Università di Pisa
Dottorato di Ricerca in Ingegneria Industriale Curriculum Ingegneria nucleare e sicurezza industriale
XXX Ciclo
Development and characterization
of novel radiochromic dosimeters
for X-rays and UV radiations
Candidato
Relatori
Ing. Andrea Marini
Prof. Francesco d’Errico
Prof. Luigi Lazzeri
Prof.ssa Maria Grazia Cascone
Coordinatore del corso
Prof. Giovanni Mengali
Ai miei genitori.
Non per retorica,
ma con vero amore.
Scripta manent.
“E capii che nella vita non volevo diventare come certe persone,
e avrei cercato con tutta la mia forza di essere come certe altre.”
(“Saltatempo”, Stefano Benni)
3
Contents
Abstract ... 9
1 Introduction ... 10
2 State of the art ... 16
2.1 Three-dimensional dosimeters for radiation therapy ... 16
2.1.1 Radiochromic gel dosimeters ... 17
2.1.2 Radiochromic plastic dosimeters ... 21
2.1.3 Polymer gel dosimeters ... 21
2.2 UV dosimeters ... 23
2.2.1 Photodiodes based radiometers ... 23
2.2.2 Spectroradiometers ... 23
2.2.3 Photomultiplier tubes... 24
2.2.4 Broadband UV radiometers ... 24
2.2.5 Polysulfone films ... 25
3 Development of a Fricke gel dosimeter based on a polyvinyl alcohol matrix chemically cross-linked with glutaraldehyde ... 27
3.1 Materials and methods ... 30
3.1.1 PVA-GTA gelation time ... 30
3.1.2 Gel volume reduction ... 31
3.1.3 PVA-GTA Fricke gel and gelatine gel preparation procedure ... 32
3.1.4 Dose-response ... 35
3.1.5 Diffusion coefficient ... 35
3.1.6 Spontaneous oxidation ... 36
3.2 Results and discussion ... 37
3.2.1 Gelation time ... 37
3.2.2 GTA influence on the initial absorbance ... 43
3.2.3 Dose-response ... 45
3.2.4 Diffusion coefficient ... 54
3.2.5 Volume reduction ... 61
4
3.2.7 Mowiol based gel ... 64
3.3 Comparison with other Fricke gels ... 75
3.4 PVA-GTA Fricke gel: final remarks ... 77
4 Redox-Phen solution: a water-based chemical dosimeter for UV and X-rays ... 79
4.1 Materials and method ... 82
4.1.1 Redox-Phen solutions preparation ... 82
4.1.2 UVA and UVB irradiation ... 84
4.1.3 X-rays irradiation ... 84
4.1.4 Solutions read-out ... 84
4.2 Results and discussion ... 85
4.2.1 Nitric acid concentration ... 87
4.2.2 Ammonium iron(III) sulfate concentration and phen/FAS ratio ... 88
4.2.3 Proposed formulation ... 94
4.3 Comparison with other UV dosimeters ... 99
4.4 Redox-Phen solution: final remarks ... 101
5 Conclusions and future perspectives ... 102
6 List of publications ... 103
5
List of figures
Figure 2.1 - Samples of the three main types of 3D chemical dosimeters. ... 16
Figure 2.2 - Fricke gel samples irradiated in the range 0-30 Gy ... 19
Figure 2.3 - Simplified schematic of a double beam spectroradiometer ... 24
Figure 2.4 - Detector head of broadband UV meter ... 25
Figure 2.5 - Polysulfone repeating unit ... 26
Figure 3.1 - Partially (left) and fully (right) hydrolyzed PVA ... 27
Figure 3.2 - PVA cross-linking by GTA ... 28
Figure 3.3 - Irradiation setup for diffusion coefficient measurements. ... 35
Figure 3.4 - Frequency-time diagram of a gel with 26.5 mM of GTA at 20 °C ... 37
Figure 3.5 - Smoothed dataset and Logistic fitting function ... 39
Figure 3.6 - Gelation point calculation ... 40
Figure 3.7- Gelation time of gels with different concentrations of GTA at 20 °C ... 41
Figure 3.8 - Gelation time of gels with 26.5 mM of GTA at different temperatures ... 41
Figure 3.9 - Two Fricke solutions with the addition of 26.5 mM of GTA ... 43
Figure 3.10 - Absorbance of Fricke solutions with xylenol orange and different amount of GTA ... 44
Figure 3.11 - Dose-response curve of the PVA-GTA gel ... 45
Figure 3.12 - Dose-response curves of PVA-GTA and gelatine gels in the range 0-30 Gy. ... 47
Figure 3.13 - Sensitivity values of repeated PVA-GTA gel batches and average value ... 48
Figure 3.14 - Intercept values of three PVA-GTA gel batches and average value ... 48
Figure 3.15 - Initial absorbance of the three gel batches and their average ... 49
Figure 3.16 - Precision of the three PVA-GTA batches ... 50
Figure 3.17 - Calculated dose from the three PVA-GTA batches ... 51
Figure 3.18 - Accuracy of the three PVA-GTA gel batches ... 52
Figure 3.19 - Diffusion mechanism of solute molecules in a hydrogel. ... 55
Figure 3.20 - Gel samples for the measurement of the diffusion coefficient ... 57
Figure 3.21 - Absorbance-position profile one hour after the irradiation (dots) and fitting equation (solid line) ... 58
Figure 3.22 - Normalized absorbance-position profiles ... 58
Figure 3.23 - Curvature parameter n of PVA-GTA-A, PVA-GTA-B and gelatine gel versus time ... 59
6 Figure 3.24 - Sketch of the influence of the crosslinking degree on the diffusion of a solute. 60 Figure 3.25 - Sketch of the diffusion of a solute inside two gels with different molecular
weights. ... 60
Figure 3.26 - Gel samples with 132.5 (left) and 265 mM of GTA (right) ... 62
Figure 3.27 - Absorbance change at 585 nm of PVA-GTA and gelatine gel stored at 5 °C .... 64
Figure 3.28 - 10% PVA GTA gel (left) and 15% PVA solution (right) ... 65
Figure 3.29 - Absorption spectra of 10%PVA-GTA gel and 15% PVA solution ... 65
Figure 3.30 - 15%Mowiol Fricke solution (left) and its absorption spectrum (right) ... 67
Figure 3.31 - Dose-response curve of 10% (Mw-A) and 12.5% (Mw-B) Mowiol-based gels68 Figure 3.32 - Coefficient of variation of the Mw-A and Mw-B gels as a function of dose ... 69
Figure 3.33 - Sketch of the impact of a blend of molecular weights on the diffusion of a solute. ... 70
Figure 3.34- Spontaneous oxidation rate of different PVA and Mowiol gels ... 73
Figure 4.1- Phenanthroline molecule (left) and ferroin molecule (right) ... 79
Figure 4.2- Redox-Phen_F solution samples irradiated with different UVA doses. ... 80
Figure 4.3 - Absorbance spectra of Redox-PHEN_B solution exposed to different UVA doses ... 85
Figure 4.4 - Absorbance spectra of Redox-Phen_H solution exposed to 1000 mJ/cm2 and a water solution with 0.2 mM of ferroin ... 86
Figure 4.5 - Comparison between UVA dose response of PHEN_A and PHEN_B samples .. 87
Figure 4.6 - UVA dose response of solutions with 0.25 mM of FAS and different phen/FAS ratios ... 88
Figure 4.7 - UVA dose response of solutions with 0.5 mM of FAS and different phen/FAS ratios ... 89
Figure 4.8 - UVA - dose-response curve of Redox-Phen_G ... 90
Figure 4.9 - UVA sensitivity of Redox-Phen solutions with 0.25 mM and 0.5 mM of FAS as a function of the phen/FAS ratio ... 91
Figure 4.10 - UVB-dose response of Redox-Phen_E, Redox-Phen_F, and Redox-Phen_H ... 92
Figure 4.11 - X-rays dose-response different Redox-Phen solutions ... 93
Figure 4.12 - Absorbance change during storage at ~5 °C ... 94
Figure 4.13 - UVA-dose response of Redox-Phen_F ... 95
Figure 4.14 - UVB - dose response of Redox-Phen_F ... 97
7 Figure 4.16 - Comparison between UVA-dose responses of Redox-Phen_F solution and Fricke gel dosimeters ... 99 Figure 4.17 - Comparison between UVB-dose response of Redox-Phen_F solution and polysulfone film ... 100
8
List of tables
Table 2.1 - Sensitivity and diffusion coefficient of different type of Fricke gels ... 20
Table 3.1 - Gel tested to evaluate the volume reduction ... 31
Table 3.2 – PVA and GTA concentrations of the tested gel ... 34
Table 3.3 - Summary of gelation times as a function of GTA concentration and temperature 42 Table 3.4 - Recommended calibration coefficient for the PVA-GTA gel ... 49
Table 3.5 - PVA molecular weight, GTA concentration and diffusion coefficients of the tested PVA-GTA gel ... 56
Table 3.6 - Volume reduction of PVA-GTA gels after 21 days ... 62
Table 3.7 - Diffusion coefficient of tested PVA gels ... 72
Table 3.8 – Dosimetric characteristics of PVA-GTA gel and other Fricke gel dosimeters ... 76
Table 4.1 - Tested Redox-Phen solutions... 83
9
Abstract
This thesis presents the development of two tissue equivalent and water equivalent chemical dosimeters for the measurement of the three-dimensional dose distribution in radiotherapy and the dose from UV sources.
