3D Dosimetric Tools in Radiotherapy for Photon Beams

The MAGIC dosimeter with formaldehyde has characteristics of tissue-equivalence to water, stability of response and high detection resolution for suitable application in 3D dosimetry for complex treatments. Especially for use in techniques of high dose rate it can verify the volume dose as a quality control in radiotherapy. The gel dosimeter with formaldehyde (MAGIC-f) has been used in simulation studies as well as in clinical [8-11].


Introduction
The technological advances to develop or improve devices for radiotherapy have increased in recent years, leading to conformality in the absorbed-dose within the tumor volume and avoiding healthy tissue. For quality assurance of the treatment, measurement of complex dose distribution from the new devices needs to be verified in the treated volume and healthy structure surrounding it.
According to ICRU the prescribed and administered dose must be within -5 % and + 7 % [1]. Many dosimetric protocols for radiotherapy recommend use of an ionization chamber like reference dosimeter, however, dosimeters like TLD, film, diode and other tools can be used although they measure the absorbed-dose at a point or in two dimensions [2,3].
A clinical system-dosimetry that can measure the dose distribution in 3D with tissueequivalent characteristics is not available. In this context, dosimetry based on gel has shown a great potential for measured dose-distribution in 3D [4][5][6][7].
The MAGIC dosimeter with formaldehyde has characteristics of tissue-equivalence to water, stability of response and high detection resolution for suitable application in 3D dosimetry for complex treatments. Especially for use in techniques of high dose rate it can verify the volume dose as a quality control in radiotherapy. The gel dosimeter with formaldehyde (MAGIC-f) has been used in simulation studies as well as in clinical [8][9][10][11].
The most common used simulation algorithms, based on Monte Carlo calculations, are ITS2, EGS4, MCNP4 and PENELOPE [12][13][14][15][16]. The algorithm for mixed transport of charged particles implemented by PENELOPE algorithm led to its use in radiotherapy, simulating several irradiations and geometry of clinical situations in radiotherapy, which have shown a good concordance with experimental measurements using different irradiation techniques [17][18][19][20]. This chapter will approach two dosimetry tools: the MAGIC-f gel dosimeter and the PENELOPE-Monte code. Also, this chapter will cover some clinical applications of the two dosimetry tools with modalities like brachytheray, radiosurgery and 3D conformal therapy.

MAGIC-f dosimeter
Gel-based dosimeters called polymer gel dosimeters have been proposed since 1954 [21][22][23][24]. In 1992, formulations like BANANA, BANG and PAG polymer gels were proposed [25,26]. The suppression of polymerization by oxygen, present in these gels, was improved with a proposition of MAGIC gel (Methacrylic and Ascorbic acid in Gelatin Initiated by Copper) [27], which allows the MAGIC polymeric gels to be prepared in normal weather conditions [28][29][30], which for higher temperatures beyond 25 °C loss stability. Thus, was add formaldehyde to the original formulation of the MAGIC, re-calling as MAGIC-f, which led to a rise in its melting point to 69 °C [31].
The monomeric compounds of the MAGIC-f dosimeter immersed in an aqueous matrix, after exposure to irradiation suffer a polymer reaction, resulting in a polymer gel matrix. This formation changes the NMR relaxation properties of the gel and can be related to the deposited energy. One way to show this change in 3D is by using magnetic resonance images.

PENELOPE code
PENELOPE (Penetration and Energy Loss of Electrons and Positron) is a package used to simulate the transport of electrons, positrons and photons in arbitrary materials and complex geometries. The package has written on a FORTRAN platform, which include characteristics of many materials, and a user file. Besides these files, the code has a database with the characteristics of various materials of interest in radiological physics [32], cross section libraries and other quantities necessary for the transport of particles [33]. The simulation algorithm is based on a model that combines numerical and analytical cross sections for different types of interactions and is applied to initial energies from 1 keV to 1 GeV. The code has been used in some applications to simulate different irradiation techniques, reproduce the dimensions of irradiation geometry, source, energy, distance and other dosimetric parameters.

