Amardeep Jagtap

Nicolas Goubet

Clément Livache

Audrey Chu

Bertille Martinez

Charlie Gréboval

Junling Qu

Erwan Dandeu

Loic Becerra

Nadine Witkowski

Loïc Becerra

Sandrine Ithurria

Fabrice Mathevet

Mathieu G Silly

Benoit Dubertret

Emmanuel Lhuillier

Short Wave Infrared Devices Based on HgTe Nanocrystals with Air Stable Performances

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

INTRODUCTION

Among potential applications of colloidal quantum dots (CQDs), their use for displays [START_REF] Xie | Quantum Dots-Converted Light-Emitting Diodes Packaging for Lighting and Display: Status and Perspectives[END_REF] and solar cells [START_REF] Konstantatos | Colloidal Quantum Dot Optoelectronics and Photovoltaics[END_REF] have certainly generated the most of interest. [START_REF] Talapin | Prospects of Colloidal Nanocrystals for Electronic and Optoelectronic Applications[END_REF] For these two applications, relatively wide band gap nanocrystals (>1.2 eV) must be used. Nonetheless, CQDs are also quite promising for the emergence of low cost Infrared (IR) devices such as detectors and photon sources. IR electromagnetic radiations in short wave IR (SWIR; 1.4 -3 μm) and in the two atmospheric transmission windows, mid wave IR (MWIR; 3 -5 μm) and long wave IR (LWIR; 8 -14 μm) are of utmost importance considering both space and civil applications; including earth environmental monitoring, night time surveillance, communications, etc. In particular, expansion to mass market of new applications, such as assistance to night driving or spectroscopic sorting, requires photodetectors with low price and relatively fast photoresponse. Current technologies are not able to achieve this combination, since quantum detectors are expensive and thermal detectors are slow. Lead chalcogenides (PbX) nanocrystals have been widely used to obtain absorption in the near infrared range. [START_REF] Hines | Colloidal PbS Nanocrystals with Size-Tunable Near-Infrared Emission: Observation of Post-Synthesis Self-Narrowing of the Particle Size Distribution[END_REF][START_REF] Mcdonald | Solution-Processed PbS Quantum Dot Infrared Photodetectors and Photovoltaics[END_REF] However, when longer wavelengths need to be addressed those materials are promptly limited by their bulk band gap. Even in the SWIR (0.8-3 µm) , the necessity of large PbX CQDs [START_REF] Pietryga | Pushing the Band Gap Envelope: Mid-Infrared Emitting Colloidal PbSe Quantum Dots[END_REF] which are of poor colloidal stability, results in films with pinholes and the associated electrical shorts when going toward vertical geometry devices. In this sense, the use of confined semi-metal materials is of utmost interest to reach colloidally stable CQDs with narrower band gap. Mercury chalcogenides (HgX) have recently generated a significant interest for the design of IR devices [START_REF] Kershaw | Narrow Bandgap Colloidal Metal Chalcogenide Quantum Dots: Synthetic Methods, Heterostructures, Assemblies, Electronic and Infrared Optical Properties[END_REF][START_REF] Lhuillier | Recent Progresses in Mid Infrared Nanocrystal Based Optoelectronics[END_REF][START_REF] Keuleyan | Mid-Infrared HgTe Colloidal Quantum Dot Photodetectors[END_REF] in the range of wavelengths from near IR 10 , telecom [START_REF] Kovalenko | Colloidal HgTe Nanocrystals with Widely Tunable Narrow Band Gap Energies: From Telecommunications to Molecular Vibrations[END_REF] (1.55 µm), mid IR [START_REF] Tang | Scalable Fabrication of Infrared Detectors with Multispectral Photoresponse Based on Patterned Colloidal Quantum Dot Films[END_REF] and up to the THz [START_REF] Lhuillier | Infrared Photodetection Based on Colloidal Quantum-Dot Films with High Mobility and Optical Absorption up to THz[END_REF] .

In this paper we focus on the so-called extended SWIR region where detection is conducted up to 2.5 µm (4000 cm-1 or 500 meV), which is of interest for night imaging based on night glow radiation. Even if the SWIR range is less demanding from a technological point of view than longer wavelength, its vicinity with the visible range makes the cost difference with visible technologies very striking. SWIR detection is currently driven by InGaAs technology, which suffers from its lack of spectral tunability and high cost. Thus, CQD based technologies may offer an interesting cost disruption for SWIR detection. [START_REF] Chen | Mercury Telluride Quantum Dot Based Phototransistor Enabling High-Sensitivity Room-Temperature Photodetection at 2000 nm[END_REF] However, some essential steps still have to be addressed before HgX nanocrystal based technologies can reach a mature level. In this paper, we address two of them, which are (i) the material and device stability toward air operation [START_REF] Lhuillier | Mid-Infrared HgTe/As2S3 FETs and Photodetectors[END_REF][START_REF] Chen | Air-Stable Infrared Photodetectors based on Spray-Deposited Aqueous HgTe Quantum Dots[END_REF] which is achieved using polymer encapsulation and (ii) dark current reduction, particularly keeping focus on room temperature operation, through the development of a photovoltaic device. For the reduction of dark current, we integrate narrow band gap HgTe CQDs with large band gap metal oxide (TiO2) in stacked layers geometry.

METHODS

Chemicals

Mercury chloride (HgCl2, Strem Chemicals, 99%), tellurium powder (Te, Sigma-Aldrich, 99.99%), trioctylphosphine (TOP, Cytek, 90%), oleylamine (Acros, 80-90%), dodecanethiol (DDT, Sigma-Aldrich, 98%), 1,2,ethanedithiol (EDT, Fluka, 98.0%), hydrochloric acid (HCl, Mieuxa, 25%), lithium perchlorate (LiClO4, Sigma-Aldrich, 98%), polyethylene glycol (PEG, Mw = 6 kg.mol -1 , Fluka), chloroform (Carlo Erba), ethanol absolute anhydrous (Carlo Erba, 99.9%), methanol (Carlo Erba, 99.8%), acetone (Carlo Erba, 99.8%), n-hexane (Carlo Erba), n-octane (SDS, 99%), toluene (Carlo Erba, 99.3%), N, N-Dimethylformamide (DMF, > 99.8 %, Sigma Aldrich), Anatase titanium oxide nanoparticles (TiO2, size: 8 -10 nm, Ti-Nanoxide HT-L/SC from Solaronix), Poly (vinyl alcohol) (PVA, Mw = 89000 -98000 kg.mol -1 , Sigma Aldrich), Poly (vinylidene fluoride) (PVDF, Mw = 180000 kg.mol -1 , Sigma Aldrich), Poly(methyl methacrylate) (PMMA), Indium tin oxide (ITO) coated glass slide (ρs = 70 -100 Ω/sq, Sigma Aldrich). All chemicals are used as received, except oleylamine, which is centrifuged before used. Mercury compounds are highly toxic. Handle them with special care.

Material synthesis 1 M TOP:Te precursor: 2.54 g of Te powder is mixed in 20 mL of TOP in a three neck flask. The flask is kept under vacuum at room temperature for 5 min and then the temperature is raised to 100 °C. Furthermore, degassing of flask is conducted for the next 20 min. The atmosphere is switched to Ar and the temperature is raised to 275 °C. The solution is stirred until a clear orange coloration is obtained. The flask is cooled down and the color switches to yellow. At room temperature, the flask is degassed again for 10 min. Finally, this solution is transferred to an Ar filled glove box for storage.

HgTe CQD synthesis: In a 100 mL three-neck flask, 513 mg of HgCl2 and 57.5 mL of oleylamine are degassed at 110 °C for 1 h. Under Ar at 80 °C, a solution containing 1.9 mL of 1 M TOP:Te and 10 mL of oleylamine is quickly injected after warming it up with heat gun. After 3 min, the reaction is quickly quenched by adding a mixture of toluene (9 mL) and DDT (1 mL), the flask is then cooled down using air flux. The nanocrystals are precipitated in ethanol and redispersed in toluene. This washing is repeated one more time. Finally, the HgTe CQDs dispersed in toluene are filtered through a 0.2 µm PTFE filter. The obtained solution is used for further characterizations and fabrication of devices.

Electron microscopy: For TEM pictures, a drop of CQD solution is drop-casted on a copper grid covered with an amorphous carbon film. JEOL 2010F is used at 200 kV for acquisition of picture. For device characterization, FEI Magellan scanning electron microscope is used.

Electrode fabrication

Au/Glass electrode fabrication: Microscope glass slides (75 × 25 × 1 mm) are cut in half and cleaned by sonication in acetone and rinsed thoroughly with isopropanol, and then oxygen plasma cleaning is carried out for 5 minutes. An adhesion primer (TI-PRIME) is spin-coated onto each substrate before AZ5214E photoresist is spin-coated and baked at 110 °C for 90 s. A mask aligner is used to expose the substrates to UV light for 2 s through a lithography mask. Black paper is kept under the glass slides to prevent light from being reflected back to the photoresist. These substrates are baked at 125 °C for 2 min to invert the photoresist and flood-exposed for 15 s with the mask aligner, again using black paper. Photoresist is developed using AZ726 developer for 20 s and rinsed with pure water. Patterned substrates are dried and cleaned with 5 min of oxygen plasma to remove photoresist residues. In a thermal evaporator, 5 nm of chromium is deposited as an adhesion promoter before 80 nm of gold is evaporated. Lift-off is conducted in an acetone bath for at least an hour. Electrodes are 2.5 mm long and spaced by 10 or 20 µm.

