Characterization of GafChromic EBT-3 film calibration for high-accuracy applications

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Stockholm University

Bachelor Thesis

Characterization of GafChromic

EBT-3 film calibration for

high-accuracy applications

Author:

Tim Melhus

Supervisor:

Dr. Fredrik Hellberg

Medical Radiation Physics Department of Physics

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Acknowledgements

First and foremost, I would like to thankDr. Fredrik Hellbergfor the incredible patience, supervision and guidance supplied during the course of this work. The support and sug-gestions provided byDr. Hellberg allowed me to not only finish this project, but also to take pride in it, for which I am truly thankful.

I also want to thank Mathias Westermark for his outstanding help regarding the irradia-tion of the radiochromic films used in this project. Without Mr. Westermark’s time and supervision, this project would not have been possible.

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Abstract

The Eu-XFEL, a 3.4 km long free electron laser situated in Hamburg, Germany was commissioned in 2017, and has since been at the forefront of cutting edge technologies. The short laser-like X-ray pulses produced within the facility can be used to film ultrafast phenomena such as the formation or breakup of chemical bonds, research the composition and structure of complex biomolecules on the atomic scale, and can even be used to study matter under extreme conditions.

Since its commissioning, a concern has been raised regarding the demagnetization of the permanent magnets present in the undulator system as a result of stray radiation. To monitor this, Gafchromic EBT-3 films along with other dosimetric tools have been installed at various points along the beamline to monitor radiation induced damages and predict the lifetime of the undulator system.

This work focuses on optimizing the calibration of Gafchromic EBT-3 films for accurate estimations of the unwanted dose absorbed in the magnetic material, and was achieved by increasing the amount of calibration measurements and segmenting the measurements, in turn performing the calibration in parts.

The results show that calibrating the EBT-3 films according to the proposed method can accurately estimate unknown doses up to 52 Gy.

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Abbreviations

RGB Red, Green and Blue

OD Optical Density

Gy Gray, unit of absorbed dose

NOD Net Optical Density

XFEL X-ray Free Electron Laser

MU Monitor Units

dpi Dots per inch

ROI Region Of Interest

SSD Source to Surface Distance

QA Quality Assurance

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1. Introduction

1.1 History and modern applications

The invention of the photograph is often credited to Joseph Nic´ephore Ni´epce, who in 1826 demonstrated the radiochromic process by projecting the view from a window onto a pewter plate coated with a light-sensitive solution of ”bitumen of Judea”[1].

Since Ni´epce’s discovery, the radiochromic process has been extensively studied and sev-eral different tools and techniques have been developed for various applications of this process. One of these applications comes from McLaughlin et al., who in 1965 reported on the development of certain derivatives of the triphenylmethane molecule, a colorless solid solution that underwent radiation induced color changes[2].

Much of the early work on radiochromic materials can be attributed to the National Insti-tute of Standards and Technology (NIST), and the following research has since established the use of radiochromic materials in the form of films as a suitable dosimeter for industrial and medical applications.

In recent years, clinical facilities all over the world have used radiochromic films for the quality assurance (QA) of intensity modulated radiation therapy (IMRT) plans while re-search facilities such as the European X-ray Free Electron Laser (Eu-XFEL) or the Linac Coherent Light Source (LCLS) use radiochromic films in order to assess radiation induced damages to their instruments.

The usage of radiochromic films stems from the advantages that they provide over other dosimeters such as thermoluminescent dosimeters (TLDs), ionization chambers (ICs), RADFET-dosimeters and semiconductor diodes.

The films allow the user to keep a permanent record of the absorbed dose in a material as opposed to TLDs, which cannot store previous dosimetric evaluations for archival pur-poses using conventional readout procedures[3].

The storage capabilities of radiochromic films, their potential of being cut into any de-sired shape, their near perfect energy independence in the keV-MeV range[4] and the unmatched spatial resolution that the films provide in dose[5, 6] in comparison to detec-tor arrays are the major advantages that the films provide over other detecdetec-tors, and the reason for using the films in conjunction with TLDs, ICs, RADFET-dosimeters and other types of dosimeters at various medical and research facilities.

The Eu-XFEL, a 3.4 km long radiation research facility located in Hamburg is just one of many such establishments. The facility has been operational since its commissioning in 2017, and consists of a 2.1 km long linear accelerator, of which the acceleration length is 1.7 km[7], followed by undulators1 _{that supply the various experimental stations with}

high intensity X-rays.

Bunches of electrons are first injected into the beamline at the electron injector (not shown in figure 1.1). The electron bunches are subsequently accelerated up to high en-ergies (up to a maximum of approximately 17.5 GeV[7]) by the superconductive linear accelerator, and finally directed into one or more of the undulators (SASE1, SASE2 or SASE3), providing the experimental stations with bunches of high intensity radiation. A visual depiction of this is shown in figure 1.1, taken from the Eu-XFEL website[8].

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Figure 1.1: Figure copied from the European XFEL website[8], depicting the Eu-XFEL beamlines and experimental stations.

The undulator segments are arrays of permanent magnets that are arranged in such a way as to create an alternating magnetic field. When the highly relativistic electrons enter a undulator segment as depicted in figure 1.1, the magnetic field acts upon the electrons via a Lorentz force, causing the electrons to accelerate perpendicularly to the direction they are traveling in. As the Lorentz force that acts upon the electron bunches constantly switches direction due to the alternating magnetic field, the electrons start moving in a sinusoidal pattern, continually accelerating and decelerating perpendicular to the direction of their motion, which according to the Larmor relationship means that they will emit part of their kinetic energy as synchrotron radiation[9]. A schematic representation of this is depicted in figure 1.4, taken from the Eu-XFEL website, depicting one undulator cell[10].

The emitted synchrotron radiation is subsequently collimated into a photon-beam, and directed to one of the experimental stations (see figure 1.1). For SASE1 and SASE2, the resulting X-ray beam has an energy withing the range of 3 keV to over 25 keV, while SASE3 acquires photon-energies between 0.26 and 3 keV[8].

Because the electron bunches are accelerated to relativistic speeds in the linear

accelerator, the emitted synchrotron radiation which has a wavelength within the X-ray spectra, is emitted in the forward direction of the electron velocity as a concentrated cone.

