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Software for 3D radiotherapy dosimetry. Validation

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Phys. Med. Biol. 59 4111 (http://iopscience.iop.org/0031-9155/59/15/4111) View the table of contents for this issue, or go to the journal homepage for more

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Institute of Physics and Engineering in Medicine Phys. Med. Biol. 59 (2014) 4111–4136

Physics in Medicine & Biology doi:10.1088/0031-9155/59/15/4111

Software for 3D radiotherapy dosimetry. Validation Marek Kozicki, Piotr Maras and Andrzej C Karwowski GeVero Co., Tansmana St. 2/11, 92-548 Lodz, Poland E-mail: [email protected] Received 9 December 2013, revised 3 April 2014 Accepted for publication 5 June 2014 Published 8 July 2014 Abstract

The subject of this work is polyGeVero® software (GeVero Co., Poland), which has been developed to fill the requirements of fast calculations of 3D dosimetry data with the emphasis on polymer gel dosimetry for radiotherapy. This software comprises four workspaces that have been prepared for: (i) calculating calibration curves and calibration equations, (ii) storing the calibration characteristics of the 3D dosimeters, (iii) calculating 3D dose distributions in irradiated 3D dosimeters, and (iv) comparing 3D dose distributions obtained from measurements with the aid of 3D dosimeters and calculated with the aid of treatment planning systems (TPSs). The main features and functions of the software are described in this work. Moreover, the core algorithms were validated and the results are presented. The validation was performed using the data of the new PABIGnx polymer gel dosimeter. The polyGeVero® software simplifies and greatly accelerates the calculations of raw 3D dosimetry data. It is an effective tool for fast verification of TPSgenerated plans for tumor irradiation when combined with a 3D dosimeter. Consequently, the software may facilitate calculations by the 3D dosimetry community. In this work, the calibration characteristics of the PABIGnx obtained through four calibration methods: multi vial, cross beam, depth dose, and brachytherapy, are discussed as well. Keywords: polyGeVero®, 3D dosimetry software, radiotherapy dosimetry, polymer gel dosimetry, 3D dosimetry, TPS verification, PABIGnx calibration (Some figures may appear in colour only in the online journal)

0031-9155/14/154111+26$33.00  © 2014 Institute of Physics and Engineering in Medicine  Printed in the UK & the USA 4111

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1. Introduction Techniques used in radiation therapy for treatment of tumors involve state-of-the-art irradiation devices that generate high-energy photon and electron beams, comprising radionuclide-based sources or sources of accelerated particles. Advanced treatment planning systems (TPSs) are used for the development of 3D radiation dose distribution, and irradiation devices are employed for precise delivery of a 3D dose distribution to a planned treatment volume. The gravity of radiation therapy necessitates that the planned dose distribution exactly matches the region being cured and spares adjacent healthy tissue. Therefore, this kind of treatment calls for effective dosimetry for accurate 3D measurements of radiation dose distribution and verification of TPSs and TPS-generated plans for the irradiation of tumors. Among the wide range of dosimetric systems for radiotherapy, polymer gel dosimetry has attracted great attention due to its high capability to measure the radiation dose distribution in three dimensions with a high resolution. Three-dimensional polymer gels are the dosimeters used in this technique. For more information on polymer gel dosimetry a reader may see, for example, a review by Baldock et al (2010), while Adamovics and Maryanski (2006) present a different form of 3D dosimetric systems. The polymer gel dosimeters are measured with different techniques, such as ultrasonography (US) (Atkins et al 2010, Mather et al 2002a, b), computed tomography (CT) (Jirasek and Hilts 2009), magnetic resonance imaging (MRI) (e.g. De Deene, 2009, De Deene 2010), and optical computed tomography (OCT) (Gore et al 1996, Doran 2009, Sobotka et al 2012). However, MRI seems to be the most advanced and useful technique for measuring the gel dosimeters of all scanning methods. The outcome of the 3D scanning of polymer gel dosimeters is raw data in the form of a set of 2D planes or 3D cubes, which are processed by most groups using, for instance, MATLAB® software (MathWorks, Inc.). This requires the ability to write different protocols for any new experiment and the ability to adapt them for a particular study. The calculation of 3D data may be laborious and time consuming as well. A solution to this problem is separate software capable of processing 3D dosimetry (and the polymer gel dosimetry) data independently of the experiment setup. The work toward such a tool was initiated and as a result the GeVero® software was obtained (Kozicki et al 2009a, b). It was capable of calculating some crucial dosimetric data for polymer gel dosimetry based on MR modality DICOM images only obtained after scanning the dosimeters. Despite its rather modest structure, it calculated linear calibration, dose distribution after application of the linear calibration, and histograms; it also allowed for comparison of two datasets based on gamma index calculations (Low et al 1998) and it could display isodoses. Another project was initiated by GeVero Co., aiming at the preparation of completely new software for 3D dosimetry of significantly expanded structure. The goal was to prepare software operating on DICOM (modality: MR, CT, US) and VFF format files and having a structure ready for other file formats, capable of fully processing 3D dosimetry data as well as storing, printing, and exporting the results as TXT, BMP files, and report forms. The main features of the presented polyGeVero® software (created in 2008–2013, using Delphi 7, Embarcadero Technologies) are: (i) fast calculating calibration equations based on linear, exponential, and polynomial functions; (ii) calculating calibration equations through different calibration approaches (described below); (iii) the brachytherapy database with the characteristics of the mostly used isotopes in brachytherapy that is adapted for the brachytherapy calibration calculations; (iv) storing the calibration equations and characteristics of the dosimeter’s calibrations in a separate database; (v) calculating dose distributions in 3D after application of the calibration equations; (vi) comparing two datasets of dose distributions, e.g. gel dosimetry dose distribution results with TPS-generated plans of dose distribution, by means 4112

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of typical tools used in radiotherapy dosimetry calculations either on the basis of 2D–2D or 3D–3D calculations; and (vii) displaying dose distributions as 3D images. This article makes the reader familiar with the software and the results of its validation. The calibration methods (multi vial, cross beam, depth dose, brachytherapy) of PABIGnx polymer gel dosimeter (Kozicki 2011) are discussed as well. 2.  Materials and methods 2.1.  Brief description of the software

