Heterogeneity phantoms for visualization of 3D dose distributionsby MRI-based polymer gel dosimetry
Yoichi Watanabea) and Rob MooijDepartment of Radiation Oncology, College of Physicians and Surgeons, Columbia University,622 West 168th Street, New York, New York 10032
G. Mark PereraDepartment of Medical Physics, Memorial Sloan Kettering Cancer Center, 1275 York Avenue, New York,New York 10021
Marek J. MaryanskiMGS Research, Inc., P.O. Box 581, Guilford, Connecticut 06437
~Received 6 June 2003; revised 28 November 2003; accepted for publication 30 January 2004;published 6 April 2004!
As radiation therapy technology is moving towards morecurate delivery of complex three-dimensional~3D! dose dis-tribution, there is an increasing demand of including thefects of heterogeneous material distribution in docalculations.1 To evaluate calculation methods we need aliable dose measurement tool. Gel dosimetry has advantover conventional dosimetry tools such as ionization chabers, solid-state dosimeters@TLD, diodes, and metal–oxide–semiconductor field effect transistor~MOSFET!# and radio-graphic films because the gel is soft-tissue equivalentworks as both tissue-equivalent medium and dose measuinstrument simultaneously.
Polymer gel dosimeters such as BANG® polymer gel~MGS Research, Inc., Guilford, CT! have been used fomany dosimetric studies and the usefulness of this typedosimeters for 3D dose measurements were demonstrate2–5
To the author’s knowledge five studies were reported totend the gel dosimetry to inhomogeneous media.6–10
The aim of this article is to study the feasibility of 3dose measurements using newly developed heteroge
975 Med. Phys. 31 „5…, May 2004 0094-2405Õ2004Õ31„5
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phantoms. The phantom was filled with BANG-3® polymergel. The phantom can be used to measure dose distribuaround air and bone inserts. We used an magnetic resonimaging ~MRI! scanner to estimate dose distributions ofirradiated phantom. The dose measurement accuracyMRI-based polymer gel dosimetry depends on the MR imaquality. MRI artifacts, in particular, susceptibility effectaround air-gap and bone, significantly influence the imaquality.11–14 Hence, first we studied the effects of MRI artfacts on measured dose distributions using three methcomparison of a measured dose distribution in a homoneous phantom with a reference dose distribution, compson of a sagittally scanned image with a sagittal imageconstructed from axially scanned data, and coregistrationMR and computed-tomography~CT! images. Next we measured dose distributions in phantoms with an air-gap abone-like material. The results of these experiments aresented in the result section.
Some recent studies deal with the image quality isswith MRI-based gel dosimetry.15–23The implication of thosefindings with the current study is presented in the discuss
976 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 976
section. Many publications exist for dose measurementinhomogeneous media. However, a few experimental reshave been published for experimental setups similar toexperiments.24–27 Our experimental results in inhomogeneous media will be compared with those published resin the discussion section. Conclusions are given in thesection.
II. MATERIALS AND METHODS
II.A. Polymer gel phantoms
When polymer gel is irradiated, polymerizatioprogresses, leading to absorbed dose-dependent strucvariation. This physical change can be detected by usinMRI scanner,28 an optical scanner,29 an ultrasound device,30
vibrational spectroscopy techniques,31,32 or an x-ray CTdevice.33 For this study we used MRI to measure spin–srelaxation time (T2). The spin–spin relaxation rate (R2),which is the inverse ofT2, is a function of absorbed dose.2,28
Therefore, MRI data can be converted to absorbed dosetributions with proper calibration.
A heterogeneity phantom containing BANG-3® polymergel was designed and manufactured. The phantom is a 1diameter and 15 cm long cylinder with two hexagonal eplates for stable horizontal positioning. It has a 6 cm diaeter and 6 cm deep cylindrical cavity on one of the flat enThis cavity can be filled with cylindrical inserts madesolid bone-like and water-equivalent materials to represtissue heterogeneity. Figure 1 is an illustration of the phtom. Note that the container has an opening of about 2diameter, through which the gel is poured into the containThe phantom container is made of oxygen-impermeaBarex® plastic ~BP, Naperville, IL!. The thickness of theBarex wall is about 0.7 mm.
BANG-3® polymer gel contained in a cylindrical vial waused to obtain a calibration relation between absorbed dand MR signal. The vial is 2.5 cm diameter and 9 cm lo
FIG. 1. Schematic diagram of the heterogeneity phantom. This drawinlustrates solid water-equivalent and bone-like inserts in the cavity. Tsetup was used only for the CT-MRI image fusion study for image distoranalysis. The locations of the planes used for the analysis are indicateddose measurements in inhomogeneous media, the top 3 cm portion ocavity was filled with a water-equivalent insert. The bottom 3 cm was filwith a water-equivalent insert or a bone-like insert. The space was left oto simulate an air cavity.
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and it is made of glass. The polymer gel for the calibratiwas taken from the same batch as that used to fill the hetgeneity phantom. All calibration vials were mounted inhomemade mounting block made of Styrofoam for Mscans.
Table I gives elemental compositions of BANG-3® poly-mer gel, water-equivalent, and bone-like materials as welwater and muscle data.34 Mass density, electron density, aneffective atomic number represent the radiological characistics of material. The BANG-3® polymer gel is composed owater, N,N8-methylen-bisacrylamide~bis!, methacrylic acid,and gelatin. BANG-type polymer gel is radiologicallequivalent to water.35 A ‘‘desensitizing’’’ compound is usedto change the gel sensitivity to absorbed dose. Hence,atomic composition of the polymer gel could be slightly dferent from the data shown in the table. The water-equivamaterial contains some heavier elements such as Mg andbut the overall characteristics including the electron denare similar to water. The bone-like material simulates humbones, in particular, the cortical bone.
