Calculations and measurements of the scintillator-to-water stopping power ratio of liquid scintillators for use in proton radiotherapy

Abstract

Liquid scintillators are a promising detector for high-resolution three-dimensional proton therapy dosimetry. Because the scintillator comprises both the active volume of the detector and the phantom material, an ideal scintillator will exhibit water equivalence in its radiological properties. One of the most fundamental of these is the scintillator’s stopping power. The objective of this study was to compare calculations and measurements of scintillator-to-water stopping power ratios to evaluate the suitability of the liquid scintillators BC-531 and OptiPhase HiSafe 3 for proton dosimetry. We also measured the relative scintillation output of the two scintillators. Both calculations and measurements show that the linear stopping power of OptiPhase is significantly closer to water than that of BC-531. BC-531 has a somewhat higher scintillation output. OptiPhase can be mixed with water at high concentrations, which further improves its scintillator-to-water stopping power ratio. However, this causes the solution to become cloudy, which has a negative impact on the scintillation output and spatial resolution of the detector. OptiPhase is preferred over BC-531 for proton dosimetry because its density and scintillator-to-water stopping power ratio are more water equivalent.

1. Introduction

Proton irradiation for cancer therapy has gained popularity in recent years due to its ability to deliver a highly conformal dose to the tumor while sparing surrounding healthy tissue, particularly distal to the tumor beyond the range of the beam. This is possible because a mono-energetic proton beam deposits most of its energy in a small volume of tissue at the end of its range, a phenomenon known as the Bragg peak. When treating patients, the energy of the proton beam is modulated so that the Bragg peaks of many different energies add to deliver the prescribed dose to a clinically relevant volume of tissue; this is known as a spread-out Bragg peak. This energy modulation poses a challenge for accurate dosimetry for quality assurance of treatment delivery: proton range depends on energy, so the beam cannot be characterized by a measurement at a single depth, and three-dimensional measurements are required for a thorough assessment. Proton treatment plans contain inhomogeneous dose distributions with steep gradients, so a dosimeter with high spatial resolution is necessary to make these measurements.

A promising area of study that could meet these requirements is three-dimensional scintillation dosimetry using liquid scintillators. These materials consist of organic solvents containing fluors, the scintillating molecules that emit visible light when exposed to radiation. The use of liquid scintillators for three-dimensional radiation dosimetry was first investigated by Kirov et al. (2005; 2000). Their work focused on dosimetry of brachytherapy eye plaques in a small detection volume. Fukushima et al. (2006) subsequently utilized scintillation for proton beam measurements. Their work was limited to range verification using a narrow block of a solid plastic scintillator. In recent years our research group has developed a large-volume liquid scintillation detector with the goal of achieving accurate and quantitative three-dimensional proton dosimetry (Archambault et al., 2012; Beddar et al., 2009; Pönisch et al., 2009; Robertson, Mirkovic, Sahoo, & Beddar, 2013). This detector exhibits many desirable characteristics, such as a linear dose response, a spatial resolution of 0.3 mm, and a temporal resolution of 0.05 s (Archambault et al., 2012). However, one aspect of this detector that has received little attention is the choice of liquid scintillator.

Water, or a solid water-equivalent plastic, is used as a phantom material to represent patient tissue for quality assurance measurements. Unlike other detector systems, three-dimensional scintillation dosimetry uses a scintillator that comprises both the active detection volume and the phantom material. For this reason, an ideal scintillator should exhibit water equivalence in its radiological properties. Many properties must be considered to fully define a material as water-equivalent, but one of the most relevant for proton radiotherapy is the ratio of its linear stopping power to that of water. This value does not depend strongly on proton energy, so it provides a concise characterization of the scintillator. The linear stopping power ratio also relates the physical thickness of a material to its water-equivalent thickness (WET). Numerical and analytical methods have been developed to calculate the WET of arbitrary materials (Newhauser et al., 2007; Zhang & Newhauser, 2009) and measurements of WET can be used to determine the linear stopping power ratio (Sánchez-Parcerisa, Gemmel, Jäkel, Parodi, & Rietzel, 2012; Zhang, Taddei, Fitzek, & Newhauser, 2010).