The polyGeVero® software is composed of four workspaces: (i) Calibration Workspace, (ii) Calibration Curve Summary Table Workspace (CCST), (iii) Gel Dosimetry Dose Distribution Workspace (GDDD), and (iv) Gel Dosimetry versus Treatment Planning System Workspace (Gel dosimetry versus TPS). They have been designed such that the user can calculate data obtained by scanning 3D dosimeters with magnetic resonance imaging, computed tomography, optical computed tomography, and ultrasonography. Consequently, VFF (presently the VFF files of VISTA Cone Beam Optical CT, Modus Medical Device, Canada) and DICOM type files are allowed for calculations; however, the structure of the software can be expanded for the other type of files as well. The outcome of calculations done in polyGeVero® can be exported as TXT and BMP files (1D and 2D graphs: signal and dose maps as well as profiles and other results) or printed and saved as BMP images or in the form of reports. In the Calibration Workspace, the user will find tools for the calculations of calibration equations based on a few calibration options: multi vials (in this method a few vials are used and usually irradiated with two to three bands of different doses); depth dose (a few vials are used to observe the build-up of the absorbed dose and its decrease along a longer axis of a vial); cross beam (the beams of ionizing radiation are crossed in a polymer gel dosimeter phantom resulting in several bands of different absorbed doses within one phantom and one plane); and brachytherapy (the method usually employs one calibration phantom irradiated with a brachytherapy isotope). In case of the brachytherapy calibration, the software is equipped with brachytherapy calibration database. This editable database comprises characteristics of most brachytherapy sources as well as algorithms for calculation of the dose versus distance relation for a source. The parameters of sources, dose rate constants, types of sources, and their models and characteristics were taken from www.physics.carleton.ca/ clrp/seed_database/ (June 2009) with the permission of the database’s authors as stated on the website (Taylor and Rogers 2008). Calibration equations that are calculated in the Calibration Workspace are stored with the calibration characteristics in the Calibration Curve Summary Table Workspace. This workspace serves as a database of calibration curves created by the user. The next workspace: Gel Dosimetry Dose Distribution, was designed for calculating the 3D cube of absorbed dose distribution (*.vec file) of a 3D dosimeter—for example, a polymer gel dosimeter—for further use in the Gel Dosimetry versus Treatment Planning System Workspace. For MR modality, raw data in the form of echo images obtained after scanning is calculated using monoexponential decay function that leads to T2 relaxation time images. These are transformed into R2 images (1/T2), which are further used for dose distribution calculations after the application of a calibration equation (exponential, linear or polynomial). The 2D dose images are transformed in a 3D dose cube as mentioned previously. Finally, the Gel Dosimetry versus Treatment Planning System Workspace is to compare two datasets of dose distributions, e.g. obtained from a 3D dosimetry, *.vec, (e.g. the polymer gel dosimetry), and a treatment planning system. The comparison of datasets is done on the basis of calculations of the gamma index, gamma angle, dose difference, and correlation (Pearson’s 4113

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coefficient) of two datasets of dose distributions as well as histogram calculations for these datasets and for the gamma index, gamma angle, and dose difference results. Profiles, isodoses, and planes of 2D dose distributions can also be viewed and compared in any desired plane (XY,YZ, ZX) in the whole 3D matrixes. Finally, for better visualization of data, polyGeVero® is equipped with tools for displaying a single 2D plane and multiple 2D planes of dose distribution in three dimensions. 2.2.  Correctness of algorithms

The correctness of the algorithms was proven by comparing the output of calculations performed by polyGeVero® with the output of calculations done by other software. For the validation of the core algorithms, the following software packages were used: OriginPro 8.1 (OriginLab Corporation, USA), Osiris 4.1.8 (Digital Imaging Unit, Switzerland), MS Excel 2002 (Microsoft Corporation, USA), Microview 2.1.2 (GE Healthcare, UK), RadiAnt DICOM viewer (Medixant, Poland), OmniPro IMRT 1.4.0.1 (Scanditronix Wellhofer, Sweden), and MATLAB® 6.5 (MathWorks, Inc., USA). The procedure adopted for the polyGeVero® validation was as follows. Correct uploading of data and reading of pixel values of DICOMs and VFF files were performed by comparing the values displayed by polyGeVero® with those displayed by Osiris, RadiAnt, and Microview for some images. For instance, the values of a randomly chosen pixel of an MR echo were compared and were equal to 343 for RadiAnt, Osiris, and polyGeVero®. A similar observation was made for a CT image and a US image: values of 31 and 81, respectively, for a chosen pixel were read in every software package. In the case of VFF files, Microview showed a value of 18.028 for a pixel, whereas polyGeVero® showed a value of 18.0277. This insignificant difference in pixel values for VFF files stems from the display of a number of significant digits by the software packages. Consequently, it was concluded that there are no differences between the results obtained by these software applications. Afterwards, the core algorithms of each Workspace were examined through the calculations of the same datasets in polyGeVero® and another selected software application. The algorithms of the Calibration Workspace, that is, the calibration curve calculations by polyGeVero®, were verified through the comparison of results with those calculated by MS Excel 2002 and OriginPro 8.1. However, the brachytherapy calibration calculations by polyGeVero® were verified by comparing the results with the data calculations by MATLAB 6.5 provided by Dr L Petrokokkinos (University of Athens, Greece; see also Petrokokkinos et al 2009). Validation of the algorithms of the Gel Dosimetry Dose Distribution Workspace, that is, the dose distribution calculations by polyGeVero®, was done. The algorithms responsible for the calculation of the dose distribution using linear, exponential, and polynomial calibration equations were tested by comparison of the results calculated by polyGeVero® with those obtained from OriginPro 8.1. The algorithms of the Gel Dosimetry versus Treatment Planning System Workspace of polyGeVero® were verified through the comparison of calculations of the same datasets performed with polyGeVero® and OmniPro IMRT software. An IMRT 3D plan (RTDose) of a brain tumor irradiation generated with the aid of an Eclipse external beam planning system as described in section 2.3.3 was used. This plan was uploaded as two datasets into polyGeVero® and OmniPro IMRT in order to calculate the gamma index, gamma angle, gamma index profiles, dose difference, correlation between two datasets, and histograms, and to represent data in the form of isodoses. The calculations were performed for two randomly chosen transverse (axial) planes of the IMRT 3D plan (XY for polyGeVero® and ZX for OmniPro IMRT) lying at different depths (depth: Z axis in polyGeVero® and Y axis in OmniPro IMRT) equal to 155.6 mm and 158 mm. 4114