Si/SiO2/Au electrodes: The surface of a Si/SiO2 wafer (400 nm oxide layer) is cleaned by sonication in acetone. The wafer is rinsed with isopropanol and finally cleaned using an O2 plasma. AZ 5214E resist is spin-coated and baked at 110 °C for 90 s. The substrate is exposed under UV through a pattern mask for 2 s. The film is further baked at 125 °C for 2 min to invert the resist. Then a 40 s flood exposure is performed. The resist is developed using a bath of AZ 726 for 32 s, before being rinsed in pure water. We then deposit a 5 nm chromium layer and 80 nm gold layer using a thermal evaporator. The lift-off is performed by dipping the film in acetone for 1 h. The electrodes are finally rinsed using isopropanol and dried by an air flow. The electrodes are 2.5 mm long and spaced by 10 µm. These electrodes are used for photoconductive device and electrolyte gated transistor measurements.

Electrolyte gating:

For electrolyte gating we first mix in a glove box, 0.5 g of LiClO4 with 2.3 g of PEG. The vial is heated at 170 °C on a hot plate for 2 h until the solution becomes clear. To use the electrolyte, the solution is warmed around 100 °C and brushed on the top of the HgTe CQD film.

Photoconductive device preparation

Ligand exchange: Inside a N2 filled glove-box, HgTe CQDs in toluene are drop-casted on pre-patterned interdigitated gold electrodes (10 µm separation) on SiO2/Si substrates. After complete drying, EDT ligand exchange is performed by dipping the film in an EDT solution in ethanol (1 -2 wt %) for 90 s and rinsing it in pure ethanol for 30 s. This process is repeated for 3 to 4 times to get homogeneous and crack filled film with a device resistance of 100 -200 kΩ.

Protective layer of PMMA/PVA/PVDF: PMMA (5 wt % in CHCl3) solution is spin-coated on substrates at 2000 rpm for 60 s, then a quick annealing step at 50 °C for 1 min is performed. In following steps, PVA (centrifuged solution at 10 wt % in water) and PVDF (10 wt % in DMF) are spin coated at 4000 rpm for 60 s and 1500 rpm for 30 s, respectively. After each step, substrates are annealed for 1 min at 50 °C. Finally, device is kept in vacuum overnight for the complete drying of encapsulation layers. Thus, obtained thicknesses for these encapsulation films are found to be 1.3 µm, 0.5 µm and 0.5 µm of PMMA, PVA and PVDF, respectively.

Photovoltaic device fabrication

ITO patterning: ITO substrates are cut into 17 × 17 mm size and thoroughly cleaned by sonication in acetone for 5 min, rinsed with acetone and isopropanol, then dried completely with dry N2 flow. AZ 5214E photoresist is spin-coated for 30 s and subsequently the substrates are baked at 110 °C for 90 s. At next stage, standard photolithography is performed using mask aligner for exposing the substrates to UV light for 5 s through a lithography mask (1 mm width). Photoresist is developed using AZ 726 developer for 40 s and immediately rinsed with de-ionized water. Thus, exposed ITO surface is completely etched out with 25 % HCl (in water) for 6 min and substrates are dipped immediately in deionized water. Then, lift-off is conducted in an acetone bath and patterned ITO substrates are cleaned with acetone and isopropanol. Finally, substrates are dried with dry N2 flow. TiO2 film preparation: 200 µL of anatase TiO2 nanoparticles solution is spin-coated on above patterned ITO substrates at 5000 rpm for 30 s. The TiO2 film is annealed at 200 °C for 15 min and its thickness is measured to be 65 nm with Dektak profilometer.

HgTe CQD film preparation and EDT ligand exchange in air free conditions: Film preparation and ligand exchange are carried out inside a N2 filled glovebox. In a typical procedure, 80 µL of concentrated HgTe CQDs (25 mg/mL) from toluene is spin coated at 2000 rpm for 30 s on above fabricated Glass/ITO/TiO2 substrates. After complete evaporation of solvent, ligand exchange is carried out by dipping the film in 1 -2 wt % EDT solution in ethanol for 90 s and rinsing it in pure ethanol for 30 s. Afterwards, a quick annealing step at 50 °C, for 1 min is carried out. This procedure is repeated for 8 -9 times to get thicker (180 -200 nm) and pin-hole free HgTe CQD film.

Au electrode deposition in air free conditions: Fabricated Glass/ITO/TiO2/HgTe substrates were transferred from glove box to the thermal evaporator chamber under N2 environment. 80 nm thick Au was evaporated at a rate of 2 -5 A°/s using shadow mask (1 mm width) technique and the mask was aligned to get a pixel of 1 × 1 mm area.

Encapsulation of device: Finally, the fabricated device is transferred back to the glove box under N2 environment. The PMMA/PVA/PVDF encapsulation films are deposited on top of device with the above mentioned protocol and the device is kept in vacuum overnight for the complete drying of encapsulation layers.

Electrical measurements DC transport:

The sample is connected to a Keithley 2634b, which controls the drain bias (VDS) between -2 and +2 V with a step of 10 mV, and measures the associated current (IDS). This measurement is made in the dark and under illumination using diodes (405 nm, power = 0.17 -22 mW, 532 nm, power = 25 mW (used for inside the glove box) and 635 nm, power = 7 mW (used for in air measurement).

Transistor measurements: The sample is connected to a Keithley 2634b, which sets the drain-source bias (VDS =10 mV), controls the gate bias (VGS) between -2 and +2 V with a step of 1 mV and measures the associated currents IDS and IGS. The measurements are repeated two times to ensure that the obtained curves are stable.

Setup and experimental condition for transient photocurrent, noise measurements and frequency dependence of the photocurrent are given in Figure S2, S7 and S8, respectively.

RESULTS and DISCUSSION

To start our discussion, we focus on the active material. We synthetize HgTe CQDs with a band edge energy at 4000 cm -1 using the Keuleyan's procedure [START_REF] Keuleyan | Synthesis of Colloidal HgTe Quantum Dots for Narrow Mid-IR Emission and Detection[END_REF] , see experimental section and Figure 1c. CQDs are actually tetrapods, see transmission electron microscopy (TEM) in Figure 1a-b. Initially, the HgTe CQDs are capped with long thiol chains (dodecanethiol: DDT), which ensures the colloidal stability of the particle. To build photoconductive film of HgTe, the exchange of these long native ligands toward shorter molecules is very critical. Herein, we used solid state ligand exchange for ethanedithiol (EDT) molecules, since we demonstrate recently that short dithiols are the best tradeoff between enhancing the mobility by carrier lifetime product and the amount of introduced traps. [START_REF] Martinez | Probing Charge Carrier Dynamics to Unveil the Role of Surface Ligands on HgTe Narrow Band Gap Nanocrystals[END_REF] After ligand exchange, we observe a broadening of the excitonic feature, as well as a significant reduction of the peak relative to the C-H bond (≈3000 cm -1 ), which confirms the efficiency of the DDT removal, see Figure 1c. Transport properties probed in an electrolyte gated field effect transistor configuration [START_REF] Lhuillier | Investigating the n-and p-Type Electrolytic Charging of Colloidal Nanoplatelets[END_REF] reveals an ambipolar behavior showing the ability of HgTe CQD film for both hole and electron conduction [START_REF] Liu | n-and p-Type HgTe Quantum Dot Films[END_REF] , see Figure 1d. The hole mobility is typically three times lower than the electron mobility.

To finish those preliminary results about the material, we have measured its electronic spectrum in absolute energy scale, see Figure 1e. The band edge energy is measured though the IR spectrum, see Figure 1c. The positions of the Fermi level and valence band from the vacuum level are determined from photoemission measurements conducted on the TEMPO beamline of synchrotron Soleil. The Fermi level lies in the upper part of the band gap (80 meV below the conduction band), which confirms the slightly more n-type nature of the material observed in transport measurement, while the vacuum level is typically 4.7 eV above the Fermi level, see Figure S1. From transient photocurrent measurement, see Figure S2, we are able to determine the Urbach energy (i.e. the characteristic energy decay of the trap distribution within the band gap) to be 35 meV. [START_REF] Martinez | Probing Charge Carrier Dynamics to Unveil the Role of Surface Ligands on HgTe Narrow Band Gap Nanocrystals[END_REF] This relatively low value is critical to obtain reasonable open circuit voltage, [START_REF] Chuang | Open-Circuit Voltage Deficit, Radiative Sub-Bandgap States, and Prospects in Quantum Dot Solar Cells[END_REF][START_REF] Zhitomirsky | Engineering Colloidal uantum Dot Solids Within and Beyond the Mobility-Invariant Regime[END_REF] with in mind the integration of the HgTe CQDs into a photovoltaic configuration device.

