Journal of the Korean Physical Society, Vol. 62, No. 4, February 2013, pp. 657∼663

Quantitative Analysis of Dose Distribution to Determine Optimal Width ofRespiratory Gating Window Using Gafchromic EBT2 Film

Sung Hyun Lee, Kum Bae Kim, Mi-Sook Kim, Hyung-Jun Yoo, Seungwoo Park, Haijo Jung and Young Hoon Ji∗

Department of Radiological Cancer Medicine, University of Science & Technology, Daejeon 305-350, Korea andResearch Center for Radiotherapy, Korea Institute of Radiological & Medical Sciences, Seoul 139-706, Korea

Chul-Young Yi

Department of Ionizing Radiation Standards, Korea Research Institute of Standards and Science, Daejeon 305-340, Korea

(Received 28 September 2012, in final form 14 January 2013)

The purpose of this study was to determine the dependence of the dose distribution on the widthof the respiratory gating window by using radiochromic Gafchromic EBT2 film. An in-house three-dimensional breathing simulator was used with a 4-s cycle and a 3-cm movement. The gamma indexand the 50, 95, and 20 – 80% dose distributions were individually analyzed with regard to static, 100(full motion), 60, 40, 30, 20, and 15% respiratory gating windows. In addition, dose differences basedon the different extents of exposure were compared and analyzed along with total beam deliverytime. Dose distributions became increasingly similar to the static value with decreasing respiratorygating window width. The extent differences from the static case for the low-dose region were notsignificant; neither were the extent differences for the high-dose region and 30, 20, and 15% gatingwindows (P = 0.388, 0.275, respectively). However, the 40% gating window showed a significantdifference (P = 0.001). Moreover, the treatment time for the 30% gating window was reduced bymore than half compared to that for the 15% gating window. Thus, the 30% window would bea reasonable choice for maximizing the range of the gating window while markedly decreasing thedose difference and the treatment time.

PACS numbers: 87.53.Dq, 87.53.Xd, 87.66.CdKeywords: Radiation therapy, Respiratory gating window, Gafchromic EBT2 filmDOI: 10.3938/jkps.62.657

I. INTRODUCTION

The goal of radiation therapy is to deliver the maxi-mum dose to the tumor and a minimal dose to normaltissues. Various methods, such as three-dimensional con-formal radiotherapy (3DCRT), stereotactic radiotherapy(SRT), intensity-modulated radiotherapy (IMRT), andimage-guided radiotherapy (IGRT), have been widelyused, and four-dimensional radiotherapy (4DRT) is cur-rently gaining acceptance in the clinical field. The emer-gence of these methods was prompted by irregular inter-nal organ movement, which may be as large as 1 – 3 cmin the chest and abdomen, caused by patient breath-ing during radiation therapy [1–3]. More specifically, theliver has been shown to move 3 cm, and the pancreas andthe kidney have been observed to move more than 2 cm[4,5]. For the lungs, the lower lobe shows predominantmovement, and in deep breathing, the diaphragm has amaximum displacement of 9.5 cm [6,7].

These respiratory motions can cause significant er-

∗E-mail: jyh328@kirams.re.kr; Fax: +82-2-970-2412

rors in radiotherapy. Conventional computed tomogra-phy (CT), commonly used for treatment planning, showssevere motion artifacts derived from the interplay be-tween the advancing scan planes and the object’s motion.To explicitly include organ and target motion in treat-ment planning, as well as to reduce the margin of plan-ning target volume (PTV), a time-resolved CT image ac-quisition method is needed. Four-dimensional computedtomography (4DCT) is performed by oversampling CTdata at each slice. During several CT tube rotations, theprojection data are collected in the axial cine mode forthe duration of the patient’s respiratory cycle. After dataacquisition has been completed at one couch position,the X-rays are turned off, and the couch advances to be-gin data acquisition again until full coverage of the scanlength is achieved. All images obtained from 4DCT, eachrepresenting a different phase of the respiratory cycle,are sorted into series of 3D images and reconstructed toprovide separate and complete volumetric information[8–10]. In this manner, radiation therapy using 4DCTtakes into account respiratory motion during imaging,planning, and radiation delivery. Therefore, respiration-

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gated radiation therapy is able to ensure dose deliveryat specific cycles and amplitudes.

