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Transcript
Int. J. Radiation Oncology Biol. Phys., Vol. 63, No. 2, pp. 577–583, 2005
Copyright © 2005 Elsevier Inc.
Printed in the USA. All rights reserved
0360-3016/05/$–see front matter
doi:10.1016/j.ijrobp.2005.05.021
PHYSICS CONTRIBUTION
DESIGN AND IMPLEMENTATION OF AN ANTHROPOMORPHIC QUALITY
ASSURANCE PHANTOM FOR INTENSITY-MODULATED RADIATION
THERAPY FOR THE RADIATION THERAPY ONCOLOGY GROUP
ANDREA MOLINEU, M.S.,* DAVID S. FOLLOWILL, PH.D.,* PETER A. BALTER, PH.D.,*
WILLIAM F. HANSON, PH.D.,* MICHAEL T. GILLIN, PH.D.,* M. SAIFUL HUQ, PH.D.,†
AVRAHAM EISBRUCH, M.D.,‡ AND GEOFFREY S. IBBOTT, PH.D.*
†
*Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, Houston, TX;
Department of Radiation Oncology, University of Pittsburgh Medical Center, Pittsburgh, PA; ‡Department of Radiation Oncology,
University of Michigan Medical Center, Ann Arbor, MI
Purpose: To design, construct, and evaluate an anthropomorphic phantom for evaluation of intensity-modulated
radiation therapy (IMRT) dose planning and delivery, for protocols developed by the Radiation Therapy
Oncology Group (RTOG) and other cooperative groups.
Methods and Materials: The phantom was constructed from a plastic head-shaped shell and water-equivalent
plastics. Internal structures mimic planning target volumes and an organ at risk. Thermoluminescent dosimeters
(TLDs) and radiochromic film were used to measure the absolute dose and the dose distribution, respectively. The
reproducibility of the phantom’s dosimeters was verified for IMRT treatments, and the phantom was then
imaged, planned, and irradiated by 10 RTOG institutions.
Results: The TLD results from three identical irradiations showed a percent standard deviation of less than 1.6%,
and the film-scanning system was reproducible to within 0.35 mm. Data collected from irradiations at 10
institutions showed that the TLD agreed with institutions’ doses to within ⴞ5% standard deviation in the
planning target volumes and ⴞ13% standard deviation in the organ at risk. Shifts as large as 8 mm between the
treatment plan and delivery were detected with the film.
Conclusions: An anthropomorphic phantom using TLD and radiochromic film can verify dose delivery and field
placement for IMRT treatments. © 2005 Elsevier Inc.
Intensity-modulated radiation therapy, Quality assurance, Anthropomorphic phantom, Cooperative groups.
structure is irradiated to a higher dose than intended, and
perhaps higher than can be tolerated.
Consequently, comprehensive quality assurance (QA) procedures are necessary (4). A QA program for IMRT should
focus on the characteristics that strain the abilities of the
procedures and equipment. For example, the nature and advantages of IMRT demand that patient positioning be considerably more precise and reproducible than for conventional
treatment. Devices to facilitate reproducible positioning and
patient immobilization are available for imaging, simulation,
and treatment equipment, and QA procedures should be implemented to ensure proper function and correct usage. Other
alignment devices, such as lasers, video systems, and ultrasound imaging systems, should be evaluated on a regular basis
to ensure their correct function.
INTRODUCTION
Intensity-modulated radiation therapy (IMRT) has gained
acceptance as an improved treatment technique for several
disease sites (1–3). Several manufacturers of radiation therapy equipment provide devices to enable the delivery of
IMRT, including multileaf collimators and inverse-planning
(optimization) treatment-planning systems. Because IMRT
offers the possibility of high dose gradients, it is possible to
deliver high doses to target volumes while maintaining low
doses to nearby critical normal structures to a much greater
extent than is the case with conventional radiation therapy.
At the same time, the high dose gradients achievable with
IMRT mean that localization of the dose distribution is
critical. Small errors in positioning of the patient can mean
that a target volume is missed or that a sensitive normal
Health and Human Services.
Acknowledgments—The authors thank the Radiation Therapy Oncology Group for its contributions, in particular Drs. Robert Kline
and James Galvin for their helpful discussions.
Received Jan 30, 2004, and in revised form May 5, 2005.
Accepted for publication May 11, 2005.