While the film presents conductive and photoconductive behaviors even in air [START_REF] Lhuillier | Mid-Infrared HgTe/As2S3 FETs and Photodetectors[END_REF][START_REF] Martinez | Probing Charge Carrier Dynamics to Unveil the Role of Surface Ligands on HgTe Narrow Band Gap Nanocrystals[END_REF][START_REF] Lhuillier | Thermal Properties of Mid Infrared Colloidal Quantum Dot Detectors[END_REF] its properties are far from stable. Even if the film is prepared in air free condition (i.e. in glove box) the conductance rises once exposed to air, see Figure 2a. This increase of the dark conductance just after exposure is not even leading to a plateau and we keep observing an increase over the next 10 days, see Figure 2e, indicating the severe degradation of the device overtime. This increase in dark conductance will be quite detrimental for photodetector device fabrication. An usual solution to overcome a large dark current is to cool down the sample to reduce the amount of thermally activated carriers. However, ligand exchanged HgTe CQD film reveals a non-monotonic behavior of the I-T curve, [START_REF] Lhuillier | Mid-Infrared HgTe/As2S3 FETs and Photodetectors[END_REF] see Figure 2b, where cooling the sample can even increase the dark conductance. It was previously demonstrated [START_REF] Lhuillier | Mid-Infrared HgTe/As2S3 FETs and Photodetectors[END_REF] that air free preparation and handling of the film prevents such degradation of the performance. To address this issue we developed an alternative solution by encapsulating the film using protective layers. Encapsulation of CQDs has recently become a major topic in particular for their use in displays. In this case, the goal of the encapsulation is to preserve the photoluminescence efficiency at high temperature, while preventing oxygen and water exposure. This can be achieved by using polymer [START_REF] Xie | Quantum Dots-Converted Light-Emitting Diodes Packaging for Lighting and Display: Status and Perspectives[END_REF] or inorganic matrix [START_REF] Wang | Quantum Dot Color-Converting Solids Operating Efficiently in the kW/cm 2 Regime[END_REF] grown in solution or by physical method such as by ALD [START_REF] Loiudice | CsPbBr3 QD/AlOx Inorganic Nanocomposites with Exceptional Stability in Water, Light, and Heat[END_REF][START_REF] Pourret | Atomic Layer Deposition of ZnO in Quantum Dot Thin Films[END_REF] or PLD [START_REF] Aubret | Nondestructive Encapsulation of CdSe/CdS Quantum Dots in an Inorganic Matrix by Pulsed Laser Deposition[END_REF] .

However, in the case of HgTe CQDs, most of these methods cannot be used. The previously mentioned methods require mild temperature (100-200 °C) annealing operations, which leads to irreversible changes in the HgTe CQD film. Figure S3a shows that above 50 °C, annealing of the HgTe CQD film leads to a significant broadening of the exciton absorption. HgTe has a much larger Bohr radius (40 nm) than many other CQD material (≈7 nm for CdSe or CsPbBr3), and as a result HgTe CQDs are strongly confined and thus very sensitive to annealing, which leads to a partial sintering of the nanoparticles. The consecutive change of particle size makes the electrical band gap of the material becoming driven by the tail absorption. As a result, thermal activation of carriers becomes even more dramatic and we observe a rise of the conductance, see Figure 2a-b andS4. Thus, only quasi room temperature conditions can be used in the case of HgTe CQDs. We choose a strategy to combine O2 and H2O insulating barrier polymer layers to prevent any oxidation of the HgTe CQD film. All steps of film preparation (deposition + ligand exchange) are conducted in air free condition. Still in glove box, a thick (1.3 µm) PMMA layer is spin coated to obtain a smooth surface. Then a PVA layer (500 nm) is used as oxygen repealing material, before a PVDF layer (500 nm) gets deposited as water insulator, see a scheme of the device as inset of Figure 2c. With such encapsulation system, no rise of the conductance is observed while the system is brought to air environment, see Figure 2c ande. Moreover, the temperature dependence of the film recovers a monotonic behavior, see Figure 2d. The Arrhenius fit of the I-T curve around room temperature leads to an activation energy of 114 meV. With such encapsulation, stable dark current and photoresponse are observed over several month time scale, see Figure 2e-f.

I-T curve of an HgTe CQD film after the film has been exposed to air. c. I-V curves of a HgTe CQD film, prepared with protective layers, and measured in glove box and after air exposure. Inset is a scheme of the HgTe CQD film device with protective layers. d. I-T curve of an HgTe CQD film prepared with protective layers, after the film has been exposed to air. e. Dark current as a function of time spent in air for a HgTe CQD film with and without protective layers. Time zero corresponds to the sample in the air-free glove box. f. Ratio of photocurrent over dark current as a function of time spent in air for HgTe CQD films with and without protective layers.

The full characterization of the protected device in planar configuration is given in figure S9 and Figure 3. The device presents a responsivity (R in A.W -1 ) in this configuration reaching 10 mA.W -1 (Figure 3a), which corresponds to internal quantum efficiency of 3%. The device present a fast response, with a 3 dB bandwidth above 10 kHz (Figure 3b), which is compatible requested dynamics for imaging. The noise current density (in in A.Hz -1/2 ) is limited by 1/f noise as expected for HgTe CQD film [START_REF] Lhuillier | Thermal Properties of Mid Infrared Colloidal Quantum Dot Detectors[END_REF][START_REF] Liu | 1/f Noise in Semiconductor and Metal Nanocrystal Solids[END_REF][START_REF] De Iacovo | Noise Performance of PbS Colloidal Quantum Dot Photodetectors[END_REF] , see figure S9c, and is typically in the range of nA.Hz -1/2 . The specific detectivity D* (i.e. signal to noise ratio) defined as

n i A R D = *
with A the optical area is typically at room temperature around a few 10 6 jones, see Figure 3d. One way to increase performance is to cool down the device. Assuming a weak temperature dependence of the mobility and given the I-T curve of Figure 2d, we estimate that detectivity around 10 8 jones can be obtained for an operating temperature of 125 K. However, to push even further the performances, it is critical to design device geometry with inherently less dark current. Switching from photoconductive mode to photovoltaic (PV) mode is a proven way to reduce the applied bias over the sample and thus the dark current. [START_REF] Guyot-Sionnest | Background Limited Mid-Infrared Photodetection with Photovoltaic HgTe Colloidal Quantum Dots[END_REF] Indeed the built in bias of the photodiode allows to operate the device at zero (or very reduced) bias, where the dark current and its associated noise should be reduced. While PbS CQDs have been intensively integrated to PV geometry, far less work have been focused on HgTe [START_REF] Im | Efficient HgTe Colloidal Quantum Dot-Sensitized Near-Infrared Photovoltaic Cells[END_REF][START_REF] O'connor | Near-Infrared Electroluminescent Devices Based on Colloidal HgTe Quantum Dot Arrays[END_REF][START_REF] Günes | Hybrid Solar Cells Using HgTe Nanocrystals and Nanoporous TiO2 Electrodes[END_REF] and especially in the SWIR range. [START_REF] Chen | Photocurrent Enhancement of HgTe Quantum Dot Photodiodes by Plasmonic Gold Nanorod Structures[END_REF] Actually glass/ITO extensively used for solar cell remains quite transparent in the SWIR range, as long as thin ITO layer are used, see figure S5. Thus, we choose to use this substrate with in mind the design of a low-cost device. Because of the pretty large work function (4.7 eV), ITO can be used as electron injector and an inverted diode structure can be built. Our PV device is made of a stack of ITO/TiO2/HgTe/Au. Since the TiO2 layer typically requires an annealing step, this configuration presents the benefit to limit the exposure of HgTe QD to high temperature. The HgTe layer typically presents a 180 -200 nm thickness and is obtained through a multilayer deposition process to ensure an efficient ligand exchange and also to fill up any possibly formed cracks, see image of the device in Figure 4a. Finally a gold top contact is used as hole extractor with a high stability toward oxygen and water exposure.

The cross sectional scanning electron microscopy (SEM) image (Figure 4a) confirms the high quality stacking of TiO2/HgTe CQD layers on ITO substrates. To obtain an air stability operation, the device is further encapsulated using the earlier proven PMMA/PVA/PVDF stack of polymer layers. A picture of the final device is shown as inset of Figure 4a. The encapsulating layers are gently removed from the external part of the gold contact (ie away from the active device) using a razor blade and cotton swab to be able to connect electrical contact.

To understand the charge transport in this device, its I-V characteristics was measured, see Figure 4b, and it clearly shows a rectifying behavior, at room temperature. Photocurrent can be generated even at zero bias, see Figure 4b.

Figure 4c compares the current modulation induced by the light for photoconductive and PV devices in two configurations. In the photoconductive mode, we see a limited current increase under illumination, see Figure 4c. The signal to noise ratio is actually limited by the large background signal (i.e. the dark current). As PV mode is used, we observe a huge decrease of the background, thanks to zero bias operation; see Figure 4b.