Static and respiration-gated radiation therapy havebeen reported to deliver doses showing differences as highas 20% of the PTV, prescribed in terms of 0.6 cm gatedout of 2.0 cm. In addition, the dose can vary by up to2.5% for non-gated plans and 1% for gated plans at thecenter of the target [11,12]. Another study has shownthat the gated profile closely matches the reference pro-file for window sizes of 0.5 mm and 1 mm while the in-tended profile is slightly altered for a 5-mm window [13].Considering this, setting the proper range for the respira-tory gating window is one of the most important factorsif radiotherapy is to deliver full coverage to the tumorand limit the dose to normal tissue as much as possible[14].

In the present study, using Gafchromic EBT2 film, weobtained 4DCT images for various phases by using anin-house 3D breathing simulator, and quantitatively ana-lyzed the differences in the dose distributions for a rangeof respiratory gating windows. We then examined theideal range of the respiratory gating window for maxi-mizing the gating efficiency.

II. MATERIALS AND METHODS

1. In-house 3D Breathing Simulator and HousePhantom

We developed a 3D breathing simulator comprisingthree integrated components: a body that contains themotor, a base that measures the breathing signal by us-ing a phantom in revolution per minute (rpm), and adigital pulse meter (Fig. 1). The body encases the en-tire system, internally protects the motor, and controlsthe up-and-down movement of the location of the motor.The base, made of Bakelite, continuously controls the fre-quency of sinusoidal motion between 10 – 30 rpm; this isdone by adjusting the pulse meter. The length, width,and height of the breathing simulator are 109, 22.5, and22 cm, respectively, and the amplitude of the motion isadjustable from 1.0 – 5.0 cm. These specifications aim tofollow the movement of the chest and the abdomen [15],the most predominant movements of internal organs. Aperformance evaluation test showed that the accuracy ofthe range and the cycle were 98.7% and 97.7%, respec-tively, that the observed positional reappearance error ofmovement was up to 1 mm, and that the time fluctuationwas 0.093 s in a cycle of 4 s.

The tunnel-shaped House phantom, 25 × 20 × 25 cm3,was a mixture of acryl and poly(methyl methacrylate).It enabled the integrative placement of the glass dosime-ter, the ionization chamber, and the optically stimulatedluminescence (OSL), as well as the alignment of the ra-diochromic film parallel to the beam, as shown in Fig. 1.

Fig. 1. (Color online) Experimental setups for (a) theHouse phantom (tunnel-shaped phantom) and for (b) the 3Dbreathing simulator with the House phantom loaded for filmexposure on the treatment couch. The second row shows thetreatment planning images obtained using the Eclipse treat-ment planning system: central slices of the (c) coronal andthe (d) sagittal views of the House phantom.

Fig. 2. Calibration curve of the Gafchromic EBT2 film forabsorbed doses ranging from 0 – 415 cGy. The goodness offit (R2) was 0.9987.

2. 4DCT Image Acquisition with RPM andClinical Treatment Plan

The 3D breathing simulator was driven with a 4-s,15-rpm cycle with a 3-cm anterior-posterior fan shapemovement and was scanned using a multislice CT scan-ner (Lightspeed RT 16, GE, Germany) [16]. The VarianReal-Time Position Management (RPM) system (Var-ian Medical Systems, Palo Alto, CA, USA) recorded thebreathing profile during with the 4DCT scan by using aninfrared (IR) camera and an external IR reflective markerplaced on top of the phantom to track the motion of thephantom. In this manner, 1520 CT images were acquired

Quantitative Analysis of Dose Distribution to Determine Optimal Width · · · – Sung Hyun Lee et al. -659-

with a slice interval of 2.5 mm and were later binned ret-rospectively according to spatiotemporal time signaturesand table positions by using Advantage 4D software (GEHealthcare, Waukesha, WI). Reconstructed images wereassigned to 1 of 10 specific respiratory phase bins, with a±5% spatiotemporal tolerance for sorting. Each bin wasreconstructed into a 3D data set representing spatiotem-porally similar images [17]. Thereafter, three directionalfields (0, 120, and 240◦) of the gated IMRT plan wereperformed using a treatment planning system (Eclipse,Varian, USA). The gross tumor volume (GTV) was de-lineated in the end-exhalation phase, where breathingmotion and motion artifacts were expected to be small-est [5]. The PTV was generated with a safety margin of5 mm [18], delivering 200 cGy to the 46.4-cm3 PTV and207.3 cGy to the isocenter. The Clinac iX system (Var-ian Medical Systems, Palo Alto, CA, USA) was usedat 6 MV and 600 MU/min, and the dose distributionsfor static (no motion), 100% (full motion), and variouswidth respiratory gating windows were analyzed. For thedelivery of the gated plan, the RPM software was usedto track the motion of the externally-mounted marker.This respiratory trace was matched with the trace ac-quired during the 4DCT scan and enabled the treatmentmachine to beam-on when the phantom entered into thegated phases.

