An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®

ARTICLE IN PRESS Physica Medica ■■ (2016) ■■–■■

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Physica Medica j o u r n a l h o m e p a g e : h t t p : / / w w w. p h y s i c a m e d i c a . c o m

Original Paper

An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife® Jae Pil Chung a,b, Se Woon Oh a,b, Young Min Seong b, Kook Jin Chun a,b,*, Hyun-Tai Chung c,** a

Department of Medical Physics, Korea University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejon 34113, Republic of Korea Center for Ionizing Radiation, Division of Metrology for Quality of Life, Korea Research Institute of Standards and Science, 267 Gajeong-ro, Yuseong-Gu, Daejon 34113, Republic of Korea c Department of Neurosurgery, Seoul National University College of Medicine, 101 Daehang-no Jongno-gu, Seoul 03080, Republic of Korea b

A R T I C L E

I N F O

Article history: Received 21 September 2015 Received in revised form 30 January 2016 Accepted 1 February 2016 Available online Keywords: Gamma Knife Single-shot dose distribution Radiochromic film Dose calibration Gamma index pass rate

A B S T R A C T

Purpose: A method of calibrating radiochromic films for Gamma Knife® (GK) dosimetry was developed. The applicability and accuracy of the new method were examined. Methods: The dose distribution for a sixteen millimeter single-shot from a GK was built using a reference film that was calibrated using the conventional multi-film calibration (MFC) method. Another film, the test film, from a different set of films was irradiated under the same conditions as the reference film. The calibration curve for the second set of films was obtained by assigning the dose distribution of the reference film to the optical density of the test film, point by point. To assess the accuracy of this singlefilm calibration (SFC) method, differences between gamma index pass rates (GIPRs) were calculated. Results: The SFC curves were successfully obtained with estimated errors of 1.46%. GIPRs obtained with the SFC method for films irradiated using a single-shot showed differences less than one percentage point when dose difference criterion (ΔD) was 2% and the distance to agreement criterion (Δd) was 1 mm. The GIPRs of the SFC method when the films were irradiated following a virtual target treatment plan were consistent with the GIPRs of the MFC method, with differences of less than 0.2 percentage points for ΔD = 1% and Δd = 1 mm. Conclusion: The accuracy of the SFC method is comparable to that of conventional multi-film calibration method for GK film dosimetry. © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Introduction The Gamma Knife® (GK, Elekta AB, Stockholm, Sweden) is a minimally-invasive stereotactic radiosurgery (SRS) device that delivers lethal radiation to intracranial lesions by directing many collimated 60Co gamma rays to a single focal point. GK treatment plans should be verified with great care because a high irradiation dose, usually between 10 Gy and 40 Gy, is delivered in a single session. Thus, accurate measurement of the absorbed dose distribution is a critical requirement and the proper calibration of radiochromic films is essential.

* Corresponding author. Center for Ionizing Radiation, Division of Metrology for Quality of Life, Korea Research Institute of Standards and Science, 267 Gajeong-ro, Yuseong-Gu, Daejon 34113, Republic of Korea. Tel.: +82 42 868 5374; fax: +82 42 868 5671. E-mail address: [email protected] (K.J. Chun). ** Corresponding author. Department of Neurosurgery, Seoul National University College of Medicine, 101 Daehang-no Jongno-gu, Seoul 03080, Republic of Korea. Tel.: +82 2 2072 3958; fax: +82 2 747 3799. E-mail address: [email protected] (H.-T. Chung).

A conventional multi-film calibration (MFC) of radiochromic films begins with a dose rate measurement using a standard radiation detector, such as an ionization chamber, to determine the irradiation time. The films are then irradiated at several preselected doses. The irradiated films are scanned using a scanner, and the pixel values of the scanned images are converted into optical density values after color channel decomposition. A calibration curve is then obtained to correlate the optical density with the absorbed dose by fitting the scatter plot of the optical densities and irradiated doses. The entire calibration process for a set of films typically requires a great deal of time, effort and care to complete because several tens of films must be evaluated. Furthermore, the entire procedure must be repeated for sets of films with different lot numbers, even if they are of the same type. Therefore, it would be desirable to develop a simple method of building a calibration curve for a new set of films using previous data without needing to repeat the entire calibration procedure. In this study, we developed and verified such a simple but novel method of film calibration for GK dosimetry using an existing calibrated film with a reference dose distribution. Once a calibration curve has been obtained for one set of films, we can

http://dx.doi.org/10.1016/j.ejmp.2016.02.001 1120-1797/© 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: Jae Pil Chung, Se Woon Oh, Young Min Seong, Kook Jin Chuna, , Hyun-Tai Chung, An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®, Physica Medica (2016), doi: 10.1016/j.ejmp.2016.02.001

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obtain a calibration curve for another set by irradiating only a single new film under the same conditions as the reference film. Methods

KRISS generated an SFC curve for Set IV and sent the results to SNUH. To assess the accuracy of the SFC method, an SNUH member calculated the GIPRs of the films that were irradiated following a virtual target treatment plan using both the SNUH MFC curve and the KRISS SFC curve.