Reprint requests to: Andrea Molineu, M.S., Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center,
Unit 547, 1515 Holcombe Blvd., Houston, TX 77030. Tel: (713)
745-8989; Fax: (713) 794-1364; E-mail: amolineu@
mdanderson.org
This work was supported by Public Health Service Grant CA
81647, awarded by the National Cancer Institute, Department of
577
578
I. J. Radiation Oncology
● Biology ● Physics
Before a patient is treated with IMRT, it is the standard of
practice to perform some form of plan verification. This
might have two or more components, generally including
the validation of data transfer and a dosimetric confirmation
of the intended dose delivery. Confirming delivery of the
intended dose requires that the treatment be delivered with
some sort of phantom containing dosimeters in place of the
patient. Inverse planning systems allow the planned intensity distribution or leaf sequences to be applied to a convenient geometrically shaped (generally elliptical or cylindrical) phantom. Dosimeters (such as ionization chambers or
thermoluminescent dosimeters [TLDs]) are then placed at
selected locations in the phantom, and the complete IMRT
sequence is delivered. Delivery of the expected dose at the
locations selected for measurement is taken as an indication
that the correct dose distribution is being delivered.
The Radiologic Physics Center (RPC) (http://rpc.
mdanderson.org/rpc/) is funded by the National Cancer
Institute to assure the cooperative study groups that conduct multi-institutional clinical trials that institutions participating in the trials have adequate QA procedures and that
no major systematic dosimetry discrepancies exist. The
RPC monitors the linear accelerator output at more than
1300 institutions and verifies dosimetry data used by the
institution, brachytherapy source strength, the calculation
algorithms used for treatment planning, and the institution’s
QA procedures. Remote monitoring procedures include the
use of mailed TLDs to verify machine output, comparison
of an institution’s dosimetry data with RPC standard data to
identify potential discrepancies, evaluation of reference or
actual patient calculations to verify the treatment-planning
algorithms and manual calculations, review of the institution’s written QA procedures and records to verify adherence to Task Group 40 (TG-40), and mailed anthropomorphic phantoms to verify tumor dose delivery for special
treatment techniques.
The RPC is a member of the Advanced Technology
Consortium (http://atc.wustl.edu; member organizations are
listed on the “Members” page), which is funded by the
National Cancer Institute to provide quality assurance for
advanced technology in radiation therapy clinical trials for
protocol groups in the United States. Among other things,
the Advanced Technology Consortium enables electronic
submission of treatment data and conducts evaluations of
protocol compliance and credentialing through the RPC.
Recently, the Radiation Therapy Oncology Group
(RTOG) and other cooperative groups have begun to evaluate the use of IMRT for treatment of patients submitted to
some clinical trials, and other study groups have indicated
their intention to begin such trials in the near future. Study
groups are interested in ensuring that their participating
institutions practice good QA so that patients treated with
IMRT are treated safely, effectively, and in compliance with
the protocol. To enter patients treated with IMRT into a
clinical trial, institutions are required to go through a credentialing process that demonstrates that they meet the
requirements of the study group. The RPC currently partic-
Volume 63, Number 2, 2005
ipates in the credentialing of institutions wishing to enter
patients into clinical trials involving IMRT. The RPC provides anthropomorphic dosimetry QA phantoms to verify an
institution’s ability to deliver IMRT treatments appropriately. This report describes the development and initial
evaluation of an anthropomorphic phantom for credentialing purposes for RTOG IMRT protocols.
METHODS AND MATERIALS
Phantom design
The IMRT head-and-neck phantom was designed to meet certain design criteria, including having an anthropomorphic outer
plastic shell so that it tests realistic anatomic clinical situations,
being lightweight so that it is inexpensive to mail, using water as
a substitute for tissue where possible, and containing a target that
includes radiation dosimeters and that can be imaged with computed tomography (CT). The outer plastic shell of the head was
purchased (The Phantom Laboratory, Salem, NY) and modified in
the M. D. Anderson Cancer Center Department of Radiation
Physics machine shop to hold the imaging/dosimetry insert in a
watertight environment. All air spaces surrounding the imaging/
dosimetry insert could be filled with water, and all modifications
used plastic so that no metal parts would interfere with the imaging
of the phantom. The exterior plastic shell was of sufficiently
realistic anthropomorphic shape that the head phantom would fit in
most treatment immobilization devices used for IMRT treatments.