3. Film Irradiation and Beam Delivery Time forVarious Setting Gating Windows

Radiochromic film (GAFCHROMICr EBT2, ISP,USA), 15 × 15 cm2, capable of measuring doses from1 – 1000 cGy, was used in this study. It was placed inthe House phantom parallel to the beam. Dose measure-ments were implemented 10 times each for static, 100(full motion), 60 (phases of 20 – 80%), 40 (phases of 30 –70%), 30 (phases of 40 – 70%), 20 (phases of 40 – 60%),and 15% (phases of 40 – 55%) respiratory gating win-dows [19]. The 50% phase was chosen as exhale becauseit is more reproducible than gating during the inhalestate [20]. The total treatment beam delivery time wasmeasured five times and averaged for each gating win-dow. Irradiated films were digitalized in the transmis-sion mode by using a flatbed scanner (Epson Expression10000XL, EPSON, Japan) at a resolution of 96 pixels perinch with no color correction and were saved as an RGBuncompressed Tagged Image File Format (tiff) [21].

4. Dose Analysis and Evaluation

Irradiated films were analyzed with the commercialfilm analysis software RIT113 (Radiological ImagingTechnology, Colorado Springs, CO, USA) to determinethe gamma index (γ), which is the magnitude of the min-imum vector difference between the reference dose distri-

bution and the measurement distribution. The compo-nents of γ are the dose and the distance, where distancecan be either a one- or two-dimensional component. Inorder to calculate γ, one calculates the magnitude of thevector from a reference point to every point in the mea-surement distribution and selects the minimum value.The value is then scaled by the dose and the distance cri-teria, such that if γ is greater than one, the measurementfails with respect to the reference distribution [22]. Theanalysis criteria for the γ map was set at a 3% relativedose difference (DD) and a 2 mm distance-to-agreement(DTA).

For the film calibration, a film with the same lot num-ber as the one previously irradiated was placed in awater-equivalent solid phantom (RW3, PTW, Germany)at a source-to-surface distance of 100 cm and a depth of5 cm and was exposed to 12 dose levels of 3 × 3 cm2.A calibration curve was obtained with the pixel valuesranging from 197 – 103.1, which correspond to dosesof 0 – 415.7 cGy. Thereafter, the pixel value was con-verted into the absorbed dose [23,24]. Each pixel wasanalyzed with MATLAB (version R2012a, Mathworks,Natick, MA, USA) to compare the line dose profiles forthe field-size region, high-dose region, and penumbra re-gion, which correspond to the lateral widths of the 50,95, and 20 – 80% isodose levels, respectively. In the caseof the penumbra region, we calculated the mean penum-bra, which means the right and the left penumbra wereaveraged. Also, the extents of the dose exposing morethan 95, 90, 80, 70, 60, 50, and 20 – 50% dose regionson the basis of irradiated dose to the target area wereanalyzed.

For each of the 10 measurements, the mean and stan-dard deviation were calculated for the gamma map re-sults, dose profile, and the extents of dose exposure. Inthe case of the standard deviation, a combined standarddeviation was calculated using the following formula:

dp =

√s2

x + s2y

2, (1)

where sp is the combined standard deviation, and sx andsy are the standard deviations being compared. For sta-tistical analysis, SPSS 17.0 (Chicago, IL) and MicrosoftExcel software (Redmond, WA) were used. A paired t-test was applied to determine the statistical differencesbetween gating cases. Differences were considered signif-icant for P < 0.05.