The purpose of this study was to evaluate the suitability of two commercially available scintillators for liquid scintillation dosimetry of proton beams. Because measurements are time-consuming and beam time is scarce on clinical proton beamlines, we first tested a simple method of analytically calculating scintillator-to-water stopping power ratios. We then measured the stopping power ratios of the two scintillators, both to determine the more water-equivalent scintillator and to assess the accuracy of the calculations. We also measured their relative scintillation outputs to ensure adequate counting statistics for proton dosimetry.

2. Methods and materials

2.1 Calculation of scintillator-to-water stopping power ratio

To calculate stopping power ratios we used the software package Stopping and Range of Ions in Matter (SRIM; www.srim.org) (Ziegler, Ziegler, & Biersack, 2010). This program calculates mass stopping power in a compound as a linear combination of the stopping powers of its atomic constituents, with a correction factor for the atomic bonding structure of the molecule. In the realm of proton therapy, SRIM has been used in such applications as calculating the required thickness of a brass collimator for a Monte Carlo study of proton scattering (Titt, Zheng, Vassiliev, & Newhauser, 2008) and calculating the required thickness of a scintillating crystal for a proton imaging device (Sipala et al., 2010).

Any compound can be added to SRIM’s compound dictionary, where it is defined by its atomic composition and the bonding structure of its light elements. The program does not support mixtures of compounds, so we first defined each component compound in SRIM’s compound dictionary and calculated its mass stopping power for 10-, 100-, and 200-MeV protons. The component compounds and their mass fractions were found in the Material Safety Data Sheets (MSDS) provided by the manufacturer, and their atomic bonding structures were found in PubChem, an online database maintained by the National Center for Biotechnology Information (http://pubchem.ncbi.nlm.nih.gov/) (Bolton, Wang, Thiessen, & Bryant, 2008).

To calculate the stopping power of a scintillator, we used a linear combination of the component mass stopping powers weighted by the mass fraction of each component in the scintillator. Linear stopping power was calculated by multiplying the mass stopping power by the measured density of the scintillator. We then calculated the scintillator-to-water stopping power ratio by normalizing the scintillator stopping power to the SRIM-calculated stopping power of water. Uncertainty in the ratio was calculated using the measured standard error of the mean for scintillator density and by assuming that σ = 5% for each SRIM-calculated stopping power. This is based on the work of Ziegler et al. (2010). In a survey of ~9000 proton stopping power measurements, they found that 68% were within 5% of the SRIM-calculated value.

2.2 Measurement of scintillator-to-water stopping power ratio

We measured linear stopping power ratios using the procedure described by Zhang et al (2010), which is based on measuring the water-equivalent thickness (WET) of several different thicknesses of a given material. The WET for a certain physical thickness of scintillator t_sc is given by

$$\mathit{WET}=t_{sc}\frac{{\overline{S}}_{sc}}{{\overline{S}}_w},$$ (1)

where S̄_sc and S̄_w are the mean linear stopping powers of the scintillator and water, averaged over the range of energies of a monoenergetic proton beam traversing the material (Zhang & Newhauser, 2009). Conceptually, the WET of a material is the difference between the range of a proton beam in water and its residual range in water when the material is placed in the beam. We measured the scintillator-to-water linear stopping power ratio by calculating the least-squares solution of equation 1 for five measurements of WET as a function of t_sc.

The WET of the scintillators was measured using the Zebra detector (IBA Dosimetry). This device consists of 180 parallel-plate ionization chambers that can measure the entire depth dose curve with a resolution of 2 mm. Dhanesar et al. (2013) found that the Zebra can accurately measure the water-equivalent range of a proton beam with an uncertainty of 0.4 mm. All measurements were repeated with and without a 1 mm water-equivalent insert to effectively improve the resolution to 1 mm. Depth dose curves were measured for a monoenergetic 200-MeV proton beam spread to a 10 × 10 cm² field size using a passive scattering system. Five rectangular containers made of 6.4 mm poly(methyl methacrylate) (PMMA) were used to hold the liquid scintillators in front of the Zebra’s entrance window (Figure 1). The internal thickness t_sc of each container was measured with a digital caliper (Table 1). For each container, depth dose curves were recorded for the proton beam transiting the container with and without the scintillator, and the WET was calculated as follows:

$$\mathit{WET}=\frac{1}{2}(r_{0+}+0.1+r_{0-})-\frac{1}{2}(r_{sc+}+0.1+r_{sc-})=\frac{1}{2}(r_{0+}+r_{0-}-r_{sc+}-r_{sc-})$$ (2)

Figure 1.