Figure 1 shows the hollow phantom head with the insert in
place. The crown of the head is removable so that the insert can be
placed into its watertight housing. The base contains a port that
allows the shell to be filled with water and is fitted with adjustable
screws so that the head can be placed on the type of headrest
commonly used by the institution.
The insert was constructed as a block of polystyrene housing
solid water targets and an acrylic organ at risk (OAR). The
planning targets were designed in collaboration with the RTOG
Medical Physics Committee to mimic an RTOG oropharyngeal
protocol (H-0022) that would have primary and secondary targets
with an OAR adjacent to the primary target. The solid water used
for the targets and acrylic used for the OAR were of slightly
Fig. 1. The intenstity-modulated radiation therapy head-and-neck
phantom, with insert in place.
Anthropomorphic QA phantom for IMRT
● A. MOLINEU et al.
579
Phantom dosimeters
Fig. 2. The dosimetry/imaging insert. The primary planning target
volume (PTV), secondary PTV, organ at risk (OAR), and holes for
the thermoluminescent dosimeter (TLD) capsules can be seen. The
axial film is placed in the cross-section shown, and the sagittal film
pieces are placed in the slits though the primary PTV.
different densities than the surrounding water and plastics for
imaging and target identification purposes. However, the differences in density and atomic number were small enough to have an
insignificant effect on treatment delivery. The insert was designed
to hold TLDs in the two planning target volumes (PTVs) and the
OAR. Radiochromic films (RCFs) were placed in the axial and
sagittal planes through the primary target and in the axial plane
through the secondary target and OAR.
Figure 2 shows the 7.5 cm ⫻ 10.5 cm ⫻ 13 cm polystyrene
insert. The primary and secondary PTVs are made of solid water
and are 5 cm long. The primary PTV is 4 cm in diameter and holds
two TLDs. One TLD is located superior to and the other inferior
to the axial film. The secondary PTV is 2 cm in diameter and has
one TLD in its center, directly inferior to the axial film. The
centers of the two PTVs are 5.2 cm apart. The OAR is made of
acrylic, is 1 cm in diameter, and extends the length of the insert. It
has one TLD in the center of its cross section, located directly
inferior to the axial film. The edge of the OAR is 0.8 cm from the
edge of the primary PTV in the posterior direction.
The locations of the RCFs can also be seen in Fig. 2. A single
sheet is placed in the axial plane. The slits through the primary
PTV and OAR indicate the placement of the two sagittal films
inferior and superior to the axial film. Figure 3 is an axial CT slice
of the phantom. Both PTVs, the OAR, and a film slit are visible.
Because the dosimeters would be irradiated during both the
imaging and the treatment delivery, TLDs were located on the
exterior of the phantom at the location of the ears during the
imaging irradiation. These TLDs were used to subtract the dose
given to the dosimeters in the phantom as a result of the
imaging process from the dose given during treatment. The
imaging dose was typically on the order of 1% of the dose given
to the PTV.
TLD-100 powder, placed in custom-built, reusable capsules, is
used as the absolute dosimeter. The capsules are small cylinders
with outer dimensions of 5 mm (height) ⫻ 5 mm (diameter), with
a 1-mm wall thickness. Each capsule holds approximately 40 mg
of powder that yields two readings. The capsules are constructed of
high-impact polystyrene that contains very little air and approximate a small sphere.
The capsules are irradiated by the remote institution and are read
at the RPC with the same technique as is used in the TLD mail-out
dosimetry program. The TLD-100 powder is taken from the TLD
powder stock used by the RPC for its mail-out dosimetry service
(5). Each batch of TLD-100 powder used in the mail-out system is
evaluated by the RPC for dose response, energy dependence, dose
uniformity, and fading. It has been shown that the accuracy of
absolute dose determined in the TLD readout system is equivalent
to ion chambers to within ⫾4% at a 90% confidence interval (6).
The TLD system is also precise to within ⫾3% and is capable of
detecting dose errors on the order of ⫾5% or greater (5). Thermoluminescent dosimeter dose readings are used to evaluate the
absolute dose delivered to the phantom, and the two capsules on
either side of the target center are used to normalize the film dose
distributions. The exceptions to the published TLD reading procedure are that a filter is used to damp the thermoluminescent
signal, and high-dose TLD standards are used because of the high
doses delivered to the phantom. Supralinearity of the thermoluminescent signal is accounted for in the dose calculations.