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2.3.  Source of data

An experimental calibration of a polymer gel dosimeter was performed in order to collect data for the verification of the polyGeVero® software’s algorithms. Also, a plan of 3D dose distribution in a polymer gel dosimeter was prepared for the same purpose with a TPS, as described below. 2.3.1. Preparation of PABIGnx.  A PABIGnx polymer gel dosimeter, which was first pre-

sented elsewhere (Kozicki 2011), was chosen in order to collect data for the verification of the polyGeVero® software’s algorithms. Details on its preparation are as follows. Poly(ethylene glycol) diacrylate (PEGDA, Mn = 700 g mol−1; Aldrich), N,N'-methylenebisacrylamide (MBA; Aldrich), gelatine (type A, 300 Bloom; Sigma), copper sulfate pentahydrate (CuSO4 × 5H2O; Chempur), ascorbic acid (AsAc; Chempur), and distilled water were used for the preparation of the dosimeter samples. Initially, MBA (4% w v − 1) was dissolved at 45 °C. Afterward, gelatine (5% w v − 1) was added in portions and the mixture was stirred until it was transparent. Next, it was cooled down to around 25 °C in order to add PEGDA (4%  w v − 1). Finally, copper sulfate pentahydrate (0.0004% w v − 1) and ascorbic acid (0.007% w v − 1) were added. After thorough mixing, the liquid composition was poured into phantoms, referred to below as calibration phantoms, and left for 24 h in order to solidify completely. The density of the gel and the elemental composition by weight were equal to 1.02 g cm − 3 at 23 °C and 10.838 1H, 7.399 6C, 1.777 7N, 79.986 8O, 9.98 × 10 − 7  − 7 29Cu, and 5.03 × 10 16S, respectively. Four calibration methods are available in polyGeVero®; however, the software is not restricted to these. These are multi vial calibration, cross beam calibration, brachytherapy calibration, and depth dose calibration. Therefore, the calibrations of PABIGnx were performed according to these methods to collect the data required for the purpose of verification of the polyGeVero® algorithms. It should be noted that the depth dose calibration did not require application of a TPS. However, it is also interesting to examine 3D dosimeters’ calibrations when applying different geometries of dose distributions toward simplification of the dosimetric method and reduction of the calibration time and total volume of the calibration gel dosimeter (and thus the cost of calibration). Thus, the other calibration methods (multi vial and cross beam calibrations) were applied as well for the purpose of data collection for the verification of the software, which required the use of a TPS. Different dosimetric phantoms were used to conform to the requirements of each calibration. Cross beam calibration and brachytherapy calibration phantoms (GeVero Co., Poland) were each filled with around 600 cm3 of the PABIGnx composition (height of the phantom: 150 mm; inside diameter: 80 mm). The brachytherapy calibration phantom was equipped with a quartz tube (outside diameter: ~4 mm; inside diameter ~2.3 mm) adapted for a plastic catheter for irradiation (plastic catheter: outside diameter: ~2 mm; inside diameter ~1.1 mm). The volume of the eight glass phantoms for the multi vial calibration was ~50 cm3 (height: 200 mm; inside diameter: 20 mm; wall thickness: 1 mm). Three depth dose calibration phantoms (GeVero Co., Poland) were filled with approximately 950 cm3 of the polymer gel composition (height: 350 mm; inner diameter: 60 mm). The choice of the brachytherapy phantom with a quartz tube adapted for insertion of the plastic catheter is explained as follows. In our preliminary studies, we used both GeVero Co. Brachytherapy calibration phantom with a quartz tube adapted for insertion of a plastic catheter and the phantom with the plastic catheter only. The effect of polymerisation and crosslinking of the gel’s components (in form of opaque cloud around the source position) was slightly larger in the case of the phantom with the quartz tube and the catheter. Although it should be 4115

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further proven experimentally, we can assume now that the plastic catheter is permeable to air and the following explanation of the observed phenomenon can be given. In the case of the phantom with a plastic catheter, the radical polymerisation processes might have been altered due to a continuous flow of oxygen into the gel volume. Once oxygen appears around growing polymer chains, the radical polymerisation is stopped. In fact, inhibition of radical polymerisation by oxygen is a well-known phenomenon. However, it seems that the oxygen infusion is low enough to allow for polymerisation of monomer ingredients at a distance closer to the catheter and higher dose rate. In fact, it is known that at a dose rate high enough, oxygen can be consumed and radical polymerisation may proceed. For this reason, the opaque cloud around the source position appeared but was smaller than for the other phantom. Furthermore, the infusion of oxygen into the plastic catheter-equipped phantom propagates on the dose sensitivity of the gel phantoms such that it is higher for phantom with the quartz tube than the plastic catheter only (0.0787 and 0.0652 1/(Gy × s), respectively). The different effects of polymerisation for two phantoms observed in this study are similar to the ones described elsewhere (Pantelis et al 2005). Based on our observations it seems, however, that PABIGnx is much less vulnerable to this effect than the former composition of PABIG. Consequently, the construction of the brachytherapy phantom with the quartz catheter is considered to be superior to the other one for those polymer gel dosimeter used, since it eliminated the aforementioned effect. 2.3.2.  Irradiation of PABIGnx calibration phantoms.  Three phantoms designed for depth dose

calibration were irradiated in a water phantom (RFA-300, Scanditronix Wellhofer, Uppsala, Sweden) to provide proper scattering conditions. The distance from the source to the inner surface of the PABIGnx phantom’s 1 mm-thick upper window (SPD) was equal to 950 mm. The field of the photon beam was equal to 100 × 100 mm, and the prescribed doses at a distance of 50 mm from the gel dosimeter’s surface (at the isocenter of the machine) were equal to 2.5, 10.0 and 35.0 Gy for the three vials, respectively. Note that the construction of the GeVero Co. depth dose phantom is such that on its top there is a 1 mm-thick window. The depth dose calibration phantom is placed in the water phantom such that this window is above the water level. Consequently, the surface of the gel matches the surface of water in the water phantom. The irradiation setup and the depth dose phantoms are presented in figure 1. The irradiation of the depth dose phantoms was performed with the aid of a Clinac 2300 CD 6-MV photon beam at 300 MU min − 1 (Varian Medical Systems, Palo Alto, CA). The parameters of irradiation were calculated after the percentage depth dose (PDD) had been measured with the aid of a CC13-S ionization chamber (Scanditronix Wellhofer, Uppsala, Sweden). The point dose (Gy), however, was measured with an FC65-G ionization chamber with a Dose 1 electrometer (Scanditronix Wellhofer, Uppsala, Sweden) at 5 cm depth, which was used for the conversion of PDD into depth dose in Gy. Combined standard uncertainty of dose measured with FC65-G ionization chamber equals to 1.5% according to the technical reports series of IAEA (TRS 2000). The so-obtained depth dose (Gy) was used afterwards for PABIGnx calibration curve calculation. The calibration phantoms that were prepared for the multi vial Calibration were placed centrally inside a cubic phantom of RW3 plates (18 × 18 × 18 cm3 cube) (Scanditronix Wellhofer, Uppsala, Sweden) (Christ 1995, Tello et al 1995). Each vial that was placed inside the phantom was additionally fixed with the application of paraffin wax. Before irradiation, the RW3 with a PABIGnx phantom was scanned (CT, Siemens, Somatom Sensation Open, 1.5 mm step) and 2D CT images were transferred to a treatment planning system (TPS). The Analytical Anisotropic Algorithm (v. 7.5.18) for photons was implemented in the Eclipse external beam planning system (Varian Medical Systems, Palo Alto, CA) in order to calculate two bands 4116

