Time-resolved imaging of prompt-gamma rays for proton range verification using a knife-edge slit camera based on digital photon counters

The experimental set-up is similar to the one described by Smeets et al (2012). A schematic representation of the setup is shown in figure 1-left. Figure 1-right shows a photograph of the actual setup installed in the gantry of treatment room 2 of the West German Proton Therapy Centre Essen (WPE), where all proton irradiations were performed. The LYSO : Ce and BGO detectors were mounted on a breadboard, at opposite sides of a cylindrical polymethylmethacrylate (PMMA) phantom. The knife-edge slit collimator was placed on a PMMA support rail in between the LYSO : Ce detector and the phantom. The PMMA phantom had dimensions of Ø15 cm  ×  20 cm and was irradiated with an 160 MeV proton pencil-beam. The Bragg peak position, defined as the distal position at which the depth-dose profile has reduced to 80% of the maximum height, was located at a depth of 15.2 cm into the phantom.

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The knife-edge slit collimator was made of a tungsten alloy with a density of 16.96 g cm⁻³. It had a thickness of 4 cm and a slit opening of 6 mm. The collimator was placed midway between the phantom axis and the mid-plane of the crystal matrix (figure 1-left), so as to project an inverse image of the prompt-gamma emission profile onto the detector with a magnification factor of 1. The distance between the beam axis (coinciding with the phantom axis) and the mid-plane of the scintillator matrix was 30 cm. The center of the slit was aligned with the expected Bragg peak position, as well as with the center of the detector. Additional measurements were made with the detector shifted by  ±3.35 cm in parallel with the beam axis (corresponding to an overlap of 8 crystals), so as to enlarge the total field-of-view (FOV) to about 13.5 cm, still centered at the Bragg-peak position. In addition to the measurements performed with the knife-edge slit collimator, measurements were also done using a completely closed collimator (i.e. a tungsten slab with a uniform thickness of 4 cm), as well as without any collimator, for characterization purposes.

All acquisitions were done with a beam current at nozzle exit of about 10 pA or 6.24   ×   10⁷ protons s⁻¹. In most measurements, the administered dose was about 10 Gy per measurement, corresponding to about 6.5   ×   10⁹ protons delivered in total. A few measurements used for timing calibrations were acquired with a 5-times higher dose, using the same beam current. It is noted that this beam current is lower than those typically used in clinical treatments, which are of the order of 1 nA. The DPC data acquisition electronics used in the present measurements (section 2.1.2) is part of a technology demonstrator kit that is not designed for high count rates. In particular, it makes use of a USB 2.0 connection to the readout computer, which forms a bandwidth bottleneck. A higher-bandwidth connection would be required to obtain sufficient system bandwidth for clinical use of a DPC-based prompt gamma camera. The DPC detector is in principle capable of processing a much higher count rate than in the current experiment (section 2.1.3).

The detectors were based on DPC modules manufactured by PDPC (DPC-MO-22–3200). Each DPC module has a total surface area of 68 mm  ×  68 mm and contains 2   ×   2 DPC arrays (DPC3200-22–44). Each of the 4 DPC arrays measures 32 mm  ×  32 mm and comprises 8   ×   8 DPC pixels at a pitch of 4 mm, each DPC pixel consisting of 3200 single-photon avalanche diodes (SPADs) or microcells (Frach et al 2009). A DPC array is assembled from 4   ×   4 independent DPC-chips, each chip containing 2   ×   2 pixels. It is equipped with readout electronics and a pair of 9-bit time-to-digital converters (TDCs). After light detection and readout, the DPC-chip outputs the total number of fired cells on each of its 4 pixels, as well as a single time stamp. One of the modules was equipped with a matrix of 256 LYSO : Ce (Lu_1.8Y_0.2SiO₅(Ce)) crystals, each crystal having dimensions of 3.8 mm  ×  3.8 mm  ×  22 mm. The other detector had a matrix of 256 BGO (Bi₄Ge₃O₁₂) crystals of 3.8 mm  ×  3.8 mm  ×  20.5 mm each. The coupling between DPC-pixels and crystals was 1-to-1 in both cases. Each BGO crystal was optically isolated, whereas light sharing was allowed between each group of 4 LYSO : Ce crystals coupled to a same DPC-chip, so as to minimize saturation of the DPC-pixels. The detector modules were cooled by Peltier elements and attached to a heat exchange plate internally flushed with running tap water. The modules were enclosed in a light-tight and moisture-free box that was continuously flushed with dry nitrogen gas. The temperature of operation of the DPC arrays was  −15 °C.

