Dr Pichandi Ashokkumar

Dr Nagappanpillai Adarsh

Dr Andrey S Klymchenko
email: andrey.klymchenko@unistra.fr

Ratiometric Nanoparticle Probe Based on FRET-Amplified Phosphorescence for Oxygen Sensing with Minimal Phototoxicity

Keywords: oxygen sensors, dye-loaded polymeric nanoparticles, phosphorescence, singleparticle fluorescence, oxygen gradients in microfluidics

Luminescent oxygen probes enable direct imaging of hypoxic conditions in cells and tissues, which are associated with variety of diseases, including cancer. Here, we

developed nanoparticle probe that addresses key challenges in the filed: it (i) strongly amplifies room temperature phosphorescence of encapsulated oxygen-sensitive dyes; (ii) provides ratiometric response to oxygen; and (iii) solves the fundamental problem of phototoxicity of phosphorescent sensors. The nanoprobe is based on 40-nm polymeric nanoparticles, encapsulating ~2000 blue-emitting cyanine dyes with fluorinated tetraphenylborate counterions, which are as bright as 70 quantum dots (QD525). It functions as a light-harvesting nanoantenna that undergoes efficient FRET to ~20 phosphorescent oxygen-sensitive platinum octaethylporphyrin (PtOEP) acceptor dyes. The obtained nanoprobe emits stable blue fluorescence and oxygen-sensitive red phosphorescence, thus providing ratiometric response to dissolved oxygen. The light-harvesting leads to ~60-fold phosphorescence amplification and makes the single nanoprobe particle as bright as ~1200 PtOEP dyes. This high brightness enables detection of dissolved oxygen at a single-particle level and imaging oxygen in cells at ultra-low nanoprobe concentration with no sign of phototoxicity, in contrast to PtOEP dye. The developed nanoprobe is successfully applied to imaging of microfluidics-generated oxygen gradient in cancer cells. It constitutes a promising tool for bioimaging of hypoxia.

Introduction

Molecular oxygen has a crucial role to supply metabolic energy to cells in aerobic respiration. [1] The deficiency of molecular oxygen, commonly referred as hypoxia, is directly related to cancer growth, neurological disorders, retinal diseases, etc, and the elevated levels of oxygen (hyperoxia) can lead to generation of reactive oxygen species and free-radicals. [2] Among existing oxygen sensing methods, such as chemical [3] and electrochemical, [4] optical methods based on luminescent probes have attracted a growing attention in recent years, since they offer reversible responses with no electrical interferences and in a relatively noninvasive manner [5] and allow fabricating devices based on films and optical fibers. [6] In this case, phosphorescence is a key mechanism to achieve oxygen sensitivity, because the triplet excited state of dyes is efficiently quenched by oxygen. [7] Particularly popular are palladium(II)-and platinum(II)-porphyrins, as well as complexes of iridium(III) and ruthenium(II). [5a, 8] However, their use as oxygen sensors meet a number of challenges, in particular quantification of the signal and phototoxicity. Although a number of phosphorescence-based oxygen probes have been developed, [5,9] their intensity-based signal is difficult to quantify, so that sophisticated fluorescence lifetime detection scheme is needed. Ratiometric optical oxygen sensors are an attractive alternative, because intensity ratio, similarly to lifetime, provides robust absolute measure of the analyte and requires rather simple detection setup. [5b, 10] For this purpose, phosphorescent and fluorescent dyes are combined together to generate Förster Resonance Energy Transfer (FRET), where phosphorescent dyes (FRET acceptors) emit in the oxygendependent manner, and fluorescent dyes (donors) provide stable oxygen-independent reference signal. [5b, 10] Molecular, FRET-based probes were reported, [11] however their design is challenging because of complex multistep synthesis, poor solubility in water and poor luminescent brightness due to donor-acceptor quenching. An attractive approach is to combine these phosphorescent dyes with fluorescent nanomaterials. The latter include conjugated polymer nanoparticles (NPs), [12] quantum dots (QDs), [13] carbon dots, [14] dyedoped silica NPs, [15] aggregation-induced emission NPs [16] and dye-loaded polymeric NPs. [17] So far, a variety of oxygen-sensitive probes combining fluorescent NPs and phosphorescent acceptor dye, has been reported mainly based on conjugated polymer NPs, [8c, 18] and, less commonly, dye-doped polymeric NPs [19] , core-shell polymeric NPs [20] and supramolecular NPs. [21] However, in these systems oxygen sensing by phosphorescent dyes generates highly reactive singlet oxygen, [22] which makes this technique phototoxic. Therefore, many of these NPs were also proposed for photodynamic therapy applications. [8c, 18d] To the best of our knowledge, design of bright nanoprobes for oxygen with minimized phototoxic effects of phosphorescent dyes remains an unexplored field.

New possibilities offer ultrabright fluorescent dye-loaded polymeric NPs, [17a] which already found different applications in single-particle tracking, [23] super-resolution imaging, [17b] single-molecule detection, [24] nucleic acid detection, [25] as well as multicolor cellular and in vivo imaging. [26] In these NPs, the problem of aggregation-caused quenching (ACQ) of encapsulated dyes was resolved by us using bulky fluorinated counterions that operate as fluorophore insulators. [17b, 27] The obtained dye-loaded polymeric NPs were up to 100-fold brighter than QDs of similar color and size. [25a, 28] The other key feature is their exceptional FRET efficiency, where NPs loaded with ~10000 dyes, so-called light-harvesting nanoantennas, can transfer energy to a single acceptor, thus amplifying its emission >1000fold. [24] Functionalization of these nanoantenna particles with DNA yielded nanoprobes for amplified detection of nucleic acids, which were >2000-fold brighter than reported FRETbased molecular probe, [25a] and sensitivity down to single molecules. [25b] Therefore, we hypothesized that the combination of these dye-loaded NPs with an oxygen-sensitive phosphorescent dye in form of a donor-acceptor FRET system would provide a facile route to oxygen sensors with drastically improved brightness. Moreover, owing to their high FRET donor capability, our NPs would require minimal number of phosphorescent dyes (acceptors) to obtain efficient FRET, which could decrease eventual phototoxic effects.

Herein, based on light-harvesting dye-loaded fluorescent nanoparticles that amplify phosphorescence of encapsulated oxygen-sensitive dye, we developed an oxygen sensor featuring high brightness, ratiometric response and low phototoxicity. We prepared 40 nm PMMA-MA NPs encapsulating an energy donor based on blue cyanine dye with bulky hydrophobic counterion (BlueCy-TPB) and oxygen-sensitive phosphorescent acceptor platinum octaethylporphyrin (PtOEP) (Figure 1). Efficient FRET from ca. 2000 donors to ca. 20 acceptors inside the particles was achieved, leading to ~60-fold phosphorescence amplification. The obtained nanoprobe emitted stable fluorescence as well as oxygensensitive red shifted phosphorescence, equivalent in brightness to ~1200 PtOEP molecules, providing ratiometric response to dissolved oxygen. This high brightness enabled oxygen sensing at the single-particle level. The oxygen nanoprobe internalized inside cells showing no sign of phototoxicity, in contrast to PtOEP dye alone. Finally, in vitro mapping of dissolved oxygen gradients in HeLa cell culture was demonstrated by a specially designed microfluidic chamber.

Results and Discussion

Design of the oxygen nanoprobe

As a polymer matrix for preparation of NPs, we selected PMMA-MA and PLGA, which were found very efficient for encapsulating different cationic organic dyes. [17b, 17c, 26, 28] PtOEP was chosen as a phosphorescent oxygen sensitive unit, which has already been used in oxygen sensors. [5b, 18b, 29] However, in our nanoprobe, we plan to encapsulate PtOEP as FRET acceptor at very low concentration in the polymer matrix together with highly concentrated FRET donors, which will serve as a light-harvesting system for amplifying phosphorescence of PtOEP and generating ratiometric response to oxygen (Figure 1). Therefore, in this study the FRET donor should be carefully selected based on the following criteria: (1) ensure efficient FRET which requires good spectral overlap of the donor emission and the PtOEP absorption, centered around 530 nm; (2) its emission should be well separated from that of PtOEP to provide a ratiometric output without any crosstalk and (3), the dye should be cationic, so that we could apply the counterion approach to prevent ACQ [17b, 26-27] and ensure efficient lightharvesting process. [24][25] Therefore, we have chosen thiacyanine dye family, which operates in the blue spectral region. [30] To provide proper encapsulation, a hydrophobic chain of 18 carbons was incorporated to the fluorophore (BlueCy). Moreover, the obtained dye BlueCy was paired with bulky hydrophobic couterion tetrakis(pentafluorophenyl)borate (F5-TPB), which has shown to be efficient against ACQ in many cationic dyes and to favor dye encapsulation into polymeric NPs. [17b, 17e, 26-27]

Donor NPs

The BlueCy dye was synthesized in three steps by modifying the reported procedure (Scheme S1). [30a] BlueCy derivative was obtained in a good yield by the condensation of quaternized 2-methyl-3-octadecylbenzo [d]thiazol-3-ium salt with quaternized 3-methyl-2-(methylthio)benzo [d]thiazol-3-ium salt in the presence of trimethylamine in absolute ethanol.

