Abbas Salhab
email: abbas.salhab@etu.uphf.fr

Julien Carlier
email: bjulien.carlier@uphf.fr

Pierre Campistron

M Neyens

Malika Toubal

Bertrand Nongaillard

V Thomy

Polydimethylsiloxane micro-channels

Keywords: Micro and Nano-technology, Wetting, Surface cleaning, Microelectronics, Nondestructive testing, Acoustics, Piezoelectric transducers, Microfluidics, Deep trench isolation

come

Introduction

In the microelectronics industry the tendency for miniaturization of the electronic components has led to the fabrication of micro and nanostructures with high aspect ratios (for example structures of hundreds of nanometers wide and tens of micrometers height). With these increasing aspect ratios it's becoming more and more difficult to achieve wet cleaning of these etched silicon structures [1] and to remove non-desired particles which can lead to defective electronic products. We developed an acoustic method [2,3] using ultra-high frequency (5 GHz) to detect the penetration of the liquid to the bottom of the etched structure and hence get information about the efficiency of the wetting (cleaning) states. Our previous results have been obtained under static wetting conditions (droplet based) while the industrial cleaning process uses a liquid dispensed in a form of jet on a rotating wafer. Thus, in order to have experimental conditions closer to industrial practice, a PDMS based micro-channel has been placed on the top of the etched silicon wafer matrix (Fig. 1 and Fig. 2) in a manner that the DTI trenches are perpendicular to the micro-channel. The industrial cleaning process is done by rotating a silicon wafer and dispensing the fluid in a form of jet on top of this rotating wafer. Due to the complexity of the industrial process we will not implement the rotation. Instead we will use micro-channel to establish a dynamic liquid flow with conditions as close as possible to the industrial process and get information on the wetting dynamic of these high aspect ratio structures. Information from the industrial process has been obtained and used in hydrodynamic calculations for our PDMS micro-channel system and are presented in the next section.

Experimental Setup

The characterization acoustic method that we developed [2] is represented in Fig. 3; it consists of sending an incident volume wave generated by a piezoelectric transducer (ZnO disc of 75 µm diameter) which is fabricated on the back of the wafer by lithography process. This same transducer receives also the reflected wave to be analyzed by a signal processor. These reflected signals or echoes could be either the reflection from the top of the pillar (A12) or from the bottom of the pillars (A11) which can give us, after analysis, information about the wetting state [2]. Our characterization method gives good separation of echoes inside the silicon due to the utilization of very small wavelengths of 1.7 µm (f = 5 GHz) for the longitudinal waves.

A PDMS micro-channel with dimensions of 3300×3100 µm 2 and thickness of 20 µm (Fig. 1 and Fig. 2(b)) is then placed on the silicon DTI structures and aligned on both the acoustic transducer and the silicon DTI structures matrix. The micro-channel is obtained by the realization of a SU-8 photoresist based mold using a laser lithography technique. After several steps (PDMS deposition in the SU-8 mold, annealing and demolding), the micro-channel adhesion to the silicon wafer is established through a surface oxidation of the PDMS (using a corona discharge).

Hydrodynamic calculations have been done to ensure that the pressure loss inside the micro-channel does not exceed 1 bar respecting the conditions that is used in the industry. DTI wafer with etch depth 4 µm will be investigated with the use of dynamic flow. The DTI matrix is etched on the silicon wafer front side and consists of nonmetric structures and aspect ratio ranging from 20 to 35.

Pressure loss and fluid speed inside the micro-channel have been calculated using Eq. 1 [4], and Eq. 2, 3, 4 [START_REF] Wehking | Electronic Theses and Dissertations[END_REF]. Parameters such as fluid speed and height have been obtained from the simulation of fluid film thickness on a rotating silicon wafer as function of distance from the wafer center (Fig. 4). At high rotational speed of wafer (ω > 800 r.p.m), Eq. 5 [START_REF] Leshev | [END_REF] shows very good corresponds with results in Fig. 4, which will be used to calculate the fluid film thickness (h); then we will take our micro-channel height as 2h to achieve the same fluid flow profile, since it is a closed channel compared to the open jet system used in cleaning industrial wafers. Different aspect ratios of DTI [1,7] within silicon wafers, and covered by a PDMS micro-channel, have been tested and subjected to different hydrodynamic conditions. Table 1 show the hydrodynamic conditions on 300 mm flat wafer and the corresponding pressure loss calculated using Eq. 4 for a micro-channel of 27 µm (2h) in thickness. We can see that the expected pressure loss is small 114.5 mbar (< 1 bar) which will not cause problems experimentally and will not cause much difference in micro-channel pressure compared to industrial atmospheric conditions used in cleaning silicon wafers.

u r = ω 2 rh 2 �1-�1-z h � � 2 � 2ϑ (1) f = 64 R e 1 2 3 + 11 24 � b a �� 2 - b a � (2)
D= 2𝑎𝑎𝑎𝑎 𝑎𝑎+𝑎𝑎 (3)
ΔP = ρ f L D 𝑢𝑢 𝑟𝑟 2 2 (4) ℎ = 0.782 × 𝑄𝑄 0.33 × 𝜈𝜈 0.33 × ω -0.67 × 𝑟𝑟 -0.67 (5)
In Here we will take the average of the radial velocity so, we will integrate ur as function of z from 0 to h and then divide it by h, it will be reduced to Eq. 6.

u r = ω 2 rh 2 3ϑ (6)
Table 1: Calculated hydrodynamic conditions applied on 300 mm wafer for water at 20˚C and at industrial flow rate of 0.12 L/min. The corresponding pressure loss is shown for a micro-channel of 27 µm in height (2h).

Q [L/min] 𝜈𝜈 [m 2 /s] ω [r.p.m] r [mm] h [µm] ur [m/s] ΔP [mbar]
0.12 1.0e -6 1500 140 13.50 0.21 114.50

Results and Discussion

The DTI [1,7] (Deep Trench isolation) silicon wafer is an etched silicon structure with trenches width of 200 nm, organized as a network of rectangles. Although the DTI wafer is made of silicon, there are two additional layers which are silicon dioxide (SiO2) and silicon nitride (Si3N4) of several tens of nanometers in thickness, present uniquely on the top surface of the trenches. The wetting dynamic on a sample wafer of 4 µm etch depth was investigated using distilled water (or mixture of ethanol and distilled water) at 20˚C. The wetting process is measured at different time intervals.

Fig. 5 shows the acoustic reflection using longitudinal waves (frequency ~4.5 GHz) for three different cases:

-First when no fluid is present in the micro-channel, -Second when we have an apparent complete filling of the micro-channel and no fluid movement for one minute. This state is called 'static case' one in Fig. 5, -And finally in the case of dynamic flow through the micro-channel for one minute at a flow rate of 55 µL/min and fluid speed of 4.67 mm/s. This is called 'dynamic case' in Fig. 5.

The first echo (A11) occurs at the bottom of the etched silicon at time of 185.1 ns and the echo from the top (A12) of the silicon surface occurs at 186 ns. We can observe that A11 is the same for all the cases and have a value of 265 µV suggesting that no acoustic energy has been absorbed by the presence of a liquid hence, no wetting occurred at the bottom of the trenches. For A12 it is equal to 360 µV in the case of no water presence and equal to 297 µV for both the static and dynamic case. These latter results suggest that both static and dynamic cases have similar wetting response. In conclusion wetting is not achieved at the bottom of trenches using distilled water both in the static and dynamic cases.

