New approaches to particle induced prompt gamma imaging

The Monte Carlo (MC) package GATE (version9.0) [38] which is based on Geant4 (version 10.5.1) simulation toolkit [37] has been used to perform simulations relevant for our prompt gamma detector development. The physics list QGSP_ BIC_ HP_ EMY [39] accounts for the processes involved in the proton beam interactions with the target material, the process of dose deposition within the target, the generation of secondary particles due to nuclear interactions, the interaction of the secondary particles within the phantom material and subsequently with the detector system involving mechanical collimators and scintillating crystals. Binary cascade and pre-compound model are used to implement the nuclear interactions depending on the proton energy, and photon evaporation model describes the decay of the excited nuclei to produce gamma. The optical sensor is not modeled in our simulations, and the reported counts and energy are based on the gamma energy deposited in the crystals. The energy dependent resolution is modeled for the KE-PET in section 4 but not for the 3DPG detector in section 6.

The simulated distributions of the 984 keV gamma in section 5 and the carbon and oxygen PG in section 6 are model dependent and not always in agreement with the experimental values, however this does not significantly impact the approaches described in this work and the designs can be further optimized.

The experiments described in this work have been performed using a coaxial HPGe detector (Canberra GC3022), although the crystal dimensions are not specified, [40] describe it to be a cylinder of 5.73 cm diameter and 5.75 cm height. The detector operated at 2500 V and the energy spectrum was collected using CAEN DT5770 MCA. The energy resolution of the HPGe GC3022 at 661 keV was measured to be 0.81%. The deteriorated energy resolution can be attributed to radiation damage, increased pressure in the cryostat, and other aging effects over 20+ years of usage; nevertheless all important gamma lines for our tests were clearly identified. Lead and tungsten collimators were used to shield the detector where necessary. The cyclotron at INER was used as a proton source for 30 MeV protons in the experiment with Ti target mounted on a water phantom described in section 5. A 230 MeV cyclotron installed at the CGMH proton facility delivered a pencil beam between the energies of 70 MeV (beam width of 4.7 mm FWHM) and 90 MeV (beam width of 7.4 mm FWHM) for a beam energy scan on a Ti marker with water phantom described in section 5.

In our simulated geometry, we irradiate a cylindrical phantom of PMMA (20 cm diameter 11.04 cm length) with the diameter comparable to a human head. An 8 cm thick tungsten knife-edge collimator is placed between the detector and the phantom with an area equal to the detector area. As seen in figure 3 (left) collimator inner gap $\mathrm{w_{1}=15\ mm}$ and the outer width $\mathrm{w_{2}=35\ mm}$ with a resulting angle of $\mathrm{28.1^{o}}$. The center of the collimator is positioned at the expected Bragg peak position for 90 MeV proton beam. In a real treatment case, the Knife-Edge PET (KE-PET) system would need to be placed in a similar manner at the Bragg peak corresponding to the highest energy of the treatment plan. For the detector, we utilize the geometry of the ASPET as seen in 3 (right) described in [19]. $\mathrm{3\times 3\times 20\ mm^{3}}$ LYSO crystals coupled directly to SiPMs with same area (3 mm $\times$ 3 mm) to form a single detector channel. A total of 512 channels (16 rows and 32 columns) are contained within one module and are readout by eight units of the 64 channel STIC asic [47] (developed in Univ. of Heidelberg) and the subsequent DAQ chain developed in-house supporting >2.5 MHz for a single module. In this work we model the detector on GATE and assume a uniform response and loss-less acquisition due to the low expected count rate.

When a gamma photon strikes any single channel, the entire energy is deposited during a photoelectric interaction, the probability of which decreases with the photon energy, and is $\sim 2\times$ lesser than Compton cross section at 511 keV. The entire energy of a high energy gamma can also be recovered if multiple interactions occur within the same crystal leading to a full recovery of the photon energy. This is the basis for using larger crystals in other PG detector designs. However, in our approach with the KE-PET, the counts of the partial energy deposited in each detector channel comprise the dominant part of the events. The counts retrieved in this manner are summed up along each vertical column of crystals.

We performed simulations of the KE-PET detection system with a 90 MeV proton beam irradiated on a cylindrical water phantom and recorded the detector information for 1 mm shifts in the phantom position from -20 mm to +20 mm.