This cone will have a centrally located intensity maximum which consists of the majority of the emitted synchrotron radiation. A fraction of the synchrotron radiation will however deviate from the central core. The overtones of X-ray flashes may hit the undulator material and deposit a dose into the material, however it is not believed that these x-ray overtones contribute to the demagnetization of the undulator segments due to their low energy[11].

The largest contributor to the demagnetization of undulator segments is thought to be halo electrons. When the electron bunches are injected into the linear accelerator, a portion of the electrons may not be contained within the core of the electron beam, but rather between the inner surface of the beam pipe and the outer surface of the core beam volume. This fraction of electrons are commonly referred to as halo electrons, since the distribution of these electrons forms a halo around the beam core. Figure 1.2 shows a simple recreation of halo electrons in 2 dimensions, copied from the bachelor thesis ”The Study of the Collimation and Radiation Effects of the Electron Beam in

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Accelerators” by Vahan Petrosyan[12].

Figure 1.2: Figure recreated from ”The Study of the Collimation and Radiation Effects of the Electron Beam in Accelerators”[12], depicting halo electrons relative to the central beam core.

Since the halo electrons are positioned closer to the permanent magnets on one side, and further away from the permanent magnets on the other side relative to the central core, the halo electrons will experience a larger electromagnetic force acting upon them. In turn, this means that the halo electrons will be bent more by the magnetic field (relative to the central core), and as such might penetrate the vacuum tube and subsequently hit the permanent magnets, depositing a dose and demagnetizing the magnets in the

process. Similarly, the electrons might interact in the vacuum tube material, producing secondary radiation which in turn might also deposit a dose into the magnets.

A simple 2 dimensional depiction of this is shown in figure 1.3.

Figure 1.3: Depiction of how the halo electrons contribute to the demagnetization of undulator cells.

TLDs, RADFET-dosimeters and radiochromic films are placed at the entrance of each undulator cell in order to provide accurate information on if and when adjustments to the beamline or permanent magnets needs to be made.

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Figure 1.4: Figure taken from the Eu-XFEL website[10], depicting one undulator cell, and the creation of soft X-rays.

1.2 Purpose of this study

As with most detectors, the radiochromic films needs to be calibrated before usage, relating the measurable quantity to the absorbed dose in the films. This calibration procedure is necessary for each batch of radiochromic films due to slight variations in humidity, temperature and storage of different batches during the manufacturing

process, however the film pieces in a batch of films are all assumed to respond uniformly to radiation exposure.

The calibration of the films is performed in a facility where the radiation exposure can be thoroughly controlled, and subsequently related to the measurable quantity. It is this calibration procedure which was investigated in this paper for various parameters

affecting the accuracy of measurements.

Previous recommendations on the type of films used in this study state that in order to save both time and film, only 6-8 calibration measurements are needed per film batch[4] to produce a reliable response function for the batches, including a piece of unexposed film.

In this work, the calibration procedure with 8 calibration measurements was compared to one with 17 calibration measurements to assess how the statistics improves with a larger number of calibration measurements, and determine whether or not the additional measurements make a significant difference when estimating the response of the films. Another approach to the post-irradiation analysis of the films was also tested and compared to the standard procedure (both 8 and 17 calibration measurements). The second approach was specifically designed to fit the calibration measurements better at higher doses, allowing for a more precise estimation of the calibration parameters, and thus increasing the accuracy of the films at doses above the recommended optimal dose range[4].

The secondary calibration method was then used to compare how well the sensitometric curve fits the calibration measurements in different intervals of absorbed dose, relative to the standard calibration method.

The calibration procedures was performed for two different batches of GafChromicTM

EBT-3 films, lot number #08141801 (batch1) and #09071704 (batch2), both of which will later on be sent to the Eu-XFEL for usage. Batch 1 was recently ordered from Ashland GafChromic2_{, while batch 2 had been laying dormant for a number of months}

before calibration.

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2. Experimental procedure

2.1 GafChromic EBT-3 films

The GafChromicTM _{EBT-3 film is the latest version of radiochromic films in the EBT}

series, and is a radiation sensitive film composed of an active layer sandwiched between two matte-polyester substrates as depicted in figure 2.1, reconstructed from the EBT-3 specification and user guide[4]. The active layer contains a marker dye, a stabilizing agent and a diacetylene monomer which acts as the active component, all of which contributes to the near perfect energy independence (< 5 % at 100 keV and 18 MeV) of the films[4].

Upon ionizing radiation exposure or thermal annealing, the active component undergoes a 1,4 polymerization process[13], in turn changing optical density depending on the specific composition of the active layer[14]. The chain-polymerization of the diacetylene molecules grows in length as more dose is absorbed by the active layer, and as a result the film grows darker[15].

Figure 2.1: Structural depiction of a Gafchromic EBT-3 film, taken from the EBT-3 specification and user guide[4].

Barring the previously mentioned advantages of GafChromicTM _{EBT-3 films, they also}

do not require any chemical processing in order to measure the absorbed dose. This provides for yet another advantage over dosimeters such as TLDs, and all that is needed to measure the dose to radiochromic films is a flatbed scanner and some software

designed for the purpose.

Previous studies have reported on a temperature dependence of the GafChromicTM

EBT-3 films[16, 17], however as both batches were stored below 25◦C before and after the calibration, this temperature dependence is not a problem.

According to the EBT-3 user specification guide, the dynamical dose range of the GafChromic films ranges from 10 cGy to 20 Gy[4], however previous studies have shown that the films can accurately measure doses up to approximately 40 Gy[18] using a multi-channel method of analyzing the films[19]. This method does however rely on the accuracy of the calibration, and is therefore subject to the investigation presented in this work.

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2.2 Optical density

Following the carefully controlled irradiation of the EBT-3 films, a flatbed scanner is used to scan the films and generate digital images of the films in a lossless image format called TIFF1_{, from which the optical density of the films can be extracted.}

The optical density (OD) is a quantitative measure expressed as a logarithmic ratio between the radiation incident upon a material and the radiation transmitted through the material, or in other words the absorbance of the material2_{, as defined by equation}

2.1 where Iunexp is the intensity of an unexposed film, and Iexp(D) is the intensity of a

film exposed to a dose D.