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Figure 1.  A depth dose calibration. (a) A view of the experiment setup; a single depth

dose GeVero Co. phantom was immersed in a water phantom and centred beneath an accelerator head. The dosimeter’s surface matches the surface of water. The opaqueness of the phantom denotes the post-irradiation effect in the gel dosimeter. (b) The phantoms as seen after irradiation with different prescribed doses; from bottom to top: 2.5, 10.0, and 35.0 Gy. (c) A view of the GeVero Co. depth dose calibration phantom with MRI plane, a position of R2 versus distance profile and a 1 mm-thick window indicated. 4117

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each with a different maximum dose with 6 cm spacing between the centers of the consecutive 3 cm-long bands. The irradiation was performed with the aid of a Clinac 2300 CD 6 MV photon beam at 300 MU min−1 (Varian Medical Systems, Palo Alto, CA; a four-field box technique was applied to irradiate each band). The doses (Gy) with corresponding standard deviations were as follows: 0.5 ± 0.0, 1.0 ± 0.0, 2.0 ± 0.0, 3.0 ± 0.0, 4.5 ± 0.0, 6.0 ± 0.0, 12.1 ± 0.1, 14.0 ± 0.1, 16.2 ± 0.1, 18.0 ± 0.1, 28.4 ± 0.1, and 30.1 ± 0.2 (the regions for the mean dose and standard deviation calculations were taken individually for each dose form the region of maximum prescribed dose and ranged from 10 × 10 to 12.5 × 12.5 mm; see also section 2.3.4). In figure 2(a), a print screen of the TPS during preparation of the irradiation plan is presented. A vial with PABIGnx is centrally located inside the RW3 multislab phantom and two bands of dose distribution can be discerned. Figure 2(b) illustrates the RW3 phantom with the dosimeter’s vial after irradiation. An accelerator head is above the phantom and opaque regions in the vial correspond to the irradiated parts of the dosimeter. A phantom designed for the cross beam calibration was irradiated according to a predefined plan. After being filled with PABIGnx, it was scanned (CT, Siemens, Somatom Sensation Open, 1.5 mm step), and 2D CT images were transferred to a TPS. The Analytical Anisotropic Algorithm (v. 7.5.18) for photons was implemented in an Eclipse external beam planning system (Varian Medical Systems, Palo Alto, CA) in order to calculate two irradiation planes of the PABIGnx polymer gel, each 35 mm thick. Each plane consisted of four fields comprising the areas of a quasi-uniform dose distribution (20 × 20 mm). Consequently, this method provided eight calibration points for the maximum doses (standard deviation is provided for each dose calculated): 2.4 ± 0.0, 5.4 ± 0.1, 7.4 ± 0.1, 9.6 ± 0.1, 13.1 ± 0.2, 22.4 ± 0.4, 30.6 ± 0.5, 37.8 ± 0.5 Gy (each dose was calculated as a mean value from 25 pixels (12.5 × 12.5 mm) taken from the center of the maximum prescribed dose). The irradiation was performed with the aid of a Clinac 2300 CD 6 MV photon beam at 300 MU min−1 (Varian Medical Systems, Palo Alto, CA). The irradiation scheme of the phantom, the phantom with PABIGnx after irradiation with the irradiation planes indicated and a cross section of a TPS-generated plan of irradiation are presented in figure 3. A brachytherapy calibration phantom with PABIGnx was irradiated with a 192Ir source (303.2 GBq; 8.2 Ci; Reference Air Kerma Rate (RAKR) 33.3 mGy h−1; capsule dimensions: 1.1 mm diameter; 5.1 mm length; source pellet dimensions: 0.6 mm diameter; 3.5 mm length; GammaMed 12i HDR, Varian Medical Systems, USA). The irradiation procedure was to deliver 10 Gy at a distance of 10 mm from the source, perpendicular to the longer axis of the source at a single dwell position. The GeVero Co. brachytherapy calibration phantom filled in with PABIGnx and irradiated is presented in figure 4(a). Note that the quartz tube is indicated in figure 4 as well as the zone of irradiation. 2.3.3.  A TPS plan of dose distribution.  A real IMRT plan of irradiation of a brain tumor was

converted into a dose distribution in a 3 dm3 PABIGnx glass phantom (3–4 mm wall thickness) imitating the human head and neck (GeVero Co. Poland) with the aid of an Eclipse external beam planning system (Varian Medical Systems, Palo Alto, CA). The setup of IMRT irradiation of the phantom was left as initially calculated for the irradiation of the tumor (inter alia: fluences, gantry parameters, and MU = 300 MU min − 1). The only exception was that the originally prescribed dose of 60 Gy/100% was reduced to 20 Gy/100%. The so-prepared 3D dose distribution plan was used for the verification of the polyGeVero® algorithms. 2.3.4. Measurements of phantoms with PABIGnx. Algorithms of calibrations calculations.  The measurements of all PABIGnx vials were performed with the aid of a Siemens

Avanto magnetic resonance (MR) whole body scanner (1.5 T; syngo MR B17 software). 4118