Single-film calibration method Multi-film calibration at KRISS (Set I) Fig. 1a illustrates the concept of the single-film calibration (SFC) method using a reference film. Here, the ‘Reference film’ is a film with a given dose distribution obtained using the MFC method, and the ‘Test film’ is the film to be calibrated. If the two films are irradiated under identical conditions, then the dose distributions on the two films will be identical. The conditions that must be matched include the dose distribution, irradiation time, position, radiation source, and phantom shape, among others. Then, even when the two films have different optical density values at a given point (ODref(x,y) and ODtest(x,y)), it is known that the two films were irradiated with the same dose at that point. Once the dose–response function of the reference film has been well defined at each point, Dref(x,y) = fMFC(ODref(x,y)), it can be assigned to the optical density of the test film at the same point, ODtest(x,y). Using pairs of data of the form (ODtest(x,y), Dref(x,y)), we can generate the dose–response curve for the test film, Dtest(x,y) = gSFC(ODtest(x,y)). Fig. 1b illustrates the procedure used to verify the accuracy of the SFC method. In this case, we have an irradiated film and two calibration curves, namely, an MFC curve and an SFC curve. We obtain two dose distributions from this single image, one by applying the MFC curve and one by applying the SFC curve. We can then calculate the gamma index pass rates (GIPR) for each dose distribution and compare them. If the GIPR values are equivalent for both dose distributions, then we can conclude that the two calibration methods are equivalent, at least for the GIPR calculation. The definition and physical meaning of the GIPR are presented in the following sections and have also been described in reference [1]. Study flow In this section, we summarize the experimental procedures to provide a general outline of the study. The detailed information regarding each procedure is presented in the following sections. First, a set of films (Set I) was calibrated using the MFC method. A nonirradiated film from Set I was irradiated at 60 Gy using the 16 mm collimator of a GK Perfexion. The dose distribution of the reference film was constructed by applying the MFC calibration curve. This film was used as the ‘reference film’ in the SFC procedure. Then, a ‘test film’ was selected from the second set of films (Set II) and irradiated at 60 Gy under the same conditions as the reference film, such that the dose distribution of the test film would be identical to that of the reference film. The test film was calibrated by correlating the optical density distribution of the test film with the dose distribution of the reference film. The GIPR of the reference film dose distribution and the GIPR of the test film dose distribution were compared with each other to assess the validity of the SFC method. The accuracy of the SFC method was also verified using several other sets of films. In order to reduce bias, the SFC curve calculation and the other processes such as the irradiation of films, MFC calibration, and GIPR calculations were performed at separate sites. Two sets of films, Set III and Set IV, were calibrated following the MFC method using the 16 mm collimator of a GK Perfexion at Seoul National University Hospital (SNUH), Seoul, Korea. Then, all images from the Set III films used in the MFC method and three films from Set IV, which were irradiated at 33 Gy simultaneously with the MFC procedure, were sent to the Korea Research Institute for Standards and Science (KRISS). KRISS performed its own MFC for Set III and built a reference dose distribution for the 33 Gy irradiation. By assigning this dose distribution to the three 33 Gy images in Set IV,

GafChromic® MD-V3 films (Lot No. A03051201) were selected for use in Set I. The films were calibrated using a 60Co irradiation system in the dosimetry laboratory at KRISS. Before irradiation, all films were scanned to obtain the non-irradiated film images. Individual films were irradiated at doses ranging from 5 to 60 Gy in increments of 5 Gy. Two films were irradiated at each dose, and the average optical density values were used in the MFC curve fitting. The irradiation time was determined by the dose rate, which was measured using the standard absolute dose measurement procedure at KRISS. A PTW TN31010 ionization chamber (PTW, Freiburg, Germany) and a Keithley 6517B electrometer (Keithley Instruments Inc., Cleveland, OH, USA) were used for the dose rate measurements. The calibration of the PTW 31010 was traceable to the International Bureau of Weights and Measures (BIPM). A Model 2105 precision barometer (MENSOR Corp., San Marcos, CA, USA) was used for pressure measurements, and an ASL F250 precision thermometer (Automatic Systems Laboratories, Croydon, UK) was used for temperature measurements. This barometer and thermometer are calibrated annually at the Center for Thermometry and the Center for Mass and Related Quantities, KRISS. The temperature and pressure measurements were performed simultaneously with the measurements of the ionization current and dose distribution. The irradiated films were scanned using a commercial flatbed scanner, the EPSON Expression 10000XL (Epson America Inc., Long Beach, CA, USA), 48 hours after irradiation. The scanned image was in TIFF format, with a resolution of 300 DPI and a 48-bit color depth (16 bits/channel). Each film was scanned ten times, and the average values were used to reduce errors introduced during the scanning process. The color channels were separated using ImageJ (National Institutes of Health, USA) and the red channel was used because it exhibits the most sensitive response in terms of optical density, as indicated by the manufacturer [2,3]. The relation between the optical density and the irradiated dose was determined by fitting the data to a third-order polynomial. The dose distribution images of the irradiated films were constructed by converting the optical densities into absorbed doses using this fit curve. Single-film calibration of Set II To irradiate the films in a Gamma Knife, we fabricated a phantom (KRISS phantom) using PMMA (poly methyl methacrylate). It was designed to measure the dose rate and dose distribution of a GK at a water equivalent depth of 8 cm (Fig. 2). The phantom was firmly fixed to a Leksell G-frame, as shown in Fig. 2c, and its center was verified through computed tomography imaging. The phantom was installed on a GK such that the center of the phantom, and thus the center of the film, was located at the radiation center of the GK. The films were cut into an octagonal shape using a stainless steel cutting jig (60.1 × 60.1 mm2) to cut them into the same shape and size. Then, the films were set into the film nest of the phantom, as illustrated in Fig. 2b. PMMA sheet spacers were used at the front and back of each film such that the film was sandwiched by the spacers and there was no air gap between the film and the nest. We marked the film, the spacer, and the film nest to keep track of the film’s orientation. The films were irradiated in the xy-plane of the GK, i.e., the plane perpendicular to the craniocaudal axis. A film from Set I (MD-V3) was irradiated to 60 Gy using the 16 mm collimator of the GK Perfexion at Yonsei University

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Figure 1. (a) A schematic diagram of the single film calibration (SFC) method. ODref (x,y) is the measured optical density and Dref (x,y) is the absorbed dose at an arbitrary point (x,y) on the reference film. Dref (x,y) is obtained using the conventional multi-film calibration (MFC) method and assigned to the optical density of the corresponding point on the test film, ODtest(x,y). The calibration curve of the test film is obtained by fitting the set of data points in the form (ODtest(x,y), Dref(x,y)). (b) The validity of the SFC method can be verified by comparing the gamma index pass rates (GIPRs) of the two dose distributions, calculated by individually applying both MFC and SFC to a single image on an irradiated film. The upper gamma index distribution is obtained by converting the optical densities of the film image into absorbed doses using the MFC method, and the lower distribution is obtained by converting the optical densities of the same image using the SFC method.