Application of the two dosimetric tools for some modalities in radiotherapy
4.1. Water-equivalent calibration of 192 Ir HDR brachytheray source using MAGIC-f gel HDR brachytherapy is a treatment technique that uses sealed radioactive sources to treat prostate, colorectal cancer and some gynecological malignancies [34,35]. The commonly used implants are of 192 Ir sources with a half-life of 74 days, emitting beta rays ranging from 530 keV to 670 keV, and a gamma ray with an energy of 370 keV [36].
Due to the energy spectrum present in this source and the high gradient dose, a proper source calibration is necessary, although vendors assign large uncertainties to the calibration values (up to  10%). The calibration protocols for HDR brachytherapy sources recommend a specification in reference to air kerma rate using ionization chamber [37,38]. Absorbed dose measurement in water has recently been proposed to calibrate 192 Ir HDR brachytherapy sources [39].
For determination of the water-equivalent calibration of an 192 Ir HDR source we used the MAGI-f dosimeter, which has been shown to be a suitable dosimeter for many treatments in radiotherapy due to its characteristics of water equivalence (effective atomic number of 7.41), spatial resolution better than 1mm and the most important characteristic of measuring dose tridimensionally. Through the MAGIC-f were determined dosimetric parameters like percentage dose depth (PDD), and calibration curve (CC).
The two dosimetric parameters, PDD and CC, were obtained with the three dosimetric tools a)thermoluminescent dosimeter, b)ionization chamber and c)PENELOPE-Monte Carlo code simulation. The results obtained with these dosimetric tools were compared with the obtained data of polymer gel [40]. Measurements for PDD determinations, in water, were carried out using TLDs (LiF-100 with dimensions: 0.9 x 0.9 x 3.1 mm 3 ) packed with plastic and a plane parallel ionization chamber (Markus type, 0.05cm³) after proper calibration. Both dosimeters were introduced in different depths (from 3 up to 12 mm) in a water phantom (figure 2). The catheter containing the HDR source was set parallel to the TLDs and the ionization chamber.

Magic gel procedures
After preparation the solution of gel, this was poured in an acrylic cylindrical phantom of 6 cm diameter, 8 cm height and 0.5 cm thickness taking care to prevent air bubbles(figure 3).
During the PDD measurement the phantom filled with the gel was kept inside the water phantom and the source was positioned at a distance of 2 cm from the gel phantom wall.
(a) (b) For gel calibration, part of the gel was poured into three cylindrical glass tubes with 5ml volume, 12mm diameter and 75 mm height, closed with a 20mm hermetic stopper inserted in a plastic cover, as shown in figure 4.
Relaxation images of the gel phantom and glass tubes were acquired using a 1.5 T scanner (Siemens, Magneton Vision) one day after the irradiation to allow enough time for gel reaction completion. A head coil and multi spin echo sequences with 16 echo times in multiples of 22.5 ms, a repetition time of 3000 ms and a matrix size of 512 × 512 pixels were used during image acquisition. The slice thickness was 2mm. The transverse relaxation rate R2 (=1/T2) was calculated by fitting the signal intensities versus the echo time pixel by pixel. The R2 maps were related to absorbed dose using a specific program developed in MatLab ® 6.5.

PENELOPE-Monte Carlo
The user code was written to describe the geometry of the source and simulate all anisotropic properties of the brachytherapy extended source. A cubic water phantom were simulated, with dimensions of 30 cm, appropriate to obtain full scattering conditions. Simulation spatial resolution was set to1 mm.