OD(D) = log₁₀ Iunexp Iexp(D) (2.1) The Net Optical Density (NOD) can be calculated using a common method described by Devic et al., expressed in equation 2.3, where Iunexp and Iexp(D) are the scanner

readings for unexposed and exposed film pieces respectively, while Ibckg is the zero-light

transmitted intensity value characterizing the background signal of the scanner[20]. As the background signal of the scanner in a dark room is expected to be small due to the lack of light in the room during the film-scanning process, Ibckg was set to 0 for the

remainder of this work, making equation 2.1 equal to equation 2.3.

N OD(D) = ODexp(D) − ODunexp (2.2)

= log₁₀ Iunexp− Ibckg Iexp(D) − Ibckg (2.3) The NOD can then be related to the dose by the suggested rational function expressed in equation 2.4[19] which depends on the absorbed dose D, as well as the calibration parameters ax, bx, and cx. The objective of calculating the NOD using equation 2.3 and

subsequently determining the calibration parameters by fitting a curve to the calibration measurements using eq 2.4, is to eventually calculate unknown doses via equation 2.5 using the calibration parameters ascertained during the calibration process, where x is the specific red, blue and green (RGB) color channels.

N OD(D) = −log₁₀ax+ bx· D cx+ D (2.4) Dx= cx· 10−N OD− ax bx− 10−N OD (2.5) Another method suggested by Devic et al. calculates the NOD of the films by equation 2.3 and fits the data points to the absorbed dose according to equation 2.6 instead, where the third term accounts for the nonlinear dose response while approaching the high dose region close to the saturation level for a given film dosimetry system[21].

Dfit = ax+ bx· N OD + cx· N ODn (2.6)

For both of these methods, there are two requirements which has to be fulfilled, and one consideration which is to be applied. The requirements are (i): The function has to be

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https://en.wikipedia.org/wiki/TIFF

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monotonically increasing with dose and (ii): the function has to go through the origin based on the definition of OD, and the consideration to be applied is that the

fitting-algorithm that is to be used to estimate the parameters of both models is chosen as the algorithm which results in the minimum relative uncertainty for the fitting parameters ax, bx and cx.

2.3 Calibration procedure and irradiation setup

The calibration method utilized in this study is akin to the proposed protocol presented in the appendix of Rebecca Titternes bachelor thesis ”GAFChromic Film Calibration For European XFEL” (2017)[22]. Small changes were made to the protocol in order to better fit the purpose of this work, however the pre handling of the film, and the calibration procedure remained the same.

One sheet of GafChromic EBT-3 film was first cut into 12 equally large pieces (10.45 cm x 2.9 cm) and 4 slightly larger pieces (10.45 cm x 3.2 cm) using a guillotine cutter. A 30 cm x 30 cm x 13.3 cm water phantom was then constructed at Karolinska

university hospital by the use of several 1 mm - 2 cm thick 30 cm x 30 cm RW3-slabs. RW3 is a white water equivalent polystyrene material with a density of 1.045 g/cm3_[₂₃_],

and the purpose of constructing this water phantom is mainly to prevent the

backscattering of radiation from the radiation table, which has a higher effective atomic number than the films. The precise height of the phantom is not of any importance as long as it is thick enough to absorb any backscattered radiation from the table.

Introducing this water phantom, which in the sense of interaction coefficients is a first approximation of the human body, will result in the build-up of dose.

A simple schematic description of the dose build-up is depicted in figure 2.2. The percentage of absorbed dose relative to the maximum dose in the phantom increases with depth (up to a certain point zmax), and thus a depth-dose curve was calculated for

the radiation source (Varian Truebeam 07, version 2) in order to determine the depth at which the films should be placed to receive 100 % of the planned dose.

Figure 2.2: Schematic description of the dose build-up. This depiction was modified after “Cunnigham –The physics of Radiology”.

Once the optimal placement of the films had been established, the stack of RW3-slabs were placed onto a treatment table, and the films were taped on top of the water

phantom as shown in figure 2.3. Another stack of RW3-slabs were then placed on top of the films in order to position the films at the depth-dose maximum. Once the film

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configuration had been setup as shown in figure 2.3 and covered with the remaining RW3-slabs, the films were irradiated using the Varian Truebeam 07 machine at a dose rate of 600 monitor units per minute3, a source to surface distance of 90 cm, a

calculated 73.227 MU/Gy and a field size of 20 cm x 20 cm.

Figure 2.3: Positioning of the films during the calibration procedure.

The doses delivered to the various film pieces used in this work were {0.0, 1.0, 2.0, 3.0, 4.0, 6.0, 8.0, 12.0, 16.0, 20.0, 24.0, 28.0, 34.0, 40.0, 46.0, 52.0 and 58.0} Gy, and the uncertainty in dose had been calculated beforehand to be approximately 2.1 % at most. At this point, the only assumption which was made was that the films would receive a uniform amount of dose when irradiated, homogeneously distributed over the surface area of the irradiated film pieces, excluding the part of the film pieces which was placed slightly outside the radiation field seen in figure 2.3. The film pieces were carefully handled individually using latex gloves, cleaned using a 80 % isopropyl alcohol and wiped with a soft microfiber cloth as to ensure the validity of this assumption and to avoid systematic errors during the film handling.

Following the radiation exposure, the films were placed inside a black envelope and stored in the envelope for 72 hours as an extra precaution to prevent any type of accidental irradiation from sunlight or any other UV-light source.

As the films darken even post-irradiation[24], it is important to wait at least 24 hours before scanning the films in order to let the polymerization-process saturate. In order to ensure complete saturation of the films response to radiation exposure, a 72-hour

waiting period was implemented before scanning the films.

2.4 Post-irradiation film analysis

Following the waiting period, the films were scanned and digitally converted to TIFF images using a flatbed Epson V800 scanner according to the procedure proposed by

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Rebecca Titternes[22], with the scanner resolution set to 2048 dots per inch (dpi) instead of the suggested 720 dpi to reduce the relative differences in NOD observed by Tagiling et al.[25].

