Ismat Ara Reshma

Margot Gaspard

Camille Franchet

Pierre Brousset

Emmanuel Faure

Sonia Mejbri

Josiane Mothe
email: josiane.mothe@irit.fr

Training Set Class Distribution Analysis for Deep Learning Model -Application to Cancer Detection

Keywords: Medical information retrieval, Image segmentation and classification, Deep learning, Class-biased training

Deep learning models specifically CNNs have been used successfully in many tasks including medical image classification. CNN effectiveness depends on the availability of large training data set to train which is generally costly to obtain for new applications or new cases. However, there is a little concrete recommendation about training set creation. In this research, we analyze the impact of different class distributions in the training data to a CNN model. We consider the case of cancer detection task from histopathological images for cancer diagnosis and derive some useful hypotheses about the distribution of classes in the training data. We found that using all the training data leads to the best recall-precision trade-off, while training with a reduced number of examples from some classes, it is possible to inflect the model toward a desired accuracy on a given class.

Introduction

The huge success of deep learning models in visual recognition [START_REF] Lecun | Deep learning[END_REF] [2] and specifically CNN, drove researchers to explore their use in computer-aided diagnosis system for cancer 1 detection from histopathological or whole slide images (WSIs) [START_REF] Bejnordi | Diagnostic assessment of deep learning algorithms for detection of lymph node metastases in women with breast cancer[END_REF] [4] [START_REF] Liu | Detecting cancer metastases on gigapixel pathology images[END_REF]. This paper contributes to this research topic with the objective to help physicians to detect metastasis by providing them the image regions in which there is a high probability of cancer and the regions where there is no cancer. In that purpose, we employ segmentation (i.e. pixel classification) of the WSIs. Segmentation facilitates readable separation of each class and eases image analysis [START_REF] Srinivasan | Segmentation techniques for target recognition[END_REF].

One of the specificities of CNN is that they need a lot of training examples [START_REF] Dernoncourt | De-identification of patient notes with recurrent neural networks[END_REF]. However, when dealing with biomedical images, precise annotation process needs both expertise and time. As a result, the image data sets that can be built are small. The problem of how to distribute the examples from the different classes to learn is not well studied.

In this paper, we tackle the challenge of deciding which types of examples would be needed to obtain the expected prediction from the trained model. Indeed, when considering segmentation problems, the trained model can be very effective on one class and poorly performing on another. Would the results be different if one class is "over-represented"? Is it better to have about the same number of examples in each class? This paper aims at answering these questions, all related to the balanced/imbalanced nature of the training set [START_REF] Buda | A systematic study of the class imbalance problem in convolutional neural networks[END_REF]. There are some studies in the literature that tackle this problem [START_REF] Buda | A systematic study of the class imbalance problem in convolutional neural networks[END_REF] [9] [10] [11] [12] as it has an adverse effect on classification accuracy.

Among the proposed methods to balance classes, the most straightforward and commonly practiced method is the oversampling of the minority class [8] [9]. However, it can lead to overfitting [START_REF] Chawla | SMOTE: synthetic minority over-sampling technique[END_REF] and concrete studies on the effects are lacking. To address the class-imbalance in metastasis detection the existing methods usually adopt random sampling to select an equal number of positive and negative examples [START_REF] Wang | Deep learning for identifying metastatic breast cancer[END_REF] [START_REF] Liu | Detecting cancer metastases on gigapixel pathology images[END_REF] and thus generate a balanced training set. However, there is no analysis to answer whether this balanced distribution is the optimal one for this task. Kubat et al. [START_REF] Kubat | Addressing the curse of imbalanced training sets: one-sided selection[END_REF] suggested downsampling.

In this paper, we consider both balanced and class-biased distributions of the training set and analyze the selection impact on the model accuracy. The result could serve for deciding which examples should be first added in the training set when there are costly to add. We study the impact on the model of a training biased by an over-represented class (what we call a class-biased training). We run a series of experiments in which we train the model in one hand with an over-representation of the cancer class and on the other hand with an over-representation of the non-cancer class. We also consider balanced sets. We found that balanced data not always lead to the best result and suggest solutions to optimize the model toward a specific accuracy on a target class.

The rest of the paper is structured as follows: we first present related work. We then describe the experimental details with results. Finally, we conclude the paper with some future directions.

Related Work

During the last decades, several studies have been done to facilitate computer-aided diagnosis for metastasis detection from WSIs. Most of the methods used classical machine learning techniques [START_REF] Gurcan | Histopathological image analysis: A review[END_REF]. Studies on utilizing deep learning on this topic are comparatively few and new. From 2015, Bejnordi et al. [START_REF] Bejnordi | Diagnostic assessment of deep learning algorithms for detection of lymph node metastases in women with breast cancer[END_REF] are organizing a worldwide challenge named CAMELYON on this topic in which most of the participants use CNN-based methods. The winning team [START_REF] Wang | Deep learning for identifying metastatic breast cancer[END_REF] utilized the 22 layers GoogleNet, employed rotation and random cropping for data augmentation and color normalization. Liu et al. [START_REF] Liu | Detecting cancer metastases on gigapixel pathology images[END_REF] utilized the updated version of GoogleNet named Inception (V3) [START_REF] Szegedy | Going deeper with convolutions[END_REF]. To avoid class-bias they selected normal and tumor classes with equal probability then extracted patch of that class from a WSI which was selected by uniformly at random; then it was followed by applying several data augmentation techniques including rotation, mirroring, and extensive color perturbation. Sonia M. et. al. [START_REF] Mejbri | Deep Analysis of CNN Settings for New Cancer Whole-slide Histological Images Segmentation: the Case of Small Training Sets[END_REF] proposed a new data set for different types of breast cancer, and an end-to-end deep learning framework for multilabel tissue segmentation utilizing their data set, while network parameters were determined with a deep analysis.

One of the common problems in machine learning is imbalanced data. In the real world, the availability of some classes makes them the over-presented majority, while the scarcity of some classes makes them the under-presented minority. This imbalance of classes representation makes the classification task challenging for a classifier. A limited amount of studies on this topic is available in the literature, especially on deep learning perspective. Some studies suggest data level modification [START_REF] Jaccard | Detection of concealed cars in complex cargo X-ray imagery using deep learning[END_REF] [17], while other studies suggest network architecture level modification [START_REF] Wang | Training deep neural networks on imbalanced data sets[END_REF]. Buda et al. [START_REF] Buda | A systematic study of the class imbalance problem in convolutional neural networks[END_REF] present a comparative study of different methods. Oversampling of the minority class is the most prescribed solution [9] [8]. Kubat et al. [START_REF] Kubat | Addressing the curse of imbalanced training sets: one-sided selection[END_REF] suggested downsampling.

To address the class-imbalance in metastasis detection task the existing methods usually adopt random sampling to select the equal number of positive and negative examples [START_REF] Wang | Deep learning for identifying metastatic breast cancer[END_REF] [START_REF] Liu | Detecting cancer metastases on gigapixel pathology images[END_REF]. However, comparative studies among the different distribution of classes in the training set are absence in this domain. In this paper, we consider this issue. The result could serve for deciding which examples should be first added in the training set when there are costly to add.

Experiments

Data Set and Setting

We use the "metastatic LN" data set from Toulouse Oncopole. The data set contains 61 WSIs (34 for training, 27 for test) of lymph nodes stained with hematoxylin and eosin (H&E), for which an expert pathologist has provided the ground truth segmented masks. The masks are annotated with 3 classes: metastasis/cancer(C), lymph-node(¬C), and other(O). Class O can be either background or histological structures not included in the first two classes C and ¬C, such as adipose or fibrous tissue. Metastasis of 16 primary cancer types and organs have been included in the data set.

Although many other parameters may influence the results, in this research we focus on analyzing the impact of the training examples and the classes they belong to. Although, the WSIs are very large in size, here we utilize them by 8 times downsampling in size to save time and memory resource during analysis. However, the full resolution images will give better result [START_REF] Liu | Detecting cancer metastases on gigapixel pathology images[END_REF]. As a network architecture of CNN, we select U-net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF]. We implement the U-net architecture using Keras [START_REF] Chollet | [END_REF] on the TensorFlow backend. In all the experiments, 20% of the training data is kept for validation. All data are normalized by scaling the pixel value from [0, 255] to [0.0, 1.0] by dividing 255. It makes the convergence of training faster [START_REF] Lecun | Efficient backprop[END_REF]. We utilize Adam [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] as an optimizer. After empirical preliminary evaluation, we set the learning rate of Adam as 1e-05. We use the "categorical cross-entropy" (original U-net) as loss function.

We extract squared overlapping patches of dimension d 2 with stride d/2 pixels from each training WSI that correspond to our training examples; we use d=384 pixels and extract 127,898 patches. We use usual recall, precision, and F-measure to evaluate the model; however, rather than considering the pixellevel evaluation, we consider non-overlapping patches of dimension 500 2 on the predicted test images' masks and make a patch-based evaluation. We compute patch-based recall, precision, and Fmeasure for each test image separately, and finally, take the average result of 27 test images to evaluate the performance of models.

Experiment Design

The statistics in Table 1 depicts that most of the pixels (78%) in the training WSIs belong to the class O.

Results

In Fig. 1 we report the results for both class C and class ¬C. The results are the average results computed from the results of 27 test WSIs. Since recall and precision varies in reverse order, it is important to report both. To evaluate the model performance by considering both recall-precision at the same time, we also report F-measure. Experiments are ordered according to the descending order of precision on class C.

From Fig. 1 we can see that recall is higher than precision for both classes; which implies that in this domain most of the error comes from false positive2 rather than false negative 3 . Another noticeable thing is, unlike it has been reported in [START_REF] Prati | Class imbalance revisited: a new experimental setup to assess the performance of treatment methods[END_REF] for 20 different data sets from UCI machine learning repository [START_REF] Frank | UCI machine learning repository[END_REF], Statlog [START_REF] Michie | Machine Learning, Neural and Statistical Classification[END_REF], and some private data sets, here balanced distribution i.e. experiments (C, ¬C, C&¬C) and (C&¬C) does not produce the best result. On the other hand, the natural distribution i.e. the one that has been used in the experiment (All) is the best trade-off maintaining distribution; it produces reasonable recall and precision for both classes C and ¬C at the same time, however not the best result producing distribution. Since in this research our main objective is helping pathologist in all cancer location detection with less false positive generation, the best trade-off maintaining distribution for both classes is not the desirable one, rather best result producing distribution for cancer (class C) class is the most desirable. For class C, the best precision is found for ¬C-biased training set i.e. for the experiment (¬C, C&¬C), while the best recall is found for C-biased training set i.e. for the experiment (C, C&¬C). However, while considering both recall and precision at the same time i.e. F-measure, ¬Cbiased distribution (¬C, C&¬C) is the best distribution, and C-biased distribution (C, C&¬C) is the worst distribution for class C. According to this result it is obvious that, in the ¬C parts of WSIs, there are some regions which look like class C parts i.e. there are some inter-class similar regions, that is why the absence of enough ¬C examples compared to class C examples in the training set (e.g. experiment (C, C&¬C)) causes false positive for cancer (C) class during test.

When considering the class ¬C, this is the other way around: the best precision is found for C-biased training set i.e. for the experiment (C, C&¬C), while the best recall is found for ¬C biased training set i.e. for the experiment (¬C, C&¬C). However, while considering both recall and precision at the same time i.e. F-measure, C-biased distribution is the best distribution for class ¬C.