The key advantage of the PV geometry compared to photoconductive operation is the increase of photocurrent to dark current ratio, as shown in Figure 4c. For the same light power density, we notice an increase of the ratio by a factor >70, as going toward the PV geometry. Performances of this PV device are reported in Figure 3 and S10 for full characterization. We would like to stress the main difference with the photoconductive geometry. First we observe a drops of the photoreponse by one order of magnitude, see Figure 3a. The latter is not due to absorption of electrode in the SWIR range, but actually due to the limited internal quantum efficiency of our device, typically 0.1%, as shown in figure S11. This demonstrates that charge extraction is still not optimized. On the other hand, the promptness of the photoresponse is preserved with a 3dB bandwidth still above the capacity of the current setup (10 kHz), see Figure 3b. As it was expected for PV geometry we notice a drastic decrease of the noise current density at low bias by more than two decades with respect to the photoconductive geometry, see Figure 3c. This results in an enhanced detectivity, which now reach 10 7 jones at room temperature. Finally the stability of the device has been checked, and the I-T curve (see figure S4c) is similar to the one obtained for photoconductive devices with protective layer, while the photodetection performance remains unchanged at least over 7 weeks.

CONCLUSIONS

We report a solution based procedure, allowing air stable room temperature operation of HgTe nanocrystals for photodetection in SWIR range over several month time scale. The procedure is based on a low temperature (50°C) approach to prevent any sintering of nanocrystals, which may potentially reduce the equivalent band gap and rise the device dark current. We demonstrate that a combination of PMMA/PVA/PVDF polymer layers prevents the previously observed degradation of performances (i.e. rise of conductance in air and non-monotonic I-T curve). We also demonstrate that PV device geometry can be effectively used to reduce the device dark current at room temperature and obtain an increase of the photocurrent to dark current ratio by a factor of 70. In all geometries, HgTe leads to fast photoresponse, with associated bandwidth above 10 kHz, which is enough for most imaging applications. By switching from photoconductive to photovoltaic device geometry, detectivity in SWIR region is found to be enhanced by 1 order of magnitude at room temperature. These results will pave the way for long term device stability and solution-based approach for promising next generation SWIR optoelectronics based on narrow bandgap HgTe CQDs.

SUPPORTING INFORMATIONS

Supporting information include details about Photoemission measurements, experimental setup for device characterization (transient photocurrent, noise, frequency response), material characterizations (temperature dependence), device and structure characterizations (optical properties of the device, band alignment)

ACKNOWLEDEGMENTS

EL thanks the support of ERC starting grant blackQD. We acknowledge the use of clean-room facilities from the "Centrale de Proximité Paris-Centre". This work has been supported by the Region Ile-de-France in the framework of DIM Nano-K (grant dopQD). This work was supported by French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, and more specifically within the framework of the Cluster of Excellence MATISSE and also by the grant Nanodose and H2DH. NG and AJ thank Nexdot for post doc funding.

Figure 1 -

 1 Figure 1 -a. and b. are low and high magnification TEM images of HgTe nanocrsytals, respectively. c. Absorption spectrum of DDT-capped and EDT-capped HgTe CQDs. d. Transfer curve (drain current as a function of gate bias) for an HgTe CQD film capped with EDT ligand probed in an electrolyte gated transistor configuration. e. Reconstructed

Figure 2 -

 2 Figure 2 -a. I -V curves of a HgTe CQD film prepared and measured in glove box and after (next hour) air exposure. b. I-T curve of an HgTe CQD film after the film has been exposed to air. c. I-V curves of a HgTe CQD film, prepared with protective layers, and measured in glove box and after air exposure. Inset is a scheme of the HgTe CQD film device with protective layers. d. I-T curve of an HgTe CQD film prepared with protective layers, after the film has been exposed to air. e. Dark current as a function of time spent in air for a HgTe CQD film with and without protective layers. Time zero corresponds to the sample in the air-free glove box. f. Ratio of photocurrent over dark current as a function of time spent in air for HgTe CQD films with and without protective layers.

Figure 3 -

 3 Figure 3 -Performances of protected photodetectors in photoconductive and photodidoe configuration a. Responsivity as a function of the applied bias under blackbody illumination (TBB= 927 °C) for a HgTe CQD film. b. Bode diagram of the photocurrent intensity for a HgTe CQD film, as a function of the light chopping frequency. c. Noise current density (at 100 Hz) as a function of applied bias for a HgTe CQD film. d. Room temperature detectivity at 100 Hz, as a function of the applied bias for a HgTe CQD film.

Figure 4 -

 4 Figure 4 -a. Cross sectional SEM image of a HgTe CQD device in photovoltaic configuration. Inset is a top view of the final device. b. I -V curve of the HgTe CQD device in photovoltaic configuration. Inset is a zoom in the zero bias region under dark condition and under illumination by a blue (405 nm) laser with a 22 mW power. C Photocurrent over dark current ratio as a function of incident power for the photoconductive device (Au/HgTe/Au) and for the PV device with an ITO/TiO2/HgTe/Au geometry.


Nathalie Lassau

Samy Ammari

Emilie Chouzenoux

Hugo Gortais

Paul Herent

Matthieu Devilder

Samer Soliman

Olivier Meyrignac

Marie-Pauline Talabard

Jean-Philippe Lamarque

Remy Dubois

Nicolas Loiseau

Paul Trichelair

Etienne Bendjebbar

Gabriel Garcia

Corinne Balleyguier

Mansouria Merad

Annabelle Stoclin

Simon Jegou

Franck Griscelli

Nicolas Tetelboum

Yingping Li

Sagar Verma

Matthieu Terris

Tasnim Dardouri

Kavya Gupta

Ana Neacsu

Frank Chemouni

Meriem Sefta

Paul Jehanno

Imad Bousaid

Yannick Boursin

Emmanuel Planchet

Mikael Azoulay

Jocelyn Dachary

Fabien Brulport

Adrian Gonzalez

Olivier Dehaene

Jean-Baptiste Schiratti

Kathryn Schutte

Jean-Christophe Pesquet

Hugues Talbot

Elodie Pronier

Gilles Wainrib

Thomas Clozel

Fabrice Barlesi

Marie-France Bellin

Michael G B Blum
email: michael.blum@owkin.com

AI-based

come

Introduction

Hospitalized COVID-19 patients are likely to develop severe outcomes requiring mechanical ventilation or high-flow oxygenation. Among hospitalized patients, 14 to 30% will require admission to an ICU, 12 to 33% will require mechanical ventilation, and 20% to 33% will die [START_REF] Myers | Characteristics of Hospitalized Adults With COVID-19 in an Integrated Health Care System in California[END_REF][START_REF] Docherty | Features of 20 133 UK patients in hospital with covid-19 using the ISARIC WHO Clinical Characterisation Protocol: prospective observational cohort study[END_REF][START_REF] Richardson | Presenting Characteristics, Comorbidities, and Outcomes Among 5700 Patients Hospitalized With COVID-19 in the New York City Area[END_REF][START_REF] Wu | Risk Factors Associated With Acute Respiratory Distress Syndrome and Death in Patients With Coronavirus Disease 2019 Pneumonia in Wuhan, China[END_REF] . Detection at admission of patients at risk of severe outcomes is important to deliver proper care and to optimize use of limited intensive care unit (ICU) ressources [START_REF] Phua | Intensive care management of coronavirus disease 2019 (COVID-19): challenges and recommendations[END_REF] .

Identification of hospitalized COVID-19 patients at risk for severe deterioration can be done using risk scores that combine several factors including age, sex, and comorbidities (CALL, COVID-GRAM) [START_REF] Liang | Development and Validation of a Clinical Risk Score to Predict the Occurrence of Critical Illness in Hospitalized Patients With COVID-19[END_REF][START_REF] Yan | An interpretable mortality prediction model for COVID-19 patients[END_REF][START_REF] Levy | Development and Validation of a Survival Calculator for Hospitalized Patients with COVID-19[END_REF][START_REF] Ji | Prediction for Progression Risk in Patients with COVID-19 Pneumonia: the CALL Score[END_REF][START_REF] Mejia-Vilet | A Risk Score to Predict Admission to Intensive Care Unit in Patients With COVID-19: The ABC-GOALS Score[END_REF][START_REF] Wynants | Prediction models for diagnosis and prognosis of covid-19 infection: systematic review and critical appraisal[END_REF] . Some risk scores also include additional markers of severity such as the dyspnea symptom, clinical examination variables such as low oxygen saturation and elevated respiratory rate, as well as biological factors reflecting multi-organ failures such as elevated Lactate dehydrogenase (LDH) values [START_REF] Levy | Development and Validation of a Survival Calculator for Hospitalized Patients with COVID-19[END_REF][START_REF] Mejia-Vilet | A Risk Score to Predict Admission to Intensive Care Unit in Patients With COVID-19: The ABC-GOALS Score[END_REF][START_REF] Xie | Association Between Hypoxemia and Mortality in Patients With COVID-19[END_REF][START_REF] Zhou | Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study[END_REF][START_REF] Lippi | Laboratory abnormalities in patients with COVID-2019 infection[END_REF] .

Beyond clinical and biological variables, computerized tomography (CT) scans also contain prognostic information, as the degree of pulmonary inflammation is associated with clinical symptoms, and the amount of lung abnormality has been associated to severe evolution [START_REF] Colombi | Well-aerated Lung on Admitting Chest CT to Predict Adverse Outcome in COVID-19 Pneumonia[END_REF][START_REF] Zhang | Clinically Applicable AI System for Accurate Diagnosis, Quantitative Measurements and Prognosis of COVID-19 Pneumonia Using Computed Tomography[END_REF][START_REF] Zhao | Relation Between Chest CT Findings and Clinical Conditions of Coronavirus Disease (COVID-19) Pneumonia: A Multicenter Study[END_REF][START_REF] Taieb | Prognostic value of visual quantification of lesion severity at initial chest CT in confirmed Covid-19 infection: a retrospective analysis on 216 patients[END_REF][START_REF] Wu | Chest CT Findings in Patients With Coronavirus Disease 2019 and Its Relationship With Clinical Features[END_REF] . However, the extent to which CT scans at patient admission add prognostic information beyond what can be inferred from clinical and biological data is unresolved.