The films were placed centrally in the scanner one by one, consistently oriented in the same manner as to avoid any orientation-based source of error[26]. The orientation of the films, as well as the absorbed dose to each piece was tracked by marking the films with a permanent marker, as shown in figure 2.4.

Once all the films had been digitally converted into a TIFF-format, a Region Of Interest (ROI) was carefully chosen for each piece as to reduce any unwanted sources of error, and subsequently cropped to the ROI as shown in figure 2.4. The ROI of each film piece was chosen as the 1300x600 pixel-region with the least variance in OD over the whole image, minimizing the errors caused by damages to the film pieces or specks of paper dust stuck to the scanner.

Damages to the films may occur when cutting the film sheets into smaller pieces, causing small air-filled gaps between the layers of the film and severely inhibiting the responsiveness to dose in that particular region as shown in figure 2.4.

Figure 2.4: One example of the ROI as well as the damages to the film that cutting them may inflict.

The cropped images were then used in conjunction with a self developed Python

program and the known exposure to each film piece in order to estimate the calibration parameters expressed in equations 2.4 and 2.6.

2.4.1 Image analysis software GFC19

The self developed python program GFC19 works by reading the red, green and blue (RGB) values of each pixel in the ROI. GFC19 then assumes a homogeneously distributed radiation exposure, and calculates the average pixel value of each color

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channel over the ROI for each film piece. Using the average RGB-intensities, a NOD-value is calculated for each film piece in all three color channels by way of equation 2.3.

An estimation of the calibration constants (ax, bx and cx) is then performed for each

color channel with a non-linear least square fit (nlLSQ). The nlLSQ was performed using the Levenberg-Marquardt algorithm4 on both response models (equations 2.4 and 2.6), after which a comparison between the response models is performed to determine which model fits the data best.

The comparison is made by computing the sum of squared residuals(P SS2

res5) defined

in equation 2.7, where Di is the measured doses, NOD(Di) is the measured NOD for a

dose Di, and f(Di) is the predicted NOD-value of the response model.

The response model whose P SS2

res demonstrated the smallest deviation from 0 was

chosen for subsequent measurements and analysis, as this indicates a better fitting curve. While calculating the sum of squared residuals, GFC19 also checks if at some point the residual distance (SSres) between the expected NOD-value and the measured

NOD-value exceeds the error of that measurement. If it does for two or more color channels at the same time, GFC19 splits the data set into two smaller data sets, and calibrates the sets separately in an attempt to reduce SS_res2 .

X SS_res2 = n X i=1 (N OD(Di) − f (Di))2 (2.7)

2.4.2 Evaluation of the new split-calibration method

In research facilities such as the Eu-XFEL or LCLS, Gafchromic EBT-3TM _{films are}

often used in conjunction with TLDs, ICs and RADFET dosimeters to estimate unknown doses absorbed in the undulators caused by halo electrons and stray

electromagnetic radiation. The films are a crucial part of of the aforementioned setup as the spatial resolution of the films is significantly better than the above-mentioned

detectors.

However as the response of the films saturate after receiving an absorbed dose of approximately 40 Gy[18], the evaluation of absorbed dose in the undulators (using Gafchromic EBT-3TM _{films) is limited to within the dose range 0-40 Gy.}

A test was therefore devised to observe how this new ”split-calibration” method would affect dosimetric evaluations.

The test was performed by removing 4 calibration measurements using a pseudo-random number generator6 _{to generate random numbers between 1 and 17 (so to ensure that the}

non-irradiated film was part of the sensitometric curve). These 4 numbers would

correspond to the index of the calibration measurements which were to be removed from the calibration data set (see section 2.3).

The remaining set of images were then calibrated using both the standard calibration method and the split-calibration method, and the resulting sensitometric curve was subsequently used to estimate the absorbed doses in the 4 films which were removed from the calibration by using a (4x4) K-nearest neighbors algorithm and averaging out the dose over the ROI.

4 https://en.wikipedia.org/wiki/Levenberg\OT1\textendashMarquardt_algorithm 5 https://en.wikipedia.org/wiki/Residual_sum_of_squares 6 https://docs.python.org/3/library/random.html

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2.5 Error analysis and uncertainty in film handling

As the images of the radiochromic films are digitally extracted, the OD of each pixel is considered to be an absolute value, meaning that the only source of uncertainty up to that point stems from the handling of the films. As such, latex gloves were worn at all times to minimize the risk of introducing sources of error such as fingerprint marks, and when needed, the films were cleaned using a 80 % isopropyl alcohol and wiped with a soft microfiber cloth.

The scanner window was also cleaned between scans using the same type of microfiber cloth, which in some cases resulted in residual cloth sticking to the scanner window, and subsequently impacting the uncertainty measurement (see figure 2.4).

Averaging the measured NOD-values also introduces an uncertainty for each film piece, estimated by the standard deviation, and is most likely a result of the non-uniformity in sensitometric response, claimed by the manufacturer to be better than ± 3 %[4].

The calculated standard deviation was subsequently propagated through equation 2.3 using the standard error propagation formula expressed in equation 2.8, where f is a function dependent on multiple independent variables x1, x2, x3 etc., and ∆x1, ∆x2,

∆x3 are their respective errors. Ultimately, the uncertainty in NOD provides weights

which are used in the nlLSQ-fit to better estimate the calibration parameters. The end results of this propagation for equation 2.4, i.e. the uncertainty in NOD for a color channel x, was thus calculated using equation 2.9.

∆f (x1, x2, x3, ...) = r ∂f ∂x1 ∆x1 2 + ∂f ∂x2 ∆x2 2 + ∂f ∂x3 ∆x3 2 + ... (2.8) σN ODx= v u u u t −σax ln(10)(ax+bx·D) 2 + −σbx·D ln(10)(ax+bx·D) 2 + σcx ln(10)(cx+D) 2 + −σD·(bx·cx−ax) ln(10)(D+cx)(bx·D+ax) 2 (2.9) There is also some uncertainty associated with the radiation source and the absorbed dose in the water phantom. This uncertainty was calculated before irradiating the films, and was done so with the use of software installed at the facility.