In summary, for the cancer class C: In a nutshell for C (resp. ¬C), to increase precision we need ¬C (resp. C) biased training, while to increase recall, we need C (resp. ¬C) biased training. The class O is predicted well whatever the experiment is. Detailed results are presented in Table 2.

Conclusions and Future Work

In this research, we analyzed the impact of class distribution in the training set for metastasis detection task from WSIs while using U-net deep learning architecture. We utilize our own data set, in which one class, the class O is over-represented compared to the two other classes C and ¬C. This class O-biased data leads us to do a series of experiments with two other artificially class-biased training data: C-biased and ¬C-biased data, and artificially balanced data as well. All these artificially created training data were created by downsampling the over presented class O and in some experiments either downsampling C or ¬C class.

We found that balanced data does not lead to the best result in this domain, rather imbalance data leads to the desired accuracy for a given class. On the other hand, while keeping all possible training examples i.e. keeping the natural distribution in the training set causes the best trade-off in recall-precision, however, does not give the best result either in diagnosis perspective. In fact, the imbalanced distribution gives the most desirable result in this domain. More specifically, for cancer class prediction, non-cancer biased training reduces the confusion due to the interclass similar region between cancer and non-cancer class, thus produces less false prediction for cancer class. Although our analysis gives a preliminary flavor of the behavior of the model towards the different distribution of classes in the training set, it demands deeper analysis. Specifically, here the number of training examples was not the same for all experiments, we will solve this issue in our future work. Moreover, here we tested the class distribution for a fixed set of network parameters, in the future, we will test the same setting for different parameter settings.

Fig. 1 .

 1 Fig. 1. Model performance for class C (top row) and ¬C (bottom row) when using different combinations of the patch categories as a training set, i.e. different distribution of the classes in the training set. Here, experiments are arranged according to the descending order of the precision on class C.

  1) class C-biased training makes recall higher, (2) class ¬C-biased training makes precision higher, (3) balanced training causes an average result, and (4) the natural distribution i.e. training with the original distribution of the training set (experiment, (All)) makes the best trade-off in recall and precision (both are reasonable at the same time). For class ¬C class: (1) most of the experiments give more than 0.95 recall, (2) class C-biased training gives the higher precision, (3) balanced training gives an average result, and (4) the natural distribution i.e. training with the original distribution of the training set (experiment, (All)) makes the best trade-off in recall and precision (both are reasonable at the same time).

Table 1 .

 1 Report on the average number (in million and percentage) of pixels of each class in the training and testset.Since the class O is (i) over-represented, (ii) not the class the pathologists focus on, it imposes us to check the impacts of some other artificial distributions of classes in our training set. To create some other artificial distributions of classes, we need to separate the class examples. In that purpose, we define several patch categories based on the pixel classes they belong to. Throughout the paper, we use the term "class" to indicate pixel type, while, "category" to indicate patch type.

		Pixel class Mean in	Mean in %
			million
	Training	C	15.2	11
		¬C	14.6	11
		O	107.4	78
	Test	C	20	14
		¬C	9.8	7
		O	114.8

Table 2 .

 2 Average results computed from the results of 27 test WSIs for the different experiments. Here, R, P, F means the recall, precision, and F-measure respectively.

Throughout the paper, "cancer" and "metastasis" are interchangeably used.

Actually belongs to negative, however, predicted as positive.

Actually belongs to positive, however, predicted as negative.


Serdar Şahin

Antonio Maria Cipriano

Charly Poulliat

Marie-Laure Boucheret

Evolution Analysis of Iterative BICM Receivers with Expectation Propagation over ISI Channels

Keywords: Bit-interleaved coded modulation, inter-symbol interference, expectation propagation, EXIT, evolution analysis

This paper investigates the dynamic behaviour of doubly iterative bit-interleaved coded modulation (BICM) receivers based on expectation propagation (EP). When implemented in the frequency domain, for single-carrier (SC) systems, such receivers achieve attractive performance-complexity tradeoffs in quasi-static wideband channels. With this category of receivers, conventional binary extrinsic information transfer (EXIT) functions are subject to a great number of parameters, including channel realizations, constellation and inner iteration parameters. Hence, this paper proposes a novel extrinsic information evolution analysis method which simplifies the receiver's EXIT function into independent inner transfer functions. The core idea is to track state-evolution dynamics of EP through numerically stable extrinsic variance/information transfer (EXVIT) functions. Numerical results attest to the accuracy of this method for tracking the asymptotic receiver behaviour.

I. INTRODUCTION

Iterative detection and decoding techniques, involving softinput soft-output (SISO) detectors and decoders, have been widely investigated to push achievable communication rate boundaries closer to their theoretical limits. Recent advances on probabilistic message passing algorithms, such as expectation propagation (EP), has led to novel iterative architectures for enabling close-to-optimal detection in a variety of interference-limited applications. The signal processing dynamics of such algorithms are often computationally intensive, and thus, predicting their behaviour is a topic of interest.

The predictability of the iterative detection dynamics is of significant importance both for facilitating algorithm design, or for physical layer link abstraction. For instance, in channel coding, density evolution (DE) was proposed for tracking the dynamics of probability density distributions (PDFs) of exchanged bit log-likelihood ratios (LLRs) between SISO modules [START_REF] Richardson | Design of capacity-approaching irregular low-density parity-check codes[END_REF], [START_REF] Boutros | Iterative multiuser joint decoding: unified framework and asymptotic analysis[END_REF]. Extrinsic information transfer (EXIT) analysis [START_REF] Brink | Designing iterative decoding schemes with the extrinsic information transfer chart[END_REF] simplified DE to an asymptotic single-parameter tracking problem, and it has lead to great achievements on the design and analysis of bit-interleaved coded modulation (BICM) systems with iterative detection.

When considering communications systems, where a codeword is subject to P independent channel realizations (due to fading, pseudo-random precoding or frequency-hopping, for instance) [START_REF] Knopp | On coding for block fading channels[END_REF], the receiver's EXIT function becomes an at least P -dimensional function. Analyzing receiver behaviour under such circumstances requires numerical Monte Carlo integration over each dimension, during the EXIT function synthesis.

Moreover, when the receiver has configurable parameters, the dimensionality of the EXIT function further increases.

This issue has been addressed for soft-input soft-output (SISO) minimum mean squared error (MMSE) linear equalizers with interference cancellation (IC) [START_REF] Tüchler | Turbo equalization using frequency domain equalizers[END_REF], by using analytical approximations and average-mutual information based EXIT models of their sub-blocks [START_REF] Kansanen | An analytical method for MMSE MIMO turbo equalizer EXIT chart computation[END_REF]- [START_REF] Visoz | Semi-analytical performance prediction methods for iterative MMSE-IC multiuser MIMO joint decoding[END_REF]. This paper generalizes this approach to non-linear turbo equalizers involving EP.

A recently proposed doubly-iterative FD equalizer, based on EP, called FD self-iterated linear equalizer with EP-based IC (FD SILE-EPIC), has been shown to achieve attractive performance-complexity trade-offs [START_REF] Şahin | A framework for iterative frequency domain EP-based receiver design[END_REF]. This receiver performs self-iterations, through the exchange of extrinsic Gaussian messages between the equalizer and the demapper modules, prior to decoding. It was shown to improve the performance upon alternative self-iterated receivers that uses hard decision or soft a posteriori probability (APP) feedback, which have been often discarded in the past to their unpredictability and due to high error propagation. These disadvantages are not a concern with FD SILE-EPIC. EP message-passing is shown to be asymptotically predictable through asymptotic mean-squared error (MSE) state-evolution functions [START_REF] Takeuchi | Rigorous dynamics of expectation-propagation-based signal recovery from unitarily invariant measurements[END_REF], [START_REF] Çakmak | Expectation propagation for approximate inference: Free probability framework[END_REF], thanks to its divergence-free "decision device" [START_REF] Ma | Iterative detection in coded linear systems based on orthogonal AMP[END_REF]. However these proofs are limited to Gaussian i.i.d. channels, and predictability of EP in general is only an experimental observation [START_REF] Şahin | A framework for iterative frequency domain EP-based receiver design[END_REF].

This paper investigates the detection dynamics of EP-based BICM receivers through extrinsic message evolution analysis. First, the conventional binary EXIT analysis is carried out in order to outline its dependency on receiver parameters and channel realizations, which makes it costly to compute. Next, a novel evolution analysis method is proposed in our context, which replaces this receiver's EXIT function with analytical receiver models and symbolwise extrinsic information/variance transfer (EXVIT) functions. The synthesis method for this approach is given, and to further illustrate the implications of our proposal, analytical expressions are given for the BPSK and Gray-mapped QPSK constellations. Finally, the asymptotic prediction capabilities of this method is illustrated with numerical results.

The remainder of this paper is organized as follows. The system model and the receiver are given in section II, and the conventional analysis method is discussed in section III. The proposed evolution analysis is discussed in section IV and its implications are assessed in section V with numerical results.

II. SYSTEM MODEL

A. Single Carrier Multi-Block Transmission with BICM

Single-carrier transmissions of P blocks of K symbols is carried out with a BICM scheme 1 . A K b -bit information block b is encoded by a rate-R c forward-error-correction code and then interleaved into a K d -bit d. This codeword is then split into P binary sequences d p , and a memoryless modulator ϕ maps each sequence to x p ∈ X K , with |X | = M and Q = log 2 M . This symbolwise operation maps the vector d p,k [d p,Qk , . . . , d p,Q(k+1)-1 ] to the symbol x p,k , and we use ϕ -1 q (x p,k ) or d p,k,q to refer to d p,kQ+q . Each transmitted block x p goes to through a possibly independent ISI channel, and the received baseband observations are y p = H p x p + w p , for p = 0, . . . , P -1, with H p the channel matrix and w p ∼ CN (0 K , σ 2 wp I K ) the additive white Gaussian noise (AWGN). Assuming H p to be a circulant matrix 2 , whose first line is the impulse response h p = [h p,0 , . . . , h p,L-1 , 0 1,K-L ], L < K being the channel spread, the frequency domain observations y p = F K y p follow

y p = H p x p + w p , (1)
where x p = F K x p , w p = F K w p and H p = F K H p F H K , with F K is the normalized K-DFT matrix with its elements given by [F K ] k,l = exp(-2jπkl/K)/ √ K, and such that F K F H K = I K . Thanks to DFT properties, H p = Diag(h p ) with h p = √ KF K h p , and the FD noise is w ∼ CN (0 K , σ 2 wp I K ).

B. Double-Loop EP Receiver: FD SILE-EPIC

EP is an approximate Bayesian inference algorithm which can be seen as an extension of loopy belief propagation which assign a PDF family to each variable node [START_REF] Minka | Divergence measures and message passing[END_REF], and computes messages by the means of the reverse-information projection.

This concept has been used to derive a doubly iterative frequency domain equalizer for BICM in [START_REF] Şahin | A framework for iterative frequency domain EP-based receiver design[END_REF], the FD SILE-EPIC. In addition to the conventional turbo loop for exchanging extrinsic LLRs between the demapper and the decoder, 1 Notations: Bold lowercase letters denote vectors: let u be a N × 1 vector, then un, n = 0, . . . , N -1 are its entries. Capital bold letters denote matrices: for a N × M matrix A, [A]n,: and [A]:,m respectively denote its n th row and m th column, and an,m = [A]n,m is the entry (n, m). I N is the N × N identity matrix, 0 N,M and 1 N,M are respectively all zeros and all ones.

