. All beams
were delivered at 200 MU/min.
E. Geometric alignment, helix and stereotaxy
Due to the nonideal trajectory of the detector during gantry rotation 共because of sagging of the detector support frame
under gravity兲 a geometric correction was performed. Projections of a cylindrical phantom41 with a helix of high-contrast
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ball bearings set into its surface were acquired for every
gantry angle to be used during MVCT reconstruction. The
motion of the support frame was known to be quite reproducible. The helix phantom was aligned using the treatment
room lasers and imaged immediately prior to the Alderson
Rando phantom. For a particular gantry angle, the projected
positions of the ball bearings on the detector give sufficient
information to calculate the three-dimensional rigid body
transformation from the treatment room 共stereotactic兲 coordinates to the detector coordinates 共u,␯兲.42 A full discussion
of this method is beyond the scope of this paper.
F. Megavoltage CT imaging
The phantom was set up on the LINAC using the same
stereotactic localization system as for kV CT and imaged and
translated so that the center of the target point, as defined by
the inverse plan, coincided with the rotation isocenter of the
LINAC. A megavoltage CT dataset was then acquired taking
120 projection at 3° intervals around the phantom. Beam
delivery was automated using the Lantis system, delivering 1
MU per projection at 200 MU/min with the gantry stationary
for each beam. The limit of 1 MU per projection was limited
by the LINAC control system, as discussed above. The detector was not automatically synchronized with the LINAC, so
images were acquired by setting the maximum integration
time available of 6400 ms and triggering the detector manually. This long integration time ensures that the entire 1 MU
pulse is captured, given that there can be a random delay of
up to 2–3 s at the start of each beam.
The CT dataset was scatter corrected using the iterative
technique described in Sec. II C, and reconstructed using a
cone-beam implementation of the Feldkamp algorithm. The
correction for the nonideal scanning geometry using the
method discussed in Sec. II E was performed during backprojection. This is preferable to rebinning the projection data,
since it removes one interpolation step, which would potentially degrade spatial resolution. Because Compton interactions dominate in the megavoltage region, the reconstructed
megavoltage images are almost linear with electron density.
However, the dose calculation algorithm used expects CT
numbers 共Hounsfield units, HU兲 so the absolute values in the
reconstructed images have to be converted. For this work,
the reconstructed megavoltage CT values were assumed to
be equal to electron density and were converted to HU using
the electron density to CT number lookup tables provided by
the CT scanner calibration. Since the same look-up table is
used to convert from CT numbers back to electron density
during the dose calculation, this step should not introduce
significant systematic error.
G. IMRT beam delivery and verification
The IMRT beams were delivered and recorded with the
flat-panel imager by acquiring sequences of images. Each
image was an average of ten frames, each frame acquired
using an integration time of 100 ms. These images could
then be summed to give images of each individual beam
segment, or the complete intensity-modulated beam for each
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gantry angle. An independent measurement of the delivered
dose in the phantom was acquired by placing radiographic
film 共Kodak X-Omat V兲 between two slices of the Rando
phantom. 共Note: this necessitated the removal of the phantom from the stereotactic positioning system, dismantling to
insert the film and repositioning. The phantom could not then
be MVCT scanned because of the presence of the film. The
geometric error arising from this process is estimated to be
1–2 mm.兲 As a final independent check, the phantom was
removed and the IMRT beams delivered, in air, directly to
the flat-panel imager. In this way, the directly measured input
fluences could be compared to the in vivo measured, scattercorrected back-projected input fluences.
H. Back-projection and dose calculation
The IMRT beam image sequences were iteratively scatter
corrected using the method described above and then
summed to give the measured primary fluence at the plane of
the detector. These primary fluence maps were backprojected through the megavoltage CT dataset to a plane 30
cm above the isocenter. Inverse attenuation corrections were
performed using the reconstructed electron density values.
IN
The input fluence ⌽u,
␯ for detector pixel u, ␯ is given by
冉 冕
IN
Primary
exp ⫹
⌽u,
␯ ⫽⌽u, ␯
冊
␮ x,y,z t x,y,z dr ,
共4兲
Primary
is the measured primary fluence. The integral
where ⌽u,
␯
is performed along the ray line r 共from the point u, ␯ to the
focus兲 over the attenuation coefficient ␮ x,y,z and pathlength
t x,y,z values for each CT voxel x,y,z traversed. The nonideal
geometry was corrected for using the same helix transformation method as for the CT reconstruction. The resultant reconstructed input fluence maps were then used, together with
the MVCT data set, as input for the convolution/
superposition dose calculation.