II.B. Experimental procedures
A heterogeneity phantom was mounted in the LeksMicro-Stereotactic system for Gamma-Knife stereotacticdiosurgery. It was irradiated with a 6 MV photon beam of aVarian 600C accelerator. It was set at 95 cm SSD to thesurface of the phantom. The field size was set to310 cm2 at 100 cm from the target.
Eight calibration vials containing polymer gel were irrdiated with 6 MV photon beam to 30, 60, 80, 100, 130, 16200, and 250 cGy, when 200 cGy was delivered to isocenThe calibration doses were 2.5, 5, 10, 15, 20, and 25when 20 Gy was delivered to isocenter. Always one vial wleft unirradiated as a control.
The heterogeneity phantom was placed in the headand scanned with a 1.5 T SIGNA® MRI scanner~GE Medi-cal Systems, Waukesha, WI!. We used the Hahn spin-echsequence~SE! with two echoes. The two-point SE sequen
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TABLE I. Elemental composition of selected materials~% by weight!.
Material Water Muscle BANG® Bone-like Water-equivalent
977 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 977
is recommended by the MGS Research and is supportedpublication.36 Recently, multispin echo sequences haemerged as pulse sequences with more accurate and hsingal-to-noise ratio~SNR! than the two-point SE sequencfor gel dosimetry.15,16,23However, we did not use those advanced pulse sequences because those are more difficimplement than the two-point SE sequence on our MRI scner. The repetition time was set to 2 s. The echo times~TE!were 20 and 100 ms. The echo times were determinereceive sufficiently large signal for expected spin–spin relation time (T2) of longer than 40 ms~or R2,25 s21). Wedid not optimize the echo times although an optimizatleads to higher SNR.15,23The field of view~FOV! was 24 cmby 24 cm. Acquisition matrix was 256 by 256. Hence, tpixel size was 0.937 mm by 0.937 mm on the image plaThe number of acquisitions per scan~NEX! was varied from1 to 3. The receiver bandwidth was 32 kHz. The frequenencoding was made in the superior-to-inferior or the left-right direction. The slice thickness varied from 2 to 5 mwith no overlap between adjacent slices. We chose tworections for the slice select axis: the phantom cylinder axisthe transverse axis perpendicular to the cylinder axis. Inarticle, MR scans using the cylinder axis as the slice seaxis is called ‘‘axial’’ and the scans in the transverse dirtion is called ‘‘sagittal.’’ Calibration vials were MRI-scanneindependently from a heterogeneity phantom, but usingsame imaging parameters.
To study MRI artifacts we used a heterogeneity phantwith water-equivalent inserts~or ‘‘simulated homogeneouphantom’’!. The phantom was irradiated to 20 Gy at 5 cdepth. It was MR scanned in both axial and sagittal dirtions. We also used a heterogeneity phantom with an air-a water-equivalent insert, and a bone-like insert as illustrain Fig. 1. This phantom was scanned with both the Mscanner and a GE Advantage CT scanner. The imagingtrix size for the CT scan was 5123512 with FOV of 28328 cm2 and 3 mm slice thickness. The pixel size was 0.5mm by 0.547 mm. The CT image of the phantom was copared with aT2-weighted MR image of the same phantoSince CT is free of the geometrical distortion of MRI,serves as a reference image for the image artifact study
We studied the effects of air-gap and bone on dose dibutions. Air inhomogeneity was modeled by placing o3-cm-thick water-equivalent insert in the cavity of the herogeneity phantom and leaving a 3-cm-thick cavity. Forbone inhomogeneity experiment, the 3-cm-thick cavity wfilled with a bone-like material. To minimize MR image atifacts due to an air-gap and high-density material such asbone-like insert, the cavity of the heterogeneity phantom wfilled with water-equivalent inserts during MRI scans. Fthese experiments we used a more clinically relevant dos200 cGy at 5 cm depth, instead of 20 Gy given to the simlated homogeneous phantoms. Note that the differenc200 cGy and 20 Gy should not change our conclusions scorrect calibration data were used for both cases.
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II.C. Analysis procedures
MRI data were transferred to a workstation for analysIn-house software was used to calculate spin–spin relaxarates. The spin–spin relaxation time was calculated by fittthe MR signal at TE520 and 100 ms with an exponentiaequation of signal decay.37
Using the data from the calibration gel vials, calibratiorelations betweenR2 and the absorbed dose were deriveThese relations were used to generate absorbed dose dbutions, which are called ‘‘measured’’ dose distributionthis article.
We developed analysis programs using MATLAB® Ver-sion 6.5 Release 13~MathWorks, Inc., Natick, MA!. Theprograms were used to convertR2 to absorbed dose usincalibration relations and to display dose distributions froboth measurements and the CadPlan treatment planningware ~Varian Medical Systems, Palo Alto, CA!.