Let x and y be two random variables, then µx

= E[x] is the expected value, σ 2 x = Var[x]
is the variance and σx,y = Cov[x, y] is the covariance. The probability of x taking a value α is P[x = α], and probability density functions (PDF) are denoted as p(•). CN (µx, σ 2

x ) denotes the circularlysymmetric complex Gaussian distribution of mean µx and variance σ 2

x . We denote φ(x; µ, σ 2 ) exp(-kw|x-µ| 2 /σ 2 )/ πσ 2 /kw where kw = 1/2 for x ∈ R and kw = 1 for x ∈ C. The mutual information between two random variables x and y is defined in bits as I(x; y) E p(x,y) [log 2 (p(y|x)/p(y)]. 2 The circulant channel matrix assumption can be satisfied in practice with signalling schemes such as cyclic prefix insertion. This model can be extended to SC frequency-division-multiple-access (FDMA) and its variants, by incorporating involved subband masks and pulse-shaping into Hp.

there is a loop for exchanging extrinsic symbols between the equalizer and the demapper. The receiver structure and exchanged quantities are illustrated in Fig 1 . At the SISO demapper, a priori and extrinsic bit LLRs are respectively denoted by L a (d p,k,q ) and L e (d p,k,q ), and a priori and extrinsic symbol estimates are respectively denoted x e p,k and x d p,k with respective residual noise variances v e and v d . Each turboiteration (TI) τ = 0, . . . , T consists of S τ self-iterations (SIs) (may depend on τ ), for s = 0, . . . , S τ , and then the decoder is updated with the extrinsic receiver LLRs.

At the initialization of a TI τ , equalizer's messages are reset, with x e(τ,s=-1) p,k = 0, v e(τ,s=-1) p = +∞, and at the initial TI, the decoder message is set to

L (τ =0) a (d p,k,q ) = 0, ∀k, j.
The SISO demodulator computes prior probability mass function (PMF) on transmitted symbols with, ∀α ∈ X ,

P (τ ) p,k (α) ∝ Q-1 q=0 exp(-ϕ -1 q (α)L (τ ) a (d p,k,q )), (2)
and then deduces the posterior PMF, ∀α ∈ X , with

D (τ,s) p,k (α) ∝ φ(x e(τ,s) p,k , α, v e(τ,s) p )P (τ ) p,k (α). (3)
The posterior PMF D

(τ,s) p,k is projected on CN (µ d p,k , γ d p ) through the EP-based reverse-information projection, with µ d(τ,s) p,k E D [x p,k ] = α∈X αD (τ,s) p,k (α), γ d(τ,s) p,k Var D [x p,k ] = α∈X |α -µ d(τ,s) p,k | 2 D (τ,s) p,k (α), γ d(τ,s) p K -1 k γ d(τ,s) p,k . (4)
Then the extrinsic symbol PDF CN (x ⋆ p,k , v ⋆ p ) is computed by dividing CN (µ d p,k , γ d p ) by the prior symbol PDF CN (x e p,k , v e p )

x

⋆(τ,s+1) p,k /v ⋆(τ,s+1) p = µ d(τ,s) p,k /γ d(τ,s) p -x e(τ,s) p,k /v e(τ,s) p , (5)
1/v ⋆(τ,s+1) p = 1/γ d(τ,s) p -1/v e(τ,s) p . (6)
However, as EP is an approximate inference algorithm, damping is used to avoid local fixed points [START_REF] Minka | Divergence measures and message passing[END_REF]. Thus, for s = 0,

x d(τ,0) p,k = x ⋆(τ,0) p,k E P [x p,k ], (7)
v d(τ,0) p = v ⋆(τ,0) p K -1 k Var P [x p,k ], (8)
which is equivalent to the conventional decoder's extrinsic feedback [START_REF] Tüchler | Turbo equalization using frequency domain equalizers[END_REF], and for s > 0, exponential smoothing is used with parameters 0 ≤ β (τ,s) ≤ 1 on the extrinsic estimates

x d(τ,s) p,k = (1 -β (τ,s) )x ⋆(τ,s) p,k + β (τ,s) x d(τ,s-1) p,k , (9)
v d(τ,s) p = (1 -β (τ,s) )v ⋆(τ,s) p + β (τ,s) v d(τ,s-1) p . ( 10
)
At the SISO equalizer, applying DFT on the demapper feedback, the extrinsic outputs are given by FD MMSE filtering

x e(τ,s) p,k = x d(τ,s) p,k + f (τ,s) p,k * (y p,k -h p,k x d(τ,s) p,k ), (11)
v e(τ,s) p = 1/ξ (τ,s) p -v d(τ,s) p , (12)
f (τ,s) p,k = h p,k /[ξ (τ,s) p (k w σ 2 wp + v d(τ,s) p |h p,k | 2 )], (13)
ξ (τ,s) p = K -1 k |h p,k | 2 /(k w σ 2 wp + v d(τ,s) p |h p,k | 2 ), (14)
where k w = 1/2 for real constellations (BPSK), else k w = 1.

At the final self iteration, extrinsic bit LLRs are computed

L (τ ) e (d p,k,q ) = ln α∈X 0 q D (τ,Sτ ) p,k (α)
α∈X 1 q D (τ,Sτ ) p,k (α) -L (τ ) a (d p,k,q ), (15)
with X b q = {α ∈ X : ϕ -1 q (x) = b}, b ∈ F 2 . These LLRs are the processed by the SISO decoder to produce L (τ +1) a (d p,k,q ).

III. CONVENTIONAL EVOLUTION ANALYSIS

A. Binary Extrinsic Information Evolution: EXIT

Extrinsic information transfer (EXIT) functions track the mutual information (MI) carried by extrinsic messages [START_REF] Brink | Designing iterative decoding schemes with the extrinsic information transfer chart[END_REF], to study the behavour of SISO modules within a BICM system.

The SISO receiver is described by the transfer function T REC , which depends on the channel realizations with

I (τ ) E,p = T REC (I (τ ) A ; h p , σ 2 wp , {β (τ,s) } Sτ s=0 ), (16)
where the prior information

I (τ ) A
and the extrinsic information I (τ ) E,p are the average MI between coded bits and respectively the a priori and extrinsic LLRs of the module. Indeed

I (τ ) A (P KQ) -1 p,k,q I(d p,k,q ; L (τ ) a (d p,k,q )) and I (τ ) E,p (KQ) -1 k,q I(d p,k,q ; L (τ )
e (d p,k,q )). The SISO decoder's EXIT function T C is similarly given by

I (τ +1) A = T DEC ({I (τ ) E } P -1 p=0 ). (17)
This is a multi-dimensional EXIT that accounts for different channel realizations over the codeword, but which provides a scalar output due to decoder's averaging effect.

Receiver EXIT functions are synthesized by isolating the concerned SISO module and feeding it prior LLRs matching the desired I A , and then computing an histogram on extrinsic LLRs, through equations ( 2)-( 3) and ( 15), to estimate I E . Hence, a prior LLR generator is needed, and the following assumption and property provide a solution to this end [START_REF] Brink | Designing iterative decoding schemes with the extrinsic information transfer chart[END_REF].

Assumption 1. A priori LLRs of a SISO module are i.i.d. with L

(τ ) a (d p,k,q ) ∼ N ( dp,k,q µ (τ ) a , σ 2(τ ) a
) , with dp,k,q = 1-2d p,k,q . Property 1. If Assumption 1 holds, as LLRs are symmetrically distributed, σ

2(τ ) a = 2µ (τ )
a , and

I(d p,k,q ; L (τ ) a (d p,k,q )) = J(µ (τ ) a ) with J(µ) 1 -L log 2 (1 + e -L )φ(L; µ, 2µ) dL.
Property 1 states that µ a needed for input LLR generation at I A can be obtained by the binary MI function J(•).

EXIT analysis has partially been carried out on FD SILE-EPIC, in order to deduce achievable rates in [START_REF] Şahin | A framework for iterative frequency domain EP-based receiver design[END_REF], and Fig. 2 illustrates its operating principle. However as T REC depends on inner iterations and its damping parameters, computing an EXIT for each possible configuration is impractical.

B. On the Asymptotic Predictability of FD SILE-EPIC

The consistent Gaussian model (Assumption 1) accurately characterizes EXIT functions for many cases, and in particular for the MAP detector, but some sub-optimal receivers' EXIT yield erroneous predictions when I A = 0. Indeed, as one SISO module's prior inputs are provided from another SISO

e (d p,k,q ) ∼ N ( dp,k,q µ (τ ) e , 2µ (τ )
e ), and µ

(τ ) e ≈ J -1 (I (τ ) E ).
The i.i.d. assumption is often true, in the large system limit thanks to interleaving, and Gaussian model holds for demapper output with BPSK and Gray-mapped QPSK constellations. However, the consistent Gaussian approximation of LLRs at the decoder output is lost across turbo iterations due to non-linear dynamics of channel decoding [START_REF] Fu | Stochastic analysis of turbo decoding[END_REF]. Hence, EXIT remains accurate for a few iterations, but its accuracy needs to be experimentally evaluated. A study has been carried out for FD SILE-EPIC in [START_REF] Şahin | A framework for iterative frequency domain EP-based receiver design[END_REF], where finite-length trajectories of average MI were in accordance with the EXIT functions.

IV. PROPOSED EVOLUTION ANALYSIS

A. Symbolwise Extrinsic Information Evolution: EXVIT

Synthesis of EXIT functions for evolution analysis of SISO receivers can be impractical as numerical integrations need to be carried out for each possible channel realization. For FD SILE-EPIC, the number of self-iterations and the damping add additional static parameters which further increase the dimensionality of the EXIT generation procedure. To alleviate this issue, a symbolwise evolution analysis method is proposed here, removing the dependence of the synthesis process on channel and on inner loop parameters.

The asymptotic behaviour of some EP-based algorithms has previously been investigated through state evolution [START_REF] Takeuchi | Rigorous dynamics of expectation-propagation-based signal recovery from unitarily invariant measurements[END_REF], [START_REF] Çakmak | Expectation propagation for approximate inference: Free probability framework[END_REF], where MSE on extrinsic estimates are tracked. Here, the BICM context with the SISO demodulator with prior information, and damping brings additional modelling complexity.

In this section, a symbolwise extrinsic parameter transfer model is proposed, which consists in characterizing

• the equalizer output (demodulator input) with modulation constrained normalized mutual information I L , • the equalizer input (demodulator output) with the covariance v d of the soft symbol feedback. The choice of these measures aims to ensure evolution analysis' ability to track evolution dynamics with sufficient accuracy, and to keep them numerically stable with values on finite intervals. Various candidate measures were evaluated for extrinsic evolution dynamics in [START_REF] Tüchler | Measures for tracing convergence of iterative decoding algorithms[END_REF]. Mutual information and second-order statistics of the extrinsic PDFs (called "fidelity" therein) are measures that maintain accuracy, by avoiding restrictive assumptions on the measured extrinsic PDFs. Regarding the numerical stability, we have I L ∈ [0, 1], and

v d ∈ [0, σ 2
x ], where σ 2 x = 1 is the average symbol power.