Please cite this article in press as: Jae Pil Chung, Se Woon Oh, Young Min Seong, Kook Jin Chuna, , Hyun-Tai Chung, An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®, Physica Medica (2016), doi: 10.1016/j.ejmp.2016.02.001

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Figure 2. (a) Schematic diagram of the outer shell of the KRISS phantom. (b) The inner film insert of the phantom. (c) The manufactured outer shell fixed to a Leksell G frame. (d) A picture of the inner phantom with an inserted film inside.

Severance Hospital (YUSH), Seoul, Korea. The irradiation time was determined by means of an absolute dose rate measurement using the measurement system described in the previous section and the KRISS phantom. This film was used as the ‘reference film’ for the SFC of the films in Set II (MD-V2, Lot No. S0628MDV2). A film from Set II was irradiated to 60 Gy under the same conditions as the reference film and was used as the ‘test film’ in the SFC method. The irradiated films, namely, the reference and the test film, were handled and scanned in the same manner as the films used in the MFC procedure at KRISS. Any rotational and translational differences between the scanned images of the test film and the reference film were adjusted using ImageJ. The rotation of the scanned images was corrected such that the vertical side of the octagon was parallel to the vertical axis (the y-axis of the GK). The reference film image was translated such that the center of the optical density peak corresponded to the center of the peak in the test image. The dose distribution of the reference film, Dref(x,y), was built by applying the MFC curve described in previous section to the optical density data from the scanned image of that film, ODref(x,y). Then, Dref(x,y) was assigned to the optical density distribution of the test film image, ODtest(x,y), point by point. This allowed us to generate data pairs in the form of (ODtest(x,y), Dref(x,y)) which should be equivalent to (ODtest(x,y), Dtest(x,y)). The calibration curve from the SFC method for the films in Set II was obtained by fitting the (ODtest(x,y), Dref(x,y)) data to a third-order polynomial. We selected a square with dimensions of 45 × 45 mm2 around the dose center as the region of interest (ROI) for data fitting. The ROI covered a dose range from approximately 10% (6 Gy) to 100% (60 Gy). For easier handling of the data set, the images were reformatted to 50 ~ 90 DPI to reduce the massive amount of collected data (approximately 2 × 105 points included in the SFC curve) to fewer than 25,000 points. Gamma index pass rate calculation One of the most useful parameters for evaluating the differences between measured and calculated dose distributions is the GIPR [1]. The gamma index, γ, is defined as follows:

Γ (rc , rm ) =

rc − rm Δd 2

2

+

[D (rc ) − D (rm )]2

γ = min {Γ (rc , rm )} ∀ {rm }

ΔD 2

(1) (2)

where rc is an arbitrary point in the calculated dose image and rm is a point in the measured dose image. Δd is the distance to agreement (DTA) criterion. D(rc) is the dose at rc , D(rm) is the dose at rm, and ΔD is the dose difference criterion. When γ ≤ 1, the corresponding point rc passes the test. The GIPR is the ratio of the number of

points that pass the test for a given set of criteria to the total number of points. Although the threshold for acceptance depends on the medical physicists practicing at each site, the measured dose distribution is typically said to be equivalent to the calculated one when the GIPR is greater than or equal to 95%. For the purpose of assessing the equivalence of the SFC method to the MFC method, we built a dose distribution for the test film by converting its optical density values into absorbed dose values using the SFC curve. The dose distribution of a 16 mm single-shot at the center of the KRISS phantom calculated using Leksell Gamma Plan version 10.1 (LGP, Elekta AB, Stockholm, Sweden) was exported to a DICOM (Digital Imaging and COmmunications in Medicine) file with a spatial resolution of 0.2 mm/pixel. The GIPRs of the test film dose distribution and the reference film dose distribution were obtained by comparing the measured distributions to the calculated dose distribution using commercial film analysis software, DoseLab Pro version 6.70b (Mobius Medical Systems, Houston, TX, USA). The separation of the red channel from the scanned film images and the conversion of optical densities into absorbed doses were also performed using DoseLab Pro for the GIPR calculations. Multi-film calibration of EBT2 films (Set IV) To verify the equivalence of the SFC method to the MFC method in a more realistic scenario, a treatment plan for a virtual target with a volume of 1.6 cm3 was prepared. The dose distributions of films irradiated following this virtual target plan were obtained using both in the MFC method and the SFC method, and the resulting GIPRs were compared. First, a set of EBT2 films (Set IV, Lot No. A07160901) was calibrated using the conventional MFC method at SNUH. The EBT2 films for MFC calibration were cut by hand into 60 × 60 mm2 squares and irradiated at the center of an Elekta Solid Water Phantom (Elekta AB, Stockholm, Sweden) using the 16 mm collimator of a GK Perfexion at SNUH. The films were fixed at a given location and rotation angle inside the Elekta Solid Water Phantom using two punch holes made in the films. Three EBT2 films were irradiated at each of eight absorbed doses, 5, 10, 15, 20, 24, 27, 30, and 33 Gy. These dose values were selected considering the facts that the maximum dose of the virtual target plan was 30 Gy and that a greater variation in dose was observed at doses higher than 15 Gy. Three nonirradiated EBT2 films were used as the control films (0 Gy) which were used to calculate the net optical densities of the irradiated films [4]. The films were stored in a refrigerator and scanned using an EPSON Expression 10000XL flatbed scanner at SNUH two weeks after irradiation. The scanned images were stored in an uncompressed TIFF format with a 300 DPI resolution and a 48 bit color depth. No