The objective of this study was to integrate clinical, biological and radiological data to predict the outcome of hospitalized patients. CT-scan information was included in multimodal scores either through deep learning models or using radiologist quantification of lesions.

Results

A total of 1,003 patients from Kremlin-Bicêtre (KB, Paris, France) and Gustave Roussy (IGR, Villejuif, France) were enrolled in the study. Clinical, biological, and CT scan images and reports were collected at hospital admission. There were 931 patients for which clinical, biological and CT-scan data were available (Supp Fig 1). A total of 506,341 images were analyzed for the 980 patients with CT-scans (average of 517 slices per scan). Radiologists annotated 17,873 images from 329 CT-scans. Summary statistics for the clinical, biological, and CT scan data are provided in Table 1.

Table 1: Population description for the KB and IGR hospitals and association between variables measured at admission and severity. Among the 1,003 patients of the study, biological and clinical variables were available for 987 individuals. Categorical variables are expressed as percentages [available]. Continuous variables are shown as median (IQR) [available]. Association with severity are reported with p-values for each center and p-value were combined with Stouffer's method. A star (*) in the column entitled "Significant association" indicates that the variable is significantly associated with severity after Bonferroni adjustment to account for multiple testing across 58 variables (treatments are excluded). For continuous variables, odds ratios are computed for an increase of one standard deviation of the continuous variable.

Variables associated with severity

We first evaluated how clinical and biological variables measured at admission were associated with future severe progression, which we defined as an oxygen flow rate of 15 L/min or higher and/or the need for mechanical ventilation and/or patient death [START_REF]Clinical management of severe acute respiratory infection when COVID-19 is suspected[END_REF] . This definition of severe progression corresponds to a score of 5 or more according to the World Health Organization evaluation of severity on a 1 to 10 scale. We computed the severity odds ratios for each individual variable, and at each hospital center (Table 1 andSupp Fig 2). When combining association results from the two centers, we found 11 variables significantly associated with severity (P <0.05/58 to account for testing 58 We then assessed the predictive value of features from admission radiology reports, and found three significant features: (i) extent of disease (OR KB 2.37 (1.97-2.86), OR IGR 1.62 (1.11-2.37), P Stouffer = 9.56e-21) and (ii) crazy paving ( OR KB 2.50 (1.82-3.44), OR IGR 2.37 (1.10-5.11), P Stouffer = 3.10e-09), associated with greater severity, and (iii) peripheral topography , associated with lesser severity (OR KB 0.54 (0.39-0.74), OR IGR 0.55 (0.23-1.31), P Stouffer = 8.21e-05).

Segmentation of CT-scans

We next trained the deep neural network AI-segment (Supp Fig 3) to segment radiological patterns and provide automatic quantification [START_REF] Ronneberger | Convolutional Networks for Biomedical Image Segmentation[END_REF][START_REF] Hara | Learning spatio-temporal features with 3D residual networks for action recognition[END_REF] of their volume, expressed as a percentage of the full lung volume. These patterns included the three distinguishable features that appear as disease severity progresses: ground glass opacity (GGO), crazy paving, and finally consolidation. AI-segment was trained on 184 patients from KB hospital (8 fully annotated scans, 176 partially annotated ones) and evaluated on 145 patients from IGR hospital (14 fully annotated scans and 131 partially annotated ones). To evaluate AI-segment , we first compared its performance to that of radiologists manual annotation. AI-segment discriminated lung regions from regions outside of the lung with an accuracy of 99.9% when evaluated on the fully annotated scans. Within the lung, the model's ability to discriminate between lesions and healthy areas had F1 values of 0.85 and 0.98 on partially and fully annotated scans. In the fully annotated scans, the predicted volumes of each lesion type had relative errors (median [min-max]) of 3.77% [0.054%-14%] for GGO, 0.96% [0.058%-4.4%] for consolidation, and 5.92% [0.41%-13%] for sane lung (no crazy paving was present in these scans). We next compared AI-segment to the information contained in the radiology reports. The F1 score measuring the ability of AI-segment to detect the presence of a lesion type per patient, was of 0.88 for GGO, 0.65 for crazy paving, and 0.75 for consolidation (Supp Table 1). Correlation between quantification of the proportion of lesions with AI-segment and the radiologist evaluation was of 0.56 (Supp Fig 5). AI-segment visual results were also consistent with radiologist observations (see Figure 1 for three representative cases). We lastly evaluated to what extent AI-segment provided biomarkers of future severity. We found that severity was significantly associated to GGO extent (OR KB 0.64 (0.54,0.76), 0.77 (0.54,1.10), P Stouffer = 1.94e-07), crazy paving extent (OR KB 1.47 (1.20-1.79), OR IGR 1.31 (0.92,1.87), P Stouffer = 6.70e-05), consolidation extent(OR KB 1.46 (1.23,1.73), 1.27 (0.89,1.82), P Stouffer = 7.61e-06) as well as total disease extent (OR KB 2.11 (1.74,2.55), OR IGR 1.90 (1.30,2.79), P Stouffer = 7.66e-16)(accounting for multiple testing). These correlations were observed in the larger KB dataset, but were not found in the IGR dataset (Supp Table 2).

Prognostic models based on CT-scan only

We next evaluated the prognostic value of variables extracted from CT scans through three different models. The first model called report combined variables from the radiological report using logistic regression. The second was based on the lesion volumes computed by AI-segment and variables were again combined with logistic regression. The third called AI-severity used a weakly supervised approach with no radiologist-provided annotations (Supp Fig 4) [START_REF] Courtiol | Deep learning-based classification of mesothelioma improves prediction of patient outcome[END_REF] . All three models were trained on 646 KB patients, validated on 150 KB patients and on the independent IGR dataset of 135 patients (Figure 2). On the validation set from KB hospital, AI-severity outperformed report (AUC AI-severity = 0.76 (0.66,0.85), AUC AI-segment = 0.67(0.56,0.77), AUC report = 0.71 (0.62,0.80)). On the independent IGR validation set, both AI-segment and AI-severity outperformed the model report (AUC AI-severity = 0.75 (0.65,0.84), AUC AI-segment = 0.70 (0.59,0.80), AUC r eport = 0.65 (0.54,0.75)). When considering alternatives outcomes consisting of either death, or death or admission to ICU, AI-severity and AI-segment were also superior to report in terms of AUC (Supp Table 3).

To interpret the weakly supervised AI-severity model, and understand what it detects within the CT scans, we evaluated to what extent the features extracted by AI-severity (internal representation) could predict clinical and radiological variables. To this end, we trained a new logistic regression with AI-severity's extracted features as input, and some clinical and radiological variables as output. AUC on the KB validation set was 0.93 (C.I. = (0.88,0.97)) for disease extent (threshold >2), 0.78 (C.I. = (0.70,0.85)) for crazy paving, 0.64 for condensation (C.I. = (0.53,0.74)) and 0.80 for GGO (C.I. = (0.65,0.94)) (Supp Table 4). It was also possible to relate internal representations of the neural networks to clinical variables. We obtained an AUC of 0.88 (C.I. = (0.82,0.94)) for predicting an age strictly larger than 60 year-old, an AUC of 0.93 (C.I. = (0.89,0.97)) for sex, and of 0.76 (C.I. = (0.68,0.84)) for predicting an oxygen saturation larger than 90%. As a comparison, a logistic regression trained on the variables from the radiology report obtained only AUC scores of 0.70 (C.I. = ( 0.61,0.78 )) for age, 0.57 (C.I. = ( 0.48, 0.67) ) for sex and of 0.68 (C.I. = ( 0.58, 0.77) ) for oxygen saturation. Simply put, this analysis shows that the internal representation of the AI-severity neural network captures clinical features from the lung CTs, such as sex or age, on top of the known COVID-19 radiology features.