As mentioned before, MR image artifacts were analyzby three methods. For the first method we compared msured dose distributions on a sagittal plane of a simulahomogeneous phantom with ‘‘reference’’ dose distributiofrom CadPlan. We used a 2.5 mm grid size in an 1123160dose matrix for CadPlan dose calculation. For the secmethod the measured dose distribution in the simulatedmogeneous phantom from a sagittal scan was compareda dose distribution reconstructed using axially scanned dFor the third method we used MR and CT images of a herogeneity phantom with an air-gap, a water-equivalentsert, and a bone-like insert. See Fig. 1 for the arrangemThe image fusion module of the Leksell GammaPlan® treat-ment planning software~Elekta AB, Stockholm Sweden! wasused to coregister the MR and CT images. The registrawas automatically done using the common fiducial markewhich are embedded in both MRI and CT localizatioframes. The accuracy of image registration is better thanpixel size, i.e., 0.94 mm. We measured displacement ofMR image relative to the CT image. Four transverse plashown in Fig. 1 were selected so that those planes pthrough the polymer gel~plane A!, the air-gap~plane B!, thebone-like insert~plane C!, and the water-equivalent inse~plane D!. The displacement was measured at four poi~Ant, Post, Left, and Right! on the outer surface of the phantom and the inner surface~or the outer surface of the cavity!of the phantom on each plane. Total number of measurempoints was 28. The current localization method as impmented in GammaPlan does not allow fusing sagittal acoronal images. Hence, the image distortion issue of satally scanned images was not studied using the MRI–image fusion method.
The SNR of MRI data affects not only the image qualbut also the uncertainty ofR2, consequently, the uncertaintof measured absorbed dose. For the currentR2 measuremenprotocol the ratio of the standard deviation ofR2, sR2
, to the
mean ofR2, ^R2&, can be estimated by using an analyticequation given as a function ofR2:
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978 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 978
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A similar equation was also given by De Deeneet al. inrelation to dose resolution.15,23 For current experiments,TE1
and TE2 are 20 and 100 ms, respectively. The ratior0 /srepresents SNR of the MR signal taken atTE1 andTE2 ~or ofthe base images!. Equation~1! can be used to obtain a neessary SNR value of MR signal to achieve a specific unctainty level of measuredR2. The SNR values were estimateby dividing the average signal intensity by the standardviation in the uniform region on aT2-weighted image takenat TE2 .37 The measurements were done for various combtions of slice thickness and NEX. The measured SNR valare compared with the required SNR to achieve a leveuncertainty in the measured dose.
SNR requirement ofR2 values can be determined frothe accuracy requirement of dose measurements. An AAtask group recommends that in 3D inhomogeneous mediacalculated doses should agree with true values withinalong the central axis and within 7% in other regions.38 Byapplying the dose resolution concept,19 we set the uncer-tainly level of dose measurements to 7% with a 52% codence level. The uncertainty of measured dose dependthe dose and the uncertainty of the calibration relation.3,39,40
When the calibration uncertainty is small, the uncertaintydose is close to the uncertainty ofR2. For simplicity we setthe required uncertainly level ofR2 to 5%.
To improve the image quality of inherently noisy Mimages, we tested several types of image filters, whichavailable on MATLAB®. We used a class of a linear filtetwo-dimensional finite impulse filter, FILTER2, with averaing and Gaussian low pass options. Also a medium filMEDFILT2, and an adaptive Wiener filter, WIENER2, wetested. All filters were applied to images consisting ofR2values. Mean and standard deviations of ten different lotions in a uniform dose region of the filtered image wecalculated. The size of neighbors used for filtering was 33 pixels.
III. RESULTS
III.A. Dose response calibration
Figure 2 shows the calibration data forR2 as a functionof absorbed dose obtained by calibration gel vials. Fig2~a! is for a simulated homogeneous phantom, to whichGy was given at the isocenter. The figure indicates thatR2 value varies from 7 to 14 s21 in the dose range betwee0 and 25 Gy. Figure 2~b! is for all other cases, to which 20cGy was given at the isocenter. This figure indicates thatR2 value ranges from 4 to 11 s21 for the dose range o0–250 cGy. The data points in Fig. 2~b! were fitted with bothlinear and quadratic equations by applying a least-squafitting method in the Regression Analysis Tool of Microso
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Excel ~Microsoft Corporation, Redmond, WA!. A quadraticequation fits the data points better as indicated by the colation determinationR2 closer to unity than that of a lineaequation. Hence, quadratic equations were used for conving R2 to absorbed dose for the data presented in this art
III.B. MRI artifacts
Measured dose distributions of a simulated homogenephantom should be the same as reference dose distribufrom CadPlan. Figure 3~a! shows line profiles of the measured dose and the reference dose on a transverse planpendicular to the central axis at depth of 5 cm. The doprofiles were plotted along the line passing through the ctral axis. The measured field width at the 80% dose levelmm wider than the CadPlan calculation. They agree eother in the 10% and 50% dose range. Figure 3~b! showsdepth-dose curves along the central axis. The MRI datathis figure were taken from a sagittal scan of the phantomboth figures there is no MR signal coming from the wat
FIG. 2. Absorbed dose vs spin–spin relaxation rate~R2!. The data wereobtained with calibration gel vials. For regression equations shown onfigures, the variabley is R2 and the variablex is absorbed dose.R2 is theR-squared value as defined in the regression analysis tool of MicroExcel® program.~a! Isocenter dose was 20 Gy.~b! Isocenter dose was 200cGy.
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979 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 979
equivalent material; consequently, the dose at those poinset to zero. The sharp edges indicate the interface betwthe water-equivalent insert and the polymer gel. The dincreases to the maximum value within two pixels~or 1.88mm! in the beam direction and within one pixel~or 0.94mm! in the transverse direction. However, the dose inbeam direction does not increase to the correct value fomm beyond the interface. Note that an averaging noise fiwas used to smooth out the measured dose profiles showFig. 3.