Some systematic errors may also exist in the Epson V8800 scanner which was used to digitally convert the films, and previous studies have suggested correcting for both dead pixels as well as scanner noise before scanning the films[20]. These corrections were however not performed in this study as the effects of these was not the subject of investigation.

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3. Results

3.1 Uncertainty in absorbed dose

The uncertainty in absorbed dose was estimated using the Varian Truebeam 07’s accompanying software at a dose rate of 600 Mu/min and a radiation energy of 6 MV. Figure 3.1 shows the acquired dose profile for the radiation source over the preset radiation field.

Figure 3.1 provides information about the field size, radiation symmetry as well as the flatness, from which the uncertainty in absorbed dose was extracted. For all calibration measurements, the uncertainty in absorbed dose was set to the largest deviation from perfect flatness, measured to be 2.05 %.

−100 −50 0 50 100 150 Position [mm] 0 20 40 60 80 100 Ab so rbe d d ose (G y) [% ]

Dose profile through central radiation axis

Dose profile

Figure 3.1: Dose profile at zmax of the radiation source with a radiation energy of 6 MV.

Graphical data acquired on Apr. 26 - 2019 from Dr. Mathias Westermark (Karolinska Institutet - Department of Medical Radiation Physics).

3.2 Number of calibration measurements

The calibration parameters estimated when using 17 calibration measurements was compared to the same parameters estimated when using 8 calibration measurements for both batches of Gafchromic EBT-3 films.

Figure 3.2 depicts the two calibration curves acquired for each batch, and the parameter comparison has been listed in table 3.1 where the relative improvement of a parameters uncertainty ∆(σP) in color channel x has has been computed as

∆(σPx) = max(100 · (1 −

σPn=17_x

σPn=8_x )) (3.1)

While the relative difference in parameter value was found to be < 7% for all color channels in both batches, the relative improvement of parameter uncertainty was found

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to be substantial for both batches when using all 17 calibration measurements, most notably in the blue color channel (see table 3.1).

(a) n=8 (b) n=17

(c) n=8 (d) n=17

Figure 3.2: Sensitometric curves for batch 1 (top) and batch 2 (bottom) when utilizing n calibration measurements.

Table 3.1: Comparison of the estimated values of the acquired calibration parameters utilizing n calibration measurements.

Color channel

Para-meter

Batch 1 Batch 2

Value (n=8) Value (n=17) ∆(σP) Value (n=8) Value (n=17) ∆(σP)

a 0.991±0.037 0.992±0.029 1.254±0.048 1.253±0.040 Red b 0.235±0.004 0.234±0.003 24.7% 0.277±0.004 0.276±0.003 17.2% c 0.992±0.040 0.996±0.034 1.255±0.050 1.257±0.045 a 1.458±0.038 1.426±0.034 1.602±0.070 1.594±0.052 Green b 0.129±0.004 0.132±0.003 15.6% 0.159±0.006 0.158±0.005 27.7% c 1.457±0.041 1.421±0.040 1.601±0.073 1.589±0.057 a 4.274±0.255 4.255±0.157 4.481±0.131 4.535±0.100 Blue b 0.319±0.009 0.319±0.005 45.3 % 0.381±0.004 0.378±0.003 28.4% c 4.287±0.277 4.296±0.178 4.485±0.137 4.555±0.109

3.3 Post irradiation analysis

The post irradiation analysis was performed twice for each batch of film, and has been split into two different parts accordingly.

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The first part of the analysis focuses on the calibration method which utilizes one calibration curve over the whole dose range. This method is the standard way to calibrate radiochromic films today, however as the dose range in this study exceeds the previously explored dose range of 0-40 Gy[18], the question is how well this method of calibration works for higher doses, or more generally, how good it is in various intervals of absorbed dose. For this reason, the second part analyzes the films according to the method described in section 2.4.1, where an additional analysis of the P SS2

res is

performed to determine whether the best-fit curve could be improved further in some intervals of absorbed dose.

3.3.1 Part 1 - Calibration performed over the whole dose range

The average NOD of each film in both batches was first calculated by equation 2.3, and fitted using a nlLSQ-fit to both model functions (equation 2.4 and 2.6) with a standard python package for non-linear least square fits1_.

The optimized curve suggested by each model function was then compared to one another by computing their respective sum of squared residuals (P SS2

res), and the

choice of model function was determined as the functions whose P SS2

res exhibited the

least deviation from 0, indicating a better fit.

For both batches, equation 2.4 provided the better fit when calibrating the films over the dose range 0-58 Gy, and the resulting calibration parameters have been listed in table 3.2. The sensitometric curve of each batch has been depicted in figure 3.3 along with a plot of their respective residuals.

Table 3.2: Calibration parameters acquired in the dose range 0-58 Gy for both batches. Used to plot the curves depicted in figure 3.3.

Color channel Calibration parameter Batch 1 Batch2 Parameter value X SS_res2 Parameter value X SS_res2 a 0.992±0.029 1.253±0.040 Red b 0.234±0.003 1.76 x 10−3 0.276±0.003 1.92 x 10−3 c 0.996±0.034 1.257±0.045 a 1.426±0.034 1.594±0.052 Green b 0.132±0.003 4.78 x 10−3 0.158±0.005 5.27 x 10−3 c 1.421±0.040 1.589±0.057 a 4.255±0.157 4.535±0.100 Blue b 0.319±0.005 5.83 x 10−4 0.378±0.003 2.11 x 10−4 c 4.296±0.178 4.555±0.109 1 https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html

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0

10

20

30

40

50

60 Dose [Gy]

0.0

0.2

0.4

0.6

0.8 NOD

Calibration curve for batch #08141801

Red channel

Green channel

Blue channel

0

10

20

30

40

50

60 Dose [Gy]

0.05

0.00

0.05 Residual

(a) Sensitometric curve of batch 1 over the dose range 0-58 Gy.

0

10

20

30

40

50

60 Dose [Gy]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 NOD

Calibration curve for batch #09071704

Red channel

Green channel

Blue channel

0

10

20

30

40

50

60 Dose [Gy]

0.05

0.00

0.05 Residual

(b) Sensitometric curve of batch 2 over the dose range 0-58 Gy.