Current radiotherapy techniques implement treatment plans based on volumetric dose distributions with complex shapes and sharp gradients. To verify the agreement between these treatment plans and the dose that is actually delivered to the patient, a dosimetric system that is truly three dimensional, sensitive to radiation in each point and tissue equivalent is required. For this purpose, we developed a radio-chromic gel based on polyvinyl alcohol (PVA) chemically cross-linked with glutaraldehyde (GTA). This gel dosimeter has high sensitivity and stability of the signal, i.e. low diffusion of the iron complex. Furthermore, it is transparent and therefore can be imaged with optical techniques, as well as with NMR. The dosimetric characteristics of the PVA-GTA gel were compared to those of a Fricke gelatine gel and to other gel dosimeters previously studied by other investigators.
Even though UVA and UVB rays are commonly adopted in many treatments for skin disease and tumors, a passive and water equivalent dosimeter for both this type of radiations does not exist. We developed an aqueous dosimeter that is sensitive to UVA, UVB and X-rays named Redox-Phen solution. This dosimeter is inexpensive and tissue equivalent, being made of 99% of water. It changes color in the visible region upon irradiation, thus it can be measured via simple optical method, and an evaluation of the exposition can be made also by naked eyes. We studied the influence of the main chemical parameters on the dose-response and storage stability of the dosimeter to select the best formulation and compare it with the performances of other UV passive dosimeters.
10
1 Introduction
During his entire life, each person is continuously exposed to ionizing radiations from natural and artificial sources. Different natural sources of radiations exist to which we are exposed day by day, and many industrial and medical applications adopt ionizing radiations too. The dangerous nature of this type of radiations is well known: the exposition to ionizing radiations can produce detrimental effects on the health of human beings due to their ability to damage DNA, and these effects can be deterministic or stochastic. A safe dose threshold exists for deterministic effects, while the more accepted model for stochastic effects is the so-called “Linear no-threshold” model (ICRP, 2007), which predicts a linear increase in the probability of a stochastic effect but not a safe level, no matter how low the exposition is. The most relevant stochastic effect is the probability to develop a mortal cancer.
Cancer is the second leading cause of death worldwide: the lifetime probability of developing a cancer is about 40% in the USA for men and women. In Italy, one man out of two and one woman out of three will develop a cancer at a certain point in their life. The lifetime
probability of dying of cancer is about 33% for men and 16% for women in Italy, and 23% for men and 19% for women in the USA. Great progress have been done in the diagnose and treatment of cancer in the last decades. The improved effectiveness of cancer treatments is testified by the drop in deaths for cancer in the last years in nations where the more advanced medical procedures are available. Cancer death dropped about 1.5% annually both in men and women in the USA between 2005 and 2014, and 1.5% for men and 0.7% for women in Italy in the period 2006-2016. (Associazione Italiana di Oncologia Medica and Associazione Italiana dei Registri Tumori, 2016; National Cancer Institute, n.d.; Siegel et al., 2016; WHO, 2017)
Despite their aforementioned dangerousness, ionizing radiations are a tool of primary importance in medicine, especially in cancer treatment. Many different procedures adopt X or gamma rays to diagnose or treat diseases. As any other artificial exposition to ionizing radiations, medical procedures that adopt ionizing radiations have to follow the key radiation protection principles known as justification, optimization and dose limitation (ICRP, 2007). Therefore, although no legal limits exist for patients, the delivered dose has to be kept as low as reasonably achievable every time a patient needs to be exposed to ensure that the positive
11 healing effect overcomes the possible health detriment. To achieve this goal the adoption of the most advanced dosimetric techniques to monitor and optimize the exposition is mandatory. These techniques and related devices need a continuous development to follow closely the fast-paced enhancement of medical apparatus.
A good example of this relationship between medical and dosimetric devices can be found in the radiation therapy field. In the USA about half of the patients with cancer receives some type of radiation therapy as part of their treatment (“Radiation Therapy for Cancer - National Cancer Institute,” n.d.). External radiation therapy is adopted in the majority of the cases. It makes use of focused beams of ionizing radiations, mainly high energy X-rays and electrons, produced by linear accelerators (LINACs) to treat the cancer volume. LINACs have become more and more complex in the last decades. The adoption of technical solutions such as rotating gantry, computerized treatment planning, multileaf collimators, intensity modulation and integrated cone beam has led to so-called 3D conformal radiation therapy. This type of external radiation therapy is able to conform the X-ray beam to the cancer shape at any entrance angle while modulating the intensity at the same time. Nowadays many different types of 3D conformal radiotherapy treatment exist: some examples are Intensity Modulated Radiation Therapy (IMRT); Volumetric Modulated Arc Therapy (VMAT); Stereotactic Ablative Radiation Therapy (SABR). All of these techniques share the ability to precisely deliver the dose to the volume to treat while sparing the surrounding healthy tissues, especially nearby organs at risk (OAR). This sparing effect is achieved creating volumetric dose distributions with complex shapes and sharp gradients. Measuring and verifying these highly discontinuous volumetric distributions is a challenging but yet necessary task.
Many dosimetric devices have been developed in the recent years in the attempt to perform the exact characterization of these complex beams: along with the well-established dosimetric techniques such as ionization chambers or film dosimeters, many other devices aim to reconstruct the dose distribution by mean of bi-dimensional arrays of point silicon dosimeters arranged on planar or cylindrical geometries.
Even though all the aforementioned instruments are commonly used worldwide, none of them is a true 3D system. All the devices used nowadays reconstruct the volumetric distribution interpolating a sampling of one or two-dimensional sparse measurements. Furthermore, many of them are made of materials that are not tissue equivalent, such as silicon.