III. RESULTS

1. Gamma Index Comparison

Figure 3 shows irradiated dose distributions, as well asthe γ index, for respiratory gating windows of 100 (fullmotion), 60, 40, 30, 20, and 15% compared to the static

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Fig. 3. Dose distribution of the first set of measurementsfor the static case (first row) and for the 100 (full motion),60, 40, 30, 20, and 15% respiratory gating windows (fromthe left side of the second row) under a simulated respiratoryperiod of 4 s. The bottom row shows comparisons of thegamma map results for γ > 1 for 100 (full motion), 60, 40,30, 20, and 15% respiratory gating windows (from the leftside) compared to the static case (criteria: 3%/2 mm, red =passing failed area).

case. The numbers of pixels for which γ% was > 1 [25]were 73.3 ± 5.5, 58.7 ± 7.0, 28.7 ± 6.5, 22.1 ± 5.4, 15.1± 3.7, and 8.3 ± 4.5%, for 100 (full motion), 60, 40, 30,20, and 15% respiratory gating windows, respectively,compared to the static value. A shorter gating windowshowed less error.

2. Comparison of Linewidth profiles

The results of averaged dose distributions along thex and the y-axes are shown in Fig. 4 for all respiratorygating windows. The results indicate that the dose dis-tributions become similar to that for the static case asthe respiratory gating window width is decreased. Theline-dose profiles on the y-axis were severely slanted tothe right, which indicates that insufficient doses were ir-radiated on the high-dose area for the cases of no gatingand large gating windows.

Differences from the static case in the linewidths of thefield-size, the high-dose, and the penumbra regions areshown in Table 1 for each gating window. The linewidthof the high-dose region showed large dose differencescompared with those of the field-size and the penumbraregions, as high as –58.3 ± 1.2% on the x-axis and –66.7± 1.6% on the y-axis in the case of full motion. Also,the penumbra region was maximally increased as high as23.3 ± 0.4% on the x-axis and 15.9 ± 0.2% on the y-axisin the case of full motion. Generally, the 15% gatingwindow showed the best agreement with the static.

3. Comparison of Irradiated Extents

The extent differences from the static case, along withthe total beam delivery time for the different gating win-dows, are shown in Fig. 5. The differences in the dose

Fig. 4. Averaged line dose profiles on Gafchromic EBT2film individually shown on the (a) x-axis and the (b) y-axis onthe center for the static and the 100% (full motion) cases, andfor various widths of the respiratory gating window. Basedon the calibration curve (Fig. 2), these were individually nor-malized to the central axis, which was irradiated at 200 cGy.

for the more than 95, 90, 80, 70, 60, 50, and 20 – 50%dose regions are depicted. In general, the extent dif-ferences decreased with decreasing gating window. Ex-tent differences of the more-than-95%-dose-distributionregion from the static case were fairly high at –71.5 ±4.7, –41.9 ± 5.5, and –27.0 ± 4.7% for 100 (full mo-tion), 60, and 40% gating windows, respectively, andgradually decreased to –14.1 ± 4.7, –13.5 ± 5.1, and–7.6 ± 5.4% for 30, 20, and 15% respiratory gating win-dows, respectively. No statistical differences from thestatic case were shown for the 30, 20, and 15% gatingwindows (P = 0.053, 0.084, 0.243, respectively) whereasthe 40% gating window showed a statistical difference inthe case of the more-than-95% extent shown in Table 2(P = 0.001). On the other hand, the extent differencesof the 20 – 50% dose-distribution region, compared tothe static case, were –3.3 ± 15.1, –3.6 ± 16.5, –2.8 ±14.6, –1.5 ± 14.6, –3.0 ± 14.0, and –4.1 ± 11.6% for 100(full motion), 60, 40, 30, 20, and 15% respiratory gat-ing windows, respectively, but the differences were not

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Table 1. Comparison of the linewidth differences determined using Gafchromic EBT2 film for the static case and for 100, 60,40, 30, 20, and 15% motion for the field-size, high-dose, and penumbra regions which correspond to the lateral widths of the50, 95, and 20 – 80% isodose levels.