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image corrections were applied during scanning [5]. The green channel of the scanned images was selected because the green channel of EBT2 films exhibits higher sensitivity in the 8 ~ 50 Gy region [6]. A constant film orientation was carefully maintained during irradiation and scanning [7]. A 6 × 6 mm2 square in the central area was selected to determine the mean optical density of each film, considering the 22 mm full width at half maximum (FWHM) of the 16 mm single-shot dose distribution. The mean optical density of all three EBT2 films irradiated at a given dose was used as the optical density at that dose. All image analyses were performed using DoseLab Pro. The MFC curve was obtained by fitting a third-order polynomial to the nine data points (ODSet_IV , D Set_IV ) using the commercial software package, Origin 2015 (OriginLab Corp, Northhampton, MA, USA). The MFC procedure for a GK Perfexion is described in more detail in reference [8]. EBT2 films irradiated following a virtual target treatment plan (Set IV) A treatment plan was prepared for the irradiation of a virtual target in a commercial anthropomorphic phantom, CIRS Model 605 (CIRS Inc., Norfolk, VA, USA), as shown in Fig. 3. For treatment planning, computed tomography images of the phantom with a dummy film inserted were obtained, as shown in Fig. 3b. The treatment plan, which consisted of five 4 mm shots, two 8 mm shots, and one 16 mm collimator shot, was designed using with LGP version 10.1 to cover a 1.6 cm3 target. The prescribed dose was 15 Gy to the 50% isodose surface. Three films from Set IV (EBT2) were cut by hand into an octagonal shape of 60 × 60 mm2 in size, without using the film cutting jig. The position and rotation of each film inside the CIRS 605 phantom were confirmed by means of three or four fiducial markers applied to the film prior to irradiation (Fig. 3c). The films were installed inside the phantom at the location defined in the treatment plan, and they were irradiated in accordance with this plan using the GK Perfexion at SNUH. The irradiated films were handled and scanned in the same manner as the calibration films. The optical density data from the scanned image of each of the virtual target irradiation films were converted into absorbed doses using the MFC curve for Set IV. Before calculating GIPR, we translated and rotated

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the measured film images with respect to the calculated dose distribution using the automatic adjustment procedure in DoseLab Pro. Because the purpose of this study was to compare the GIPRs obtained using the SFC method and the MFC method rather than to evaluate the accuracy of the plan, we could concentrate more on the differences between the two calibration methods and less on the effect of any misalignment of the films and/or images in the GIPR calculations. The GIPRs were obtained under various calculation criteria by comparing the measured dose distributions to the LGP dose distribution. Single-film calibration of EBT2 films (Set IV) To obtain an SFC curve for Set IV, we chose three films from Set III (MD-V3, Lot No. 06061402) to obtain a reference dose distribution. They were irradiated to 33 Gy using the 16 mm collimator of the GK Perfexion at SNUH. The dose distributions of these films were constructed by converting their optical densities using a calibration curve obtained via a conventional MFC method. Three films from Set III were irradiated at each of the following doses: 5, 10, 15, 20, 24, 27, and 30 Gy. Three non-irradiated films from Set III were used as 0 Gy films. These 27 films, including the three films from Set III that were irradiated to 33 Gy as described above, were scanned at SNUH, and the images thus obtained were sent to KRISS. KRISS obtained an MFC curve for the Set III films using the same method applied for the MFC of Set I. The average dose distribution of the three 33 Gy films from Set III was used as the reference dose distribution for the SFC of Set IV. The three Set IV films (EBT2) that were irradiated to 33 Gy during the MFC of Set IV were chosen as the test images for the SFC of Set IV. The scanned images of these three 33 Gy films from Set IV were sent to KRISS. The average optical densities of these three films were used as the test optical density distribution and compared to the reference dose distribution determined for the three 33 Gy films from Set III. There was no measurable translational or rotational misalignment between the films because they were fixed in place by two rods passing through two punch holes in each film. To construct data pairs in the form of (ODSet_IV, DSet_III), eight doses (5, 10, 15, 10, 24, 27, 30, and 33 Gy) were selected, as in the MFC method, and the optical densities of the test films irradiated at each dose were collected with a 0.5 Gy bin width. This simplification was introduced to facilitate the handling of the data and to ensure that they were as comparable as possible for both calibration methods. Nine data points, including the 0 Gy point, were fitted to a thirdorder polynomial using Origin 2015, and the fitted curve was used as the SFC curve for Set IV. The SFC curve for Set IV was sent to SNUH, and the optical density images of the three Set IV films irradiated following the virtual target plan were converted into absorbed doses using this SFC curve. The GIPRs for the measured dose distributions obtained using the SFC curve for Set IV were calculated by comparing the measured distributions to the calculated dose distribution. The GIPRs for the dose distributions obtained using the SFC curves and the GIPRs for the dose distributions obtained using the MFC method were compared to assess the equivalence of the two calibration methods. Results Verification of the SFC using a single-shot plan

Figure 3. (a) A CIRS Model 605 anthropomorphic phantom fixed to a Leksell G frame. (b) A calculated treatment plan for a virtual target with a volume of 1.6 cm3 inside the phantom. (c) An EBT2 film irradiated using this treatment plan with 15 Gy at the 50% surface.