12 A true three-dimensional dosimeter is defined by the so-called “Resolution-Time-Accuracy-Precision (RTAP) criteria” introduced by Oldham et al. (2001) and extensively discussed in many other works (Oldham, 2015, 2014; Oldham et al., 2001; Schreiner, 2015). According to them, a 3D dosimeter has to be capable of delivering «a 3D dosimetric analysis of a treatment plan with 1 mm isotropic spatial resolution, within 1 hour, with an accuracy of within 3% of the true value, with 1% precision».
The only dosimeters nowadays available that fulfill all these criteria are the 3D chemical dosimeters. These dosimeters are based on the quantification of changes in the concentration of chemical species induced by the interaction with ionizing radiations. The ability of these systems to measure the dose stems from their chemical properties, hence all their volume is sensitive to radiations. The volumetric dose distribution can be reconstructed imaging the dosimeter with nuclear magnetic resonance (NMR) or optical computed tomography (optical CT). The dosimeter registers the spatial dose information continuously throughout its volume rather than sampling it, then a high spatial resolution can be achieved.
Three main class of 3D chemical dosimeters have been proposed by various investigators in the last decades: radiochromic gels, radiochromic plastics, and polymer gels (Schreiner, 2017). This thesis illustrates the development and optimization of a new radiochromic gel dosimeter based on a matrix of polyvinyl alcohol (PVA) cross-linked with glutaraldehyde (GTA). The main aim of the work was to realize a so-called Fricke gel that could overcome the main issues that have impaired the use of these dosimeters so far. In fact, despite Fricke gels have been the first radiochromic gel dosimeters that have been proposed (Gore and Kang, 1984), their affirmation as a widespread tool has been hindered by two main phenomena that happen in the dosimeter: the diffusion of ions inside the matrix, that will blur the initial volumetric dose distribution as the time passes and eventually lead to the loss of spatial information, and the spontaneous oxidation of ferrous ions that limits the shelf life of the dosimeter.
Polyvinyl alcohol has been proposed as a matrix for Fricke gel by Chu and colleagues in 2000 (Chu et al., 2000). PVA has been regarded as a favorable alternative to natural polymers, mainly gelatine and agarose, that was used in all the previously published studies because it is a synthetic polymer produced with high purity and stringent tolerances on chemical characteristics. Natural polymers available on the market usually contain more impurities and greater differences can exist between different batches, hence the reproducibility of these gel
13 has always been a critical aspect. PVA is water soluble and non-toxic. Different routes exist to create a gel from a PVA solution (Peppas, 1987), a process also known as cross-linking. Chu and colleagues (2000) proposed to adopt a physical method that creates a gel by freezing and thawing a PVA water solution repeatedly. Even though effective, this method creates gels that are translucent or opaque, depending on the freezing temperature, it is laborious and may lead to gel with a non-uniform structure due to thermal gradients, especially in large volumes. We hereby propose a PVA based gel dosimeter that is cross-linked with a chemical reaction. The cross-linking agent GTA is added to a water-based PVA solution: GTA reacts with PVA linking together different molecules and creating a network that yields a transparent hydrogel that can be imaged with both optical and magnetic techniques. The production process is extremely simple since it does not need additional steps after the mixing of all the chemical reagents. The initial fluid solution that eventually turns into a gel can be cast in volumes of any shape and size. The diffusion of ions in the irradiated gel is one of the lowest ever obtained in a Fricke gel so far, while the sensitivity is higher than the gel proposed by Chu and colleagues (2000).
In the second part of this thesis, the development of a new water-based chemical dosimeter for UV radiation and X-rays is presented. UV radiation is the part of the light spectrum with a wavelength between 10 and 400 nm. The UV region is where the transition between non-ionizing and non-ionizing radiation occurs. To define exactly if a radiation is non-ionizing or not is tricky since different atoms and molecules have different ionization values. The conventional transition between UV and X-rays has been fixed at a wavelength of 10 nm, equal to an energy of 124 eV. However, the first ionization energy of oxygen and hydrogen is equal to 12.1 and 13.6 eV, and an average energy of 33 eV is required to ionize a water molecule (considering also other possible interactions, such as excitation). Therefore, the value of 33 eV is sometimes regarded as the transition between non-ionizing and ionizing radiations, especially if biological effects are of interest. The most energetic part of the UV spectrum is thus ionizing, while the mid and lower part is not. Nevertheless, all the UV spectrum has in common with ionizing radiations the ability to damage the DNA and promote cancer. As for ionizing radiations, damages induced by UV radiations are not related to energy transfer in the form of heat: they arise from the chemical changes induced in the DNA molecules directly by the radiation or by indirect mechanisms, such as the creation of highly reactive chemical
14 species that eventually interact with the DNA (Matsumura and Ananthaswamy, 2004; National Toxicology Program, 2016; Sinha and Häder, 2002).
The UV spectrum is conventionally divided into sections of different wavelengths. This subdivision is somehow arbitral and various values of transition wavelengths between one UV class and the following are adopted in different science fields. In biology and human health-related fields the most accepted categorization subdivides the UV spectrum in UVA, from 315 to 400 nm; UVB, from 280 to 315 nm and UVC, from 100 to 280 nm (Brian L Diffey, 2002; Tobiska and Nusinov, 2007).
UVB and UVC photons produce direct damages to DNA, hence they have been regarded for long as carcinogenic agents. Even though UVA cannot produce such a direct damage, they can promote the creation of highly reactive chemical species, such as hydroxyl and oxygen radicals, that in turn can create DNA ruptures. Therefore, recently cancer-promoting effect of UVA has been reconsidered. Chronic UVA exposure may result in the accumulation of DNA lesions and also increase or multiply UVB-mediated DNA damage (Svobodová et al., 2012). The main source of human UV exposition is sunlight. Despite its dangerousness, UVC is of little concern for human safety as long as sun irradiation is involved, since almost all of the UVC photons that reach the Earth are shielded by the atmosphere. On the other hand, the solar UV spectrum that reaches the Earth surface is made approximately of 95% of UVA and 5% of UVB (Brian L. Diffey, 2002).
As for ionizing radiation, UVA and UVB photons are used extensively in medicine. They find vast adoption in the treatment of skin diseases and skin cancer via phototherapy, often in conjunction with specific drugs such as psoralens (PUVA and PUVB therapy).
Many electronic devices exist that can measure UV radiant exposure, the dosimetric quantity of interest in photobiology, but they are non-water equivalent, usually mono-dimensional point devices. Although personal dosimeters for UV radiations do exist, many studies concentrated on the possibility to create a UV dosimeter to monitor sunlight exposition. Among this dosimeters, polysulfone films are the most common ones (Davis et al., 1976). UVB rays are the most dangerous part of the sunlight spectrum, therefore polysulfone films, being sensitive to wavelengths between 320 and 290 nm, have been regarded as a convenient personal dosimeter. Nevertheless, as previously noted UVA exposition poses potential hazards too, and medical applications use both UVA and UVB radiations (Lapolla et al.,
15 2011; Wainwright et al., 1998). Therefore, a dosimeter that can measure both UVA and UVB radiation may be of interest in many medical and environmental applications.
In the second part of this research, we developed a water equivalent passive chemical dosimeter named Redox-Phen solution that is sensitive to all the three main type of photons adopted in therapeutic treatment, i.e. UVA, UVB, and X-rays. The proposed dosimeter is a water solution that changes its color upon irradiation. This change is proportional to the energy deposited by the radiation in the volume and it occurs in the visible region, thus it can be quantified with simple optical measurements. A first evaluation can also be made with the naked eye, whereas polysulfone films develop their signal in the UV, thus being invisible to humans and needing special reading apparatus.
