Schiano Di

Lombo Magali

Cavalie Isabelle

Camilleri Virginie

Perrot Yann

Gagnaire Beatrice

Affiliations

Gagnaire B Tritiated

Tritiated thymidine internalization in zebrafish early life stages: joint use of experimental procedures and microdosimetry Running title: Tritiated thymidine internalization in zebrafish

Keywords: Tritium, zebrafish, microdosimetry, organically bound tritium, internalization, DNA, tritiated thymidine

internalization in zebrafish embryo and larva: joint use of experimental processes

Introduction

Tritium is the only hydrogen isotope with radioactive properties (1). It is a β-emitter that has a half-life of 12.3 years, and a mean energy of 5.7 keV. Considering that it is a hydrogen isotope, its physico-chemical properties are the same than that of hydrogen, meaning it could be found in every environmental compartments (2). In the environment, tritium can be found in three main forms: free in the water (HTO), gaseous tritium (HT) and organically bound tritium (OBT), where tritium replaces hydrogen in an organic molecule. Tritium is produced by natural and anthropogenic processes. In the environment, its main anthropogenic sources are nuclear industries such as nuclear power plants, which routinely release tritium as HTO [START_REF] Arcanjo | Assessing tritium internalisation in zebrafish early life stages: Importance of rapid isotopic exchange[END_REF][START_REF] Chen | Radiation quality of tritium[END_REF][START_REF] Jaeschke | Bioaccumulation of tritiated water in phytoplankton and trophic transfer of organically bound tritium to the blue mussel, Mytilus edulis[END_REF]. Tritium levels in all the environmental compartments have been monitored in France for many years, highlighting basal levels of 0.12 to 0.86 Bq/L [START_REF]Livre blanc du Tritium & bilan des rejets de tritium pour les INB[END_REF][START_REF] Irsn | Actualisation des connaissances acquises sur le tritium dans l'environnement[END_REF]. Under a radioactive influence, tritium levels were of 1 to 61 and 5 to 35 Bq/L in the Rhône and Garonne rivers, respectively .When the tritium enters the biological tissues, it can be found in three different forms: Tissue Free Water Tritium (TFWT), where tritium is trapped in the tissue water; exchangeable-organic tritium (eOBT), where a tritium is bound to oxygen, sulfur, nitrogen or phosphorous; and nonexchangeable organic tritium (neOBT), where tritium is bound to a carbon atom [START_REF] Jaeschke | Tissue-specific incorporation and genotoxicity of different forms of tritium in the marine mussel, Mytilus edulis[END_REF]. The latter is the tritium form that has the highest biological half-life.

Considering that tritium can enter living organisms, many studies have focused on internalization measurements, both on the field and in the laboratory [START_REF] Arcanjo | Assessing tritium internalisation in zebrafish early life stages: Importance of rapid isotopic exchange[END_REF][START_REF] Jaeschke | Bioaccumulation of tritiated water in phytoplankton and trophic transfer of organically bound tritium to the blue mussel, Mytilus edulis[END_REF][START_REF] Jaeschke | Tissue-specific incorporation and genotoxicity of different forms of tritium in the marine mussel, Mytilus edulis[END_REF][START_REF] Mccubbin | Incorporation of Organic Tritium (3H) by Marine Organisms and Sediment in the Severn Estuary/Bristol Channel (UK)[END_REF][START_REF] Gagnaire | Effects of in situ exposure to tritiated natural environments: A multi-biomarker approach using the fathead minnow, Pimephales promelas[END_REF][START_REF] Gagnaire | Effects of in vivo exposure to tritium: a multi-biomarker approach using the fathead minnow, Pimephales promelas[END_REF][START_REF] Kim | Tritium uptake in rainbow trout (Oncorhynchus mykiss): HTO and OBT-spiked feed exposures simultaneously[END_REF]. A study focusing on the HTO internalization in zebrafish embryos and larvae have shown that tritium does incorporate in the tissue of the animals at a fast rate, and is mainly found in the form of TFWT [START_REF] Arcanjo | Assessing tritium internalisation in zebrafish early life stages: Importance of rapid isotopic exchange[END_REF]. It was also shown that when living organisms are exposed to both HTO and OBT, high tritium levels were found in mussel and fish ((9.92 -22.9)x10 4 Bq/kg and (2.10 -24.00)x10 4 Bq/kg, respectively) [START_REF] Mccubbin | Incorporation of Organic Tritium (3H) by Marine Organisms and Sediment in the Severn Estuary/Bristol Channel (UK)[END_REF]. Multiple studies have also focused on the internalization differences between HTO and OBT, highlighting the fact that OBT contributes more to the absorbed tritium dose compared to HTO [START_REF] Jaeschke | Tissue-specific incorporation and genotoxicity of different forms of tritium in the marine mussel, Mytilus edulis[END_REF][START_REF] Gagnaire | Effects of in situ exposure to tritiated natural environments: A multi-biomarker approach using the fathead minnow, Pimephales promelas[END_REF][START_REF] Gagnaire | Effects of in vivo exposure to tritium: a multi-biomarker approach using the fathead minnow, Pimephales promelas[END_REF][START_REF] Kim | Tritium uptake in rainbow trout (Oncorhynchus mykiss): HTO and OBT-spiked feed exposures simultaneously[END_REF]. Those studies also showed that both compounds behave differently, with TFWT reaching equilibrium with the external activity concentration while OBT does not, leading to longer depuration rates measured in the latter case.

Tritiated organic compounds as tritiated thymidine have been used in order to better understand biological mechanisms. As thymidine is a thymine precursor, DNA internalization is expected, leading to its use in studies focusing on DNA synthesis [START_REF] Duque | Different Effects of Bromodeoxyuridine and [3H]Thymidine Incorporation into DNA on Cell Proliferation, Position, and Fate[END_REF][START_REF] Gray | Rates of incorporation of radioactive molecules during the cell cycle[END_REF][START_REF] Hopwood | Transport of thymidine during the cell cycle in mitotically synchronized CHO cells[END_REF][START_REF] Naito | Cell cycle related [3H]thymidine uptake and its significance for the incorporation into DNA[END_REF][START_REF] Peterson | Extracellular matrix alters the relationship between tritiated thymidine incorporation and proliferation of MC3T3-E1 cells during osteogenesis in vitro[END_REF][START_REF] Plagemann | Thymidine transport by Novikoff rat hepatoma cells synchronized by double hydroxyurea treatment[END_REF][START_REF] Zajicek | Studies on the in vitro incorporation of tritiated thymidine into ascites tumor cells[END_REF]. Many of those studies have shown that as expected, significant tritium levels could be measured in the cell and in the DNA after an in vitro exposure of those cells to the labelled nucleoside. Two of those studies also highlighted the fact that thymidine enters the cell via the salvage pathway, also known as facilitated diffusion [START_REF] Hopwood | Transport of thymidine during the cell cycle in mitotically synchronized CHO cells[END_REF][START_REF] Peterson | Extracellular matrix alters the relationship between tritiated thymidine incorporation and proliferation of MC3T3-E1 cells during osteogenesis in vitro[END_REF]. When thymidine reaches the cell, two competing mechanisms occur. Either the thymidine is directly transformed into thymine, leading to its degradation before it can be internalized into the DNA, or it is rapidly phosphorylated and joins the derivative pool, which is the intermediate between the thymidine internalization in the cell and its internalization in the DNA [START_REF] Hopwood | Transport of thymidine during the cell cycle in mitotically synchronized CHO cells[END_REF][START_REF] Naito | Cell cycle related [3H]thymidine uptake and its significance for the incorporation into DNA[END_REF][START_REF] Zajicek | Studies on the in vitro incorporation of tritiated thymidine into ascites tumor cells[END_REF]. While a major part of the thymidine is directly transformed into thymine before being taken out of the cell, thymidine phosphorylation is still significant, as it enables the DNA synthesis. But while the thymidine phosphorylation is fast, it is still dependent on the thymidine transport system that is itself dependent on the cell cycle. Indeed, it seems that the tritiated thymidine internalization in the cell is almost null in the G1-phase, before strongly increasing when the cells reach the S-phase and decreasing when the cells enter the G2-phase [START_REF] Gray | Rates of incorporation of radioactive molecules during the cell cycle[END_REF][START_REF] Hopwood | Transport of thymidine during the cell cycle in mitotically synchronized CHO cells[END_REF][START_REF] Naito | Cell cycle related [3H]thymidine uptake and its significance for the incorporation into DNA[END_REF][START_REF] Plagemann | Thymidine transport by Novikoff rat hepatoma cells synchronized by double hydroxyurea treatment[END_REF]. As explained above, these studies concluded that tritium linked to thymidine can enter the cell and the DNA.

Quantification tools as liquid scintillation can be used in order to obtain more information on radioactive levels in different organisms. But, in order to understand all the damages that can occur after an exposure to radiation, this information is not sufficient. Biological effects and internalization should be linked to an actual value of energy deposited. When considering that the sensitive volume is the cell, the energy deposit by decay will have a marked stochastic nature. Microdosimetric formalism is then relevant in order to obtain information on the imparted energy distribution at the microscopic level [START_REF] Tang | Influence of chromatin compaction on simulated early radiation-induced DNA damage using Geant4-DNA[END_REF]. Indeed, microdosimetry gives the formalism necessary to describe the distribution of the energy depositions that occur stochastically in a given target, and it can be used to analyse the imparted energy at the cell scale [START_REF] Cruz | Microdosimetry: Principles and applications[END_REF][START_REF] Kellerer | Concepts of microdosimetry II. Probability distributions of the microdosimetric variables[END_REF]. Such cellular simulations are even more important when considering beta-emitters as tritium [START_REF] Chen | Radiation quality of tritium[END_REF][START_REF] Tang | Influence of chromatin compaction on simulated early radiation-induced DNA damage using Geant4-DNA[END_REF][START_REF] Chao | Cellular-and micro-dosimetry of heterogeneously distributed tritium[END_REF][START_REF] Morstin | Microdosimetry of Tritium[END_REF][START_REF] Ünak | Microdosimetry of tritium and carbon-14 in different materials[END_REF]. Indeed, a study has proven that microdosimetric simulations can highlight important differences in energy depositions in materials as Teflon® or water [START_REF] Ünak | Microdosimetry of tritium and carbon-14 in different materials[END_REF]. This study showed that the range of betarays emitted from tritium were 35 times shorter than the one emitted from Carbon-14, with the total energy released by tritium being absorbed in spherical volumes of Teflon or water way smaller than in the case of Carbon-14. As beta-rays emitted by tritium cannot travel high distances (i.e. around 7 µm in soft tissues for the most energetic rays), the calculated absorbed doses in the decay vicinity of H-3 were found to be very high, thus showing that microdosimetric considerations are important for the evaluation of the radiolytic effectiveness of beta-emitters as tritium [START_REF] Chao | Cellular-and micro-dosimetry of heterogeneously distributed tritium[END_REF][START_REF] Ünak | Microdosimetry of tritium and carbon-14 in different materials[END_REF]. Other studies also highlighted differences between HTO and OBT by the means of microdosimetry [START_REF] Chen | Radiation quality of tritium[END_REF][START_REF] Chao | Cellular-and micro-dosimetry of heterogeneously distributed tritium[END_REF][START_REF] Morstin | Microdosimetry of Tritium[END_REF]. Significative differences were found between HTO and OBT, specifically when the target size gets smaller, partly because OBT is heterogeneously distributed in the organism, leading to more complex microdosimetric cases.