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3.3.2 Part 2 - Split calibration

The split-calibration procedure was performed according to the method described in section 2.4.1 due to the results presented in the residual plots of figure 3.3.

For batch 1, the curve was split at a dose of 6.0 Gy due to the residual of that calibration point exceeding the error of that measurement in both the red and green color channels, and batch 2 was split at a dose of 8.0 Gy for the same reason, in both the red and green color channels.

As a result of this split-calibration,P SS2

res was found to be substantially reduced in

both batches (by as much as a factor of 103_{), suggesting a better calibration.}

Figure 3.4 depicts the computed split-calibration for both batches of Gafchromic EBT-3 films, and the optimized calibration parameters have been listed in tables 3.3 and 3.4. As with the calibration performed over the whole dose range (0-58 Gy), equation 2.4 once again proved to be the better model function in the dose interval 0-6 Gy and 0-8 Gy for batch 1 and batch 2 respectively.

In the dose range 6-58 Gy and 8-58 Gy respectively, the sum of squared residuals

computed when utilizing equation 2.4 was found to be approximately 6- and 14 % better than P SS2

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0 10 20 30 40 50 60 Dose [Gy] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

NOD

Calibration curve for batch #08141801

Red channel Green channel Blue channel 0 10 20 30 40 50 60 Dose [Gy] 0.025 0.000 0.025

Residual

(a) Optimized sensitometric curve of batch 1, split over the dose ranges 0-6 Gy and 6-58 Gy.

0 10 20 30 40 50 60 Dose [Gy] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

NOD

Calibration curve for batch #09071704

Red channel Green channel Blue channel 0 10 20 30 40 50 60 Dose [Gy] 0.025 0.000 0.025

Residual

(b) Optimized sensitometric curve of batch 2, split over the dose ranges 0-8 Gy and 8-58 Gy.

Figure 3.4: Resulting sensitometric curves from performing an nlLSQ-optimization in two dose-intervals.

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Table 3.3: Calibration parameters acquired for batch 1

Dose interval Color channel Calibration parameter Parameter value P SS2 res a 0.894±0.006 ≤ 6.0 Gy Red b 0.252±0.001 7.05 x 10−7 c 0.894±0.006 a 1.572±0.047 ≤ 6.0 Gy Green b 0.105±0.010 1.39 x 10−5 c 1.573±0.049 a 3.132±0.362 ≤ 6.0 Gy Blue b 0.405±0.034 1.63 x 10−5 c 3.135±0.369 a 2.667±0.130 > 6.0 Gy Red b 0.212±0.001 2.18 x 10−5 c 5.211±0.365 a 0.509±0.207 > 6.0 Gy Green b 0.148±0.004 9.9 x 10−4 c -1.260±0.667 a 4.263±0.616 > 6.0 Gy Blue b 0.315±0.008 2.84 x 10−4 c 4.042±0.982

Table 3.4: Calibration parameters acquired for batch 2

Dose interval Color channel Calibration parameter Parameter value P SS2 res a 1.130±0.014 ≤ 8.0 Gy Red b 0.295±0.002 4.30 x 10−6 c 1.130±0.014 a 1.851±0.034 ≤ 8.0 Gy Green b 0.117±0.006 1.21 x 10−5 c 1.850±0.035 a 3.909±0.236 ≤ 8.0 Gy Blue b 0.417±0.017 9.86 x 10−6 c 3.913±0.240 a 4.600±0.500 > 8.0 Gy Red b 0.241±0.004 4.01 x 10−5 c 9.063±1.275 a -0.190±0.105 > 8.0 Gy Green b 0.186±0.002 1.34 x 10−4 c -3.464±0.340 a 5.343±0.618 > 8.0 Gy Blue b 0.367±0.005 7.33 x 10−5 c 5.628±0.987

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3.4 Dosimetric evaluation

The evaluation of the split-calibration method was performed as described in section 2.4.2. For batch 1, the four randomized measurements which were removed from the calibration process and subsequently used for the comparison of the calibration methods were the films which received 8.0, 24.0, 40.0 and 52.0 Gy, and similarly, for batch 2, the films irradiated with 4.0, 12.0, 20.0 and 46.0 Gy were removed from the calibration process.

Tables 3.6 and 3.5 lists the resulting calibration parameters obtained during this testing, and table 3.7 lists the estimated dose (Dmethod_estimated) of each calibration method, as well as the reference dose Dref as calculated by the Varian Truebeam V2 used at Karolinska

university hospital.

The split-calibration method proved to yield the closest match to the reference dose in most cases by a small margin at the cost of a larger uncertainty, however for the larger doses, this comparison favoured the split-calibration method considerably.

Table 3.5: Calibration parameters acquired by the developed split-calibration technique for both batches.

Color channel Calibration parameter Dose interval Parameter value (Batch 1) Dose interval Parameter value (Batch 2) a 0.882±0.010 1.128±0.015 Red b ≤12.0 Gy 0.255±0.002 ≤8.0 Gy 0.295±0.003 c 0.881±0.011 1.128±0.016 a 1.563±0.030 1.849±0.039 Green b ≤12.0 Gy 0.107±0.005 ≤8.0 Gy 0.118±0.007 c 1.564±0.032 1.849±0.041 a 3.179±0.207 3.908±0.284 Blue b ≤12.0 Gy 0.399±0.017 ≤8.0 Gy 0.417±0.021 c 3.182±0.214 3.912±0.290 a 3.629±0.256 4.935±0.397 Red b >12.0 Gy 0.207±0.001 >8.0 Gy 0.238±0.003 c 8.330±0.816 9.826±0.997 a -0.574±0.239 -0.208±0.181 Green b >12.0 Gy 0.158±0.002 >8.0 Gy 0.187±0.002 c -5.706±1.065 -3.524±0.581 a 3.069±1.147 5.513±0.779 Blue b >12.0 Gy 0.327±0.009 >8.0 Gy 0.366±0.007 c 2.020±2.170 5.854±1.222

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Table 3.6: Calibration parameters acquired by the standard calibration technique for both batches, where the number of calibration measurements are 13.