Fig. 6 shows the acoustic reflection response when there is a circulating mixture of ethanol and distilled water (40% and 60% in volume respectively) during one minute through the microchannel, as well as the static state for one minute using this mixture. The flow rate was 38 µL/min and the fluid speed was 3.23 mm/s (dynamic case). The first observation is that the two curves, static and dynamic cases, coincide with each other which suggest that there may be no difference in the results between the two states (same results obtained with distilled water). The first echo (A11) has a value of 238.1 µV in the case of circulating fluid (ethanol + distilled water), while is it 265.7 µV where no fluid is present in the micro-channel which suggests the penetration of mixture to the bottom of nano-trenches. The top echo (A12) was 259.5 µV for the case of mixture and equal to 359.5 µV for the case of no fluid present. The impact of the value of (A11) implies that this mixture of ethanol and distilled water is able to wet the bottom of the nano-trenches which has not been seen in the case of distilled water. This can be related to the lower surface tension of ethanol.

At 20˚C ethanol has a surface tension of 21.78 mN/m, while that of distilled water is equal to 72.75 mN/m. This lower value makes it easier for ethanol to penetrate high aspect ratio structures and hence induces better cleaning. Acoustic Reflection Coefficient. Calculation of the acoustic reflection coefficient is done using the acoustic reflection measurements. The acoustic reflection coefficient is defined as the ratio of the acoustic reflection of a surface when fluid is present to the acoustic reflection when no fluid is present. Fig. 7 shows the values for two cases; the bottom and top of the DTI trenches. Variation of the reflection coefficient is a direct effect of the mechanical impedance which is related to changing ethanol concentration [START_REF] Royer | Ondes élastiques dans les solides: Tome 1[END_REF].

We performed an experimental measurement of the contact angle on a flat surface of the DTI wafer (Non-etched surface), and we obtained a value of 60˚, which signify that the surface is slightly hydrophilic. In the case of the bottom DTI shown in Fig. 7, with water as the fluid circulating the micro-channel a value of 0.98 has been obtained which suggests that wetting is not achieved. For ethanol concentration between 40% and 50% (leading to a surface tension comprises between 26.2 mN.m -1 and 25 mN.m -1) the reflection coefficient decreases rapidly to 0.89, then it increases to reach 0.91 for pure (100%) ethanol. These values obtained are higher than those obtained by Carlier et al. [START_REF] Carlier | [END_REF] which are 0.86 to 0.87 for 40% to 50% concentration of ethanol and 0.9 for pure ethanol; this suggests that wetting is impartial and non-definitive with ethanol.

For the case of the top surfaces of DTI, the reflection coefficient change in similar manner as in the case of bottom surfaces of DTI, the lower values in this case may be related to the presence of the fluid which absorbs part of the acoustic energy and hence, decreases it. There are two values to explore here, the value of 0.83 for water and 0.79 for the pure ethanol. To explain these values we performed a measurement with static droplet on the flat surface (non-etched surface) of the DTI wafer. The values obtained using the droplet measurements are 0.83 and 0.88 respectively for water and pure ethanol. These values are smaller than what we expect for silicon/water and silicon/ethanol interfaces, which are normally 0.86 and 0.90 respectively. This difference can be related to the presence of other layers on the top of the silicon DTI, namely two layers which are silicon dioxide (SiO2) and silicon nitride (Si3N4) of tens of nanometers each in thickness. These layers are used in the semiconductor industry during the wafer production and etching operation and are present on top of the DTI trenches but, not inside the etched DTI. The presence of these additional layer changes the mechanical impedance of the system (piezoelectric transducer + DTI wafer) which affects the value of the reflection coefficient. For pure ethanol we have a value of 0.79 which is lower than the reference flat surface value 0.88, this difference could be explained by the presence of fluid inside the DTI trenches due to the lower surface tension of ethanol compared to water, this presence of ethanol absorbs part of the acoustic energy during reflection and hence lower the reflection coefficient. We can conclude that for the case of the bottom of the DTI structures, the wetting is never totally achieved using distilled water, and is partial and non-definitive in the case of adding ethanol. This could be related to the network pattern collapse Fig. 8 (a), or due to air trapped in the bottom of Vshaped DTI trenches Fig. 8 (b). The results obtained both for the bottom and top DTI requires a simulation code for simulating the acoustic response traversing the different layers of the DTI wafer, so as to obtain the values of the reflection coefficients depending on the state of wetting.

Conclusion

An experimental bench has been established for the first time wetting characterization using Lab-On-Chip integration acoustic transducers/ PDMS micro-channels and DTI structures. The first results show that given conditions (same concentration of water/ethanol mixture), led to the same wetting conditions in static and in dynamic states. We are currently studying the behavior using different mixtures of ethanol and water (therefore intermediate surface tensions), and with different hydrodynamic parameters applied on different aspect ratio structures. Also, a simulation code of the acoustic reflection coefficient inside the silicon wafer is currently being developed, which will enable us to predict the different wetting states. We will also investigate the drying phenomena by injecting gases (air or nitrogen for example).

  the above equations, ur the radial velocity of the fluid [m/s], ω is the rotational speed [rd/s], r the radial distance from the wafer center [m], z is the vertical distance from the surface of the wafer to the top of the fluid film height given as function of h [m], υ the kinematic viscosity [m 2 /s], f friction coefficient, Re is the Reynolds number, a and b are the cross sectional dimensions of the micro-channel (width and thickness respectively) [m], ΔP is the pressure loss from inlet to outlet inside the micro-channel [bar], ρ being the density of the fluid [Kg/m 3 ], L is the length of the micro-channel [m], D is the hydraulic diameter [m], and Q is the flow rate used in industrial process [m 3 /s].

Figure 1 :Figure 2 :

 12 Figure 1: Schematic drawing of the PDMS micro-channel with dimensions given in micrometers.

Figure 3 :

 3 Figure 3: Emission and reception of acoustic wave through silicon using piezoelectric transducer fabricated on the back of the wafer.

Figure 4 :Figure 5 :

 45 Figure4: Simulation of the fluid film thickness (h) on a flat rotating silicon wafer (without DTI trenches) as function of the distance from the wafer center for rotating speed of 1000 r.p.m.[10]

Figure 6 :

 6 Figure 6: Acoustic reflective wave response off the DTI matrix using longitudinal waves and a mixture of ethanol and distilled water (40%, 60%) as the fluid in both dynamic (fluid moving) and static (fluid present not moving inside micro-channel).

Figure 7 :Figure 8 :

 78 Figure 7: Experimental measurements of the acoustic reflection coefficient on the bottom and top of the DTI using different ethanol/water mixtures.

Acknowledgements

This work was supported in part by the STMicroelectronics-IEMN Common Laboratory and in part by the French RENATECH Network on Micro and Nanotechnologies.


Philippe Pognonec

Axel Gustovic

Zied Djabari

Thierry Pourcher

Fellow, IEEE Michel Barlaud

Mitotic index determination on live cells from label-free acquired quantitative phase images using a supervised autoencoder

Keywords: Mitotic index, non-invasive cell monitoring, Quantitative Phase Imaging (QPI), Supervised autoencoder. !

Mitotic index determination on live cells from label-free acquired quantitative phase images using a supervised autoencoder

INTRODUCTION

Somatic cells constitute the vast majority of our body. These cells may have to multiply to allow our organism to maintain normal homeostasis. Growth occurs through a very tightly regulated process called the cell cycle. During this process, a cell ultimately divides into two identical cells within one or two days. Deregulation of the cell cycle may result in cell death [START_REF] Rubin | The cell cycle and cell death[END_REF] or in uncontrolled cell growth leading to cancer [START_REF] Vermeulen | The cell cycle: a review of regulation, deregulation and therapeutic targets in cancer: Cell cycle regulation and deregulation[END_REF]. In addition, exposure to toxic compounds may also result in alteration to cell growth or cell death [START_REF] Zhang | Cell toxicity mechanism and biomarker[END_REF].