Multimodal prognostic models and ScanCov score

Lastly, we evaluated whether CT scans have a prognostic value beyond what can be inferred from clinical and biological characteristics alone. To this end, we sought to compare the performance of trimodal CT scan/clinical/biological models to a bimodal clinical/biological model ( C & B ). Using a greedy search approach to include optimal variables, we therefore incorporated clinical and biological variables into report and named the resulting trimodal model the ScanCov score. Coefficients and transformations required to compute the 6-variable ScanCov score are available in Supp Table 6. Through the same method, we also made a trimodal version of AI-segment , and AI-severity (Supp Fig 6, Supp Table 5). We evaluated the models' performances on three outcomes: the initial WHO-defined high severity outcome of "oxygen flow rate of 15 L/min or higher, or need for mechanical ventilation, or death", as well as two other outcomes "death or ICU admission", and "death". For each outcome and validation set, both ScanCov and AI-severity performed better than the bimodal biological/clinical C & B model (Figures 2 &3, Supp Table 3). The gain of performance when compared to the C & B model was larger for the KB hospital ( median AUC increase of 4.0% for AI-severity and of 3.6% for ScanCov) than for the IGR hospital (median AUC increase of 1.5% for AI-severity and of 0.4% for ScanCov) . For the model AI-segment , the median increase of AUC was of 0.5% for the KB hospital and of 1.9% for the IGR hospital. 3). The median difference (averaged over outcomes) between the AUC of AI-severity and of other scores ranged between 5% (COVID-GRAM) and 15% (CALL) at KB and between 10% (COVID-GRAM) and 26% [START_REF] Colombi | Well-aerated Lung on Admitting Chest CT to Predict Adverse Outcome in COVID-19 Pneumonia[END_REF] at IGR. The median difference (averaged over outcomes) between the AUC of AI-segment and of other scores ranged between 2% (COVID-GRAM) and 12% (CALL) at KB and between 5% (COVID-GRAM) and 24% [START_REF] Colombi | Well-aerated Lung on Admitting Chest CT to Predict Adverse Outcome in COVID-19 Pneumonia[END_REF] at IGR. Similarly, the median difference (averaged over outcomes) between the AUC of ScanCov and of other scores ranged between 4% (COVID-GRAM) and 14% (CALL) at KB and between 5% (COVID-GRAM) and 24% [START_REF] Colombi | Well-aerated Lung on Admitting Chest CT to Predict Adverse Outcome in COVID-19 Pneumonia[END_REF] at IGR. Among alternative scores, the COVID-GRAM score provided the largest value of median AUC (Figure 3, Supp Table 3). When averaging AUC (median) over outcomes at KB, the range of AUC increase when comparing COVID-GRAM to other scores was between 0.5% (MIT analytics) and 10% (CALL); range of AUC increase at IGR was between 7% (MIT analytics) and 10% [START_REF] Colombi | Well-aerated Lung on Admitting Chest CT to Predict Adverse Outcome in COVID-19 Pneumonia[END_REF] . The COVID-GRAM score was also the only alternative scoring system we considered that includes CT scan information. Of all the features within the radiologists' report, disease extent was the most strongly associated to prognosis (Table 1). We therefore further investigated this feature to confirm that it brings additional prognostic information that is not otherwise captured in any clinical or biological variable. In the KB dataset, the three variables that were the most correlated with disease extent were LDH (r = 0.52, C.I. = (0.45,0.58)), CRP (r = 0.45, C.I. = (0.39,0.51)), and oxygen saturation (r = -0.43, C.I. = (-0.49,-0.37)) (Supp Table 7). We then regressed the severity outcome with disease extent and the three correlated variables and found that significant predictors included oxygen saturation (P = 1.57e-07) and disease extent (P = 0.01), whereas statistical evidence for association was weak for LDH (P = 0.06) and absent for CRP (P = 0.26). The statistical evidence for association between disease extent and severity was also found (P = 9.85e-08) when accounting for the five additional variables of the ScanCov score, which were also significantly related with the outcome (Age P = 1.49e-06, Oxygen saturation P = 2.83e-08, Sex P = 0.035, Platelet P = 0.001, Urea = 9.77e-05). This confirms that the radiological feature of disease extent brings unique prognostic information.

To further evaluate the ScanCov score, individuals in the top tercile were assigned in a high risk group. We found that the survival function of the individuals at high risk was significantly different from the survival function of the other individuals (Figure 4, P = 2.90e-07 at KB, P = 5.38e-08 at IGR for a log-rank test). When considering a binary classification consisting of a high-risk group and a medium or low risk group, we obtained positive predictive values (or precision) of 54% (KB) and 68% (IGR), negative predictive values of 85% (KB) and 80% (IGR), specificities of 78% (KB) and 91% (IGR), and sensitivities of 65% (KB) and 48% (IGR).

Discussion

Taken together, these results show that unique future disease severity markers are present within routine CT scans performed at admission, and that these scans provide useful and interpretable elements for prognosis.

Looking back on the prognostic clinical and biological variables, we found 11 of these significantly associated with severe evolution, which is consistent with previous studies [START_REF] Lippi | Laboratory abnormalities in patients with COVID-2019 infection[END_REF][START_REF] Henry | Chronic kidney disease is associated with severe coronavirus disease 2019 (COVID-19) infection[END_REF][START_REF] Ruan | Clinical predictors of mortality due to COVID-19 based on an analysis of data of 150 patients from Wuhan, China[END_REF] . First, looking at clinical characteristics, we confirmed that male and older persons are more at risk [START_REF] Williamson | OpenSAFELY: factors associated with COVID-19-related hospital death in the linked electronic health records of 17 million adult NHS patients[END_REF] . A lthough BMI is a known risk clinical factor for severe COVID [START_REF] Williamson | OpenSAFELY: factors associated with COVID-19-related hospital death in the linked electronic health records of 17 million adult NHS patients[END_REF] , it was not associated with severity here. Discussion with clinicians however indicated that the data capture may have been biased, with emergency room doctors inputting height and weight more frequently for obese patients. Second, looking at clinical examination variables, we found that respiratory rate, diastolic pressure, and oxygen saturation are clinical variables associated with severity. These associations may reflect physician decisions taken for ICU triage. Inclusion criteria for critical care triage include (i) requirement for invasive ventilatory support characterized by an oxygen saturation lower than 90%, or by respiratory failure, or (ii) requirement for vasopressors characterized by hypotension and low blood pressure [START_REF] Sprung | Adult ICU Triage During the Coronavirus Disease 2019 Pandemic: Who Will Live and Who Will Die? Recommendations to Improve Survival[END_REF] . Third, looking at comorbidities, we confirmed the results of several meta-analyses [START_REF] Wang | Does comorbidity increase the risk of patients with COVID-19: evidence from meta-analysis[END_REF][START_REF] Henry | Chronic kidney disease is associated with severe coronavirus disease 2019 (COVID-19) infection[END_REF][START_REF] Lippi | Hypertension and its severity or mortality in Coronavirus Disease 2019 (COVID-19): a pooled analysis[END_REF][START_REF] Wang | Comorbid Chronic Diseases and Acute Organ Injuries Are Strongly Correlated with Disease Severity and Mortality among COVID-19 Patients: A Systemic Review and Meta-Analysis[END_REF] that showed that chronic kidney disease and hypertension are linked to severity. We however did not find significant associations for other comorbidities previous associated with severity, such as diabetes, and cardiovascular diseases [START_REF] Wang | Does comorbidity increase the risk of patients with COVID-19: evidence from meta-analysis[END_REF][START_REF] Gupta | Clinical considerations for patients with diabetes in times of COVID-19 epidemic[END_REF] . While we expected cancer patients to have more severe outcomes because they are generally older, with multiple co-morbidities and often in a treatment-induced immunosuppressive state [START_REF] Liang | Cancer patients in SARS-CoV-2 infection: a nationwide analysis in China[END_REF][START_REF] Miyashita | Do patients with cancer have a poorer prognosis of COVID-19? An experience in New York City[END_REF][START_REF] Dai | Patients with cancer appear more vulnerable to SARS-COV-2: a multi-center study during the COVID-19 outbreak[END_REF] , we did not find this association. Several factors can explain this. Each cohort was not optimally balanced to conclusively study the association between cancer and severity: IGR admitted mostly cancer patients (80% of the patients) while KB admitted very few cancer patients (7%). Fourth, looking at COVID symptoms, we did not find any significantly associated with severity. Dyspnea is a prominent symptom that has been repeatedly associated with severity and our results are compatible with a positive association with severity but we may lack a large-enough sample size to be significant [START_REF] Liang | Development and Validation of a Clinical Risk Score to Predict the Occurrence of Critical Illness in Hospitalized Patients With COVID-19[END_REF][START_REF] Li | The Clinical and Chest CT Features Associated With Severe and Critical COVID-19 Pneumonia[END_REF][START_REF] Du | Predictors of mortality for patients with COVID-19 pneumonia caused by SARS-CoV-2: a prospective cohort study[END_REF] . Last, looking at biological measures, we found that inflammatory biomarkers, LDH and CRP are related to severity [START_REF] Zhou | Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study[END_REF][START_REF] Li | Risk factors for severity and mortality in adult COVID-19 inpatients in Wuhan[END_REF][START_REF] Ruan | Clinical predictors of mortality due to COVID-19 based on an analysis of data of 150 patients from Wuhan, China[END_REF] . We also found association with neutrophil and urea, the later being explained by the fact that high urea is indicative of kidney disfunction. Thrombocytopenia (low platelet count) was not significantly associated to severity, possibly because of lack of statistical power and stringent correction for multiple testing, but association betwen thrombocytopenia and severity was in the expected direction and platelet counts are included in the 6-variable ScanCov score and in the trimodal models AI-segment and AI-severity .