Schematic and photograph of the experimental setup used to measure the scintillator-to-water stopping power ratios. The 3.2 mm acrylic sheet in the photograph was used to protect the Zebra from spills, and was in place for all measurements.

Table 1.

Internal thicknesses of the five acrylic containers used to measure stopping power ratios. The standard error of the mean for each container was less than 0.05 mm.

Container	Internal thickness tsc (mm)
1	10.23
2	15.35
3	20.70
4	24.18
5	30.56

In this equation, r is the distal 90% beam range in centimeters calculated from one depth dose curve. The subscripts + and − indicate curves recorded with and without 1 mm of buildup in place, and the subscripts 0 and sc indicate curves recorded for the proton beam transiting the container without and with the scintillator. Distal 90% beam ranges were calculated by fitting the Bortfeld model to the depth dose curve (Bortfeld, 1997). This model is an analytical equation for the depth dose curve given by the product of a Gaussian and a parabolic cylinder function. It includes parameters to account for the range-energy relationship, the reduction in fluence with depth from nuclear interactions, range straggling, and the energy spectrum of the beam.

To calculate the uncertainty of scintillator-to-water linear stopping power ratio measurements, we first determined σ_tsc and σ_WET. We calculated σ_tsc from repeated measurements of t_sc, and we calculated σ_WET by assuming that σ_r = 0.4 mm for each range measurement in equation 2 (Dhanesar et al., 2013). Because the ratio is calculated as a least-squares solution, we could not use simple uncertainty propagation methods. Instead, we simulated 100,000 stopping power ratio measurements using σ_tsc and σ_WET to add randomly-generated, zero-mean Gaussian noise to our t_sc and WET measurements. We then calculated the uncertainty of the stopping power ratios as the standard deviation of these simulated measurements.

2.3. Measurement of scintillation output

Scintillation output was measured with an electron-multiplying charge-coupled device camera (Luca S, Andor Technology, South Windsor, CT). The camera was housed at one end of an elongated box made of gray polyvinyl chloride, with a 7 × 7 × 16 cm³ transparent acrylic container at the other end to hold the scintillator (Figure 2). The box was positioned such that the scintillator occupied the center of a spread-out Bragg peak with a width of 10 cm and a field size of 10 × 10 cm². During irradiation, the room lights were turned off and the entire setup was covered with black felt to reduce contamination by ambient light. Each image was recorded for 20 seconds during the delivery of 15 cGy. Corresponding non-irradiated background images were recorded before each irradiation and subtracted from the irradiated images.

Figure 2.

Schematic of the experimental setup for the measurements of scintillation output. The acrylic container holds about 0.8 L of the scintillator.

The camera has defective pixels from exposure to radiation, which show up as extremely high pixel intensities in the image files. To correct this, a 3 × 3 pixel² median filter was applied to every image before processing. Each image was recorded three times, and calculations were made using the average pixel intensities. The scintillation output was quantified as the mean pixel intensity of a 59 × 23 pixel² region of interest (ROI) in the center of the radiation field. The cross-sectional area of the scintillator volume included in this ROI was approximately 1.1 cm². To evaluate the level of photon scatter within the scintillator, the mean pixel intensity was also measured in an ROI inside of the scintillator tank but outside of the radiation field. This ROI measured 15 × 115 pixel². The cross-sectional area of the scintillator volume included in this ROI was approximately 1.4 cm².

2.4. Materials

Two liquid scintillators were investigated in this study. The first, BC-531 (Saint-Gobain Ceramics & Plastics, Valley Forge, PA), has been used previously for proton dosimetry. (Beddar et al., 2009). The second, OptiPhase HiSafe 3 (PerkinElmer, Waltham, MA) is being evaluated as a replacement for future scintillator detectors because its density is nearer to water than that of BC-531. The chemical compositions of these two scintillators are shown in Table 2. Unlike BC-531, OptiPhase is miscible with water at high concentrations, which should further improve its water equivalence. In this study we evaluated BC-531, OptiPhase, and solutions of OptiPhase with approximately 25% and 50% water by volume. The densities of the scintillators were measured with a 500 μL pipette and a digital scale (Table 3).