The two different calibration schemes described in Sec.
Primary
II B were used to derive ⌽u,
, providing two different
␯
dose reconstructions. For the relative method each measured
beam was scatter corrected to produce primary fluence at the
detector plane, the relative calibration was applied and the
input fluence estimated by back-projecting through the
MVCT cube and correcting for attenuation. The input fluence
maps were converted to monitor units such that total number
of monitor units was the same for the reconstruction as for
the original plan. This was done by applying a single weighting factor to all of the reconstructed input fluence maps, thus
maintaining the ‘‘measured’’ relative beam weights. The relative beam weights are therefore independent of the original
plan. The dose was calculated using the same convolution/
superposition algorithm as for the original plan and the dose
distribution normalized at a reference point in the center of
the target volume. For the absolute method, the primary fluence at the detector plane was scatter corrected and converted to absolute dose using the single calibration factor
derived from a small region of interest at the center of the
detector. These absolute numbers 共Gy兲 were back-projected
and attenuation corrected as described above, and used as
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tions are less than ⫾0.3 mm 共⫾0.5 pixel兲. Detector rotations,
although very small, are also fully corrected for.
B. Beam segments
FIG. 3. The effect of gantry sag, measured using the helix phantom. The
movement of the projected position of the isocenter in the lateral and axial
directions are shown as a function of gantry angle. Distances are quoted at
the plane of the isocenter.
direct input to the dose calculation with no further correction. The output of the planning system is then given directly
in Gray and, again, no further scaling was applied.
III. RESULTS
A. MVCT images and geometric correction
A sample reconstructed slice from the MVCT dataset is
presented in Fig. 2. For the purposes of comparison with the
neighboring kV CT image, several MVCT slices have been
averaged to give comparable slice thicknesses. The bone
contrast in the image is noticeably lower, since contrast in
the MV image results almost solely from electron density
variations, rather than changes in atomic number. Figure 3
shows the gantry sag effect. The shift in the projected position of the isocenter is shown as a function of gantry angle.
Shifts of ⫾6 mm in the u 共lateral兲 direction are clearly seen
at the plane of the isocenter. As would be expected, shifts in
the axial direction are far smaller. After correction all devia-
Figure 4 parts 共i兲–共vii兲 show in vivo measured beam segments for a sample beam from one direction 共108°兲. Due to
the small size of these beams, no image contrast is visible
within each subfield 共one beam element, or Bixel, is 1 cm
⫻1 cm at the isocenter兲. The collimator positions 共field
edges兲, however, are very easily visible and could be used
for on-line monitoring of the delivery hardware performance.
The intensity-modulated distribution resulting from the sum
of the beam segments is then displayed in panel 共viii兲 共scatter
corrected and back-projected through the MVCT cube to
yield input fluence兲. For comparison, the ‘‘ideal’’ model of
the intensity-modulated produced by the inverse planning
system is displayed in panel 共ix兲. This is provided simply to
give an idea of the shape of the ideal beam. For a numerical
comparison, this ‘‘ideal’’ fluence should be convolved with a
model accounting for the radiation source size and the point
spread function of the detector.
C. Input fluence matrices
As a test of the scatter correction, back-projection, and
inverse attenuation methods, line sections through both the
relative reconstructed and the directly measured 共in air兲 input
fluences matrices are presented in Fig. 5. The line sections
are the average over a 2 mm wide strip through the center of
the 108° beam both 共a兲 parallel and 共b兲 perpendicular to the
MLC leaf travel direction. The positions of the line sections
are indicated in Fig. 4, panel 共ix兲. All distances are quoted at
the plane of the isocenter. Generally very good agreement is
seen between the directly measured and reconstructed sections, with the greatest discrepancy occurring at the rightmost peak of Fig. 4共a兲. This good level of agreement is a
direct indication that the iterative scatter correction and backprojection methods work correctly, with the scatter corrected
and back-projected fluence map matching the directly measured one. It should be noted, however, that, because the
FIG. 4. Measured fluences for each separate field comprising an IMRT beam 共108°兲. Beam delivery starts
with the field shown in panel 共i兲 and proceeds from 共ii兲
to 共vii兲. Panel 共viii兲 shows the total measured input fluence and panel 共x兲 shows the prescribed ‘‘ideal’’
intensity-modulated beam model used by the inverse
planning system.