For each case, energy thresholds are set on energy spectrum (see figure 4 (a)) of each detection channel to obtain the counts. Counts from the detectors in the same depth are summed up. A 1D depth distribution of these counts is then plotted for each case of phantom-shift as seen in figure 4 (b) and the peak positions are obtained with a Gaussian fitting function. Twice the value of the statistical error representing a 95 % confidence interval is reported as the error bar for the peak position. The peak positions recorded in this manner for various shifts of the phantom are corrected from the central value by subtracting for each position the value of the peak position at the central position where the collimator center coincides with the NIST range for 90 MeV protons at 55.6 mm. The corrected peak positions for various phantom shifts are shown in figure 4 (c). The three cases shown are when the energy threshold set on each detector channel is 250 keV, 511 keV and 1 MeV. For an input of $\mathrm{2\times 10^{9}}$ protons, we can estimate the peak position to within $\pm$0.7 mm with a 95% confidence interval for the region presented with the 1 MeV threshold setting. The deviation of the corrected peak positions noted by the detector from the expected phantom shift position is plotted in figure 4 (d). The range shifts measured by the detector are close to the real shifts in the phantom position in the region of -5 mm to +5 mm. For higher values of shifts on either side, up to 4 mm deviation can be seen. We can account for the larger areas by performing a calibration of the systematic deviations of the peak positions at various proton energies.

The thickness of the collimator, the gap at the narrowest and widest regions of the KE collimator and the distance of the collimator from the beam and the detector are the major factors that affect the detected image for a given gamma energy at a given location along the beam axis. Placing the collimator closer to the phantom causes a higher magnification in the generated image.

In the current work we establish that a PET module can be conveniently adapted to develop a practical range-verification system. In order to further improve the positional resolution of the KE-PET, detector channels in coincidence can be tagged into clusters. The centroid of the cluster can be used to better localize the position.

A beam test was conducted at a 30 MeV proton facility in INER using a HPGe detector (described in section 2.2) to identify the characteristic gamma energy lines and their relative expression in the gamma spectrum. The dominant PG line expected from $\mathrm{{}^{48}Ti*->g.s}$ is the 984 keV gamma [52].

The major lines of the Ti target are 158 keV, 308 keV, 984 keV along with minor lines at 880 keV, 1.3 MeV.

A titanium marker in the experimental test was subsequently placed along with a water phantom (water enclosed in a 0.1 mm thick PET bottle) to observe the Ti gamma emission against a water backround by irradiating the protons at different locations. As seen in the figure 5 (a), the major and minor gamma lines emitted by the $\mathrm{{}^{48}Ti}$ target can be discerned against the water background. When the proton beam is irradiated at positions close to the Ti target, the gamma lines produced by Ti are dominant in the spectrum. As the position of the beam irradiation is moved away from the Ti target, the PG lines emitted by water are seen to be the major contributors while the intensities of the Ti gamma lines reduce to zero. On 5 (b) the values plotted are the integrated counts in the energy spectrum about the region of interest of $\mathrm{\pm 2\sigma}$ from each peak including the background contribution. In this figure a high level of contrast can be seen in the counts at 984 keV. The details of the detector are described inn section 3

Figure 5 (c) describes the energy spectrum shown in a 2D histogram for gamma energy bins along X axis and the different positions (0-5) of irradiation along the y axis. The lines corresponding to $\mathrm{{}^{12}C}$ at 4.438 MeV and $\mathrm{{}^{16}O}$ at 6.129 MeV are clearly visible along with their single and double escape peaks. For position-0 which at which the protons are directly incident on the Ti target, the 984 keV gamma line is prominent, while the gamma lines from water ($\mathrm{{}^{16}O^{*}->g.s:6.129\ MeV}$, $\mathrm{{}^{16}O(p,3p2n)^{12}C^{*}->g.s:4.438\ MeV}$) have a lower intensity. The strong 511 keV line from PAG generation within the water phantom can be noted in figure 5 (b). The main conclusion from the low energy measurement with Ti placed on top of a water phantom is that the major gamma lines resulting from the Ti marker have the energies under 1 MeV and can be easily discerned from a water background.

This test was repeated at a higher energy in Chang Gung Memorial Hospital by probing the water phantom (8 cm $\mathrm{\times}$ 8 cm area and 30 cm depth, ) containing a 3 mm thick Ti target placed between 42 mm and 45 mm from the beam entrance, with various proton energies (70MeV - 90 MeV).