GatingStatic

100%60% 40% 30% 20% 15%

window (full motion)

X (cm) 10.7 ± 0.2 6.2 ± 0.2 8.3 ± 0.5 9.2 ± 0.3 9.6 ± 0.2 10.0 ± 0.3 10.2 ± 0.4

Field size D (%) –42.1 ± 0.3 –22.4 ± 0.5 –14.0 ± 0.4 –10.3 ± 0.3 –6.5 ± 0.4 –4.7 ± 0.4

region Y (cm) 9.0 ± 1.0 10.1 ± 0.9 9.3 ± 1.1 9.1 ± 1.1 8.9 ± 1.0 8.6 ± 1.0 8.7 ± 1.1

D (%) 12.2 ± 1.3 3.3 ± 1.5 1.1 ± 1.5 –1.1 ± 1.4 –4.4 ± 1.4 –3.3 ± 1.5

X (cm) 4.8 ± 0.3 2.0 ± 1.2 4.2 ± 1.4 4.7 ± 0.9 4.7 ± 1.0 4.6 ± 0.9 4.7 ± 1.1

High dose D (%) –58.3 ± 1.2 –12.5 ± 1.4 –2.1 ± 0.9 –2.1 ± 1.0 –4.2 ± 0.9 –2.1 ± 1.1

region Y (cm) 5.4 ± 0.9 1.8 ± 1.3 3.3 ± 1.5 4.5 ± 1.0 4.6 ± 1.2 4.7 ± 1.6 4.8 ± 1.4

D (%) –66.7 ± 1.6 –38.9 ± 1.7 –16.7 ± 1.3 –14.8 ± 1.5 –13.0 ± 1.8 –11.1 ± 1.7

X (cm) 3.0 ± 0.1 3.7 ± 0.4 3.5 ± 0.3 3.4 ± 0.2 3.4 ± 0.2 3.4 ± 0.2 3.4 ± 0.3

Penumbra D (%) 23.3 ± 0.4 16.7 ± 0.3 13.3 ± 0.2 13.3 ± 0.2 13.3 ± 0.2 13.3 ± 0.3

region Y (cm) 4.4 ± 0.0 5.1 ± 0.2 4.5 ± 0.3 4.3 ± 0.3 4.3 ± 0.3 4.3 ± 0.3 4.4 ± 0.2

D (%) 15.9 ± 0.2 2.3 ± 0.3 –2.3 ± 0.3 –2.3 ± 0.3 –2.3 ± 0.3 –0.0 ± 0.2

Abbreviations: X: x-axis direction; Y: y-axis direction, D: linewidth difference compared to the static case

Table 2. Comparison of extent differences between gatingwindows from 100 to 15% and the static case for a dose dis-tribution region of more than 95% and a dose distributionregion of 20 – 50%.

Gating More than 95% region 20 – 50% region

window D (%) P D (%) P

100%–71.5 ± 4.7 0.000 –3.3 ± 15.1 0.289

(full motion)

60% –41.9 ± 5.5 0.000 –3.6 ± 16.5 0.289

40% –27.0 ± 4.7 0.001 –2.8 ± 14.6 0.314

30% –14.1 ± 4.7 0.053 –1.5 ± 14.6 0.366

20% –13.5 ± 5.1 0.084 –3.0 ± 14.0 0.292

15% –7.6 ± 5.4 0.243 –4.1 ± 11.6 0.181

Abbreviations: D: extent difference compared with static.

statistically significant (P = 0.289, 0.289, 0.314, 0.366,0.292, 0.181, respectively). The right y-axis of Fig. 5indicates the beam delivery times for the correspondinggating windows. The beam delivery time is relativelyincreased as the width of the gating window is reduced,and 7 more time is needed for the 15% window than forno-respiratory-gated therapy.

IV. DISCUSSION

In general, determination of the gating window shouldtake into account several factors, including the duty cy-cle, the extent of tumor motion, and the setup uncer-tainty. From a dosimetric point of view, narrow gating

Fig. 5. Comparisons of differences from the static casefor seven different dose exposures to the Gafchromic EBT2film for 100% (full motion) and various widths of respiratorygating windows. The percent of dose area is based on theplanned dose of 200 cGy to the PTV. The y-axis on the rightside indicates the treatment beam delivery time for the samegating window.

windows are beneficial. Increasing the dose rate may re-duce the treatment time, allowing for a smaller gatingwindow, but the cost of this is a reduced duty cycle [10].On the other hand, increasing the dose rate does notalways reduce the dosimetric error for a moving target[26]; therefore, a maximal increase in the dose rate is nota recommended way for reducing treatment time. Froma clinical point of view, the advantage of reducing thegating widow will be negated when the window becomesmuch smaller than the setup uncertainty, which deter-mines the PTV margin. For this relationship, an opti-

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mal gating window that balances the decrease in normaltissue sparing with the increase in duty cycle should bedetermined.