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Partridge, Ebert, and Hesse: IMRT verification by 3D dose reconstruction
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TABLE I. A comparison of dose/volume statistics for planned and measured,
reconstructed dose distributions for the target and organ at risk. The maximum, minimum, mean, and standard deviations in the dose D are given as
percentages of the plan normalization value. The volumes of the target and
organ at risk receiving more than 30% of the plan normalization dose and
less than 90% of the reference dose are quoted as percentages of the total
volume of each structure.
Target 共plan兲
Target 共recon.兲
OAR 共plan兲
OAR 共recon.兲
FIG. 5. Line sections though the input fluence of the 108° intensitymodulated beam are shown in 共a兲 the MLC leaf-travel direction for the
central leaf pair, and 共b兲 normal to the MLC leaf-travel direction. The relative positions of the line sections are indicated in Fig. 4, panel 共ix兲. The
point used to define the maximum for relative beam normalization is shown
in panel 共a兲. The ‘‘ideal’’ intensity-modulated beam is shown simply for
reference. Panel 共c兲 shows the effective water thickness of the phantom
calculated by back-projection for the 108° beam 共the lateral direction along
the central axis of the detector兲. All distances are quoted at the isocenter.
relative normalization scales each beam according to this
peak intensity, the normalization point in this beam is probably shifted systematically down because of the small effective field size of the peak.
Because the two sections are taken from two separate deliveries, it is unclear whether the small differences seen are
Medical Physics, Vol. 29, No. 8, August 2002
D min
共%兲
D max
共%兲
D mean
共%兲
D stdev
共%兲
vol.⬎30
共%兲
vol.⬍90
共%兲
81.6
89.5
0
0
108.7
108.6
93.4
96.4
101.3
101.4
10.7
12.2
3.0
3.4
23.2
24.6
100
100
13.9
14.7
0.4
0.2
99.6
98.9
the result of physical differences in the delivered fluence, or
arise as an artifact of uncertainty in the measurements and
calculations. The accuracy of the these measurements is estimated to be in the region of ⫾1 mm, ⫾2% dose 共relative兲.
An assessment of the repeatability of the delivery system is
beyond the scope of this work. Panel 共c兲 shows the effective
water thickness of the phantom as seen by the 108° beam.
The values were calculated by back-projecting through the
MVCT cube along the central axis of the detector in the u
共lateral兲 direction. Water thickness was obtained by ray tracing the raw ‘‘electron density’’ values in the MVCT cube 共i.e.
before conversion to HU兲 and dividing the sum by the effective attenuation coefficient of water for a 6 MV beam.
The relative back-projected input fluence matrices were
normalized using to the maximum recorded fluence in each
beam 共the sum of the maximum fluences of all beams is
defined to be 100%兲. Table II shows the results of this process, and compares the resulting values to the normalization
values originally produced by the planning system. Some
clear discrepancies are seen between the two sets of figures,
with the high planned weightings of the 36° and 324° beams
reduced and the values of the remaining beams correspondingly increased. One reason for this may be that peak values
for very small peaks (1 cm⫻1 cm) in the measured, reconstructed fluence matrices are not well reproduced, as shown
earlier in figure 5a兲. It should also be noted that the prescribed beam weightings, given in terms of monitor units, do
not account for the difference in output factor that will be
seen in the different-sized field measurements. For a beam
TABLE II. Relative beam weightings for the five IMRT beams. The planned
beam weighting were generated by the inverse planning system. The ‘‘measured’’ weightings are the relative maximum values of the measured, backprojected input fluence matrices for each beam.