The counterion, iodide, was then exchanged with hydrophobic fluorinated anion, tetrakis(pentafluorophenyl) borate (F5-TPB) to obtain a target dye salt BlueCy-TPB. The final product and intermediates have been characterized by standard analytical procedures

(Figure S1-S5).
BlueCy-TPB showed absorption and emission bands centered around 425 and 475 nm, respectively, which is characteristic for the blue cyanine dyes with thiazole moities. [30c] The dye exhibited negligible fluorescence with a quantum yield (QY) of 0.1 -0.3 % in organic solvents such as dioxane, methanol, etc (Table S1). Interestingly, a considerable enhancement in the fluorescence was observed in aqueous medium with a quantum yield of 6.1 %, probably due to the aggregation-induced emission (AIE). [16a, 16c-f, 31] The aggregation in water was evidenced by the formation of a new absorption band at the shorter wavelength region (Figure 2A). To prove that the observed enhancement in the fluorescence intensity in aqueous medium arise from the restriction of molecular rotation in aggregates, [16a, 31b] we measured fluorescence properties in highly viscous medium, glycerol. As expected, the dye showed marked enhancement in the quantum yield up to 21 % (Table S1), which confirms the restriction of rotation around the methine bond between two benzothiazoles. The fluorescence enhancement is known for complexes of cyanine dyes with DNA, [32] as well as for other cationic dyes associated with bulky counterions. [27c, 33] In our case, this property is important for enhancing emission of the dye once it is encapsulated into the rigid polymer matrix of NPs. Next, we prepared BlueCy dye-loaded polymeric NPs by using our recently developed protocol of charge-controlled nanoprecipitation. [17a-c, 23] For this purpose, a solution of the polymer (PLGA or PMMA-MA) and BlueCy-TPB in dioxane/acetonitrile mixture was rapidly added into aqueous media (20 mM phosphate buffer, pH 7.4). The BlueCy-TPB is expected to co-precipitate together with the polymers due to its high hydrophobicity brought by the long C18 alkyl chain and the bulky hydrophobic counterion, leading encapsulation inside the particles. [17a-c, 26-27, 28] Absorption spectra revealed that nanoprecipitation of the dye with PLGA or PMMA-MA resulted in the narrow absorption spectra, similar to that in dioxane, whereas in control conditions without the polymer, a clear blue-shifted shoulder appeared probably due to aggregation of the dye in the buffer (Figure 2A). These results provide the first indication that the dye was blended with the polymer after the nanoprecipitation. In case of PLGA and PMMA-MA, bearing a negatively charged carboxylate, NPs of 33±2 and 45±2 nm diameter were formed, respectively, according to dynamic light scattering (DLS) (Figure 2B). The polymeric NPs maintained their monodispersity and small size upon increasing the BlueCy-TPB dye loading from 0.6 to 12 wt% with respect to the polymer (Figure 2B, Table S2). In case of PMMA-MA NPs with 12 wt% of BlueCy-TPB, the transmission electron microscopy (TEM) suggested the formation of uniform spherical particles with an average size of 40 nm (Figures 2C andS6), in line with the DLS data. Based on the diameter of NPs (40 nm) we can calculate particle volume (33500 nm 3 ) and, then, assuming the BlueCy-TPB dye loading at 12 wt% (100 mM dye concentration) and polymer density of 1 g/ml, we can estimate that ~2000 donor dyes are encapsulated per NP. By contrast, DLS data revealed that BlueCy with small inorganic counterions such as iodide (BlueCy-I) showed drastic increase in the particle size with dye loading (Table S2). These data are in agreement with our earlier reports, showing that with small inorganic anions, the cationic dyes are adsorbed a the NPs surface leading to particle aggregation. [17b, 27] The QY values of the NPs were found to be as high as 35% for PMMA-MA NPs at 0.6% dye loading. However, the increase in the dye loading produced a gradual decrease in QY of NPs, which can be due to ACQ at high dye loading (Figure 2D). In line with this observation, the mean lifetime of the BlueCy-TPB in PMMA-MA NPs also gradually decreased from 2.31 ± 0.15 ns to 1.10 ± 0.09 ns with the increase in the dye loading from 0.6 to 12 wt% (Figure S7). At low BlueCy-TPB loading, the fluorescence decay was biexponential, dominated by the long-lived component (Table S3). At higher dye loading, new short-lived decay component appeared (0.16-0.18 ns) and the amplitudes of the short-and medium-lived components gradually increased. In addition, the decay time of long-lived component decreased from 2.53 ns to 1.63 ns with increase in dye loading from 0.6 to 12 wt%.

The observed multi-exponential decay at high dye loading, in line with earlier works on rhodamine-loaded NPs, [17b, 24] indicates a complex quenching process, which probably includes both dark states (corresponding to the short-lived component) and those quenched by excitation energy transfer (medium-lived component, 0.84 ns at 12 wt% loading).

Nevertheless, the QY values remained relatively high in PMMA-MA NPs, namely 17% even at 12 wt% dye loading BlueCy-TPB, whereas the salt with small anion, BlueCy-I, in PMMA-MA NPs showed systematically lower QY values (Table S2). This result highlights the importance of the bulky hydrophobic counterion F5-TPB to prevent ACQ. [17a, 17b, 27a, 27b] Moreover, BlueCy-TPB-loaded PMMA-MA NPs displayed significantly higher QY values compared to PLGA NPs (Figure 2D), which according to our earlier studies indicates lower level of dye clustering in PMMA-MA NPs. [28] Therefore, in the next steps we focused our research on BlueCy-TPB-loaded PMMA-MA NPs.

Then, the single-particle fluorescence of the PMMA-MA NPs immobilized on the glass surface was characterized, using wide-field microscopy. BlueCy-TPB NPs appeared as fluorescent spots and their intensity increased with the dye loading (Figure 3). Remarkably, single-particle brightness of PMMA-MA with 12 wt% BlueCy-TPB was found to be 70-fold higher than that of QDs of similar emission wavelength (QD525). This result was supported by estimated theoretical brightness, [17a] N(number of dyes) x ε(molar absorptivity) x QY (quantum yield): 2000 (N) × 6.7×10 4 M -1 cm -1 (ε) × 0.173 (QY) = 2.30×10 7 M -1 cm -1 for BlueCy-TPB NPs (Table S4) and only 1 (N) × 3.70×10 5 M -1 cm -1 (ε) × 0.69 (QY) = 2.55×10 5 M -1 cm -1 for QD525 at 395 nm excitation (based on data from the provider, ThermoFisher Scientific). However, our NPs are ~2-fold larger than QD525 (~40 nm vs 15-20 nm), which should be taken into account in this comparison. On the other hand, the size of fluorescent core in our NPs can be tuned to much larger extent within 9-100 nm, [17c, 23] which makes them flexible for different applications.

Preparation and validation of oxygen nanoprobe

Further, we prepared FRET NPs by introducing platinum octaethylporphyrin (PtOEP), an oxygen sensitive unit (Figure 1), acting as an energy acceptor for BlueCy-TPB. DLS and TEM data confirmed formation of small NPs around 40 nm size (Figure 4A, Figure S6). In the obtained NPs, the absorption spectrum of the PtOEP with a maximum at ∼535 nm (Qband) overlapped efficiently with the emission profile of the donor, BlueCy-TPB (Figure S8), suggesting that this is a good FRET pair. Indeed, increase in the PtOEP loading in BlueCy-TPB NPs (increase in the acceptor/donor ratio) decreased gradually the donor emission at 485 nm, accompanied by an increase in the PtOEP emission band at 650 nm, which is a clear indication of FRET from of BlueCy-TPB to PtOEP (Figure 4B). Fluorescence lifetime measurement also supported the occurrence of FRET process in the BlueCy-TPB/PtOEP NPs (Table S3): Average lifetime of BlueCy-TPB decreased from 1.10±0.09 ns to 0.87±0.07 ns in the presence of PtOEP, in line with the intensity-based steady-state measurements. The presence of acceptor decreased decay times only for medium-and long-lived components (to 0.63 and 1.42 ns, respectively), which corroborates with the FRET processes occurring on a similar time scale. Remarkably, an increase in the donor loading from 0.6% to 12% for a constant acceptor (PtOEP) loading of 0.071 wt% (1 mM) also resulted in a growth of FRET efficiency from 4% to 18% (Figure 4C). These observations indicate the cooperative effect of the donor dyes, showing the light-harvesting phenomenon. According to our earlier studies, at higher dye loading, the donor dyes start to communicate, so that the excitation energy undergoes fast migration up to the energy acceptor. [24] By analyzing excitation spectra of the FRET NPs ( 12wt% BlueCy-TPB) at the emission wavelength of the acceptor, we found that the antenna effect (AE) was 60±5. This indicates that with the light-harvesting process the acceptor emission can be amplified up to 60-fold. The AE value is directly linked to number of donors (nD) and acceptors (nA), their corresponding extinction coefficients (D and A, respectively) and FRET efficiency (E): AE = nD×D×E/(nA×A×100). [34] Using FRET efficiency based on donor intensity changes, the estimated value of AE = 2000×67000×18/(20×45000×100) = 27 (method 1, Figure 4D). It is significantly lower than the experimental value, indicating that observed FRET efficiency is underestimated and should be ~40% for AE = 60. The donor intensity does not take into account the dark states of self-quenched dyes that contribute to FRET without emitting in the donor channel. [35] Then, we made a theoretical calculation of FRET efficiency, assuming a multi-chromophoric system with randomly distributed noncommunicating donors. [START_REF]Principles of Fluorescence Spectroscopy[END_REF] Based on overlap integral between emission band of donor NPs and PtOEP absorption band, the calculated Forster radius was found to be 3.6 nm. For 2000 donors and 20 acceptors confined in 40-nm particle, the theoretical FRET efficiency was 16%, giving even lower estimated AE = 24 (method 2, Figure 4D). The much higher experimental AE value is probably linked to donor-donor excitation energy transfer, which ensures energy migration within multiple donors up to reaching the proximal acceptor. [24, 25b] To examine the response of our FRET NPs, consisting A:D loading ratio of 1:100, to molecular oxygen, we exposed their suspensions in buffer to the flow of oxygen (oxygenated) and nitrogen (deoxygenated) gases. The observed emission at 650 nm for the FRET NPs in air-saturated solution got quenched in the oxygenated conditions, whereas it was significantly enhanced after the nitrogen purging (Figure 5A). Oxygenation/deoxygenation conditions produced strong effect on the acceptor emission, with almost negligible influence on the donor one. This result indicates that the observed PtOEP emission corresponds to phosphorescence, which is in line with the observed long acceptor emission lifetimes on the time scale of microseconds (Figure 5D) and the literature data for PtOEP. [START_REF] Izakura | [END_REF] Observation of phosphoresce at room temperature is remarkable phenomenon that attracted strong attention recently. [38] In our NPs, it was observed for two reasons. First, oxygen diffusion is largely slowed down in polymers (diffusion coefficient is 2.7-5.5×10 -9 cm 2 s -1 in PMMA vs 2.5×10 -5 cm 2 s -1 in water), [11a, 39] which decreases collisional quenching of PtOEP triplet state, thus favoring its phosphorescence. Second reason is the light-harvesting phenomenon that amplifies emission of PtOEP. Importantly, oxygenation produced 90% change in the ratio between donor fluorescence and acceptor phosphorescence, showing high sensitivity of the oxygen nanoprobes.