Table 2.

The chemical components found in the two scintillators and their mass fractions.

Scintillator	Component	Mass fraction
BC-531	Linear alkylbenzene	0.95
	Pseudocumene	0.05
	Fluorsa	< 0.003
OptiPhase HiSafe 3	Nonylphenolethoxylate	0.3
	2-(2-butoxyethoxy)ethanol	0.08
	Diethanolaminephosphoric acid ester	0.08
	Diisopropyl naphthalene	0.5
	2,5-diphenyloxazole	0.02
	1,4-bis-(2-methylstyryl)-benzene	0.02

^aThe exact molecule is not given, but the mass fraction is very small, so this component was neglected in SRIM calculations

Table 3.

Measured densities of the scintillators used in this study.

Scintillator	Measured density (g/cm3)
BC-531	0.869 ± 0.004
100% OptiPhase	0.963 ± 0.003
75% OptiPhase, 25% water	0.969 ± 0.002
50% OptiPhase, 50% water	0.986 ± 0.002

4. Results

4.1 Calculation of scintillator-to-water stopping power ratio

The results of the SRIM calculation of scintillator-to-water stopping power ratios are shown in Figure 3. The uncertainty in the calculated mass stopping powers was assumed to be σ = 5%. This is based on the work of Ziegler, Ziegler, & Biersack (2010): in a comparison of ~9000 experimental values and SRIM calculations, they found that 68% of proton stopping power measurements were within 5% of the SRIM-calculated values. The scintillator densities and their uncertainties used to calculate the linear stopping powers are shown in Table 3. Water was assumed to have a density of exactly 1 g/cm³.

Figure 3.

SRIM calculations of the scintillator-to-water linear stopping power ratios for 10-, 100-, and 200-MeV protons. A ratio of 1 means the scintillator’s stopping power is water-equivalent. The ranges of these proton energies in water are 0.1, 7.7, and 25.9 cm (Berger, Coursey, Zucker, & Chang, 2005).

4.2 Measurement of scintillator-to-water stopping power ratio

The results of the measurements of the scintillator-to-water linear stopping power ratios are shown in Figure 4. The ratios were calculated as the least-squares solution of equation 1. Their uncertainties were calculated as the standard deviations of many repeated calculations of the stopping power ratio with zero-mean Gaussian noise added to our measured WET and t_sc values. We calculated σ_WET from equation 2 with σ_r= 0.4 mm (Dhanesar et al., 2013), and we used σ_tsc = 0.2 mm from repeated measurements of container thicknesses.

Figure 4.

Measured scintillator-to-water linear stopping power ratios for 200-MeV protons. A ratio of 1 means the scintillator’s stopping power is water-equivalent.

4.3 Measurement of scintillation output

The results of the scintillation output measurements are shown in Figure 5. Figure 6 shows colormaps of the images on which these measurements were made with the two ROIs overlaid in black.

Figure 5.

Relative scintillation output of the scintillators, measured by the mean pixel intensity of one ROI in the radiation field and one ROI inside the scintillator, but outside the radiation field. All values are normalized to the in-field BC-531 measurement. The standard error of the mean was less than 10⁻⁵ for all measurements.

Figure 6.

Colormaps of scintillation output: (a) BC-531; (b) OptiPhase; (c) OptiPhase, 25% water; (d) OptiPhase, 50% water. The black rectangles show the ROIs used for measurements of scintillation output in and out of the radiation field.

5. Discussion

5.1 Calculation of scintillator-to-water stopping power ratio

As expected, the stopping power ratios do not depend strongly on proton energy, though they do decrease slightly with increasing energy. 200 MeV represents an approximate upper limit to the energies used in proton radiotherapy. Given that the largest changes in proton stopping power occur in the Bragg peak, it is likely that these ratios change more dramatically at energies below 10 MeV. However, protons in this energy range will travel less than 0.1 mm in human tissue, so large deviations in the stopping power ratio would be of little importance to dosimetric or range measurements.