Relative beam weighting 共%兲
Beam angle
共degrees兲
Planned
From measured input fluence
36°
108°
180°
252°
324°
29
14
16
15
27
26
18
17
16
23
1854
Partridge, Ebert, and Hesse: IMRT verification by 3D dose reconstruction
FIG. 6. Surface renderings of the 90% isodose surfaces for 共a兲 the planned
dose distribution and 共b兲 the reconstructed relative dose distribution.
comprised of many small subfields, the measured fluence
would be expected to be lower than a corresponding simple
field with the same number of monitor units.
A possible source of systematic error in the backprojection is the assumption in Eq. 共4兲 that attenuation is a
simple exponential function of thickness t. For the small,
centrally placed fields used in this study, significant off-axis
changes is beam spectrum and beam-hardening in the phantom are not expected, but for application to more realisticsized fields the effect of this approximation should be studied
further. Off-axis beam quality and beam hardening are taken
into account in the detector calibration and scatter
correction—using a linear-quadratic model described in Eq.
共1兲—but the coefficients B and C from Eq. 共1兲 cannot be
used directly to model the beam alone, since they contain
information about both the beam and spatial changes in gain
and nonlinearity of the detector itself.
1854
FIG. 7. Cumulative dose/volume histograms of the planned and reconstructed relative dose distributions in the target and organ at risk, as generated by the treatment planning system, are shown.
very small fields. Again, this problem is highlighted in this
case by the use of a very small target volume.
A more quantitative examination of the differences between the planned and relative reconstructed dose distributions is gained from comparing the cumulative dose-volume
histograms 共DVHs兲 of the target and organ at risk, as presented in Fig. 7. The DVHs show the effect of smoothing in
the reconstructed dose distribution with a uniformly slightly
higher dose to the OAR. The slight target underdose in the
reconstruction is a result of the superior–inferior truncation
discussed above. Despite these obvious differences, generally good agreement is seen between the two sets of DVHs,
indicating good agreement between the plan and the reconstruction.
Figure 8 shows a contour plot of a transverse slice
through the center of the target volume. Isodose lines for the
planned and reconstructed dose distributions are overlaid,
D. Relative isodose comparisons
Figure 6 shows surface renderings of the planned and reconstructed 90% isodose surfaces, viewed from 共approximately兲 the anterior direction. The two surfaces are drawn to
exactly the same scale. By inspection, it can be seen that the
broad shape and size of the two surfaces are very similar,
indicating that the measured dose distribution is similar to
that planned. Two obvious differences, however, are visible:
first the measured distribution is generally smoother than the
plan calculation and, second, the measured distribution is
truncated in the superior–inferior direction. Any blurring of
the measured data caused by either x-ray or optical scattering
within the flat-panel detector, or by the finite spatial resolution of the detector, is, of course, not modeled by the planning calculation. These smoothing effects do not seem to
seriously degrade the reconstructed dose distribution. The
truncation of the measured, reconstructed dose distribution is
caused by the large beam penumbras parallel to the MLC
leaf-travel direction, as seen in Fig. 5共b兲. The output factors
used in the planning calculation are not well tested for these
Medical Physics, Vol. 29, No. 8, August 2002
FIG. 8. Isodose contour plots of the planned 共solid兲 and relative reconstructed 共dotted兲 dose distributions. A transverse plane through the treatment
isocenter is shown. The outlines of the target, organ at risk, and external
body contour are shown in gray.
1855
Partridge, Ebert, and Hesse: IMRT verification by 3D dose reconstruction
showing the 60%, 75%, 90%, and 100% contours, together
with the outlines of the organ at risk, target, and phantom
surface. Because of the careful geometric calibration procedure used, the absolute positions of the two dose distributions are accurately known, making a direct comparison of
the spatial distributions possible. A very good reproduction
of the 90% isodose contour is seen, with agreement to within
⫾2 mm in most places. The mean difference between the
planned and reconstructed dose cubes, calculated for a centrally placed volume of interest 14.3 cm⫻14.3 cm
共transverse兲⫻6.6 cm 共axial兲 was 0.6% with a standard deviation of ⫾2.3% 共calculated with a voxel size of 2.24⫻2.24
⫻3.0 mm3 兲, this is in good agreement with the results of
Kapatoes.32,33 The position of the 60% isodose contour is
less well reproduced, with the reconstruction showing the
dose distribution to be shifted out by 3– 4 mm in some
places, although this could be an effect of the different dose
gradients present at 60% and 90%.