In current-gated RT, the gating window is generallydecided empirically without specific knowledge of thecharacteristics of each gating window. Numerous studiesindicate the gating technique is associated with a betteroutcome than non-gated RT, but few studies have ac-counted for an optimal range of the gating window [11,12, 27, 28]. One study suggested that a 1-mm gatingwindow would be optimal as it might reduce the totaltreatment time compared to a 0.5-mm window, whichwas based on the similarity of the results for the 0.5-mmand the 1-mm gating windows [13]. The 1-mm gatingwindow, however, has a 6.7% duty cycle and is a fairlythin gating window for clinical application.

The present study used the common commercial EBT2film to focus on the ability of the gated operation for vari-ous gating windows. We observed that varying extents ofdose exposure, as well as the x-axes and the y-axes beamprofiles, approached the results for the static case as thesize of the respiratory gating window was decreased. The15% respiratory gating window showed an 8.3 ± 4.5%gamma index difference and a 7.6 ± 5.4% extent dif-ference from the static case, so that the 15% respiratorygating window could be regarded as the ideal gating win-dow width among previously-used gating window. How-ever, a gating duty cycle of 30 – 50% was reported tolead to a 4 to 15 times increase in delivery time [29,30],and a 7 times increase was observed for the 15% window,compared to no-respiratory-gated therapy. In addition,the duration time, which is the exposure time per cycle,became shorter as the range of the gating window wasdecreased, and the number of cycles needed to deliver allplanned doses would be more than that needed to deliverdoses with larger respiratory gating windows. Therefore,the unexpected systematic errors that exist for every cy-cle would accumulate and have a negative effect on theresults.

This study showed that the 100% (full motion) to 15%gating windows had no statistically significant extent dif-ferences compared to the static case for the 20 – 50% dosedistribution region. In the high-dose region, however, ex-tent differences from the static case for the 40% gatingwindow were statistically significant (P = 0.001) whereasthose for the 30%, 20%, and 15% gating window were notstatistically significant (P = 0.388, 0.275, respectively).For the 30% gating window, the extent difference wasfairly reduced, and the treatment time was reduced bymore than half compared to that for the 15% gating win-dow. In this point of view, the 30% respiratory gatingwindow should be a reasonable choice for maximizing therange of the gating window. In a clinical point of view,however, it is important to mention that no statisticaldifference does not mean no dosimetric difference. InFig. 4(b), both the under-dose region in the target areaand the over-dose region around the target area were in-creased compared to the static case. An under-dose in

the target area would increase the probability of can-cer recurrence, and an over-dose would increase normal-tissue toxicity. Therefore, whether to increase the PTVmargin under the minimum normal-tissue-toxicity condi-tion or to increase the treatment time by using a smallerwidth of the gating window should be carefully consid-ered.

This study was based on an assumption that the pa-tient remained immobile during gated delivery, which isnot the case in an actual clinical situation. The pa-tient always moves to some extent during the treat-ment period, and this affects the quality of the deliv-ered dose. The American Association of Physicists inMedicine (AAPM) Task Group 76 [15] emphasized thenecessity for a respiratory gating device to adequatelysimulate cyclical motion similar to human respirationand to provide an adequate number of detectors for doseanalysis. A limitation of our work is that the movementof the breathing simulator, which had a fan-shaped tra-jectory, is not perfectly identical to organ movement. Adetermination of the correlation between the anatomicalchanges and the breathing phases on a patient basis isplanned as a future work. Another limitation is that fora radiochromic film, such as the EBT2 film, which hascomplex handling procedures due to its sensitive spectralcomposition, positioning and orientation in the digitiz-ing process are very difficult because of the asymmetricgeometry of the composite grains and the non-uniformresponses of different directions. However, various cor-rection methods are available for addressing these issues[31–33].

V. CONCLUSION

The gating technique using 4D-CT is an evolving tech-nique that aims to improve dosimetric beam delivery. Inthis work, we quantitatively investigated the dose dis-tribution for various respiratory gating windows and de-termined the optimal window for different beam deliverytimes. These results are useful because they allow usto exploit the effectiveness of gated-radiation therapy bysuggesting explicit window sizes.

ACKNOWLEDGMENTS

This work was supported by the Korean government’sMinistry of Education, Science and Technology (MEST).

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