The main objective of this study was to quantify tritiated thymidine internalization in zebrafish in its early life stages. With this purpose, the tritiated thymidine internalization in the organisms was studied by means of experimental procedures and microdosimetric simulations. The use of both approaches was also chosen in order to answer another objective: showing how experimental processes and simulations could complete each other. Zebrafish was chosen as it is a convenient laboratory species, with adults being able to spawn hundreds of eggs in a single spawning, and the genome of this species being fully sequenced [START_REF] Spence | The behaviour and ecology of the zebrafish, Danio rerio[END_REF][START_REF] Scholz | The zebrafish embryo model in environmental risk assessment-applications beyond acute toxicity testing[END_REF]. Early developmental stages were chosen as they are considered as being more sensitive to a large range of chemicals. Also, the first developmental stages have already been studied, giving u the required information for the microdosimetric simulations [START_REF] Fraysse | Development of a zebrafish 4-day embryo-larval bioassay to assess toxicity of chemicals[END_REF][START_REF] Kimmel | Stages of embryonic development of the zebrafish[END_REF]. In order to study the tritium internalization in the zebrafish embryos and larvae, zebrafish embryos were exposed to a large range of tritiated thymidine activity concentrations (2.21x10 3 to 5.95x10 5 Bq/mL). During those exposures, individuals were sampled after different exposure times in order to have more information on the internalization kinetics. Moreover, individuals were sampled after 1 and 4 days of exposure in order to quantify the tritium internalization in the whole individual, but also in its DNA, which was quantify after extraction. Finally, microdosimetric simulations were made in order to obtain more information on the imparted energy at a cellular level, giving more information on which cells could be more at risk when chronically exposed to tritiated thymidine.

Material and methods

Fish

All experimental procedures performed in this study were previously approved by IRSN Animal Care Committee and followed French regulations for animal experimentation (protocol P2019-19; registration number of IRSN laboratory: C13-013-07). Four months old wild-type zebrafish (AB genetic background) were supplied by Paris Sorbonne University (France) and were kept in a zebrafish housing system (Zebtec Techniplast® Stand Alone) with a 12:12h light:dark cycle photoperiod. The fishes were fed three times a day with Gemma Wean 0.3 (Skretting). Water parameters were monitored daily (pH 7.5 ± 0.2; conductivity 400 ± 20 µS.cm -1 , temperature 27.5 ± 0.2 °C). As males and females were kept in different tanks, the mating was done every three to four weeks to ensure that the fishes had a good reproductive capacity and that the females stayed in good health. All matings were done in the husbandry using the water from the housing system and using fishes that were between 4 and 13 months old.

Embryo exposure and tritium contamination

Exposures to different tritium activities were done separately to ensure that there was no cross-contamination between the different glass crystallisers. Embryo medium was prepared using InstantOcean sea salt at a concentration of 60 mg/L [START_REF] Westerfield | The zebrafish book : A guide for the laboratory use of zebrafish Danio (Brachydanio) rerio[END_REF]. The embryo medium was used as the negative control condition and to dilute the tritiated thymidine source. Tritiated thymidine solution (97% purity, 185 MBq, PerkinElmer, Courtaboeuf, France) was diluted in embryo medium to obtain final activity concentrations varying between 2.21 x 10 3 and 5.94 x 10 5 Bq/mL.

The exposure was designed from the protocol described in Arcanjo et al [START_REF] Arcanjo | Assessing tritium internalisation in zebrafish early life stages: Importance of rapid isotopic exchange[END_REF]. At 3.5 hpf, zebrafish eggs were placed in two glass crystallisers covered with Parafilm at a density of two eggs per mL of tritiated thymidine solution or embryo medium. The eggs were kept in the dark in thermo-regulated incubators (Heraterm, ThermoScientific) at 27 ± 1 °C for 4 days. At 48 h, 80 % of the water medium was renewed with fresh solutions. Tritium-free water (Abatilles water, France) was also placed in the incubators (40 mL/beaker) in order to monitor tritium exchanges in the incubator. Temperature (°C) and relative humidity (%) were monitored every 30 minutes during the exposure (HOBO data logger U12, Onset).

Tritium measurements were made on the medium (3 replicates/crystalliser, once a day, 10 µL of medium in 990 µL of tritium free water), on the tritium-free water (1 replicate/beaker, once a day, 1 mL) and on the eggs and larvae (24 and 96 hpe, hours post exposure). Blank measurements were made on tritium-free water (Abatilles water, France).

After adding 19 mL of the liquid scintillation cocktail (Ultima Gold LLT, Perkin Elmer), the liquid scintillation measurements were done using a Quantulus (Quantulus 1220, Perkin Elmer) monitored by WinQ (1220-307 WinQ, Perkin Elmer). Each measurement was done three times and lasted 20 minutes. The data were processed using the EasyView software.

The results were expressed as Bq/mL.

Internalization measurements

Tritium internalization kinetics and barrier function of the chorion

Tritium kinetics measurements were realised on 10 to 15 individuals that were exposed during 1 to 96 hours (1; 3; 6; 20; 22; 24; 48; 72 and 96 h) to tritiated thymidine at a concentration activity of (4.2 ± 0.3)x10 4 Bq/mL. For the negative control, only 3 individuals were sampled at each time point. The internalization was measured according to a protocol modified from the one described by Arcanjo et al. [START_REF] Arcanjo | Assessing tritium internalisation in zebrafish early life stages: Importance of rapid isotopic exchange[END_REF]. Briefly, 10 to 15 individuals were sampled and individually dried on a filter (RA 1.2, Millipore). With a needle, the egg was rolled over the filter while the larva was only gently taped on the filter.

Once the sample was dry, it was placed in a liquid scintillation tube. One mL of soluene-350 (Perkin Elmer) was added to the sample that was then left to heat for 48 hours at 55 °C. In a next step, 35 µL of glacial acetic acid (Sigma Aldrich) was added, followed by 19 mL of Ultima Gold LLT scintillation liquid (Perkin Elmer). All results were expressed as Bq/sample. After 48 hours of exposure to solution with tritium activity concentrations of 3.4x10 3 and 4x10 4 Bq/mL, two types of samples were dried and mineralized. Firstly, 15 whole embryos were dried as explained above. Secondly, 15 other individuals were sampled and the chorion was carefully removed before sampling the larvae and drying it by taping it on a filter. All samples were mineralized following the process explained above. Results were processed using the EasyView software and were expressed as Bq/sample.

Tritium internalization measurements: 24 and 96 hours of exposure

The internalization measurements were realised on 20 to 30 individuals that were exposed during 24 hours (24 hpe) to tritiated thymidine at concentration activities ranging from 2x10 3 to 6.5x10 5 Bq/mL (0.2; 3.3; 4.9; 6.5; 6.6; 9; 11; 15; 33 and 65x10 4 Bq/mL).

For the negative control, only 6 individuals were sampled at each time point. The internalization was measured according to a protocol modified from the one Arcanjo et al.

(3). Briefly, 30 embryos were sampled and individually dried on a filter (RA 1.2, Millipore) as explained above. Briefly, 10 to 15 tubes were used for total tritium measurement and another 10 to 15 were used to measure OBT. For total tritium measurement, samples were processed as described above and for the OBT measurements, samples were firstly dried in opened tube for 48 h at 55 °C before following the same protocol described for total tritium quantification. All samples were measured using a Quantulus monitored by WinQ.

The results were processed using the EasyView software. For the larvae exposed for 96 hours to the same activity concentrations, only 10 to 15 samples were dried and only the total tritium internalization was measured.

Results were expressed in Bq/kg (fresh weight) using weight data presented by Arcanjo et al. [START_REF] Arcanjo | Assessing tritium internalisation in zebrafish early life stages: Importance of rapid isotopic exchange[END_REF]. Dose rate (DR, µGy/h) were calculated using the equation:

𝐷𝑅 = (𝐷𝐶𝐶 𝑒𝑥𝑡 × 𝐴 𝑤 ) + (𝐷𝐶𝐶 𝑖𝑛𝑡 × 𝐴 𝑂 ) (1)
where Aw is the tritium content in the water (Bq/mL), DCCext is the calculated dose coefficient related to external exposure (μGy/h per Bq/g), AO is the tritium content in the organism (Bq/g, fresh weight) and DCCint is the calculated dose coefficient related to internal exposure (μGy/h per Bq/g). The dose coefficients (DCs) were calculated by analytical procedure using EDEN v3 (developed by IRSN ( 31)), following the hypothesis that tritium is homogeneously distributed in the organism. These DCs and weights used are presented in Table 1. Concentrations factors (CF, mL/g) were calculated following this equation:

𝐶𝐹 = 𝐴 𝑂 𝐴 𝑤 (2)
Where AO is the tritium content in the organism (Bq/g, fresh weight) and Aw is the tritium content in the water (Bq/mL).

DNA extraction and tritium measurements

DNA was extracted from zebrafish embryos and larvae following the DNeasy ® Blood & Tissue Kit (Kiagen). Briefly, 3 pools of 25 control embryos (or 18 larvae) and 5 pools of 25 contaminated embryos (or 18 larvae) were sampled after being rinsed with clean embryo medium that was then removed and replaced by 200 µL of a Buffer ATL/Proteine K mix (90:10, v/v). 200 µL of Buffer AL were added, followed by 200 µL of Ethanol (> 96 %). The mixture was then added to a DNeasy Mini spin column placed in a 2 mL collection tube. The sample was centrifuged for 1 min at 6000 g at room temperature. The supernatant was then discarded and then spin column was placed in a new 2 mL collection tube before adding 500 µL of Buffer AW1 and centrifuging the sample at 6000 g for 1 min.

The supernatant was discarded, and the spin column was added to a new 2 mL collection tube. Buffer AW2 (500 µL) was added in the column and the sample was centrifuged for 3 min at 20000 g. The column was placed in a 2 mL microcentrifuge tube and the DNA was eluted by adding 50 µL of Buffer AE to the center of the spin column membrane. The DNA was left to incubate at room temperature for 1 minute before being centrifuged for 1 min at 6000 g.