The LYSO : Ce and BGO crystal matrices have comparable (i.e. within 4% variation) total attenuation cross sections for photons between 1 MeV and 10 MeV (Berger and Hubbell 2010). Given the higher light output and lower decay time of LYSO : Ce (41 ns versus 300 ns for BGO), the LYSO : Ce detector was used for the time-of-flight (TOF) measurements. Due to technical reasons, one DPC array of the BGO detector was not operational.

Data acquisition with DPCs is regulated by a programmable trigger and validation logic (Frach et al 2009, 2010). The trigger logic is implemented on pixel level, and the trigger threshold is defined as the number of sub-pixels (one-fourth of a pixel) that must be fired to create a time stamp. Triggering on the 1st or 2nd fired sub-pixel is best suited for fast timing applications. We used the 2nd sub-pixel threshold in all of the measurements performed in this work.

Upon triggering, the DPC-chip enters into the validation phase, i.e. it keeps counting during a certain validation interval, to check whether it reaches a given validation threshold. Upon validation, the DPC-chip continues acquiring for an additional time, the integration interval, after which it is read out and recharged/reset. If the validation threshold is not met, the integration and readout phases are skipped. Therefore, the optimum trigger and validation settings depend on the application, measurement conditions, and crystal type, size, and coupling. The settings should reduce the dead-time due to system readout and/or resets of dark count-induced triggers, while maximizing the detection efficiency at the same time.

In the present work, the validation interval was set to 40 ns for the measurements with BGO, and to 10 ns for the LYSO : Ce measurements without RF synchronization. The validation threshold was set to a 2-OR validation pattern for the BGO measurements, and an 8-OR validation pattern for the LYSO : Ce measurements. This validation conditions only need to be satisfied by one sub-pixel (the four subpixels are connected through a logical OR), while each sub-pixel is subdivided into 8 logical validation regions. A 2-OR validation scheme requires that 2 mutually exclusive groups of 4 validation regions each have at least one fired microcell, whereas the 8-OR scheme requires one fired microcell per validation region (Tabacchini et al 2014). The expected number of fired cells on a pixel at the time of validation is 5.3   ±   2.5 for the 2-OR validation pattern and 59   ±   17 for the 8-OR validation pattern (Tabacchini et al 2014). Thus, stricter validation settings were used for LYSO : Ce than for BGO since LYSO : Ce has a higher light yield and a faster decay time. A higher validation threshold could, however, be used with the BGO detector, without compromising the detection efficiency. The integration times used in our measurements were 1285 ns for BGO and 165 ns for LYSO : Ce without RF synchronization, so as to accumulate counts during approximately 4 decay time constants in each case. Finally, DPC saturation was reduced in the measurements with LYSO : Ce by using the lowest available excess voltage, viz. 2.2 V above tile breakdown voltage, whereas for BGO a typical excess voltage of 2.9 V was used.

For the measurements with TOF discrimination, the acquisition electronics of the LYSO : Ce detector module were synchronized with the cyclotron RF. This was done by converting the 106 MHz RF wave into a clock signal, which was then used as a reference clock by the acquisition electronics, instead of the 200 MHz internal DPC clock. In this way, the registration time of each event relative to the phase of the RF cycle could be obtained from the TDCs in the DPC-chip. The acquisition time settings used in this case were different from the ones used in the previous measurements, as the acquisition times are integer multiples of the reference clock. Specifically, the validation interval used in the experiments with RF synchronization was 18.9 ns and the integration interval was 160.4 ns. (As a result, the total measurement time changed by less than one percent.)