Beyond these clinical and biological variables, chest CT-scans provided additional markers of disease severity. Significant features include the total extent of lesions, the presence of crazy paving pattern lesions, and the proportion of consolidation lesions when measured with automatic segmentation. Although the extent of disease severity and consolidation are known to be associated with severity [START_REF] Colombi | Well-aerated Lung on Admitting Chest CT to Predict Adverse Outcome in COVID-19 Pneumonia[END_REF][START_REF] Taieb | Prognostic value of visual quantification of lesion severity at initial chest CT in confirmed Covid-19 infection: a retrospective analysis on 216 patients[END_REF][START_REF] Yuan | Association of radiologic findings with mortality of patients infected with 2019 novel coronavirus in Wuhan, China[END_REF][START_REF] Zhang | CT features of SARS-CoV-2 pneumonia according to clinical presentation: a retrospective analysis of 120 consecutive patients from Wuhan city[END_REF][START_REF] Li | CT image visual quantitative evaluation and clinical classification of coronavirus disease (COVID-19)[END_REF][START_REF] Li | Association of 'initial CT' findings with mortality in older patients with coronavirus disease 2019 (COVID-19)[END_REF][START_REF] Liu | CT manifestations of coronavirus disease-2019: A retrospective analysis of 73 cases by disease severity[END_REF][START_REF] Ye | Chest CT manifestations of new coronavirus disease 2019 (COVID-19): a pictorial review[END_REF] , our study discovered its association with crazy paving, a precursor of consolidation lesions. Initial damages to the alveoli, as well as protein and fibrous exudation, explain the early onset of GGO. As the disease progresses, more and more inflammatory cells infiltrate the alveoli and interstitial space, followed by diffuse alveolar lesions and the formation of a hyaline membrane, which results in a crazy paving appearance, which is then followed by consolidation on the CT examination [START_REF] Xu | Pathological findings of COVID-19 associated with acute respiratory distress syndrome[END_REF][START_REF] Tian | Pulmonary Pathology of Early-Phase 2019 Novel Coronavirus (COVID-19) Pneumonia in Two Patients With Lung Cancer[END_REF] . Correlation results between the proportion of each lesion type and severity reflects this sequencing, as GGO proportions are negatively related with severity, while crazy paving and consolidation proportions are positively correlated to severity (Supp Table 2).

Compared to a radiologist's reporting and quantification of lesions, there are several advantages to capturing CT-scan information through deep learning models. Good reproducibility is a key element for imaging biomarkers such as disease extent, and visual inspection of images introduces variability that can hinder its clinical application [START_REF] Hagiwara | Variability and Standardization of Quantitative Imaging: Monoparametric to Multiparametric Quantification, Radiomics, and Artificial Intelligence[END_REF] . Additionally, the consolidation feature, which has been repeatedly associated with COVID severity [START_REF] Li | The Clinical and Chest CT Features Associated With Severe and Critical COVID-19 Pneumonia[END_REF][START_REF] Yuan | Association of radiologic findings with mortality of patients infected with 2019 novel coronavirus in Wuhan, China[END_REF][START_REF] Li | Association of 'initial CT' findings with mortality in older patients with coronavirus disease 2019 (COVID-19)[END_REF][START_REF] Liu | CT manifestations of coronavirus disease-2019: A retrospective analysis of 73 cases by disease severity[END_REF][START_REF] Ye | Chest CT manifestations of new coronavirus disease 2019 (COVID-19): a pictorial review[END_REF] , was not found to be associated with severity with a simple presence/absence radiologist coding, whereas correlation was evident once pulmonary consolidation was quantified with automatic segmentation. Another advantage is that radiologists are faced with the challenge that large numbers of cases must be read, annotated and prioritized in a COVID-19 pandemic. AI analysis of radiological images has the potential to reduce this burden and speed up their reading time. Finally, unimodal prognosis scores obtained with deep learning models trained on CT-scans are more predictive of severity than manually extracted radiological features. We indeed showed that internal representation of the AI-severity neural network captures clinical information from CT scans, and this can can be particularly useful when some clinical or lab measurements are missing.

Our reported prognostic values for CT-scan-based models (AUC range of 0.70 -0.80) are lower than the 0.85 AUC reported in the previously published Zhang et al study [START_REF] Zhang | Clinically Applicable AI System for Accurate Diagnosis, Quantitative Measurements and Prognosis of COVID-19 Pneumonia Using Computed Tomography[END_REF] . We hypothesize that this is due to use of different outcome definitions, as well as different patient characteristics in the study cohorts (age, severity at admission, etc). Hospital admission criteria vary between countries and hospitals; for instance, proportion of deaths in our French KB and IGR cohorts was of 16-17%, while it was of 39% in the Zhang et al study [START_REF] Zhang | Clinically Applicable AI System for Accurate Diagnosis, Quantitative Measurements and Prognosis of COVID-19 Pneumonia Using Computed Tomography[END_REF] . When applying other previously published scores to the KB and IGR datasets, we found smaller AUC scores than reported values in the original papers. This difference can again be explained by differing patient characteristics, and different measures of severity between studies [START_REF] Yan | An interpretable mortality prediction model for COVID-19 patients[END_REF][START_REF] Mejia-Vilet | A Risk Score to Predict Admission to Intensive Care Unit in Patients With COVID-19: The ABC-GOALS Score[END_REF][START_REF] Colombi | Well-aerated Lung on Admitting Chest CT to Predict Adverse Outcome in COVID-19 Pneumonia[END_REF][START_REF] Liang | Development and Validation of a Clinical Risk Score to Predict the Occurrence of Critical Illness in Hospitalized Patients With COVID-19[END_REF][START_REF] Ji | Prediction for Progression Risk in Patients with COVID-19 Pneumonia: the CALL Score[END_REF] Our evaluation of the different trimodal models that included CT scan information in addition to clinical and biological information revealed the added prognostic value of CT scans. Interestingly, while CT scan disease extent was correlated to biological and clinical severity biomarkers such as CRP levels, tissue damage (LDH) and oxygenation -highlighting some information redundancy between data modalities [START_REF] Li | The Clinical and Chest CT Features Associated With Severe and Critical COVID-19 Pneumonia[END_REF] -disease extent was still significantly associated with severity even after accounting for these other severity markers, confirming the unique added value of CT-scans. Beyond AI modeling, our study shows that the 6-variable ScanCov score integrating a radiological quantification of lesions with key clinical and biological variables provides accurate severity predictions, and can rapidly become a reference patient scoring approach.

Methods

Description of the retrospective study Data including CT-scans, were collected at two French hospitals (Kremlin Bicêtre Hospital, APHP, Paris denotes as KB and Gustave Roussy Hospital, Villejuif denoted as IGR). CT scans, clinical, and biological data were collected in the first 2 days after hospital admission. This study has received approval of ethic committees from the two hospitals and authors submitted a declaration to the National Commission of Data Processing and Liberties (N° INDS MR5413020420, CNIL) in order to get registered in the medical studies database and respect the General Regulation on Data Protection (RGPD) requirements. An information letter was sent to all patients included in the study. We stopped to update information about patient status on the 5th of May. Among the 1,003 patients of the study, two patients asked to be excluded from the study. Forchheim). All patients were scanned in a supine position during breath-holding at full inspiration. The acquisition and reconstruction parameters were of 120kV tube voltage with automatic tube current modulation (100-350 mAs), 1 mm slice thickness without interslice gap, using filtered-back-projection (FBP) reconstruction (SOMATOM Drive) or blended FBP/iterative reconstruction (Discovery or Optima). Axial images with slice thickness of 1 mm were used for coronal and sagittal reconstructions.

Radiology reports

COVID-19 associated CT imaging features were obtained from radiologist reports that follow the guidelines of several scientific societies of radiology (French SFR, STR, ACR, RSNA) regarding the reporting of chest CT findings related to COVID-19 [START_REF] Simpson | Radiological Society of North America Expert Consensus Statement on Reporting Chest CT Findings Related to COVID-19[END_REF] . The template of the radiologist report ( https://ebulletin.radiologie.fr/actualites-covid-19/compte-rendu-tdm-thoracique-iv-0 ) was available the 17th of March and the reports were completed retrospectively for the patients who were admitted to the hospital before that date. CT imaging characteristics were evaluated to provide the five following variables : (i) ground glass opacity (GGO) (rounded / non rounded / absent) that is defined as an increase in lung density not sufficient to obscure vessels or preservation of bronchial and vascular margins, (ii) consolidation (rounded / non rounded / absent) that occurs when parenchymal opacification is dense enough to obscure the vessels' margins and airway walls and other parenchymal structures, (iii) the crazy-paving pattern (present/absent) that is defined as ground-glass opacification with associated interlobular septal thickening 51 , (iv) peripheral topography (present/absent) that corresponds to the spatial distribution of lesions in the one-third external part of the lung, and (v) inferior predominance (present/absent) that is defined as a predominance of lesions located in the lower segments of the lung. A rounded pattern (for GGO and consolidation) is defined as a lesion presenting a well delineated shape. In addition to the five CT imaging features, radiologists assessed the extent of lung lesions according to the evaluation criteria established by the French Society of Radiology (SFR) [START_REF]La société d'Imagerie Thoracique propose un compte-rendu structuré de scanner thoracique pour les patients suspects de COVID-19[END_REF] . Disease extent can be: absent / minimal (<10%) / moderate (10-25%) / extensive (25-50%) / severe (>50%) / critical >75%. The coding absent / minimal / moderate extensive / severe / critical was based on a quantitative variable with values of 0 / 1 / 2 / 3 / 4 / 5. Variables were automatically extracted from the report using optical character recognition.