DNA concentration (µg/mL) was measured using the Qubit ® dsDNA Broad Range Assay Kit (ThermoFisher Scientific). All samples are treated individually, and two DNA standards (0 and 100 ng/µL in TE buffer) were added. In each 0.

Microdosimetry simulations

In the formalism used in this study, the energy released to a volume is the imparted energy noted ℇ. It is the sum of all the elementary energy deposits in this volume coming from a primary particle (in our case an electron from the decay) and from all the secondary particles. For each cell, ℇ is a stochastic variable, also leading to different specific energies (z) which is the microdosimetric quantity equivalent to the absorbed dose. It is worth pointing out that absorbed dose D corresponds to the ratio between the mean value of the deposited energy in the matter and the mass of the volume where the deposition occurs.

In this work, simulations were computed using Geant4 Monte Carlo toolkit version 10.06 as well as its extension, Geant4-DNA. This extension proposes, among other things, physical models at very low energy for the simulation of the track structure (i.e. the spatial distribution of the interactions points) in liquid water and which is thus well adapted to microdosimetry [START_REF] Agostinelli | Geant4-a simulation toolkit[END_REF][START_REF] Allison | Recent developments in Geant4[END_REF][START_REF] Incerti | The geant4dna project[END_REF][START_REF] Incerti | Comparison of GEANT4 very low energy cross section models with experimental data in water[END_REF][START_REF] Bernal | Track structure modeling in liquid water: A review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit[END_REF][START_REF] Incerti | Geant4-DNA example applications for track structure simulations in liquid water: A report from the Geant4-DNA Project[END_REF]. Geant4 Monte Carlo toolkit has been chosen as both ellipsoidal and spherical cells are usable, which is not the case with MIRDcell, but different studies showed that Geant4 can be used instead of MIRDcell as the results obtained are comparable [START_REF] Incerti | Geant4-DNA example applications for track structure simulations in liquid water: A report from the Geant4-DNA Project[END_REF][START_REF] Salim | Dosimetry assessment of theranostic Auger-emitting radionuclides in a micron-sized multicellular cluster model: A Monte Carlo study using Geant4-DNA simulations[END_REF]. For microdosimetric calculation the shape and size of the target volume have a strong impact on the distribution of the imparted energy. In order to simulate the cells present in the zebrafish embryos and larvae, an individual cell was represented as a sphere or an ellipsoid made of liquid water, considering the majority of zebrafish cells are of those shapes. The radius chosen were from 0.25 to 10 µm (0.25; 0.5; 1.25; 2.5; 5; 7.5; 10 µm) for the spherical cells and from 0.5 to 15 µm (0.5; 2.5; 5; 7.5; 10; 12.5; 15 µm) for the ellipsoidal ones [START_REF] Kellerer | Concepts of microdosimetry II. Probability distributions of the microdosimetric variables[END_REF][START_REF] Braat | Characterization of zebrafish primordial germ cells: Morphology and early distribution of vasa RNA[END_REF][START_REF] Ciruna | Planar cell polarity signalling couples cell division and morphogenesis during neurulation[END_REF][START_REF] Concha | Oriented cell divisions and cellular morphogenesis in the zebrafish gastrula and neurula: a time-lapse analysis[END_REF][START_REF] Easter | The Development of Vision in the Zebrafish (Danio rerio)[END_REF][START_REF] Field | Formation of the digestive system in zebrafish. ii. pancreas morphogenesis☆[END_REF][START_REF] Glickman | Shaping the zebrafish notochord[END_REF][START_REF] Grandel | The development of the paired fins in the Zebrafish (Danio rerio)[END_REF][START_REF] Kane | The zebrafish epiboly mutants[END_REF][START_REF] Kimmel | Specification and Morphogenesis of the Zebrafish Larval Head Skeleton[END_REF][START_REF] Li | Zebrafish: A Model System to Study Heritable Skin Diseases[END_REF][START_REF] Liu | Chemical-induced craniofacial anomalies caused by disruption of neural crest cell development in a zebrafish model[END_REF][START_REF] Mizoguchi | Sdf1/Cxcr4 signaling controls the dorsal migration of endodermal cells during zebrafish gastrulation[END_REF][START_REF] Murakami | Zebrafish protocadherin 10 is involved in paraxial mesoderm development and somitogenesis[END_REF][START_REF] Schmitt | Early-eye morphogenesis in the zebrafish, Brachydanio rerio[END_REF][START_REF] Shin | Neural cell fate analysis in zebrafish using olig2 BAC transgenics[END_REF][START_REF] Yin | Convergence and extension movements mediate the specification and fate maintenance of zebrafish slow muscle precursors[END_REF]. The radius chosen for the ellipsoidal cells corresponds to the smallest of the three axes, the other characteristic dimensions being taken equal to twice this radius (x = radius; y = 2xradius; z = 2xradius). Simulations were made in liquid water on one cell of interest made of liquid water while considering the presence of its neighbour cells, with the cell of interest being in the middle of a 3-D cell cluster. The presence of the neighbour cells was taken into consideration as a study made on the tritiated thymidine incorporation in rhesus monkeys (Macaca mulatta) showed that labelled cells are usually close to each other, forming bands [START_REF] Duque | Different Effects of Bromodeoxyuridine and [3H]Thymidine Incorporation into DNA on Cell Proliferation, Position, and Fate[END_REF]. For those neighbour cells, it was taken into account that electrons released by tritium during its decay can only travel up to 6 µm in liquid water [START_REF] Carsten | Tritium in the Environment[END_REF] and the cells located at a distance greater than 6 µm were therefore not taken into account. For those simulations, 10 6 electrons were being released in the cell of interest but also in its neighbours. The simulation scheme is represented in Figure 1. As a large number of electrons were used in the simulations, the simulation is quite robust, and its statistic error is 1.5 %.

From these simulations, the probability of having an imparted energy for one tritium disintegration from 50 to 18500 eV (with a 50 eV bin) was obtained. This energy scale was chosen considering that electrons emitted by tritium during its decay have a maximum energy of 18.6 keV [START_REF] Carsten | Tritium in the Environment[END_REF]. These simulations also indicated the mean imparted energy in each cell, the imparted energy having the highest probability and the maximum energy that could be deposited in the cell. In this work, the mean imparted energy will be expressed in eV per disintegration and represented as a function of the radius of the cell.

Statistical analyses

Statistical analyses were performed using RStudio with PMCMR, car and lmtest packages. All data were expressed as mean ± SD (Standard Deviation). Packages as ggplot2, ggpubr, ggmisc and scales were used to represent the data as graphs. The normality of data distribution and the homogeneity of the variances were verified using the Shapiro-Wilks and Levene tests (p < 0.05). For the water tritium content during the experiment, a two-way ANOVA was performed with crystallizer and time as factors. When necessary, this test was followed by a Tukey post-hoc test (p < 0.05). To compare the total tritium and OBT contents in the zebrafish embryos and larvae, t-test or Wilcoxon test were performed (p < 0.05). Lastly, to compare the concentration factors between each experiment, a one-way ANOVA was performed, followed by a Nemenyi post-hoc (p < 0.05) when necessary. To compare the tritium concentrations measured in the DNA between the different tritium activity concentrations, the Kruskal-Wallis test was performed, followed by a Bonferroni post-hoc test (p < 0.05).

Results

Tritium internalization in zebrafish early stages

Tritium internalization kinetics and barrier function of the chorion

Tritium internalization kinetics measured after the first experiment are presented in Fig. 2A. These results gave the general trend, showing that there was a first significant increase in the internalization between 0 and 1 hour of exposure. The internalization then reached a threshold between 1 and around 6 hours of exposure. It then increased again between 6 and 24 hours of exposure before slowing down before 48 hours of exposure.

Considering the large standard deviations measured at 22, 24 and 48 hours, the experiment was repeated using a similar activity concentration (4.0x10 4 instead of 4.5x10 4 Bq/mL) and more individuals (15 instead of 10) were sampled. The results are exposed in Fig. 2B. These results confirmed the trend already observed after the first experiment, and tritium activity concentrations in the sample statistically different between samples exposed for 1 and 24 hours (p < 0.001).

In order to verify the hypothesis of the chorion acting as a barrier, the activity was measured by removing the chorion of half of the individuals after 48 hours of exposure, before mineralization. For both external activities tested, the activity measured in the individual without the chorion was significantly lower than the activity measured in the individual with the chorion (2.03 vs 44.71 and 11.09 vs 171.17 Bq for 3.3x10 3 and 4x10 4 Bq/mL, respectively; p < 0.001).

Tritium internalization in embryos and larvae

Activity concentrations measured in the crystallizers at the beginning of the experiment, measured external activity concentrations and calculated internal dose rates after 24 and 96 hours of exposure are presented in Table 2. Some data are missing either because they were not planned to be measured, or because there was a technical issue during the experiment. The results showed that for embryos and larvae, the internal dose rate increased with the external activity, but this increase did to seem to be linear. Also, it can be pointed out that the standard deviations for this parameter were higher for embryos compared to larvae. Considering that the increase of the dose rate with the external activity concentration did not seem to be linear, the dose internal dose rate was plotted against the external activity concentration, and those plots are presented in Fig. 4 and Fig. 5. For embryos (Fig. 4) as for larvae (Fig. 5), the tritium internalization seemed to follow a sigmoidal curve, with an exponential increase leading to a saturation point at an external activity concentration of around 2 to 2.5x10 5 Bq/mL.

The form of the incorporated tritium was also studied by measuring the total tritium and OBT fractions, separately. The results are presented in Table 3. As showed in the table, there were no statistical differences between the total tritium and OBT dose rates (p > 0.05).

Tritium internalization in DNA

Tritium incorporation in the DNA from embryos and larva exposed to three tritium activities was measured and the results are presented in Table 4. Tritium incorporation in the DNA was visible even at the lowest external activity concentration measured (3.46x10 3 Bq/mL). The results also showed that as for the tritium incorporation in the whole embryo and larvae, the internalization process seemed to be complete after 24 hours of exposure, as there was no significant differences between the tritium activity concentrations in the DNA at 24 and 96 hours of exposure (p > 0.05).

Microdosimetry of tritium in zebrafish cells

For all cells, the highest probability was reached for the lowest imparted energy per disintegration (0-50 eV), and this was observed for all cells, with no effect of their shape or their size (Fig. 6). For all cells, the probability rapidly decreased while the energy increased, until the imparted energy reached 250 eV.Bq -1 . At this point, the probability increased, reaching a maximum for imparted energies of 250 and 350 eV.Bq -1 in ellipsoidal and spherical cells, respectively. After this point, the probability decreased exponentially while the imparted energy increased. For both cell shapes, the increase of the cell radius was linked to a decrease in the probability linked to the smallest deposited energies. Cells with the lowest radius also reached a null probability for lower energies than cells with higher radii.