We investigated the influence of the main chemical parameters on linearity and sensitivity of the response of various Redox-Phen solutions and selected the formulation with the best overall performances.
16
2 State of the art
2.1 Three-dimensional dosimeters for radiation therapy
The last decades have seen a continuous increase in the complexity of medical linear accelerators (LINACs) for radiation therapy. In response to this, a new type of dosimeters has been proposed in the effort to characterize the complex volumetric dose distributions produced by the more advanced among these new apparatus and validate treatment plans. To do this, high and isotropic spatial resolution and adequate precision and accuracy are needed. The idea of a three-dimensional phantom made of a tissue equivalent material that is also sensitive to radiation in each point dates back to the work of Gore and colleagues, that firstly proposed in 1984 to use the well-known Fricke solution dispersing it in a gelling matrix (Gore and Kang, 1984). Gore demonstrated that the radiation-induced chemical changes in the gel could be imaged by NMR techniques. Since then, gel dosimetry became a thriving research field and many different types of 3D chemical dosimeters have been proposed. Among them, three main types gained affirmation and are the most relevant nowadays: radiochromic gels, radiochromic plastics and polymer gels (Figure 2.1). The main aspect of these three types of 3D chemical dosimeters will be discussed briefly hereafter. (Baldock, 2017; Ibbott, 2004; Lepage and Jordan, 2010; Oldham, 2015; Schreiner, 2015, 2004)
Figure 2.1 - Samples of the three main types of 3D chemical dosimeters. From left to right: a) radiochromic gel dosimeter; b) polymer gel dosimeter; c) radiochromic plastic. Pictures from Oldham (2015) and Schreiner (2015)
17
2.1.1 Radiochromic gel dosimeters
Radiochromic gels are the evolution of the first gel dosimeter proposed by Gore and colleagues. The initial idea was to disperse the so-called Fricke solution in an agarose gelling matrix. Fricke solution, an acidic water solution of an iron salt, was one of the first dosimeter ever proposed (Fricke and Morse, 1927). Before the irradiation, the solution contains only Fe2+ ions that are oxidized to Fe3+ by the interaction of ionizing radiation with the dosimeter. The final concentration of Fe3+ ions is proportional to the absorbed dose. Since the amount of iron in the solution is negligible if compared to the total mass, radiations interact almost exclusively with the water bulk creating radicals, hence the Fricke solution is tissue and water equivalent. Radicals are highly reactive chemical species that eventually interacts with the ferrous ions and oxidize them (radical species will be indicated with the symbol after their chemical formula). When the solution is irradiated, water is decomposed:
Hydrogen atoms then react with oxygen to produce the hydroperoxy radical:
After this initial interaction between ionizing radiation and water different chemical routes may lead to the oxidation of a ferrous ion. Some of them are:
18 Regardless of the chemical route, the final concentration of Fe3+ ions is proportional to the energy deposited in the dosimeter by the radiation. The relationship that links the change in Fe3+ concentration to the dose is:
[ ] (
)
Where D is the dose, G (Fe3+) is the chemical yield of Fe3+ (expressed as ions produced per 100 eV), ρ is the density in kg/l, NA is Avogadro’s number and is the number of Joules per
electron volt.
The Fe3+ concentration of Fricke solution is usually evaluated by spectrophotometric measurements since Fe3+ has absorption peaks at 224 nm and 304 nm. The gel, on the other hand, could be imaged by NMR to retrieve both the dose and its spatial distribution, since the magnetic properties of iron ions changes with the oxidation state. The polymeric matrix keeps the ions in the position where they were oxidized for a certain time so that not only the dose but also its spatial distribution could be reconstructed. This first attempt to create a 3D dosimeters was impaired by the high diffusion of the small iron ions inside the matrix, that limited to about 1 hour the useful time to image the irradiated gel before the spatial information was lost. Furthermore, this problem was amplified by the long sampling time needed for an NMR reading.
Different authors proposed to modify the standard formulation of Fricke solutions and gels by the addition of chelating agents (Appleby and Leghrouz, 1991; Rae, 1996). A chelating agent is a molecule that can form two or more coordination bonds with one metal ions. Xylenol orange (XO) is the most used chelating agent in Fricke gels: when added to the Fricke solution XO chelates the Fe3+ ions creating a chemical species that has an intense absorption peak at 585 nm. A Fricke solution with the addition of XO can be infused in a gelling matrix to obtain a gel that changes its color from yellow-orange to deep purple upon irradiation (Figure 2.2).
19 Figure 2.2 - Fricke gel samples irradiated in the range 0-30 Gy(from left to right) with 5 Gy increments.
This gel dosimeter, known as Fricke or Ferrous Xylenol gel (FXG), is by far the most studied and adopted radiochromic gel dosimeter. Xylenol orange made possible to image FGX gels with optical CT (Kelly et al., 1998), a technique that demonstrated lower imaging time and higher accuracy and spatial resolution than NMR (Oldham et al., 2001).
The introduction of xylenol orange had also a massive impact on diffusion: the chelated molecule is much bigger than the Fe3+ ion alone, then its movement inside the polymer network is slower (Rae, 1996; Schreiner, 2004).
The three main matrixes that have been studied are agarose, gelatine, and PVA. Agarose has been the first adopted polymer (Appleby et al., 1986; Gambarini et al., 1999; Healy et al., 2003), but it has been soon replaced by gelatine due to its transparency and lower dissolving temperature (Bero et al., 2000; Davies and Baldock, 2008; Hazle et al., 1991). PVA has been regarded as a convenient alternative to agarose and gelatine because of its chemical simplicity and purity (Chu et al., 2000; Hill et al., 2002). A comparison between the typical value of sensitivity and diffusion coefficient of gels made by natural polymers and PVA is reported in Table 2.1.
20 Table 2.1 - Sensitivity and diffusion coefficient of different type of Fricke gels
Gel matrix
Sensitivity
(Gy
-1)
Diffusion
coefficient
(mm
2h
-1)
20% PVA hydrogel
(Chu et al., 2000)
0.046
0.14
20% functionalized PVA
(Smith et al., 2015)
0.014
0.13
Natural polymers
(various types and concentrations)
(Chu et al., 2000; Davies and Baldock,
2008; Kron et al., 1997; Rae, 1996)
0.065 - 0.075
0.3 - 2.2
FX gels are easy to prepare and show adequate dose sensitivity. However, subtle variations in dose responses have been reported between batches and within research groups. Two main sources of variation come from xylenol orange, whose chemical purity may differ from batch to batch and between different manufacturers (Liosi et al., 2017), and from deformities in the production procedures. The oxygen content, for example, is a parameter that greatly influences the response of the dosimeter, and different procedures may lead to differences in the final oxygen concentration (Davies and Baldock, 2008; DeAlmeida et al., 2014; Olsson et al., 1989; Schulz et al., 1990). Another aspect that impaired the practical adoption of FXG dosimeters is the spontaneous oxidation of Fe2+ ions. The conversion from Fe2+ to Fe3+ occurs spontaneously even in the absence of stimulation because the ferric state is the more stable one. Since that, the shelf life of FXG is not long enough to make them commercially available. Thus, FXG gels need to be prepared in a chemistry lab a brief time ahead of their use, and this makes them impractical for many medical centers.