Results and conclusions
Calibration curves for HDR 192 Ir source using TLD, ionization chamber and MAGIC gel are shown in figure 5.
The three dosimeters showed linearity with relative dose with correlation coefficients (R) of 0.9948, 0.9959 and 0.9971 for CI, TLD and the gel respectively. Maximum uncertainty of 3.5 % was found for measurements with the TLD for 10 Gy and a maximum uncertainty of 0.8 % was found for 10 Gy using the other dosimeter. The CC curve obtained with the TLDs did not show sensitivity for low doses (0.5 Gy) and MAGIC gel presented a background dose, approximately of 1.3 s -1 , which was subtracted for PDD measurements.
The calibration curve obtained with the Magic-f gel for the HDR 192 Ir source shows that it is possible to calibrate this source in water as stipulated in the protocol for external source [41]. Since, the gel is constituted by 90% water, effective-atomic-number of 7.41, which can be represent interaction of radiation with the water.
For PDD determinations, dose map distributions were obtained with MAGIC-f in a few planes as shown in figure 6.
The PDD curves were determined through percentage absorbed dose in depth, Dd, relative to the absorbed dose in the maximum depth, Dm, as show in equation 1 The dose maps were obtained through the relaxation images and analysed with the program, in MatLab  developed to relate the nuclear resonance signal of the image with the absorbed dose.  From the percentage depth dose and calibration curve results it can be concluded that the MAGIC polymeric gel can be used as dosimeter in routinely clinical procedures and can be used to check the calibration of 192 I sources in an water-equivalent medium as part of the assurance quality in HDR brachytherapy.

Dose-distribution of small fields through the MAGIC-f dosimeter and PENELOPE code
Some techniques in radiotherapy, like intensity-modulated radiation and stereotactic radiosurgery, use small radiation fields and higher dose-radiation. Since the dosimetry of the small fields is more critical than that for large fields, due to no-equilibrium conditions created as consequence of the secondary electron track length and the real source size project from the collimator to the phantom or patient. Other complication is the perturbation of the level of disequilibrium, which is inducted bye the dosimeter when introduced in the track of the radiation fields. Thus, due these characteristics of the small fields, an accurate dose verification of the delivery dose of the small radiation fields is required [42][43][44][45].
The aim of this application is evaluate the response of MAGIC-f dosimeter, after being exposed to a conformal irradiation technique using a small field to compare the results with PENELOPE code through two dimensional dosimetric parameters [46].

Treatment planning system (TPS)
The TPS BrainSCAN 5.31, was used to plan a conformal irradiation with the tomography images of the cylindrical phantom, with 9 irradiation fields from 0° to 340°. The prescribed dose was determined through the calculated algorithm using pencilbeam for 16 Gy in 100% of the target volume.

MAGIC-f gel and PENELOPE code
The solution of Magic-f gel was poured in a cylindrical phantom of PPMA with dimensions of 12 cm diameter, 18 cm height and thickness 0.5 cm. The phantom containing the gel was placed at source-phantom center distance of 100 cm, figure 8, from the linear accelerator (Siemens MEVATROM with multileaf MX2), irradiated with 9 fields of 6 MV photon beam, each one of 1 x 1 cm 2 , to a total dose of 16 Gy. The experimental irradiation was made in the same irradiation conditions as the TPS.
PENELOPE simulations were used to determine the percentage depth dose, beam profile and a conformational dose distribution in the same irradiation and geometry condition made by the MAGIC-f.
After the irradiation, the reading was performed through MRI using a 3 T scanner and head coil. Relaxation images were obtained using a multi spin echo sequence with 16 echo times in multiples of 22.5 ms, a repetition time of 3000 ms and a matrix size of 256 × 256 pixels. The slice thickness was 2mm for each slice. The two dose distributions obtained with the gel and PENELOPE were compared through beam profiles for each irradiated field.