B. Transfer Function Synthesis for EXVIT Analysis

As equalizer's extrinsic estimates are unbiased and decorrelated [START_REF] Ma | Iterative detection in coded linear systems based on orthogonal AMP[END_REF], and EP is asymptotically Bayes optimal [START_REF] Takeuchi | Rigorous dynamics of expectation-propagation-based signal recovery from unitarily invariant measurements[END_REF], the following assumption is considered. Assumption 3. The extrinsic symbol outputs of the equalizer are i.i.d. and x e p,k = x p,k + w e p,k with w e p,k ∼ CN (0, v e p ). Property 2. If Assumption 3 holds, then the constrained AWGN capacity is ψ X (v e p ) I(x e p,k ;

x p,k ) = Q -r(v e p ) with r(v e ) = x e log 2 x∈X φ(x e k ; x, v e ) φ(x e k ; x k , v e ) φ(x e k ; x k , v e ) dx e k .
ψ X (•) depends on X , and it does not have a closed form in general. It can be obtained by using Monte Carlo integration.

Hence, the transfer function of the equalizer is defined as

I (τ,s) L,p = T EQU (v d(τ,s) p ; h p , σ 2 wp ), (18)
under Assumption 3, with the analytical transfer function

T EQU (v d(τ,s) p ; h p , σ 2 wp ) ψ X (v e(τ,s) p )/Q, (19) where v e(τ,s) p
is given by equations ( 12)-( 14). To capture the non-linear demapping and EP-feedback behaviour with an extrinsic mutual information information to variance transfer function, the dynamics of the extrinsic symbol PDF CN (x

d(τ,s) p,k , v d(τ,s) p
) is tracked, given the prior information I (τ ) A , and the extrinsic equalizer I (τ,s) L,p . The EP-based feedback from the demapper is modelled with

v d(τ,s+1) p = T EP (I (τ,s) L,p , I (τ ) A , v d(τ,s) p ; β (τ,s) ), (20)
with T EP T Damp • T EP* and where T Damp analytically models damping and T EP* characterizes the behaviour of CN (x

⋆(τ,s) p,k , v ⋆(τ,s) p
). In detail, eq. ( 10) applies damping with

T Damp (v ⋆ p , v d(τ,s) p ; β (τ,s )) (1 -β (τ,s) )v ⋆(τ,s) p + βv d(τ,s) p ,
and the transfer of the pure extrinsic symbols is obtained, following Assumptions 1 and 3, given I L and I A , with with

T EP* (I L , I A ) [1/γ d (I L , I A ) -1/v e ] -1 , (21)
γ d (I L , I A ) 1 KM K-1 k=0 xk∈X f γ (x k , x e k , L a,k ) dL a,k dx e k , f γ (x k , x e k , L a,k ) γ d k (x k , x e k , L a,k )φ(x e k ; x k , v e ) Q-1 q=0 φ(L a,k,q ; (1 -2ϕ -1 q (x k ))µ a , 2µ a ), (22) γ d k (x k , x e k , L a,k ) α∈X |α - α ′ ∈X α ′ D k (α ′ )| 2 D k (α), (23)
D k (α) = Z -1 k φ(x e k ; α, v e ) Q-1 q=0 exp(-ϕ -1 q (α)L a,k,q ), (24)
Z k is such that α∈X D k (α) = 1, µ a = J -1 (I A ), v e = ψ -1 X (QI L ) and L a,k = [L a,k,0 , . . . , L a,k,Q-1 ].
While T EP* has no closed form in general, it only depends on X and on K.

Finally, to complete the characterization of FD SILE-EPIC, SISO demapper's extrinsic LLR output needs to be characterized with respect to the final self-iteration estimates. Following Assumption 3, the EXIT function of a SISO demapper is used

I (τ ) E,p = T DEM (I (τ ) A , I (τ,Sτ ) L,p
).

(25)

In conclusion, symbolwise EXVIT analysis consists in applying transfer functions T EP and T EQU successively, on each block p to obtain {v d(τ,Sτ ) p } P -1 p=0 and then {I (τ,Sτ ) L,p } P -1 p=0 , starting with v d(τ,-1) p = 1, ∀p. Then, the extrinsic output of the overall receiver is {I (τ ) E,p } P -1 p=0 , computed with T DEM . Unlike EXIT analysis, EXVIT has analytical dependence on channel realizations {h p , σ 2 wp } P -1 p=0 and on {β (τ,s) } Sτ s=0 . Numerical integrations are only needed for the two-dimensional T EP* and T DEM functions, which only depend on X and on K.

C. Simplifying the decoder's EXIT function

The decoder's EXIT function in eq. ( 17) requires as many inputs as P , the number of channel realizations over the codeword, which elevates synthesis complexity. A similar issue is noted for evolution analysis of BPSK MIMO systems in [START_REF] Yuan | Evolution analysis of iterative LMMSE-APP detection for coded linear system with cyclic prefixes[END_REF]. The problem is identical from the MI point of view, hence the following assumption is made to address it. Assumption 4. The decoder behaviour is identical for inputs {L e (d p,k )} K-1 k=0 , p = 0, . . . , P -1 and for { Le (d k ′ )} KP -1 k ′ =0 , if they have the same average MI with respect to d.

Thus the SISO decoder's EXIT function is reduced to single dimensional mapping with the effective mutual information

I (τ +1) A = T DEC P -1 P -1 p=0 I (τ ) E . (26)

D. Analytic evolution analysis for BPSK/QPSK

This section provides analytical derivation of T EP* for BPSK constellation (extension to Gray-mapped QPSK is straightforward). Due the symmetry of the constellation, and i.i.d. LLRs,

γ d k (x, x e k , L a,k ) = γ d k (1,
x e , L a ), x e = 1+w e , w e ∼ N (0, v e ), and L a = µ a + w a , with w a ∼ N (0, 2µ a ). Then

γ d (w e , w a ) γ d k (1, x e , L a ) = 1 -|µ d (w e , w a )| 2 , (27)
µ d (w e , w a ) α αD(α) = tanh 1 2 (µ d + w d ) , (28)
µ d µ a + 2/v e , w d w a + 2w e /v e , (29)
with Gaussian integrals therein can be approximated analytically with an n th q order Gauss-Hermite quadrature [START_REF] Steen | Gaussian quadratures for the integrals ∞ 0 e -x 2 f (x)dx and b 0 e -x 2 f (x)dx[END_REF].

µ a = J -1 (I A ), v e = ψ -1 X (I L ) = 2/J -1 (I L ). APP covariance is γ d (I L , I A ) = 1-E

V. RESULTS AND CONCLUSION

In the following, BPSK and QPSK EXVIT functions are evaluated analytically, with n q = 15, and 16-QAM EXVIT, and all EXIT functions are given by Monte-Carlo evaluations.

First, the accuracy of the proposed EXVIT model is evaluated by comparison with the measured MI trajectories of a coded BPSK system with K b = 16384. The closeness of transfer functions to the measured MI trajectories indicates the accuracy of an analysis method. Equivalent EXIT functions in Proakis C channel, [0.23, 0.46, 0.69, 0.46, 0.23], are plotted in Fig. 4, for a signal-to-noise ratio (SNR) of 5 dB. Both EXVIT and EXIT transfer functions appear to be close the MI trajectories for the first few turbo-iterations, hence both methods manage to predict initial turbo-iterations fairly well. Besides, there is a relatively slight difference between both curves, hence they would predict similar decoding thresholds or achievable rates.

Next, to assess the accuracy of EXVIT for predicting more quantitatively, transmissions of K b = 16384 bits over a 10tap Rayleigh fading channel with uniform power profile is considered with β = 0.3. The codeword, obtained with the recursive convolutional code [1, 5/7] 8 is subject to P = 8 channel realizations, and the decoder's bit error rate (BER) and packet error rate (PER) are quantified with regards to its input prior information,. Finite-length simulations are drawn with solid lines on Fig. 5, and EXVIT is used to track the evolution of the extrinsic information of the equalizer, which is fed into the decoder, and to predict the corresponding error rate performance. Predictions appear to be close to the actual Monte-Carlo simulations, for QPSK and 16-QAM constellations, at the zeroeth and the first turbo-iterations. These results attest to the accuracy of the proposed method.

In conclusion, this paper proposes a method for the symbolwise extrinsic analysis of an EP-based, highly non-linear receiver's behaviour. This approach replaces the EXIT function of the receiver, with inner EXVIT functions having analytical dependence on the channel and the receiver parameters. The receiver is shown to be predicted with adequate accuracy over multi-block channels only with a few numerical integrations and independently of the modulation format.

Fig. 1 .

 1 Fig. 1. Double-loop turbo equalization structure.

Fig. 3 .

 3 Fig. 3. Proposed evolution analysis model for T REC .

Fig. 5 .

 5 Fig. 5. BER and BLER prediction with analytical EXVIT.

  we,wa [|µ d (w e , w a )| 2 ], and the

	1
	0.9
	0.8
	0.7
	0.6
	0.5
	0.4
	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	Fig. 4. EXIT & EXVIT functions with [1, 5/7] 8 recursive convolutional code.


Noémie Guirandy

Béatrice Gagnaire

Sandrine Frelon

Thomas Munch

Nicolas Dubourg

Virginie Camilleri

Isabelle Cavalie

Magali Floriani

Caroline Arcanjo

Sophia Murat

El Houdigui

Noemie Guirandy

Simon

REFERENT Olivier

Adverse effects induced by chronic gamma irradiation in progeny of adult fish not affecting parental reproductive performance

Keywords: reproduction, irradiation exposure, zebrafish, risk assessment

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Gamma radiation represents a potential health risk to biota, due to its ability to ionize molécules in tissue. Ionizing radiation is known to induce oxidative stress, DNA damage and apoptosis, which therefore constitute usual molecular markers for evaluating toxicity mechanisms [START_REF] Gagnaire | External gamma irradiation-induced effects in early-life stages of zebrafish, Danio rerio[END_REF][START_REF] Jaafar | Long-Term Effects of Ionizing Radiation on Gene Expression in a Zebrafish Model[END_REF][START_REF] Knowles | An investigation into the effets of chronic radiation on fish[END_REF][START_REF] Kumar | Effects of gamma radiation on the early developmental stages of Zebrafish (Danio rerio)[END_REF]Simon et al. 2011b;[START_REF] Sinha | Radio-protective dosimetry of Pangasius sutchi as a biomarker, against gamma radiation dosages perceived by genotoxic assays[END_REF]. Significant effects in animals (fish, nematode, Daphnia) in terms of survival, reproduction and development have been observed [START_REF] Adam-Guillermin | Genotoxic and reprotoxic effects of tritium and external gamma irradiation on aquatic animals[END_REF][START_REF] Buisset-Goussen | Effects of chronic gamma irradiation: A multigenerational study using Caenorhabditis elegans[END_REF][START_REF] Gagnaire | External gamma irradiation-induced effects in early-life stages of zebrafish, Danio rerio[END_REF][START_REF] Knowles | An investigation into the effets of chronic radiation on fish[END_REF][START_REF] Parisot | DNA alterations and effects on growth and reproduction in Daphnia magna during chronic exposure to gamma radiation over three successive generations[END_REF]Simon et al. 2011b). Moreover, damage effects in fish have mainly been observed for early life stages, which are considered as the most vulnerable to ionizing radiation. Embryogenesis, in addition to gametogenesis and organogenesis, can be affected by ionizing radiation due to the high rate of cell division, proliferation and differentiation (Hurem et al. 2017a;[START_REF] Hurem | Parental exposure to gamma radiation causes progressively altered transcriptomes linked to adverse effects in zebrafish offspring[END_REF]) and enable the consequences of irradiation to be assessed.