For both cell shapes, the specific energy per Bq computed with Geant4-DNA could be linked to the cell radius (R² ≥ 0.99; Fig. 7). The equations computed for the spherical and ellipsoidal cells can be found in the equations ( 3) and ( 4), respectively. z is the mean imparted energy and r is the cell radius. For an equivalent radius, the specific energy for 1 Bq of tritium in a spherical cell was lower than the specific energy in an ellipsoidal cell.

For both cell shapes, the specific energy decreased when the cell radius increased.

𝑧 = 0.0956𝑥 -2.607 (3)
𝑧 = 0.2766𝑥 3 (4)

Discussion

Tritium internalization kinetics

The results highlighted that there are three steps in the internalization kinetics of tritiated thymidine in embryos and larvae. Briefly, the results showed a first internalization between 0 and 1 hour of exposure, and a second significant internalization between 6 and 24 hours of exposure. The internalization can then be considered as complete as there were no statistical differences between the activity concentration after 24 and 48 hours. These results are in accordance with another study made on HTO, where tritium internalization kinetics showed that a steady-state appeared between 1 and 24 hours of contamination (3).

These results are even more interesting considering that the embryos were exposed from the same time (3 to 3.5 hours post fertilization), showing that despite differences in behaviour between OBT and HTO, internalization kinetics stay the same [START_REF] Jaeschke | Tissue-specific incorporation and genotoxicity of different forms of tritium in the marine mussel, Mytilus edulis[END_REF][START_REF] Kim | Tritium uptake in rainbow trout (Oncorhynchus mykiss): HTO and OBT-spiked feed exposures simultaneously[END_REF].

The last part of the kinetic was the significant decrease between 48 and 72 hours of exposure. This could be explained by the hatching that occurred between 48 and 72 hpf, transforming embryos into larvae. We hypothesised that the main fraction of tritium was adsorbed on the chorion, and not internalized in the embryo, which would show a barrier effect of the chorion. This hypothesis was confirmed by the second part of the experiment, with tritium levels being significantly higher in embryos with chorion compared to dechorionated embryos. This result was in accordance with previous studies. The zebrafish chorion has a 3.5 µm thickness and is divided between 3 different layers of different compositions [START_REF] Bonsignorio | Structure and macromolecular composition of the zebrafish egg chorion[END_REF]. It also contains pores that have a size of 0.17 µm², and its structure is consistent with the roles that have been assigned to its different compartments: diffusive exchange of gases and physical protection, flexible filter for transport of materials and protection against microorganisms [START_REF] Scholz | The zebrafish embryo model in environmental risk assessment-applications beyond acute toxicity testing[END_REF][START_REF] Rawson | Field emission scanning electron microscopy and transmission electron microscopy studies of the chorion, plasma membrane and syncytial layers of the gastrula-stage embryo of the zebrafish Brachydanio rerio: a consideration of the structural and functional relationships with respect to cryoprotectant penetration[END_REF]. Considering its composition, its possible barrier function in case of external exposure to pollutants has been investigated, and multiple studies demonstrated that intake of pollutants as polystyrene nanoparticles, lindane or depleted uranium was limited by the chorion [START_REF] Scholz | The zebrafish embryo model in environmental risk assessment-applications beyond acute toxicity testing[END_REF][START_REF] Van Pomeren | Exploring uptake and biodistribution of polystyrene (nano)particles in zebrafish embryos at different developmental stages[END_REF][START_REF] Bourrachot | The effects of waterborne uranium on the hatching success, development, and survival of early life stages of zebrafish (Danio rerio)[END_REF].

Tritium internalization in whole zebrafish embryos and larvae

While studying the tritium internalization, measurements after 24 hours of exposure also showed that tritium is nearly totally internalised in its organic form, which is not surprising considering that tritiated thymidine is an organically bound tritium form. In general, the fact that tritium seemed to be mainly internalised in its organic form strictly differs from HTO studies performed on fish species as rainbow trout (Oncorhynchus mykiss) and zebrafish [START_REF] Arcanjo | Assessing tritium internalisation in zebrafish early life stages: Importance of rapid isotopic exchange[END_REF][START_REF] Kim | Tritium uptake in rainbow trout (Oncorhynchus mykiss): HTO and OBT-spiked feed exposures simultaneously[END_REF]. Indeed, in the rainbow trout study, Kim et al. showed that significant OBT levels were only obtained after feeding the trout with OBT-spiked food, while a simple HTO exposure in the medium led to high total tritium levels, but no OBT.

Arcanjo et al. also showed that the OBT levels were lower after 24 hours of exposure compared to 96 hours of exposure, and that at both times, OBT levels were significantly lower than total tritium ones (3). Those results confirm the main hypothesis of differences in the internalization of OBT and HTO in zebrafish embryos and larvae. These findings are in accordance with a study focusing on tritiated glycine internalization in the mussel [START_REF] Jaeschke | Tissue-specific incorporation and genotoxicity of different forms of tritium in the marine mussel, Mytilus edulis[END_REF]. It showed that the internalization pattern was different from the one observed in the case of HTO, with a repartition between the different body compartments being different between tritiated glycine and HTO. A few studies focusing on the internalization of OBT through the food chains in different species of fish are also in accordance with our results [START_REF] Mccubbin | Incorporation of Organic Tritium (3H) by Marine Organisms and Sediment in the Severn Estuary/Bristol Channel (UK)[END_REF][START_REF] Gagnaire | Effects of in situ exposure to tritiated natural environments: A multi-biomarker approach using the fathead minnow, Pimephales promelas[END_REF][START_REF] Gagnaire | Effects of in vivo exposure to tritium: a multi-biomarker approach using the fathead minnow, Pimephales promelas[END_REF].

Indeed, those studies, performed on the field and in the laboratory, showed that OBT activity concentrations measured in the fish were higher after the fishes were fed tritiated feed, and that the exposure to HTO did not lead to the measurement of significant OBT levels compared to TFWT. All those studies also confirmed that the depuration rates were lower for OBT compared to HTO.

Relationship between the internal dose rate and the external activity concentration

Our study showed that the internal dose rate increased exponentially with the external activity concentration before reaching a saturation point. Such results are not surprising, considering those findings had already been made by different studies based on the tritiated thymidine incorporation in different cells. For example, a study focusing on tritiated thymidine internalization in hyperploid Ehrlich ascites tumor cells showed that in the process of incorporating thymidine in the DNA, a precursor pool is formed [START_REF] Zajicek | Studies on the in vitro incorporation of tritiated thymidine into ascites tumor cells[END_REF]. One study focusing on the same tumor cells found that there was an exponential increase in the tritium internalization when the pool activity concentration increases [START_REF] Naito | Cell cycle related [3H]thymidine uptake and its significance for the incorporation into DNA[END_REF][START_REF] Cleaver | Investigations into the incorporation of [3H]thymidine into DNA in L-strain cells and the formation of a pool of phosphorylated derivatives during pulse labelling[END_REF]. Literature also reported the existence of a saturation point. A study showed that when the thymidine concentration increased in the external medium, the DNA internalized fraction decreased exponentially, thus showing that even at large concentration of thymidine, the internalization will saturate. This is in accordance with the assumption that DNA synthesis depends on a balanced supply of 4 nucleotides, and that the excess of one of those same nucleotides should not cause unbalanced synthesis. Those findings were then confirmed by two other studies, one of them specifying that the excess thymidine might be released out of the cell by a feedback mechanism [START_REF] Hopwood | Transport of thymidine during the cell cycle in mitotically synchronized CHO cells[END_REF][START_REF] Cleaver | Investigations into the incorporation of [3H]thymidine into DNA in L-strain cells and the formation of a pool of phosphorylated derivatives during pulse labelling[END_REF]. A special care has to be put in such comparisons, as the studies presented above were made using synchronous cell suspensions, which is different from a living organism during its development, where cells are being created at a fast rate [START_REF] Kimmel | Stages of embryonic development of the zebrafish[END_REF]. It is also important to take into account that the internalization measured in these studies was the direct DNA internalization, while our study mainly focused on the internalization in the whole fish.

Tritium internalization in the zebrafish DNA

Our study highlighted the fact that even after an exposure to the lowest tritium activity concentration, a significant tritium incorporation could be measured in the DNA. This is in accordance with a study focusing on the incorporation of tritiated glycine in the marine mussel. It showed that after an exposure to an activity concentration close to our lowest activity concentration, the tritium activity concentration measured in the DNA was similar to the ones we measured in our embryos and larvae (0.05 to 0.2 Bq/µg vs 0.16 to 0.25 Bq/µg, respectively) [START_REF] Jaeschke | Tissue-specific incorporation and genotoxicity of different forms of tritium in the marine mussel, Mytilus edulis[END_REF].

Multiple in vitro studies have focused on the DNA synthesis rate by using tritiated thymidine incorporation as a synthesis marker [START_REF] Hopwood | Transport of thymidine during the cell cycle in mitotically synchronized CHO cells[END_REF][START_REF] Naito | Cell cycle related [3H]thymidine uptake and its significance for the incorporation into DNA[END_REF][START_REF] Peterson | Extracellular matrix alters the relationship between tritiated thymidine incorporation and proliferation of MC3T3-E1 cells during osteogenesis in vitro[END_REF][START_REF] Zajicek | Studies on the in vitro incorporation of tritiated thymidine into ascites tumor cells[END_REF][START_REF] Cleaver | Investigations into the incorporation of [3H]thymidine into DNA in L-strain cells and the formation of a pool of phosphorylated derivatives during pulse labelling[END_REF]. In the present study, tritium incorporation in DNA was completed after 24 hours of exposure. Other studies confirmed a rapid incorporation of tritium in DNA (less than one hour) [START_REF] Zajicek | Studies on the in vitro incorporation of tritiated thymidine into ascites tumor cells[END_REF][START_REF] Cleaver | Investigations into the incorporation of [3H]thymidine into DNA in L-strain cells and the formation of a pool of phosphorylated derivatives during pulse labelling[END_REF]. A study also highlighted the fact that after one hour of incubation, the radioactivity present in the medium was no longer available for the cell, which could explain the fact that even after the renewal of the medium after 48 hours, no more incorporation was induced [START_REF] Zajicek | Studies on the in vitro incorporation of tritiated thymidine into ascites tumor cells[END_REF].