To further prove that the enhanced phosphorescence from PtOEP arise due to FRET from the BlueCy-TPB donor, we have carried out a control experiment with NPs containing 0.071 wt% (1 mM) of PtOEP alone. In comparison to FRET NPs, PtOEP-loaded NPs showed negligible phosphorescence signal when excited at 405 nm or 535 nm, corresponding to direct excitation of the acceptor (Figure S9). The latter confirms that the observed amplified phosphorescence signal in FRET NPs is due to the light-harvesting phenomenon, where multiple donors pump the excitation energy to few acceptors. Even in the deoxygenated condition, control PtOEP-loaded NPs showed ~50-fold weaker phosphorescence when compared to the FRET NPs (Figure S9), in line with the observed high value of antenna effect. Finally, the reversibility of the system has been checked by the alternate purging of oxygen and nitrogen that showed stable and reversible ratiometric response of the FRET NPs (Figure 5B). The quantitative detection of molecular oxygen was then carried out by monitoring the ratiometric emission response of the BlueCy-TPB/PtOEP nanoprobe with regard to the successive decrease in oxygen concentration in the solution, using sodium sulfite (Na2SO3), a well-known oxygen scavenger. [40] By decreasing the oxygen concentration of the solution from 7.5 mg/mL to 0.03 mg/mL, quantified by an optical probe for dissolved oxygen, we observed a gradual ratio change through enhancement in the acceptor phosphorescence, without altering the donor fluorescence (Figure 5C). This decrease in the oxygen concentration also produced a gradual increase in the phosphorescence lifetime of the acceptor from 60 µs to 138 µs (Figure 5D, Table S5). The ratiometric response of BlueCy-TPB/PtOEP NPs to oxygen in the presence of BSA (48 µM) and FBS (10%), components of biological media, was nearly the same as in phosphate buffer (Figure S10). The observed invariant FRET and the ratiometric response to oxygen show that both donor and acceptor components are well encapsulated inside PMMA-MA NPs, without their detectable leakage, which makes this nanoprobe compatible with biological media.

Then, to evaluate ratiometric response of the nanoprobe to oxygen at the single-particle level, the immobilized BlueCy-TPB/PtOEP NPs (12 wt%, PMMA-MA) at the glass surface were imaged with a microscope by collecting signals simultaneously at the donor (490-560 nm) and acceptor channels (640-670 nm) after exciting the donor (at 395 nm). The control NPs (BlueCy-TPB) without acceptor appeared as very bright spots in the donor channel with poor emission in the acceptor channel. Interestingly, for the BlueCy-TPB/PtOEP NPs, we were able to detect the single-particle phosphorescence in the acceptor channel even under airsaturated conditions (Figure 6). The decrease in the intensity at the donor channel compared to the control sample (BlueCy-TPB alone), confirmed FRET from BlueCy-TPB to PtOEP.

In the deoxygenated conditions (with sodium sulfite), the emission in the acceptor channel drastically increased and became higher than the donor channel, so that the pseudo-color in the merged images changed from green to yellow. The distinct changes in the two-color merge and ratiometric images (Figure 6, Figure S11) suggest the ability of our nanoprobe operate as the oxygen sensor at the single-particle level. This become possible thanks to the light-harvesting process providing ~60-fold phosphorescence amplification of 20 encapsulated PtOEP dye in the NP, leading single-particle phosphoresce equivalent to ~1200 PtOEP dyes.

Validation in live cells and phototoxicity

After incubation with HeLa cells for 3 h at 37 °C, nanoprobe showed dotted emission in both donor and acceptor channels located inside the cells. This dotted emission is in agreement with the previous studies on polymeric and other NPs, [13b-d, 17b, 26] suggesting localization of the nanoprobe in the endosomes and lysosomes. Indeed, it is well established that NPs below 100 nm enter cells by endocytosis. [41] The presence of signal in the acceptor channel, colocalized with the donor channel (Figure 7A), as in our single-particle studies (Figure 6), suggested that the nanoprobe remained intact inside the cells, in line with the observed stability FRET nanoprobe in BSA and serum (Figure S10).

High brightness of the nanoprobe with amplified phosphorescence of PtOEP per particle allowed us to observe detectable signal in the acceptor channel at very low concentration of PtOEP (1 nM) in cells. This low concentration should significantly decrease phototoxicity of our system compared to PtOEP alone. To verify this, we incubated HeLa cells with our nanoprobe or the PtOEP dye and irradiated under same excitation power at their respective excitation wavelengths (395 nm for NPs and 550 nm for the PtOEP). Remarkably, to obtain the similar signal-to-background ratio at the phosphorescence (acceptor) channel, 500-fold higher concentration of PtOEP alone was needed (500 nM) compared to that used with the nanoprobe. This large concentration difference is in line ~1200-fold higher phosphorescence brightness of the nanoprobe compared to PtOEP dye. In these conditions, 5 min irradiation resulted in dramatic morphological alternations in cells incubated with PtOEP dye (Figure 7B), indicating its high cytotoxicity. In sharp contrast, no signs of cytotoxicity were detected in cells incubated with nanoprobe (Figure 7C). The latter result can be explained by 500-fold lower effective concentration of PtOEP photosensitizer used with the nanoprobe in cells as well as the shielding effect of the polymer particle that physically separates the encapsulated photosensitizer from the cellular environment.

Imaging oxygen gradients in cancer cells

Then, in order to model hypoxia in cells, we designed a setup with a stable gradient of oxygen based on microfluidic plate (µ-ibidi) compatible with cell culture and fluorescence microscopy. From one outlet of the 50-mm long channel, the oxygen scavenger was added and the outlet was sealed, creating an oxygen restricted area, while the other end was exposed to air, providing oxygen abundant area (Figure 8A). Initially, we have optimized the addition of the oxygen scavenger into this microfluidic setup by using sodium dithionite reducing agent and Nile Red, presenting a chromogenic RedOx behavior (Figure S12). [42] Then, using the optimized protocol we applied oxygen gradient in the microfluidic chamber with HeLa cells seeded and incubated for 3h with our nanoprobes. Initially, using the two color detection mode, we imaged both ends of the chamber. Remarkably, a strong fluorescence signal from the FRET donor channel and a low signal from the acceptor channel were observed in the oxygen abundant area, whereas in the oxygen restricted end, enhanced phosphorescence at the acceptor channel was observed (Figure 8B), corresponding to significantly stronger acceptor/donor ratio in the hypoxic region (Figure 8C). This result shows that our nanoprobe exhibits ratiometric response to dissolved oxygen directly inside the cells. To further map the gradient of oxygen in HeLa cells within the microfluidic channel, we performed multiple images with 1 mm interval along the channel from the oxygen abundant to oxygen-restricted end. Within the defined length, we observed the gradual enhancement in the phosphorescence at the acceptor channel, accompanied by some decrease in the donor channel (Figure 8D). The gradient between normoxic and hypoxic regions was clearly visible in the merged images as a gradual change in emission color from green to yellow and then orange-red (Figure 8D). Finally, a large scale "panorama" two-color image of the microfluidic channel revealed a profile of this oxygen gradient (Figure 8E).

Conclusion

Existing optical molecular probes for dissolved oxygen suffer from a number of fundamental limitations: (i) limited brightness of used phosphorescent dyes; (ii) need for complex detection schemes based on fluorescence lifetime and (iii) intrinsic photo-toxicity of phosphorescent dyes because of singlet-oxygen generation. Here, we introduce organic polymeric nanomaterials that undergo efficient FRET from large ensemble of encapsulated energy donor dyes (light-harvesting nanoantenna) to oxygen-sensitive phosphorescent unit and function as ratiometric nanoprobes for dissolved oxygen, which overcome the mentioned limitations. The light-harvesting nanoantenna particle is composed of a specially designed blue cyanine with bulky fluorinated counterions encapsulated inside poly(methyl methacrylate-co-methacrylic acid) (PMMA-MA) NPs. The resulted 40 nm dye-loaded NPs encapsulating ca. 2000 dyes with good fluorescence quantum yield (17%) showed 70-fold higher brightness than QD525. Then, encapsulation into this light-harvesting nanoantenna of an oxygen-sensitive acceptor (PtOEP) at low concentration (1:100 acceptor : donor ratio) result in efficient FRET, so that the NPs emits both fluorescence of the donor and phosphorescence of the acceptor. The relative intensity of the phosphorescence band increases with decrease in oxygen concentration, which enables quantitative ratiometric measurements of oxygen in solution. Light-harvesting from bright fluorescent nanoparticle leads to ~60-fold amplification of PtOEP phosphorescence at room temperature and makes single particles as bright as 1200 PtOEP. Our approach with light-harvesting dye-loaded polymeric NPs is different from earlier studies on conjugated polymer NPs that also exploited FRET to PtOEP, [18b] because we aimed to achieve an efficient FRET with minimal amount of encapsulated acceptor. Indeed, in the previous representative work, [18b] bright phosphorescence of NPs was achieved by encapsulating ~5500 PtOEP acceptors per particle, whereas in the present work, phosphorescence equivalent of >1000 dyes per particle was achieved with only 20 PtOEP acceptors. This amplified phosphorescence of the nanoprobe enables detection of dissolved oxygen at the single particle level and ratiometric imaging oxygen in cells at ultra-low concentration of encapsulated PtOEP (1 nM). As a result, the obtained NPs do not show any sign of phototoxicity even after 5 min irradiation of the nanoprobes. By contrast, free PtOEP dye, which required much higher concentration (500 nM) to achieve comparable phosphorescence signal from the cells showed strong phototoxicity. The developed nanoprobe was successfully applied to ratiometric imaging in a culture of cancer cells of stable oxygen gradient generated by a microfluidic setup. The high brightness, the ratiometric response and low phototoxicity make the developed nanomaterial a promising tool for imaging hypoxia, which is ubiquitously present in numerous pathologies.

Figure 1 .

 1 Figure 1. Concept of light-harvesting nanoparticle encapsulating BlueCy-TPB/PtOEP for ratiometric detection of oxygen. A) Molecular structures of the cyanine donor dye (BlueCy) with its counterion F5-TPB and of the porphyrin acceptor dye (PtOEP). B) Schematic representation FRET-based ratiometric oxygen nanoprobe.

Figure 2 .

 2 Figure 2. Characterization of BlueCy-TPB dye and its polymeric NPs. A) Absorption and emission spectra of BlueCy-TPB dye in dioxane, phosphate buffer (pH 7.4) and in NPs of different loading. B) Plot showing the size by DLS for different loading of BlueCy-TPB. C) Representative TEM images of the PMMA-MA NPs with and without BlueCy-TPB (12 wt% dye loading, counter stained with uranyl acetate). D) Dependence of fluorescence quantum yield on the dye loading.

Figure 3 .

 3 Figure 3. Single-particle evaluation of BlueCy-TPB NPs under wide-field fluorescence microscopy. A) Fluorescence images of NPs with different dye loading and QD525 immobilized on a glass surface. In the case of QDs, the intensity was multiplied by 10-fold to make the signal visible. B) Corresponding 3D representation graphs. All imaging conditions were identical for dye-loaded NPs and QDs. The excitation wavelength is 395 nm. Scale bar is 10 µM.

Figure 4 .