The MFC dose–response curve for the Set I (MD-V3) films obtained at KRISS is presented in Fig. 4a along with the third-order polynomial curve fit (adjusted R2 = 0.9997). The optical density data from the reference film that was irradiated to 60 Gy at YUSH (Fig. 5a) were converted into absorbed doses (Fig. 5b) using this fitted curve. This dose distribution was used as the reference dose distribution

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Figure 4. (a) Multi-film calibration plot for the Set I (MD-V3) films obtained at KRISS. The solid line represents the curve fitted to the measured data. (b) A scatter plot of the optical density values from the test film that was irradiated to 60 Gy (Set II, MD-V2) and the corresponding absorbed doses assigned based on the reference film (Set I, 60 Gy). The solid line represents the single-film calibration curve obtained by fitting the data to a third-order polynomial. The twelve data points shown here correspond to the twelve doses used in the multi-film calibration of Set I.

for the SFC of Set II. It was assigned to the optical density image of the test film (Set II) that was irradiated under conditions identical to those used to irradiate the reference film at YUSH. The data pairs consisting of the optical density values for the test film and the dose values for the reference film are plotted in Fig. 4b. These pairs were fitted to a third-order polynomial (adjusted R2 = 0.9997). To simplify the calibration procedure, the twelve doses (5–60 Gy in increments of 5 Gy) that were selected for the MFC of Set I were used, and the corresponding optical densities were collected with a 0.5 Gy bin width. The third-order polynomial fit to these twelve points was used as the SFC curve to determine the dose distribution of the test film. The SFC curve obtained from these twelve points was essentially identical to the curve obtained using approximately 21,000 points, as shown in Fig. 4b. The origins of the dose–response curves shown in Fig. 4a and b differ because of the use of different definitions of the optical density. The optical densities represented in Fig. 4a are the net optical densities determined by subtracting the optical density of the non-irradiated film from the optical density of an irradiated film. By contrast, the optical den-

sities in Fig. 4b were obtained from the images of the irradiated films without performing background subtraction using the non-irradiated images. The obtained dose values were not affected by the definition of the optical density, however, because it is equivalent to a choice of the absolute scale. Accurate film alignment is an important issue in SFC, because the SFC procedure relies on point-to-point matching. To check how much displacement could exist between the film and the film nest, we measured the sizes of both. The measured width of the 12 films cut using the film cutting jig was (59.817 ± 0.088) mm, and the height was (59.860 ± 0.094) mm. The width of the film nest was measured to be (60.060 ± 0.026) mm, and the height was (60.056 ± 0.027) mm. The estimated displacements between the film and the film nest were (0.243 ± 0.092) mm in width and (0.196 ± 0.098) mm in height. Because these estimated displacements represent the average worst-case values, we assumed that the misalignment between the reference film and the test film was less than 0.25 mm. The errors from this film misalignment would also have been somewhat compensated by the translation and rotation of one scanned image for

Figure 5. (a) The scanned image of the reference film (60 Gy, Set I). It was irradiated using the 16 mm collimator of a GK Perfexion at Yonsei University Severance Hospital. The area inside the dotted line corresponds to the dose distribution that was used as the reference dose distribution for the single-film calibration of Set II. (b) The dose distribution of the reference film obtained in the multi-film calibration of Set I. (c) The three-dimensional dose distribution of the reference film with contour lines at increments of 3 Gy.

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Table 1 Gamma index pass rates given various calculation criteria. Criteria

16 mm single-shot

Virtual target plan

Δd (mm)

ΔD (%)

MD-V3, MFC (%)

MD-V2, SFC (%)

EBT2, MFC (%)

EBT2, SFC (%)

2 2 2 1 1 1

3 2 1 3 2 1

99.7 98.8 96.9 99.7 98.3 94.6

99.9 98.7 93.1 98.7 97.6 89.3

100.0 ± 0.0 100.0 ± 0.0 100.0 ± 0.0 99.9 ± 0.1 99.6 ± 0.3 99.2 ± 0.4

100.0 ± 0.0 100.0 ± 0.0 100.0 ± 0.0 99.9 ± 0.1 99.7 ± 0.3 99.4 ± 0.5

alignment with the other image, as described in the Methods section. The estimated displacement from our alignment tests was less than 0.2 mm (less than 2 pixels at a resolution of 300 DPI) for GK single-shot images. Thus, the effect of the potential offset and rotation of the films on the GIPRs was considered to be negligible; a detailed description is provided in the following Alignment of films and images section. Before the gamma index was calculated, a dose normalization factor was applied to the films that were irradiated at YUSH to compensate for the dose difference between KRISS and YUSH. Because the purpose of this study was to perform a relative comparison between the SFC and the MFC procedures, this common multiplication factor does not affect the conclusions of this study. Points with doses larger than 20% (12 Gy) of the maximum dose were considered to suppress the irrelevant dose points in the local gamma index calculation. The DTA calculation resolution was 1 mm/pixel, the search range was twice the DTA criterion, and the number of contour lines was 30. Table 1 shows the GIPRs obtained by varying the gamma index calculation criteria as follows: ΔD from 1% to 3% and Δd from 1 mm to 2 mm. The GIPRs of the test film dose distribution (MDV2, SFC) were consistently in agreement with those of the reference film (MD-V3, MFC), with differences of less than 1 percentage point when the calculation criteria were ΔD ≥ 2% and Δd ≥ 1mm . When the ΔD was set to 1%, the difference between the two films increased to between 3.8 and 5.3 percentage points. Considering the fact that the typical acceptable mechanical accuracy limit of SRS is

7

1 mm and the dose rate error range is 3%, it can be concluded that the SFC method yields results that are equivalent to those of the MFC method.