The literature also enabled us to obtain more information on the potential mechanisms leading to the tritiated thymidine incorporation into the zebrafish DNA. Most studies mention the formation of a phosphorylated thymidine pool [START_REF] Naito | Cell cycle related [3H]thymidine uptake and its significance for the incorporation into DNA[END_REF][START_REF] Zajicek | Studies on the in vitro incorporation of tritiated thymidine into ascites tumor cells[END_REF][START_REF] Cleaver | Investigations into the incorporation of [3H]thymidine into DNA in L-strain cells and the formation of a pool of phosphorylated derivatives during pulse labelling[END_REF]. This formation is an intermediate step towards the DNA incorporation. A study showed that the pool size is dependent on the tritium external activity concentration, and that an equilibrium is formed between this pool and the external medium in terms of activity concentration [START_REF] Cleaver | Investigations into the incorporation of [3H]thymidine into DNA in L-strain cells and the formation of a pool of phosphorylated derivatives during pulse labelling[END_REF]. Another study also highlighted that while the thymidine is transformed into phosphorylated derivatives before being incorporated into the DNA, there is a competing mechanism in which thymidine is directly transformed into thymine, the latter then being degraded and pushed out of the cell [START_REF] Zajicek | Studies on the in vitro incorporation of tritiated thymidine into ascites tumor cells[END_REF]. Thymidine is usually mainly transformed into thymine, and only a smaller fraction is incorporated into the DNA.

An important factor to take into account was that those two studies also showed that the cell cycle has a crucial role in the DNA synthesis and the tritiated thymidine incorporation into the DNA [START_REF] Naito | Cell cycle related [3H]thymidine uptake and its significance for the incorporation into DNA[END_REF][START_REF] Cleaver | Investigations into the incorporation of [3H]thymidine into DNA in L-strain cells and the formation of a pool of phosphorylated derivatives during pulse labelling[END_REF]. Indeed, it seems that the precursor pool activity varies with the cell cycle, and that there is a significant increase in the S-phase and a small decrease in the G2-phase. Those observation, combined with the fact that the G1 cells are unable to take up thymidine, show that only cells in the S-phase can incorporate tritiated thymidine into the DNA. As mentioned above, our study focused on the in vivo exposure of zebrafish embryos and larva to tritiated thymidine, while most studies used to understand the underlying incorporation mechanisms were in vitro studies, most of them using synchronous cell suspensions. Differences in mechanisms could be discovered, as our study focuses on zebrafish embryos and larvae, organisms that undergo multiple cellular divisions, and that have a high renewal cell rate ( 29) More experiments would thus be needed in order to confirm the mechanisms associated with the tritiated thymidine incorporation in the whole fish and its DNA.

Microdosimetry

The simulations highlighted that low energy deposits had the highest probability, and that this probability decreased when the energy deposit increased. The spectrum also showed that the cells with the smallest radii have a higher probability of being a target for low energy deposits. Indeed, the maximum probability, only observed for the lowest energy deposit values, decreased when the cell radius increased (e.g. the probability of observing a small energy deposit for a spherical cell with a 0.25 µm radius was around 3 times higher than the one measured for a spherical cell with a 1.25 µm radius). After comparison of our spectrum with the one representing the kinetic energy of tritium (Supplementary Information, Figure S1), it seemed that, as highlighted by Morstin et al. in a microdosimetry study focusing on tritium, the low energy deposits were caused by low-energy electrons [START_REF] Morstin | Microdosimetry of Tritium[END_REF]. Other microdosimetry studies also showed that for a same volume, the number of deposition events decreased when the energy increased [START_REF] Turner | Comparative Study of Electron Energy Deposition and Yields in Water in the Liquid and Vapor Phases[END_REF][START_REF] Liamsuwan | Microdosimetry of low-energy electrons[END_REF][START_REF] Tung | Low-energy electron interactions with liquid water and energy depositions in nanometric volumes[END_REF], which explains the results obtained in this study. In the smallest volumes (i.e. the cells with the lowest radius), only the low-energy electrons deposited their energy, because their deposit events were closer to each other. For electrons with a higher energy, the deposit events were farer from each other, meaning the risk of leaving the cell before depositing a significant amount of energy increased.

Those studies also explained another fact observed in our studies. After a small decrease of the probability when the imparted energy increased, an increase was observed, with the probability reaching a maximum at around 250 and 350 eV.Bq -1 (for spherical and ellipsoidal cells, respectively). This increase was only visible for smaller cells (0.25-0.5 and 0.5 µm for spherical and ellipsoidal cells, respectively). After comparison of those spectrum with simulations made on cells with "no neighbours" (i.e. the electrons were only released in the cell of interest; Supplementary Information, Figure S2), it seemed that this increase was due to the presence of electrons in the neighbour cells. The microdosimetry studies presented above highlighted the fact that for a same volume, the number of deposition events decreased when the electron energy increased [START_REF] Morstin | Microdosimetry of Tritium[END_REF][START_REF] Turner | Comparative Study of Electron Energy Deposition and Yields in Water in the Liquid and Vapor Phases[END_REF][START_REF] Liamsuwan | Microdosimetry of low-energy electrons[END_REF][START_REF] Tung | Low-energy electron interactions with liquid water and energy depositions in nanometric volumes[END_REF]. This shows that the increase mentioned above should be caused by electrons with a slightly higher energy than the electrons causing the maximum probability.

Considering those two information, the increase reaching a maximum at around 250 and 350 eV.Bq -1 should be caused by electrons with a slightly higher energy. Indeed, electrons with a higher energy travel longer paths between two interactions (i.e. energy deposits), causing a high proportion of the deposits to be out of the cell of interest. But when the electron starts its path in a neighbour cells, the chances that it ends its path, and thus deposits more energy, in the cell of interest, increases with increasing kinetic energy, thus increasing the probability of an energy deposit as shown in the spectrum. But as explained above, this increase was only visible for small cells. This is due to the fact that high-energy electrons could also deposit more energy in larger cells, considering that the cell radius was sometimes bigger than the distance that electrons released by tritium during its decay can travel (i.e. 6 µm) [START_REF] Carsten | Tritium in the Environment[END_REF]. Thus, the deposits caused by electrons released in the neighbour cells that ended their path in the cell of interest represent a smaller proportion of the total energy deposit measured in the cell, which explains that the increase was not visible on the final spectrum.

The simulations also highlighted the fact that there was a non-linear relationship between the specific energy calculated in the cell and its radius. This is very interesting as it means that the specific energy can be calculated using the formula presented in Eq [START_REF] Arcanjo | Assessing tritium internalisation in zebrafish early life stages: Importance of rapid isotopic exchange[END_REF] and ( 4) for cells with radii ranging from 0.25 to 10 µm and from 0.5 to 15 µm (for spherical and ellipsoidal cells, respectively). Finally, the relationship between the specific energy and the cell radius showed that for an equal radius, the specific energy was lower in a spherical cell compared to an ellipsoidal one. This was expected, considering that the higher the mass of the target, the lower the specific energy will be. In the case of the cells studied here, for a same radius r, the volume of our ellipsoid is smaller than the volume of our sphere ( πr 3 , respectively), which means that its mass is also smaller than the mass of the sphere.

Considering the fact that smaller cells present a higher probability of being the target of energy depositions closer to each other, it seems that those cells would be at a greater radiological risk than others. Indeed, several studies showed that low-energy electrons and more specifically tritium caused deleterious effects in zebrafish and other aquatic species [START_REF] Jaeschke | Tissue-specific incorporation and genotoxicity of different forms of tritium in the marine mussel, Mytilus edulis[END_REF][START_REF] Arcanjo | Effects of tritiated water on locomotion of zebrafish larvae: a new insight in tritium toxic effects on a vertebrate model species[END_REF][START_REF] Arcanjo | Tritiated water exposure disrupts myofibril structure and induces mis-regulation of eye opacity and DNA repair genes in zebrafish early life stages[END_REF][START_REF] Beaton | Correlated responses for DNA damage, phagocytosis activity and lysosomal function revealed in a comparison between field and laboratory studies: Fathead minnow exposed to tritium[END_REF][START_REF] Adam-Guillermin | Genotoxic and Reprotoxic Effects of Tritium and External Gamma Irradiation on Aquatic Animals[END_REF]. Considering the dimensions of the different cell types in the early-life stages of the zebrafish, the hypothesis is that smaller cells as dermal cells, chondrocytes or eye cells would be at a greater risk than notochord or mesodermal cells (i.e. 0.5 to 2 and 10 to 20 µm radii, respectively), considering that the energy deposits would be closer to each other [START_REF] Easter | The Development of Vision in the Zebrafish (Danio rerio)[END_REF][START_REF] Glickman | Shaping the zebrafish notochord[END_REF][START_REF] Li | Zebrafish: A Model System to Study Heritable Skin Diseases[END_REF][START_REF] Liu | Chemical-induced craniofacial anomalies caused by disruption of neural crest cell development in a zebrafish model[END_REF][START_REF] Yin | Cooperation of polarized cell intercalations drives convergence and extension of presomitic mesoderm during zebrafish gastrulation[END_REF].

Conclusion

This study successfully gave supplementary information on tritiated thymidine internalization in living organisms. We confirmed that after exposure of zebrafish early life stages to different tritiated thymidine activity concentrations, significant tritium levels could be measured in the whole fish and its DNA. We also confirmed that as for HTO, the internalization process is rapid, with the maximum activity concentration being measured in the sample after 24 hours of exposure. We also proved that tritium is completely internalized in its organic form, but that the chorion acts as a barrier to prevent the entrance of tritiated thymidine in the embryos. Though, significant levels could still be measured in the embryos once the chorion was removed. We also showed that the internal dose rate calculated for the embryos and larvae increased following a sigmoidal trend when the external activity concentration increased. This showed that there does not seem to be a gap between in vivo and in vitro studies when it comes to the tritiated thymidine internalization in the cells. Microdosimetric studies confirmed that the energy deposition probability and the mean energy deposited depend on the size of the cell considered, as well as its shape.

It was shown that the energy imparted to the smallest cells came from the electrons with the lowest energy, thus increasing the risk of observing damages in those cells. It was also possible to find a linear fit between the mean imparted energy in the cell and the logarithm of its radius, highlighting that the quantity of energy deposited is proportional to the volume of the cell.

Tables

  5 mL tube, 190 µL of the dsDNA BR Reagent/dsDNA BR Buffer mix (1:199, v/v) were mixed with 10 µL of the DNA sample. Each sample was vortexed before being incubated in the dark at room temperature for 5 minutes. The Qubit ® 3.0 Fluorometer was used to measure the DNA concentration in the sample. Extracted DNA (25-35 µL) was mixed with Abatilles water (965-975 µL) and the tritium activity concentration was measured following the protocol already presented for the tritium liquid measurements.

Table 4 .FiguresFigure 1 .

 41 Figures

Figure 2 .