It is thus of utmost importance for biologists to monitor cell growth. This is usually done either with molecular tools on cell lysates, or via flow cytometry performed on isolated cells placed in suspension and processed with a FACS machine (Fluorescence-activated cell sorting) [START_REF] Adan | Flow cytometry: basic principles and applications[END_REF]. While both methods have advantages, they both interfere with the cells being monitored. Molecular analysis requires cell killing to obtain a workable lysate that is used to quantify molecular markers of the cell cycle. Flow cytometry, while being able under specific conditions to keep cells alive, will strongly interfere with the physiology of cells due to the extensive manipulations inherent to the FACS procedure [START_REF] Andrä | An Evaluation of T-Cell Functionality After Flow Cytometry Sorting Revealed p38 MAPK Activation[END_REF].

Quantitative Phase Imaging (QPI) is a well established imaging technology that only requires short bursts of low intensity white light that are relatively harmless to living cells compared to fluorescence. QPI cameras produce phase images that are processed to extract biologically significant features. The optical phase differences measured after light propagates through biological samples are a direct reflection of the dry matter encountered along the optical path. Many reviews focus on this technique [START_REF] Kemper | Digital holographic microscopy for live cell applications and technical inspection[END_REF], [START_REF] Kim | Principles and techniques of digital holographic microscopy[END_REF], [START_REF] Lee | Quantitative Phase Imaging Techniques for the Study of Cell Pathophysiology: From Principles to Applications[END_REF], [START_REF] Marquet | Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders[END_REF], [START_REF] Park | Quantitative phase imaging in biomedicine[END_REF] [START_REF] Park | Gradient-coherent strong regularization for deep neural networks[END_REF], [START_REF] Kasprowicz | Characterising live cell behaviour: Traditional label-free and quantitative phase imaging approaches[END_REF], [START_REF] Zangle | Live-cell mass profiling: an emerging approach in quantitative biophysics[END_REF], [START_REF] Popescu | Quantitative phase imaging of cells and tissues, ser. McGraw-Hill biophotonics[END_REF]. The QPI strategy used here does not require temporally coherent illumination and can thus be used with conventional microscope sources, such as halogen lamps [START_REF] Bon | Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells[END_REF]. It accurately measures increases in the growing cell mass [START_REF] Aknoun | Living cell dry mass measurement using quantitative phase imaging with quadriwave lateral shearing interferometry: an accuracy and sensitivity discussion[END_REF]. We previously showed that these and other features derived from QPI, associated with proximal machine learning methods, accurately recognize HeLa cells experimentally blocked in early S and M phases [START_REF] Pognonec | Non Invasive Live Cell Cycle Monitoring using Quantitative Phase Imaging and Proximal Machine Learning Methods[END_REF] following thymidine and nocodazole treatments, respectively. The S and M phases of the cell cycle correspond to the beginning of chromosome duplication (DNA synthesis) and to the onset of cell division (mitosis), respectively. Stemming from this observation, we reasoned that we should be able to perform mathematical testing on normal (untreated) exponentially growing cell populations to characterize cells undergoing mitosis. This was performed with a supervised deep neural autoencoder. As presented in this work, our algorithms were able to identify cells with a very high accuracy from QPI-derived features. To biologically validate these computed results, we compared the phenotypes of the cells present in the predicted M class (Mitosis) to images of the same identical cells obtained with a regular CMOS camera in the presence of a permeant dye emitting light under fluorescent illumination. This dye specifically labels cellular nucleic acids (mainly DNA present in chromosomes). We could thus validate the coherence of the computed classification. Deep neural networks have proven their effectiveness in bioinformatics for both classification and feature selection [START_REF] Min | Deep learning in bioinformatics[END_REF], [START_REF] Zhang | Deep learning-based multi-omics data integration reveals two prognostic subtypes in high-risk neuroblastoma[END_REF]. Autoencoders were introduced into the field of neural networks decades ago and their most efficient application was dimensionality reduction [START_REF] Hinton | Autoencoders, minimum description length and helmholtz free energy[END_REF], [START_REF] Goodfellow | Deep learning[END_REF]. Stacked autoencoders were successfully used for denoising [START_REF] Vincent | Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion[END_REF], and fault classification [START_REF] Wang | Deep learning for fault-relevant feature extraction and fault classification with stacked supervised auto-encoder[END_REF].

An autoencoder is a discriminative model which maps feature points to a high dimensional space to labels in a low dimensional latent space. Let us recall that variational autoencoders (VAEs) [START_REF] Kingma | Auto-encoding variational bayes[END_REF], [START_REF] Kingma | Semi-supervised learning with deep generative models[END_REF] encourage the latent space to fit a prior distribution, like a Gaussian. These classical priors in the latent space are chosen for their computational simplicity rather than their compatibility with the latent structure and thus can lead to inaccurate latent lowdimensional representations of data. Recently Barlaud and Guyard proposed a non-parametric supervised Autoencoder framework [START_REF] Barlaud | Learning a sparse generative nonparametric supervised autoencoder[END_REF] where they relaxed the parametric distribution assumption in the latent space to learn a non-parametric data distribution of clusters. This supervised network encourages the latent space to fit a distribution learned with the clustering labels rather than a parametric prior distribution. In this paper, we point out the following specific contributions:

• We estimate a new Mitosis reference cells using a hand made microscopy approach without any invasive chemical treatment.

•

We use the efficient new autoencoder classification [START_REF] Barlaud | Learning a sparse generative nonparametric supervised autoencoder[END_REF] method instead of the classical Douglas-Rachford method [START_REF] Pognonec | Non Invasive Live Cell Cycle Monitoring using Quantitative Phase Imaging and Proximal Machine Learning Methods[END_REF] [START_REF] Barlaud | Robust classification with feature selection using an application of the Douglas-Rachford splitting algorithm[END_REF].

The paper is organized as follows: Section 2 deals with live cell cycle monitoring. In section 3 we develop the autoencoder classification method. In section 4 experimental results are provided on real biological datasets with a discussion in section 5. Finally in section 6 we conclude the paper.

LIVE CELL CYCLE MONITORING

The cell cycle is a biological process ultimately resulting in cell division, yielding two daughter cells with exactly the same genetic content. This highly regulated process is of the utmost importance and is a direct reflection of cell growth. It consists in four phases:

• The mitotic phase per se (M-Phase), in which nuclei loose their membrane, nucleoli disappear and chromosomes are physically sorted to be equally split among two identical daughter cells. These new cells then enter:

• The G1 phase, in which the cell nucleus is reorganized following cell division. The entry into the G1 phase requires the passage of a checkpoint ("Spindle checkpoint") where cells verify that division occurs as planned. If not, cells cannot proceed to G1. The G1 phase is associated with the formation of nucleoli, sub-nuclear structures that produce ribosomal RNAs required for the synthesis of proteins from transcribed DNA, as well as for the normal physiology of the cell. DNA transcription into RNA restarts to support cellular functions. Following the G1 phase and after another checkpoint validating their well being, the cells proceed to:

• the S phase, in which DNA is replicated. This phase is associated with an increase in cell size and mass. After chromosomal duplication, cells enter:

• the G2 phase, in which there is a last checkpoint before entering the M-Phase again.

