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Optimization of a multipoint plastic scintillator dosimeter for high dose rate brachytherapy

Purpose: This study aims to optimize and characterize the response of a mPSD for in vivo dosimetry in HDR brachytherapy. Methods: An exhaustive analysis was carried out in order to obtain an optimized mPSD design that maximize the scintillation light collection produced by the interaction of ionizing photons. Several mPSD prototypes were built and tested in order to determine the appropriate order of scintillators relative to the photodetector, as well as their length as a function of the scintillation light emitted. Scintillators BCF-60, BCF-12 and BCF-10 constituted the mPSD sensitive volume.Each scintillator contribution to the total spectrum was determined by irradiations in the low energy range.For the best mPSD design, a numerical optimization was done in order to select the optical components that better match the light emission profile. The optimized dosimetric system was used for HDR brachytherapy dose determination. The system performance was quantified in term of signal to noise ratio and signal to background ratio. Results: It was determined that BCF-60 should be placed at the distal position, BCF-12 in the center and BCF-10 at proximal position with respect to the photodetector.This configuration allowed for optimized light transmission through the collecting fiber, avoiding inter-scintillator excitation and self-absorption effects.The optimized luminescence system allowed for signal deconvolution using a multispectral approach, extracting the dose to each element while taking into account Cerenkov stem effect.Differences between the mPSD measurements and TG-43 remain below 5%. In all measurement conditions, the system was able to properly differentiate the produced scintillation signal from the background one. Conclusions: A mPSD was constructed and optimized for HDR brachytherapy dosimetry, enabling real time dose determination, up to 6.5cm from the 192Ir source.


I. INTRODUCTION
In brachytherapy, radioactive sources are placed a short distance from the target. The high dose gradients near brachytherapy sources (10% or more per millimeter for the first few centimeters from the source) provide a level of protection to healthy tissues surrounding the target. Despite the short distances involved in this modality, brachytherapy is not free from errors, which can be caused by humans (e.g., incorrect medical indication, source strength, patient identification, catheter, or applicator) or by failures in the treatment system (e.g., mechanical events) 1 . Even small errors in the source positioning can result in harmful consequences for patients. Systematic implementation of precise quality control and quality assurance protocols helps to improve treatment quality, and routine use of real-time verification systems and in vivo dosimetry are even more helpful in determining whether there are deviations from the prescribed dose during treatment delivery. Performing these tasks requires a precise and accurate detector whose presence does not perturb the particle fluence and the physics interactions. Tanderup et al. 2 reviewed different detectors for potential use for in vivo brachytherapy dosimetry. The selection of the appropriate dosimetric system is a compromise between different requirements and constraints of the detector as well as the application sought.
Plastic scintillator detectors (PSDs) are a promising detector for obtaining accurate realtime radiotherapy dose measurements. Previous studies have demonstrated that PSDs can accurately measure dose in external beam radiotherapy and that they have high spatial resolution, linearity with dose, energy independence in the megavolt energy range, and water equivalence 3-12 . In addition, some authors have found PSDs to be feasible for use in brachytherapy applications [13][14][15][16][17] . Despite the aforementioned advantages, PSDs response is affected by the stem effect and temperature dependence. Temperature dependence was long considered to be negligible, but recent studies showed that, depending on the type of scintillator, changes on the order of 0.6% per degree Celsius should be expected 9,18 . Moreover, a large fraction of the light collected by PSDs consists of Cerenkov radiation, which is especially undesirable in high dose rate (HDR) brachytherapy. Cerenkov radiation can cause large errors in dose reporting; therefore, numerous investigations have developed methods to remove Cerenkov radiation from the scintillation light collection procedure 6,11,12,[19][20][21][22] .
Most studies that have characterized PSDs have been conducted using an optical fiber connected to a single point of measurement as the sensitive volume. Multiple scintillation sensors attached to a single optical chain have been used, but their application is limited to measurements made within 3 cm of an HDR brachytherapy source 22-24 . New multipoint PSDs (mPSDs) could assess the dose at multiple points simultaneously, thereby improving treatment quality and accuracy. The multi-hyperspectral filtering method proposed by Archambault et al. 22 led to the conception of an mPSD in which each scintillator has an independent signal. Such an arrangement would allow simultaneous determination of the absorbed dose at different locations in a volume 23-25 .
The purpose of this study was to evaluate the performance of an mPSD in terms of sensitivity and accuracy, resulting in a thorough optimization of the optical chain, with applications in in vivo HDR brachytherapy in mind. To achieve this goal, 3 steps were followed. First, the base system was experimentally characterized. Second, the mPSDs system was numerically optimized to maximize the mPSDs performance. Finally, it was characterized the optimized system.