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Figure 2.  Multi vial calibration. (a) TPS (Eclipse External Beam planning)-generated dose distribution for this type of calibration. The RW3 multislab phantom, with a centrally placed calibration vial with PABIGnx dosimeter, is visible in the TPS at different geometries. Two bands of dose to be delivered to the dosimeter’s vial can be discerned. (b) The RW3 phantom with the dosimeter’s vial as seen with the naked eye after irradiation (an accelerator head is above the phantom). The vial is partially removed from the phantom to illustrate the effect of irradiation (opaque regions). (c) A print screen of the polyGeVero® Gel dosimetry versus TPS workspace to illustrate the method of the multi vial calibration calculations. A TPS dose (Data 1) and R2 PABIGnx (Data 2) distributions are uploaded and synchronized in 3D. The profiles for the two datasets along the X axis are to help in the selection of a region of interest for the dose and R2 bands. The histogram window contains calculated data for the ROIs: minimum, maximum and mean dose and R2 values with standard deviations, as well as number of points taken for the calculations. Note that this workspace will naturally name the R2 PABIGnx data as dose distribution. However, it should be treated as R2 (1/s) distribution—see explanation in section 2.3.4. 4119

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Figure 3.  A cross beam calibration. (a) TPS generated dose distribution for this type of calibration. There are two planes of irradiation and four square regions of different doses at each plane. (b) A cross beam calibration GeVero Co. phantom filled with PABIGnx polymer gel dosimeter after irradiation (­ Clinac 2300 CD) according to the TPS plan. Two planes of MR measurements are indicated. (c) XY plane (TPS) across the middle part of irradiated region as indicated in B (plane 1) and three profiles along X, Y and Z axes visualised by polyGeVero software. The pink square indicates the region of interest (ROI) for one of four regions of this plane from which a mean dose is calculated for the calibration purpose.

A radiofrequency (RF) head coil was used for the vials of the multi vial, brachytherapy, and cross beam calibrations, whereas an RF head and neck coil was used for the depth dose Calibrations. Before scanning, all samples were kept in an air-conditioned room 4120

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Figure 4.  Brachytherapy calibration. (a) GeVero Co. brachytherapy calibration phan-

tom with PABIGnx after irradiation. A quartz tube is fixed centrally inside the phantom. The zone of irradiation is located in the central part of the dosimeter. The MR planes were set to be perpendicular to the longer axis of the phantom as indicated. (b) The polyGeVero calculated R2 plane that is perpendicular to the longer axis of the quartz tube. The plane crosses the active part of the 192Ir source in its middle and serves for the R2 versus distance calculations. The R2 is calculated as a mean value of the pixels located on a circle of a radius equal to a distance chosen, as indicated.

with the MR device. Any transfer of the gel dosimeter vials after preparation or irradiation or during MR scanning was done with the aid of isothermal bags. A 16-equidistant-echo multi-slice sequence was optimized with respect to SNR, bearing in mind a desired resolution of scanning and limited time for the measurement. Specifically, a repetition time (TR) was equal to 4040 ms, the first echo was 50 ms, and the last one 4121

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was 800 ms. After MR scanning, 2D MR echo slices were used for calculations of the spin-spin relaxation time (T2) and corresponding R2 (1/T2) planes with polyGeVero®. The data were processed employing only 14 echoes after discarding the first two following our unpublished findings that showed that the first two echoes’ pixel values clearly deviated from the remaining 14 echoes pixel values that could be fitted with monoexponential decay function. These findings are in agreement with those published elsewhere (De Deene et al 2000). Afterwards, the calculations of the calibration curves were performed with polyGeVero® and compared with the results of calculations obtained with the other software. MR scanning of three depth dose calibration phantoms was as follows. One 5 mm-thick plane was received for each vial (in-plane resolution: 0.98 × 0.98 mm). The plane crossed the vial along its long axis exactly in the middle. For the purpose of the depth dose calibration calculations a single profile of R2 versus distance was taken from the central part of this plane (each R2 value corresponds to 1 pixel; no standard deviation was calculated contrary to the other calibration methods). A scheme indicating the plane’s and the profile’s positions is presented in figure 1(c). The polyGeVero® depth dose calibration algorithms allow for calculations of the R2 versus dose relation thanks to the option of Profile/Depth. It gives the user the possibility of matching the R2 versus distance with the dose versus distance to get the calibration relation. The dose versus distance is measured with ionizing chamber in a water phantom (refer to section 2.3.2) at the same irradiation conditions as in the case of the depth dose PABIGnx phantoms’ irradiation figure 1 and afterward is imported to the Profile/Depth workspace for further calculations. In the case of the vials for multi vial calibration, a single slice at a central plane of the phantom crossing two irradiated regions and comprising the maximum absorbed dose was measured (slice thickness 4 mm; in-plane resolution: 0.52 × 0.52 mm). The polyGeVero® algorithm of this calibration method, partially illustrated in figure 2(c), is as follows. The central plane of the phantom obtained after MR scanning is uploaded to GDDD Workspace in order to calculate *.vec file. Note that the *.vec file option is designed in polyGeVero® for the calculations of 3D dose cube. However, for the purpose of multi vial calibration it can be used for the calculation of 2D vec file of R2 (1/s) distribution. Once this file is created, it is imported in the Gel Dosimetry versus TPS Workspace as Data 2 figure 2(c). Note that the Gel dosimetry versus TPS Workspace will naturally name the R2 PABIGnx Data 2 as dose distribution that can be misleading at first glance. Simultaneously, a TPS plan of dose distribution is imported in the same Workspace as Data 1 figure 2(c). Using the Move option in this Workspace as well as the Synchronise Mode, profiles for these datasets and isodoses display, the two datasets are aligned in 3D (note that the polyGeVero® is equipped with an option of automatic spatial alignment of two 3D datasets and it can be used instead of the Move option on condition that the fiducial markers are used stuck on the vials for the polyGeVero® to calculate an isocentre point during the *.vec file calculations). The next step is to select a region of interest (ROI) for every dose and R2 band. If a ROI is selected for a dose band, a corresponding ROI for R2 band will be selected automatically. Every ROI should correspond to the region of maximum dose figure 2(c). Once ROIs are selected for one dose and R2 bands, the histogram option is initialized, which results in calculations of dose, and R2 maximum, minimum, and mean values for the ROIs as well as standard deviations and number of points used for the calculations are shown figure 2(c). The described operations should be repeated for all bands and vials that result in R2 and dose values for the preparation of the calibration relation. The phantom for Cross Beam Calibration was scanned to obtain two planes perpendicular to the vial’s long axis and crossing the irradiated regions in their middle parts, which comprised four square fields of different doses (each plane) figure 3(b). The slice thickness was 4122