Monitoring the cell cycle allows direct evaluation of cell growth, but no method is currently available to do so without interfering with normal cell growth. Fluorescence-Activated Cell Sorting (FACS) is very powerful for monitoring cell cycling, but requires non-physiological cell handling and/or cell labeling with exogenously expressed fluorescent proteins [START_REF] Andrä | An Evaluation of T-Cell Functionality After Flow Cytometry Sorting Revealed p38 MAPK Activation[END_REF]. We investigated whether high resolution quadri-wave lateral shearing interferometry, that allows quantitative linear retardance and birefringence measurements on biological samples could allow non-invasive monitoring of the cell cycle in populations. The QPI strategy, presented in [START_REF] Aknoun | Living cell dry mass measurement using quantitative phase imaging with quadriwave lateral shearing interferometry: an accuracy and sensitivity discussion[END_REF], [START_REF] Aknoun | Quantitative phase microscopy for non-invasive live cell population monitoring[END_REF], only requires short bursts of low intensity white light which appears to have a negligible effect on cell physiology. The optical phase difference measured when photons exit a biological sample is a direct reflection of the dry mass present in the sample being analyzed. It has been shown for example that the mass increase associated with cellular cell cycle progression (2N toward 4N chromosomes) can be accurately determined [START_REF] Rubin | The cell cycle and cell death[END_REF]. In addition, the characteristic cell rounding associated with the late G2 phase is also easily detected by QPI [START_REF] Aknoun | Quantitative phase microscopy for non-invasive live cell population monitoring[END_REF]. Biologists partners [START_REF] Pognonec | Non Invasive Live Cell Cycle Monitoring using Quantitative Phase Imaging and Proximal Machine Learning Methods[END_REF] have investigated how reliable this approach would be to monitor a live cell population under the microscope. They first setup a controlled system in which HeLa cells were synchronized into the early S phase (double thymidine block) and late G2/mitosis (nocodazole block) [START_REF] Aknoun | Living cell dry mass measurement using quantitative phase imaging with quadriwave lateral shearing interferometry: an accuracy and sensitivity discussion[END_REF]. Cells were classically labeled with Hoechst 33342 to visualize nuclei by fluorescence imaging with the dye. Multiple fields were then acquired in parallel with a regular CMOS camera (Zyla 5.5) to visualize the blue Hoechst fluorescence, and with a SID4Bio camera to acquire quantitative phase images. Typical images of cells obtained by Fluorescent labeling and Phase imaging are presented in Figure 1 and2. In this work, we focused on the classification of mitotic cells. These cells, or more precisely their percentage among the whole population, represent the so-called mitotic index [START_REF] Hoffman | Wright's Hypothesis: Its Relation to Volume Growth of Tissue Cells and Mitotic Index[END_REF]. It is a reliable reflection of the growth of a cell population. To avoid the bias of chemically arrested cells, training sets were obtained by supervised selection of cells undergoing mitosis. This strategy allowed us to monitor in a completely non-invasive manner the growth of a living cell population in real time by following the mitotic index. Since the cells are kept alive under a robotic imaging station allowing QPI time-lapse acquisitions, screening of the effect of pharmacological substances of interest becomes possible in the absence of any manipulation other than interferogram treatment and mathematical processing.

METHOD: NON-PARAMETRIC SUPERVISED AU-TOENCODER FRAMEWORK

Let X be the dataset, as a m × d data matrix made of m line samples x 1 , . . . , x m . Let y i = j, j ∈ [1...k] be the label, indicating that the sample x i belongs to the j-th cluster. Projecting the data in the lower dimension latent space is crucial to be able to separate them accurately. In this paper we propose to use a deep neural network autoencoder framework. Let us recall that the encoder (or discriminative part) of the autoencoder map features points of a high dimensional space to a low dimensional latent space in and that the decoder maps feature points of a low dimensional space to a high dimensional latent space. Figure 3 depicts the main constituent blocks of our proposed approach. We have added to our autoencoder a "soft max" block to compute the classification loss. Let Z, the latent space, X the reconstructed data (Figure 3) and W the weights of the neural network. The goal is to compute the weights W minimizing the total loss which depends on both the classification loss and the reconstruction loss. Thus we propose to minimize the following criterion to compute the weights W of the autoencoder [START_REF] Barlaud | Learning a sparse generative nonparametric supervised autoencoder[END_REF].

Loss(W ) = φ(Z, Y ) + λψ( X -X) s.t. W 1 ≤ η. (1)
Where φ(Z, Y ) is the classification loss in the latent space and ψ( X -X) is the reconstructed loss. We also introduce a constrained regularization loss W 1 ≤ η for features selection [START_REF] Condat | Fast projection onto the simplex and the l1 ball[END_REF], [START_REF] Perez | A filtered bucket-clustering method for projection onto the simplex and the 1 -ball[END_REF]. The parameter λ weights the classification loss and the reconstruction loss. We use the Cross Entropy Loss for the classification loss function. We use the robust Smooth 1 (Huber) Loss [START_REF] Huber | Robust statistics[END_REF] as reconstruction loss function ψ. The size of the latent space is the number of clusters.

The authors of [START_REF] Zhou | Deconstructing lottery tickets: Zeros, signs, and the supermask[END_REF] proposed a double descent algorithm as follows: after training a network, set all weights smaller than some threshold to zero, rewind the rest of the weights to their initial configuration, and then retrain the network from this starting configuration but keeping the zero weights frozen (untrained). In order to minimize our global criterion 1, we use the modified double descent algorithm proposed by Barlaud and Guyard [34] where they replaced the thresholding by the 1 projection.

Algorithm 1 Projection on the 1 norm-proj 1 (V, η) is the projection on the 1 -ball of radius η, ∇φ(W, M 0 ) is the masked gradient with binary mask M 0 , and f is the ADAM optimizer, γ is the learning rate

Input: W * , γ, η for n = 1, . . . , N (epochs) do V ← f (W, γ, ∇φ(W )) end for W := proj 1 ((V, η) Output: W, M 0 Input: W * for n = 1, . . . , N (epoch) do W ← f (W, γ, ∇φ(W, M 0 )) end for Output: W
In this paper, we used a linear fully connected network (LFC) with an input layer of d = 15 neurons, one hidden layers (64 neurones) followed by a ReLU activation function and a latent layer of dimension k. We have implemented our sparse learning method using a constraint approach in the PyTorch framework. The losses are averaged across observations for each mini-batch. We chose the ADAM optimizer [START_REF] Kingma | a method for stochastic optimization[END_REF], as the standard optimizer in PyTorch. We have used the default parameters of the Pytorch software or previous publications. However two parameters must be tuned. The parameter η is determined by the maximum accuracy after cross-validation. The "minibatch" parameter is a compromise between the computational cost and accuracy. In our case the computational cost is not an issue and we have privileged the accuracy with a low value of "mini-batch". We used the Captum method [START_REF] Lundberg | A unified approach to interpreting model predictions[END_REF] to compute the weights of features. First we learn a neural network using the mitoses and G1/S reference cells and a part of the control dataset. Then we save the best learned network with a sense of accuracy. Finally we use this best learned network to predict the labels and probabilities on the control data.