The setup is shown in 6 (left) where the Ti target was placed inside a water phantom positioned on the treatment couch. 5 cm thick lead shields were placed adjacent to the water phantom facing the detector with a 2 cm window centered at the Ti target. The HPGe detector was positioned 46 cm away from the Ti marker shielded by lead bricks 5 cm thick and a circular entrance window of $\mathrm{2\ cm}$ diameter. The measurement was performed with different energies of proton beam for different runs. The beam currents and irradiaiton period were different for each proton energy - currents in the range of 0.27 nA to 0.42 nA, and irradiation period between 123 s and 196 s as shown in table 1.

The proton energy was then converted into a corresponding value of the R80 position which is the distal position with 80% of the peak dose value. In the region of 960 keV to 1000 keV, a linear+Gaussian function is fitted to account for the background to obtain the counts of 984 keV gamma. The presence of the 984 keV gamma line as a function of the R80 value of the incident beam can be seen in figure 6 (right). The R80 position for the incident beams were estimated based on MC simulated depth doses for the test beam setup of the water phantom with titanium marker for various input proton energies. As seen in figure 6 d the counts 984 keV gamma originating from $\mathrm{{}^{48}Ti}$ increase from 30% to 67% of the maximum value when the proton range falls within the extent of the implanted marker.

In order to assess the possibility of applying the fiducial markers for range verification in a clinical setting it is necessary to estimate the expected counts which depend on the production cross-sections. We performed experimental measurements on two elements $\mathrm{{}^{48}Ti}$ since titanium can be good candidate for bio-compatible implants.

In an experimental test at INER, we measured the differential cross sections for the dominant PG lines at a $\mathrm{90^{o}}$ angle from a $\mathrm{{}^{48}Ti}$ target 0.1 mm thick and 50 mm $\times$ 50 mm area. 30 MeV protons were attenuated down to the desired proton energy before hitting the target. The prompt gamma emission was measured by a HPGe detector (described in section 2.2) placed 27.6 cm away from the target. The HPGe detection efficiency was measured against standard sources which matched with the region of interest as seen in figure 7 a. The PG lines of interest were then fitted against the background spectrum measured without target and the counts were normalized against the beam current, irradiation time, the detection efficiency and the target thickness.

In order to calculate the energy dependent production cross-section of gamma we consider that the target area is larger than the beam, which is true for our measurement. We only consider prompt gamma in our calculations. The energy dependent cross section for each prompt gamma line can be estimated using equation 5.1.

where E is the proton energy, $\mathrm{\sigma(E,90^{o})}$ is the differential cross section at 90^o, $\mathrm{N_{det}(E)}$ is the number of gamma detected, $\mathrm{\eta_{det}}$ is the detection efficiency, $\mathrm{\rho}$ is the material density, $\mathrm{N_{A}}$ is the Avogadro constant, $\mathrm{A}$ is the atomic mass, and $\mathrm{dx}$ is the thickness of the target.

The differential cross-sections measured at 90^o can be seen in figure 7 c and d for titanium and steel targets. We estimated a peak values of $\mathrm{28\ mb.sr^{-1}}$ for 984 keV (15 MeV protons), $\mathrm{32\ mb.sr^{-1}}$ at 309 keV (10 MeV protons) and $\mathrm{34\ mb.sr^{-1}}$ at 158 keV (21.9 MeV protons) impinging on a 0.1 mm thick, 50 mm $\times$ 50 mm area target of $\mathrm{{}^{48}Ti}$. In comparison, the 6.129 MeV PG from $\mathrm{{}^{16}O}$ and the 4.44 MeV PG from $\mathrm{{}^{12}C}$ from an oxygen target have differential cross sections values at $\mathrm{90^{o}}$ of around $\mathrm{11\ mb.sr^{-1}}$. The most reliable PG line from iron is the 1238 keV line resulting from an excited state of $\mathrm{{}^{56}Fe}$ and has a peak value of $\mathrm{14\ mb.sr^{-1}}$ as seen in figure 7 d. The low energy line at 158 keV with a peak at $\sim$10 MeV would be more sensitive to noise.

Based on the measured dependence and the expected counts, Ti marker based range verification can be found to be a practical approach. Stainless steel is another interesting candidate for this application.

In order to maximize the signal to noise ratio in a clinical application it would be necessary to employ larger crystals and utilize readout electronics with higher data acquisition rates. Anti-Compton shielding will be effective in suppressing the high energy gamma that leave the primary crystal, and also to reduce the neutron induced gamma which can come from larger angles with respect to the detector-target line of sight. There is sufficient scope to explore other options such as pixellated detectors or even miniaturized detectors that can be mounted closer to the fiducial marker.