21
2.1.2 Radiochromic plastic dosimeters
The idea to use plastic for a radiochromic dosimeter has been proposed in 2003 by Adamovics and Maryanski (Adamovics and Maryanski, 2006, 2003). In the most used formulation polyurethane is used to create a solid matrix that is infused with a halogenated free radical initiator and leuco-malachite-green leucodye (LMG). The interaction with ionizing radiation create radicals that oxidize LMG to malachite green, thus turning the plastic from transparent to green. This dosimeter is known with its commercial name PRESAGE™ and can be imaged with optical CT but not with NMR. Since malachite green absorbs light rather than scatter it, the dosimeter shows high contrast. The polyurethane matrix is more transparent than natural polymers usually adopted for gels and being solid it is diffusion free and does not require an external casing. (Oldham, 2015)
PRESAGE™ showed a linear dose response up to 100 Gy, while the energy and dose rate dependence of the response is still under debate (Yates et al., 2011). Sensitivity showed differences from batch to batch and even within the same batch between dosimeters of different volumes (Oldham, 2015). A darkening effect over time has been reported by different authors, but it seems not to depend on the dose and then it can be modeled and accounted for (Juang et al., 2013; Nasr et al., 2015; Schreiner, 2015).
PRESAGE™ radiochromic plastic is commercially available, so there is no need for a chemical lab to prepare the dosimeter on site.
2.1.3 Polymer gel dosimeters
Polymer gel dosimeters are based on the radiation-induced polymerization of monomers dispersed in an aqueous gel matrix, usually agarose or gelatine (Baldock, 2017). The effect of ionizing radiations on monomers and polymer have been extensively studied in many works in the fifties and seventies (Alexander et al., 1954; Boni, 1961; Hoecker and Watkins, 1958) but the development of polymer gels for radiotherapy came later from the work of Maryanski and colleagues (Maryanski et al., 1994). They proposed to use the polymerization of acrylamide and N,N’-methylene-bis-acrylamide (bis) monomers dispersed in agarose as an alternative to Fricke gel dosimeters.
Jirasek summarized the many chemical reactions that occur in a polymer gel exposed to ionizing radiations and that are the mechanism behind this type of dosimetric gels (Jirasek et
22 al., 2009). In the first place, water radiolysis creates several different radicals that react with monomers and start the polymerization. The so formed polymers then grow in length via different reactions that link new monomers or different polymers one to the other in a chain reaction, since their terminal vinyl group remains available. This process, that produces also heat, can be halted by the interaction of the polymer chain with another chain termination, with gelatine or with primary radicals.
Polymer gel dosimeters do not suffer diffusion problem, hence the post-irradiation distribution of polymers is stable, and they can be imaged both with NMR and optical CT. Even so, the performance of polymer gels with optical CT are less satisfactory if compared with radiochromic gels and plastic, because in these gels light is scattered instead of being absorbed: the higher stray light produces lower contrast and accuracy. The main issue with the use of these gels has been their sensitivity to oxygen. Being based on the chemistry of free radicals, they have to be created in oxygen-free environments and preserved from any contact with atmospheric oxygen that may impair the polymerization, reducing their accuracy and creating artifacts (De Deene et al., 2000; Gustavsson et al., 2004). Therefore their production process is much more complicated than FXG gels. Furthermore, the chemicals they are made of are highly toxic, while the reagents used for Fricke gels are not.
A fundamental step forward for this type of gels has been the development of a formulation known as MAGIC that is not sensitive to oxygen inhibition and thus can be created and used in a normally oxygenated environment (Fong et al., 2001). MAGIC polymer gel is made of methacrylic acid, ascorbic acid, gelatine, and copper. Ascorbic acid binds free oxygen contained within the aqueous gelatine matrix into metallo-organic complexes in a process initiated by copper sulfate, thus scavenging it and preventing the polymerization inhibition effect.
Polymer gels have been the more adopted gel dosimeters, and many studies used them to verify treatment plans (Baldock et al., 2010; Ibbott, 2004). Some polymer gels are available on the market (“MGS Research Inc,” n.d.).
23
2.2 UV dosimeters
The vast majority of UV dosimeter are electronic devices that measure the changes in electrical quantities such as voltage or current. These instruments are sensitive and precise, but they are not water equivalent, being made of a material such as silicon, and they are usually mono-dimensional point devices. Thus, their response may vary sharply with the angle of incidence of the radiation. Furthermore, they are active systems, so they need some source of electric power to function.
The most relevant passive UV dosimeters are polysulfone films. These measure the UV radiant exposure by the darkening of the exposed plastic film, that changes its absorbance at a certain wavelength upon irradiation.
The characteristics of the main devices used to measure UV radiation will be exposed briefly hereafter.
2.2.1 Photodiodes based radiometers
Photodiodes sensitive to wavelengths from about 200 nm up to about 1000 nm are used in many radiometers. Photodiodes by themselves are sensitive to the whole light spectrum, then filters are used to cut the wavelength outside UV. The UV light is converted into a current that is proportional to the UV dose.
2.2.2 Spectroradiometers
Spectroradiometers measure the power distribution of a source at each wavelength of the spectrum. This information leads to the radiometric, photometric and colorimetric characterization and calibration of the source. Spectroradiometers usually are portable devices that do not need a computer connected to them to work. A schematic of a spectroradiometer is reported in Figure 2.3, where the essential components are shown:
the input optics gathers the electromagnetic radiation from the source; the monochromator separates the light into its component wavelengths; the detector itself;
24 the control and logging system that gather the data and store them
Figure 2.3 - Simplified schematic of a double beam spectroradiometer
2.2.3 Photomultiplier tubes
Photomultipliers tubes (PMT) are devices that produce a current proportional to the incident UV light by mean of a photocathode, that converts the striking photons into electrons. These electrons are accelerated in a void tube and multiplied in number by many dynode stages, then they are collected and the produced current is registered. PMTs are highly sensitive devices, thanks to their ability to multiply the initial signal, and their technology is well established, being used in many applications.
2.2.4 Broadband UV radiometers
A broadband UV radiometer (BBUV meter) is an instrument that measures the total (spectrally integrated) radiation, over a spectral band in the UV region from a UV source. Essentially, two types of broadband measurement are required, depending on the application: spectrally weighted and absolute. Spectrally weighted measurements evaluate the radiation according to the action spectrum, which is the rate of a physiological activity plotted against the wavelength of light, of the photovoltaic, photochemical or photobiological phenomenon under investigation. This requires the BBUV meters to have a relative spectral responsivity
25 matched to the action spectrum of the phenomenon of interest. Compared with spectral measuring instruments such as spectroradiometers, BBUV meters are much more cost-effective and simpler to use. They are also more portable, robust and faster. However, their inability to resolve the spectrum components and inevitable spectral mismatching to the desired spectrum may lead to significant and unexpected measurement errors if they are not calibrated and used under the same UV sources. The most common type BBUV meters operate in the wavelength range between 250 nm and 400 nm. Such instruments consist of a detector head, an electronic circuit, and a display unit. The head contains a photodetector (usually a UV-enhanced silicon photodiode) with a UV filter, a limiting aperture, and a front diffuser (see Figure 2.16).
Figure 2.4 - Detector head of broadband UV meter
2.2.5 Polysulfone films
Polysulfone is a thermoplastic polymer (Figure 2.5) that can withstand oxidation induced by heat and high energy radiations and can be produced in thin films.
When exposed to UV radiation, these films undergo degradation and their mechanical and optical properties changes. The plastic darkens upon UV irradiation, and its absorbance at 330 nm is related to UV dose with a monotone relationship (Davis et al., 1976).