In terms of ecological risk assessment (ERA), endpoints on the impact on adult reproduction performance (reproductive success, fecundity, fertility) and on development of early stages (growth, survival) remain the main useful endpoints in characterising the ecological consequences of pollutants, including ionizing radiation. Radiological protection criteria are largely based on data from acute exposure experiments of adult organisms, thus information on the effects of ionizing radiation during sensitive life stages and after chronic exposure are lacking (Hurem et al. 2017a;Hurem et al. 2017b). Overall, few data are available concerning the effects of ionizing radiation in fish. The ecological screening benchmark for a generic ecosystem of 10 pGy h-1 based on the HDR5 (Hazardous Dose Rate for 5% of the species) for radioactive substances was built with five EDR10 (Effect Dose Rate related to a change of 10% for a particular effect) from fish, which involved values ranging from 47 to 20,881 pGy h"1 [START_REF] Garnier-Laplace | A multi-criteria weight of evidence approach for deriving ecological benchmarks for radioactive substances[END_REF]. This generic benchmark dose rate was proposed by the European project, ERICA, for the screening of potential radiological effects [START_REF] Brown | The ERICA Tool[END_REF]. For freshwater and chronic y external exposure, applying a safety factor of 50 to the lowest EDR10 (reproductive endpoint: 516 pGy h-1) led to a predicted no-effect value of 10 pGy h-1 [START_REF] Garnier-Laplace | First derivation of predicted-no-effect values for freshwater and terrestrial ecosystems exposed to radioactive substances[END_REF]. Derived considerationreference levels (DCRLs) i.e., "the dose rate band within which there is likely to be some chance of deleterious effects occurring to individuals of such type of a given type of Reference Animal and Plant (RAP)" indicate a possible reduction of reproductive success for dose rates ranging between 40 and 4,000 pGy h-1 for trout [START_REF] Icrp | Protection of the environment under different exposure situtations[END_REF].

Firstly, the EDR10 did not include the assessment of adult reproduction performance.

Secondly, none of these fish species belong to the cyprinid family. Thirdly, the consequence of parental exposure for offspring generations have not yet been taken into account in the ERA. However, multigenerational studies have become of great interest [START_REF] Buisset-Goussen | Effects of chronic gamma irradiation: A multigenerational study using Caenorhabditis elegans[END_REF]Hurem et al. 2017a;[START_REF] Lemos | Single Low-Dose Ionizing Radiation Induces Genotoxicity in Adult Zebrafish and its Non-Irradiated Progeny[END_REF][START_REF] Parisot | DNA alterations and effects on growth and reproduction in Daphnia magna during chronic exposure to gamma radiation over three successive generations[END_REF]. For fish, the progeny of adult zebrafish exposed to 53 mGy h-1 (60Co gamma radiation) for 27 days showed a 100 % mortality rate occurring at the gastrula stage (Hurem et al. 2017a). Thus, parental exposure can lead to hereditary effects in offspring, probably due to epigenetic mechanisms [START_REF] Herrâez | Paternal contribution to development: Sperm genetic damage and repair in fish[END_REF]Hurem et al. 2017a;[START_REF] Lemos | Single Low-Dose Ionizing Radiation Induces Genotoxicity in Adult Zebrafish and its Non-Irradiated Progeny[END_REF].

As fish are known to be the most radiosensitive organisms among the poikilothermic aquatic animals [START_REF] Garnier-Laplace | First derivation of predicted-no-effect values for freshwater and terrestrial ecosystems exposed to radioactive substances[END_REF], zebrafish, or Danio rerio, were chosen in the present research as a cyprinid model for assessing gamma radiation effects on reproduction performance and larval development. Zebrafish have been widely used for examining effects of ionizing radiation [START_REF] Choi | Radioadaptive response induced by alpha-particleinduced stress communicated in vivo between zebrafish embryos[END_REF][START_REF] Choi | Embryos of the zebrafish Danio rerio in studies of non-targeted effects of ionizing radiation[END_REF][START_REF] Gagnaire | External gamma irradiation-induced effects in early-life stages of zebrafish, Danio rerio[END_REF]Hurem et al. 2017a;Hurem et al. 2017b;[START_REF] Mcaleer | Novel use of zebrafish as a vertebrate model to screen radiation protectors and sensitizers[END_REF][START_REF] Ng | Photon hormesis deactivates alpha-particle induced bystander effects between zebrafish embryos[END_REF]Simon et al. 2011b;[START_REF] Yum | Effects of alpha particles on zebrafish embryos[END_REF]) in addition to transgenerational effects (Hurem et al. 2017a;[START_REF] Kamstra | Ionizing radiation induces transgenerational effects of DNA methylation in zebrafish[END_REF].

Indeed, breeding success, high fecundity and rapid development are the main advantages of this model in performing multigenerational studies [START_REF] Lawrence | The husbandry of zebrafish (Danio rerio): A review[END_REF][START_REF] Simon | Exploring ecotoxicological fish bioassay for the evaluation of uranium reprotoxicity[END_REF].

In this study, adult zebrafish were exposed to four dose rates (0, 0.5, 5 and 50 mGy h-1, 137Cs gamma radiation) over 10 days. The dose rates were higher than those in "hot spots" measured in freshwater ecosystems around Chernobyl (< 0.2 mGy h"1) [START_REF] Bonzom | Effects of radionuclide contamination on leaf litter decomposition in the Chernobyl exclusion zone[END_REF][START_REF] Fuller | Reproduction in the freshwater crustacean Asellus aquaticus along a gradient of radionuclide contamination at Chernobyl[END_REF][START_REF] Lecomte-Pradines | Soil nematode assemblages as bioindicators of radiation impact in the Chernobyl Exclusion Zone[END_REF][START_REF] Lerebours | Impact of Environmental Radiation on the Health and Reproductive Status of Fish from Chernobyl[END_REF]. Reproduction was initiated and the progeny were then exposed or not to the same dose rates over 96-120 hours.

The objectives of this study were to evaluate (i) the adult reproductive performance, (ii) the effects in the progeny of irradiated parents and (iii) the responses at the molecular and organism level. Effects on adults were assessed by reproductive performance and genotoxicity (comet assay). Effects on the progeny were assessed using the survival rate (%) and the genotoxic and oxidative stress effects. The progeny were also placed in non-irradiated conditions (F1 recovery) over 120 hours to evaluate the impact of adult irradiation on the progeny (generational effects).

Complementary objectives concerned the increase of the exposure duration on the effects and the time necessary to obtain reproductive resilience: for the two lowest dose rates tested (lowDR: 0.5, 5 mGy h-1), adult F0 exposure duration was increased to 24 days; for the highest dose rate (highDR: 50 mGy h-1), 10 day-irradiated adults (F0) were placed in non-irradiated conditions over 63 days (F0 recovery). Adult performance, progeny survival and molecular effects were also evaluated during these complementary experiments.

MATERIALS AND METHODS

Fish husbandry

The project (APAFIS#15821) was authorized by the IRSN ethics committee N°81 (EU 0520) in an application under the directive 2010/63/UE relating to animal care. The study was conducted on wild-type zebrafish that were kept, reproduced and irradiated in a zebrafish housing system (Zebtec Tecniplast stand Alone, Varese, Italy) with recirculating fresh water.

Adult fish were acclimatised over 2-3 weeks to tap water + 20% demineralized water renewed daily (Aquadem, Veolia, France) (pH=7.4 ± 0.2, conductivity = 398 ± 2 qS cm-1, T=28.4 ± 0.3 °C), with a 14 h light/10 h dark cycle photoperiod. The fish were fed ab libitum twice a day with commercial flakes (Tetramin®).

Adult and embryo exposure

Figure 1 shows the exposure duration and endpoints for the experiments. Nominal dose rates were 0.5 and 5 mGy h-1 for the low dose experiment (lowDR) and 50 mGy h-1 for the high dose experiment (highDR). As both experiments (lowDR and highDR) were not carried out at the same time, control fish conditions were implemented for each experiment. Gammarays were emitted from a 137Cs source (444 GBq, 662 keV, IRSN-MICADO-Lab platform). Dose rates were simulated using MCNP5 software and measured using thermoluminescent dosimeters (Chiyoada Technologies, Japan) and the values represented between 91.1 and 100.8% and between 80 and 120% of the nominal low DR and high DR values, respectively. Two control conditions were kept in a separate room (60-80 nGy h"1).

The population density of adult fish was 0.7 L g"1. For the low dose rate experiment (lowDR), 20 adult fish per condition (female: 0.66 ± 0.13 g, n=24, male: 0.50 ± 0.065 g, n=11) were irradiated over 10 and 24 days. For the high dose rate experiment (highDR), 24 adult fish per condition (female: 0.38 ± 0.06 g, n=6, male: 0.40 ± 0.07 g, n=6) were irradiated over 10 days. To keep the radiation exposure as long as possible, the daily control of abiotic parameters (pH, conductivity, Temperature), the animal welfare and the feeding process were carried out in less than one hour, five times per week. During this hour, irradiation was stopped in order to access to the tanks. Food was supplied to the fish twice a day by automatic suppliers. During the weekends, the control of these parameters was achieved through the use of cameras, allowing animal welfare to be monitored without interrupting the irradiation. The preparation of reproduction and egg collection required stopping the irradiation during four hours. After 24 d of exposure, the adults from lowDR were sacrificed and the gonads were collected. After 10 d of exposure, six adults from highDR were sacrificed and the gonads were collected. Six other adults were introduced into non-irradiation conditions (F0 Recovery).

For each reproduction event, embryos were obtained from 10 spawning genitors (i.e. replicates) for lowDR and 12 genitors (i.e. replicates) for highDR per condition. Each group, consisting of one male and one female, was placed in specific spawning aquariums to avoid egg predation in the zebrafish housing system. Adults were irradiated during reproduction.

After spawning, the egg viability (3-4 hpf, hours post fertilisation) of each spawn was confirmed when the blastula stage was reached. The embryos (2.6 ml/egg) were then reintroduced into small beakers (0=9 cm) in the zebrafish housing system to be irradiated (at the same dose rate as the adult groups (F1 irradiated group) or without irradiation (F1 Recovery group) and larvae were fed starting from 5 dpf (days post fertilisation) (artificial commercial food ST-1, Aqua Schwarz GmbH). The culture medium of the embryos was the same as that of the adults and 10% was replenished daily.

Ecologically-representative endpoints for adults

For the lowDR experiment, adult F0 reproductive performance (n=10 couples per condition) was assessed after 10 and 24 days of exposure for both dose rates tested. Endpoints concerned the reproductive success (number of couples that spawned), the fecundity (number of eggs per female) and the egg survival rate at 3 hpf (fertilization rate). For the highDR experiment, F0 reproductive performance was assessed after 10 days of irradiation (n=12 couples per condition) and after 6, 36 and 63 days in non-irradiated conditions (F0 Recovery, n=6 couples) (Figure 1).