Radiochromic films (GAFChromic MD-55-2 film; Nuclear Associates, Carle Place, NY) were used to measure dose distributions
and field localization. Radiochromic film is approximately tissue
equivalent and has no significant angular dependence (7). It is
relatively insensitive to room light and thus easy to work with in
the mail-out program. Radiochromic film was investigated for dose
response, fading, energy independence, and uniformity and was
Fig. 3. Computed tomographic slice of phantom.
580
I. J. Radiation Oncology
● Biology ● Physics
Table 1. Reproducibility results for the TLD doses averaged
for three irradiations
TLD
Average (cGy) ⫾ SD
Primary PTV (superior)
Primary PTV (inferior)
Secondary PTV
Organ at risk
714 ⫾ 8.1
804 ⫾ 10.8
663 ⫾ 6.7
178 ⫾ 2.8
Abbreviations: TLD ⫽ thermoluminescent dosimeter; SD ⫽
standard deviation.
Volume 63, Number 2, 2005
the normal tissue could not receive more than 110% of the primary
PTV prescription dose. The phantom was placed on the treatment
couch and positioned with lasers and phantom fiducials. The dose
was delivered with a nine-field step-and-shoot arrangement with
the 6-MV X-ray beam of a Varian Clinac 2100CD (Varian Medical Systems, Palo Alto, CA). Once each treatment was delivered,
the dosimeters were removed, and new ones were placed in the
phantom without disturbing the phantom position on the treatment
couch. The phantom was then re-irradiated. A total of three phantom irradiations were delivered.
Data comparison
found to have high spatial resolution and low spectral sensitivity,
making it well suited to measuring IMRT-produced high dosegradient radiation fields (8, 9).
Two sheets of RCF were placed in the insert in the axial and
sagittal planes. The sagittal film was cut into two pieces, allowing
the axial film to intersect it at the center of the primary target.
Small holes were drilled in the dosimetry insert to allow two
localization marks to be made on each piece of film. These marks
uniquely specify the location and orientation of the films with
respect to the targets.
The recommendations for the handling and evaluation of RCF
for use in dosimetry were followed (7). Films were scanned with
a 633-nm laser densitometer (Personal Densitometer; Molecular
Dynamics, Sunnyvale, CA) with a scanning resolution of 0.1 mm.
Films irradiated in the phantom were scanned on a ground glass
scanning bed to eliminate interference-pattern artifacts found with
use of the standard polished glass scanning bed. A mask was
created for the scanning bed to exclude light contamination. This
film-scanning system is based on the technique used by Dempsey
et al. (10). Films were scanned at least 36 hours after irradiation to
avoid documented reverse-fading effects (7). All films from the
same lot were stored together so that they had the same temperature, light, and non–treatment-related radiation exposure history. A
dose–response curve from 0 Gy to 30 Gy was measured for each
lot of film used in this analysis. The dose–response curve was used
to correct for any nonlinearity in the dose response of the film. The
variations in film sensitivity were previously measured at the RPC
by irradiating multiple sheets of film from the same lot to determine reproducibility of the film response. A background film from
the same lot and order was included and scanned with all treatment
films. A 12-bit TIFF (tagged image file format) image file was
generated from the film scan in an array of optical density (OD)
values ranging from 0 to 4095. The background OD values were
subtracted from each irradiated film. The average background OD
was 0.24. Profiles through the center of the primary PTVs and
OARs were generated according to localization marks on each
film. These profiles were normalized to the TLD results. Pixel
averaging was used to smooth the profiles (11).
The phantom was mailed to 10 institutions wishing to participate in an RTOG IMRT protocol. Each institution was instructed
to image the phantom, design a treatment plan in accordance with
the prescription outlined above, and treat the phantom according to
the plan. Each institution irradiating the IMRT head-and-neck
phantom was instructed to provide dose calculations and dose
distribution information for comparison with the TLD and RCF
measurements. The institution was asked to outline the TLD powder and report the minimum, mean, and maximum dose to the TLD
capsule. The institution was also asked to provide dose distributions in the planes corresponding to the location of the films. The
treatment plan was compared with the measured dose profiles and
TLD results in the two planes of measurement.