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equal to 3 mm and the in-plane resolution was 1.02 × 1.02 mm. The polyGeVero® Cross Beam Calibration algorithm is analogous to the one of the multi vials calibration. First, two datasets of TPS dose and R2 MR distributions are uploaded and synchronized in 3D in the Gel dosimetry versus TPS Workspace. Next, ROIs are selected for eight areas of maximum dose and corresponding R2 using the approach described for the Multi Vial Calibration. For this purpose, the analysis of profiles for the irradiation areas in X, Y, and Z directions was performed as well figure 3(c). The position of one ROI can be seen in figure 3(c) for one of four areas of an irradiation plane from which a mean dose is calculated using the histogram option. Once the doses and corresponding R2 values are calculated, the R2 versus dose calibration relation is obtained. The brachytherapy calibration phantom was scanned so that the whole irradiated region was covered. Two-dimensional planes were received perpendicularly to the catheter’s (and the quartz tube) longer axis figure 4(a). The slice thickness was set to 1 mm and the in-plane resolution was 1.02 × 1.02 mm. Based on the MR images obtained the polyGeVero® brachytherapy calibration algorithm created 3D R2 cube and calculated the mass centre of the irradiated part of PABIGnx. Note that the mass center is the center of the active part of the source. Afterward, the MR plane at which the center is located was searched and displayed by polyGeVero ­figure 4(b). The next step of the brachytherapy calibration algorithm is to search for the relation of R2 versus distance from the mass center. This is performed as indicated in figure 4(b). At each distance chosen, R2 is calculated as a mean value of pixels located on a circle of a radius equal to this distance. The R2 versus distance is related by the polyGeVero® algorithm to the dose versus distance in order to obtain the brachytherapy calibration dependence of R2 versus dose. For the dose versus distance relation calculation for the particular brachytherapy source, an option of Brachycalibration Dose versus Distance must be chosen. The calculations are performed automatically based on the line approximation approach (Rivard et al 2004) after indication of the source model, Air Kerma Strength, r step for geometry factor calculation, radial dose function, and time of irradiation of the PABIGnx phantom. For the purpose of verification of the main polyGeVero® algorithms, the MR data received as previously described for the phantoms with PABIGnx were sufficient, and therefore the verification results for these data are presented below. However, it should be noted that the algorithms were also examined with very good results for the data obtained from scanning the dosimeter phantoms with CT (Picker, PQ 2000; scanning conditions: KVP (Peak KV) = 120; slice thickness = 1.5 mm; x-ray tube current (mA) = 150; pixel spacing = 0.2 mm). Some phantoms were also scanned with US (Siemens, Antares) in order to obtain any data of this modality. It should be noted, however, that due to the restrictions of this scanning technique and poor results obtained, the calculations of the PABIGnx present no scientific value in terms of the calibration characteristics. Nevertheless, the correctness of calculations done with polyGeVero® was confirmed for this modality as well. The polyGeVero® algorithms were also successfully validated for the VFF type files (the example VFF files were obtained through the courtesy of Modus Medical Devices, Inc.). The validation of the algorithms was performed by comparing the calculations with those done using MS Excel 2002 and Origin Pro 8.1. 3.  Results and discussion 3.1.  Validation of the software 3.1.1. Algorithms of calibration workspace.  The main algorithms in this Workspace include calculations of cross beam, multi vials, depth dose, and brachytherapy calibrations. For the MR modality of DICOM images, the correctness of the relaxation rate calculation, 4123

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2.5 MSExcel 2002 + Origin Pro 8.1 ® polyGeVero

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dality. The profile was calculated for PABIGnx polymer gel phantoms irradiated such that at 50 mm depth the absorbed dose was equal to 10 Gy. The polyGeVero® results are compared with those obtained with the aid of MS Excel 2002 and Origin Pro 8.1.

R2, for the depth profiles along the depth dose calibration phantoms was examined. Three phantoms with irradiated PABIGnx to doses of 2.5, 10, and 35 Gy at 50 mm were scanned as described previously. We found that the R2 profiles obtained by polyGeVero®, MS Excel 2002, and OriginPro 8.1 are alike; one of them is shown in fi ­ gure 5 as an example result. This proved the correctness of the calculation of the relaxation rate by the software under examination. Afterward, the algorithms for calculation of the calibrations were examined. The results are presented in figures 6(a)–(d). For all calibration methods under examination, we observed that the results of polyGeVero® match those obtained through the calculations with the other software. It should be noted that the complexity of the brachytherapy calibration calculations required separate algorithms, which were prepared independently in MATLAB® (provided by Dr L Petrokokkinos; University of Athens, Greece; see also Petrokokkinos et al 2009) and applied for the same dataset as for the calculations in polyGeVero®. The comparison of the results in figure 6(d) shows no difference between the calibrations calculated with the two software packages. It should be noted, however, that the calculations of the brachytherapy calibration with polyGeVero® may take approximately two to three minutes (including uploading raw data), which is definitely not the case for the calculations done with the aid of MATLAB®. A concise discussion of the calibration results for PABIGnx can be found in section 3.3. 3.1.2.  Algorithms of gel dosimetry dose distribution workspace.  This Workspace comprises a

range of tools adapted for transformation of DICOM or VFF raw data obtained from scanning of a 3D dosimeter into a 3D cube of dose distribution. The core algorithms include calculation of dose distribution after application of a calibration equation and transformation of a 3D dose cube into a formatted cube adapted for further calculations in the next Workspace. Of outmost importance was the verification of algorithms responsible for transformation of raw data into radiation dose distribution results. The same algorithms in this Workspace are used for relaxation rate calculations as in the Calibration Workspace. Since they were verified as described in section 3.1.1, we focused 4124

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tion; (b) cross beam calibration; (c) depth dose calibration; (d) brachytherapy calibration. Origin Pro 8.1 and MS Excel 2002 were used for the calculations of (a)–(c), and MATLAB 6.5 was used for the calculations of (d). The calibration results of the PABIGnx polymer gel dosimeter are presented for the MR modality. Inset in C is a comparison of all calibrations for PABIGnx obtained with polyGeVero®.