 4 Figure 4. Characterization of FRET NPs. A) TEM image of BlueCy-TPB/PtOEP NP. B) Emission spectra of BlueCy-TPB/PtOEP NPs loaded with different amounts of the acceptor dye (PtOEP) and constant (12 wt%, 100 mM) BlueCy-TPB donor loading. C) Plot of FRET efficiency of NPs with varied donor but constant acceptor (0.071 wt%, 1 mM) loading. (D) Antenna effect obtained for optimized FRET NPs (12 wt% Donor, Donor : Acceptor ratio 100:1) obtained experimentally (from excitation spectra), based on calculation based on experimental FRET efficiency (Method 1) and based on calculation based on theoretical FRET efficiency (Method 2).

Figure 5 .

 5 Figure 5. Oxygen sensing experiments using BlueCy-TPB/PtOEP NPs in phosphate buffer solution at pH 7.4. A) Ratiometric response in emission spectra of BlueCy-TPB/PtOEP NPs towards the change in oxygen concentration in the solution. Oxygen concentration was varied by purging oxygen and nitrogen gases. B) Ratiometric plot of emission intensities between acceptor and donor to the number of alternative purging of oxygen and nitrogen, to confirm the stability and reversibility of the BlueCy-TPB/PtOEP NPs as the oxygen probe. Changes in C) emission spectra and D) phosphorescence lifetime of BlueCy-TPB/PtOEP NPs by the successive variation of oxygen concentration in the solution.

Figure 6 .

 6 Figure 6. Single-particle evaluation of BlueCy-TPB/PtOEP NPs under wide-field fluorescence microscopy. The microscopic images and the corresponding 3D representation of the donor and acceptor channel for BlueCy-TPB (Donor NPs) and BlueCy-TPB/PtOEP NPs (FRET NPs) after the excitation at 395 nm, in the air saturated and deoxygenated solutions. Scale bar; 10 µM.

Figure 7 .

 7 Figure 7. Internalization of nanoprobes and phototoxicity test. A) Fluorescence microscopy images of HeLa cells after incubation for 3 h with BlueCy-TPB/PtOEP nanoprobe (1 nM of PtOEP) at the donor (<640 nm) and acceptor (>640 nm) channels and their composite with bright-field images. B,C) Comparison of phototoxicity under the microscope for PtOEP dye alone (B) vs BlueCy-TPB/PtOEP NPs (C). B) Microscopic images (acceptor channel) and bright field images of HeLa cells after incubation for 3 h with PtOEP NPs (500 nM) and irradiation at 550 nm for 5 min. C) Corresponding images for BlueCy-TPB/PtOEP NPs (1 nM of PtOEP), after 5 min irradiation at 395 nm. The irradiation power density was kept the same (10 W cm -2 ) for both excitation wavelengths; the concentration of PtOEP dye alone was increased in order to reach signal intensity values similar to that for the nanoprobe. Scale bars: 10 µM.

Figure 8 .

 8 Figure 8. In vitro imaging of oxygen gradient in a microfluidic plate using BlueCy-TPB/PtOEP NPs with wide-field fluorescence microscopy. A) Schematic representation of stable oxygen gradient generation in the microfluidic slide. B) Fluorescence microscopic

Acknowledgements

This work was supported by Marie Curie post-doctoral research grant (MSCA-H2020-IF, NanoOxySens 705826) and European Research Council ERC Consolidator grant BrightSens 648528. P.A. acknowledges Senior Postdoctoral Fellowship grant sponsored under RUSA 2.0. The authors thank A. Russer and C. Crucifix for help with electron microscopy, K. Trofymchuk for help with theoretical FRET calculations, L. Richert for help with TCSPC measurements, A. Reisch for fruitful discussions and J. Valanciunaite for technical support.

Experimental Section

The Experimental Section is available at the Supporting Information.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Conflict of interest

The authors declare no conflict of interest.

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The table of contents


A Etxebeste
email: ane.etxebeste@creatis.insa-lyon.fr

D Dauvergne

M Fontana

J M Létang

G Llosá

E Munoz

J F Oliver

É Testa

D Sarrut

CCMod: a GATE module for Compton Camera imaging simulation

Keywords: Monte Carlo, simulation, gamma imaging, Compton camera

Compton cameras are gamma-ray imaging systems which have been proposed for a wide variety of applications such as medical imaging, nuclear decommissioning or homeland security. In the design and optimization of such a system Monte Carlo simulations play an essential role. In this work, we propose a generic module to perform Monte Carlo simulations and analyses of Compton Camera imaging which is included in the open-source GATE/Geant4 platform. Several digitization stages have been implemented within the module to mimic the performance of the most commonly employed detectors (e.g. monolithic blocks, pixelated scintillator crystals, strip detectors...). Time coincidence sorter and sequence coincidence reconstruction are also available in order to aim at providing modules to facilitate the comparison and reproduction of the data taken with different prototypes. All processing steps may be performed during the simulation (on-the-fly mode) or as a post-process of the output files (offline mode). The predictions of the module have been compared with experimental data in terms of energy spectra, angular resolution, efficiency and back-projection image reconstruction. Consistent results within a 3-sigma interval were obtained for the energy spectra except for low energies where small differences arise. The angular resolution measure for incident photons of 1275 keV was also in good agreement between both data sets with a value close to 13 • . Moreover, with the aim of demonstrating the versatility of such a tool the performance of two different Compton camera designs was evaluated and compared.

Introduction

Compton Cameras (CCs) are actively collimated gamma-ray imaging devices which have been originally designed for astronomy applications. Their first application in medical imaging was proposed in [START_REF] Todd | A proposed γ camera[END_REF]). Thenceforth, there has been an interest in their application in the field of nuclear medical imaging [START_REF] Han | Statistical performance evaluation and comparison of a Compton medical imaging system and a collimated Anger camera for higher energy photon imaging[END_REF][START_REF] Seo | Optimal geometrical configuration of a double-scattering Compton camera for maximum imaging resolution and sensitivity[END_REF][START_REF] Harkness | Optimisation of a dual head semiconductor Compton camera using Geant4[END_REF][START_REF] Karimian | Design of a new Compton camera by Monte Carlo method and assessment its important parameters affecting image quality[END_REF][START_REF] Alnaaimi | Performance evaluation of a pixellated Ge Compton camera[END_REF], Odaka et al. 2012[START_REF] Calderón | Evaluation of Compton gamma camera prototype based on pixelated CdTe detectors[END_REF][START_REF] Fontana | Compton camera study for high efficiency SPECT and benchmark with Anger system[END_REF]). In addition, there is also a growing interest in their use to image the prompt gamma emission produced during proton therapy for in-vivo range assessment [START_REF] Richard | Design guidelines for a double scattering Compton camera for prompt-gamma imaging during ion beam therapy: A Monte Carlo simulation study[END_REF][START_REF] Peterson | Optimizing a three-stage Compton camera for measuring prompt gamma rays emitted during proton radiotherapy[END_REF][START_REF] Kormoll | A Compton imager for in-vivo dosimetry of proton beams-a design study[END_REF], Polf et al. 2015[START_REF] Hilaire | Proton therapy monitoring by Compton imaging: influence of the large energy spectrum of the prompt-γ radiation[END_REF][START_REF] Solevi | Performance of MACACO Compton telescope for ionbeam therapy monitoring: first test with proton beams[END_REF][START_REF] Rohling | Requirements for a Compton camera for in vivo range verification of proton therapy[END_REF].

In nuclear medicine, Single Photon Emission Computed Tomography (SPECT) Anger gamma-camera is nowadays one of the most widespread imaging techniques for diagnosis. The main drawback of this technique is that the sensitivity is inversely proportional to the spatial resolution due to the use of mechanical collimation. In order to overcome this limitation, the use of active collimation systems such as CCs has been proposed. They usually consist of several position and energy sensitive gamma ray detectors arranged in scatterer and absorber planes working in time coincidence. Using the kinematics of Compton scattering, the origin of the gamma-ray can be constrained to a cone surface. As a result of the intersection of different cones, information of the activity distribution can be obtained.

However, to our knowledge, commercial devices have only been proposed for astronomy or for envirommental measurements in homeland security but not for medical applications, even if several prototypes have been built [START_REF] Llosá | Results of a first demonstrator prototype of a Compton prostate probe[END_REF][START_REF] Seo | Development of double-scattering-type Compton camera with double-sided silicon strip detectors and NaI(tl) scintillation detector[END_REF][START_REF] Alnaaimi | Performance evaluation of a pixellated Ge Compton camera[END_REF], Takeda et al. 2012[START_REF] Kurosawa | Prompt gamma detection for range verification in proton therapy[END_REF][START_REF] Kishimoto | Demonstration of threedimensional imaging based on handheld Compton camera[END_REF][START_REF] Mccleskey | Evaluation of a multistage CdZnTe Compton camera for prompt gamma imaging for proton therapy[END_REF][START_REF] Thirolf | A Compton camera prototype for prompt gamma medical imaging[END_REF], Golnik et al. 2016[START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF][START_REF] Lee | Prototype system for proton beam range measurement based on gamma electron vertex imaging[END_REF]. The high performance required in terms of energy, spatial and time resolution when CCs are employed in medical applications together with the complexity of the image reconstruction algorithms have prevented them from becoming a commercial medical imaging system. These gamma-ray imaging devices need to be further investigated and optimized to reach the clinical standards for which accurate Monte Carlo (MC) simulations are required.

MC simulations play an essential role in the design and optimization of these systems [START_REF] Richard | Design guidelines for a double scattering Compton camera for prompt-gamma imaging during ion beam therapy: A Monte Carlo simulation study[END_REF], the validation of reconstruction algorithms [START_REF] Andreyev | Resolution recovery for Compton camera using origin ensemble algorithm[END_REF]) and the extrapolation of the behaviour of these devices to unavailable situations in order to predict their potential [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF]. Several particle-tracking MC simulation software packages have been used to simulate CCs, such as CIS [START_REF] Lee | CIS: a GUI-based software system for Monte Carlo simulation of Compton camera[END_REF], MEGAlib [START_REF] Zoglauer | MEGAlib-the medium energy gamma-ray astronomy library[END_REF], GAMOS [START_REF] Arce | GAMOS: A Geant4-based easy and flexible framework for nuclear medicine applications[END_REF][START_REF] Harkness | A Compton camera application for the GAMOS Geant4-based framework[END_REF]), Geant4 [START_REF] Richard | Design guidelines for a double scattering Compton camera for prompt-gamma imaging during ion beam therapy: A Monte Carlo simulation study[END_REF][START_REF] Peterson | Optimizing a three-stage Compton camera for measuring prompt gamma rays emitted during proton radiotherapy[END_REF][START_REF] Rohling | Requirements for a Compton camera for in vivo range verification of proton therapy[END_REF][START_REF] Fontana | Compton camera study for high efficiency SPECT and benchmark with Anger system[END_REF], SWORD [START_REF] Novikova | Designing sword-software for optimization of radiation detectors[END_REF] or BEAMnrc/EGSnrc [START_REF] Sinclair | Simulations of a scintillator Compton gamma imager for safety and security[END_REF]. GATE/Geant4 [START_REF] Jan | GATE V6: a major enhancement of the GATE simulation platform enabling modelling of CT and radiotherapy[END_REF][START_REF] Sarrut | A review of the use and potential of the gate Monte Carlo simulation code for radiation therapy and dosimetry applications[END_REF]) is an open-source and collaborative simulation platform dedicated to medical physics applications which is based on the well established general purpose Geant4 software [START_REF] Allison | Recent developments in Geant4[END_REF]. Nowadays, GATE is commonly used for emission tomography simulations [START_REF] Gillam | Monte-Carlo simulations and image reconstruction for novel imaging scenarios in emission tomography[END_REF], notably due to the broad range of experimental settings that can be simulated by using macro language. GATE already contains dedicated modules for SPECT and PET imaging.