Finally, the DPCs were operated at a constant temperature (−15 °C, see section 2.1.2) to maintain stable detection efficiency throughout all measurements. Cooling reduces the dark-count rate and, therefore, the dead-time induced by triggers originating from dark counts. The dark-count rate was further reduced by switching off the 5% (160) cells with the highest dark-count rate (Frach et al 2009). The remaining average dark-count rate was about 50 s⁻¹ per cell, measured with the BGO crystals coupled to the sensor tiles. It is noted that the temperature of operation was simply set as low as practically achievable; in this initial study we did not yet study or optimize the detector performance as a function of the operating temperature.

The average count rate obtained per DPC-chip was 0.88 kcps for LYSO : Ce and 0.42 kcps for BGO, in terms of overall validated events, as energy and time-of-flight selection was applied offline. In the case of LYSO : Ce, the chip count rate within the acceptance time-of-flight window (see section 2.2.2) was 0.25 kcps. The total trigger rate (validated and non-validated triggers) was 0.22 Mcps for both detectors, mainly due to dark counts.

The maximum (validated) event rate that the DPC-chips can process is 1.3 Mcps when operated at a 200 MHz clock, which scales with the clock frequency. However, the bandwidth of the DPC-sensor is artificially limited by the event storage available on the tile FPGA. Currently, the sensor can handle a maximum of about 120 kcps per chip when operating at the default 200 MHz clock frequency. Therefore, these detectors may be capable of acquiring an eventual 100 times higher validated-event count rate, which could be expected at a clinical beam current of 1 nA, provided that there are no bandwidth limitations on the interface between the acquisition electronics and the readout computer. With the present implementation, using the 106 MHz external clock for TOF discrimination, the bandwidth was reduced to about half of the 120 kcps per chip, due to the longer clock cycles. A possible way to increase the sensor bandwidth while ensuring synchronization to the cyclotron RF, would be to operate the sensors with a frequency double of that coming from the external clock. This would likely reduce the chip dead time and would increase FPGA bandwidth, eventually enabling to measure using typical clinical beam currents and cyclotron RF, with TOF discrimination.

Energy calibration was performed by measuring specific gamma lines from the following radioactive sources: ¹³⁷Cs (661.7 keV), ⁶⁰Co (1173 keV; 1333 keV), ²²Na (511 keV; 1275 keV), and ²⁴Na (1369 keV; 2754 keV; sum peak 4123 keV). The calibration was done on a per-pixel basis so as to normalize the response for each crystal. However, the counts were summed over each DPC-chip, since event acquisition is performed on a per- DPC-chip basis and since inter-crystal light sharing occurs within each DPC-chip, especially in the LYSO : Ce detector. Pixel assignment was done using the 'winner-takes-all' method, i.e. by selecting the brightest pixel within the DPC-chip.

Prior to energy calibration we corrected the measured number of fired microcells per pixel for saturation to improve linearity. Saturation occurs due to the limited number of available cells, each of which can detect only one photon per scintillation event. A correction was implemented using the 'simple model' proposed by van Dam et al (2012), which takes into account optical crosstalk (Frach et al 2009) as well as dark count contributions over the total acquisition time. In the present case, we used a total crosstalk probability of 0.16, in accordance with Tabacchini et al (2014).

Upon saturation correction the LYSO : Ce detector presented good proportionality up to 1333 keV. In first instance we therefore used a linear energy calibration obtained from fitting the ²²Na and ⁶⁰Co peak positions, such that the ratios of saturation-corrected photon counts to energy equaled 4.3   ±   0.4 keV⁻¹ (mean  ±  standard deviation). With this calibration, which normalized the response of each crystal, the peak positions up to 4123 keV (²⁴Na sum peak) were re-calculated (energy_extrapolated) from the global spectra, i.e. the spectra obtained from all detector pixels. We thus derived a DPC-chip/pixel-independent energy correction function for the LYSO : Ce detector, by fitting a second-order polynomial to the true energy values, E, as a function of the extrapolated energy peak values, E_extrap. These values (E, E_extrap) and the energy correction curves are presented in figure 2.