Results and conclusions
The two dosimetric tools were validated through comparison PDD and BP curves. The determination of the PDD was made through the equation 1. The PDD curves are shown in the figure 9 for an irradiation field of 1 x 1 cm 2 , source-phantom center distance of 100 cm with energy of 6 MV and absorbed dose of 5 Gy.
The PDD curves obtained with the two dosimetric tools show the same behavior. Maximum differences of 6.5 % were found in 10.1 cm depth comparing the two curves.  The BP curves obtained with the two dosimetric tools show the same behavior, with maximum differences of 4.3 %, where compare both curves in distances more than size of the irradiation field. Inside the irradiation field (1 cm 2 ) the maximum difference was of 0.9 %.
The dose-distributions to a conformal irradiation technique obtained with tool dosimeters, gel and PENELOPE, are showed in the figure 11. The dose-distributions obtained were compared through the BP, as show in figure 12.
(a) (b) The comparisons between gel and PENELOPE showed maximum differences of 0.91% inside the isodose of 50% .For isodose major of 50% the difference was up to 12.3%. From the results obtained it can be infer that the response of the MAGIC-f polymeric gel is suitable and can be used routinely as a dosimeter in clinical procedures using small fields, especially in radiosurgery.

Gamma index comparison for the conformal dose-distribution trough dosimetric tools
The modern radiotherapy imposes high level of accuracy to deliver absorbed-dose in a complex way, which depends on beam energy, field size, geometry of the irradiation target and others aspects. Thus, the generated dose-distributions must be checked rigorously, both for administered and delivered dose distributions.
MAGIC-f gel with high spatial resolution, effective-atomic-number close to water and an ability to measure the dose in 3D and also, PENELOPE code are available with a high concordance and estimate measurement of dose distribution in 3D.
Comparisons of dose-distributions obtained with the simulation and experimental measures can be analyzed through a beam profile, as showed in the section 4.2, which give us a limited information of that comparison. A subtraction pixel by pixel of the dose map technique can offer more information but is not related the tolerance of the position. The gamma index is a technique that relates to tolerance with the dose and position within a limited range [47,48]. Dose-distributions obtained with the MAGIC-f gel and PENELOPE simulation were compared through the technique of gamma index [49].

Materials and methods
The dose-distributions obtained with the MAGIC-f gel and PENELOPE code were compared by determining gamma index () test. A program was developed in MalLab  , which calculated the gamma index; following the parameters of distance-to-agreement (DTA) and the tolerance of dose difference. The DTA determines the comparison tolerance of localization of one pixel from the MAGIC-f dose-distribution to the pixels within circumference, for an established radius, from the PENELOPE dose-distribution. Likewise, the dose tolerance parameter determines the comparison tolerance of dose value of one pixel from the MAGIC-f dose-distribution to the dose values to pixels within circumference, for an established radius, from the PENELOPE dose distribution.
Thus, the formulation for determining the  values, combining the two criteria: DTA and dose tolerance, are expressed in the equation 3:

Results and conclusions
As shown in the section 4.4, we obtained dose-distributions for the conformational irradiation of 9 fields of 1x1 cm 2 , using the Magic-f gel and the PENELOPE code.
Both dose-distributions were compared using the gamma index test through the program developed using the criteria of DTA of 3 mm and dose tolerance of 3 %. Figure 13 show the  map, with maximum values up to 2.5. Analyzing a central region, target volume, of 1 cm diameter from the dose-distribution obtained by the gel and PENELOPE code, 100% of the dose values pass the test under gamma index conditions. Although for regions farther than 1 cm only 57% of the dose values pass this test, which present gamma index values more than 1.
The results have shown that the response of MAGIC-f gel has a concordance with the simulated values in the central region. To improve the gel response some studies will be done to minimize the difference in region with high dose gradient and low doses to that hereafter it can be used like a dosimeter routinely in clinical procedures.

Monte Carlo simulation of MAGIC-f gel for radiotherapy using PENELOPE
A way to study and predict MAGIC-f gel results is the use of computational simulation as the Monte Carlo method. From the codes more commonly used in radiotherapy is the PENELOPE code. This code allows the "construction" of materials trough the use of the compound's chemical composition (i.e., elements present and stoichiometric index, or weight fraction, of each element), mass density, mean excitation energy and energy and oscillator strength.