In this work, we present an extension of GATE toolkit with the aim of supporting CC simulations. This new Compton Camera Module (CCMod) facilitates the investigation of CC systems and realistic comparisons between different prototypes in an environment that allows to simulate several imaging devices, radiotherapy treatments and perform dosimetry calculation in the same framework. As an example, simulations of protontherapy beam lines [START_REF] Grevillot | A Monte Carlo pencil beam scanning model for proton treatment plan simulation using GATE/Geant4[END_REF][START_REF] Grevillot | GATE as a Geant4-based Monte Carlo platform for the evaluation of proton pencil beam scanning treatment plans[END_REF]) are already available and may be used to generate realistic distributions of promptgammas [START_REF] Gueth | Machine learningbased patient specific prompt-gamma dose monitoring in proton therapy[END_REF][START_REF] Huisman | Accelerated prompt gamma estimation for clinical proton therapy simulations[END_REF]) that may be investigated with CCs. Moreover, GATE already contains specific modules for medical physics simulations, which allow to easily insert a voxelized CT image from a DICOM file or to read and analyze list mode format among others. In this work, the predictions of CCMod have been compared with experimental data taken with MACACO prototype built at IFIC-Valencia [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF]. The developed tools have been employed to illustrate their capability to characterize and enhance experimental data by developing dedicated filtering criteria to reduce the fraction of background events. Furthermore, the performance of two different CCs has been characterized in terms of efficiency and angular resolution showing the versatility of this open-source module.

Materials and Methods

All the simulation studies included in this work were performed with Geant4 version 10.5 and GATE version 8.2.

Compton Camera module

2.1.1. Compton Camera principles. CCs employ electronic collimation based on Compton kinematics. A conventional CC is comprised of a scatterer and an absorber detector layer working in time coincidence. Ideally, the gamma-ray undergoes a Compton interaction in the closest detector layer, referred to as scatterer, where the recoil electron deposits its energy, and the scattered photon is absorbed in the absorber. Using the kinematics of Compton scattering the incident trajectory of the gamma-ray can be constrained to a cone surface. However, in experimental data there is a non-negligible percentage of invalid events that contribute to the background such as partial energy absorption events (recoil electron or scattered photon escape), incorrectly ordered interactions and randoms.

CCs typically consist of low-Z material for the scatterer and high-Z material for the absorber in order to maximize the probability of Compton scattering in the scatterer and photoelectric absorption of the scattered photon in the absorber. The energy resolution of the scatterer is particularly important to accurately determine the scattering angle. To this end, a low Z material is also of special interest to reduce the effect of Doppler energy broadening, Compton profile, due to the initial momentum of the bound electron [START_REF] Ordonez | Doppler broadening of energy spectra in Compton cameras[END_REF].

In most proposed designs, the device is comprised of a scintillator detector for the absorber and one or several detector layers for the scatterer based on different technologies such as scintillator crystals coupled to compact SiPM/MPPC arrays [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF][START_REF] Kishimoto | Demonstration of threedimensional imaging based on handheld Compton camera[END_REF], semiconductor detectors [START_REF] Seo | Development of double-scattering-type Compton camera with double-sided silicon strip detectors and NaI(tl) scintillation detector[END_REF][START_REF] Thirolf | A Compton camera prototype for prompt gamma medical imaging[END_REF], Golnik et al. 2016[START_REF] Lee | Prototype system for proton beam range measurement based on gamma electron vertex imaging[END_REF][START_REF] Fontana | Compton camera study for high efficiency SPECT and benchmark with Anger system[END_REF] or gaseous detectors [START_REF] Kurosawa | Prompt gamma detection for range verification in proton therapy[END_REF]). In addition, CCs composed only of semiconductor detector layers [START_REF] Alnaaimi | Performance evaluation of a pixellated Ge Compton camera[END_REF], Takeda et al. 2012[START_REF] Mccleskey | Evaluation of a multistage CdZnTe Compton camera for prompt gamma imaging for proton therapy[END_REF] have been successfully built and tested.

The aim of CCMod is to provide a framework where different system configurations can be easily simulated in a medical environment. It was designed to model the most common CC configuration with a scatterer and an absorber. However, it can be adapted to accommodate other designs such as one single position sensitive detector system that acts as scatterer and absorber at the same time [START_REF] Lehner | 4π Compton imaging using a 3-D position-sensitive CdZnTe detector via weighted list-mode maximum likelihood[END_REF][START_REF] Mihailescu | SPEIR: a Ge Compton camera[END_REF][START_REF] Maier | Second generation of portable gamma camera based on Caliste CdTe hybrid technology[END_REF][START_REF] Montémont | NuVISION: a portable multimode gamma camera based on HiSPECT imaging module[END_REF]) that can be of interest in homeland security applications.

2.1.2. GATE module. CCMod has been implemented as a dedicated GATE actor that follows the same structure to store and process the interaction of particles as the SPECT and PET scanner systems [START_REF] Jan | GATE V6: a major enhancement of the GATE simulation platform enabling modelling of CT and radiotherapy[END_REF]. Portions of the geometry are designated as Geant4's sensitive detectors where interactions are recorded. Here, the absorber and scatterer layers store information about all particle interactions from now on referred to as hits. A hit contains the interaction process type (Compton, photoelectric, ionization...), the layer name, the position interaction, the deposited energy, the time and information on parent particle among others.

Individual detector layer responses obtained from the aggregation of the hits are referred to as singles. The singles are then sorted in time and associated in coincidences. Finally, the singles within each coincidence are ordered generating a sequence coincidence. This sequence determines the cone surface. This processing from interactions to cone information is divided into three different steps namely digitizer, sorter and coincidence sequence reconstruction which are explained in detail in sections 2.1.3 to 2.1.5. At each step the corresponding output data (hit collection, singles, coincidence, sequence coincidence) are available to the user. All processing steps may be performed during the simulation (on-the-fly mode) or on the simulation output files (offline mode).

A similar data format for hit collection and singles as for SPECT and PET modules has been used to be able to share the digitizer modules and sorter between the different imaging devices. Hence, some of the already available modules for SPECT and PET systems [START_REF] Jan | Gate: a simulation toolkit for PET and SPECT[END_REF]), e.g. energy resolution, time resolution, energy window, spatial resolution, and dead-time, can be directly applied in CCMod. Several new modules, briefly described in section 2.1.3, have been developed to meet the needs of some of the most commonly employed CC configurations. The features included in these additional modules, that can be equally applied to SPECT/PET systems, can be of interest to simulate more accurately and further understand the acquired data also in those imaging modalities.

2.1.3. Digitizer. The digitizer consists of applying sequentially a chain of modules to the hit collection to mimic the individual detector response creating the singles. In order to reproduce accurately the response of a detector, the modules that compose the digitizer chain must be carefully selected.

With the aim of modeling the response of the most commonly employed detectors in CCs such as semiconductor, pixelated and monolithic scintillator detectors (see 2.1.1), several modules have been implemented. These modules can be classified into three different categories. The first one corresponds to those that spatially regroup hits to take into account the characteristics of the signal generation in the detector such as grid discretization module which simulates the response of pixelated or strip detectors. The second one corresponds to modules that modify the observable values of the singles such as Depth of Interaction (DoI) modeling or 3-dimensional spatial resolution module. The last category comprises those modules that filter the singles such as energy threshold modules. Figure 1 shows the general structure of the digitization chain divided into the aforementioned three categories applied to a 5-hit-collection composed of three photon interactions, two Compton scattering and a photoelectric absorption, and two secondary electronic interactions. As an example, the response of a monolithic block readout by position sensitive photo-detectors is approached by applying a hit regrouping module to collect the total energy deposited by the hits and provide the energy weighted centroid position.

Since in CCs different detector layers have usually different roles and characteristics, these modules have been designed so that they can be applied locally to a specified sensitive volume. In addition, with the aim of recovering Compton kinematics, a module that provides the information of the incident photon before and after each interaction has been developed. Additional modules can be easily added by the users to take into account unforeseen situations in specific configurations.

The digitization of optical photons has not been considered in CCMod. The performed simulations do not include the generation and transport of optical photons which highly increase the computational cost [START_REF] Bonifacio | A time efficient optical model for GATE simulation of a LYSO scintillation matrix used in PET applications[END_REF]). However, several digitization modules, such as DoI module which models the influence of the light distribution on the 3-dimensional spatial resolution of the detector, have been implemented aiming at reproducing the response of scintillator crystals.

2.1.4. Sorter. In Geant4, events are created sequentially. However, singles are not necessarily arriving to the sorter in chronological order. Therefore, they are ordered by their simulation time value before being sorted in time, generating coincidences when they are detected within the same Time Coincidence Window (TCW). To this end, the sorter developed in GATE for PET systems [START_REF] Strydhorst | Redesign of the GATE PET coincidence sorter[END_REF] has been adapted for CCMod. By default, Single Window method is selected where as long as a coincidence window is opened, no other single can open its own coincidence window. Multiple Window method is also available as for PET systems. An additional option has been included to allow only singles in the absorber layer to open its own window (absorber coincidence trigger). The criterion set for CC coincidence processing acceptance is that at least two of the singles within the TCW are recorded in different detector layers.

Coincidence Sequence Reconstruction (CSR).

The CSR is a coincidence processor which modifies the order of the singles within a coincidence to generate a sequence coincidence. In CCs, CSR plays an essential role since the correct sequence of singles is necessary to determine the correct cone surface where the source is located. By default, the singles within a coincidence are ordered according to their detection time, i.e by increasing time-stamp value. This policy is referred to as ideal. However, since the time resolution of the detector layers is generally not good enough to identify the correct interaction sequence, different policies are adopted. CCMod includes several policies namely random, distance to the source and the above described ideal policy. The distance to the source policy orders the singles by increasing distance to the source in the perpendicular direction to the camera, i.e. first singles in the first layer. Furthermore, a policy based on the so-called revan analyzer from MEGAlib [START_REF] Zoglauer | MEGAlib: simulation and data analysis for low-to-medium-energy gamma-ray telescopes[END_REF], known as Classic Coincidence Sequence Reconstruction (CCSR) has been included.