Verification of the SFC using a virtual target plan The calibration curves for Set IV that were obtained using the MFC and SFC procedures are presented in Fig. 6a. Both data sets were fitted to third-order polynomials. The adjusted R2 values were 0.99962 for the MFC and 0.99997 for the SFC (Fig. 6a). For the purpose of comparing the MFC and SFC curves, 10 arbitrary optical density values (OD = −17,500 × log10(Intensity/65535)) defined in DoseLab Pro, ranging from 6000 (~5 Gy) to 15,000 (~35 Gy) in increments of 1000, were selected. The doses corresponding to these 10 values were calculated using the MFC and SFC methods. Fig. 6b plots the 10 resulting points with the MFC doses on the horizontal axis and the SFC doses on the vertical axis. These points were fitted to a straight line. In the ideal case, the SFC and MFC methods would produce the same values at every point, and the line should have a slope of one and pass through the origin. The fitted result was DSFC = 0.99948 * DMFC + 0.2891 (adjusted R2 = 0.99982). The median difference between two methods at the chosen 10 points was −0.8 ± 2.6%, with the SFC doses being approximately 0.8% larger than the MFC doses. The largest difference (−7.8%) was observed at the lowest dose point (~5 Gy), whereas the errors in the moderateto high-dose region ( ≥ 14 Gy ) were less than 1.0%. Because the lowdose region (<5 Gy) is not of practical interest for the verification of most GK radiosurgery plans and the absolute dose difference was small (<0.4 Gy), the relatively large difference between the SFC and MFC calibration curves in this range can be neglected. The GIPRs of the EBT2 films irradiated following the virtual target plan are presented in Table 1. Points with doses larger than 20% (6 Gy) of the maximum dose were considered in the gamma index calculation. The agreement was very good, with a difference of 0.2 percentage points for Δd = 1 mm and ΔD = 1%. These results indicate that the physical quantities determined using the SFC method are equivalent to those obtained using the MFC method, at least in Gamma Knife film dosimetry.

Figure 6. (a) Dose calibration points and fitted curves for the multi-film calibration (MFC) and single-film calibration (SFC) of Set IV (EBT2). Both curves are third-order polynomials fitted to corresponding data set. (b) A scatter plot showing the doses calculated using the MFC method on the horizontal axis and doses by the SFC method on the vertical axis. The solid line represents a linear fit to the data.

Please cite this article in press as: Jae Pil Chung, Se Woon Oh, Young Min Seong, Kook Jin Chuna, , Hyun-Tai Chung, An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®, Physica Medica (2016), doi: 10.1016/j.ejmp.2016.02.001

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Table 2 Standard uncertainties (1σ) in the conversion parameters for the radiochromic films. Uncertainty component

Type A (%)

Type B (%)

Optical density measurement using the scanner Intensity resolution Uniformity of the radiochromic film Temperature and relative humidity measurement Alignment of the KRISS phantom with the irradiation center of the GK Fitting error from misalignment Fitting error from bias in the dose distribution Calibration curve fitting Combined standard relative uncertainty

0.10

0.02 0.002 0.50 0.056 0.20 0.16 0.19 1.33

1.46

Uncertainty analysis A detailed uncertainty budget based on the relative standard uncertainties for the fitted parameters of the calibration curves of the radiochromic films for dose conversion is tabulated in Table 2. The contributing uncertainty components were classified as either statistical (type A) or systematic (type B) uncertainties [9], and their values are listed. The optical density measurement uncertainty includes the measurement uncertainty of the pixel values obtained using the scanner. The intensity resolution uncertainty is the uncertainty related to the determination of the bit of an image located between two adjacent pixel values in a 0~65535 pixel value distribution. The uncertainty in the uniformity of the radiochromic films is related to the intrinsic property of the spatial non-uniformity of a film in a selected ROI. The fitting error from misalignment is related to the positioning uncertainty of the film inside the nest. The fitting error from bias in the dose distribution represents the uncertainty arising from the uneven distribution of data points in the optical density versus dose curve. Errors related with the film alignment and the data point distribution are described in detail in the following sections. The calibration curve fitting uncertainty is the overall uncertainty introduced during the fitting procedure performed to obtain the calibration curve. Alignment of films and images There was no measurable misalignment between the films irradiated in the Elekta Solid Water phantom because they were fixed in place by two cylindrical rods. The maximum possible rotation of the films inside the KRISS phantom was less than 0.5°, and the effect of this small rotation could be neglected because of the cylindrical symmetry of the single-shot GK dose distribution in the xy plane. With the intent of evaluating the effects of film and/or image translation, we generated SFC dose–response curves using intentionally shifted images. We shifted the image of the reference film (33 Gy, MD-V3) in increments of 0.282 mm (one pixel at 90 DPI), resulting in shift distances 0.28 mm, 0.56 mm, 0.85 mm, and 1.13 mm. The fitting results for the dose versus optical density curves obtained from the misaligned images were compared with the curve for the un-shifted image data, as shown in Fig. 7. As the shift of the image increased, the spread of the dose–optical density data became broader and the adjusted R2 values of the fitted curve worsened (Table 3). It is natural that this artificial difference became larger as the shift increased. The fitted curve itself, however, did not change considerably, as shown in Fig. 7f. This is because the dispersed data points were almost evenly distributed around the fit curve for the un-shifted image. The dose distribution of the sixteen-millimeter single-shot was a broad peak with a FWHM of 22 mm in the x- and y-directions. When the shift was much smaller than this FWHM, most of the area of the peaks still overlapped. Suppose that the peak of the test image