II.A.1. Experimental set-up
The optical chain in the proposed system has components that (1) generate scintillation light in the mPSD, (2) detect the scintillation light, and (3) analyze the signal.
The scintillating fibers used in this study were the plastic scintillators BCF-10, BCF-12, and BCF-60 from Saint Gobain Crystals (Hiram, OH, USA). Figure 1 shows the design schematic of a typical mPSD. The scintillators were separated from each other by 1 cm of clear optical fiber (Eska GH-4001, Mitsubishi Rayon Co., Ltd., Tokyo, Japan). The same type of fiber was also used to conduct the scintillating light to the photodetector surface.
(Here, clear refers to a fiber in which no scintillation light is produced.) Figure 1 shows an mPSD with 2 scintillators, but both 2-point and 3-point mPSDs were explored in this study. All optical interfaces (scintillators and clear optical fibers) were polished using a SpecPro automated optical fiber polisher (Krell Technologies, Neptune City, NJ, USA) with successive grain sizes of 30 µm, 9 µm, 3 µm, and 0.3 µm. The detectors were constructed using a previously described coupling technique 26 . It was verified that the polishing and coupling techniques were reproducible within margins of less than 5%. Each 1-mm-diameter detector prototype was made light-tight using a black polyether block amide jacket from Vention Medical (Salem, NH, USA). The scintillating tip was sealed with a mixture of epoxy and black acrylic paint.

II.A.2. Irradiation measurements
This study was designed to cover energy ranges of clinical interest. Several measurements were carried out in the low-energy range using an Xstrahl 200 X-ray therapy system (Xstrahl Ltd., Camberley, UK) to avoid Cerenkov light emission. Continuous beam irradiations with a tube current of 10 mA were performed according to the specifications shown in Table I.
Three beam energies were used during these irradiations.
The mPSD response was then assessed for HDR brachytherapy. A Flexitron HDR after-

II.A.3. mPSD design optimization
The purpose of this step was to identify the best configuration of scintillators in an mPSD.
Interchangeable radiosensitive tips containing the scintillators were coupled to a clear optical fiber, which conveyed the light signal to the photodetector. We built and tested more than 20 prototype 2-point and 3-point mPSDs using various combinations of scintillator positions and lengths to determine (1) the optimal position for each scintillator within the fiber and (2) the optimal length of each scintillator.
To evaluate the effect of scintillator position on the recorded signal, the lengths of the scintillators inside the radiosensitive tips were kept identical, but the positions of the scintillators inside the fiber were altered. Each scintillator was placed in a distal, central, or proximal position relative to the photodetector surface. To determine the optimal scintillator length in terms of the scintillation light produced and spatial resolution, each scintillator was varied in length from 3 to 14 mm. The hyperspectral approach 22 dictated a balanced signal contribution from each scintillator to the overall light collection, while the spatial resolution of the dose required as small as possible detection elements. For each possible combination of scintillator number, position, and length, the total emission spectrum was obtained from simultaneous irradiation of all the scintillators in the fiber. Then, in order to obtain their individual contributions to the total emission spectrum, each scintillator was individually irradiated. Lead blocks were used to shield the neighboring scintillators from the incoming radiation. This analysis was performed under a fixed irradiation condition.
An energy of 120 kV was selected to avoid Cerenkov light production. The spectrometer was cooled to -20 • C, and the integration time was 40 s. Background signals acquired prior to exposures were subtracted from the scintillation light.

II.A.4. Cerenkov radiation removal
The stem effect, which can have 2 sources, is always present in PSDs. The first source is direct excitation of the polymer chain, or fluorescence, from the plastic optical fiber guides, and the second is Cerenkov light production. Therriault-Proulx et al. 29  Therriault-Proulx et al. 14,15 showed that when an HDR brachytherapy source is within 10 mm of the optical fiber and more than 25 mm from the scintillator, Cerenkov removal is necessary. Their study in a water phantom demonstrated that an error on the order of 25% could be expected if stem effect removal is not performed. They also showed that in conditions where the source is placed close to the scintillator and far from the optical fiber, the stem effect is negligible. The further the source moves away from the scintillator and closer to the optical fiber, the more important the stem effect becomes 15 . In our study, multiple probes were read by a single clear collecting optical fiber; thus, it was used a single removal method, the hyperspectral filtering technique proposed by Archambault et al. 22 .
Dose calculation in mPSDs is based on the assumption that the recorded signal results from the linear superposition of spectra; no self-absorption interactions among the scintillators composing the mPSD are considered 22 . The idea behind this formalism is that once the light emission of each component at different wavebands is known, the total signal recorded can be decoupled, and the signal fraction contributed by each scintillator can be determined.
In equation (1), m is a vector of L elements, R is the response matrix of dimensions, and x is a vector of N elements representing the photon flux (the number of photons emitted for a given emission source, either scintillating elements or any other source of light). L represents different wavelength filters or channels. The number of measurement channels L should be equal to N + 1. The additional channel is included to take into account the stem effect, which should be removed from the measured signal 14 .
The dose d i;k received by the scintillator during irradiation is directly proportional to the number of scintillation photons in the absence of losses (quenching); for this reason, of measurements whose goal is to determine the absorbed dose, not the calibration factor, which is already known at this stage.