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The energy correction functions obtained with and without cluster processing appear to be different, yielding: E = 0.991E_extrap  −  8   ×   10⁻⁶E²_extrap, and E = 0.969E_extrap + 2.3   ×   10⁻⁵E²_extrap, respectively, where all energy values are expressed in units of keV. Event clustering was performed by summing up the energies of all DPC-chips with time-stamps spaced less than 5 ns apart, for the LYSO : Ce detector. Most probably these events originate from the same gamma quantum, which may undergo interactions in more than one DPC-chip. Omitting the clustering procedure results in a slight underestimation (~4%) of the extrapolated energy values at 2754 keV, which could be attributed to saturation. In contrast, if cluster processing is applied, there is an overestimation by about 4% at 2754 keV and 4123 keV, suggesting that energy overestimation outbalances saturation in this case. Presumably, this overestimation could be due to light sharing between neighbor DPC-chips. The per-pixel energy calibration may overestimate the energy in the presence of light sharing, because energy calibration curves have been derived from energy spectra of single-DPC-chip clusters (i.e. one DPC-chip validated per cluster window on whole detector).

In the case of the BGO detector we observed considerable inter-chip and inter-pixel response variations. Furthermore, lack of proportionality could be observed at 1275 keV already, with about 6% deviation of the saturation-corrected photon counts relative to the extrapolation from the 511 keV line. Possible reasons for this are the optical isolation between BGO crystals within a same DPC-chip and/or a (slight) mismatch between the crystal footprints and the DPC-pixels surfaces. For this detector, we therefore chose to apply a chip/pixel-dependent energy calibration curve, calculated by fitting a second-order polynomial to the positions of the five energy peaks from ¹³⁷Cs, ²²Na, and ²⁴Na, such that the curves of the saturation-corrected photon counts, c, as a function of energy, E, yielded: c = p₀ + p₁E + p₂E², with p₀ = 22   ±   26, p₁ = 1.1   ±   0.1 keV⁻¹ and p₂ = (−4   ±   1)  ×  10⁻⁵ keV⁻² (mean  ±  standard deviation). Since BGO has a lower timing resolution compared to LYSO : Ce, a longer clustering window of 20 ns was applied for that detector, which was sufficient to collect chip-events with energies as low as a few hundreds of keV.

The resulting (global) energy spectra measured with point sources are shown in figure 3 for both detectors. Both here and in the remaining of this work, energy spectra are presented with cluster processing, except in section 3.1, figure 6, where specified. The insets in figure 3 show the position of the 4123 keV sum peak of ²²Na, which is clearly resolved for LYSO : Ce (figure 3-left) but hardly noticeable for BGO (figure 3-right). The FWHM of the gamma peaks at 511 keV, 1369 keV, 2754 keV, and 4123 keV was 12%, 11%, 10%, and 8%, for LYSO : Ce, respectively, and for BGO it was 19%, 14%, and 13% at 511 keV, 1275 keV, and 2754 keV, respectively. The BGO point-source spectra were obtained with a higher validation threshold than used in the prompt-gamma measurements (8-OR validation pattern instead of 2-OR), which lowered the detection efficiency but did not affect the peak positions.

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Time calibration of the LYSO : Ce detector was done to allow accurate time-of-flight (TOF) discrimination. The two TDCs on each DPC-chip run on half the system clock frequency, in opposition of phase, and have a resolution of 19.5 ps and a range that spans approximately 10 ns. In this particular case, the system clock of 200 MHz was replaced by a clock pulse derived from the 106 MHz cyclotron RF signal, resulting in nearly no overlap between the TDC time stamps, meaning the valid time stamps were given alternatively from TDC1 or TDC2. The TDC outputs provided a direct measure of the TOF of the detected events, relative to the arrival time of the proton bunch, due to the correlation of the proton arrival times with the phase of the RF signal (RF-pulsed beam delivery). It is noted that part of the 9.4 ns long RF wave period (not more than 30%) was not registered due to a firmware filter that rejected events with invalid combinations of TDC1 and TDC2 values, which had not been adapted to the 106 MHz operating clock by the time of the experiment. Nevertheless, the available TDC range was sufficient to apply the TOF discrimination, and the use of an adequate delay line ensured that the prompt signal fell within that range.