Ecologically-representative endpoints and oxidative stress analysis for progeny

For both experiments, the progeny survival rate (%) was assessed after 24 and 48 h in the control, irradiated and non-irradiated (recovery) conditions. Complementary experiments consisted of irradiating 3 hpf-eggs at 50 mGy h"1 over 96 h (30 eggs from three spawns per condition) to measure the survival rate.

For the lowDR experiment, two pseudo-replicates of 80 eggs originating from three spawns per condition including the control, irradiated and non-irradiated conditions, were followed to measure the progeny survival rate over 1, 2, 10 and 22 d. For the highDR experiment, 30 eggs from six spawns of the three conditions were tracked over 5 d (120h).

For the highDR experiment, photographs of 72 hpf-larvae were recorded. Morphology (whole body size, surface of yolk reserve), malformations and cardiac edema were then assessed using software (Danioscope image analysis system version 10.0, Noldus). Analyses were made on 10 72 hpf-larvae per condition after 10 d F0 exposure (F0Irr. 10d) and after F0 recovery at 6 days (T10d+R6d) and at 36 days (T10d+R36d).

Reactive oxygen species (ROS) production was measured in F1-progeny from the lowDR experiment using a protocol adapted from Hurem et al, (2017) and [START_REF] Gagnaire | External gamma irradiation-induced effects in early-life stages of zebrafish, Danio rerio[END_REF] Given the high larval mortality rate, no measurements were made during the highDR experiment. ROS production was determined using the fluorescent probe (2', 7'dichlorodihydrofluorescein diacetate (H2DCFDA, Sigma-Aldrich, St. Louis, USA)) in 10 larvae per condition (larvae exposed from 3-4 hpf to 4 or 10 days originating from 10 d-adult and 24 d-adult reproduction). Through the oxidation of H2DCFDA in dimethylsulfoxide (DMSO, Sigma-Aldrich, St. Louis, USA) water by ROS (mainly H2O2) the molecule was converted into 2', 7' dichlorodihydrofluorescein (DCF), which is highly fluorescent. The reported wavelengths for the measurement of DCF fluorescence are 500 nm for excitation and 525 nm for emission (TECAN Infinite M1000, Switzerland).

Genotoxic effects in progeny and adult

The genotoxic effects induced by gamma irradiation in the developmental stages (1 d, 4 d, 10 d for lowDR and 1 d for highDR experiments) and in gonads (10 d, highDR experiment) of zebrafish were evaluated using the alkaline comet assay as described in Sing et al, (1998) (1988) with modifications (Simon et al. 2011a;[START_REF] Simon | Toxicokinetic and toxicodynamic of depleted uranium in the zebrafish, Danio rerio[END_REF]. After centrifugation (110 g, 10 min, 8 °C, Eppendorf, 5427R, Germany), pellets were suspended in 1 mL of L15-HEPES and used immediately. Cells were counted on a Malassez cell and their viability was assessed using trypan blue. Two hundred nucleoids per slide were analysed at *400 magnification under a fluorescence microscope (Nikon Eclipse E600) equipped with a 515 560 nm excitation filter. Comet pictures were analysed using Comet IV software (Perceptive Instruments). This assay was performed on three pools of ten 24-hpf eggs, on 10 individual 96-hpf larvae and on three pools of whole gonads per sex and per condition. The Tail Moment was defined as the percentage of DNA in the tail multiplied by the length between the centre of the head and tail.

Statistical analysis

All data are presented as means ± SD with significance taken atp<0.05. A comparison between the control and irradiation or recovery exposures was performed. Before the statistical analyses, the normality and homogeneity of the variance were tested using the Shapiro-Wilks and Fisher tests, respectively. The T-test and one or two ways-ANOVAs were used when data were normally distributed. The non-parametric test (Kruskal-Wallis) was used when data were not normally distributed.

RESULTS

There were no instances of adult fish mortality during the experimental periods (control, low DR and high DR experiments).

Cumulative doses after exposure conditions

For the LowDR experiment, cumulative doses in adults ranged between 120 and 2880 mGy after 10 and 24 days of exposure, respectively. For the highDR experiment, the cumulative dose in adults was 12 Gy (SD Table 1). For the progeny, maximal cumulative doses ranged from 264 to 2640 mGy for the lowDR experiment and 6 Gy for the highDR experiment (SD Table 1).

Adult performance (reproductive success, fecundity, total egg number and 3hpf-egg mortality)

For the highDR experiment, all females (n=12 per condition) spawned after 10 days of exposure. For the lowDR experiment (n=10 per condition), reproductive success was 100% and 80% for both the irradiated conditions and control conditions, respectively.

Figure 2 shows the fecundity (number of eggs per female) after 10 days of exposure for both experiments. High inter-individual variability was observed in all conditions. A significant difference (Kruskal-Wallis, p=0.03) was observed between 0.5 mGy h-1 (240 eggs ± 132) and control (364 eggs ± 123) conditions. In the control LowDR, 43% of all spawns ranged between 101 and 300 eggs and 57% of spawns had higher than 300 eggs. At 0.5 mGy h-1, 20% of all spawns produced less than 100 eggs. At 5 mGy h-1, no significant difference in fecundity (413 eggs ± 148) was observed even though 89% of spawns had more than 300 eggs. At the high dose rate (50 mGy h-1), a change in the size of spawns was also observed, with an increase in the number of spawning events (75%, 9/12), providing between 101 and 300 eggs compared to the control (42%, 5/12). A significant difference was observed between both control fish fecundity (lowDR: 364 eggs ± 123 per female (n=7) versus the highDR: 203 ±117 eggs per female (n=12), p=0.042 Kruskal-Wallis test) and egg quantity distribution.

The quality of oocytes was assessed by the survival 3hpf-progeny, indicating the number of fertilized versus non-fertilized eggs. The survival rate at 3 hpf remained high (>89%) without any significant difference between exposure conditions (SD Figure 1). Over the 50 spawns monitored, only two presented a survival rate ofless than 80%. Almost 85% of the spawns presented a survival rate of 90-100%.

Reproductive success after 24 days of lowDR exposure was not impacted by irradiation; 80, 90 and 100% of couples reproduced for the controls, 0.5 and 5 mGy h-1, respectively. The significant difference in fecundity previously observed after 10 days between the control and 0.5 mGy h-1 was not observed after 24 d of exposure. Fecundity was 375 ± 102, 289 ± 138 and 357 ± 138 eggs per female for the controls, 0.5 and 5 mGy h-1, respectively. In the controls, 37.5% of spawns contained between 101 and 300 eggs and 62.5% contained more than 301 eggs, as observed after 10 days. At 5 mGy h-1, 75 % of spawns presented more than 301 eggs, as previously observed after 10 days of exposure. The survival rate at 3 hpf-egg was close to the one measured after 10 days of adult exposure.

Progeny survival and size

Figure 3 shows F1 progeny survival rate (%) measured at 24 and 48 h for all exposure conditions of both experiments. For the lowDR experiment, the survival rate was higher than 87%, with no significant difference between the conditions. For the highDR experiment, a significant difference was observed between the control and larvae exposed to 50 mGy h-1 for 24 h (p=0.02) and 48 h (p=0.006). Significant differences were also observed between the control and F1 recovery conditions for both times (p=0.015 and p=0.006 for 24 and 48 h, respectively). Figure 4 shows the survival rate (%) in F1 progeny originating from the lowDR experiment. Survival rates were higher than 80% and 60% at 2 and 10 d, respectively, for all exposure conditions. No significant effect of treatments and control was observed in the progeny coming from 10 d-irradiated adults. Similar results were observed for the progeny coming from 24 d-irradiated adults. A significant différence was observed between 5 and F1R5 (Kruskal-Wallis test: p=0.049, n=6) at 22 days of exposure. No significant differences were observed for the hatching rate (%) at 48 h (data not shown).

For the irradiated and non-irradiated (F1 Recovery) larvae (Figure 5), 100% died after 120 h of highDR exposure, although the average survival rate for the control condition was 84 ± 11%. In the control condition, the mortality rate was low and remained constant from 24 hpf. F1 irradiated (51%) and F1 Recovery (58%) survival rate at 24 hpf was low compared to the control and ranged between 16 to 96%, indicating a high spawn variability (SD Figure 2). Drastic effects seemed to appear more rapidly for F1 irradiated larvae than for F1 Recovery larvae (SD Figure 2).

Figure 6 shows the survival rate (%) in F1 progeny coming from the highDR experiment where adults were placed in non-irradiated exposure conditions (F0 Recovery) over 63 days. Fish were induced to spawn after 6, 36 and 63 days. Drastic effects of adult irradiation on survival progeny rate lasted for at least 6 days (35 ± 22, n=11 spawns) and until 36 days (48 ± 37, n=8 spawns). All larvae alive at 48 h from F0R0d, F0 R6d and F0 R36d, died at 96 h. After 63 days in non-irradiated conditions, the progeny survival rate remained high (>85%, n=11 spawns) and no significant difference was observed compared to the control until 96 h.

For the highDR experiment, the body sizes of F1 irradiated and F1 Recovery larvae decreased significantly compared to the control (Figure 7). Similar results were also observed for nonirradiated 72 h-larvae originating from F0 recovery conditions after 6 days. After 36 d in nonirradiated conditions (F0 R36d), the body sizes of non-irradiated progeny showed no significant difference compared to the controls although 100% of mortality at 120 h was observed. The surface of vitellus and pericardia area also showed no statistical différence with the controls (data not shown).

Oxidative stress

Figure 8 shows ROS production in F1-progeny coming from the lowDR experiment.

Irradiation at 5 mGy h-1 led to an increase of ROS production in 4 d-exposed larvae coming from 24 d-adult exposure. However, F1 R progeny exposed over 4 d at both dose rates showed a significant increase in ROS production for larvae coming from 10 d-and 24 d-adult exposure. No effects were observed in larvae (irradiated and recovery) exposed over 10 d (Figure 10B).

Genotoxic effects

Figure 9 shows DNA damage measured in progeny coming from 24 d-adults in the lowDR experiment, expressed by the tail moment. The progeny were placed in irradiated and non-irradiated conditions (F1 Recovery) over 10 days. Significant DNA damage was noticed at 4 d for irradiated (0.5 mGy h"1: 11.3 ± 4.3%; 5 mGy h"1: 14.4 ± 2.1%) and non-irradiated larvae (F1R: 0.5 mGy h-1: 8.4 ± 3%) compared to the controls (x10). At 10 d, the tail moment showed no difference between the conditions.

Figure 10A shows DNA damage expressed by the tail moment in the progeny coming from 10 d-adult fish from the highDR experiment. The progeny was collected in irradiated and non-irradiated conditions (F1 Recovery) for 24 h. The high mortality rate did not allow larval collection at 4 and 10 d. A significant increase of the tail moment was observed between the control, irradiated (x6.5) and non-irradiated (x5) conditions. 10B-C shows DNA damage in the gonads of males and females after 10 days of irradiation. DNA damage increased for both sexes compared to the control. The effects were more pronounced for males (x3) than for females (x1.7).

DISCUSSION

In the present work, embryo-larval and adult fish stages were exposed to 0.5, 5 and 50 mGy h"1 (137Cs gamma radiation) to augment the dataset of gamma ray effects after parental and progeny exposure.