EXPERIMENTAL RESULTS

Datasets

The following work was done on widely used HeLa cells, an immortalized cell line derived in 1953 from an epidermoid carcinoma of the cervix [START_REF] Scherer | Studies on the propagation in vitro of poliomyelitis viruses: iv. Viral multiplication in a stable strain of human malignant epithelial cells (strain HeLa) derived from an epidermoid carcinoma of the cervix[END_REF]. Hoechst 33342 labeling allows visualization of nuclei by fluorescence, and clearly detects in a proliferating population mitotic structures where chromosome condensation reaches a peak (see Figure 4, Panel A, arrows). First, both visible (fluorescent labeling) and phase images were processed with software (CellProfiler for fluorescent images [START_REF] Carpenter | CellProfiler: image analysis software for identifying and quantifying cell phenotypes[END_REF], and BioData (Phasics) for QPI) to extract multiple features stored as matrix (the X matrix defined in section 3), in which each line corresponds to a detected cell/nuclei and each column displays the values of a specific feature (diameter, phase value, ...) for all the cells. In our experiment we have 15 features for QPI images: 8 features related to QPI Interferograms (Dry mass, Phase max, Phase min ...) and 7 features related to geometry of the cell (Surface, ...) [START_REF] Pognonec | Non Invasive Live Cell Cycle Monitoring using Quantitative Phase Imaging and Proximal Machine Learning Methods[END_REF]. Note that we obtain at least equivalent accuracy using 15 QPI features as when we used 65 fluorescent features [START_REF] Pognonec | Non Invasive Live Cell Cycle Monitoring using Quantitative Phase Imaging and Proximal Machine Learning Methods[END_REF]. Datasets were retrieved from cell segmented after interferogram processing. Each data set consists of one row per identified cell, and multiple columns corresponding to the multiple features calculated. These features have been described in [START_REF] Aknoun | Living cell dry mass measurement using quantitative phase imaging with quadriwave lateral shearing interferometry: an accuracy and sensitivity discussion[END_REF]. Interferogram processing of the same field acquired via QPI produces the image shown in Panel B, where cells have been segmented. One can clearly see that the two mitotic cells visualized by nuclear staining correspond to cells with a high density signal, as pointed out by the green arrows. Double arrow labeled "2" points to a cell in which chromosomes have migrated to the just separated two daughter cells at the end of mitosis. The data set were normalized as follows [START_REF] Van Den Berg | Centering, scaling, and transformations: improving the biological information content of metabolomics data[END_REF]: i) Logtransformation of the datas for the following main benefits: Reducing heteroscedasticity and thus the bias on regression, transforming multiplicative noise into additive noise and ii) Classical column zero mean.

In this paper, we provide experiments using three specific databases:

•

The first dataset was presented in [START_REF] Pognonec | Non Invasive Live Cell Cycle Monitoring using Quantitative Phase Imaging and Proximal Machine Learning Methods[END_REF]. Briefly, HeLa cells were grown either in standard condition (Control cells, containing all phases of the cell cycle), or in the presence of chemicals to enriched the population in Mitosis phase (with nocodazole treatment) or in G1/early S phase (with double thymidine block). This dataset consist in 1163 G1/S reference cells and 9871 control cells (no chemical treatment).

•

The second dataset was also built from HeLa cells. To avoid the bias resulting from mitotic nocodazole enrichment, we manually identified more than 150 cells entering mitosis and followed them with our imaging station, acquiring interferograms every 3 minutes until the end of mitosis, resulting in thousands of mitotic cell images. In parallel, we also acquired interferograms on the general HeLa population. This dataset consist in 1581 Mitotic reference cells and 84,411 control cells.

•

In the third database, we use the 1581 Mitotic reference cells of the second database and 50,000 control cells from an acquisition performed on another day.

First experiment using chemical blocking

Initial results were published by the authors using a Douglas-Rachford classification method [START_REF] Pognonec | Non Invasive Live Cell Cycle Monitoring using Quantitative Phase Imaging and Proximal Machine Learning Methods[END_REF], [START_REF] Barlaud | Robust classification with feature selection using an application of the Douglas-Rachford splitting algorithm[END_REF]. Interestingly, we observed during this first study that the 15 QPI features used were at least as reliable as the 61 fluorescence features in term of classification accuracy. Mean accuracy Fluorescence = 89.24 and mean QPI accuracy = 91.86. This is why we now work exclusively with a QPI camera. In the present paper, we use a non parametric supervised autoencoder [START_REF] Barlaud | Learning a sparse generative nonparametric supervised autoencoder[END_REF]. The main benefits of the autoencoder is to improve the classification accuracy on the same dataset used in our original work (see Table 1) and to compute the latent space. Table 1 shows that the autoencoder outperforms Douglas-Rachford accuracy by 6.34% on the Mitosis, and by 7.46% on the G1/S cells.

Figure 5 of the train latent space in the training set demonstrates that Phase features allow the separation of the different populations according to their localization in the cell cycle. Interestingly, M phase cells (blue) form a characteristic sub-population, allowing for accurate calculation of the proportion of cells in mitosis, i.e. the determination of the proliferation status of the cell population monitored in Figure 6 of the test latent space . This demonstrated that cells arrested in the M phase by nocodazole block or in the early S phase by double thymidine block, form homogeneous populations.

The Table 2 shows a lower than expected Mitotic index (3%). For these mitotic cells the expected index is usually close to 7% [START_REF] Varia | Alignment of Mitotic Chromosomes in Human Cells Involves SR-Like Splicing Factors Btf and TRAP150[END_REF]. It should be kept in mind that the nocodazole-treated cells used for training arrests cells in the M phase at a very specific point as shown on Figure 2. Indeed, nocodazole interferes with spindle formation which is required to bring individual chromosomes together to form the equatorial plate. The lack of kinetochores activates the spindle assembly checkpoint, and arrests the cycle in the prometaphase, that ultimately leads to apoptosis. Later stages of mitosis are thus not found in a nocodazole-blocked population: metaphase, anaphase, and telophase stages are missing. Thus training for mitosis on a nocodazole-blocked population will only identify early stages of mitosis. This is confirmed by the dotplot presented in Figure 7, using 2 QPI features (Cell surface and Phase average). Nocodazole arrested cells are in blue, and Control cells are in green.

The plot shows both Control and Nocodazole treated cells and the Nocodazole cloud is located in the continuity of the small isolated cloud seen in Control cells. Phenotypic observation of these cells demonstrates that most of them are mitotic cells. Thus, it is clear that Nocodazole-treated cells do not exactly superimpose with Control mitotic cells. This is the reason for the lower than expected Mitotic index when using Nocodazole-treated cells as a training set. As expected, some of the cells from the control population presented feature values similar to those of the 2 blocked populations, since there are cells in the early G1-S phase as well as cells in the M phase in the control population. We thus proposed to visually select cells undergoing mitosis and to acquire their images every 3 minutes with time-lapse imaging using the QPI camera. This allowed us to build a robust bank of bona fide mitotic cells.

Second experiment using biologist-supervised mitoses selection

Once this bank of mitotic cells was built, we followed the same strategy as described above using our autoencoder approach to identify mitotic cells. We decided to focus on mitotic cells for two reasons: i) mitoses, the percentage of which in a population is a https://www.overleaf.com/project/60032669b0517552d480edb5convenient marker of cell growth, are relatively quick events, representing roughly 5% of the cell cycle duration for this cell line, with very characteristic changes in phenotype; ii) the G1-S phase is a process that evolves slowly, lasting for more than 50% of the length of the cell cycle. In contrast to mitosis, there is no clear-cut change in phenotype, making it more difficult to unambiguously identify. This experiment is illustrated by a pytorch code available at https://github.com/Gustoaxel/Cell-Cycle

Results on the second dataset

Figure 8 and9 show that the distribution in the latent space of the training and test sets are similar and different to Gaussian distributions. Note that the mitoses cluster is more compact than the control cluster. The explanation for this observation is likely the fact that mitotic cells undergo a very abrupt and specific change of their morphology, while non-mitotic cells undergo a slow and progressive evolution of their phenotype.