 2 Figure 2. Tritium activity (Bq/sample, mean ± SD, n = 9-10) measured in individual samples after various exposure times to a tritium at an activity concentration of 4.5x10 4 Bq/mL (top panel). The experiment repeated (bottom panel) on 15 individuals after a 1, 20, 24 and 48 h of exposure to a tritium at an activity concentration of 4x10 4 Bq/mL (Kruskal-Wallis, a<b<c<d, p < 0.05, a corresponds to the basal tritium levels in the individual (< DL)).

Figure 3 .

 3 Figure 3. Tritium activity (Bq/sample, n = 15) measured in 51 hpf zebrafish embryo before and after the chorion removal. Those individuals were sampled after a 48 hour exposure to tritium at activity concentrations of 2.4x10 3 (A, left panel) and 4.0x10 4 (B, right panel) Bq/mL (statistical analysis: t.test, a<b, p < 0.05).

Figure 4 .

 4 Figure 4. Variations in the internal dose rate (µGy/h, n=10-15) measured in zebrafish embryos after 24 hours of exposure to tritiated thymidine activity concentrations ranging from 2x10 3 to 6x10 5 Bq/mL. The graph was also zoomed around the 0 to 1.5x10 5 Bq/mL region.

Figure 5 .

 5 Figure 5. Variations in the internal dose rate (µGy/h, n=10-15) measured in zebrafish larvae after 96 hours of exposure to tritiated thymidine activity concentrations ranging from 2x10 3 to 6x10 5 Bq/mL. The graph was also zoomed around the 0 to 1.5x10 5 Bq/mL region.

Figure 6 .

 6 Figure 6. Energy deposited (eV, probability) in spherical (A) and ellipsoidal (B) cells of different radius (µm) by 1 Bq of tritium. Those results were obtained by the simulation of 10 6 electrons released in those same cells and their direct neighbours.

Figure 7 .

 7 Figure 7. Specific energy (Gy) computed in spherical (circle) and ellipsoidal (square) cells of different radii (µm). The lines correspond to the equation representing the specific energy as a function of the radius of the spherical (dotted line) and ellipsoidal (dashed line) cells.

Table 1 .

 1 Calculated dose coefficients for internal and external exposures (uGy/h per Bq/g) and fresh masses used in the dose rate calculations. Fresh masses have been measured and reported by Arcanjo et al. (3).

	Exposure	DCCext	DCCint	Fresh mass
	duration (h)	(µGy/h per Bq/g)	(µGy/h per Bq/g)	(mg)
	24	1.26x10 -5	2.24x10 -3	1.18
	96	1.73x10 -5	2.24x10 -3	0.25

Table 2 .

 2 External activities (Bq/mL, n = 2-3 crystallizers) and dose rates (µGy/h, n = 10-15) measured in the water and the zebrafish embryos and larvae after 24 and 96 hours of exposure.Results are expressed as mean ± SD. -means that these data were not acquired during the corresponding experiment, or that the data could not be kept because of an issue in the experiment.

		After 24 hours of exposure	After 96 hours of exposure
	Starting	External
			Dose rate	External activity
	activity (10 3	activity (10 3			Dose rate (µGy/h)
			(µGy/h)	(10 3 Bq/mL)
	Bq/mL)	Bq/mL)
	2.21	2.42 ± 0.38	15.50 ± 8.41	2.73 ± 0.56	6.03 ± 1.48
	3.46	2.61 ± 0.30	17.38 ± 4.29	3.32 ± 0.08	15.19 ± 13.16
	6.87	7.08 ± 1.29	22.09 ± 9.01	7.06 ± 0.36	22.75 ± 15.99
	30.73	31.11 ± 0.20	121.58 ± 67.59	31.30 ± 1.96	65.36 ± 13.62
	36.26	30.96 ± 0.23	120.48 ± 34.82	35.26 ± 0.31	76.80 ± 8.89
	36.92	42.77 ± 4.97	234.78 ± 157.76	-	-
	39.52	39.94 ± 0.06	263.34 ± 117.59	-	-
	41.15	40.02± 1.15	252.06 ± 134.36	40.36 ± 4.99	98.88 ± 46.88
	45.35	39.03 ± 3.73	282.21 ± 209.45	46.46 ± 2.70	83.36 ± 21.09
	65.77	-	-	59.09 ± 3.41	103.76 ± 36.23
	67.22	66.71 ± 1.19	267.36 ± 134.98	-	-
	90.61	82.89 ± 1.65	615.71 ± 196.04	105.85 ± 10.58	70.14 ± 26.25
	111.78	102.84 ± 3.00	785.28 ± 285.75	118.49 ± 5.68	146.24 ± 90.39
	321.45	311.15 ± 8.15	907.86 ± 472.67	324.77 ± 10.16	663.98 ± 102.49
	594.79	659.06 ± 28.91 1328.94 ± 485.48	627.40 ± 53.41	592.27 ± 60.42

Table 3 .

 3 Total tritium and OBT dose rates (µGy/h, n=10-15) measured in the zebrafish embryos after 24 hours of exposure. Results are expressed as mean ± SD. -means that these data were not acquired during the corresponding experiment, or that the data could not be kept because of an issue in the experiment. (t.test or Wilcoxon test, p < 0.05).

	Starting activity	Total tritium dose rate	Total tritium dose rate
	concentration (Bq/mL)	(µGy/h)	(µGy/h)
	3.63x10 4	120.48 ± 34.82	131.08 ± 49.82
	3.21x10 5	907.86 ± 472.67	1046.63 ± 485.67
	5.95x10 5	1328.94 ± 485.48	1462.89 ± 597.58

This study, being a part of a larger project, helped setting the perspective of using three of the activity concentrations studied and presented in this paper (7.5x10 3 ; 4x10 4 and 1.1x10 5 Bq/mL) in order to study the toxic effects of tritiated thymidine on zebrafish in its early life stages. Those activity concentrations were chosen as they lead to internal dose rates already used to study HTO and chronic gamma irradiation toxicity (22, 170 and 466µGy/h).

Acknowledgements

The authors would like to acknowledge IRSN for funding this project, as well as IRSN colleagues for their help on the experiments (Olivier Armant, Pierre Techer and Noëmie Guirandy), animal care (Elsa Cantabella) and liquid scintillation measurements (Daniel Orjollet). electrons released in those same cells.

Supplementary Information


Ludovic Duponchel
email: ludovic.duponchel@univ-lille.fr

Alexandre Cugerone

Manuel Muñoz

Vincent Motto-Ros
email: vincent.motto-ros@univ-lyon1.fr

Diagnosis and correction methods for spectral interference in the framework of LIBS imaging

Keywords: Spectral interferences, Diagnosis, Correction, Signal unmixing, Laser-Induced Breakdown Spectroscopy (LIBS), Imaging

Laser-Induced Breakdown Spectroscopy (LIBS) has become a powerful imaging technique for elemental characterization in analytical chemistry due to its advantages over other techniques. Major, minor, and trace elements are detected with high measurement dynamic, a low limit of detection and a high acquisition rate, allowing for the quick analysis of large sample surfaces. Today, chemometric tools are commonly used to ensure the most comprehensive and unbiased exploration of such spectroscopic data. However, the integration of the signal from a wavelength assumed to be specific to the element of interest remains the basic

tool for generating a chemical distribution map from a hyperspectral dataset. This classical approach is based on a strong assumption, the specificity of the chemical information on the spectral domain being considered. Any spectral interference inevitably result in the generation of a biased distribution image. In this publication, we demonstrate how Principal Component Analysis (PCA) can diagnose the potential presence of a spectral interference and how Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) can ultimately correct it if necessary using a LIBS imaging dataset obtained from the analysis of a complex rock sample. The proposed approach combines the simplicity and effectiveness of the integration method with the diagnostic and correction capabilities of chemometric tools, providing a comprehensive solution for spectral interference in LIBS imaging.

INTRODUCTION

Laser-Induced Breakdown Spectroscopy (LIBS) is increasingly establishing itself as a powerful imaging technique for the elemental characterization of complex materials in analytical chemistry [START_REF] Gardette | Laser-Induced Breakdown Spectroscopy Imaging for Material and Biomedical Applications: Recent Advances and Future Perspectives[END_REF]. This is due to a set of advantages that few analytical techniques can match today. Beyond a relatively simple sample preparation, this technique allows for the detection of major, minor, and even trace elements (from % to ppm for many elements). In addition to this high measurement dynamic and the low limit of dectection, its acquisition rate can now reach up to 1000 Hz, i.e. 1000 LIBS spectra acquired in one second. As a consequence, multiple square centimeters of a sample surface is possible to analyse in few hours, while maintaining a spatial resolution of approximately 10 microns. Under these conditions, we can easily end up with over a million spectra acquired on a sample, and it is only natural that chemometric tools are more and more exploited to ensure the most comprehensive and unbiased exploration. This includes unsupervised methods such as Principal Component Analysis (PCA) [START_REF] Moncayo | Exploration of megapixel hyperspectral LIBS images using principal component analysis[END_REF][START_REF] Finotello | HyperPCA: A powerful tool to extract elemental maps from noisy data obtained in LIBS mapping of materials[END_REF], clustering (such as k-means) [START_REF] Nardecchia | Detection of minor compounds in complex mineral samples from millions of spectra: A new data analysis strategy in LIBS imaging[END_REF][START_REF] Kiss | Imaging margins of skin tumors using laser-induced breakdown spectroscopy and machine learning[END_REF], and signal unmixing (such as Multivariate Curve Resolution -Alternating Least Squares, MCR-ALS) [START_REF] Nardecchia | Data fusion of LIBS and PIL hyperspectral imaging: Understanding the luminescence phenomenon of a complex mineral sample[END_REF][START_REF] Nardecchia | LIBS and Raman image fusion: An original approach based on the use of chemometric methodologies[END_REF] to name just a few. The last two references cited is also an opportunity to highlight another advantage of LIBS imaging, namely its multimodality through fully optical instrumentation on a single microscope. The LIBS community is well aware today that the use of multivariate tools derived from chemometrics allows for simultaneous exploitation of all the wavelengths in the spectral domain with the least possible prior assumptions. However, it should be remembered that, as any spectroscopic imaging technique, the basic tool for generating a chemical distribution map from a hyperspectral dataset is the integration of the signal from a wavelength (or a small spectral range around it) assumed to be specific to the element in question [START_REF] Fabre | Advances on microLIBS and microXRF mineralogical and elemental quantitative imaging[END_REF][START_REF] Marina-Montes | Aerosol analysis by micro laser-induced breakdown spectroscopy: A new protocol for particulate matter characterization in filters[END_REF]. It is an opportunity to emphasize that we should not oppose chemometric tools and this classical approach, but instead use them in parallel during an exploration as they provide different perspectives on our complex samples. On the other hand, the simplicity of the integration method should not make us forget that it is based on a strong assumption, which is the specificity of the chemical information on the spectral domain being considered. This assumption is all the more important in spectroscopic imaging, since any spectral interference, i.e., the presence of any unwanted chemical species in the considered spectral range, will inevitably result in the generation of a biased distribution image. Such an image could, for example, show overconcentrations of the element of interest or even, in the worst case, areas that appear to contain it when it is not present. This highlights the crucial role of spectral specificity in this imaging context. Based on the richness of emission lines contained in a LIBS spectrum and their low bandwidth, it would be a mistake to believe that an isolated and characteristic wavelength of the element of interest is always possible to find. Indeed, we remind here the excellent detection limits of LIBS but also the chemical complexity of the samples we analyze. Moreover, even if we always have a preconceived notion about the presence of certain elements in a given sample, it is difficult to know all the elements present within it. In fact, our goal is to strive for this objective when we implement such a spectroscopic technique. This does not mean that we should abandon this signal integration method for generating our elemental maps. Indeed, it remains fast and most of the time effective and relevant, but we should combine a diagnostic method to detect the presence of any interference in the investigated spectral domain. Based on a positive diagnosis, it will then be necessary to propose a correction strategy for this interference in order to obtain a corrected image for the element of interest. The entire purpose of this publication is to address these two points, namely the diagnosis and correction of spectral interferences. The main interest of our approach lies in the fact that we do not develop new chemometric algorithms to address this issue. We propose to use only PCA and MCR-ALS, not over the whole spectral domain as it is usually done, but only over a restricted spectral range around the wavelength of the element of interest. Based on a LIBS imaging dataset obtained from the analysis of a complex rock sample composed of germanium and gallium zoned sphalerite, we will demonstrate how PCA can be used to diagnose the potential presence of spectral interference, as well as how MCR-ALS can ultimately correct it.