Figure 4 shows two-dimensional isodose distributionstained by both measurements and calculations. The distrtions are plotted on a sagittal plane. The beam entersphantom at the left. There is no measured data insidecavity, which was filled with water-equivalent inserts. Aaveraging filter was applied to the measured data.
The isodose distribution given in Fig. 4~a! was obtainedby scanning the phantom in the sagittal direction. The figshows that measured 20% and 50% isodose lines agreethe calculation except at the right edge of the plot. Measu80% and 90% isodose lines extend further towards the dostream direction~or in the right direction in the figure! be-yond the water-equivalent material. Furthermore, the msurement shows about 5%–10% lower dose than
FIG. 3. 1D dose profiles measured with BANG-3® polymer gel dosimeterand the reference profiles by CadPlan®. The cavity of the heterogeneityphantom was filled with water-equivalent material to model a homogenemedium. The averaging filter was applied to the measured dose data~a!Along the line perpendicular to the beam axis at a depth of 5 cm.~b! Alongthe beam axis.
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calculation in the region within 10 mm from the downstreaside of the cavity filled with water-equivalent material.
Figure 4~b! shows isodose distributions on a sagittal plafor both measurement and calculation. The measured ddistribution for this figure was obtained by reconstructing tsagittal image from axially scanned data. Measured 2050%, and 80% isodose lines are in good agreement withcalculation. At the right edge of the phantom the 20% a50% isodose lines show erroneous falloff of absorbed do
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FIG. 4. 2D dose distributions measured with BANG-3® polymer gel dosim-eter ~solid lines! and the reference distributions by CadPlan~dashed lines!.The distributions are plotted on a sagittal plane along the central axis obeam. The cavity of the heterogeneity phantom was filled with waequivalent material to model a homogeneous medium.~a! The measureddose map was obtained from a sagittal MRI scan.~b! The measured dosemap was reconstructed from axially scanned MRI data.
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980 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 980
The isodose lines at the right side of the water-equivainsert indicate a slow increase of the dose instead ofexpected rapid rise at the interface. This is mainly causedthe 3 mm transverse slice thickness~or the partial volumeeffect!. The 90% isodose line of the measured distributdoes not close in the downstream side of the waequivalent insert and indicates artifacts.
Figures 4~a! and 4~b! show that the 100% isodose lines dnot touch the sidewall of the cavity, where the watequivalent material is inserted. This indicates the effectsthe insert material on the measured dose.
Table II gives the displacement of MR images relativeCT images obtained by the MRI–CT image fusion methThe data indicate less than 2 mm positional differences aspecific points in the phantom. Most points showed a dcrepancy smaller than 1 mm. Considering the precisionthese measurements, about 1 mm, we do not observe sigcant differences in the displacement at interfaces ofpolymer gel ~plane B!, bone-polymer gel~plane C!, andwater-polymer gel~plane D!. Hence, the spatial distortioeffects of the transverse MR image on the measured ddistribution are not important for the current study.
FIG. 5. Percentage standard deviation ofR2 vs R2 for various SNR valuesof T2-weighted image.
TABLE II. Measured spatial shift of MR image relative to CT image. Eigpoints on transverse planes A, B, C, and D illustrated in Fig. 1 are localon the images. The measurement tool on the GammaPlan® treatment plan-ning software was used to measure the distance between correspopoints on CT and MRI images. Negative numbers imply that the MR imis shifted to left or to anterior relative to CT image. Unit is millimeters.
Plane A B C D
Outer Ant ,1.0 ,1.0 ,1.0 ,1.0Post 1.0 21.4 21.0 22.0
Right 21.2 1.2 21.2 21.5Left ,1.0 ,1.0 ,1.0 ,1.0
Inner Ant NA 21.5 ,1.0 ,1.0Post NA 21.0 ,1.0 1.0
Right NA ,1.0 20.5 21.0Left NA 21.0 21.7 21.0
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III.C. Image quality
We measured the SNR ofT2-weighted images for varioucombinations of the slice thickness (Dz) and NEX. The mea-sured SNR values were about 30, 50, and 70(Dz, NEX)5(2 mm, 2), ~3 mm, 2!, and~5 mm, 3!, respec-tively. Figure 5 presents a theoretical result for the perceage ratio of the standard deviation ofR2 to the mean ofR2as a function ofR2 for SNR530, 50, 70, and 120. The figurindicates that the percentage ratio is a strong function ofR2for a fixed SNR. It shows that a SNR higher than 120needed to achieve smaller than 5% uncertainty in theR2range of our interest, i.e.,R255 – 25 s21. Therefore, a fur-ther increase of SNR is required for a more precise dmeasurement with MRI-based gel dosimetry.
To further improve image quality, we tested noise filteTable III shows the standard deviation ofR2 values for sev-eral noise filters. The ‘‘averaging’’ filter reduces the noilevel ~or the standard deviation! the most. Also we examinedif an independent application of a noise filter to the dataTE520 ms and TE5100 ms before calculatingR2 reducesthe noise level. We did not observe any significant improment in noise reduction. Hence, for the best filtering wecided to apply the averaging filter toR2 ~or dose! data when-ever necessary.
III.D. Dose distributions around heterogeneities
Figure 6 shows measured dose distribution in a heteroneity phantom, for which 6 cm diameter and 3-cm-thick clindrical air-gap was created beyond the 3-cm-thick watequivalent material. Figure 6~a! shows that the dose in thdownstream direction beyond the air-gap increases becof decreased photon attenuation in air. The line dose proat 10 mm from the air-polymer gel interface~or z5210 mm) given in Fig. 6~b! shows that the dose beyond thair-gap is 11% larger than the dose in the region not beythe air-gap. There is no observable buildup region atinterface of air-gap and the polymer gel.