Color channel Calibration parameter Parameter value (Batch 1) Parameter value (Batch 2) a 0.979±0.030 1.251±0.045 Red b 0.235±0.003 0.275±0.004 c 0.982±0.035 1.254±0.049 a 1.437±0.040 1.606±0.056 Green b 0.130±0.004 0.160±0.005 c 1.432±0.047 1.601±0.061 a 4.095±0.129 4.524±0.124 Blue b 0.324±0.005 0.378±0.004 c 4.123±0.144 4.543±0.134

Table 3.7: Estimated doses of the test films using both calibration methods with 13 calibration measurements.

Batch 1 Batch 2

Dref [Gy] Dstandardestimated [Gy] D split

estimated [Gy] Dref [Gy] D

standard estimated [Gy] D split estimated [Gy] 8.0±2.05% 7.36±4.81% 7.62±4.54% 4.0±2.05% 4.06±5.27% 4.04±3.86% 24.0±2.05% 24.84±10.22% 23.83±23.72% 12.0±2.05% 11.85±7.17% 12.49±22.96% 40.0±2.05% 38.85±15.89% 40.22±24.14% 20.0±2.05% 19.15±9.36% 19.95±21.73% 52.0±2.05% 40.68±19.64% 53.38±25.43% 46.0±2.05% 41.21±20.18% 47.71±22.97%

3.5 Calibration uncertainties

When performing the calibration and averaging out the NOD-value over each film piece, the assumption that each piece has been homogeneously irradiated to within 3%[4] was made, and with this averaging, an uncertainty for each measurements was computed by the standard deviation.

Subsequently, the standard deviation of each measurements was propagated through expression 2.8 which provided weights when computing the sensitometric curve. Figure 3.5 depicts the comparison of the errors obtained by both calibration methods visually. The gray areas in both figure 3.5a and 3.5b represents the sensitometric curves obtained when using the split-calibration method including their respective errors, as listed in tables 3.3 and 3.4, while the red, green and blue areas correspond to the standard calibration method and its associated errors as listed in table 3.2.

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0 10 20 30 40 50 60 Dose [Gy] 0.0 0.2 0.4 0.6 0.8

Net optical density

Calibration errors of batch #08141801

Red channel Green channel Blue channel

(a) Error comparison between the standard calibration method and split-calibration method for batch 1 0 10 20 30 40 50 60 Dose [Gy] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Net optical density

Calibration errors of batch #09071704

Red channel Green channel Blue channel

(b) Error comparison between the standard calibration method and split-calibration method for batch 2

Figure 3.5: Error comparison between the standard calibration method and the split-calibration method of both batches.

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4. Discussion

Starting with section 3.2, the results presented in table 3.1 indicates precisely what was expected from a statistical point of view, that more calibration measurements yield a better overall result1_{. Increasing the number of calibration measurements was found to}

result in substantially lower uncertainties in all color channels (15.6 %-45.4 % for batch 1 and 17.2 %-28.4 % for batch 2) as well as providing a better estimation of the

calibration parameters themselves. The latter comparison was made by computing the sum of squared residuals for each color channel in the cases where the number of calibration points (n) was set to 8 and 17, and was found to be lower when utilizing 17 calibration measurements.

While the improvement may differ depending on the batch being calibrated, it is expected that each batch will exhibit a similar improvement in both calibration parameter and their respective uncertainties.

The currently available documentation (21/06-2020) on Gafchromic EBT-3 films state that in order to save both time and film, only 6-8 calibration measurements per batch are needed to ensure a reliable dosimetric evaluation in the dose range 0-20 Gy[4]. At research facilities such as the Eu-XFEL and LCLS where it is critical to keep track of the absorbed dose delivered to the undulators however, there is no guarantee that the dose will lie within this dose range, and as such, a new recommendation of 12-17 calibration measurements in a larger dose range is therefore proposed here.

Assuming that the film pieces used for the purpose of calibration are large enough such that an ROI can be chosen without including damaged regions of the films (see figure 2.4), one sheet out of the 10 contained in each batch2 _{will be enough to calibrate the}

whole batch.

Irradiating the films in this work took roughly 2 hours, however it is estimated that by using a radiation source with a similar dose rate to the Varian Truebeam 07 used in this work (approximately 8.2 Gy/min), the calibration time per batch assuming 17

calibration measurements in the dose range 0-60 Gy, could be performed within 45 minutes excluding the waiting period mentioned in section 2.3.

Apart from the improved statistics, increasing the amount of calibration measurements from 6-8 to 12-17 would also allow the user to utilize the newly developed

split-calibration method if needed, at the cost of a small amount of time. This in turn could be beneficial when estimating unknown doses, especially for larger doses,

according to the small sample size presented in table 3.7.

The standard calibration procedure was applied to both batches, fitting a sensitometric curve to the data according to both equation 2.4 and 2.6. For both batches, equation 2.4 yielded the best fitting curve, determined as the functions whose sum of squared

residuals exhibited the smallest deviation from 0.

Looking at the sensitometric curves presented in figures 3.3a and 3.3b, a pattern of over-and underestimation can be observed for both the red over-and green color channels. For both batches, the green curve underestimates the films response to radiation in the approximate dose range 8-20 Gy, and overestimates the response for doses above 40 Gy. The opposite is true for the red color channel, which overestimates the response in the

1

https://scientificallysound.org/2016/03/03\protect\penalty-\@M/ how-does-sample-size-affect-precision-of-estimates/

2

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approximate dose range 8-20 Gy, and underestimates the response to radiation for doses above 40 Gy.

The same behaviour can not be observed for the blue color channel which fits the

calibration data within one standard deviation over the whole dose range, and exhibits a P SS2

res roughly one order of magnitude less than the red and green color channels, in

turn suggesting that estimating an unknown dose with a single-channel method (the blue color channel) may actually be more accurate compared to the multi-channel method in these dose intervals.

In the optimal dose range however, specified by the manufacturer as 0-10 Gy[4], the sensitometric curves matches the calibration data well enough to accurately estimate unknown doses via the multi-channel method within a few percent, and the same can be said for the approximate dose interval 20-40 Gy, although to a lesser degree as the films are designed to be used within the dose interval 0-20 Gy.