Table 4 shows that the top 3 features are phase features which means that they are more efficient than geometric As expected, we found a significantly higher proportion of cells in mitosis compared to that found using the nocodazole-blocked population, since all stages of the M phase were present in the training set, as seen in Table 5 and Figure 10. More than 80,000 cells are plotted (Figure 10). The dense green zone close to the origins corresponds to small cellular debris. 5, in good agreement with the mitotic index calculated for exponentially growing HeLa cell populations by manual counting [START_REF] Varia | Alignment of Mitotic Chromosomes in Human Cells Involves SR-Like Splicing Factors Btf and TRAP150[END_REF]. This demonstrates the robustness of the approach. Table 6 was obtained with the same training set, but on a dataset produced with the same cell line on another day. The averaged mitotic index obtained was 7.1%, very similar to that of Table 5. This demonstrates that as long as the same exact acquisition settings are used (exposure, magnification, ...), the learned autoencoder can be used on multiple new acquisitions without any significant changes in the calculated mitotic index.

DISCUSSION

Exponentially growing cell populations grow because cells undergo mitosis. The mitotic index is defined as the percentage of cells undergoing mitosis in a cell population. There are many ways to determine the mitotic index, but only QPI allows non-invasive monitoring of the mitotic index. Using the strategy reported here, it is now feasible to screen chemical banks on live cell populations using high-throughput microscopy. The effect of these chemicals on the population growth/differentiation/cell death will be reflected by changes in their mitotic indexes. This should be of great interest for pharmacological studies to identify biologically active compounds. This work demonstrates that Quantitative Phase Imaging is a very powerful and non-invasive way for biologists to monitor live cell populations with a relatively standard imaging station consisting of an automated microscope in a CO2 thermostated and water-saturated incubation chamber. Classically, biologists interested in following cell populations under live conditions have had to rely on either "vital" labeling, as with the DNA intercalating agent Hoechst 33342, or exogenously expressed proteins tagged with a fluorescent domain. However, it is well known that "vital" dyes are quick to alter cell physiology, as seen with Hoechst 33342 mentioned above [START_REF] Purschke | Phototoxicity of Hoechst 33342 in time-lapse fluorescence microscopy[END_REF]. Similarly, while very useful, fluorescent fusion proteins result in many possible artifacts and toxicity, and thus cannot be considered physiological. [START_REF] Ansari | Cellular GFP Toxicity and Immunogenicity: Potential Confounders in in Vivo Cell Tracking Experiments[END_REF] The camera used in this study does not capture classical photonic images, but rather records interferograms of the live cells by measuring regular white light phase gradients created when going through biological samples. From these interferograms, several cell features are extracted. Since each cell type has its own phenotype, it is necessary to first build a mitotic reference data set for each cell type analyzed. Mathematical treatment of the cell features provides a very accurate supervised classification of existing subpopulations. This means that without any treatment of the cells, biologists are now able to calculate the proportion of cells going through mitosis, in a way reminiscent of the widely used FACS systems. In contrast to FACS analyses, the cells remain untouched in culture during the whole process, which can theoretically last as long as needed. In other words, all questions dealing with cell growth and phenotypic changes in cell populations exposed to any treatment of interest can now be reliably addressed in real time since normal cell physiology will not be affected by anything else but the tested products. While our approach should theoretically be usable with other QPI methodologies, we do not have access to these other systems. The only sure way to validate our concept to these other QPI methodologies would be to try it. Toxicity testing and drug development should be made more straightforward with this approach. In addition, screening costs will be kept as low as possible due to the absence of any treatment or manipulation other than computerized treatment of descriptors extracted from interferogram analyses, and mitotic index calculation with our new autoencoder algorithm.

Deep learning networks are of particular interest for classification analysis. Variational autoencoders are of increasing interest. Herein we show how a new supervised autoencoder can be of particular interest for cell monitoring.

CONCLUSION

In this paper we point out the following contributions:

•

We shows that we now have a way to monitor live cell populations in a completely non-invasive manner thanks to the association of QPI technology with mathematical treatment of the QPI produced interferograms.

• As reported earlier [START_REF] Paweletz | Fine structural studies of early mitotic stages in untreated and nocodazole-treated HeLa cells[END_REF], we confirm here that while convenient to produce training sets, chemical blockade of the cell cycle with nocodazole will only detect early stages of the M phase, which is too restrictive for the preparation of datasets representative of the whole mitotic process. Training on naturally occurring mitoses is thus necessary for the algorithm to accurately classify all mitotic events.

• Combining a hand made efficient mitosis reference and a new supervised autoencoder we obtained a very high accuracy classification of 98.6%. This result in an accurate Mitotic index estimation (7%) (more reliable as compared to chemical blocking) compared to state of the art results reported in the literature.

• A straightforward application, among others, will be live real-time high-throughput pharmacological screening of molecule banks. In addition to its easy implementation, this approach records changes in populations throughout the experiment, for example in response to changes in culture conditions. The proportion of mitoses in cell populations exposed to the tested chemicals will be a reliable reflection of any effect of the screened molecules on cellular proliferation.

Fig. 1 .

 1 Fig. 1. "Fluorescence versus Phase imaging, G1 and S phases in HeLa Cells". G1 (top row): 2 representative cells before DNA synthesis are shown as seen by Fluorescence ("Fluo", left) and Phase ("QPI", right) imaging. S (bottom row) illustrates cells undergoing DNA synthesis. The cells are larger, and the nucleoli are more visible (pointed out with green stars) with Fluorescence labeling and in Phase imaging. White scale bar: 10µm.

Fig. 2 .

 2 Fig. 2. "Fluorescence versus Phase imaging, M phase". Left pair: Cell blocked during mitosis following nocodazole treatment. The green stars point to chromosomes blocked in prophase, the first stage of mitosis.Chromosome visualization in Phase imaging is possible but difficult (contrast was enhanced) compared to Fluorescence imaging (where labeling is chromosome specific). However, the phase analysis of the image unambiguously indicates a bona fide mitotic cell. Right pair: Control cell in metaphase (second stage of mitosis), with densely packed chromosomes highly visible in Fluorescence imaging, equatorial plate also distinguishable in QPI (contrast was enhanced).

Fig. 3 .

 3 Fig. 3. Autoencoder framework

Fig. 4 .

 4 Fig. 4. "Fluorescence versus Phase imaging", Panel A: Fluorescence labeling of nuclei, Panel B: Phase imaging. The arrows point to cells in the M phase, clearly visualized with both fluorescence and phase imaging. The equatorial plate, corresponding to chromosome alignment during metaphase can be seen both with fluorescence and phase imaging (arrows 1 and 3). Double arrow "2" points to chromosomes migrating to the two daughter cells at the end of mitosis. Scale bar: 50µm.

Fig. 5 .

 5 Fig. 5. Latent space train on the first dataset using chemical datas selection: Mitosis (blue) and G1/S cells (orange).

Fig. 6 .

 6 Fig. 6. Latent Space test using chemical datas selection: Mitosis (blue) and G1/S cells (orange)

Fig. 7 .

 7 Fig. 7. "Mitotic versus Nocodazole-generated mitotic cells": Cell surface versus Phase average dotplot with both Control (green) and Nocodazole-treated cells (blue). The Nocodazole mitotic cloud is further out than the Control mitotic cloud.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Latent Space on the training data set: Mitosis (blue)

Fig. 10 .

 10 Fig. 10. "Mitotic cells in an exponentially growing population": Cell surface versus Phase average dotplot, showing both mitotic (blue) and nonmitotic cells.