An alternative measure of the difference between the
planned and reconstructed dose distributions was calculated
by applying a tolerance rule. The two distributions were said
to be within tolerance if, for a given point in one distribution,
a sufficiently similar dose was found within a short distance
from the other distribution. In x,y,z dose space, this criterion
is equivalent to specifying points within a four-dimensional
hyperellipse with semiaxes equal to the tolerances in x,y,z
and dose. Using levels of ⫾2 mm, ⫾2% and a similar volume of interest to that used above 共bounding the high-dose
region兲, 32.3% of the volume of interest is out of tolerance.
Increasing the tolerance to ⫾3 mm, ⫾3% the percentage out
of tolerance drops to 7.3%, with values of 1.9% and 0.56%
for ⫾4 mm, ⫾4% and ⫾5 mm, ⫾5%, respectively. This
method is effectively the same as the ␥ distribution method
described by Low et al.43 with the hyperellipse reduced to a
two-dimensional figure with semiaxes equal to the dose difference ⌬D M and distance to agreement ⌬d M in the notation
of Low et al.
1855
FIG. 9. Isodose contour plots of the dose distributions measured with film
共solid兲, the relative reconstruction from the EPID measurement 共dashed兲 and
originally planned 共dotted兲. The plane of the film—and hence the section
through the planned and reconstructed dose cubes—was inclined at 15° to
the transverse plane. The distance along the vertical axis is therefore not
strictly in the anterior–posterior direction and is marked AP* accordingly.
Note: because of the inclination of the film, the section shown above is not
the same as that displayed in Fig. 8.
F. Absolute dose reconstruction
The results of the absolute dose reconstruction are shown
in Fig. 10. A clear systematic error is present, with the absolute dose at the reference point calculated to be 1.055 Gy,
compared to a value of 1.022 Gy in the original plan. A line
section through the treatment isocenter in the RL direction is
shown in panel 共b兲. The ⫾1.7% 1 SD error bars indicated are
estimated just from the uncertainty in the absolute calibration
共⫾0.9%兲 and errors in measurement. No attempt has been
made to estimate the accuracy of the electron density conversion and dose calculation. An estimation of the robustness
and repeatability of absolute dose measurements with a-Si
flat-panel detectors is beyond the scope of this work.
IV. DISCUSSION
E. Comparison of relative reconstruction with film
The dose measured directly by film, relative dose reconstructed from the EPID measurement and planned doses are
shown in Fig. 9. The section is inclined at an angle of 15° to
the transverse plane, intersecting close to the center of the
target volume but moving gradually superior in the anterior
direction. Again, agreement of the 90% isodose contours are
good, being within ⫾3 mm most of the time. The 60% isodose 共high gradient兲 is again less accurate, deviating by up to
5 mm in some places. There are several additional sources of
error in this comparison, including the accuracy of the film
developing and scanning process, errors associated with removing and repositioning the phantom between the two measurements, and the uncertainty in locating the exact oblique
section through the reconstructed dose cube. There was also
no method available of accurately registering the dose distribution measured by the film with the reconstruction, so the
two distributions shown in Fig. 9 were aligned by eye.
Medical Physics, Vol. 29, No. 8, August 2002
The accurate reconstruction of in vivo dose delivery relies
on high-quality treatment-time, anatomical information. For
the phantom study presented here, megavoltage CT was used
to acquire this information. Because of limitations of the
LINAC control system, the dose delivered to the phantom was
unfeasibly high for clinical use. To avoid severe undersampling artefacts in the Feldkamp CT reconstruction, 120 projections were required, which with a minimum of 1 MU per
projection gives 120 MU. The time taken to automatically
acquire a complete CT dataset was also about 17 min. In the
future, is it hoped that data will be acquired using continuous
gantry rotation, making it possible to reduce the dose per
projection and acquire the complete dataset in 1–2 min.