Coincidence processing modules already available for PET systems, such as deadtime or memory buffer can also be employed in the CCMod.

Comparison with experimental data

2.2.1.

MACACO prototype The predictions of CCMod were compared with experimental data taken at IFIC-Valencia with the first version of MACACO (Medical Applications CompAct COmpton camera) prototype [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF]). The prototype is based on LaBr 3 monolithic crystals coupled to SiPMs. The system setup, the so-called configuration 1 in [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF], was composed of two layers separated by 50 mm. Both layers were made of monolithic scintillator crystals coupled to SiPM arrays with active area elements of 3×3 mm 2 . The crystal sizes were 27.2×26.8×5 mm 3 and 32.0×36×10 mm 3 for the first and second layer respectively. The first layer was based on four Hamamatsu MPPC S11830-3340MF monolithic arrays whereas the second one was based on an older version S11064-050P(X1) with larger gaps between the pixels. More details can be found in [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF].

A second version of the prototype is currently under development based on higher performance SiPM arrays with the aim of improving the energy resolution of the prototype. The SiPM, model S13361-3050AE-08, is based on TSV (Through Silicon Via) technology. Further information is available in [START_REF] Barrio | Performance improvement tests of MACACO: A Compton telescope based on continuous crystals and SiPMs[END_REF]).

The reported measurements, unless otherwise stated, were taken with the first version of the prototype and a 22 Na source of 847 kBq activity located in the center of the first plane at a perpendicular distance of 53 mm (see figure 2). The acquisition discriminator threshold applied at pixel level was set about 70 keV for each plane (sum of the values in all 64 pixels) [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF].

Simulation characteristics

Geometry Two sets of simulations were performed to reproduce the experimental data: a simplified geometry in which only the volumes corresponding to the sensitive detector layers (scintillator crystals) were included and another one in which additional insensitive components of the prototype i.e. crystal encapsulation, crystal holder, PCBs (printed circuit boards) and the SiPMs, were included in order to take into account their contribution to photon scattering. The compositions, densities and thicknesses of these materials are not exactly known and they were not optimized. The camera was simulated in air. Both geometries are shown in figure 2. Processing The first step of the processing was the digitization of the hits to reproduce the response of the detector-layers, see section 2.1.3. The digitization chain was designed with the aim of modeling the experimental response of a monolithic crystal coupled to a SiPM matrix with an acquisition discriminator threshold applied at pixel level. Following the general structure shown in figure 1, a hit regrouping module was firstly applied. The clustering module was selected to group the hits within an acceptance distance of 3 mm, which corresponds to the SiPM pixel size. Then, the maximum deposited energy in a SiPM pixel of the array (E c effect,i ) was approximated analytically without the generation and transport of optical photons using the MPM, namely the Model of Pixel response for a SiPM array coupled to a Monoblock, see figure 1. This effective energy at pixel level was obtained for each cluster by weighting its energy by the fraction of the solid angle subtended by a virtual pixel centered at the cluster X-Y position at the readout surface of the crystal. Then, the conventional adder was applied to generate a single signal per layer and per event where the energy corresponds to the total deposited energy of all the clusters in the layer and the position to the energy weighted centroid position. Pile up effect was not included since it was negligible in the experimental data.

After the hit regrouping modules, energy and spatial resolution modules were applied. The energy resolution was set to 8.5% at 511 keV in the first layer, with an energy dependence following the inverse square root law policy. In the second layer however a slightly worse resolution of 12.5% at 511 keV was set to match the experimental data. The influence of the temperature variations on the energy resolution was not modeled. Regarding the transverse spatial resolution, a 2 mm Gaussian blurring was applied. In this work, the DoI uncertainty was modelled as an exponential function with a coefficient of -0.3507 mm -1 [START_REF] Cabello | Simulation study of PET detector limitations using continuous crystals[END_REF]) and a value of 8 mm FWHM at the entrance of the crystal. However, different models were tested for DoI, such as dual layer model or Gaussian blurring for the DoI uncertainty, yielding equivalent results.

Finally, a local threshold was applied at pixel level where if at least the effective energy of one of the clusters (E c effect,i ) was above the threshold the whole event was accepted for processing. Due to the uncertainties in the applied experimental discriminator threshold which was set to get a global energy threshold in each layer of above ∼70 keV [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF], and the simplified model employed to reproduce it, discrepancies between the simulated and experimental accepted singles distribution are expected. In order to minimize them, a slightly higher global energy threshold of 85 keV was also applied to the total energy deposition in each layer to both data sets.

After the digitization process, the generated singles were sorted using a TCW of 50 ns. The singles within the sequence coincidence were ordered by increasing axial distance to the source, i.e. first singles in the first layer. It was considered that the majority of coincidences corresponds to forward scattering in the scatterer followed by an interaction in the second layer.

Source 22 N a source was simulated with an activity of 847 kBq and a diameter of 0.5 mm that correspond to the experimental values. The source was embedded in a plastic phantom that represents the source encapsulation and facilitates the positron annihilation.

The intrinsic activity of 138 La of the LaBr 3 crystal and naturally occurring radioactive materials were not included since the detected count rates due to the natural radioactivity were negligible (<1%) compared to those generated by the employed external source. Natural radioactivity can be included in the simulation with an additional source.

Physics list and cuts

The option 4 of the standard electromagnetic physics list, which includes Doppler broadening effect, was selected. The employed model for Compton scattering for energies below 20 MeV was LowEPComptonModel [START_REF] Brown | A low energy bound atomic electron Compton scattering model for Geant4[END_REF] with G4EMLOW7.7 database. Atomic de-exitation processes such as fluorescence, Auger and PIXE (Particle-Induced X-ray Emission) effects were activated for all volumes (sensitive and insensitive materials). Cuts values were set to 0.1 mm which corresponds to one order of magnitude less than the smallest dimension of the sensitive detectors.

Time A simulation time of 200 s was set leading to around 20000 accepted coincidences. The simulation lasted around 14 hours on a single Intel(R) Xeon(R) CPU E5-2620 @ 2.00GHz.

Figures of Merit

The verification was made through the comparison of different figures of merit namely energy spectra of singles, energy spectra of coincidences, scattering angle, angular resolution and efficiency.

In addition, reconstructed images obtained from the back-projection onto the plane of the source were compared.

Scattering angle

The estimated scattering angles obtained from the Compton kinematics θ C were compared to the ones obtained from geometrical method θ G following eq. ( 1a) and eq. ( 1b) respectively:

cos(θ C ) = 1 - m e c 2 E 1 E 0 (E 0 -E 1 ) (1a) cos(θ G ) = g 10 • g 21 | g 10 || g 21 | (1b)
where E 1 is the energy deposited in the Compton scattering, E 0 is the incident energy, m e is the rest mass energy of the electron, g 10 is the vector that goes from the source position to the first interaction position and g 21 from the first interaction to the second interaction position. Due to the error associated with the manual positioning of the source in the experimental set-up, the position of the source was corrected taking into account the reconstructed image.

For the comparison with experimental data, the initial energy E 0 was estimated from the sum of the energy deposition in the layers. When the total deposited energy was below 600 keV, E 0 was assigned to the 511 keV photon and otherwise to the 1275 keV photon.

Angular Resolution

The error distribution of the scatter angles was computed as the difference between θ G and θ C [START_REF] Zoglauer | Doppler broadening as a lower limit to the angular resolution of next-generation Compton telescopes[END_REF][START_REF] Seo | Experimental performance of double-scattering Compton camera with anthropomorphic phantom[END_REF], Odaka et al. 2012[START_REF] Mizumoto | A performance study of an electron-tracking Compton camera with a compact system for environmental gamma-ray observation[END_REF]. The Angular Resolution Measure (ARM) value is given by the FWHM of the distribution. Its magnitude is related to the resolution of the final image. Therefore, it enables to study the resolution excluding the dependence of the reconstruction methods.

In order to fit the non-Gaussian distribution of the ARM, different functions have been employed in the literature: a Voigt function (a convolution of the Gaussian and Lorentzian distributions) [START_REF] Seo | Experimental performance of double-scattering Compton camera with anthropomorphic phantom[END_REF], Odaka et al. 2012), a Lorentzian function [START_REF] Mizumoto | A performance study of an electron-tracking Compton camera with a compact system for environmental gamma-ray observation[END_REF] or a superposition of different Lorentzian functions [START_REF] Zoglauer | Doppler broadening as a lower limit to the angular resolution of next-generation Compton telescopes[END_REF]. In this work, the ARM value was obtained by fitting the distribution with a Lorentzian function.

Relative detection efficiency The relative detection efficiency was calculated as the fraction of events emitting a photon within the solid angle subtended by the first detector layer that produces a detected coincidence. In order to compare the obtained value with the experimental value reported in [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF] for the 1275 keV photons of the 22 Na source, the coincidences with a total deposited energy comprised between 600 and 1350 keV were selected.

CCMod as a facilitator towards more accurate results

CCMod can be employed to better understand the experimental data and to get more accurate results. The ground-truth provided by the developed tool on a validated simulation can be employed to define ad-hoc filters based on observable values to improve experimental data by reducing the fraction of invalid events.

In this section, the developed simulation was employed to illustrate the capability of the CCMod to characterize the signature of the deposited energy of random coincidences. This type of invalid events was chosen for illustration purposes. The studied experimental data were taken with a 22 Na source which leads to several photons per decay (511 keV and 1275 keV). Therefore, the information of the primary photon that produces each interaction, included in the CCMod, was employed to distinguish between random coincidences generated by the detection of different photons coming from the same decay process (same event identification) and photons coming from two different decays (different event identification).

In addition, the angular error distribution was studied to evaluate the impact of the energy threshold applied experimentally and to characterize the energy signature of the events with large angular error value with the aim of reducing the fraction of background events.

Comparison of the performance of different prototypes

The comparison of the performances between MACACO and CLaRyS prototypes was performed. The CLaRyS collaboration includes four institutions: Institut de Physique Nucleaire de Lyon (IPNL), Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé de Lyon (CREATIS), Centre de Physique de Particules de Marseille (CPPM) and Laboratoire de Physique Subatomique et Cosmologie de Grenoble (LPSC). The prototype under development by the CLaRyS collaboration is described below.