The results of SRIM calculations of linear stopping power were strongly influenced by the densities of the scintillators. However, their atomic compositions certainly play a role also. BC-531 is composed entirely of hydrogen and carbon, while OptiPhase contains oxygen as well. With its density of 0.96 g/cm³ compared to BC-531’s 0.87 g/cm³, OptiPhase is more closely matched to water in both characteristics.

5.2 Measurement of scintillator-to-water stopping power ratio

A comparison of the SRIM-calculated and measured stopping power ratios is shown in Table 4. Every calculation had an error within 4%. Measurement confirmed the SRIM calculation that BC-531 would have the least water-equivalent linear stopping power. Even without the addition of water,

Table 4.

Comparison of calculated and measured scintillator-to-water linear stopping power ratios for 200-MeV protons.

	Calculated	Measured	% Error
BC-531	0.892 ± 0.063	0.878 ± 0.012	1.59
OptiPhase	0.959 ± 0.068	0.993 ± 0.012	−3.42
OptiPhase, 25% water	0.966 ± 0.068	1.000 ± 0.012	−3.40
OptiPhase, 50% water	0.984 ± 0.070	0.999 ± 0.012	−1.50

OptiPhase showed deviations from water of less than 1%, which is better than SRIM’s prediction of about 4%. Interestingly, the measured linear stopping power ratio of OptiPhase with 25% water was slightly closer to 1 than that of OptiPhase with 50% water. However, both values were so close to 1 that this discrepancy can be attributed to experimental error.

Our error analysis for the measured stopping power ratios takes into account the uncertainty in measurements of container thicknesses and the scintillators’ water-equivalent thicknesses, as well as the additional uncertainty introduced by the least-squares curve fitting process. However, another source of uncertainty when comparing our calculated and measured values is the fact that the measurements are not truly point measurements at 200 MeV. The WET values used for the least-squares solution are related to the physical thickness t_sc by the energy-averaged stopping power ratio as the protons transit the scintillator (see equation 1). However, a 200-MeV proton transiting 4.3 cm of water (2 × 0.64-cm acrylic plus t_sc for our thickest container) loses only about 20 MeV. Stopping power ratios are relatively constant at these energies, so the energy averaging should not introduce much error into these measurements.

5.3 Measurement of scintillation output

The addition of water to OptiPhase had the unexpected result of causing the solution to become cloudy (pure OptiPhase and BC-531 are both clear). This effect increased with the concentration of water (Figure 7). The cloudiness causes increased scatter of scintillation photons within the scintillator, leading to the increased observed light output in the out-of-field ROI in the two solutions of OptiPhase and water shown in Figure 5.

Figure 7.

One liter of OptiPhase, 25% water (left) and one liter of OptiPhase, 50% water (right). Pure OptiPhase is clear, but it becomes cloudy when mixed with water.

This cloudiness reduces the overall scintillation output and limits the volume of the scintillator from which a useful signal can be obtained. It would also cause a significant reduction in the spatial resolution of the detector. This can be seen in the rounded contours of Figure 6c and especially 6d, which were recorded with the 7-cm length of the scintillator volume occupying the flat region of a 10-cm spread-out Bragg peak.

6. Conclusions

SRIM calculations of stopping power ratios were fairly accurate, with errors of less than 4%. Defining the component molecules of a scintillator for SRIM calculations is straightforward, and the information required to do so is readily available from the MSDS and the PubChem database. These calculations can provide an easy initial characterization when evaluating liquid scintillators for proton dosimetry but should not be relied upon for precise comparisons.

OptiPhase HiSafe 3 is the preferred liquid scintillator for proton dosimetry because its stopping power and density are more water-equivalent than those of BC-531. Diluting OptiPhase with water achieves a slight improvement with an acceptable loss in scintillation output. However, dilution is not necessary because the linear stopping power of pure OptiPhase is already water-equivalent. Dilution with water is, in fact, undesirable because it causes the solution to become cloudy, which would significantly degrade the detector’s spatial resolution due to increased scatter of scintillation photons.