While the single-channel method (blue color channel) may improve dosimetric

evaluations in the approximate dose interval of 8-20 Gy compared to the multi-channel method, the same can not be confirmed for doses above 40 Gy. This is because the response of Gafchromic EBT-3 films become unreliable after receiving a dose of approximately 40 Gy due to the saturation of the films sensitivity[18], whether a multi-channel method or a single-channel method is applied.

Due to the residuals depicted in figure 3.3, the newly developed split-calibration

method, comprehensively described in section 2.4.1, was applied to the calibration data. The software developed for this, GFC19, was built to split the data set into two

distinguished data sets at the first point where the residuals of two or more

measurements exceeds the error of those measurements. GFC19 then calibrates each data set according to equations 2.4 and 2.6, and compares the model functions to each other to return the best fitting model function.

Batch 1 was split at 6.0 Gy and batch 2 was split at 8.0 Gy. For both batches and in all intervals of absorbed dose, equation 2.4 provided the better fitting model function, and their respective calibration curves have been depicted in figure 3.4.

In both cases, the split-calibration method has gotten rid of the over- and

underestimation of NOD that can be observed in figure 3.3, indicating a more accurate calibration, and thus a more precise estimation of absorbed doses in the intervals 8-20 Gy and 40+ Gy. The same observation can also be made when comparing the sum of squared residuals listed in table 3.3 and 3.4 to the sum of squared residuals listed in table 3.2, which also indicates a better fit over the whole dose range.

In the optimum dose range (0-10 Gy[4]), the difference in P SS2

res between the

split-calibration method and the standard calibration method was found to be minimal (≤ 2%) indicating that in situations where the absorbed dose is known to be

approximately 10 Gy or less, such as in the QA of IMRT-plans, the standard calibration method is close to equivalent to the split-calibration method, and should therefore be used as this saves some time. In the interval 10-20 Gy, the difference in P SSres2 for the

two calibration methods was found to be 5-12 % in favour of the split-calibration method depending on color channel, which should mean that the split-calibration

method is better at estimating doses in this interval. However, as shown in table 3.7, the standard calibration method outperforms the split-calibration method at the

measurement of 12.0 Gy (batch 2). The reason for this is unknown, and as only one test was run on a limited data set, no conclusion as to why this is the case can be drawn.

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In situations where the applied dose is unknown, or known to be above the dynamical dose range (0.1-20 Gy[4]), it is recommended to use the split calibration method as this allows for a more accurate dosimetric evaluation (see table 3.7).

A glaring problem with the split-calibration method however is the discontinuity at the point where the data set is split. This method assumes that the model function

expressed in equation 2.4 is a purely mathematical function used to describe the

behaviour of the films, rather than having any sort of physical meaning or interpretation behind it, and therefore, splitting the calibration should not present any problem.

As to the dosimetric evaluation, table 3.7 lists the doses estimated when using both calibration methods, as well as the dose delivered to the films according to the Varian Truebeam 07.

The test cases were chosen at random using a pseudo-random number generator to remove any bias, and in all cases except where Dref = 12.0 Gy, the split-calibration

method was found to be more accurate than the standard calibration method.

For the larger doses included in these test cases (40.0 Gy and 52.0 Gy for batch 1, as well as 46.0 Gy for batch 2), the difference between the ”true” dose (Dref) and the dose

estimated using standard calibration methods estimation was as much as 22 %, while the same difference when using the split-calibration method was found to be less than 4 %. This means that even at doses above 40 Gy, the Gafchromic EBT-3 films can be used as a reliable dosimeter, in disagreement with previously published work[18]. The uncertainties obtained when utilizing the different calibration methods for both batches have been visually depicted in figure 3.5, and listed along with their respective calibration parameters in tables 3.3, 3.4 and 3.2.

The expectation when comparing the different methods to each other was that the split-calibration method would exhibit a more accurate estimation of parameter uncertainty in the upper end of the dose range, and a larger but more accurate error estimation of unknown doses. This is because the error in absorbed dose was assumed to have a constant value of 2.05 %, which means that larger absorbed doses will have a larger absolute error. In turn, calibrating the batches by computing the nlLSQ-fit over the whole dose range will be heavily weighted towards the lower end of the dose

spectrum, and thus the nlLSQ-fit would underestimate the error in calibration parameters.

When calibrating the films according to the split-calibration method, the weighting of the films is specific to that interval of absorbed dose, and accordingly a higher

uncertainty in that interval is expected.

As figure 3.5 shows, this is not necessarily true (see the red color channel in figure 3.5a or the green color channel in figure 3.5b). Estimating unknown doses using the

multi-channel method does however echo the expectations, and yields higher uncertainties when using the split-calibration method to estimate these doses as expected (see table 3.7).

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5. Conclusion

In conclusion, increasing the amount of calibration measurements from 8 to 17 was shown to optimize the sensitometric curve for each batch of Gafchromic EBT-3 films in terms of uncertainty and accuracy (a 15.6 % - 45.3 % and 17.2 % - 28.4 % improvement for batch 1 and 2 respectively). Regardless of where the EBT-3 films may be used as a dosimeter, as many calibration measurements as possible should be utilized to ensure maximum measurement accuracy.

The additional measurements also allows the user to calibrate the batches according to the newly developed split-calibration method, yielding more accurate dosimetric

estimations of films exposed to approximately 20 Gy or more. In situations where the absorbed dose is unknown, or known to be above the dynamical dose range of

Gafchromic EBT-3 films[4], the split-calibration method is recommended to be used for accurate dosimetry, while doses below approximately 20 Gy can be reliably estimated using the standard calibration method.

The new split-calibration method was also shown to be able to estimate doses up to 52 Gy in disagreement with previously published work[18]. The estimations of high doses were shown to be much better in terms of accuracy when using the split-calibration method compared the standard calibration method.

Both batches calibrated with the split-calibration method were shown to accurately estimate the reference doses to within 4 %, however as the uncertainties in these estimations are large (approximately 25.43 % for batch 1 and 22.97 % for batch 2), further investigations are needed to conclude whether the accuracy of the presented results are due to random luck, or if the uncertainty in these doses have been severely overestimated.

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Characterization of GafChromic EBT-3 film calibration for high-accuracy applications

Stockholm University

Bachelor Thesis