was shifted slightly to the right; its right-hand side was then compared with the lower value of the reference peak, and its lefthand side was compared with the higher value. Because the peak was symmetric about its center, the decrement on the right-hand side was nearly equal to the increment on the left-hand side. Therefore, the resulting data distribution was symmetric about the unshifted data. The dose differences caused by the image shifts were estimated by calculating the standard deviation of the dose difference, σ (ΔD fit ) , and the maximum dose difference, ΔD fit ,Max , from the unshifted curve; these values are presented in Table 3. In our study, the estimated misalignment distance was less than 0.25 mm, and the related dose error was 0.16%. For this comparison, twenty arbitrary optical density values were selected. Because the estimated misalignment distance in our study was less than 0.25 mm, we used the 0.28 mm shifted data for error estimation, which yielded a dose error of 0.16%. The effect of the image shifts on the GIPRs was also assessed by using the fitted curves to obtain dose distributions for the three EBT2 films irradiated following the virtual target plan, and the results are given in Table 4. There were no meaningful differences in the GIPR values when the image shift was 0.28 mm. The differences remained within the range of statistical errors even when the shift was increased to 1.13 mm. Uneven distribution of the data points in SFC In the SFC method, there is a higher density of data points in areas with a steep dose gradient than in areas with a shallow gradient, as shown in the frequency distribution plot for the SFC of the EBT2 films (Fig. 8a). To estimate the effect of this uneven distribution, we artificially generated an evenly distributed data set by interpolating from the uneven data. The dose estimations obtained in the two cases (the fits to the original data and the evenly distributed data) are compared in Fig. 8b. As seen in Fig. 8b, the dose estimation results for the two cases exhibited little difference. The estimated dose difference, σ(ΔDfit), between the two cases was 0.034 Gy, corresponding to a 0.19% difference. The maximum difference between the two fitted curves is 0.08 Gy in the high dose region (33 Gy). Discussion Simplifying film calibration procedures by using a reference film with a varying dose distribution is not an uncommon approach in quality assurance for conventional linear accelerator (LINAC) radiotherapy and robotic radiosurgery using a CyberKnife® [5,10,11]. Chang et al. showed that the SFC method using a percent depth dose distribution yielded dose distributions for a 60o wedged 6 MV photon field with errors of less than 4% [10]. To the best of the authors’ knowledge, however, the current study is the first to apply the SFC method for GK dosimetry. We used the dose distribution from the 16 mm collimator of a GK Perfexion instead of the wedge field dose of a LINAC. There are several advantages of using this 16 mm singleshot distribution as the reference for SFC. Because the single-shot irradiation using a GK is a very stable process using fixed collimators, its dose distribution is also very stable and can be verified with high accuracy (1 mm/1%) [8]. The center of the single-shot can be easily determined by analyzing the dose distribution, with a positional accuracy of down to less than 0.5 mm [12]. Furthermore, the dose distribution in the xy plane of a GK is a nearly cylindrically symmetric, meaning that the error from the rotation of the measured films is negligible. The GIPRs for the virtual target plan obtained for the EBT2 films calibrated using the SFC method were consistent with those of the MFC method, with differences of less than 0.2 percentage points for

Please cite this article in press as: Jae Pil Chung, Se Woon Oh, Young Min Seong, Kook Jin Chuna, , Hyun-Tai Chung, An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®, Physica Medica (2016), doi: 10.1016/j.ejmp.2016.02.001

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Figure 7. Dose–response curves of (a) the un-shifted image, (b) the 0.28 mm shifted image, (c) the 0.56 mm shifted image, (d) the 0.85 mm shifted image, and (e) the 1.13 mm shifted image. (f) Comparison of the five fitted curves. The data points shown here are arbitrary points for comparison with the fitted results. Plots (a)–(e) were generated using the commercial software package, TableCurve 2D 5.01.

Please cite this article in press as: Jae Pil Chung, Se Woon Oh, Young Min Seong, Kook Jin Chuna, , Hyun-Tai Chung, An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®, Physica Medica (2016), doi: 10.1016/j.ejmp.2016.02.001

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Table 3 Dose differences between the shifted-image calibration curves and the curve for the un-shifted image. Shift σ(ΔDfit) ΔD fit ,Max R2

0.00 mm – – 0.9997

0.28 mm 0.02 Gy 0.06 Gy 0.9988

0.56 mm 0.03 Gy 0.09 Gy 0.9957

0.85 mm 0.06 Gy 0.19 Gy 0.9898

1.13 mm 0.11 Gy 0.33 Gy 0.9812

Δd = 1 mm and ΔD = 1%. Considering that the typical acceptable range of accuracy in SRS is 1 mm/3%, this result confirms that the SFC method is sufficiently accurate to be used in clinics. The GIPRs calculated in the case of the 16 mm single-shot were also acceptable under the 1 mm/3% criteria, showing a difference of 1.0 percentage point. However, this difference was much larger than that for the virtual target plan and increased to 5.3% for the 1 mm/1% criteria. This finding caused us to modify our strategy for testing the SFC method. Originally, we had planned to calibrate the primary films at KRISS and build an MFC calibration curve. After irradiating only two films (the reference film and the test film) at another site under the same conditions, we obtained the SFC curve at KRISS using these two films. However, a problem was encountered during dose normalization, because the irradiation at KRISS followed the standard protocol of TRS 398, whereas the GK irradiation could not satisfy the conditions of TRS 398 [13,14]. Differences in various

conditions, such as the beam quality, source-to-chamber distance, phantom characteristics, and beam direction, necessitated a dose normalization factor between KRISS and the other site. Although this conversion factor did not affect the current results, because the purpose of this study was the relative comparison of the SFC and MFC methods, we decided to irradiate all the films at the same site. The relatively large discrepancies between the two calibration methods for the 16 mm single-shot might stem from the fact that the GIPRs were calculated for different types of films, namely, MDV3 and MD-V2. According to the manufacturer’s specifications [2], the non-uniformity of MD-V3 films is <3%, superior to the <8% nonuniformity of MD-V2 [3]. In general, a more uniform film yields better agreement with calculations. There are also other differences in the characteristics of the different types of films that could result in unexpected errors during the SFC process. By contrast, when the virtual target plan was assessed, the GIPRs were evaluated for films of the same type (EBT2) calibrated using the two different methods. Additionally, all films were irradiated at a single site, and thus, there was no need for a dose normalization factor. Although the first test scheme should be acceptable because we compensated for the dose difference with a normalization factor, it seems more desirable to irradiate both the reference and test film at the same site. This change in the SFC procedure does not considerably affect the simplicity of the process because it is sufficient

Table 4 Gamma index pass rates for the EBT2 films irradiated following the virtual target plan. The dose distributions of the films were obtained by applying the SFC curves calculated from the shifted reference film images. Δd (mm)

ΔD (%)

