Determination of the Range and Spread-Out Bragg Peak Width of Proton Beams Using a Large-Volume Liquid Scintillator.

Purpose
To determine the range, spread-out Bragg peak (SOBP) width, and output of a passive-scattering proton beam with a liquid scintillator detector, without the need for quenching correction.


Materials and Methods
The depth-light profiles of 3 beam energies (140, 160, and 180 MeV) with 6 SOBP widths at each energy, produced in a 20 × 20 × 20-cm3 liquid scintillator tank, were collected by a charge-coupled device camera. By defining landmarks on the light signals, measured ranges and SOBP widths were acquired. A linear dependence was found between nominal and measured properties, and calibration factors were obtained by comparing those properties. The daily output stability and reproducibility of the liquid scintillator detector were studied by conducting 8 repeated measurements over 2 weeks in a 60Co beam.


Results
The beam ranges were determined with submillimeter accuracy without the need for any correction. The maximum difference between the measured and nominal range was 1.0 mm. The mean difference between the measured and nominal SOBP widths after correction was 0.1 mm (σ = 1.8 mm), with a maximum difference of 3.5 mm. The light output was reproducible with an SD of 0.14%.


Conclusions
The method described here makes it possible to quickly and accurately determine the range and SOBP width of a passive-scattering proton beam in a liquid scintillator, without the need for quenching correction. In addition, the detector proved to be reliable over time, showing good output consistency with a high degree of precision.


Introduction
By imaging a large volume of organic scintillator during proton irradiation, it is possible to image proton beams with high spatial resolution in nearly real time. Scintillator detectors exhibit a combination of characteristics, including high spatial resolution, water equivalence, and 3-dimensional dimensionality, which are particularly advantageous for proton beam measurements [1,2]. Solid plastic scintillators were used to verify proton beam range [3], and large, liquid-scintillator detectors were used to measure the range and lateral profiles of proton beams [4].
Measurements of beam range, spread-out Bragg peak (SOBP) modulation, and beam output are an important component of regular quality assurance for passive-scattering proton facilities. However, the large number of beam energies and range modulator http://theijpt.org wheels makes it difficult to measure these beam properties on a regular basis. Multilayer ionization chambers are useful tools for rapidly performing such measurements, but they are expensive and have relatively coarse spatial resolution.
Scintillator detectors have submillimeter resolution and the ability to measure the depth profile of an SOBP in a single measurement. Unfortunately, the response of organic scintillators is dependent on the linear energy transfer (LET) of the proton beam, leading to a decreased signal in the Bragg peak, a phenomenon known as quenching. The LET of passivescattering proton beams increases nonlinearly with depth throughout the SOBP, leading to depth-dependent quenching of the light signal. Quenching correction of scintillator response in proton beams is possible and has been demonstrated [5]. However, quenching correction is difficult and labor-intensive and adds additional uncertainties to dosimetric measurements.
The beam range and SOBP width are typically defined in terms of a percentage of depth dose at the proximal and distal ends of the SOBP. For example, at the MD Anderson Proton Therapy Center, the SOBP width is the distance between the proximal 95% and the distal 90% of the SOBP, and the range is defined by the distal 90% and 10% depths [6]. The output is typically defined at the center of the SOBP. Although quenching obscures the landmarks traditionally used to define beam range, SOBP width, and beam output, other useful dosimetric landmarks are present in the depth-light profiles of scintillator SOBP measurements. In this article, we present a method to relate landmarks in the scintillator depth-light profile to the beam range and SOBP width. This makes it possible to determine the beam range and SOBP width directly from the depthlight profile, without the need for quenching correction. We also present data showing the reproducibility of the measured light intensity for a given radiation dose, illustrating the potential of volumetric scintillation detectors for beam output verification.

Liquid Scintillator Detector
The liquid scintillator detector system consists of a 20 3 20 3 20-cm 3 tank of liquid scintillator (BC-531, Saint-Gobain, Courbevoie, France) confined in a light-tight enclosure. The liquid scintillator has a density of 0.869 and a refractive index of 1.47. Its light emission peak is centered at 425 nm, and the decay time of the scintillation light emission is 3.5 nanoseconds. To collect the light emitted by the liquid scintillator, a charge-coupled device (CCD) camera (Luca S 658M, Andor Technology, Belfast, Ireland) is placed 70 cm from the edge of the tank, perpendicular to the beam direction as shown on Figure 1 [7]. The CCD camera has a resolution of 658 3 496 pixels with a pixel size of 10 lm.