Figure 7 shows measured dose distribution in a heteroneity phantom, for which the air-gap in Fig. 6 was replacwith a bone-like insert. Figure 7~a! shows that the dose in thdownstream direction beyond the bone decreases due tohanced photon attenuation in the bone region. Figure 7~b!shows a line dose profile along a line perpendicular tocentral axis atz540 mm. In the figure, one can see a 10decrease in dose behind the bone region compared to
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TABLE III. The effects of image filters on noise level. Means and standdeviations ofR2 values are calculated by digitizing ten points in a unifordose region.
981 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 981
dose in the region not behind the bone. Figure 7~a! alsoshows a dose buildup region~i.e., a dose increase from 50%to 80% in 5 mm! near the bone-polymer gel interface in thdownstream direction.
IV. DISCUSSIONA comparison of measured dose distributions with cal
lated dose distributions on a sagittal plane in the simula
FIG. 6. 1D and 2D dose distributions measured with BANG-3® polymer geldosimeter. The cavity of the heterogeneity phantom was filled with one 3thick water-equivalent insert and an open space was left to model a 6 cmdiameter and 3 cm thick cylindrical air gap in water.~a! 2D dose distributionon a sagittal plane.~b! 1D dose profile along a line perpendicular to thz-axis atz5210 mm in ~a!.
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homogeneous phantom shows the artifacts on the measdose map. The rapid dose falloff in the right edge of tphantom seen in both Figs. 4~a! and 4~b! indicates the effectsof oxygen,36,41–43which will be discussed later in this section, and the effects of theB1-field inhomogeneity near theedges of the head coil.3,18,21,22The erroneous dose buildup ithe downstream side of the water-equivalent material seethose figures stems from the susceptibility effects in M
m
FIG. 7. 1D and 2D dose distributions measured with BANG-3® polymer geldosimeter. The cavity of the heterogeneity phantom was filled with a waequivalent insert and a bone-like insert model bone heterogeneity in w~a! 2D dose distribution on a sagittal plane.~b! 1D dose profile along a lineperpendicular to thez-axis atz540 mm in ~a!.
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982 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 982
images. There was a shallow air-gap~about 2 mm thick!between the water-equivalent block and the phantom cawall during the simulated homogeneous phantom expments. The left-right direction was the frequency encoddirection for Fig. 4~a! and the slice-select direction for Fig4~b!. It is well known that the geometry and the signal intesity near the interface between water and air in a cylindrcavity are distorted in the frequency encoding direction athe slice-select direction.12 To minimize the susceptibility ef-fects due to a narrow air-gap, a special attention was pairemove the gap between the heterogeneity insert and theity wall for later experiments. This enabled us to obtain msured dose distributions, especially, of the air-heterogencase as shown in Fig. 6~a!, free of the incorrect dose buildup
We showed that the SNR of the base images withcurrent MRI protocol was at most 70 and it must be 120higher to achieve 5% uncertainty level with theR2 value.The requirement of the 5% uncertainty was determinedachieve 7% uncertainty of measured dose. This requiremis reasonable as long as the uncertainty with the calibrarelation is small. However, the coefficients in a fitting eqution of the calibration data very often suffer from 1%higher uncertainty. For example the calibration data psented in Figs. 2~a! and 2~b! show the scattering of datpoints such that no single equation fits all data points pfectly. Furthermore, the uncertainty of estimated dosemore pronounced for smallerR2 values.15,23,40 Hence, theuncertainty level of theR2 value required to yield the specific dose uncertainty is smaller than 5%. Consequentlyrequired SNR value is even larger than 120.
For this study we used a two-point method, for which tMR signal is sampled at two echo times. We increased Sof the base images by using NEX as large as 3, increathe slice thickness, and decreasing the number of slicetaking sagittal scans. However, these methods arestrained by necessary spatial resolution and available sning time. Decreasing the bandwidth can also increaseSNR at the cost of more pronounced susceptibility effect37
Optimization of the echo spacing and the acquisition fractcan increase the SNR.15,23 For example, the SNR of measured dose is the largest for theR2 range of 7 – 13 s21 whenone usesTE1520 ms andTE25140 ms, and the acquisitiofraction of 0.226~or taking three times more data acquisitioat TE2 than atTE1). Further increase of the SNR is achievby taking the spin–spin relaxation decay data at more ttwo points at the cost of increased scan time. Optimizingecho spacing or the number of echoes increases thefurther. More advanced multispin echo sequences sucCPMG and the turbo spin echo sequence44 allow us to takethe decay signal at more than two echo times withoutcreasing the scan time. However, those image sequenceaccompanied with some technical drawbacks such as anhomogeneousB1-field due to stimulated echoes and the teperature rise of gel due to radio-frequency~RF! heating.23
Therefore, applications of these advanced pulse sequencdose measurements in heterogeneous media must befully evaluated by simultaneously considering SNR and iage artifacts. Such a study will be undertaken in the futu