TABLE 1

 1 Comparison of Accuracy of Mitosis and DNA detection using either Douglas-Rachford or Autoencoder algorithm

		Mitosis G1/S
	Douglas Rachford Accuracy %	91.83	88.34
	Autorencoder Accuracy %	98.17	95.8

TABLE 2

 2 Number of detected Mitotic and G1/S cells

	Training cells	600	650	700	750	800
	Testing cells	10,426 10,394 10,305 10,320 10,303
	Mitotic cells	422	332	350	342	332
	Mitotic Index 4.04	3.19	3.39	3.31	3.12
	G1/S Cells	86	102	70	67	67

TABLE 3

 3 Accuracy of detection of Mitoses

	Autoencoder Mitosis
	Accuracy %	98.6
	TABLE 4
	Selected features
	Features		Weights
	P hase -avg(nm)		0.87
	P hase -StdDev(nm)		0.83
	P hase -median(nm)		0.77
	Surf ace(micron2)		0.40
	Optical -volume(micron3)	0.32
	P hase -max(nm)		0.30
	Surf ace -density(pg/micron2)	0.25
	Dry -mass(pg)		0.19
	features for classification.

TABLE 5

 5 Number of detected mitotic cells of the second dataset Results on the third dataset This mitotic bank, or sub-portions of it, yielded the same proportion of mitotic cells when used as training on different control populations. The averaged mitotic index was 7.3% in Table

	Testing cells	5,000 10,000 20,000 40,000 80,000
	Mitotic cells	356	723	1,450	2,841	6,123
	Mitotic index 7.1	7.2	7.3	7.1	7.7
			TABLE 6
	Number of detected mitotic cells on the third dataset
	Testing cells	5,000 10,000 20,000 40,000 50,000
	Mitotic cells	366	767	1,362	2,756	3,449
	Mitotic index 7.3	7.7	6.8	6.9	6.9

ACKNOWLEDGMENTS

This work has been supported by the French Agence National de la Recherche (ANR), through the ANR-14-CE17-0017 grant. We are indebted to Dr. B. Wattellier who kindly provided us with the Phasics QPI camera used in this study.


Amal Fekkar

Camille Emprou

Christine Lefebvre

Gilbert Ferretti

Olivier Stephanov

Daniel Pissaloux

Anne Mcleer

Anne-Claire Toffart

Sophie Rousseaux

Saadi Khochbin

Sylvie Lantuejoul

Séverine Valmary- Degano

Thoracic NUT carcinoma: common pathological features despite diversity of clinical presentations

Keywords: NUT, carcinoma, BRD, thorax

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

INTRODUCTION

NUT carcinoma (NC), formerly known as NUT midline carcinoma, is an aggressive, poorly differentiated subtype of carcinoma [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF] defined by the presence of acquired chromosomal rearrangement of the NUTM1 gene (NUclear protein in Testis Midline carcinoma family member 1) localized on chromosome 15q14, with other genes including BRD4 and, to a lesser extent, BRD3 [START_REF] Haack | Diagnosis of NUT Midline Carcinoma Using a NUT-specific Monoclonal Antibody[END_REF]. NC is underdiagnosed, mainly because of a nonspecific morphology, and its true incidence is therefore unknown [START_REF] French | NUT midline carcinoma[END_REF]. NC was first described in the 1990s and has been reported primarily in the head and neck, and mediastinum of young individuals [START_REF] Evans | Pathologic Characteristics of NUT Midline Carcinoma Arising in the Mediastinum[END_REF].

Nevertheless, it is now established that NC arises in multiple sites and affects patients of all ages, with no gender predilection [START_REF] Chau | An Anatomical Site and Genetic-Based Prognostic Model for Patients With Nuclear Protein in Testis (NUT) Midline Carcinoma: Analysis of 124 Patients[END_REF]. NC is usually locally invasive and widely metastatic at diagnosis [START_REF] Bauer | Clinicopathologic Features and Longterm Outcomes of NUT Midline Carcinoma[END_REF]. Despite therapy, median survival time is as low as 6.7 months and the estimated 2-year progression free survival is only of 9% [START_REF] Bauer | Clinicopathologic Features and Longterm Outcomes of NUT Midline Carcinoma[END_REF]. As NC resembles other poorly differentiated carcinomas, this diagnosis should be considered in case of poorly differentiated tumour [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF] and verified by immunohistochemistry using a highly sensitive and specific NUT monoclonal antibody, which typically shows a speckled nuclear staining. Demonstration of a specific chromosomal rearrangement by molecular analyses such as RT-PCR or FISH [START_REF] Evans | Pathologic Characteristics of NUT Midline Carcinoma Arising in the Mediastinum[END_REF] is no longer mandatory, even though FISH is commonly used to confirm the NUMT1 rearrangement.

With the aim of drawing attention to the common morphological features that can help pathologists to consider this rare diagnosis, we report 3 cases thoracic NC with diverse clinical presentations.

Case report 1

A 29-year-old female with no past history was admitted in 2010 for dyspnoea, haemoptysis and left supraclavicular pain. Thoracic, abdominal and pelvic computed tomography (CT) showed left mediastinal, left pulmonary and latero-uterine tumours with pleural and peritoneal effusions. Biopsy of the latero-uterine mass revealed an undifferentiated homogeneous proliferation, made of small-to-medium round malignant cells arranged in diffuse sheets. Nuclei harbour a vesicular chromatin and prominent nucleoli. A high mitotic rate was noted as well as many neutrophils within the stroma. At immunohistochemical analysis, tumour cells stained positively for CD45, CD43 and CD138 and were negative for epithelial markers, suggesting a haematological proliferation. The patient underwent chemotherapy with cytarabine and mitoxantrone. In the absence of any response to treatment, radical resection of the latero-uterine tumour was performed, whose analysis confirmed initial findings (Figure 1). Tumour karyotype showed a t(15;19) translocation. Diagnosis of NC was therefore considered, and confirmed by immunohistochemistry with the NUT monoclonal antibody and by RT-PCR revealing a BRD4-NUTM1 gene fusion. Despite chemotherapy with cisplatin and etoposide, the patient died within 2 weeks.

Case report 2

In 2018, a 19-year-old female presented with a 3 months history of neck pain with anorexia and weight loss. Contrast-enhanced CT showed a pathological fracture of C4 associated with a large pulmonary mass within the right lower lobe, extending to the inferior middle mediastinum (Figure 2) and many other lytic bone lesions. Microscopic examination of a biopsy performed on the left iliac wing showed an undifferentiated malignant tumour infiltrated by many neutrophils. The proliferation was composed of small to intermediate-sized cells with a monomorphic appearance and prominent nucleoli. Necrosis and high mitotic index were observed. Immunohistochemistry showed expression of cytokeratins, synaptophysin and epithelial membrane antigen by the tumour cells. In the absence of any clear diagnosis, NUT immunohistochemistry was performed, demonstrating a strong, speckled nuclear staining in >80% of tumour cells. FISH showed a rearrangement of the NUTM1 gene in 80% of tumour cells. Despite chemotherapy (cisplatin and etoposide) and antalgic radiotherapy, the patient died less than 2 months after diagnosis.

Case report 3

A 51-year-old non-smoking male with no remarkable medical history presented in 2019 with a lung mass in the right lower lobe. Histological analysis showed a proliferation of poorly differentiated small to intermediate tumour cells. Many neutrophils infiltrated the tumour (Figure 3). Immunohistochemistry was positive for p40 and negative for TTF1, CD56, chromogranin and synaptophysin. PD-L1 showed a weak membranous positivity in 5% of tumour cells. ROS1 and ALK were negative. Neutrophilic infiltration of this poorly differentiated tumour was suggestive of the diagnosis of NUT carcinoma. Diagnosis was confirmed by immunohistochemistry and FISH. Despite chemotherapy with cisplatine and navelbine, the patient developed brain metastases and passed away 5 months after diagnosis.

DISCUSSION

Diagnosis of NUT carcinoma (NC) is difficult because this tumour lacks specific features in terms of risk factors or clinicopathological presentation. This case series suggests that in the presence of a poorly differentiated thoracic tumour, NC should be considered, especially when neutrophils infiltrate the tumour.