immediately on validation of the algorithms for calculation of the dose distribution using linear, exponential, and polynomial calibration equations. The same DICOM files were used as in the case of cross beam calibration and the relaxation rate was calculated in polyGeVero®. Afterward, an R2 profile across one plane was imported into OriginPro 8.1 for further calculations of the dose profile in this software. For the same R2 profiles, we obtained dose profiles in polyGeVero®. The following equations were used for dose profile calculations: R2 = 0.0975 × D + 1.0246; R2 = 1.111 × Exp(0.0574 × D) − 0.0004557 and R2 = 0.08247 × D + 0.00303 × D2 − 0.000178 × D3 + 2.18 10 − 6 × D4 + 1.04113. The results of the comparison of dose profiles calculations in the two software packages are presented in figure 7. It was concluded that both software packages calculate dose distributions alike. Consequently, the correctness of polyGeVero® algorithms for dose distribution calculations was confirmed. 3.1.3. Algorithms of gel dosimetry versus treatment planning system workspace.   The algorithms of polyGeVero® were validated through comparison of calculations with those performed in OmniPro IMRT for the same datasets. The results obtained are shown in figure 8. The gamma index indicates the difference between two dose distributions, e.g. calculated and measured dose 4125

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files, that were performed with the aid of OriginPro 8.1 and polyGeVero®. Dose profiles were calculated using (a) linear, (b) exponential, and (c) fourth-degree polynomial calibration equations (results calculated for data obtained for the MR modality). 4126

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and OmniPro IMRT. Two sets of TPS-generated data were uploaded to polyGeVero® and OmniPro IMRT and the following were obtained: (a) gamma index (left: polyGeVero®; right: OmniPro IMRT); (b) gamma index example profiles crossing the isocenter and drawn along the X and Y(Z) planes presented in (a) as well as the gamma index histogram for the two datasets; (c) gamma angle (left: polyGeVero®; middle: polyGeVero® with altered gamma angle algorithm (see explanation in section 3.1.3); right: OmniPro IMRT); (d) difference between the two datasets (left: polyGeVero®; right: OmniPro IMRT); and (e) isodoses (left: polyGeVero®; right: OmniPro IMRT). 4128

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distributions, with respect to the acceptance criteria. Therefore, polyGeVero® was equipped with the gamma index (γ) algorithm based on the description provided by Low et al (1998): γ(1) ( rm ) = min{ Γ ( rm,   rc ) } ∀ { rc } r 2 ( rm, rc ) δ 2 ( rm,   rc ) (2) ( rm,   rc ) = Γ + 2 2 ΔdM ΔD M r(3) ( rm,   rc ) = rc − rm δ(4) ( rm,   rc ) = Dc ( rc ) − Dm ( rm )

where:rm is a single measurement point, coordinates (xm, ym, zm); rc is spatial location of the calculated distribution relative to the measured point, coordinates (xc, yc, zc); δ is the difference between dose values on the calculated (DC ( rc )) and measured distributions (Dm ( rm )), respectively, and ΔD M, ΔdM—see below. For the gamma index calculations, the dose-difference, ΔD M, and the distance-to-­ agreement, ΔdM, criteria were set to 3% and 3 mm, respectively. The pass/fail criterion of calculation for the gamma index is  ≤ 1 for pass and  > 1 for fail. In figure 8(a), gamma index calculations obtained for polyGeVero® and OmniPro IMRT are presented. From the comparison of the colored planes for the two software packages, one can draw conclusions about the similarities in gamma index values (note that the color scales of these software packages differ slightly, which can be misleading at first glance). For instance, at x = 0 and y = 0 mm for polyGeVero® and x = 0 and z = 0 mm for OmniPro IMRT, the gamma index value is equal to 0.244 and 0.24, respectively. Pixel-by-pixel comparison was also performed for more detailed assessment. The outcome in the form of gamma index profiles along the X and Y(Z) axes and a gamma index histogram is shown in figure 8(b). The mean gamma index values calculated by polyGeVero® and OmniPro IMRT are equal to 0.264 (SD = 0.3) and 0.26 (SD = 0.24), respectively. Following analysis of these results, we concluded that there is no significant difference between calculations of the gamma index by polyGeVero® and OmniPro IMRT. The gamma angle, defined as the angle between the δ axis, representing the difference between the measured and calculated doses, and the vector Γ , according to a description by Low et al (1998), can show the difference between the calculated and measured dose distribution due to ΔD M or ΔdM. Therefore, the gamma angle can be helpful in understanding the differences between two datasets of dose distributions. It points to the parameter mostly influencing the gamma index value ΔD M or ΔdM. If the gamma angle changes from to 45° to 0°, the vector Γ tends to the δ axis, which expresses the gamma index affected mainly by ΔD M. Consequently, for the gamma angle values from 45° to 90° (the vector Γ tends to ΔdM plane), the influence of ΔdM on the gamma index predominates. Thus, this helpful analysis of the gamma angle was included in polyGeVero® calculation options. The results of gamma angle calculations in polyGeVero® and OmniPro IMRT are presented in figure 8(c). Although at first glance the results seemed to be similar, thorough analysis revealed a distinctive difference between the gamma angle values calculated by both software packages. We assumed that OmniPro IMRT algorithms define the gamma angle in another way to the definition provided by Low et al (1998). It seemed that in this software the angle is between the vector Γ and the ΔdM plane. Thus, at the points x = 0, y = 0 in polyGeVero® and x = 0, z = 0 in OmniPro IMRT, the gamma angles are equal to 0° and 90°, respectively. To confirm our supposition, the gamma angle algorithm of polyGeVero® was temporarily altered to comply with the assumed one of OmniPro IMRT and 4129

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Table 1.  A test results of calculations speed in polyGeVero®.

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Calibration

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2 min 15 s

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MR images:16-echo based Layers: 62 Spacing: 1.5 × 1.5 × 1.5 mm Number of pixels of 1 layer: 16384

Gel dosimetry versus TPS TPS dose cube: Spacing: 2.5 × 2.5 × 2.4 mm Number of l­ayers: 100 Number of pixels of 1 layer: 5460 Gel dosimeter dose cube: Spacing: 1.5 × 1.5 × 1.5 mm Number of layers: 92 Number of pixels of 1 layer: 16384 Time required for completion of the test

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the calculations were performed again. As a result, we obtained the same gamma angle plane in polyGeVero® as in the case of OmniPro IMRT figure  8(c). The gamma angle algorithm in polyGeVero® has been left as originally prepared according to the description by Low et al. Both gamma index and gamma angle calculations in polyGeVero® can be performed in various modes. Namely, one can calculate these in 2D or 3D mode; additionally, one data can be calculated versus the other data and the other way round. Besides, these calculations can be performed for different areas of data including all planes at once. In case of 2D mode for gamma index and gamma angle, the calculations are performed for e.g. two XY planes selected for two datasets and Z direction (a spatial shift between them) is neglected according to Low et al (1998). The 3D mode introduced in polyGeVero® 4130