To achieve this a single module consisting of two stages of collimators is presented as shown. A two stage collimation achieves better localization than a single stage as illustrated schematically in figure 9 (a). In order to image a patient the collimator needs to be sufficiently far to accommodate the patient size. For the presented work we chose the dimensions $\mathrm{D_{1}=30\ cm}$ and $\mathrm{D_{2}=33\ cm}$. The collimator gap is $\mathrm{w_{1}}$ and the region of interest within the target that is projected towards the detector is represented by $\mathrm{w_{2}}$. In order to restrict $\mathrm{w_{2}}$ to a smaller region, the ratio $\mathrm{\frac{D_{1}}{D_{2}}}$ needs to be minimized along with $\mathrm{w_{1}}$. A larger value of $\mathrm{D_{1}+D_{2}}$ in turn leads to a lower detector efficiency.

In our chosen design, the crystal for each module is a LYSO with $\mathrm{7\ cm\times 4\ cm\times 10\ cm}$ where the longest dimension 10 cm is in the axial direction, 7 cm is the crystal thickness along the radial direction and 4 cm in the theta direction. The choice of these dimensions is a compromise between detection efficiency for a single module, the ability to combine several sectors of detector, and cost considerations.

The effect of collimator width has been studied for different collimator gaps that can achieve a millimeter level collimation. As seen in figure 9 (b) , the best position resolution was achieved for a 1 mm gap collimator at the cost of detection efficiency. The position resolution reported is the FWHM value of the distribution shown in figure 9 (b) which is the response function of the detector when a point source is moved along the axis of interest. We have verified the effect of collimation experimentally using a NaI detector where two stage collimator of 5 mm gap yields a resolution of 9.7 mm FWHM for 511 keV gamma and 10.6 mm FWHM for 1.27 MeV gamma from a $\mathrm{{}^{22}Na}$ source. A single stage collimator in comparison provides a FWHM positional resolution of 19 mm for 511 keV gamma and 24.6 mm for the 1.27 MeV gamma. The incident position uncertainty can be calculated as a function of the collimator gap and the distance between the collimators. Figure 9 (b) shows the spatial resolution of the single module for various collimator gaps.

In order to increase the detection efficiency, multiple modules are added by shifting the original module along the azimuthal plane. This results in a planar sector of detectors focusing on the same point. This is shown in figure 9 (c). In order to identify the depth distribution of the prompt gamma we need to identify several points with a similar level of detection efficiency. Multiple sectors are arranged with equal angle between consecutive sectors about the beam axis ($\mathrm{\theta}$ direction) as seen in 9 (d). A linear offset is then introduced for each sector with respect to the previous sector along the beam axis. Since each sector is designed to observe a specific region of the beam axis, multiple sectors with a linear offset will cover a larger range of positions along the beam.

A detector model with 8 sectors covering 120 degrees with 3 modules per sector was simulated on GATE. The module dimensions were as described in section 6.1 with a collimator gap $\mathrm{w_{1}=2.5\ mm}$. Consecutive sectors are separated by 15 degrees about the beam axis, and linearly spaced along the beam axis by 2.5 mm. All the eight sectors put together cover a region of interest 17.5 mm along the beam axis in a continuous arrangement, or in discrete arrangement if a larger region of interest is desired.

A cubical water phantom (8 cm $\times$ 8 cm $\times$ 15 cm) was irradiated with 40 MeV protons with a range of 14.9 mm. A total of $\mathrm{1\times 10^{10}}$ protons were irradiated on the sample. Each sector observed the gamma originating from a 2.5 mm window along the beam axis. The spectrum recorded by each spectra is further analyzed to identify the PG peaks corresponding to $\mathrm{{}^{16}O}$ and $\mathrm{{}^{12}C}$ to estimate the counts. The counts from each sector contribute to the counts at a given depth along the beam axis, these are plotted in figure 10 (right).

Optimal strategy to position the detectors in order to best recover the depth distribution is currently being investigated. The positions of the module and the detector design used in this simulation were in keeping with realistic clinical requirements. The separation of the front face of the detection system from the beam axis is 30 cm since the detector cannot be positioned arbitrarily close to the patient.

Based on the simulated distribution of the detector counts it can be established that the beam currents and irradiation times utilized in a treatment setting can gather enough statistics to measure the count distributions of the gamma lines. When this approach is used for 3DPG application to image a smaller target sample in a non-clinical environment, the design parameters can be adapted to achieve a much higher efficiency at a better positional resolution, along with a bigger range of positions. A detection system with a $\mathrm{4\pi}$ coverage with 24 sectors can image 24 depth positions simultaneously.