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In addition to the MR image artifacts and low SNR theare other factors affecting the image quality and the accurof measured dose. Here we discuss the effects of oxyOxygen inhibits the polymerization; hence, the region whigh oxygen concentration may show erroneously low doAir can flow into the phantom inlet cavity through a smagap of the vessel cap. Then the oxygen molecules in thediffuse into the polymer gel. This explains the low measurdose in the right-edge of the phantom as seen in Figs.~a!and 4~b!. Also the container wall contains oxygen, whiceventually diffuse into the gel. Maryanskiet al.36 found adeterioration of dose distribution in the vicinity of a container wall and the authors concluded that it is causedoxygen that permeated through the container wall. TBarex® plastic, which we used as the container materialthe phantom, is known to have very small permeabilityoxygen molecules. The data show that the gas permeabof oxygen through Barex® ~See BP website at www.barex.com! is 0.3– 0.6 cm3 mm/m2/day/bar at 23 °C. It was shownthat the oxygen concentration should be less than 0.1 mggel in order to minimize the effect of the polymerizatioinhibition by oxygen.42 Using the model presented by Qadet al.,45 we estimated the time required to reach the oxygconcentration of 0.1 mg/l to be about 4 days. Therefore,oxygen effect does not have a significant impact on theresponse to the absorbed dose near the container surfalong as the experiment is done within about 4 days afterphantom was filled with polymer gel. This rough estimatiis further supported by the facts that Fig. 6~a! shows no dosebuildup region in the downstream side of the air-gap and100% isodose lines touching the cavity wall. These indicno oxygen effects near the vessel wall. Meanwhile, Fig. 3~a!as well as the 100% isodose lines in Figs. 4~a! and 4~b!shows the dose falloff near the cavity wall. Therefore, toxygen effects can alter the measured dose near vesseland need a special attention for heterogeneity experimen
Shahineet al.26 observed a dose increase of 10% relatto a homogeneous medium beyond a 53533 cm3 air-gapfor a 10310 cm2 field size and 6 MV photon beam. Theobserved a dose buildup only when the width of the air-gis equal or larger than the field size. Their results are content with our results given in Figs. 6~a! and 6~b!.
Wanget al.25 give Monte Carlo simulation results for thdose distribution beyond a finite size aluminum block3533 cm3) for a 10310 cm2 field size and a Co-60 beamTheir results show an approximately 10% dose differenalong the lateral direction perpendicular to the beam axiscm beyond the backface of the heterogeneity region. Tfollow-up article by the same authors gives both measument and Monte Carlo calculation results for a dose disbution around a finite size bone (333310 cm3) for a 10310 cm2 field size and 6 MV photon beam. The line profialong the central axis given in the article indicates a buildbeyond the bone region. Their results agree with our obvations, for which we saw a 10% decrease in dose beyonbone-like material and a dose buildup. Hepworthet al.6 alsoobserved the buildup behind a bony-structure by using adosimeter.
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983 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 983
V. CONCLUSIONS
We have studied the feasibility of measuring 3D dosimric structures around heterogeneity using a polymerphantom and MRI. We have shown the effects of MR imaartifacts caused by inserting a foreign material in a phanfilled with BANG-3® polymer gel. We found that the geometrical distortion of MR image is less than 2 mm. Withomuch attention on unintentional small air-gaps and oxygcontamination of the polymer gel, measured absorbed dcan be in error by as large as 10% near the interface ofheterogeneity and the polymer gel. Despite these limitatioour experiments have qualitatively demonstrated the effof an air-gap and a bone on the dose distributions. Thesults were consistent with published results. Furtherhancement of the SNR and better quantification of MR afacts will help to reduce the uncertainty of measured ddistributions. Once such improvement is accomplished,phantom can be used to systematically study 3D dosimestructures around heterogeneity by varying beam type~pho-tons or electrons!, beam energy, field size, and the size amaterial of heterogeneity.
ACKNOWLEDGMENTS
The authors would like to thank Dr. Yuan-Guang Xu fkindly reviewing the original manuscript and anonymous rerees for their expert comments on the manuscript. Thissearch was supported by the RSNA Research and EducFoundation Seed Grant Program~November 2000–Octobe2002!.
a!Electronic mail: [email protected] Treatment Planning Collaborative Working Group, ‘‘Role ofhomogeneity corrections in three-dimensional photon treatment pning,’’ Int. J. Radiat. Oncol., Biol., Phys.21, 59–69~1991!.
2M. J. Maryanski, G. S. Ibbott, P. Eastman, R. J. Schulz, and J. C. G‘‘Radiation therapy dosimetry using magnetic resonance imaging of pmer gels,’’ Med. Phys.23, 699–705~1996!.
3M. Oldham, I. Baustert, C. Lord, T. A. Smith, M. McJury, A. P. Warington, M. O. Leach, and S. Webb, ‘‘An investigation into the dosimeof a nine-field tomotherapy irradiation using BANG-gel dosimetryPhys. Med. Biol.43, 1113–1132~1998!.
4D. A. Low, J. F. Dempsey, R. Venkatesan, S. Mutic, J. Markman, E. MHaacke, and J. A. Purdy, ‘‘Evaluation of polymer gels and MRI as a 3dosimeter for intensity-modulated radiation therapy,’’ Med. Phys.26,1542–1551~1999!.
5Y. De Deene, C. De Wagter, B. Van Duyse, S. Derycke, B. MerssemW. De Gersem, T. Voet, E. Achten, and W. De Neve, ‘‘ValidationMR-based polymer gel dosimetry as a preclinical three-dimensional vfication tool in conformal radiotherapy,’’ Magn. Reson. Med.43, 116–125 ~2000!.
6S. J. Hepworth, M. McJury, M. Oldham, M. J. Morton, and S. J. Dor‘‘Dose mapping of inhomogeneities positioned in radiosentive polymgels,’’ Nucl. Instrum. Methods Phys. Res. A422, 756–760~1999!.