26 Figure 2.5 - Polysulfone repeating unit
The main advantage of this material stems from its sensitivity at different wavelengths that resembles the erythema action spectrum of human skin and then provides a good measure of the erythema risk (Kollias et al., 2003). Furthermore, it is inexpensive and suitable to produce thin film badges, making it appealing for personal UV dosimetry. Along with these aspects, few drawbacks have to be highlighted. The change in the absorbance of polysulfone films is in the UV region, thus it is not possible to evaluate it by naked eyes and specific equipment are needed to measure it, e.g. a UV-vis spectrophotometer. The absence of sensitivity to UVA make these films adequate for personal dosimetry, but they cannot be used in those situations when this part of the UV spectrum has to be measured, e.g. in research or medical applications.
27
3 Development of a Fricke gel dosimeter based
on a polyvinyl alcohol matrix chemically
cross-linked with glutaraldehyde
Polyvinyl alcohol (PVA) is a synthetic polymer used in industrial, commercial, medical and food applications. Its idealized formula is [CH2CH(OH)]n. The monomer “vinyl alcohol” is
theoretically the enol form of acetaldehyde but cannot exist as a monomer in practice. PVA is soluble in water but relatively insoluble in organic solvents. Its physical characteristics depend on its grade of hydrolysis, hence PVA is usually divided in partially or fully hydrolyzed (Figure 3.1).
Figure 3.1 - Partially (left) and fully (right) hydrolyzed PVA
Other parameters, such as molecular weight, solubility, flexibility and tensile strength of the final product may be varied during the production process. PVA is a safe material to work with, being non-toxic (DeMerlis and Schoneker, 2003).
PVA-water solutions are transparent and can be turned into hydrogels by physical methods, such as freezing-thawing cycles, with high doses of ionizing radiations or with chemical methods, i.e. adding to the solution a cross-linking agent (Hassan and Peppas, 2000; Peppas, 1987). A PVA hydrogel made with the freezing-thawing method was firstly proposed by Chu and colleagues as an alternative to natural polymers for the production of Fricke gels (Chu et al., 2000).
28 This chapter presents the development of a Fricke gel based on the chemical cross-linking of a PVA water solution with glutaraldehyde (GTA). GTA is a bi-functional aldehyde with the formula C5H8O2. When added to an acidic PVA water solution, GTA bonds hydroxyl groups
of different PVA chains creating an acetal bond (Figure 3.2). If the number of bonds is high enough a continuous matrix is created, hence the viscous PVA solution is turned into a hydrogel.
Figure 3.2 - PVA cross-linking by GTA
This chemical route shows many advantages over the physical process of repeated freezing-thawing cycles:
the process is simple and reproducible. No additional steps are needed after the mixing of all the chemical reagents
the whole process only takes 4 to 8 hours, depending on the adopted PVA dissolution method
the gel is transparent, hence it can be imaged both by optical and NMR techniques the gel has a homogeneous structure and can be easily produced in different shapes
and volumes
29 We evaluated the gelation time as a function of different temperatures and GTA concentrations, the dose response and the stability over time of the gel as well as its diffusion coefficient. We compared the obtained results with a well-established gelatine based Fricke gel (Davies and Baldock, 2008) and with literature data. We named the gel dosimeter PVA-GTA gel.
30
3.1 Materials and methods
3.1.1 PVA-GTA gelation time
As a first step, we characterized the influence of two main parameters, temperature, and GTA concentration, on the gelation time of the PVA-GTA gel to find a hydrogel formulation that can be easily synthesized and that can efficiently host the chemical dosimeter. A reasonably long gelation time is a desirable property because it allows the correct mix of the reagents and makes possible to create phantoms of different shapes and volumes. We measured the gelation time with a scanning vibrating needle curemeter (RAPRA technology LTD, Shrewsbury, UK), an instrument that samples the resonance frequency and amplitude of a vibrating probe that is put in contact with the gel, with a sampling time defined by the user. The testing procedure is described hereafter.
Two stock solutions are prepared with analytical grade reagents (Sigma-Aldrich) and bi-distilled water:
Solution A: 1.4 ml of concentrated sulfuric acid (96%) into a final volume of 100 ml; Solution B: 2 ml of 25% glutaraldehyde (GTA) solution and 0.5 ml of Solution A into
a final volume of 10 ml of bi-distilled water
Ten grams of PVA 99% hydrolyzed with molecular weight 85000-124000 (Sigma-Aldrich) are dissolved in 80 ml of bi-distilled water. The dissolution is performed keeping the solution at 120 °C in an autoclave for an hour in a sealed bottle. After retrieving the solution from the autoclave, the PVA sediments on the bottom of the bottle, therefore the solution is mechanically stirred for 30 minutes until it is homogeneous. While stirring, the water-PVA solution is allowed to cool down to the desired temperature (25, 20 or 15 °C). When this temperature is reached, 9.5 ml of Solution A and 10, 5 or 2.5 ml of Solution B are added. If needed, the volume is made up to 100 ml adding the missing water and the solution is stirred until it is homogeneous. All the solutions contain a final concentration of sulfuric acid equal to 25 mM and 13.25, 26.5 or 53 mM of GTA. The PVA-GTA solution is quickly poured in a becher that is then placed in a thermostatic bath set at the selected temperature. The probe of the curemeter, a flat round disc, is placed in contact with the surface of the solution and the measurement is started. The sampling time is set to 200 ms and the measure lasts for 6 hours.
31
3.1.2 Gel volume reduction
PVA hydrogel cross-linked with GTA may shrink upon gelation. We prepared different gel samples (Table 3.1) to evaluate the amount of volume reduction as a function of the GTA concentration and the PVA molecular weight, i.e. the length of the polymer chains. Gels were produced with the procedure exposed in the previous paragraph. Preliminary observations confirmed that the shrinkage is isomorph: the gel preserves the shape of the container it was poured in before the gelation. Thus, we measured the reduction of the volume pouring a known volume of PVA-GTA solution in a cylindrical becher and letting it set. Once the solution turned into a gel we covered its free surface with paraffin oil to prevent evaporation of water from the hydrogel and stored the sample at room temperature (about 20 °C). After 21 days we removed the gel from the becher, we dried it with paper and measured its final dimensions with a caliper
Table 3.1 - Gel tested to evaluate the volume reduction
Molecular weight (·103) GTA (mM)
13-23 26.5 31-50 26.5 31-50 132.5 31-50 265 85-124 26.5 85-124 53 85-124 132.5 85-124 265
32
3.1.3 PVA-GTA Fricke gel and gelatine gel preparation procedure
We obtained the PVA-GTA Fricke gel infusing the Fricke solution and xylenol orange in the PVA-GTA hydrogel. We tested several types of PVA-GTA gel to verify the influence of the cross-linking degree, the concentration of PVA and its molecular weight on the diffusion of the xylenol-iron complex. To verify the influence of the impurities on the performances of the PVA-GTA gel two type of polyvinyl alcohol were used, both purchased by Sigma-Aldrich. The first type has an ash content ≤ 1.2% and will be simply identified as “PVA” from now on. The second type has an ash content ≤ 0.5% and we will refer to it with its commercial name “Mowiol”. Table 3.2 summarizes the characteristics of the polymer used in each gel type, along with the final concentration of PVA and GTA. The final concentrations of other reagents were the same in each sample: 25 mM of sulfuric acid; 0.5 mM of ferrous ammonium sulfate and 0.165 mM of xylenol orange tetrasodium salt. The preparation process was the same for each type of gel, and it is described hereafter along with the preparation procedure of a gelatine gel used as a reference.