Figure 4 illustrates two exemplary time histograms derived from the TDC outputs of DPC-chips placed at two different locations that, upon projection through the slit, correspond to positions 13 mm proximal or distal to the proton range on the beam axis. In both cases, a peak can be observed between about 2 ns and 4 ns, which is attributed to the prompt gamma signal. The DPC-chip that looks at the region distal to the proton range registers fewer prompt counts, which are mainly attributed to prompt gammas that are scattered or that pass through the collimator without interacting. The prompt peaks are superimposed on a broad background, which is mainly attributed to neutron-induced gammas and neutrons. This slowly-increasing background peaks at time stamps posterior to the prompt arrival time and spans over the entire RF-range, most likely due to overlay of neutrons generated by a given proton bunch onto successive pulses (Biegun et al 2012).

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TOF calibration was based on determining the prompt peak position for every DPC-chip. For this purpose, we fitted all time spectra (after applying a 3 MeV low-energy cutoff) by a Gaussian function plus a linear baseline in the range between  −1.95 ns and +1.76 ns relative to the maximum of the histogram. Thus, the background is approximated by a linearly rising slope and the prompt gamma peak by a Gaussian curve. The solid curves in figure 4 are examples of such fits. As illustrated by this figure, the prompt gamma peak position is chip-dependent, which is due to the clock skews between different chips of the DPC array (van Dam et al 2013). Furthermore the sum of the proton travel time and the prompt gamma time-of-flight depends on the positon within the phantom at which the prompt gamma quantum is created (Biegun et al 2012). These effects were corrected for by placing the TOF selection window symmetrically around the mean of the Gaussian fit of each DPC-chip.

The prompt gamma peak would be very narrow, in the order of 150 ps (Biegun et al 2012), if all protons would enter the phantom simultaneously. In practice, however, the prompt gamma peak is convoluted with the proton bunch width, i.e. the arrival time-spread of the protons within each RF cycle, as well as with the time resolution of the prompt gamma detector. In the present experiments, the (single-) detector time resolution is relatively small: viz. about 255 ps FWHM for 511 keV photons using 2nd photon triggering (Degenhardt et al 2012). Moreover, it is expected to decrease with increasing prompt gamma energy (Seifert et al 2012). Therefore, the width of the Gaussian fits is mostly determined by the proton bunch width and had an average value of 1.1 ns FWHM. Hence, TOF discrimination was implemented by rejecting events that did not fall within a time window of 1.5 ns width, centered at the calculated Gaussian mean for each DPC-chip. In cases were clustering was performed, the TOF discrimination was applied post-clustering on the time stamp of the DPC-chip that registered the highest energy only.

Figure 7 shows a comparison of simulated and measured profiles, the latter without cluster processing, for both the LYSO : Ce and BGO detectors. The profiles measured with LYSO : Ce are shown taking into account only the upper half of the detector, in order to be directly comparable to the BGO case and to resemble more closely the simulation results, in terms of statistical fluctuations. Furthermore, the lower detector half of LYSO : Ce presents more background counts, presumably due to the presence of the treatment bed (see section 3.2.2) that was not modeled in the simulations.

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In general, both the experiments and the simulations indicate that the profiles obtained with LYSO : Ce and BGO are comparable in terms of the overall number of counts, but that the BGO profile contains slightly less background counts in comparison to the LYSO : Ce case, possibly due to a lower sensitivity of BGO to neutrons. By comparing the closed-collimator profiles and the open-collimator profiles beyond the Bragg peak, it seems that the simulations slightly underestimate the background, which is expected because the materials in the surroundings, such as the patient bed, are not taken into account in the simulations. However, the simulated open-collimator profile proximal to the Bragg peak is about 6% higher on average than the measured one, for both detectors.