7S. Olberg, A. Skretting, O. Bruland, and D. R. Olsen, ‘‘Dose distributimeasurements by MRI of a phantom containing lung tissue equivacompartments made of ferrous sulphate gel,’’ Phys. Med. Biol.45, 2761–2770 ~2000!.
8P. A. Love, D. G. Lewis, and C. W. Smith, ‘‘Analyzing dose distributionfrom a treatment planning system, Monte Carlo simulations and polygel measurements,’’ inThe Proceedings of the XIIth International Conference on the Use of Computers in Radiation Therapy (ICCR), edited byW. Schlegel and T. Bortfield~Springer, Heidelberg, 2000!, pp. 386–388.
9F. Gum, J. Scherer, L. Bonger, M. Solleder, B. Rhein, and M. Bo‘‘Preliminary study on the use of an inhomogeneous anthropomorp
Medical Physics, Vol. 31, No. 5, May 2004
-elem
tnsehes,tse--
i-eeic
d
-e-ion
n-
e,-
k
n,
i-
,r
nt
r
,ic
Fricke gel phantom and 3D magnetic resonance dosimetry for verificaof IMRT treatment plans,’’ Phys. Med. Biol.47, N67–N77~2002!.
10K. Vergote, Y. De Deene, F. Claus, W. De Gersem, B. Van Duyse,Paelinck, E. Achten, W. De Neve, and C. De Wagter, ‘‘Applicationmonomer/polymer gel dosimetry to study the effects of tissue inhomoneities on intensity-modulated radiation therapy~IMRT! dose distribu-tions,’’ Radiotherapy and Oncology67, 119–128~2003!.
11K. M. Ludeke, P. Roschmann, and R. Tischler, ‘‘Susceptibility artefactsNMR imaging,’’ Magn. Reson. Imaging3, 329–343~1985!.
12M. C. Oehler, P. Schmalbrock, D. Chakeres, and S. Kurucay, ‘‘Magnsusceptibility artifacts on high-resolution MR of the temporal boneAJNR Am. J. Neuroradiol.16, 1135–1143~1995!.
13H. Jara, J. A. Soto, B. Yu, P. C. Hentzen, G. H. van Yperen, and EYucel, ‘‘Multisection T1-weighted hybrid-RARE: A pulse sequence fMR imaging of the entire liver during suspended respiration,’’ MagReson. Med.36, 767–774~1996!.
14J. F. Schenck, ‘‘The role of magnetic susceptibility in magnetic resonaimaging: MRI magnetic compatibility of the first and second kindsMed. Phys.23, 815–850~1996!.
15Y. De Deene, R. Van de Walle, E. Achten, and C. Dewagter, ‘‘Mathemcal analysis and experimental investigation of noise in quantitative mnetic resonance imaging applied in polymer gel dosimetry,’’ Signal Pcess.70, 85–101~1998!.
16I. C. Baustert, M. Oldham, T. A. Smith, C. Hayes, S. Webb, and M.Leach, ‘‘Optimized MR imaging for polyacrylamide gel dosimetryPhys. Med. Biol.45, 847–858~2000!.
17Y. De Deene, C. De Wagter, W. De Neve, and E. Achten, ‘‘Artefactsmulti-echo T2 imaging for high-precision gel dosimetry: I. Analysis acompensation of eddy currents,’’ Phys. Med. Biol.45, 1807–1823~2000!.
18Y. De Deene, C. De Wagter, W. De Neve, and E. Achten, ‘‘Artefactsmulti-echo T2 imaging for high-precision gel dosimetry: II. AnalysisB1-field inhomogeneity,’’ Phys. Med. Biol.45, 1825–1839~2000!.
19C. Baldock, M. Lepage, S. A. Back, P. J. Murry, P. M. Jayasekera,Porter, and T. Kron, ‘‘Dose resolution in radiotherapy polymer gel dosetry: Effect of echo spacing in MRI pulse sequence,’’ Phys. Med. B46, 449–460~2001!.
20Y. De Deene and C. De Wagter, ‘‘Artefacts in multi-echo T2 imaging fhigh-precision gel dosimetry: III. Effects of temperature drift during scaning,’’ Phys. Med. Biol.46, 2697–2711~2001!.
21Y. De Deene, ‘‘Fundamentals of MRI measurements in gel dosimetry,The Proceedings of DOSGEL 2001, 2nd International ConferenceRadiotherapy Gel Dosimetry, edited by C. Baldock and Y. De Deen~Queensland University of Technology, Brisbane, Australia, 2001!, pp.49–65.
22M. Lepage, P. S. Tofts, S. A. Back, P. M. Jayasekera, and C. Bald‘‘Simple methods for the correction of T2 maps of phantoms,’’ MagReson. Med.46, 1123–1129~2001!.
23Y. De Deene and C. Baldock, ‘‘Optimization of multiple spin-echo squences for 3D polymer gel dosimetry,’’ Phys. Med. Biol.47, 3117–3141~2002!.
24E. R. Epp, A. L. Boyer, and K. P. Doppke, ‘‘Underdosing of lesioresulting from lack of electronic equilibrium in upper respiratory air caties irradiated by 10 MV x-ray beams,’’ Int. J. Radiat. Oncol., Biol., Phy2, 613–619~1977!.
25L. Wang, C. S. Chui, and M. Lovelock, ‘‘A patient-specific Monte Cardose-calculation method for photon beams,’’ Med. Phys.25, 867–878~1998!.