As a first step in the preparation of the gels, four stock water solutions are prepared with analytical grade reagents (Sigma-Aldrich) and bi-distilled water:
Solution A: 1.4 ml of concentrated sulfuric acid (96%) into a final volume of 100 ml; Solution B: 1.96 g of ferrous ammonium sulfate and 2 ml of concentrated sulfuric acid
(96%) into a final volume of 100 ml;
Solution C: 0.63 g of xylenol orange tetrasodium salt into a final volume of 50 ml; Solution D: 1 ml of 25% glutaraldehyde (GTA) solution and 0.5 ml of Solution A into
a final volume of 10 ml of bi-distilled water.
Solution A and Solution C are prepared in advance and kept in a refrigerator at ~5 °C, Solution B, and Solution D are always prepared the same day of the gel to minimize spontaneous oxidation of Fe2+ ions and self-polymerization of GTA.
The required amount of PVA is dissolved in 80 ml of bi-distilled water. The dissolution is performed keeping the solution at 120°C in an autoclave for an hour in a sealed container. After retrieving the solution from the autoclave, the PVA sediments on the bottom of the
33 container, therefore the solution is mechanically stirred for 30 minutes until it is homogeneous. While stirring, the water-PVA solution is allowed to cool down to 20 °C and, when this temperature is reached, 8 ml of Solution A, 1 ml of Solution B, and 1 ml of Solution C are added and the solution is further stirred for 5 minutes.
At this point, 2.5 ml or 10 ml of solution D are added, depending on the desired final concentration of GTA. An amount of water yielding a final 100 ml volume is added if needed. The solutions are homogenized stirring them for 5 more minutes and then they are poured in standard polystyrene cuvettes with 1 cm optical path. The cuvettes are kept in the dark at 20°C for one hour to allow gelation, then they were placed in a refrigerator at ~5 °C.
A widely used formulation of gelatine gel was also prepared to compare the performance of PVA-GTA gel with it. For this purpose, 3 g of Type A porcine skin gelatine are dissolved under stirring in 89.5 ml of bi-distilled water at 50 °C. After 20 minutes, the gelatine is fully dissolved and the solution is allowed to cool down to 20 °C. Next, 8.5 ml of Solution A, 1 ml of Solution B and 1 ml of Solution C are added. After 5 minutes of stirring, the solution is homogeneous and can be poured in cuvettes with 1 cm optical path which are then placed in the refrigerator in the dark, to let the gel set.
Both PVA and gelatine gels were always prepared one day before the irradiation experiments and kept in the refrigerator at ~5 °C. They were brought to room temperature one hour before irradiation and reading.
34 Table 3.2 – PVA and GTA concentrations of the tested gel
Gel name
Matrix
Molecular
weight
GTA
(% w/v) (·103) (mM)PVA-A
PVA 10%
85-124
6.625
PVA-B
PVA 10%
85-124
26.5
PVA-C
PVA 10%
31-50
26.5
PVA-D
PVA 10%
13-23
26.5
Mw-A
Mowiol 10%
125
26.5
Mw-B
Mowiol 12.5%
125
33.125
MIX-A
Mowiol 10%
30% 27
30% 61
40% 125
26.5
MIX-B
Mowiol 12.5%
30% 27
30% 61
40% 125
33.125
Gelatine
Gelatine 3%
-
-
35
3.1.4 Dose-response
To assess the sensitivity of the PVA gel, we irradiated the PVA-GTA gel in the range 0-35 Gy with a LINAC RapidArc DHX Varian (Varian Medical Systems, Palo Alto, CA, USA) at the Santa Chiara Hospital in Pisa (Italy). We closed the cuvettes with plastic stoppers and sealed them with Parafilm (Bemis NA, Neenah, WI, USA), then we submerged the cuvettes under 1 cm of water to assure electron equilibrium (dose build-up) conditions. We used X-rays produced with an accelerating potential of 6 MV and a 10x10 cm2 square irradiation field. One hour after the irradiation, we measured the absorbance of the samples at a wavelength of 585 nm with a Cary-60 UV-VIS spectrophotometer (Agilent Technologies, Santa Clara, CA, USA).
3.1.5 Diffusion coefficient
To measure the diffusion coefficients of the gels we delivered 10 Gy to 4 partially shielded cuvettes, as shown in Figure 3.3. We covered two-thirds of the cuvettes with 5 cm of lead, while the last third was left unshielded. A 1.2 cm layer of Plexiglas surrounded the cuvettes to ensure electron equilibrium.
36 We collected absorbance-position profiles 1, 4, 7, and 10 hours after the irradiation with a Cary-4000 UV-VIS spectrophotometer (Agilent Technologies, Santa Clara, CA, USA). equipped with a moving tray. We measured the absorbance along the cuvette longitudinal axis at 1 mm steps and over 1 mm wide adjacent sections. We kept samples refrigerated at about 5 °C after the irradiation and between measurements. To account for spontaneous oxidation, we left 4 samples not irradiated, they were measured at each time step and the mean of their absorbance profiles was subtracted from the irradiated ones.
3.1.6 Spontaneous oxidation
To evaluate the spontaneous oxidation of the PVA-GTA gel we measured the absorbance of 5 cuvettes at 585 nm with a Cary-60 UV-VIS spectrophotometer right after their production. We measured the change in the absorbance reading the cuvettes at different time steps for 21 days. We stored the cuvettes in the dark at about 5 °C in a fridge. Before each measurement, we took the samples off the fridge and kept them at room temperature for 30 minutes.
37
3.2 Results and discussion
3.2.1 Gelation time
Once GTA has been added to a PVA acidic water solution the viscosity increases as the cross-linking proceeds. We wanted to verify that the gelation takes enough time so that the gel can be homogenized and poured into the desired container after all the reagents have been mixed. This may be of particular interest if a large uniform phantom has to be produced
The gelation point is defined as the transition from a viscous solution to an elastic solid. We defined the gelation time as the interval between the addition of GTA and the gelation point. The gelation point can be found in the frequency-time diagrams, gelation curve for now on, obtained with the curemeter (Figure 3.4) since the resonance frequency of the curemeter probe is directly related to the elastic modulus of the material it is in contact with.
38 The S-shaped diagram reflects the gelation process and its phases: at the beginning, the frequency does not change, since each GTA molecule firstly bonds only one PVA chain. Hence, no bonds or very few of them exist between different polymer chains. Therefore, PVA chains can still move freely. Macroscopically this means that the system is still a solution, i.e. it can still flow freely even though the viscosity is increasing. After this phase, the GTA molecules that have already linked one PVA chain start to create the second bond with another PVA chain, and this is represented by the toe of the curve: after this point, the modulus sharply increases in a short time. After the toe, the system is not a solution anymore, but a gel with low elastic modulus. The cross-linking process continued for several hours, while more and more bonds between different PVA chains are created by GTA. This produces an increase in the elastic modulus of the gel, that became stiffer as the process goes by. This is reflected by the quasi-linear increasing of the resonance frequency of the probe. When almost all of the GTA molecules have created a bond on each of their sides, the diagram exhibits a shoulder, since the modulus increasing slows down and it tends to its asymptotic value.
For all the aforementioned, the gelation point corresponds to the toe of the gelation curve, therefore this is the point after which the mixture cannot flow freely anymore. To find it we first made a smoothing of the raw curves obtained from the instrument with a Savitzky–Golay filter to reduce the noise. We used the OriginPro code (OriginLab Corporation, Northampton, Massachusetts, USA) for this data processing and the following. We used a so-called “Logistic” sigmoid curve to fit the datasets obtained after the smoothing:
( )
Equation 3.1
where and are the initial and final values, is the center of the curve and p a parameter. Figure 3.5 is an example of the good agreement between one of the dataset and the fitting function. The Logistic function fitted effectively all the datasets, with an R2 always greater than 0.98.