NC is a tumour reported to arise in various sites, with a predilection for the head and neck and mediastinum [START_REF] Sholl | Primary Pulmonary NUT Midline Carcinoma: Clinical, Radiographic, and Pathologic Characterizations[END_REF]. NC corresponds to up to 18% of all poorly differentiated carcinomas of the upper aerodigestive tract, particularly the sinonasal region [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF]. Neither tobacco smoking nor viruses play a pathogenic role [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF]. NC morphology is that of a poorly differentiated carcinoma, with a distinctly monomorphic, clonal appearance, displaying a focal squamous differentiation with abrupt keratinization in 33-40% of cases [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF]. Tumour cells demonstrate frequent mitoses and single cell or geographic necrosis. The histologic features of NC are characteristic by the monomorphism of the cells, separation artefacts with a fried egg appearance with lack of nuclear moulding, the abrupt squamous differentiation and, notably, the presence of infiltrating neutrophils [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF]. In our 3 cases, the neutrophilic infiltrate was prominent and represents an important feature pointing towards this diagnosis. NC expresses with few exceptions cytokeratins and is usually diffusely positive for p63 antibody. Although rare, neuroendocrine markers and even TTF1 may be found positive and should not be used to rule out the diagnosis of NC and to favour the diagnosis of SCLC [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF]. NC shows a positive immunostaining with the anti-BRG1 antibody, which makes it possible to exclude a deficient SMARCA4 / BRG1 tumour which is part of a novel group of undifferentiated tumours described in the latest WHO classification [START_REF] Lokuhetty | Thoracic Tumors, WHO Classification of Tumours[END_REF]. In 2009, the C52B1 monoclonal antibody raised against the NUT protein was developed [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF]. This antibody is highly specific, and does not stain other human tumours than NC [START_REF] Haack | Diagnosis of NUT Midline Carcinoma Using a NUT-specific Monoclonal Antibody[END_REF]. To be regarded as positive, NUT immunostaining must harbour a typical nuclear punctate pattern in more than 50% of tumour cells [START_REF] Bishop | Cytopathologic features of NUT midline carcinoma: A series of 26 specimens from 13 patients: Cytopathology of NUT Midline Carcinoma[END_REF]. Using FISH as a "gold standard", immunohistochemistry has a sensitivity of 87%, a specificity of 100%, a negative predictive value of 99% and a positive predictive value of 100% [START_REF] French | NUT midline carcinoma[END_REF]. FISH allows the detection of NUTM1 rearrangements but is unable to identify the fusion partner of NUTM1 [START_REF] French | NUT midline carcinoma[END_REF]. For NUMT1 fusion detection by RT-PCR, specific probes have to be used. Most of the time, only BRD3-or BRD4-NUT fusions are detected by RT-PCR [START_REF] French | NUT midline carcinoma[END_REF]. RNA sequencing techniques allowing NUTM1 rearrangement detection without the knowledge of the partners could be interesting to discovery of new or unusual fusions. Such an identification is relevant as a recent study indicates that BRD3-NUT variants could be associated with a better survival than BRD4-NUT [START_REF] Chau | An Anatomical Site and Genetic-Based Prognostic Model for Patients With Nuclear Protein in Testis (NUT) Midline Carcinoma: Analysis of 124 Patients[END_REF]. To date, chemotherapy does not improve outcome of patients with NC [START_REF] Bauer | Clinicopathologic Features and Longterm Outcomes of NUT Midline Carcinoma[END_REF]. However, a precise diagnosis remains critical since experimental studies have revealed the molecular basis of the oncogenesis induced by the BRD4-NUT fusion protein and identified new potential specific therapeutic strategies. NUT is a testis-specific factor and the recent generation of a mouse model where this gene is invalidated has shown that NUT recruits p300 to induce a genome-wide histone hyperacetylation which occurs in late differentiating male germ cells before histone-toprotamine exchange [START_REF] Shiota | Nut Directs p300-Dependent, Genome-Wide H4 Hyperacetylation in Male Germ Cells[END_REF]. In the case of BRD4-NUT fusion protein, NUT keeps its ability to recruit p300, leading to the creation of hyperacetylated chromatin domains (BRD4-NUT foci) [START_REF] Reynoird | Oncogenesis by sequestration of CBP/p300 in transcriptionally inactive hyperacetylated chromatin domains[END_REF]. Cellular CBP/p300 are sequestered in these foci, making them unavailable for the various cell signalling involving these enzymes such as p53 acetylation in response to genotoxic assaults [START_REF] Reynoird | Oncogenesis by sequestration of CBP/p300 in transcriptionally inactive hyperacetylated chromatin domains[END_REF]. Therefore, any therapeutic approach leading to the dispersion of these BRD4-NUT foci could be considered as a valid therapeutic solution. With this regard, small molecules directly targeting the BDR4 portion of BRD4-NUTM1, called bromodomain inhibitors, drive terminal differentiation of NC cells in vitro and could thus inhibit BRD-NUTM1 oncogene expression [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF][START_REF] Sholl | Primary Pulmonary NUT Midline Carcinoma: Clinical, Radiographic, and Pathologic Characterizations[END_REF]. Interestingly, among four patients with BRD4-NUTM1 fusions treated with the OTX015/MK-8628 bromodomain inhibitor, two of them had a rapid response with tumour regression and symptomatic relief, and one had relative tumour stabilization [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF]. In addition, a small molecule inhibitor of CBP/p300 has been newly developed, which leads to a clear dispersion of the BRD4-NUTM1 and p300 foci [START_REF] Reynoird | Oncogenesis by sequestration of CBP/p300 in transcriptionally inactive hyperacetylated chromatin domains[END_REF]. Based on the fact that the expression of BRD4-NUTM1 is associated with globally decreased histone acetylation, histone deacetylase inhibitors (HDACi) could also represent promising targeted therapeutic agents by restoring chromatin acetylation and hence dispersing the oncogenic BRD4-NUT foci [START_REF] French | NUT Carcinoma: Clinicopathologic features, pathogenesis, and treatment: NUT Carcinoma[END_REF]. These promising treatments reinforce the importance to identify NC among other undifferentiated neoplasms especially thoracic SMARCA4-deficient undifferentiated tumours, which are poorly sensitive to cytotoxic chemotherapy regimen and which unfortunately do not have a targeted therapy [START_REF] Lokuhetty | Thoracic Tumors, WHO Classification of Tumours[END_REF].

In conclusion, our observation suggests to consider the diagnosis of NUT carcinoma in patients presenting with a poorly differentiated chest malignant tumour, especially in the presence of neutrophilic infiltration. The availability of a highly specific monoclonal antibody makes the diagnosis easy to perform by immunohistochemistry. FISH remains the "gold standard" for diagnosis, but does not allow the identification of the fusion partner. RNA based assays such as RT-PCR or RNA sequencing can allow the detection of the fusions transcripts provided they suitably designed. Prognosis remains extremely poor, but targeted therapies seem promising in patients harbouring BRD4-NUTM1 variants.

Legends of figures.

Figure 1 .

 1 Figure 1. (A) The right radical adnexectomy leads to a tumour resection showing a diffuse

Figure 2 .

 2 Figure 2. (A) Axial contrast-enhanced CT images: A1-large heterogeneous soft tissue mass in

Figure 3 .

 3 Figure 3. A-Morphological aspects (Hematoxylin-Eosin-Saffron stain): diffuse growth of

Acknowledgements

We thank Prof. Bruno Degano for critically editing the manuscript and Dr. Houda Kaddioui for her help in implementing the figures.