Zebrafish as a relevant model for multigenerational studies

Reproduction was achieved for almost all couples and with a high egg survival rate (93 ± 7 % at 3 hpf for both control conditions, n=19), confirming the relevance of this model for multigenerational studies [START_REF] Lawrence | The effects of feeding frequency on growth and reproduction in zebrafish (Danio rerio)[END_REF][START_REF] Simon | Exploring ecotoxicological fish bioassay for the evaluation of uranium reprotoxicity[END_REF]. Differences in reproductive performances were observed between the controls used in both lowDR and highDR experiments. The body weights of the control adults in both experiments was significantly different and could explain the differences in fecundity. Indeed, zebrafish fecundity, and more generally reproduction performance, can be influenced by the quality of the diet, the female body size and environmental enrichment [START_REF] Karga | Effect of different feeds on the growth, survival and reproductive performance of zebrafish, Danio rerio (Hamilton, 1822)[END_REF][START_REF] Lawrence | The husbandry of zebrafish (Danio rerio): A review[END_REF][START_REF] Lawrence | The effects of feeding frequency on growth and reproduction in zebrafish (Danio rerio)[END_REF][START_REF] Wafer | Effects of environmental enrichment on the fertility and fecundity of zebrafish (Danio rerio)[END_REF]. It is important to note that although zebrafish reproduce easily in laboratory conditions, assessing inter-individual variability of reproductive performances requires a large number of couples.

No effect of irradiation was observed on adult reproduction performance

For the testes dose rates, irradiation did not alter the reproductive capacity. Many pollutants which contribute to oxidative stress are known to alter reproductive performance, indicating that this physiological function may be sensitive to changes in the environment [START_REF] Fabbender | Reproductive and genotoxic effects in zebrafish after chronic exposure to methyl methanesulfonate in a multigeneration study[END_REF][START_REF] Newman | Embryonic oxidative stress results in reproductive impairment for adult zebrafish[END_REF][START_REF] Simon | Exploring ecotoxicological fish bioassay for the evaluation of uranium reprotoxicity[END_REF][START_REF] Wang | Disruption of zebrafish (Danio rerio) reproduction upon chronic exposure to TiO2 nanoparticles[END_REF].

Perturbation of reproduction was previously observed in other fish species. [START_REF] Woodhead | The effects of chronic irradiation on the breeding performance of the guppy, Poecilia reticulata (osteichthyes Teleostei)[END_REF] demonstrated that the total fecundity of guppies (Poecilia reticulata) was markedly reduced at dose rates of 1.7, 4 and 12.7 mGy h-1 without drastic impacts on the mortality rate and survival of offspring. [START_REF] Rackham | Effects of Chronic y-irradiation on the gonads of adult Ameca Splendens (Osteichthyes: Teleostei)[END_REF] demonstrated that spermatogenesis of adult butterfly splitfins (Ameca splendens) was disrupted (no production of sperm) after 7.3 mGy h-1 of exposure over 52 days and that developing oocytes were less sensitive to the effects of radiation than spermatogenesis. [START_REF] Knowles | An investigation into the effets of chronic radiation on fish[END_REF] observed a significant decrease in adult zebrafish in the mean number of eggs per spawn after 30 days at 7.4 mGy h-1. Compared to this study, the toxic modes of action seem to be strongly influenced by the biological model and the experimental conditions of the dose rates. Under our experimental conditions, adult zebrafish stage did not exhibit sensitivity.

Drastic effects from irradiation on progeny survival were observed and transferred from adult fish

Drastic effects on progeny were only observed after high dose rate exposure and certainly had a detrimental effect at the population level. After exposure of adults to 5 mGy h-1 over 10 or 24 days (cumulative dose rates of 1.2 and 2.8 Gy, respectively), no effect on progeny survival rate was observed until after 22 days. The range of these induced effects (5 50 mgGy h-1) is narrow and encourages us to more precisely determine the EDR10. The nonirradiated progeny of 27 d-F0 exposed to 53 mGy h-1 (34.3 Gy) previously showed a 100% mortality rate occurring at the gastrulation stage (8 hpf) (Hurem et al. 2017a). In this study, drastic effects appeared at a lower cumulative dose (12 Gy) for the same dose rate. These results raise questions regarding the best criteria (cumulative dose versus dose rate) for measuring gamma radiation exposure in the ERA.

The experimental design for the lowDR and highDR experiments did not allow the identical cumulative dose to be obtained. It could potentially be beneficial to vary the duration of exposure (1d at 50 mGy h-1; 100d to 0.5 mGy h-1) to compare the effects obtained at the same cumulative dose.

Adverse effects seemed to be due to adult exposure since (i) irradiated and recovery progeny showed identical effects compared to the control, and (ii) direct irradiation of embryos at this high dose rate did not cause significant mortality as confirmed in this study and by Simon et al, 2011. Vertebrate embryos are particularly sensitive to ionizing radiation, due to a high rate of cell division and migration [START_REF] Hu | Developmental toxicity and oxidative stress induced by gamma irradiation in zebrafish embryos[END_REF]Hurem et al. 2017a;[START_REF] Jarvis | DNA damage in zebrafish larvae induced by exposure to lowdose rate y-radiation: détection by the alkaline comet assay[END_REF][START_REF] Rhee | Gamma irradiation-induced oxidative stress and developmental impairment in the hermaphroditic fish, Kryptolebias marmoratus embryo[END_REF]. The sensitivity of early stages (development and antioxidant enzymes activities) has already been demonstrated; 6hpf-embryos were more sensitive than 12-and 24-hpf embryos to gamma irradiation (0.01-1 Gy) [START_REF] Hu | Developmental toxicity and oxidative stress induced by gamma irradiation in zebrafish embryos[END_REF]). However, we demonstrated here that the sensitivity of the progeny to ionizing radiation was particularly high when they originated from irradiated parents.

Parental effects observed in the highDR experiment were reversible, as they disappeared when adults were placed in non-irradiated conditions for between 36 and 63 days.

These results suggest F0 recovery of reproductive capacity. The F0 adults zebrafish exposed to 53 mGy h-1 during 27 days (31 Gy) and placed in non-irradiated conditions failed to produce viable offspring 1.5 year after irradiation (Hurem et al. 2017a). The differences in terms of experimental design and cumulative dose between the present study and that of Hurem et al. (2017) encouraged us to elucidate the mechanisms behind the transfer from adult to progeny and the F0 recovery induction over time.

The earliest stages of embryonic development rely on maternai products that are generated during oogenesis and supplied to the egg. Yolk lipoprotein nutrients, vitamins, hormones, mRNA transcripts, and DNA methylation statuses have been identified as markers of egg quality. The damage to these maternal products could also explain the drastic effects observed in the progeny. Note that the period of maternal control of embryonic development varies among animals and could explain difference of ionizing radiation effects between species [START_REF] Abrams | Early zebrafish development: It's in the maternal genes[END_REF][START_REF] Vastenhouw | The maternal-to-zygotic transition revisited[END_REF]). Among transferred maternal products, cortisol is essential for early development [START_REF] Faught | Maternal stress-associated cortisol stimulation may protect embryos from cortisol excess in zebrafish[END_REF][START_REF] Nesan | Role of glucocorticoid in developmental programming: Evidence from zebrafish[END_REF][START_REF] Nesan | Maternal Cortisol Mediates Hypothalamus-Pituitary-Interrenal Axis Development in Zebrafish[END_REF]). Then, de novo synthesis of cortisol starts after hatching (48 hpf) [START_REF] Nesan | Maternal Cortisol Mediates Hypothalamus-Pituitary-Interrenal Axis Development in Zebrafish[END_REF]. Finally, elevated cortisol levels in embryos leads to the same effects (mortality, pericardial oedema and heart malformation) [START_REF] Nesan | Embryo exposure to elevated cortisol level leads to cardiac performance dysfunction in zebrafish[END_REF] observed in this study.

Moreover, high levels of cortisol in females may directly impact estradiol production, possibly affecting vitellogenin production and its incorporation into the oocyte, leading to drastic effects in the progeny. In this study, we hypothesize that the high dose rates of gamma irradiation could have led to an alteration of the cortisol deposition and its transfer to eggs, which may have resulted in altered offspring phenotypes.

ROSproduction and genotoxicity after irradiated and recovery conditions

From potentially toxic mechanisms, the genotoxicity and ROS induction were assessed.

Gamma irradiation is known to induce ROS formation in zebrafish larvae [START_REF] Gagnaire | External gamma irradiation-induced effects in early-life stages of zebrafish, Danio rerio[END_REF][START_REF] Jarvis | DNA damage in zebrafish larvae induced by exposure to lowdose rate y-radiation: détection by the alkaline comet assay[END_REF]. In this study, ROS production compared to the control was increased after 4 d of exposure of larvae originating from adults exposed during 10 and 24 days. Recovery larvae showed ROS production, without being irradiated. ROS production was higher in F1 recovery larvae than in irradiated larvae (originating from F0-10d). Once again, adult exposure led to high ROS production in larvae. This would seem to be a conséquence of an effect inherited from the parents. Results were similar to those observed in other exposure conditions (dose rate, recovery duration) by Hurem et al, 2017. As no effect was observed in 10 d-larvae, the oxidative stress induced by gamma irradiation seems to be transitory. The activities of antioxidant enzymes are known to change in a developmental stage-dependent manner. However, larval ROS production in 4 d larvae was increased by gamma irradiation and persisted in F1 recovery condition. We hypothesized that under our experimental conditions, irradiation of the progeny led to an induction of protective agents that could counteract ROS production and re-establish a healthy cellular redox balance. Antioxidant enzyme activities could be assessed in further experiments in 10 d-irradiated larvae to test this hypothesis. Significant genotoxic effects were observed at 4 d-irradiated and non-irradiated progeny coming from adults exposed in the lowDR experiment (0.5 and 5 mGy h"1) during 24 days.

High inter-individual variability was however observed for the lowDR experiment, preventing the highlighting of significant differences.

Genotoxicity has previously been demonstrated in eggs exposed to gamma rays in chronic or acute experiments [START_REF] Gagnaire | External gamma irradiation-induced effects in early-life stages of zebrafish, Danio rerio[END_REF][START_REF] Kumar | Effects of gamma radiation on the early developmental stages of Zebrafish (Danio rerio)[END_REF]Simon et al. 2011b) or to non-radioactive pollutants [START_REF] Kosmehl | DNA damage induced by genotoxicants in zebrafish (Danio rerio) embryos after contact exposure to freeze-dried sediment and sediment extracts from Laguna Lake (The Philippines) as measured by the comet assay[END_REF][START_REF] Vicquelin | A new spiked sediment assay using embryos of the Japanese medaka specifically designed for a reliable toxicity assessment of hydrophobic chemicals[END_REF]. In this study, tail moment values were comparable to those measured in eggs/larvae exposed over 4 d at 24 mGy h-1 [START_REF] Gagnaire | External gamma irradiation-induced effects in early-life stages of zebrafish, Danio rerio[END_REF]. Thus, these results suggest an increase in the intensity of genotoxic effects due to parental irradiation and confirm the molecular effects inherited from the parents. The genotoxic effects decreased at 10 d, suggesting a better efficiency of DNA repair mechanisms at this larval stage, potentially related to a better efficiency of the antioxidant System. It would be interesting to measure some of the DNA repair mechanisms (as gamma H2AX activity) in order to confirm this hypothesis.