Ratios of the RPC’s measured TLD dose to the institution’s
reported mean dose to the TLD powder were determined for the
TLDs in the primary and secondary PTVs. Film profiles through
the center of the primary PTV were scaled to the TLD dose values.
The subsequent film profile results were then plotted against the
dose profile data taken from the institution’s treatment-planning
computer-generated isodose lines. The distance between the measured dose gradient and the institution’s calculated dose gradient
was determined in the region between the OAR and the primary
PTV. It was measured at three levels (25%, 50%, and 75% of the
difference between the maximum and minimum measured doses in
the region between the OAR and the primary PTV) and averaged.
RESULTS
Phantom dosimetry reproducibility
To determine how well the TLD results could be
reproduced, a benchmark treatment plan for the phan-
Reproducibility studies
The phantom was imaged at M. D. Anderson Cancer Center in
an ACQSIM CT scanner (Philips Medical Systems, Cleveland,
OH), and a benchmark treatment plan was generated with the
Corvus planning system (NOMOS, Sewickley, PA). The dose
prescription, which was a factor of 10 lower than the RTOG
protocol, was 6.6 Gy to at least 95% of the primary PTV and 5.4
Gy to at least 95% of the secondary PTV. Only 1% or less of the
primary and secondary PTVs could receive less than 93% of the
prescription dose. The OAR was to receive less than 4.5 Gy, and
Fig. 4. A plot of a right–left profile comparing three irradiations of
the phantom done in the same evening with the predicted treatment
planning values (black circles). PTV ⫽ planning target volume.
Anthropomorphic QA phantom for IMRT
● A. MOLINEU et al.
581
Table 2. Ratio of the RPC TLD dose to the institution’s reported dose and dose profile displacement analysis for the 10 institutions
that irradiated the phantom
Institution
1
2
3
4
5
6
7
8
9
10
Average
% SD
Primary PTV
(superior)
Primary PTV
(inferior)
Secondary
PTV
Profile
displacement (mm)
Organ at risk
0.97
0.93
1.04
0.96
1.09
1.01
1.02
0.98
1.04
1.04
1.01
4.8
1.04
0.96
—
1.00
1.07
1.03
1.03
0.98
1.04
1.05
1.02
3.5
1.10
0.93
1.01
0.98
1.11
0.99
1.00
0.97
1.06
1.04
1.02
5.7
1.3
2.0
1.0
⬍0.1
3.3
3.7
2.3
⬍0.1
0.7
4.0
1.8
1.5
0.99
0.82
1.16
—
1.35
1.10
0.95
0.88
1.09
1.18
1.07
15.6
Abbreviations: RPC ⫽ Radiologic Physics Center; PTV ⫽ planning target volume. Other abbreviations as in Table 1.
tom was designed. The plan was delivered three times
in one evening. There was minimal disturbance to the
phantom setup between irradiations. The combined
TLD results from these irradiations are shown in Table 1.
The percent standard deviation was ⬍1.6% for each of
the four measurement points. A representative film pro-
Fig. 5. A plot of (a) a superior–inferior profile taken from a sagittal film; (b) a right–left profile taken from an axial film;
and (c) an anterior–posterior profile taken from an axial film. The black points are the institution data taken from the
treatment plan, and the gray line is the film data. The film data closely agree with the institution plan on all three profiles.
PTV ⫽ planning target volume.
582
I. J. Radiation Oncology
● Biology ● Physics
Volume 63, Number 2, 2005
Fig. 6. A plot of (a) a superior–inferior profile taken from a sagittal film; (b) a right–left profile taken from an axial film;
and (c) an anterior–posterior profile taken from an axial film. The black points are the institution data taken from the
treatment plan, and the gray line is the film data. The superior–inferior film data show that the phantom was shifted in
the inferior direction between planning and treatment. The anterior–posterior graph includes the regression lines used
to find displacement. The levels of measurement are marked with arrows. There is an average displacement of 2 mm
in the anterior–posterior direction. PTV ⫽ planning target volume.
file that compares the three irradiations is shown in Fig.
4.
To determine the reproducibility of our film-scanning
system, the films from one irradiation were scanned three
times. For each scan, profiles in the two planes were normalized to unity at the center of the primary PTV. The
profiles from the three scans were compared in a highgradient region at a level of 75%. The maximum uncertainty
in film reproducibility for the three scans was ⫾0.35 mm.