MATERIAL AND METHODS

Origin of the sample and its preparation

The rock sample studied was collected in the Pyrenean Axial Zone, in the Arre Pb-Zn vein deposit which was investigated to understand the concentration of associated critical elements such as Ge and Ga [START_REF] Cugerone | Redistribution of germanium during dynamic recrystallization of sphalerite[END_REF]. This rock contains sphalerite (ZnS) minerals deformed by regional metamorphism, which show heterogeneous distribution and zonation in Ge and Ga. The rock sample was prepared as a 30 µm polished thin section. It is mostly composed of quartz, metamorphic micas and light-, to dark-brown sphalerite mineral enriched in germanium (up to ~ 600 ppm Ge) and gallium (up to ~ 150 ppm Ga; LA-ICP-MS analyses [START_REF] Cugerone | Behavior of critical metals in metamorphosed Pb-Zn ore deposits: example from the Pyrenean Axial Zone[END_REF]). The zoning in germanium and gallium appears very complex with microscale Ge-Ga rich patches, and a recent micro-, to nano-scale study shows the ubiquitous occurrence of Ge-Cu minerals in sphalerite, hosting most of the germanium (i.e., briartite; [START_REF] Fougerouse | Nanoscale distribution of Ge in Cu-rich sphalerite[END_REF]).

LIBS instrumental setup and spectral acquisition

The used LIBS experimental setup has already been described in several papers [START_REF] Sancey | Laser spectrometry for multi-elemental imaging of biological tissues[END_REF][START_REF] Cáceres | Megapixel multi-elemental imaging by Laser-Induced Breakdown Spectroscopy, a technology with considerable potential for paleoclimate studies[END_REF][START_REF] Motto-Ros | Precise alignment of the collection fiber assisted by real-time plasma imaging in laser-induced breakdown spectroscopy[END_REF].

Briefly, the experiment was conducted by using a Nd:YAG laser with a 8 ns pulse duration, operating at 100 Hz at the fundamental wavelength (Centurion GRM, Quantel). A typical energy of 0.6 mJ per pulse was used. The laser beam was focused onto the sample by a 15x magnification objective. In this configuration, the crater size was typically 7 µm in diameter for one shot. The measurements were performed at room temperature, under ambient pressure, and with an argon gas flowing the plasma region (0.8 l/min). The laser scanning was performed line by line in raster scan mode with the use of a motorized XYZ stage. The step size between two consecutive acquisitions was 13 µm. The light emitted by the plasma was collected by a quartz lens and focused onto the entrance of a round-to-linear fiber bundle (composed of 19 fibers, each with a 200 μm core diameter) connected to the spectrometer. The spectrometer model was a Shamrock 500 spectrometer (Andor Technology) coupled with an intensified charge-coupled device (ICCD) camera (iStar, Andor Technology). This spectrometer was equipped with a 1200 l/mm grating to cover (blazed at 300 nm) the 260-300 nm spectral range with a resolution around 0.08 nm. This range was selected for detecting in priority germanium (Ge), gallium (Ga), zinc (Zn), iron (Fe), silicon (Si) and aluminum (Al). The ICCD cameras was synchronized to the Q-switch of the laser. The LIBS acquisition was performed with a delay of 700 ns and a gate of 5000 ns. Finally, a homemade software developed in the LabVIEW environment was used to control the entire setup, allowing automatic sequences of any selected regions of interest with a preset lateral resolution. The spectral dataset considered in the following represent 1.2 million of spectra (sequence of 2400x500) and was recorded in less than 4 hours.

Interference diagnosis and correction

In order to address the proposed issue, we suggest using PCA and MCR-ALS sequentially.

Thus, PCA will be used to determine whether there is a spectral interference present in the considered spectral domain, and if so, the MCR-ALS method will enable us to separate the spectral contribution of the interferent and the element of interest. The goal here is not to develop these two very classical chemometric approaches in detail, but rather to reintroduce them briefly and focus on specific aspects of this diagnostis and interference correction.

PCA was first developed by Pearson in 1901 [START_REF] Pearson | On lines and planes of closest fit to systems of points in space[END_REF] and later by Hotelling in 1933 [START_REF] Hotelling | Analysis of a complex of statistical variables into principal components[END_REF]. It is a widely used statistical method that aims to simplify the complexity of a high-dimensional data by transforming it into a lower-dimensional space. It is a technique for identifying patterns and relationships in data by reducing the dimensionality of the dataset while retaining the most important information. PCA achieves this by extracting the principal components, which are linear combinations of the original variables that capture the maximum amount of variance in the data. The resulting components are orthogonal and uncorrelated, making it easier to analyze and interpret the data. The singular value decomposition (SVD) [START_REF] Golub | Calculating the Singular Values and Pseudo-Inverse of a Matrix[END_REF], which was developed in the 1960s, is undoubtedly the most widely used method for PCA today. Given D, an n  m matrix containing n spectra, each defined by m wavelengths, its singular value decomposition is calculated as follow:

D = U.S.V t (eq. 1)
The matrix U (of size n  p) contains the p scores of each spectrum, which are their new coordinates in the PCA space. The maximum value that p can take is simply the minimum between the values of n and m. In particular, if we chose this maximum value for p, we could express 100% of the total variance of the matrix D. However, we will see later why we never want to extract 100% of the total variance and thus this maximum allowed number of components. In the context of spectroscopic imaging, the scores are usually represented as scores maps in order to observe their spatial distributions over the sample region of interest [START_REF] Moncayo | Exploration of megapixel hyperspectral LIBS images using principal component analysis[END_REF]. However, this is not really the information that we will be exploiting in this work. Actually, the diagnosis of a potential spectral interference will focus on the utilization of matrices S and V. The matrix S (of size p  p) contains the singular values arranged in decreasing order along its diagonal. Then, squaring the first singular value gives the variance expressed by the first principal component.

The same apply to the successive eigenvalues associated with their principal component. Our goal, when we use PCA, is to find the number of significant principal components that best describe our original data. Thus, we are searching for the intrinsic dimension of our dataset, known as the rank of matrix D, which actually corresponds to the number of independent spectral sources present in it. This rank is obtained through the observation of all the calculated eigenvalues, as represented in what is called a scree plot. If the matrix D contained noiseless data, the evaluation of its rank would be trivial since it would simply correspond to the number of non-zero eigenvalues. This specific situation is depicted in the eigenvaluaes scree plot of Figure 1a, for which we clearly have an observable rank of 2. As part of a PCA applied to a small wavelength range, this would indicate here the presence of two spectral contributions and thus a potential interference between two signals. When we explore experimental data, they inevitably contain noise. This noise accounts for a certain explained variance that will be associated with its own eigenvalues. This situation is shown in Figure 1b, for which we have relatively low noise on our spectral data, indicating a good signalto-noise ratio. In these actual conditions, there are no longer any zero eigenvalues, and we must find a threshold eigenvalue below which we will consider that the principal components are no longer significant. This task remains fairly simple here since the eigenvalues associated with the noise are found on a distinct plateau separated from the first two significant singular values.

When the signal-to-noise ratio further decreases, the eigenvalues associated with the noise will increase to approach those corresponding to the chemical information. The plateau will no longer be observed as shown in Figure 1c but the "elbow" of the graph where the eigenvalues seem to level off will help us to select the threshold. As we can see, this technique allows us to estimate the rank of a matrix and therefore the number of spectral contributions present in the explored spectral domain. The final choice of this rank will of course not be based solely on this observation of eigenvalues, but also on a consistent spectral confirmation found in the principal components contained in the V t matrix (of size p  m). So to summarize, if the estimated rank of the D matrix is 1, there will be no interference and we can proceed directly and unambiguously with signal integration for generating an elemental map. Otherwise, interference will occur and we will need to apply a source separation method (such as MCR-ALS) to generate a corrected elemental map free from this perturbation, which we describe in the next section.

The MCR-ALS method was developed in the 90s to unmix complex signals acquired in analytical chemistry [START_REF] Tauler | Multivariate curve resolution applied to second order data[END_REF][START_REF] Tauler | Selectivity, local rank, three-way data analysis and ambiguity in multivariate curve resolution[END_REF]. The goal of a signal unmixing technique is quite simple as from only a set spectra (potentially containing mixtures), it is possible to simultaneously extract all spectra of pure species present in the chemical system being studied and their relative contributions in each spectrum. It should be emphasized here that this unmixing is achieved without any prior knowledge of the chemical system or even the particular shape of the spectra. So based on the previous rank estimation k > 1, this source separation method allows to decompose the data matrix D (of size n  m) considering a bilinear model:

D = C.S t (eq. 2)
with C (of size n  k) the pure contribution matrix and S t (of size k  m) the matrix containing pure spectra. MCR uses constrained alternating regressions to obtain this decomposition. Only the non-negativity constrain on C and S is used during the calculations, which is natural for LIBS spectral data. For instance, if we had an element that could potentially interfere with another element (i.e., a rank equal to 2), matrix C would allow us to obtain specific distribution images for each element, while matrix S t would help us confirm the consistency of the spectral information taken into account. The computations necessary for PCA and MCR-ALS were executed using the MATLAB environment. However, readers who are intrigued by this methodology can readily explore other programming languages since these algorithms are classical in nature. It should be noted that only raw data will be used in proposed chemometric pipeline.