Irradiation of adults at high dose rates led to significant genotoxic effects on irradiated and non-irradiated progeny as early as 1 d, unlike results obtained at lower dose rates.

However, the levels of genotoxic effects at 1 d remained lower than the ones measured at 4 d in the lowDR experiment which did not lead to a high mortality rate. The comparison between the different stages of development remains difficult and we have to take into account possible differences in reparation mechanism induction between the different stages to explain the relationship between mortality and genotoxicity effects. We suggest that the early live stage could be more sensitive than the later life stage.

High irradiation exposure led to significant genotoxic effects on adult gonads. However, the effects were lower than those measured after low uranium waterborne exposure [START_REF] Simon | Toxicokinetic and toxicodynamic of depleted uranium in the zebrafish, Danio rerio[END_REF]). Significant differences were also observed in the controls between males and females, as previously observed in other studies [START_REF] Simon | Toxicokinetic and toxicodynamic of depleted uranium in the zebrafish, Danio rerio[END_REF]. Moreover, irradiation effects seemed more pronounced for males than for females. Further studies may be completed by the determination of genotoxicity levels in zebrafish sperm, allowing a better link with genotoxicity observed in the progeny, as proposed by [START_REF] Reinardy | Cobalt-induced genotoxicity in male zebrafish (Danio rerio), with implications for reproduction and expression of DNA repair genes[END_REF]. Indeed, during spermatogenesis, chromatin is processed and packaged and contact between DNA and nuclear matrix is reorganized. Furthermore, the epigenetic pattern is also totally remodelled and transcription is stopped. All these events contribute to the control of embryo development in the early-life stages [START_REF] Herrâez | Paternal contribution to development: Sperm genetic damage and repair in fish[END_REF].

CONCLUSION

These results on fish reproductive performance after gamma irradiation provide additional information for ERAs. Drastic effects on progeny and consequently on population levels were observed at dose rates between 5 and 50 mGy h-1, confirming the DCRL values.

However, it is important to note a difference in the sensitivity between the trout reference organism and the Danio rerio, the model organism in our study. Moreover, this study highlights that parental exposure leads to significant effects in the progeny at the molecular level (ROS, genotoxicity), even at low dose rates (0.5 m Gy h-1). The consequences of these molecular effects will need to be studied following chronic exposure. The results encourage us to take into account the consequences of transmitted generational (i.e. heritable) effects for the determination of DCRL values. This study improves our understanding of the consequences of multigenerational exposure conditions for a better radioprotection of aquatic ecosystems. It confirms the difference in sensitivity of model species and identifies a narrow range of occurrence of drastic effects. It also acts as an incentive to acquire new data from multigenerational chronic exposure at low dose levels. For each exposure condition, a control condition was included. For the lowDR experiment (0.5, 5 mGy h-1), adults were exposed over 24 days. Reproduction was assessed after 10 and 24 days of irradiation. The progeny were then placed in irradiated and non-irradiated (F1 Recovery) exposure conditions over 10 and 22 days. For the highDR experiment (50 mGy h-1), adults were exposed over 10 days. The progeny were then placed in irradiated and nonirradiated (F1 Recovery) exposure conditions over 120 hours. 10d-irradiated adults were placed in non-irradiated exposure (F0 Recovery) over 63 days. Reproduction was assessed after 6, 36 and 63 days in F0 recovery conditions. The progeny were placed in non-irradiated exposure conditions over 96 hours for each time point (6, 36 and 63 days). For lowDR experiment (control, 0.5, 5, R0.5, R5 mGy h-1), survival rate was calculated from 3 spawns (with 2 pseudo-replicates, 1 male+1 female).

For highDR experiment (control, 50, R50 mGy h-1), survival rate was calculated from 6 spawns (1 male+1 female). a: p=0.024,b: p=0.015,c: p=0.006,d: p=0.006;a>b>c>d). Figure 4. Survival rate (%) of F1 progeny over time for lowDR experiment. Data are means ± SD of two replicates of 80 eggs for 3 spawns per condition. (Kruskal-Wallis test: 5 versus F1R, a: p=0.049, n=6). A. F1 progeny coming from adults irradiated during 10 days. Immediately after spawning, F1 progeny was placed in irradiated and in non-irradiated (F1R Recovery) exposure conditions during 22 days. B. F1 progeny coming from adults irradiated during 24 days. Immediately after spawning, F1 progeny was placed in irradiated exposure conditions during 10 d. Figure 5. Survival rate (%, n=6) of F1 progeny (3-4 hpf) over time. Progeny came from 10dirradiated adults for highDR experimentation. F1 Progeny were placed in irradiated and nonirradiated (F1R, Recovery) exposure conditions over 120 h. (Kruskal-Wallis test: Treatment versus Control, a: p=0.006, b: p=0.006, c: p=0.003, d: p=0.003; e=0.003, f: p=0.003). Figure 6. Individual (points) and average (histograms, means ± SD) survival rates (%, n=4-6) of F1 progeny after 24 and 48 h. Progeny came from adults irradiated during 10 days and then placed in non-irradiated conditions (F0R, Recovery) during 63 d. (Kruskal Wallis test, Treatment versus Control, a: p=0.015 n=12, b: p=0.0060 n=11, c: p=0.05 n=8, e: p=0.0058 n=11, f: p=0.05 n=11). Figure 7. Body length (mm) and typical aspect of F1 progeny at 72 h. F1 progeny came from adults exposed during 10d (Irr. 10d) and 10d followed by 6 days (F0 Irr. 10d+F0R 6d) and 36 days in non-irradiated (F0 Irr. 10d+F0R 36d) conditions. (Kruskal Wallis test, Treatment versus Control, *, p<0.05, F0Irr. 10d p=0.002 n=20; 0.0049 n=20, F0 Irr. 10d+F0R 6d, p=0.00007 n=33, F0 irr. 10d+F0R 36d, p=0.077, n=85). Figure 8. ROS production measured in larval exposed during 4 d coming from F0 adults exposed during 10 (A1) and 24d (A2) and in larval exposed during 10 d coming from F0 adults exposed during 24 d (B) of lowDR experiments. Nd: not determinate n=20 per condition, Anova test *, p<0.05. Figure 9. DNA damage (Tail moment) in F1 progeny after 1, 4 and 10d of exposure. Progeny came from adults irradiated during 24d for lowDR experiment. Progeny (3-4 hpf) were placed in irradiated and non-irradiated (F1R, Recovery) conditions. Kruskal Wallis test, *, p<0.05. Figure 10. DNA damage (tail moment) in progeny (A: 1d, irradiated and non-irradiated exposure (F1R, Recovery)) and in gonads of F0 adults (B: female, C: male) coming from highDR experiment. Kruskal Wallis test: *, p<0.05.

Figure 1. Exposure duration, conditions and endpoints for the lowDR and highDR experiments. For each exposure condition, a control condition was included. For the lowDR experiment (0.5, 5 mGy h-1), adults were exposed over 24 days. Reproduction was assessed after 10 and 24 days of irradiation. The progeny were then placed in irradiated and nonirradiated (F1 Recovery) exposure conditions over 10 and 22 days. For the highDR experiment (50 mGy h-1), adults were exposed over 10 days. The progeny were then placed in irradiated and non-irradiated (F1 Recovery) exposure conditions over 120 hours. 10 d-irradiated adults were placed in non-irradiated (F0 Recovery) exposure conditions over 63 days. Reproduction was assessed after 6, 36 and 63 days in F0 recovery conditions. The progeny were placed in non-irradiated exposure conditions over 96 hours for each time point (6, 36 and 63 days). For the lowDR experiment (control, 0.5, 5, R0.5, R5 mGy h-1), the survival rate was calculated from 3 spawns (with 2 pseudoreplicates, 1 male+1 female).

For the highDR experiment (control, 50, R50 mGy h-1), the survival rate was calculated from 6 spawns (1 male+1 female).

Figure legends Figure 1 .

 legends1 Figure legends

Figure 2 .

 2 Figure 2. Fecundity (number of egg per female) of F0 adults measured after 10 days of

Figure 3 .

 3 Figure 3. Individual (points) and average (histograms, means ± sd) survival rates (%,) of F1

Figure 2 .

 2 Figure 2. Fecundity (number of eggs per female) of F0 adults measured after 10 days of exposure for both the lowDR and highDR experiments (Kruskal-Wallis test: Treatment versus Control, * p=0.03). n=numberof spawns.

Figure 3 .

 3 Figure 3. Individual (points) and average (histograms, means ± sd) survival rates (%, n=xx) of the F1 progeny at 24 and 48 h. F1 progeny came from adults irradiated during 10 days for all experiments. F1 R: F1 recovery condition, i.e. progeny spawned by irradiated adults and placed in non-irradiated conditions.

  (Kruskal-Wallis test: Treatment versus Control, a: p=0.024, b: p=0.015, c: p=0.006, d: p=0.006; a>b>c>d).

Figure 4 .

 4 Figure 4. Survival rate (%) of F1 progeny over time for the lowDR experiment. Data are means ± SD of two replicates of 80 eggs for 3 spawns per condition. Kruskal-Wallis test: 5 versus F1R 5, a, n=6, p=0.049 A. F1 progeny coming from adults irradiated over 10 days. Immediately after spawning, the F1 progeny was placed in irradiated and in non-irradiated (F1R Recovery) exposure conditions over 22 days.B. F1 progeny coming from adults irradiated over 24 days. Immediately after spawning, the F1 progeny was placed in irradiated exposure conditions over 10 d.

Figure 5 .

 5 Figure 5. Survival rate (%) of 6 F1 progeny (3-4 hpf) over 120 h. The progeny came from 10 d-irradiated adults from the highDR experiment. The F1 Progeny were placed in irradiated and non-irradiated (F1R, Recovery) exposure conditions over 120 h. (Kruskal-Wallis test: Treatment versus Control, a: p=0.006, b: p=0.006, c: p=0.003, d: p=0.003; e:=0.003, f: p=0.003).

Figure 6 .

 6 Figure 6. Individual (points) and average (histograms, means ± SD) survival rates (%, n=4-6) of F1 progeny after 24 and 48 h. The progeny came from adults irradiated over 10 days and then placed in non-irradiated conditions (F0R, Recovery) over 63 d. Kruskal Wallis test: Treatment versus Control a: p=0.015 n=12, b: p=0.0060 n=11, c: p=0.05 n=8, e: p=0.0058 n=11, f: p=0.05 n=11.

Figure 7 .

 7 Figure 7. Body length (mm) and typical aspect of F1 progeny at 72 h. The F1 progeny came from adults exposed over 10 d (Irr. 10 d) and 10 d followed by 6 days (F0 Irr. 10d+F0R 6d) and 36 days in non-irradiated (F0 Irr. 10d+F0R 36d) conditions. Kruskal Wallis test, Treatment versus Control *, p<0.05, F0Irr. 10d p=0.002 n=20; 0.0049 n=20, F0 Irr. 10d+F0R 6d, p=0.00007 n=33, F0 irr. 10d+F0R 36d, p=0.077, n=85.

Figure 9 .

 9 Figure 9. DNA damage (Tail moment) in the F1 progeny after 1, 4 and 10 d of exposure. The progeny came from adults irradiated over 24 d for the lowDR experiment. The progeny (3-4 hpf) were placed in irradiated and non-irradiated (F1R, Recovery) conditions. Kruskal Wallis test, Treatment versus Control *, p<0.05.