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software includes Z direction as well, which means that the calculations take into account a spatial shift between the selected planes (analogously, the 3D mode serves for the dose difference and correlation parameters calculations). In 2D and 3D mode, r parameter is given by the following equations (5) and (6), respectively: r(5) = ( x m − xc )2 + ( ym − yc )2 r = ( x m − xc )2 + ( ym − yc )2 + ( zm − z c )2 (6)

The polyGeVero® software allows quick calculations of the dose difference between two datasets for all planes at once. We have compared this kind of calculation with the results from OmniPro IMRT. The two software packages show the same results; for instance, at x = 0, y = 0 (mm) for polyGeVero® and x = 0, z = 0 (mm) for OmniPro IMRT, the dose difference is equal to  − 0.146 Gy. The results are presented in figure 8(d). Analogously to the dose difference results, we have obtained the same results from drawing isodoses and calculations of correlation for two examined datasets in polyGeVero® and OmniPro IMRT. For the correlation between two datasets, the calculated values were equal to 0.999 and 0.9988 for the former and latter software packages, respectively. The results showing the same way that isodoses are drawn by the two software applications are presented in figure 8(e). 3.2.  Speed of calculations in polyGeVero®

In view of the previously presented results, it is believed that the ease of calculations with the aid of polyGeVero®, in contrast to the complexity of MATLAB® calculations that require writing separate protocols for any new experiment, does not require further discussion. However, the speed of calculations is also a determinant of good software. Therefore, in this section, the results of a corresponding test presenting how fast polyGeVero® calculates data are shown. The calculations were performed with a computer of the following specifications: processor AMD Phenom™ II X4 965 3.4 GHz, RAM: 4 GB, operating system: 64 bit Win 7. The following pattern was adopted. First, the depth dose calibration was calculated in the Calibration Workspace based on three calibration phantoms as presented above. The calibration characteristics were exported to a database (Calibration Curve Summary Table Workspace) and the depth dose linear calibration equation was selected for calculations of dose distribution in the Gel Dosimetry Dose Distribution Workspace. In this workspace, a 3D cube of dose distribution was calculated for the head and neck phantom mentioned in this work. Next, the cube and the corresponding TPS plan of dose distribution for the head and neck phantom were imported to the Gel dosimetry versus TPS Workspace. The most complex calculations in this Workspace is the gamma index or gamma angle. Therefore, we present the speed of calculation of these parameters. The results of the test are shown in table 1. As it can be concluded from the analysis of the test results, all operations required around thirteen minutes. It should be noted that the longest operations are those by the user, for instance indication of a folder location with raw data to be calculated and typing additional information required by the software for the description of the calculations such as irradiation source, date of irradiation, etc. The calculations of gamma index and gamma angle in 3D for a relatively large sample of head and neck took less than 0.5 minute. Note also that during the test, the occupancy of the random access memory (RAM) and the processor (CPU) was monitored. CPU occupancy raised from 3% to 25%, whereas RAM occupancy did not change at all. We did not observe any malfunctioning of the computer during the test caused by calculations. 4131

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3.3. PABIGnx calibration: discussion

The very first data on the PABIGnx polymer gel dosimeter and its calibration after irradiation with a nonmedical device equipped with 60Co and measurement using 0.5 T nuclear MR was obtained earlier (Kozicki 2011). In this study, however, the dosimeter was exposed to the medical ionizing radiation sources and after imaging with 1.5 T MR the calibration characteristics were obtained with polyGeVero®. From the point of view of a medical physicist a simplification of a dosimetric method is an asset. The calibration data obtained were analyzed bearing this in mind and are briefly discussed in the following. The results for the calibration methods are presented in figures 6(a)–(d). Additionally, in the inset of figure 6(c), all calibrations are in one graph to illustrate the similarities between them. In table  2, the calculated parameters of the linear and polynomial calibration equations as well as linear and dynamic dose response assessed for PABIGnx are provided for all calibration methods (linear dose range was assessed by analyzing the change of the Pearson’s coefficient and dose sensitivity (slope) of R2 versus dose relation at different dose ranges). The results for multi vial calibration of the PABIGnx polymer gel dosimeter are presented in figure 6(a). The character of the curve is analogous to the one of cross beam and depth dose calibration. It can be seen that around the dose of about 35 Gy, the gel dosimeter saturates. The linear part is up to about 18 Gy. Despite the limited number of points, the cross beam calibration curve figure 6(b) indicates a dynamic dose response region. It is clear that PABIGnx composition saturates at around 40 Gy, as shown below for the depth dose calibration. A low number of calibration points prevents it from drawing firm conclusions about the exact dose range of the linear part; however, it is definitely below 22 and above 13 Gy. In case of the depth dose calibration method figure 6(c), three calibration vials allowed for covering the dose response region of PABIGnx polymer gel dosimeter. A dynamic and linear dose response of the polymer gel was assessed to be around 40 Gy and between 16 and 18 Gy, respectively. For the brachytherapy calibration phantom, the analysis of the R2 versus dose figure 6(d) lead to the conclusion that the dynamic range is up to around 35 Gy, whereas, the dosimeter’s linear dose response is up to 16–18 Gy. It should be noted that different calibration methods proposed for PABIGnx (depth dose, cross beam, and multi vial) gave similar results. The dose sensitivity parameter of PABIGnx (table 2) is similar for these calibration methods. This gives a chance that the methods might be used alternatively, thus allowing for reduction calibration time or total volume of the dosimeter; however, further statistical studies are required to confirm the findings on these calibration methods as well as the calibration curves parameters calculated and the dose response ranges assessed. It should be noted that the Brachytherapy calibration results clearly depart from the other ones (inset in figure 6(c)), which is discussed as follows. It was observed that the depth dose calibration method was less time consuming than the multi vial calibration and longer to perform than the cross beam and brachytherapy calibration. The number of calibration points obtained through this method was significant (210 points in this study). However, the cross beam calibration method is faster and easier to perform. By altering the calibration phantom, e.g. by increasing slightly its dimensions and so the volume of the polymer gel, one can add 1–2 irradiation planes, thus increasing the calibration points by four to eight points in order to better cover low-dose regions and the region around the bending after the linear part. Multi vial calibration is more complex to perform and is time consuming in comparison with cross beam and depth dose calibrations. The number of points constituting the curve depends on the number of the calibration vials. After irradiation of a vial, it has to be replaced with another one, which prolongs the experiment. The brachytherapy calibration, which is relatively fast and easy to perform, had one important advantage in that a great number of points (190 points in this study) were received after 4132

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