The image quality required for verification must be sufficient to resolve low-contrast soft tissues 共⬃2% contrast兲 with
sufficient spatial resolution for position verification 共1–2
mm兲. There is a tradeoff between noise and spatial resolution
in CT reconstruction, giving less noisy reconstructed images
if spatial resolution restrictions can be relaxed. For example,
1856
Partridge, Ebert, and Hesse: IMRT verification by 3D dose reconstruction
FIG. 10. Panel 共a兲 shows a contour plot of the planned 共solid兲 and absolute
reconstructed 共dotted兲 dose distributions, isodose contours are shown in cGy
for a transverse plane through the treatment isocenter. The outlines of the
target, organ at risk, and external body contour are shown in gray. Panel 共b兲
is a line section through the treatment isocenter in the RL direction.
for the data acquisition system described in this paper, 0.27
MU per projection and 120 projections gives a signal-tonoise ratio 共SNR兲 4.2 in a reconstructed image with 0.6
⫻0.6⫻0.6 mm3 voxels, whereas increasing the voxel size to
1.2⫻1.2⫻1.2 mm3 increases the SNR to 16.9. 共Note: for this
example the dose per projection delivered to the phantom
was still 1 MU, although only 0.27 MU per projection was
used for the reconstruction.兲
A possible source of systematic error in the dose calculation arises from the conversion of reconstructed ‘‘MVCT
numbers’’ to HU. The assumption made in this work that the
MVCT reconstruction was linear in electron density may be
inaccurate for a number of reasons: 共i兲 any inaccuracy in the
scattered radiation correction process will lead to ‘‘cupping
artefacts’’ in the CT reconstruction, with radial changes in
the effective CT number; 共ii兲 uncorrected nonlinearities in
detector response could lead to reconstructed values that are
not exactly linear in electron density; and 共iii兲 uncertainties
in the calibration of the detector could lead to inaccuracies in
the reconstructed absolute electron density. A possible future
method for improving both the reconstructed image quality
and reconstructed CT number accuracy would be to use an
Medical Physics, Vol. 29, No. 8, August 2002
1856
elastic matching technique to fuse the MVCT and planning
CT data.
The effect of the CT set on the dose calculation was studied by running the same dose calculation, with the same
共planned兲 input fluence matrices and substituting the kV and
MV CT cubes. For the superposition calculation, no significant differences were observed, indicating that the conversion from electron density to CT number does not introduce
significant inaccuracy. The choice of planning algorithms,
however, was found to be important. Dose calculations were
performed using the kV CT dataset and the planned input
fluence matrices for both the standard pencil-beam algorithm
and the convolution/superposition algorithm mentioned in
Sec. II A. Significant differences in the calculated dose were
seen, particularly in the region close to the entry of the 108°
and 252° beams, which show the greatest deviation from
normal incidence to the phantom. Because of this, the
convolution/superposition algorithm was used for all results
presented in this paper. By using the same planning calculation for both the plan and the verification measurement, the
comparison should be independent of the dose calculation
algorithm. This is in contrast to other transit dose calculation
methods, where a separate dose deposition algorithm is
used.35 The generally good agreement between the film measured doses and the results of the convolution/superposition
algorithm indicates that this algorithm performs reasonable
well, although it would be interesting to compare the measured, reconstructed dose to a full Monte Carlo dose calculation. A further discussion of dose calculation is given by
Ahnesjö,44 but is outside of the scope of this work.
The scatter correction technique described requires an estimate of the water-equivalent thickness of the patient in the
beam’s eye view. For the work described here this was calculated performed iteratively from an EPID image, although
it could also have been calculated directly by ray tracing
through the MVCT cube. An advantage of using the iterative
technique is that the scatter correction is not dependent on
the MVCT and verification using ‘‘portal dose images’’ could
be carried out without the need for MVCT, as demonstrated
by McNutt et al.21 Use of the iterative technique also makes
the resulting thickness map independent of errors in the reconstructed MVCT number and does not require the assumption of a single effective attenuation coefficient to convert to
thickness. 共Note: the MVCT reconstruction is not independent of the scatter correction, since the CT projections are
scatter corrected.兲 With a larger detector, an increase in the
patient-to-detector distance should be possible, resulting in a
smaller scatter fraction and less severe scatter correction
problem.