26B. H. Shahine, M. S. A. L. Al-Ghazi, and E. El-Khatib, ‘‘Experimentaevaluation of interface doses in the presence of air cavities compwith treatment planning algorithms,’’ Med. Phys.26, 350–355~1999!.
27L. Wang, M. Lovelock, and C. S. Chui, ‘‘Experimental verification ofCT-based Monte Carlo dose-calculation method in heterogeneous ptoms,’’ Med. Phys.26, 2626–2634~1999!.
28M. J. Maryanski, J. C. Gore, R. P. Kennan, and R. J. Schulz, ‘‘NMrelaxation enhancement in gels polymerized and cross-linked by ioniradiation: a new approach to 3D dosimetry by MRI,’’ Magn. Reson. Iaging11, 253–258~1993!.
29M. J. Maryanski, Y. Z. Zastavker, and J. C. Gore, ‘‘Radiation dose dtributions in three dimensions from tomographic optical density scannof polymer gels: II. Optical properties of the BANG polymer gel,’’ PhyMed. Biol. 41, 2705–2717~1996!.
30M. L. Mather, A. K. Whittaker, and C. Baldock, ‘‘Ultrasound evaluatio
ddo
in
nim
dys
r-tio
Dos
si
anon
io-
h,
el
er-
ofte
kio,ari,ly-iol.
Gon.
l,’’
984 Watanabe et al. : Heterogeneity phantoms for visualization of 3D dose distributions 984
of polymer gel dosimeters,’’ Phys. Med. Biol.47, 1449–1458~2002!.31M. Lepage, A. K. Whittaker, L. Rintoul, and C. Baldock, ‘‘1HNMR an
FT-Raman study of the radiation-induced modifications in radiationsimetry polymer gels,’’ J. Appl. Polym. Sci.79, 1572–1581~2001!.
32L. Rintoul, M. Lepage, and C. Baldock, ‘‘Radiation dose distributionpolymer ges by Raman spectroscopy,’’ Appl. Spectrosc.57, 51–57~2003!.
33J. V. Trapp, S. A. Back, M. Lepage, G. Michael, and C. Baldock, ‘‘Aexperimental study of the dose response of polymer gel dosimetersaged with x-ray computed tomography,’’ Phys. Med. Biol.46, 2939–2951 ~2001!.
34ICRU, Photon, Electron, Proton and Neutron Interaction Data for BoTissues, ICRU Report 46~International Commission on Radiation Unitand Measurements, Bethesda, MD, 1992!.
35P. Keall and C. Baldock, ‘‘A theoretical study of the radiological propeties and water equivalence of Fricke and polymer gels used for radiadosimetry,’’ Australas. Phys. Eng. Sci. Med.22, 85–91~1999!.
36M. J. Maryanski, R. J. Schulz, G. S. Ibbott, J. C. Gatenby, J. Xie,Horton, and J. C. Gore, ‘‘Magnetic resonance imaging of radiation ddistributions using a polymer-gel dosimeter,’’ Phys. Med. Biol.39, 1437–1455 ~1994!.
37E. M. Haake, R. W. Brown, M. R. Thompson, and R. Venkatesan,Mag-netic Resonance Imaging: Physical Principles and Sequence De~Wiley, New York, 1999!.
38B. Fraass, K. Doppke, M. Hunt, G. Kutcher, G. Starkschall, R. Stern,J. Van Dyke, ‘‘American Association of Physicists in Medicine Radiati
Medical Physics, Vol. 31, No. 5, May 2004
-
-
n
.e
gn
d
Therapy Committee Task Group 53: Quality assurance for clinical radtherapy treatment planning,’’ Med. Phys.25, 1773–1829~1998!.
39M. Oldham, M. McJury, I. B. Baustert, S. Webb, and M. O. Leac‘‘Improving calibration accuracy in gel dosimetry,’’ Phys. Med. Biol.43,2709–2720~1998!.
40C. Baldock, P. Murry, and T. Kron, ‘‘Uncertainty analysis in polymer gdosimetry,’’ Phys. Med. Biol.44, N243–N246~1999!.
41S. J. Hepworth, M. O. Leach, and S. J. Doran, ‘‘Dynamics of polymization in polyacrylamide gel~PAG! dosimeters:~II ! modeling oxygendiffusion,’’ Phys. Med. Biol.44, 1875–1884~1999!.
42Y. De Deene, N. Reynaert, and C. De Wagter, ‘‘On the accuracymonomer/polymer gel dosimetry in the proximity of a high-dose-ra192Ir source,’’ Phys. Med. Biol.46, 2801–2825~2001!.
43J. Uusi-Simola, S. Savolainen, A. Kangasmaki, S. Heikkinen, J. PerU. Abo Ramadan, T. Seppala, J. Karila, T. Seren, P. Kotiluoto, P. Sorvand I. Auterinen, ‘‘Study of the relative dose-response of BANG-3 pomer gel dosimeters in epithermal neutron irradiation,’’ Phys. Med. B48, 2895–2906~2003!.
44A. Bankamp and L. R. Schad, ‘‘Comparison of TSE, TGSE, and CPMmeasurement techniques for MR polymer gel dosimetry,’’ Magn. ResImaging21, 929–939~2003!.
45S. S. Qadry, T. H. Roshdy, D. E. Knox, and E. M. Phillips, ‘‘Modedevelopment for O~2! and N~2! permeation rates through CZ-resin vialsInt. J. Pharm.188, 173–179~1999!.