39 Figure 3.5 - Smoothed dataset and Logistic fitting function
We defined the gelation point, i.e. the toe of the curve, as the intersection between the horizontal asymptote and the tangent to the curve in its center, i.e. its inflection point (Figure 3.6).
Figure 3.7 shows a comparison between the gelation curve of three gels with 13.25, 26.5 and 53 mM of GTA at 20 °C. These values corresponds to 0.5, 1 and 2 ml of 25% GTA solution every 100 ml of final solution volume. The figure demonstrates that the toe of the curve occurs sooner in gels with a greater amount of cross-linking agent. The time to reach the final asymptote is also shorter in gels with more GTA. Figure 3.8 shows the gelation curves of gel with 26.5 mM of GTA at 15, 20 and 25 °C. This figure demonstrates that gelation time decreases as the temperature increase.
40 Figure 3.6 - Gelation point calculation
Table 3.3 summarize the gelation times of gels with different concentrations of GTA and different gelation temperatures. All the tested GTA concentration-temperature combinations showed a gelation time of several minutes. Nevertheless, the viscosity of the PVA-GTA solution starts to increase right after the addition of GTA and becomes quite high while the solution approaches the gelation point, therefore the time really available to pour the solution in the desired container is smaller than the actual gelation time. We advise to use two third of the gelation time as the time available to cast the gel and defined this interval as working time in Table 3.3. Even so, there is enough time for a correct mixing of the reagents and to pour the gel for each tested formulation. Interestingly, solutions with 26.5 mM of GTA or less do not turn into a gel if they are kept at 15 °C or below (see also Figure 3.8). This may be useful to create phantoms with large volumes or complex shapes: reagents can be mixed keeping the solution at about 15 °C, then the temperature may be slowly raised after the casting.
41 Figure 3.7- Gelation time of gels with different concentrations of GTA at 20 °C
42 Table 3.3 - Summary of gelation times as a function of GTA concentration and temperature
GTA
(mM)
Temperature
(°C)
Gelation time
(min)
Working time
(min)
13.25
15
none
none
26.5
15
none
none
53
15
30
20
13.25
20
75
50
26.5
20
35
24
53
20
25
16
13.25
25
25
16
26.5
25
20
13
53
25
10
6
43
3.2.2 GTA influence on the initial absorbance
An unexpected side effect of the adoption of GTA as the cross-linking agent was an increase in the initial absorbance of Fricke gels or solutions after the addition of the GTA to the mixture. We noted that GTA simply stored in a fridge at about 5 °C produced a fast oxidation of part of the Fe2+ ions when added to the PVA water solution and thus an increase in the absorbance that is evident to the naked eyes (Figure 3.9). This effect is mild if the GTA comes from a bottle opened since few days, while it is very pronounced if the GTA comes from a container that was opened more than two weeks before.
Figure 3.9 - Two Fricke solutions with the addition of 26.5 mM of GTA: new GTA (right) and old GTA (right)
The quantity of ferrous ions oxidized is proportional to the amount of GTA and the effect becomes more severe depending on how much time the GTA has been exposed to air. Figure 3.10 shows the change of absorbance of Fricke solutions with the same concentration of reagents of the PVA-GTA gel and with different concentrations of GTA. Two sets of Fricke solutions were made, one with the addition of GTA from a bottle opened right before the production of the samples and one from a bottle that has been opened and stored in a fridge for a month. The two types of GTA will be called “new” and “old” for sake of simplicity. Figure 3.10 shows clearly that when old GTA is added to a Fricke solution the absorbance immediately increases and that this increase is proportional to the amount of GTA. The oxidation produced by new GTA is far less pronounced, yet still measurable.
44 Figure 3.10 - Absorbance of Fricke solutions with xylenol orange and different amount of GTA
It is known that GTA undergoes self-polymerization, and the process can be accelerated if GTA is stored improperly (Dow, n.d.; Prentø, 1995). It is not clear if the products of this polymerization, i.e. dimerized or polymerized GTA, are responsible for the fast oxidation of Fe2+ ions or if some other byproducts of the polymerization are. One point that has to be stressed is that many studies state that GTA can be stored below room temperature for months and no appreciable degradation will occur, while we noticed this fast oxidation effect after 15-30 days of storage in a fridge at about 5 °C. Self-polymerization of GTA seems not to occur or to be drastically slowed in absence of oxygen. Storage under an inert gas is an effective method to extend the shelf-life of GTA. A simpler method is to freeze the GTA solution (“Glutaraldehyde Fixative,” 2012; Rasmussen and Albrechtsen, 1974). We froze the GTA solution and tested it after 6 months adding it to a Fricke solution and found an oxidation comparable to that produced when the reagent was new. After this period, the oxidation produced by the GTA increased even if it was stored frozen. Hence, GTA can be stored
45 frozen up to 6 months. Repeated freezing-thawing cycles seem not to produce degradation of the GTA solution, as pointed out also by various investigators (Dow, n.d.; Prentø, 1995; Rasmussen and Albrechtsen, 1974). For the production of all the gels tested in this work we always used GTA from bottles opened right before the samples preparation or GTA stored frozen for not more than 6 months and thawed before the gel preparation.
3.2.3 Dose-response
Figure 3.11 shows the dose-response curve of the PVA-GTA gel in the dose range 0-35 Gy. Each point is the mean of the absorbance at 585 nm of five samples. Error bars (1 standard deviation) are included in the plot symbols The curve is a sigmoid with deviations from linearity at low doses, below 1 Gy, and high doses, above 30 Gy.
46 The shoulder that appears above 30 Gy is a saturation effect due to the finite amount of the available chemicals inside the gel: the amount of available Fe2+ ions and xylenol orange molecules decreases as the dose increases. Xylenol orange concentration, being the lowest one, is the parameter that determines the maximum absorbance, hence the onset of saturation. Recently Liosi and colleagues (Liosi et al., 2017) demonstrated that the non-linearity below 1 Gy is due to the existence of different xylenol orange complexes with various stoichiometric ratios and different absorbance spectra.
Taking into account all the aforementioned phenomena, we modeled the dose-response curve of PVA-GTA with a sigmoid curve of the type (Boltzmann function):
( )
Equation 3.2
were is the measured change in the absorbance at 585 nm, and are the minimum and maximum values, is the inflection point and k is the steepness of the curve. The function fits well the data, with R2 grater then 0.99. The dose can be calculated from the measured change of absorbance at 585 nm with the equation:
(
) Equation 3.3
Even though the previous equation takes correctly into account all the phenomena that occur in the gel when it is exposed to increasing doses, a simple linear model is more convenient to use. Furthermore, in many clinical applications the range of interest is between 5 Gy and 30 Gy, thus this is the typical dose range studied in the majority of the works in gel dosimetry. In this range, it is possible to use a simple linear relationship to evaluate the dose absorbed in the gel. Figure 3.12 illustrates the dose-response of PVA-GTA and gelatine gel between 5 and 30 Gy. Figure 3.12 shows also a linear regression for each data set, showing that both gels have a linear response in the selected range, with R2 greater than 0.99.
47 Figure 3.12 - Dose-response curves of PVA-GTA and gelatine gels in the range 0-30 Gy.
The dose is calculated from the change in absorbance by the simple equation:
Equation 3.4
where is , i.e. the slope of the linear regression, and is the intercept.
Dose-response of Fricke gel is known to depend on preparation conditions, therefore differences can arise from batch to batch. We repeated the entire calibration process on three different gel batches, from preparation to reading, to evaluate the reproducibility of calibration parameters. We used a least squares linear regression to fit the three data set, finding the parameters of Equation 3.4 along with their standard deviations. Figure 3.13 and