A major problem with understanding the differences between planned 3-D dose distributions and the measured, reconstructed distributions presented in the last section, is the
large number of possible sources of error. An attempt has
been made in the method described here to remove or isolate
as may of these as possible, but giving unambiguous reasons
for the remaining discrepancies is still difficult. The method
of localization using a stereotactic frame and the treatment
room lasers is the standard method of localization for IMRT
1857
Partridge, Ebert, and Hesse: IMRT verification by 3D dose reconstruction
at DKFZ. For head and neck patients treated in face masks, it
has been shown to be accurate to within 3 mm. For this
work, the phantom was attached directly to the stereotactic
frame and accuracy is estimated to be within 1–2 mm. The
relative agreement between dose distributions was generally
good, indicating that this method is promising for relative
IMRT verification. Significant problems exist with using
such a method for accurate, absolute dosimetry.
The major limitation of the work presented was the small
size of the flat-panel detector available. This necessitated the
use of a small phantom and correspondingly small target
volumes and intensity-modulated fields. For a full assessment of the likely clinical accuracy of this technique, further
investigations should be carried out with a larger detector
共40 cm⫻40 cm detectors are commercially available, replacing the 20 cm⫻20 cm research prototype described here兲.
The work described here has been restricted to the use of
megavoltage CT to acquire anatomical information immediately pretreatment. The dose reconstruction method, however, is equally applicable to other CT data. For example,
kilovoltage cone-beam CT integrated into the treatment
36
LINAC or ‘‘CT on rails’’ could also be used 共where a conventional CT scanner is placed in—or very close to—the
treatment room, and the patient scanned immediately before
treatment, while immobilized兲. An obvious area of future
work is the development of strategies for using such on-line
anatomical information to modify treatment plans, in socalled ‘‘adaptive radiotherapy.’’ The kind of information provided by the in vivo dose reconstruction method described
here could provide useful input for developing these adaptive
radiotherapy strategies.
V. CONCLUSIONS
A proof-of-principle study has been presented describing
a method of making three-dimensional, in vivo dosimetric
measurements of IMRT beams. A sample IMRT treatment
was inverse planned on the neck section of an Alderson
Rando phantom and delivered. The position of the phantom
at the time of treatment was recorded by taking a megavoltage CT scan. The IMRT beams were delivered using the
multiple-static field technique and measured using a flatpanel imager. Measured fluence was converted to primary
fluence at the plane of the detector using an iterative technique to correct for phantom scatter. This primary fluence
was then back-projected through the MVCT reconstruction
of the phantom—using an inverse attenuation correction—to
get an estimate of the input fluence. The 3-D dose distribution was calculated using the same convolution/superposition
algorithm as for the original plan. Both absolute and relative
dose reconstructions were shown.
Verification measurements at various stages of the process
were presented. First, the individual multiple-static field segments were shown. Next, the derived input fluence distributions were compared with directly measured input fluences,
showing good agreement. The results of the relative dose
reconstruction were analyzed using dose/volume histograms
of the defined target and ‘‘organ at risk’’ and contour plots of
Medical Physics, Vol. 29, No. 8, August 2002
1857
planar sections though the 3-D distributions. Agreement between the planned and reconstructed relative dose distributions were found to be mostly within ⫾2 mm and areas of
low dose gradient, rising to 3– 4 mm in higher gradient regions. The overall deviation between the planned and reconstructed dose distributions had a mean of 0.6% with a standard deviation of ⫾2.3%. The discrepancy between the
reconstructed and planned absolute dose at the reference
point was 0.033 cGy 共5.5%兲.
ACKNOWLEDGMENTS
The authors would like to thank the following people,
who have made valuable contributions to this work: Simeon
Nill and Rolf Bendl for help with and access to the Virtuos
and KonRad planning systems, Christian Scholz for the
convolution-based dose calculation, Lothar Spies for the
scatter correction, and Burkhard Groh for the detector characterization and spectral response modeling. The authors are
also very grateful to Phil Evans from the Institute of Cancer
Research, London, for comments on this work and for the
use of their Monte Carlo code. The authors are also grateful
to the referees for suggesting the use of an absolute dose
reconstruction and drawing attention to Ref. 43. This work
was carried out under Deutsche Forschungsgemeinschaft
Project No. DFG SCHL 249/8-1.
a兲
Electronic mail: [email protected]
Present address: MRC Systems GmbH, Hans-Bunte-Str. 10,
D-69123 Heidelberg, Germany.
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