Measurements
The measurements were conducted at the MD Anderson Proton Therapy Center on a passive-scattering proton beam gantry. The gantry was set at 2708 to irradiate the tank from the left, and the left edge of the tank was placed at isocenter. The measurements consisted of 3 different beam energies and 6 different SOBP widths for each energy, as listed in Table  1. Only beam ranges that did not exceed the water-equivalent thickness of the tank were measured. Deeper ranges can be measured using additional buildup in front of the tank.
The passive-scattered proton beam was collimated to 10 3 10 cm 2 and delivered to the liquid scintillator detector. For each field, 25 monitor units were delivered and the light intensity signal was integrated for a 15-second acquisition time.
The reproducibility and daily output stability of the liquid scintillator detector were studied by making 8 repeated output measurements in a 10 3 10-cm 2 60 Co beam during the course of 2 weeks. A 60 Co source was used because its output is more reliable than a proton beam. Each output measurement was obtained from the temporal median of thirty 10-second acquisitions, from which a light intensity profile was extracted. The output was measured as the average value for 100 pixels at the center of the profile, corresponding to a length of 3 cm.

Treatment Planning System Data
To compare quenched depth-light intensity profiles from the liquid scintillator with the actual absorbed dose profiles in water, a treatment planning system (TPS), Eclipse (version 11.1, Varian Medical Systems, Palo Alto, California), was used to calculate the dose for a single passive-scattering proton beam. The dose in water for a 10 3 10-cm field was calculated with a geometry matching the experimental setup of the liquid scintillator detector.

Data Processing
As demonstrated by Robertson et al [8], the use of a CCD camera and scintillator tank introduces several optical artifacts. For this work, we followed the method described by these authors to correct for background noise, stray radiation, vignetting, distortion, blurring, refraction, and perspective effects. The corrected measurements were aligned with the TPS data, including an offset to account for the lack of scintillation signal in the tank wall. The position in the beam direction was scaled by 0.869 to account for the density difference between the scintillator and water. Finally, the light signal was normalized to the dose from the TPS dose profile at a depth of 5 cm. At this depth, quenching or tank edge artifacts do not affect the light signal.

Analysis
The range and SOBP width were determined with a simple geometrical approach, which was applied directly to the scintillation signal without correcting for quenching. Landmark points in the depth-light profile were identified and were correlated to the range and SOBP width for each beam. The nature of the correlation was determined by comparing the measured values of these depth-light distribution landmarks to the nominal range and SOBP width as defined in the TPS.  The following method, defined here in 5 steps, was applied to the 18 measurements listed in Table 1. Figure 2 illustrates the steps of the method (note that Figure 3 shows only the SOBP region of the light signal to clearly illustrate the geometrical method).
A line is fit to the distal edge of the light signal where it reaches 50% of the maximum, as demonstrated by line 1 in Figure 2.
The line from step 1 is shifted to a shallower depth by a shift factor (line 2 in Figure 2). The shift factor is defined as a percentage of the x-intercept of line 1. The intersection of line 2 with the light signal provides a point on the distal edge of the SOBP where the light signal does not vary with the SOBP width (point B in Figure 2). In this region, only the highest-energy, pristine Bragg peak contributes to the shape of the SOBP. Because this peak is always present, this region can be considered constant for a given beam range, whatever the width of the SOBP. The value of the shift factor was varied, and its effect on the results was studied.
Step 3. Figure 2). The light signal reaches a maximum near the end of the shallowest, pristine Bragg peak's range. Here, the LET first rises from its low value in the proximal buildup region, and as a result, the quenching effect begins to be important. The LET continues to increase with depth, causing a corresponding decrease in the light signal. As a result, the maximum point of the light signal marks the proximal end of the dose plateau. A 3term Gaussian quadrature was used to fit the light signal to accurately locate the maximum in the presence of noise (line 3 in Figure 2).

The maximum of the light signal is identified (point A in
Step 4. Figure 2). The intersection of this line with line 1 determines a final point that we called the measured range (point C in Figure 2).

A line is drawn between point A and B (line 4 in
Step 5. The measured SOBP width is defined as the distance on the x-axis between the maximum defined in step 3 (point A) and the measured range (point C).
Measured ranges and SOBP widths were determined for each of the 18 beam measurements. The 18 measured ranges were compared with the 3 nominal ranges, and the 6 SOBP widths measured for each of the 3 energies were compared with the nominal widths. (C) The light signal and step 5, the measured SOBP width is defined as the distance on the x-axis between the maximum defined in step 3 (point A) and the measured range (point C).