Materials and methods
The components of MAGIG-f gel (water, gelatin, methacrilic acid, copper sulfate, ascorbic acid and formaldehyde) and its characteristics, like atomic number, density and molar mass, were input into the PENELOPE 2008 code to build the MAGIC-f.mat and water.mat material files and for the simulation of PDDs and the conformal treatment. The simulations used 2 x 10 9 primary particles and 0.01mm 2 pixel size.
For experimental measurements were used MAGIC-f dosimeter. Relaxometry, weightened in T2, with a 3.0 T, NMR Philips tomography and head coil were used for the readings of the gel samples. The images were acquired with a multi spin-echo sequence with 16 echo times, TE=20ms, TR=4000ms, matrix of 256 x 256 pixels, slices of 3mm thickness. The MR images were processed and analysed with a program developed in MatLab  , that produces R2 maps.

PDDs and dose-distribution
Simulated PDDs were used to evaluate the MAGIC-f.mat constructed by the code. Simulation conditions were 10 x 10 cm 2 field size and 100 cm source-skin distance (SSD) for photon beams of 6 MV and 10 MV and phantoms of 30 x 30 x 20 cm 3 "filled" with both simulated materials.
Experimental PDDs were determined using MAGIC-f gel and ionization chamber (IC) of 0.6 cc for 6 MV and 10 MV beams. The measurements with the gel were performed using glass tubes of 16 cm length and 1 cm diameter filled with gel. The irradiations were carried out using PPMA cube filled with water and the glass tubes positioned in the center of the volume. A dose of 10 Gy in conventional irradiation conditions for both beams was used.
For the measurement of a coplanar dose-distribution, the gel was poured into a PPMA cylindrical phantom of 10 cm diameter and 15 cm height. The irradiation of the phantom was made with 5 fields of 1 x 1 cm 2 , with a Varian 2100 linear accelerator gantry angles of 0° to 180°. The target was chosen in the center of the cylinder, at 100 cm SSD. The phantom was irradiated with 10 MV beam with2 Gy per field. The conformal irradiation was simulated using PENELOPE code in the same irradiation conditions. Both distributions were also compared through the dose profile.

Results and discussions
PDDs and dose-distribution For the 6 MV beam, a comparison between experimental gel and water (IC) shows a maximum difference of 3.20% until 10 cm depth. Beyond 10 cm the maximum difference is 5.72% in 12.5 cm. The same comparison was performed for the 10 MV beam and a maximum difference of 1.93% was found until 10 cm depth and of 2.62% at 14cm depth.
The maximum differences between experimental and simulated values are 1.46% (0.5 cm depth) and 4.3% (17cm depth) for 6 MV beam. Maximum differences of 2.14% (1 cm depth) and 3.8% (18cm depth) were found for the 10 MV beam.
The study of conformal dose distributions for 10 MV using 5 fields was performed through simulation using MAGIC-f.mat, shown in the figure 15.a. and experimentally using MAGIC-f gel dosimeter as shown in the figure 15.b. Figure 16 shows the dose profiles obtained from both distributions.
(a) (b)  A maximum difference of 0.5% in a radial distance of 0.55 cm inside the field (approximately half the irradiation field) was found and beyond that distance the differences between the dose distributions are less than 7%.
The simulations using PENELOPE code showed similar behaviors with the experimental values. Although discrepancies were found, specifically in the dose-distribution in regions of low doses, this study shows that the code can be used to simulate the components of the MAGIC-f gel for these energies. More over, the MAGIC-f.mat file can be useful for studies of response and comparison of the gel.

Conclusions
The validation of the MAGIC-f gel and PENELOPE through the dosimetric parameters, percentage depth dose and beam profile showed that that both dosimetric tools present similar behavior.
The use of two dosimeters for all radiotherapy modalities present in this work showed great concordance, although discrepancies were found in experimental measurements, using the MAGIC-f gel, and the simulations obtained with the PENELOPE code.
From the results obtained it can be infer that the response of the MAGIC-f polymeric gel and simulation by PENELOPE-Monte Carlo code are suitable and can be used routinely as a dosimeter, in case of the gel, and in the way to study or predict the response and shape of dose-distribution by the simulation.