Phantom irradiation
Ten institutions irradiated a phantom as part of an initial
evaluation program. The TLD dose results from these irradiations are shown in Table 2. The results are presented as
the ratio of the RPC TLD reading to the average dose to
TLD as predicted by the institution. Table 2 also shows the
displacement results in the region between the OAR and the
primary PTV for the 10 institutions.
Two of the TLD results are missing because the primary
PTV inferior TLD for Institution 3 was lost, and Institution
4 was not able to give a mean dose to the OAR TLD
capsule. There was agreement between the doses measured
by TLD and those reported by the institutions in the PTVs,
with the largest standard deviation being 5.7% for the results in the secondary PTV. The dose agreement in the OAR
was not as close, with an average TLD/institution ratio of
1.07 and a standard deviation of 15.6%. The OAR TLD
results correlate fairly well with the profile displacement
results. The dose gradient in the region between the OAR
and the primary PTV is very steep, and any small displacement will result in a large difference in dose delivery to the
OAR. In all cases, the RPC TLD dose fell between the
minimum and maximum doses reported by each institution
for each measurement point.
Gross TLD differences in the PTVs and OARs can indicate errors in positioning the phantom before irradiation.
Anthropomorphic QA phantom for IMRT
The institutions were asked to treat the phantom as if it were
a real patient and to pay special attention to setup accuracy.
An error of more than 200% was seen in the OAR TLD for
one institution. Visual inspection of the RCF suggested that
the phantom had been shifted in the anterior direction relative to the plan, resulting in the large dose difference seen
with the TLD. This mistake was confirmed by the institution. Further analysis of errors in IMRT treatment-planning
systems that were confirmed by phantom irradiations was
done by Cadman et al. (12). Cadman et al. indicated in their
article that improper modeling of rounded multileaf collimator leaf ends might result in significant dose discrepancies.
The results in Table 2 were used to develop TLD and
profile displacement criteria in collaboration with RTOG.
Institution 5 was not included in the data analysis to develop
the acceptance criteria because it reported a point dose to
the TLD, not an average dose. Institution 5 was unable to
retrieve the necessary data owing to an upgrade in treatment-planning software at the institution between the time
of phantom irradiation and TLD evaluation. The evaluation
criteria were set at ⫾7% for the primary and secondary
PTVs. This value was 1.64 times the standard deviation,
excluding Institution 5. The profile displacement criterion
for the dose gradient between the OAR and the primary
PTV was set at ⫾4 mm, which is the range of average
displacements, once again excluding Institution 5. Film
profiles from the axial film were taken through the center of
the primary PTV in the anterior–posterior and right–left
directions. A profile in the superior–inferior direction was
taken from the sagittal film. The profiles were normalized to
the TLD results from the primary PTV. Criteria have not yet
● A. MOLINEU et al.
583
been determined for the right–left and superior–inferior
profiles, so these films were analyzed qualitatively.
Figure 5 shows three film profiles from an institution with
fairly good film-to-plan agreement. A significant dose gradient was observed in the OAR region. The size of the TLD
is large compared with the gradient. A small shift in position
can cause large differences in the dose in the OAR region.
The profile shown in Fig. 6 is an example of poor filmto-institution agreement. The film results show that the
phantom was shifted 8 mm in the inferior direction relative
to the treatment plan. The institution that delivered this
treatment has agreed to irradiate the phantom again.
DISCUSSION
A lightweight anthropomorphic phantom was developed
to test dose delivery for IMRT head-and-neck treatments.
Thermoluminescent dosimeters and RCF were used as dosimeters. Criteria for the phantom results were agreed upon
by the Advanced Technology Consortium and RTOG. The
TLDs in the primary and secondary PTVs have a 7%
acceptance criterion. Also, the agreement between film
measurements and the institution data in the dose gradient
region between the primary PTV and OAR must be at least
4 mm. The TLD can detect error on the order of ⫾5%.
Because the TLD is larger than dose gradients typically seen
in IMRT treatment plans, the size will be modified in the
future. Because of the high dose gradients, one-dimensional
film profiles do not give a complete dose analysis. A twodimensional comparison would provide a more comprehensive method of determining how the treatment delivered
corresponded with the treatment planned.
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