Measured Range
For a nominal range of 102 mm, all the measured ranges were found to be in a 0.05-mm window (range, 102.46-102.51 mm) corresponding to a d ¼ 0.05 mm, with d representing the distance between the highest and lowest measured ranges. Similar results were observed for a range of 130 mm (d ¼ 0.14 mm) and a range of 150 mm (d ¼ 0.29 mm). Table 2 shows the effect of the shift factor (defined in step 2 of our analysis) on the precision of the measured ranges. For the 3 nominal ranges and 5 different shift factors, we measured the d, as defined previously. As expected, with shift factors closer to 1 comes better precision in the measured range. This is due to the intersection point B being located very close to the distal edge of the light signal, where the intensity does not depend on the SOBP width.
The measured ranges also proved to be close to the nominal ranges, with differences of , 0.5 mm for the 102 mm range, , 1.0 mm for the 130 mm range, and , 0.7 mm for the 150 mm range. The mean difference was 0.6 mm (r ¼ 0.2 mm). A linear fit was applied between the measured ranges and the nominal ranges with a very good agreement: Y ¼ ð1:0060:01Þx þ ðÀ0:2761:16Þ; R 2 ¼ 0:9999

Measured Spread-Out Bragg Peak Width
A similar analysis was performed on the measured SOBP widths. In that case, the measured SOBP widths did not match the nominal widths very closely, with a mean difference of 9.17 mm (r ¼ 4.01 mm), 15.62 mm (r ¼ 7.86 mm), and 16.99 mm (r ¼ 9.70 mm), for ranges of 102, 130, and 150 mm, respectively. However, a linear fit for all three sets of measurements showed a clear linear relationship between the measured and nominal SOBP widths (R 2 ¼ 0.9995, 0.9960, and 0.9964, respectively, for ranges 102, 130, and 150 mm). The slope of the linear fit was used as a correction factor to scale the measured SOBP width to match the nominal value. After that correction, the measured and nominal SOBP widths agreed within , 3.5 mm. Table 3 summarizes the differences between the measured and nominal beam characteristics.

Output Stability
The light output was shown to be stable with a relative SD of the integrated light at the center of the profile of 0.14%.

Discussion
The geometrical method developed in this study provided accurate measurements of the beam range in passive-scattering proton beams. The measured SOBP widths did not match the nominal values, but a linear relation was found between the measured and nominal widths. This implies that a set of preliminary measurements could provide these linear relations, which could, thereafter, be used as correction factors to determine the SOBP width with high accuracy during periodic beam measurements. The beam output and proximal 95% variability at the MD Anderson Proton Therapy Center were found to be , 2% [6]. We do not anticipate that this variability will affect the outcome of the method described here. Overall, this method could improve the efficiency of quality assurance for passive-scattering proton beams, enabling morefrequent verification of the range and SOBP width than is currently performed. In comparison with commercially available systems, such as, the Zebra (IBA Dosimetry, Bartlett, Tennessee) [9], the liquid scintillator detector system described here provides a higher, submillimeter resolution (versus 2 mm resolution), the measurement of an integral depth-dose curve (versus central axis depth-dose), and a reduced cost.
We anticipate the setup time of an optimized detector configuration in a typical treatment room to be around 15 minutes. The analysis of the measurements is then performed in a few seconds, giving an accurate measurement of the range and SOBP width. Because the light output from the liquid scintillator is reproducible, the detector could also be used to check the day-today output consistency of the proton beam, by comparing the light intensity in a reproducible region to previous measurements at the same spatial point.

Conclusion
The geometric approach used in this study provides a fast and efficient method to measure the beam range and SOBP width for passive-scattering proton beams without the need for quenching correction factors. By fitting the quenched depth-light signal with simple linear and Gaussian functions, the range of each measurement could be directly determined with submillimeter accuracy.
The detector system and measurement approach described in this study can be used to quickly and accurately evaluate the range and width of a SOBP and to verify the reproducibility of the beam output. These properties make it a potentially valuable and time-efficient tool for daily and monthly passive-scattering proton-beam quality assurance.

ADDITIONAL INFORMATION AND DECLARATIONS
Conflicts of Interest: The authors have no conflicts of interest to disclose.