The CLaRyS Compton Camera prototype

The CLaRyS prototype was originally designed and optimized for hadrontherapy purposes. However, the simulated geometry of the absorber corresponds to the one presented in [START_REF] Fontana | Compton camera study for high efficiency SPECT and benchmark with Anger system[END_REF], which was adapted to be as close as possible to a commercial SPECT-Anger camera device (GE Healthcare Infinia system). The scatterer detector is composed of seven parallel double sided silicon strip detectors (DSSDs) separated by 10 mm distance from each other. The absorber, 210 × 280 × 30 mm 3 in size, is composed of 6 × 8 BGO streaked blocks. Each block was simulated as an 8 × 8 pixel matrix. The distance between the last silicon plane (center) and the center of the absorber is 150 mm. The DSSDs are 90 × 90 × 2 mm 3 in size with 2 × 64 strips in a 1.4 mm pitch. The camera was simulated in air.

Processing. Different digitization chains were applied to model the responses of scatterer and absorber layers following the specifications described in [START_REF] Fontana | Compton camera study for high efficiency SPECT and benchmark with Anger system[END_REF]. Regarding the scatterer, a grid discretization module was applied to model the charge collection of the DSSDs where 64 strips of 1.3 mm active size in a 1.4 mm pitch were simulated in each transverse direction. An activation threshold of 50 keV was set at strip intersection level. An energy resolution of 2.5% at 200 keV with an energy dependence following the inverse square root law policy was additionally applied. Regarding the absorber layer, the scintillator crystal was simulated with 6 × 8 blocks made of 8 × 8 pixels each with an active area of 4.375 mm 2 in size. The readout was performed at block level. The signal of each block corresponded to the total energy deposition taking into account the 64 pixels, and the position was given by the energy weighted centroid position. An activation threshold of 100 keV was set at the block level. An energy resolution of 21% at 662 keV with an energy dependence following the inverse square root law policy was set to match the experimental performance. In both cases, the transverse spatial resolution was determined by the applied discretization module and the DoI was set to the center of the detector layer. After the digitization process, the singles were sorted in time using the same TCW value as in MACACO prototype (50 ns). For the CSR, forward scattering policy was also selected.

Multiple coincidences may contain useful information about the source in CLaRyS prototype since it is composed of several scatterer layers and a pixelated absorber. However, for comparison purposes with the MACACO configuration composed of two monolithic crystals, only coincidences composed of one single in each detector type were considered.

The physics list and cuts described in 2.2 were applied.

Evaluation

The performance of both prototypes was studied in terms of detection efficiency normalized to the geometrical acceptance of the scatterer (relative detection efficiency) and ARM. The relative detection efficiency for CLaRyS prototype was studied for coincidences composed of two singles. To this end, monochromatic point-like gamma sources related to radioemitters already suggested for nuclear medicine applications [START_REF] Fontana | Compton camera study for high efficiency SPECT and benchmark with Anger system[END_REF] emitting in a range comprised between 245-2614 keV were employed. The source was located 53 mm far from the surface of the first layer as for MACACO experimental data. In order to make a fair comparison the passive structure of MACACO prototype was not included in this study. An acquisition time of 200 s and an activity of 847 kBq were simulated. The computational time for CLaRyS prototype was between 3 and 6 hours depending on the incident energy whereas for MACACO prototype was around 2 hours on a single Intel(R) Xeon(R) CPU E5-2620 @ 2.00GHz.

Results

Comparison with MACACO experimental data

3.1.1. Energy spectra of singles In order to evaluate if the structure of the prototype plays a significant role in the measurements, the energy spectrum of the singles was studied. The comparison of the spectra between experimental data and the two sets of simulations, the simplified one and the one that includes part of the passive structure of the prototype, without applying any energy threshold is shown in figure 3(a) and figure 3(b) for the first and the second layer respectively.

In the singles spectra we can observe the photo-peaks, at 511 keV and 1275 keV, together with the Compton edges in each detector layer. In addition, the absorption of the photons undergoing back-scattering outside the studied detector layer, with energies around ∼170 keV and ∼213 keV respectively, can be clearly seen. The energy spectrum of both simulation types above the first photo-peak was equivalent. However, when the structure of the prototype was considered, there was an increment of detected singles at low energies resulting in a better agreement with experimental data. In both detector layers, the recovered intensity of the back-scattering fronts was higher and better matching the experimental data. Moreover, for the second detector layer, the Compton edge was also better recovered. Hence, all of the following simulations include the passive material.

Another difference that can be found in figure 3(a) and figure 3(b) was the lack of events depositing an energy below ∼100 keV in experimental data with respect to the simulations. This effect is due to the discriminator threshold applied at individual SiPM pixel level for the experimental acquisition, which does not result in a unique global threshold value at the total deposited energy. The value for the simulated discriminator, applied at the estimated deposited energy at pixel level using the MPM, was adjusted independently for each detector layer. Figure 3(c) and figure 3(d) show the comparison of the spectrum of the singles between the experimental and simulated data for different threshold values in each detector layer. The local threshold value was set in each detector layer as high as possible avoiding the rejection of the events that were experimentally accepted which results in a value of 3 keV in the first and 1 keV in the second layer to the estimated deposited energy at pixel level. Regarding the scatter angle, data can be classified into sequence coincidences that give rise to the diagonal line (θ G =θ C ) and the rest which are found outside the diagonal. The former consists of true sequence coincidences produced by one gammaray whereas the latter encompasses coincidences that degrade the image quality such as incorrectly ordered coincidences (due to back-scattering), partial absorption and random coincidences. The percentages of these invalid coincidences are shown in table 1 where randoms were divided into coincidences generated by different photons coming from the same decay, noted Single Decay Random (SDR) and coming from two different radioactive decays, noted Two-Decay Random (TDR). Among invalid coincidences four features can be identified according to figure 5, three clearly visible horizontal lines and a vertical curved line. The horizontal lines corresponding to θ C 0.40 rad and θ C 1.05 rad come from an incorrect order in the sequence coincidence when forward scattering is assumed, for 1275 keV and 511 keV incident photons respectively. While θ C 0.75 rad is caused by random coincidences with a full absorption of 511 keV photon in the first layer. Finally, the vertical curved line has its origin in the underestimation of the initial energy of the gamma-ray when the total deposited energy is below 600 keV and the incident gamma ray corresponds to the 1275 keV photon. This feature is clearly visible when ideal resolution is applied in the simulation (see figure 5(b)). It is worth noting that in the experimental data taken with the second version of MACACO prototype shown in figure 5(d), this feature is also visible. 6 for (a) 511 keV and (b) 1275 keV estimated incident energy and for (c) all the coincidences showing a good agreement between experimental and simulated data. For 511 keV incident energy, a second peak towards negative values is shown which mainly corresponds to the events with incorrect order or an underestimation of the initial energy. The ARM was studied for 1275 keV estimated incident energy. The obtained value for the experimental data was (13.5 ± 0.2) • whereas for simulated data was (13.4 ± 0.2) • .

Energy spectra of coincidences

Relative detection efficiency

The obtained relative detection efficiency value for 1275 keV incident photons was about 2.6× 10 -3 for simulated data, whereas the measured value in a similar configuration reported in [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF]) was about 1.9×10 -3 . An acceptable agreement was obtained between simulated data and the experimental reference value acquired with a similar configuration, especially considering that the crude analytical model of the discriminator threshold was adjusted to accept more events than in the experimental scenario (see figure 3) which led to an overestimation of the detection efficiency of the system.

(rad) C θ - G θ 2 - 1.5 - 1 - 0.5 - 0 0.5 1 1.5 2 Normalized counts 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Experimental Simulated (a) (rad) C θ - G θ 2 - 1.5 - 1 - 0.5 - 0 0.5 1
3.1.6. Back-projection onto the plane of the source Figure 7(a) and 7(b) show reconstructed images composed of 101×101 pixels of 1 mm×1 mm each from the back-projection onto the plane of the source of 1275 keV estimated incident energy photons for experimental and simulated data respectively. A bias was presented in the reconstructed axial position for the experimental data where the source was reconstructed ∼12 mm closer to the first detector layer than for the simulated data.

The comparison of the normalized projections between both data sets along x and y orthogonal directions is shown respectively in figure 7(c) and 7(d) when the simulated source is centered at 53 mm from the first layer. A displacement of about 4 mm in the y direction is presented in the reconstructed experimental data (figure 7(d)) which is probably due to an error in the manual positioning of the source. The comparison of the normalized projections between both data sets when the source is located at the reconstructed experimental axial position, 41 mm from the first layer, along x and y orthogonal directions is shown respectively in figure 7(e) and 7(f) showing a better agreement.

Towards more accurate results: simulation-based energy widow optimization

Figure 8 shows the energy spectra of the coincidences assuming forward scattering generated by the different products of the decay of a 22 Na source of 847 kBq activity: 511 keV annihilation photons, 1275 keV gamma-rays, SDR and TDR. The coincidences produced after a decay different than β + (such as electron capture), which can be neglected, are also shown and labeled "others".

In order to minimize the SDR, the simulation allows to suggest an upper limit for the deposited energy in each layer and in the summed energy spectrum. In this study such limit corresponds to about 1200 keV in each layer and to 1350 keV in the summed energy spectrum. These acceptance windows reduce the SDR in a 21.4% and the TDR in a 16.0%. In addition, the rejection of the coincidences with a deposited energy in the first layer comprised in (490, 550) keV range will further reduce them in a 10.2%, at the cost of rejecting 1.5% of good coincidences.

The angular error distribution of coincidences, excluding randoms (SDR, TDR), was studied for different low energy thresholds. Figure 9 energy of 511 keV and 1275 keV for different pairs of energy threshold values applied to the detector layers. It can be observed that when an energy threshold of 85 keV was applied to both layers, which is in accordance with the reported value applied experimentally in [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF], the number of coincidences for the incident energy of 511 keV with small angular error ("small error" peak) was drastically reduced with respect to the distribution obtained without any energy threshold. For an incident energy of 1275 keV, the applied threshold rejected only about 10% of the coincidences. This result points out the need for low energy thresholds, especially in the first layer for relatively low gamma energies.

Regarding the angular error distribution, coincidences were classified into two groups delimited by ∼3σ, where σ is the standard error of "small error" peaks.

Coincidences with a large angular error value (≥3σ), considered as invalid coincidences in this study, represented the ∼33% of the total coincidences. The energy signature of these two data sets was characterized through the comparison between the deposited energy in the absorber (E 2 ) and the deposited energy in the scatterer (E 1 ), see figure 10. Two empty regions can be identified in the "small error" peak diagram (figure 10(a)) associated with the two incident energies of the photons, 511 keV and 1275 keV. It turns out that the lower limits of the E 1 for these regions correspond approximately to the energies of recoil electrons associated with scattered photons that can not be detected due to the limited angular coverage of the absorber. For each incident energy, above this E 1 upper limit only back-scattering coincidences or coincidences with multiple interactions in the scatterer layer can been found. In our configuration, an upper energy threshold of 150 keV applied to the scatterer for the estimated incident energy of 511 keV reduced the fraction of the studied invalid coincides in a ∼62%. Whereas an upper threshold of 700 keV for the estimated incident energy of 1275 keV reduced the fraction of the studied invalid coincidences in a ∼6%.