II.B. Optimization of the light collection system
In the second step, we sought the appropriate optical components for the light detection system used during measurements. Having a complete spectral characterization led us to perform a numerical analysis to determine the optical chain that would allow optimal scintillation light collection.
In our experimental set-up, scintillation light was read by an assembly of PMTs, which were coupled to a set of dichroic mirrors and filters that deconvolved the collected light into spectral bands. PMTs were chosen as the photodetectors because they have a high signalto-noise ratio (SNR) and readout speed that overcomes many of the sensitivity issues of To quantify the sensitivity of the dosimetry system, it was evaluated the SNR and signalto-background ratio (SBR) associated with each scintillator during HDR brachytherapy measurements. Figure 3 is a representation of a typical signal pulse, showing the magnitudes that were used in SNR and SBR determination: µ s , the mean signal; µ b , the mean background signal; σ s the signal standard deviation; and σ b the background standard deviation.
The SNR is a commonly used metric for characterizing the global performance of optoelectronic systems. In case of PSD performance assessment, the noise term includes Cerenkov radiation. A few SNR studies using PMTs as the photodetector have been performed [32][33][34] .
The scintillator SNR as function of dose rate was obtained using equation 4, where the numerator represents the mean signal for a determined irradiation in a fixed time, and the denominator is the standard deviation in a homogeneous background region. SBR was determined according to equation 5 and is the proportion between the mean signal value and the mean background value for a fixed irradiation time.

III.A. mPSD signal proportion and optimal configuration
The initial investigations were performed with a 2-point mPSD configuration. Each scintillator spectrum was measured independently. Figure 4 graphs the individual spectra with intensities normalized to a 1-mm scintillator length. As shown in the figure, the scintillation intensity was strongest in the BCF-10 scintillator, whereas the BCF-60 scintillator had the weakest scintillation intensity.
In all the tested combinations, the scintillators individual spectra evidenced no selfabsorption or cross-excitation effects. The main differences observed related to the position occupied by each scintillator inside the fiber. Table II   9% when coupled to a BCF-12 scintillator. Therefore, this combination of scintillators and positions is recommended for a 2-point mPSD.
The signal analysis demonstrated that the lower-wavelength scintillator should always be placed closer to the photodetector and the less-energetic scintillator in the distal position.
Because of the Stokes shift, the absorption spectrum always has a lower wavelength range than the emission spectrum. If the aforementioned configuration is not used, inter-scintillator excitation and self-absorption effects take place, and as a consequence, the light transmission through the collecting fiber is not optimal. To exemplify this effect, 3-point mPSDs with 2 different configurations of scintillator positions inside the fiber were constructed. Their spectral distributions are shown in Figure 5. Figure  neighboring scintillators, whose photon intensities were higher than they were in the optimal configuration ( Figure 5b). Hence, in the subsequent experiments, we used mPSDs in which the scintillators were placed inside the optical fiber in increasing order of energy from distal to proximal positions.
In the case of a 3-point mPSD composed of 3 mm of BCF-60 at the distal position, BCF-12 in the center, and BCF-10 at the proximal position, we observed no self-absorption or cross-excitation effects, but the scintillators independent signals were not balanced at all.
As shown previously, the scintillation process is more efficient in BCF-10 than in the other scintillators, accounting for almost 80% of the total signal. The intensities of BCF-12 and BCF-60 were closer to one another, with 17% and 10% of the total signal, respectively.

III.B. Optimal scintillator length
The amount of measured scintillation light depends on the scintillator size, the coupling method, the fiber core size, and the numerical aperture. To determine the optimal length of each scintillator, 9 different 3-point mPSD prototypes were constructed. Figure 6 shows the contributions of individual scintillator signals for each of the 3-point mPSDs and specifies the length of each scintillator in millimeters. As indicated by the shadowed region in Figure   6, detector configurations P6 to P9 provided the required balanced signals for optimal hyperspectral deconvolution. P9 was selected as the optimal detector because it also minimized Length (mm)  P1  P4  P6  P7  P8  P9  BCF10 3  11  4  1  3  3  BCF12 3  11  6  5  7  6  BCF60 3  10  13  14  11  variations in sensor length. In the P9 mPSD, the BCF-10 scintillator was 3 mm long, the BCF-12 scintillator was 6 mm long, and the BCF-60 scintillator was 7 mm long.