It should be noted that an incoming particle that gives rise to multiple interactions on different pixels of a same DPC-chip was counted only once in the measured profiles, in contrast with the simulated profiles, in which each pixel was scored independently. This is not expected to have a major effect on the overall simulated counts, relative to the measurements. Taking into account the simplicity of the simulations, which do not take into account factors like additional background radiation and radiation scattering due to the materials in the vicinity of the detector, simulations and measurements are found to agree well. The agreement between simulation and measurements of closed collimator signal are in line with the recent results reported in Perali et al (2014) and in contradiction with the older ones reported in Smeets et al (2012). This further indicates that MCNPX seems rather efficient at reproducing not only the prompt gamma signal, but also the closed collimator signal.

Furthermore, the profiles measured with BGO present remarkable fluctuations, larger than what would be expected on the basis of Poisson noise only. These fluctuations are similar in magnitude in both the open and closed collimator cases. Moreover, the pattern of these fluctuations is very similar in these two cases, suggesting that they may result from differences in the sensitivity of different BGO crystal columns aligned in parallel with the knife-edge slit. To further investigate this, a correction to the open-collimator profile was attempted, by subtracting the difference between the measured closed-collimator profile and the corresponding average. Indeed, the resulting profile is much smoother and shows a greater degree of similarity with the simulated BGO profile. A similar effect can be observed for the LYSO : Ce case, although less pronounced.

One possible reason for the observed fluctuations in the uncorrected profiles could be the presence of systematic errors in the pixel assignment. Given that relatively large differences exist between the energy calibration curves of different BGO pixels especially, compared to the LYSO : Ce case, pixel assignment plays an important role in determining whether or not the detected event falls within the energy selection window. This effect is reduced when clustering processing is applied, as will be shown in the following section.

Overall, the agreement between simulations and measurements is quite satisfactory and reinforces that there are no important dead-time losses, as would be expected at the relatively low count rates under consideration. Given the present acquisitions settings and the measured count rate per DPC-chip, we expect that each DPC-chip is busy with event processing (acquisition, readout and recharge) for less than 2% of the time on average.

Figures 8 and 9 show the measured profiles obtained with clustering of DPC-chip-events, decomposed into 1 MeV wide energy windows up to 8 MeV, for the LYSO : Ce and BGO detectors, respectively. In the interest of clarity, only profiles without uniformity correction are presented in these figures and in the remainder of this section. It should be noted that, without uniformity correction, the profiles obtained with cluster processing present less fluctuations compared to those without cluster processing (section 3.2.1). The highest correlation with the BP position, in terms of the slope of the distal falloff region, is observed for the energy range from about 3 MeV to about 7 MeV for LYSO : Ce, and from about 3 MeV to about 8 MeV for BGO. It is to be noted, however, that the number of counts per proton falls down by an order of magnitude above 6 MeV.

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The falloff in the number of counts of the LYSO : Ce profile, relative to its maximum, is higher if TOF discrimination is applied, while the overall number of counts is reduced by a factor of 2.6, in the energy range from 3 MeV to 7 MeV.

As expected, the falloff steepness decreases below about 3 MeV in all cases studied, due to the prevalence of the background counts that result from neutron interactions in the collimator, as well as from scattered prompt gammas that are not efficiently discarded by TOF discrimination. Above 8 MeV, there is a prevalence of neutron counts and, therefore, there is little correlation between the detected profiles and the depth-dose distribution (Smeets et al 2012).

The relation between the number of counts proximal and distal to the Bragg peak position can be used as a measure of the signal-to-background (S/B) ratio. Thus, the profiles measured with the detector centered at the expected beam range were interpolated with a sigmoid curve, by fitting them with the four-parameter complementary error function previously described by Henriquet et al (2012):

$$\begin{eqnarray}&&a+b\cdot \text{erfc}\left\{c(z-d)\right\}\end{eqnarray} \tag{ 1 }$$

where z represents the depth into the phantom and a, b, c and d are fit variables. The profiles were corrected for non-uniformities using the corresponding closed-collimator profiles (see section 3.2.1) prior to the fitting, and the first and last pixel columns were excluded from the fit. The signal-to-background ratio was estimated as the ratio of the difference between the two asymptotes of the curve to the lower asymptotic value. These values are presented in table 1, for different energy windows.