The capability of the CCMod to define ad-hoc filters based on observable values to reduce the fraction of invalid coincidences was illustrated for the studied prototype.

Comparison of the performance of different prototypes

The relative detection efficiency and the angular resolution were studied as a function of the energy for both CC systems, MACACO and CLaRyS. 11 shows the relative detection efficiency for both systems for different detection energy thresholds. The results for the reported energy threshold of 85 keV for MACACO and the described operational thresholds for CLaRyS (50 keV to the scatterer and 100 keV to the absorber) are shown in filled markers. The results for a lower energy threshold of 10 keV applied to each detector type are shown in empty markers.

Efficiency Figure

Figure 11 shows that a higher energy threshold leads to a larger reduction of the efficiency at low energies. This effect is more significant for MACACO prototype due to the smaller scattering acceptance angle which reduces the maximum allowed deposited energy in the first layer (in accordance with figure 9). In this low energy region, the detection efficiency increases as the energy increases. If the applied threshold is low enough, a second energy region (700-1000 keV) can be seen with an opposite behavior due to the decreasing photon interaction probability. This region is more visible for CLaRyS prototype since it is composed of thinner scatterer layers of lower atomic number material. Finally, for high incident energies, the contribution of pair creation to the detected efficiency may be non-negligible. This contribution can be clearly observed for MACACO prototype when the low energy threshold was applied (blue empty square markers).

In general, the relative detection efficiency for CLaRyS prototype was always higher than for MACACO prototype mainly due to a three times thicker absorber and about two times higher scattering acceptance angle. It should also be noticed that MACACO does not have an optimized geometry, but just reproduces the experimental prototype layout and characterization results.

Angular resolution measure

Figure 12 shows the ARM as a function of the incident energy for both prototypes. It monotonically decreases with increasing energy. The only exception was found for the highest energy considered due to the higher probability of pair creation events which reduces the signal to noise ratio. The ARM value for CLaRyS was always better than for MACACO prototype, with a reduction of about a factor ∼4 for energies of 1 MeV.

Discussion and conclusions

CCMod, a flexible alternative to simulate CCs, has been developed within GATE/Geant4 as a complement to the already existing PET and SPECT systems. We think that this generic module within GATE not only provides the tools for data analyses but will benefit from the broad range of medical experimental settings that can be conveniently simulated using macro language. CCMod has been designed to employ the same data structures, i.e. hits, singles and coincidences, as PET and SPECT systems. Thereby, the digitization modules may be applied interchangeably to all imaging devices. Moreover, additional modules can be added by users to take into account unforeseen situations. All the processing can be performed either on-the-fly or offline by the post-processing of simulation output files.

The predictions of CCMod were compared with experimental data in terms of energy spectra, angular resolution, efficiency and back-projection image reconstruction. The spectra of singles were used to assess the impact of the passive material and to adjust the discriminator threshold, at pixel level, in each detector independently. We observed that the passive material of the prototype (boards, holders...) played an important role in the scattering, resulting in a non-negligible contribution at low energies in both layers. The main parts were simulated improving the match with the experimental data. However, there was an underestimation of the passive material surrounding the sensitive detectors that was reflected in the simulated spectra of the singles. On the other hand, the employed analytical model to reproduce the experimental discriminator threshold at pixel level accepted slightly more events, mainly at low energies, than the one employed in the experimental data. This mismatch was more significant in the second layer due to its geometrical characteristics (thicker detector with smaller Aspect Ratio, ratio of length of the side of the detector to thickness). A good agreement between both simulated and experimental data regarding the spectra of the coincidences and the ARM was obtained despite small differences at low energies. The detection efficiency was compared to the measured value reported in [START_REF] Muñoz | Performance evaluation of MACACO: a multilayer Compton camera[END_REF]) in a similar configuration. The obtained detection efficiency was higher by a factor ∼1.4 than the experimental one which can be considered in good agreement due to the unknown experimental discriminator threshold that was rather underestimated to avoid the rejection of events registered experimentally. Regarding the back-projection image reconstruction, a good agreement was obtained between both data sets regardless of the small differences related to the error in the manual positioning of the source in the experimental data. In addition, the developed simulation was employed to identify undesired coincidences and reduce them by inferring filtering criteria, based on deposited energy, that can be applied to the experimental measurements with the prototype.

CCMod was employed to predict the response of the prototype under development by the CLaRyS collaboration and compare it with the performance of MACACO experimental prototype regarding the relative detection efficiency and the ARM. In general a higher efficiency was obtained for CLaRyS prototype than for MACACO prototype mainly due to a three times thicker absorber and about two times higher scattering acceptance angle. Regarding the ARM, the performance was about four times better for CLaRyS prototype with and angular resolution of about 2.3 degree at 1 MeV, mainly due to a better energy resolution in the scatterer. The main objective of this study was to show the ability of the developed module to simulate and reproduce the results of different existing prototypes, not to draw conclusions about their performances. It is worth noting that the two employed prototypes are in different development stages. MACACO is an experimental prototype driven by existing detector size and available funding resources at the time of construction, which is being improved, whereas CLaRyS is a prototype under construction which has not been assembled yet for acquisitions in coincidence between the two types of detectors.

In summary, a dedicated GATE Compton camera module has been developed which has been satisfactorily compared with experimental data and employed to study the performance of different prototypes. This extension of GATE will allow to easily compare under the same analyses the performance of different CC systems in medical experimental setting such as hadron therapy monitoring or nuclear medicine using CTbased patient phantoms. This module, CCMod, will be available in the next GATE release.

Figure 1 :

 1 Figure 1: Scheme of the digitization chain applied to a 5-hit-collection where x hit i

Figure 2 :

 2 Figure 2: Simulated geometry. Left, geometry with the main parts of the passive materials of the experimental set up included. Right, simplified geometry.

Figure 3 :

 3 Figure 3: Simulated and experimental singles energy spectra with and without including the passive structure in (a) layer 1 and (b) layer 2. Comparison between experimental and simulated energy spectra when the passive material is included and different values for the local threshold are applied in (c) layer 1 and (d) layer 2.

  The comparison of the energy spectra of the coincidences between experimental and simulated data is shown in figure4. From left to right, the deposited energy in the first detector layer, in the second detector layer and the summed deposited energy are shown. The shaded area around the experimental data values corresponds to 3-sigma interval considering Poisson distribution.

Figure 4 :

 4 Figure 4: Simulated and experimental energy spectra of the coincidences.

Figure 5 :

 5 Figure 5: θ C (Compton kinematics angle) vs θ G (geometrical method) for (a) experimental data, (b) simulated data assuming ideal energy and spatial resolutions, (c) applying experimental energy and spatial resolution and (d) experimental data taken with the second version of MACACO prototype.

Figure 6 :

 6 Figure 6: Angular error distribution for (a) 511 keV, (b) 1275 keV estimated energy incident photon coincidences and (c) all the coincidences.

Figure 7 :

 7 Figure8shows the energy spectra of the coincidences assuming forward scattering generated by the different products of the decay of a 22 Na source of 847 kBq activity: 511 keV annihilation photons, 1275 keV gamma-rays, SDR and TDR. The coincidences produced after a decay different than β + (such as electron capture), which can be neglected, are also shown and labeled "others".In order to minimize the SDR, the simulation allows to suggest an upper limit for the deposited energy in each layer and in the summed energy spectrum. In this study such limit corresponds to about 1200 keV in each layer and to 1350 keV in the summed energy spectrum. These acceptance windows reduce the SDR in a 21.4% and the TDR in a 16.0%. In addition, the rejection of the coincidences with a deposited energy in the first layer comprised in (490, 550) keV range will further reduce them in a 10.2%, at the cost of rejecting 1.5% of good coincidences.The angular error distribution of coincidences, excluding randoms (SDR, TDR), was studied for different low energy thresholds. Figure9(a) and figure 9(b) show respectively the angular error distribution for impinging photons with an estimated

Figure 8 :

 8 Figure 8: Deposited energies (a) in the first layer (E 1 ), (b) in the second layer (E 2 ), (c) 2D diagram E 2 vs E 1 and (d) summed energy spectrum of the coincidences.

Figure 9 :

 9 Figure 9: Angular error distribution for (a) 511 keV and (b) 1275 keV estimated incident energy. THR G pair of values represents the energy threshold applied to the deposited energy in the first and second layer respectively.

Figure 10 :

 10 Figure 10: 2D diagram E 2 versus E 1 for coincidences with (a) small angular error and (b) large angular error delimited by three times the value of the standard error of the distribution.

Figure 11 :

 11 Figure 11: Relative detection efficiency as a function of the energy for CLaRyS (red circular markers) and MACACO (blue square markers) prototypes. The results for the low energy threshold are shown in empty markers.

Figure 12 :

 12 Figure 12: ARM as a function of the incident energy for CLaRyS (red circular markers) and MACACO (blue square markers) prototypes. The results for the low energy threshold are shown in empty markers.

Table 1 :

 1 Percentages of the different types of coincidences. The results for true coincidences are also shown for each incident energy (E 0 ).

		E 0 =511 keV E 0 =1275 keV	all
	Coincidences	7842 (39.1%) 8517 (42.4%) 20079
	Single Decay randoms (SDR)	-	-	15.4%
	Two Decay randoms (TDR)	-	-	3.1%
	Back-scattering	13.9%	4.6%	18.5%
	Forward-scattering (FSC)	25.2%	37.8%	63.0%
	FSC with full absorption	14.8%	7.3%	22.1%
	FSC with partial absorption	10.0%	21.1%	31.1%
	FSC with incorrect E 0 estimation	0.4%	9.4%	9.8%
	3.1.4. ARM The error of the scattering angle was studied by means of ARM and
	compared between experimental and simulated data. The angular error distribution is
	shown in figure

Acknowledgments

This work was performed within the framework of the SIRIC LYriCAN Grant INCa-INSERM-DGOS-12563, the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the ANR, the Ministerio de Ciencia, Innovación y Universidades (FPA2017-85611-R) and IFIC Severo Ochoa Excellence centre (SEV-2014-0398). This Project has received funding from the Labex PRIMES (ANR-11-LABX-0063) of Université de Lyon and PIC 2018 programme under the reference CSIC № 2018FR0032 and CNRS PICS08272.