2 2 2 1 1 1

3 2 1 3 2 1

GIPR (%) 0.00 mm

0.28 mm

0.56 mm

0.85 mm

1.13 mm

100.0 ± 0.0 100.0 ± 0.0 100.0 ± 0.0 99.9 ± 0.1 99.7 ± 0.3 99.4 ± 0.5

100.0 ± 0.0 100.0 ± 0.0 99.9 ± 0.1 99.9 ± 0.1 99.7 ± 0.2 99.4 ± 0.2

100.0 ± 0.0 100.0 ± 0.0 99.9 ± 0.1 99.8 ± 0.2 99.6 ± 0.2 99.3 ± 0.2

100.0 ± 0.0 100.0 ± 0.0 100.0 ± 0.1 99.8 ± 0.2 99.6 ± 0.2 99.2 ± 0.3

100.0 ± 0.0 100.0 ± 0.0 100.0 ± 0.0 99.8 ± 0.2 99.5 ± 0.2 99.0 ± 0.3

Figure 8. (a) A frequency-count plot of the distribution of the original dose data from the SFC of the EBT2 films. The sum of the counts is 21,055, the average count frequency is 334, the total number of bins is 64, and the bin width is 0.5 Gy. (b) A plot comparing the dose estimation results obtained by fitting the uneven (original) dose data and the evenly distributed dose data. The doses calculated from the original data are represented on the horizontal axis, and the doses calculated from the evenly distributed data are represented on the vertical axis. This plot was generated for the optical density range of 0.1 ~ 0.7 in increments of 0.03.

Please cite this article in press as: Jae Pil Chung, Se Woon Oh, Young Min Seong, Kook Jin Chuna, , Hyun-Tai Chung, An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®, Physica Medica (2016), doi: 10.1016/j.ejmp.2016.02.001

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to perform the MFC only once, and subsequently new sets of films can be calibrated using the SFC method. Conclusion A simple single-film calibration method, which involves comparing a test film with a reference film that has been calibrated using the conventional multi-film calibration method, was developed for Gamma Knife film dosimetry. The accuracy of the single-film calibration method was verified by applying it to films irradiated following a virtual target radiosurgery plan. When the reference and test films were irradiated under the same conditions, the gamma index pass rate obtained in the single-film calibration agreed well with that achieved via multi-film calibration, within the acceptable error range for stereotactic radiosurgery. Acknowledgements This work was supported partly by the Ministry of Science, ICT and Future Planning (MSIP) under the research project ’Development of absorbed dose dosimeter based on microfluidic calorimeter and absolute measurement technology of absorbed dose to water in nonstandard radiotherapy fields’ with grant number 2015M2A2A4A02044753 and partly by the Korea Research Institute of Standards and Science under the research project ’Development of Measurement Standards for Medical Radiation’ with grant number 15011045. This study was also supported by the grant 04-2014-0490 from the Seoul National University Hospital Research Fund.

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[2] ISP Technologies Inc. GAFCHROMIC® MD-V3 Dosimetry Media. ; [accessed 28.05.15]. [3] ISP Technologies Inc. GAFCHROMIC® MD-V2-55 Radiochromic Dosimetry Film for High-Energy Photons. ; [accessed 28.05.15]. [4] Aldelaijan S, Alzorkany F, Moftah B, Buzurovic I, Seuntjens J, Tomic N, et al. Use of a control film piece in radiochromic film dosimetry. Phys Med 2015. http://dx.doi.org/10.1016/j.ejmp.2015.12.004. [5] Lewis D, Micke A, Yu X, Chan MF. An efficient protocol for radiochromic film dosimetry combining calibration and measurement in a single session. Med Phys 2012;39:6339–50. [6] Devic S. Radiochromic film dosimetry: past, present, and future. Phys Med 2011;27:122–34. [7] Alnawaf H, Butson MJ, Cheung T, Yu PKN. Scanning orientation and polarization effects for XRQA radiochromic film. Phys Med 2010;26:216–19. [8] Park JH, Han JH, Kim CY, Oh CW, Lee DH, Suh TS, et al. Application of the gamma evaluation method in Gamma Knife film dosimetry. Med Phys 2011;38:5778– 87. [9] Korea Research Institute of Standards and Science. Guideline for the expression of measurement uncertainty: KRISS-99-0070-SP. Dae-Jeon. Korea; 1999. [10] Chang L, Chui CS, Ding HJ, Hwang IM, Ho SY. Calibration of EBT2 film by the PDD method with scanner non-uniformity correction. Phys Med Biol 2012;57:5875–87. [11] Blanck O, Masi L, Damme MC, Hildebrandt G, Dunst J, Siebert FA, et al. Filmbased delivery quality assurance for robotic radiosurgery: commissioning and validation. Phys Med 2015;31:476–83. [12] Maitz A, Wu A, Lunsford LD, Flickinger JC, Kondziolka D, Bloomer WD. Quality assurance for Gamma Knife stereotactic radiosurgery. Int J Radiat Oncol Biol Phys 1995;32:1465–71. [13] Andreo P, Burns DT, Hohlfeld K, Huq MS, Kanai T, Laitano F, et al. Absorbed Dose Determination in External Beam Radiotherapy: An International Code of Practice for Dosimetry based on Standards of Absorbed Dose to Water. Technical Report Series No. 398. Vienna, Austria: IAEA; 2004. [14] Chung HT, Park Y, Hyun S, Choi Y, Kim GH, Kim DG, and Chun KJ. Determination of the absorbed dose rate to water for the 18-mm helmet of a gamma knife. Int J Radiat Oncol Biol Phys 2011;79:1580–7.

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Please cite this article in press as: Jae Pil Chung, Se Woon Oh, Young Min Seong, Kook Jin Chuna, , Hyun-Tai Chung, An effective calibration technique for radiochromic films using a single-shot dose distribution in Gamma Knife®, Physica Medica (2016), doi: 10.1016/j.ejmp.2016.02.001