Table 1 confirms that the S/B ratio improves as the low-energy threshold is increased from 1 MeV to 3 MeV in all cases. Using an energy window from 3 MeV to 6 MeV, the BGO profiles have a S/B ratio of 0.8, about 60% higher than the value of 0.5 found for the LYSO : Ce case without TOF discrimination. The use of TOF discrimination increases the S/B of the LYSO : Ce profiles to 1.6 using the same energy window. The TOF-resolved LYSO : Ce detection therefore presents a 2-fold increase in S/B, in regard to the BGO case. In what concerns the high-energy threshold, we did not observe important changes in S/B by increasing it from 6 MeV to 8 MeV. Nevertheless, the profile counts increase on average by 20% for BGO and by 11% for LYSO : Ce without/with TOF discrimination, respectively, and therefore it may be beneficial to increase the high-energy threshold if clustering is performed.

Maps of the count rate registered per crystal and the corresponding profiles are illustrated in figures 10 and 11, respectively, for the BGO detector and the LYSO : Ce detector with and without TOF discrimination, using an energy window of 3 MeV–6 MeV in all cases. In figure 11, also the closed-collimator profiles are shown, as well as the profiles measured at two adjacent longitudinal detector positions that were added to increase the total field-of-view. In the latter profiles, the values of the edge pixel-columns were excluded to account for the observed systematic mismatches of the crystal count rates in the overlapping regions. Specifically, 2 pixel-columns were removed at each edge of the LYSO : Ce detector without TOF discrimination, 1 pixel-column for the same detector with TOF discrimination, and 2 pixel-columns on the left-most edge (on graph) for the BGO case.

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The count-rate map obtained with LYSO : Ce (figure 10-left) shows a higher number of counts per proton in the lower half of the detector surface, compared to the upper part. This effect is reduced by applying TOF discrimination (figure 10-center), suggesting that the intensity offset is mostly due to background counts, for example gamma rays generated by neutrons interacting in the materials of the patient bed onto which the setup was placed.

By comparing the measured profiles shown in figure 11 to the ones presented in figure 7, we observe that cluster processing increases the detection efficiency of LYSO : Ce by 39% in the energy window between 3 MeV and 6 MeV, whereas for BGO this increase is 6–7% only. In case TOF discrimination is applied, the efficiency of LYSO : Ce increased by 30% with clustering. The higher efficiency increase in LYSO : Ce, compared to BGO, may be explained by the fact that the LYSO : Ce detector registers more DPC-chips per clustered event than the BGO one (specifically, 3.8 versus 3.3 chips per event for LYSO : Ce versus BGO, respectively, in the energy window between 3 MeV and 6 MeV), and that BGO presents higher efficiency. This is not unexpected given that the coefficient for photoelectric absorption of BGO is more than 1.5 times higher than that of LYSO : Ce in the energy range between 0.3 MeV and 6 MeV (Berger and Hubbell 2010). We did not observe relevant changes in the S/B ratios due to cluster processing.

Overall, our results indicate that BGO benefits from a higher gamma-to-neutron sensitivity compared to LYSO : Ce, resulting in a better S/B if no TOF discrimination is applied. Nevertheless, TOF selection appears to be the most effective way of rejecting background, rendering TOF-resolved LYSO : Ce detection the best option evaluated.

Given that TOF rejection of neutron-induced background relies on the difference in travel time between gammas and neutrons on their way to the collimator, the efficiency of TOF selection is expected to increase even further for larger distances between the beam and the collimator. However, at large distances background reduction efficiency by a 1.5 ns TOF window may not exceed the limit of 84%, estimated by considering an homogeneous distribution of background time stamps over the 9.4 ns RF period, caused by the larger transit time spread of neutrons and the superposition of the background counts from consecutive proton bunches. Nevertheless, given that a 15 cm distance between the PG camera and the beam axis is close to the lower limit of what can be achieved in practice, the present efficiency of about 74% is very satisfactory.