RESULTS AND DISCUSSION

We have selected this complex rock sample here to illustrate different interference situations that can be observed on both major and minor elements, as well as different signal structures.

The mean spectrum of the dataset in question is shown in Figure 2a, where we can see the elements Si, Zn, Fe, Mg, Al, and Ge. The first element of interest in this study is silicon, whose most intense emission line is located around 288.158 nm. Unfortunately, from the mean spectrum, it is apparent that numerous spectra in the dataset are certainly saturated at this wavelength. This saturation is related to the detector's dynamic range, and therefore to the maximum value it can effectively measure under these given acquisition conditions. It is, of course, unacceptable to use a saturated signal since the acquired value is no longer proportional to the concentration of the element in question. We could of course implement a correction procedure for this saturation, as we have done in our previous work by considering a statistical imputation [START_REF] Nardecchia | Saturated signals in spectroscopic imaging: why and how should we deal with this regularly observed phenomenon?[END_REF], but that is not the strategy that interests us here. Figure 2b provides an integration image obtained by considering a spectral domain from 288.0721 to 288.2621 nm (i.e. the most intense line of Si). Although the spectra may be saturated, such an image allows observation of the areas of the sample that contain silicon and mostly correspond in our case to quartz and micas. However, this saturation phenomenon breaks the concentration dynamic that we should potentially observe with a representation that is quite binary, meaning without too much detail that doesn't really account for the fine variations in Si concentration between the pixels of the image. Just like in photography, we could also say that the image is saturated. Of course, such a situation is unsuitable if our goal is to accurately report the full complexity of our sample, and it is only natural that we need to work on another emission line of silicon, specifically centered at 263 nm. We can zoom in on this spectral region in the mean spectrum of Figure 2a. It can be observed that the average intensity of the silicon emission line is much lower, which avoids the previous saturation problem. As a consequence, the new Si distribution map obtained from the signal integration over the 263.0432 -263.1922 nm spectral range (Figure 2c) seems to highlight more details in the Si-rich mineral phases. On the other hand, a new observation of the mean spectrum in Figure 2a shows that we might have another issue because numerous iron contributions are observed in this spectral sub-domain, and there is a probability that it could interfere with the considered silicon line. This hypothesis is far from unfounded, as shown in Figure 2c where a certain concentration of Si, outside the Si-rich mineral phases seems now to be observed, whereas it was almost absent in the same area in Figure 2b. So, let's get to the heart of the matter of this publication as we need to diagnose this potential interference between Fe and Si. The goal here is not to perform a PCA on the entire spectral domain as usual, but only on a range from 261.2526 nm to 263.9793 nm that encompasses the contribution of silicon which is of interest to us. Figure 3 shows the eigenvalues scree plot resulting from this analysis. Distinguishing the eigenvalues related to noise from the first two that represent chemical information is a straightforward task. This rank of 2 indicates that there is indeed an interference between two signals in this reduced spectral domain. This information is corroborated by the information contained in the first two principal components and their associated scores maps (Figure 4). Firstly, it should be noted that the first two principal components effectively capture the chemical information contained within the dataset, as they together account for approximately 99.68 % of the total variance. Overall, the first principal component highlights the areas of the sample where there is relatively more Si and at the same time less Fe. The second principal component, on the other hand, highlights the phenomenon of interference with a derivative shape observed around 263 nm, and more specifically a positive contribution located at 263.0858 nm and another negative one at 263.1709 nm. Based on this diagnosis of interference between Si and Fe in this spectral domain, it is now appropriate to attempt to separate their respective spectral contributions in order to obtain an image of Si distribution that is consistent with the analytical reality of the sample. It is certainly a task that cannot be performed by PCA since by construction the principal components are perpendicular, which is never the case between two elemental spectra. This is how we will use a spectral unmixing method in the next step, specifically the MCR-ALS method based on a rank equal to two and a non-negativity constraint on the profiles during the decomposition optimization. Moreover, default values for the number of iterations and convergence criterion have been considered in this work because they are suitable for the vast majority of LIBS spectral datasets. Figure 5 displays the two pure spectra extracted from matrix S t and the two asscociated distribution maps extracted from matrix C. The pure component 1 corresponds perfectly to the spectrum of silicon, which indeed exhibits a single emission line in this spectral range centered around 263.13 nm. The pure component 2, on the other hand, perfectly extracts the spectrum of iron with its numerous emission lines, the most intense one being located around 263.11 nm. It is obvious that the interference between these two elements could not be more important, since there is an almost complete overlap between this last emission line and that of silicon, the two being separated by 0.0212 nm in these measurement conditions. This result is all the more remarkable as we make no assumptions about the shape of the pure spectra or even the profile of the emission lines during this decomposition of the data set. There should be no ambiguity on this point, as MCR-ALS is a data-driven analysis that has nothing to do with a spectral fitting procedure. Thus, the extrac-tion of the first pure map allows us to see the distribution of silicon without the spectral interference of iron. By comparing this map to that of Figure 2c, it is easy to understand that in the latter we were simultaneously observing the contributions of both elements, while we thought we were only observing silicon. Finally, if we revisit the Si distribution map extracted by MCR-ALS, we can still observe that there is a low concentration of Si outside the Si-rich mineral phases, which corresponds to trace amounts of Si in sphalerite minerals (i.e., the Fe-rich areas), and which could not have been detected otherwise than by this procedure. From this first example, we can thus see the simplicity and effectiveness of the proposed methodology, first in diagnosing interference and also in its correction, as well.

Let us now turn our attention to a second scenario focused on the search for a minor element in this same sample, namely gallium. Actually, based on the knowledge that geologists have about this particular sample, gallium is an element that could potentially be present in small quantities. This element is known to have an emission line around 394.42 nm, but it potentially interferes with iron which is particularly present in this sample. Figure 6a shows the mean spectrum of the dataset between 294.3042 nm and 294.6399 nm, on which a single line appears to be observed. Figure 6b provides a distribution map obtained by integrating the signal on this spectral range. We notice that this distribution map is quite similar to the iron one extracted by MCR-ALS, as depicted in Figure 5. At first glance, everything suggests that only iron is present on this spectral window. In order to perform a more thorough diagnosis, we conduct a PCA on this spectral domain, with Figure 7a displaying the calculated eigenvalues. In this scenario, only one eigenvalue appears to be significant, which seems to support our previous observations. However, this is not consistent with the first two principal components shown in Figure 7b. In fact, if the rank was indeed 1, the second component should only show noise and certainly not be structured as it is here. Moreover, we can see the specific derivative shape characteristic of an interference between two peaks in the second principal component.

The rank is therefore once again equal to 2. At first glance, one might think that using the scree plot is not a good strategy for evaluating the rank of the spectral data matrix. Actually, this technique is very effective when the variance of the chemical species is much greater than the noise one. It was particularly the case in the first scenario between Si and Fe, where principal components 1 and 2 expressed 76.55 and 23.12 % of the variance, respectively, with 0.33 % of residual variance associated with noise. In this new case, components 1 and 2 expressed 82.37 and 5.12 % of the variance, respectively, with 7.51 % of residual variance associated with noise.

Actually, we do have a contribution from gallium expressed in the second principal component, but its low concentration results in a very small variance compared to the noise, making it impossible to detect it solely from the scree plot. In summary, rank evaluation has therefore to be done by associating the observation of the eigenvalues scree plot and principal components. As a final step, the MCR-ALS extractions considering this rank of 2 are given in Figure 8. So the first pure component extracts an iron emission line, while the second extracts the gallium one, both separated by only 0.063 nm. The first extracted map effectively shows the distribution iron as already seen before. More interestingly here, we can observe the distribution of gallium in the second extracted map even though its concentration is very low but nevertheless well localized in certain areas of the mineral phase considered. By observing the extracted spectra, it could be surprising to have emission lines for Fe and Ga that are quite comparable in intensity.

In fact when using the MCR-ALS method, there is naturally what is called an intensity ambiguity on the extracted pure spectra. In order to remove it, we enforce the extracted spectral profiles to have a norm equal to 1 during the optimization. That is why the extracted intensities for Fe and Ga in Figure 8 appear very close. This is not very serious in this specific context, as the main goal is to identify emission lines by their maximum. However, if we wanted to give a quantitative character for a comparison of the two maps, we would need to rescale them as these two emission lines have different spectroscopic properties. The latter result further highlights the value of the proposed approach, as it is impossible to generate an unbiased distribution map of gallium using the classical integration method.

CONCLUSIONS

LIBS imaging, thanks to its high acquisition speed and sensitivity, is now an elemental imaging technique that has its place among the analytical characterization tools for complex materials. Similar to other spectroscopic imaging techniques, its fundamental principle is based on integrating the signal at a particular wavelength of the element to be imaged. Although a LIBS emission line has a limited bandwidth, the complexity of the explored samples and the richness of LIBS spectral information inevitably induce interference problems. In order to be able to generate representative compound distribution images that are consistent with analytical reality, it is therefore necessary to check if such interference is present, and if so, propose an appropriate signal correction. Through two different scenarios, we first demonstrated how to use PCA to estimate the rank of a spectral matrix, which is the number of independent signals it can contain. The rank was then used to diagnose the presence of interference around the emission line that we wanted to exploit. We also observed that an effective evaluation of this rank can only be achieved through simultaneous interpretation of the eigenvalues scree plot and the principal components, especially when the compound of interest has a low concentration and/or the signal-to-noise ratio is limited. It was subsequently demonstrated that based on confirmed interference, the MCR-ALS method could resolve this issue by separating the contributions of the target element and the interferent both spectrally and spatially.

Figure 1 :

 1 Figure 1: Eigenvalues scree plots considering different levels of noise: a) noiseless data, b) a good sig-

Figure 2 :

 2 Figure 2: A first exploration of the dataset. a) The mean spectrum of the dataset over the whole spectral range and the two spectral integration regions consid-

Figure 3 :

 3 Figure 3: The eigenvalues scree plot obtained from PCA applied on the 261.2526 -263.9793 nm spec-

Figure 5 :

 5 Figure 5: Extractions of the two pure spectral profiles and the two associated distribution maps.

Figure 6 :

 6 Figure 6: a) The mean spectrum of the dataset between 294.3 and 294.65 nm and, b) , nm and

Figure 7 :

 7 Figure 7: a) The eigenvalues scree plot obtained from PCA applied on 294.3042 -294.6399 nm spec-