III.C. Optimized light collection system
Following the determination of the optimal length, the numerical optimization allowed us to determine the best combination of components to be used for the measurements of the light collection system. Figure 7 shows a schematic of the appropriate arrangement of the components of the light collection system obtained from these calculations.
This assembly filtered the total emission spectrum from the mPSD to produce a filtered spectrum entering each PMT. Figure 8 shows each channel's filtered spectrum and the total emission spectrum of the scintillation light generated by the P9 mPSD. Each measurement channel produced a voltage value that, when converted into dose, was proportional to the scintillation light generated by each scintillator without the Cerenkov radiation. A signal was generated each second, so no signal integration in time was required.
The study done by Therriault-Proulx et al. 25 in HDR brachytherapy, uses the same scintillating elements described in this work (BCF-10, BCF-12, and BCF-60; Saint-Gobain  is limited to HDR brachytherapy measurements within 3 cm from the source. The system here proposed is able to accurately perform dose measurements beyond 3 cm with a high collection efficiency as described in the following sections.

III.D. mPSD brachytherapy implementation
Dose distributions in terms of distance to an HDR brachytherapy source were obtained, with the P9 mPSD calibrated at 1.5 cm from the 192 Ir source. This calibration distance represented a compromise between measurement uncertainties and positioning errors. Andersen et al. 35 demonstrated that positioning uncertainty dominates in measurements close to the source, whereas measurement uncertainty dominates at long distances. In order to ensure that we had enough data in the response recording, a source dwell time of 60 s was used at each dwell position. Figure 9 shows dose rate readings for each scintillator, and III.E. Evaluation of scintillation signal and system sensitivity Figure 10a shows the SNR in terms of dose rate for each scintillator in detector P9.
According to the Rose criteria, proper recognition (detection) of an object strongly depends on SNR, only becoming possible when SNR exceeds 5; detection performance degrades as SNR approaches zero 36 . Thus, an SNR of 5 was the minimum sensitivity considered in this study. The BCF-10 and BCF-12 scintillators produced an SNR greater than 5 at all distances to the source. At dose rates below 22 mGy/s, the SNR produced by the BCF-60 scintillator fell below 5. These data suggest that, with regard to SNR, the dosimetric system characterized in this study is sensitive enough to measure dose rates above 22 mGy/s. To evaluate how well the dosimetric system differentiated a signal pulse from the background signal, SBR values were calculated at each dose rate. It is important to mention that in order to determine the background signal; several signal acquisitions were performed without irradiation. From this analysis, it was obtained a µ b ± 0.16 %. To properly differentiate signal from background, a minimum SBR of 2 is required. Figure 10b shows the SBR results obtained for each scintillator in the mPSD. The SBR for the BCF-10 scintillator  fell below the SBR cutoff value for dose rate values of around 6 mGy/s, with an SBR of 1.8. SBR is directly proportional to the photon fluence from scintillation, which is in turn proportional to the scintillator volume. According to the previously determined optimal mPSD design, the length of the BCF-10 scintillator was only 3 mm. The dose rate range could be extended by increasing the length of the scintillator, but at the cost of spatial or temporal resolution. As the background signal was almost constant in the explored dose rate range, all the scintillators evidenced almost perfectly linear behavior.

IV. CONCLUSIONS
In this study, we optimized an mPSD system that can be used clinically in HDR brachytherapy. We found that the scintillation light emission per millimeter of scintillator was more efficient in BCF-10 than in BCF-12 or BCF-60 scintillators. Furthermore, we experimentally determined the appropriate position of each scintillator inside the fiber: the scintillating element with the lower wavelength should be placed closer to the photodetector, whereas the scintillator with the longer wavelength (less energy) should be placed distally. In a 2-point mPSD, the most balanced signal was obtained with BCF-10 placed proximally and BCF-60 placed distally. We also evaluated a 3-point mPSD consisting of BCF-10, BCF-12, and BCF-60 scintillators. The best prototype used 3 mm of BCF-10, 6 mm of BCF-12, and 7 mm of BCF-60. Those dimensions were determined not only on the basis of light emission balance, but also with the aim of improving the detectors spatial resolution. Finally, an optimal light collection system was evaluated in HDR brachytherapy simulations. The evaluated mPSD produced minimal deviations in dose rate readings, and analysis of SNR and SBR showed that the detector provided accurate real-time dose measurements. Center for editing our manuscript.