Annotation scenario of CT scans by radiologists

Two radiologists (4 and 9 years of experience) examined and annotated 307 anonymized chest scans independently and without access to the patient's clinic or COVID-19 PCR results. All CT images were viewed with lung window parameters (width, 1500 HU; level, -550 HU) using the SPYD software developed by Owkin. Regions of interest were annotated by the radiologists in four distinct classes : healthy pulmonary parenchyma, ground glass opacity, consolidation, crazy-paving. The presence of organomegaly was also notified when present, as a binary class. When multiple CT images were available for a single patient, the image to analyze was selected using the SPYD software. One AI and imaging PhD student also provided full 3D annotation of the four classes on 22 anonymized chest scans using the 3D Slicer software.

Statistical analysis

When detecting association with the severity outcome, odds ratio and P-values (two-sided tests) were computed separately for each hospital using logistic regression ( glm function of the R statistical software). P-values from the two different hospitals were pooled using the Stouffer meta-analysis formula accounting for the two different sample sizes. For association between severity and each variable, we considered Bonferroni correction accounting for 58 variables and 62 variables when also considering imaging markers obtained with AI-segment . To compute confidence intervals for AUC values, we considered DeLong method [START_REF] Delong | Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach[END_REF] . Survival functions were obtained using Kaplan-Meier estimators.

The AI-segment pipeline for lesion segmentation from CT scans was based on 3 segmentation networks: 3D Resnet50 54 , 2.5D U-Net, and 2D U-Net [START_REF] Ronneberger | Convolutional Networks for Biomedical Image Segmentation[END_REF] . U-Net consists of convolution, max pooling, ReLU activations, concatenation and up-sampling layers with sections: contraction, bottleneck, and expansion. ResNet contains convolutions, max pooling, batch normalization, and ReLU layers that are grouped in multiple bottleneck blocks. All models were trained on CT scans provided by Kremlin-Bicêtre (KB) and evaluated on annotated CT scans from Institut Gustave Roussy (IGR). The dataset was divided into two categories: Fully Annotated Scans (FAS) composed of 22 scans (8 from KB and 14 from IGR) and Partially Annotated Scans (PAS) composed of 307 scans (176 from KB and 131 from IGR). PAS contains a total of 7,374 annotated slices and 24,476,521 annotated pixels, i.e. 24 slices per PAS and 3,319 pixels annotated per slice on average. 2D U-Net was trained for left/right lung segmentation and 3D ResNet and 2.5D U-Net were used for lesion segmentation. 3D ResNet50 was trained on 8 KB FAS (i.e. 3,704 slices) . Inputs for the 3D ResNet consist of a height and a width of 128, and a depth of 32. We initialized the 3D ResNet with pretrained weights [START_REF] Chen | Med3D: Transfer Learning for 3D Medical Image Analysis[END_REF] . We then trained the network with Stochastic Gradient Descent for parameter optimization and an initial learning rate of 0.1 with a decay factor of 0.1 every 20 epochs. The network was trained for a total of 100 epochs. For the 2.5D U-Net, we first pretrained the network on a left-right lung segmentation task using the LCTCS dataset [START_REF] Yang | Autosegmentation for thoracic radiation treatment planning: A grand challenge at AAPM 2017[END_REF] . The network was then trained on the KB dataset using Adam optimization algorithm with a learning rate, weight decay, gradient clipping and learning rate decay parameters of 1e-3, 1e-8, 1e-1, and 0.1 (applied at epochs 90 and 150) for 300 epochs. While the validation set remains the same as when evaluating the 3D resnet50 model, 176 KB PAS scans were added to the 8 KB FAS, in the training set. PAS were only added to the 2.5D U-Net training set due to the incompleteness of the annotated volume in the scans which would not satisfy the volumetric requirements of the 3D ResNet50 input. Finally, for the left/right lung segmentation, the 2D U-Net was trained on the 8 KB FAS. Similarly to 2.5D U-Net, Adam optimization algorithm was used with a learning rate, weight decay, gradient clipping, learning rate decay, and number of epochs of 1e-3, 1e-8, 1e-1, 0.1 (applied at epoch 70), and 104. Both 2.5D U-Net and 2D U-Net used affine transformation and contrast change for data augmentation while 3D ResNet50 used affine transformation, contrast change, thin plate splines, and flipping. 3D ResNet and 2.5D U-Net are trained through the minimization of a cross entropy loss and 2D U-Net minimized a binary cross entropy loss. All training was performed on NVIDIA Tesla V100 GPUs using Pytorch as a coding framework. During the validation phase, ensemble inference [START_REF] Baldeon Calisto | AdaEn-Net: An ensemble of adaptive 2D-3D Fully Convolutional Networks for medical image segmentation[END_REF] was performed on all available scans by averaging lesion masks, which were predicted from the 3D ResNet and 2.5D U-Net models, using arithmetic mean.

We evaluated AI-segment on three distinct aspects. First, we evaluated its ability to perform accurate segmentation. To this aim, we computed F1 scores for the PAS (partially annotated scans) and FAS (fully annotated scans), of the IGR test set, when discriminating lesions versus sane areas inside the lung. Micro-averaging was used to limit the effect of class imbalance for the three different lesion types. We also reported the accuracy to discriminate background versus lung regions using FAS where background regions outside of the lung were annotated. Second, we evaluated its ability to estimate the proportion of each lesion type per scan. To this aim, we computed the median, minimum and maximum of the absolute value of the difference between the ground truth percentage of each lesion type obtained from radiologists' annotations and the estimated ones, on the 14 available FAS of the IGR dataset. Third, we evaluated to what extent AI-segment reproduces the analysis reported by radiologists. To this aim, we first compared the binary decision 'presence or absence of a lesion type' of AI-segment to the radiologist report considered as ground truth. A lesion type was detected by AI-segment when its estimated volumetry, averaged over both lungs, was above a certain threshold. The difference was then evaluated in terms of detection accuracy and F1 score, for two threshold values, using all scans of the IGR dataset (Supp Table 1). Then, we compared disease extent as evaluated by radiologists to the one predicted by AI-segment (Supp Fig 5) .

Machine learning models for severity classification based of CT scans ( AI -severity)

The AI -severity model was defined as an ensemble of two sub-models, as illustrated in Supp Fig 4. Each sub-model predicted disease severity from CT scans without using any expert annotations at the slice level. Preprocessing of the data consisted of resizing the CT scans to a fixed pixel spacing of (0.7mm, 0.7mm, 10mm) and applying a specific windowing on the HU intensities. Each sub-model is composed of two blocks: a deep neural network called feature extractor and a penalized logistic regression. The two sub-models feature extractors are an EfficientNet-B0 [START_REF] Tan | Rethinking Model Scaling for Convolutional Neural Networks[END_REF] pre-trained on the ImageNet public database and a ResNet50 60 pre-trained with MoCo v2 61 on one million CT scan slices from both Deep Lesion 62 and LIDC 63 . Each of these networks provide an embedding of the slices of the input CT scans into a lower-dimensional feature space (1280 for EfficientNet-B0 and 2048 for ResNet50). For the ResNet50-based sub-model, we reduced the dimension of the feature space using a principal component analysis with 40 components before applying logistic regression. A different windowing was applied on the CT scans before the feature extractor : (-1000 HU, 600 HU) for EfficientNet-B0 and (-1000 HU, 0 HU), (0 HU, 1000 HU) and (-1000 HU, 4000 HU) for ResNet50. Predictions of AI-severity were obtained by averaging predictions of the submodels using equal weights. Optimisation of the architecture of the network (preprocessing, feature extraction or model architecture and training, feature engineering, model aggregation) was performed using a 5 fold cross validation on the training set of 646 patients from KB.

CT scans may contain devices such as catheters (EKG monitoring, oxygenation tubing...) that are easily detectable in a CT and can bias prediction of severity ( i.e. detecting the presence of a technical device associated with severity instead of detecting the radiological features associated with severity). In order to ensure that medical devices do not affect feature extraction, all voxels outside of the lungs were masked using a pre-trained U-Net lung segmentation algorithm 64 .

Multivariate models to predict severity

The different models that combine multiple features to predict severity were fitted using logistic regression ( AI-segment , trimodal AI-segment , report , trimodal report/ScanCov , trimodal AI-severity ). Models were trained using cross validation with 5 folds on the training dataset of 646 patients from KB, and folds were stratified by age and severity outcome. Variables that were available for less than 300 patients of the training set (conjugated bilirubin and alanine) were not used. For the remaining variables, missing values were imputed by the average over patients of the training set. L2 regularization was applied when fitting logistic regression. The regularization coefficient was determined by maximizing the average AUC over the 5 cross-validation folds, using a range of different values ranging from 0.01 to 100. XGBoost algorithm was also evaluated but did not show superior performance on this dataset. We use pandas and scikit-learn to manipulate data, train and evaluate machine learning algorithms 65 .

To select variables in the multivariate models, we considered a forward feature selection technique (Supp Fig 6). The first variable included in the model is the variable which provides the largest AUC values. Then, we computed AUC values for all models with two variables including the first one that has already been included. We continued this procedure until all variables were included. Performances of the models increased quickly when the first variables were included and then AUC values reached a plateau (Supp Fig 6). We used the elbow method to select the parsimonious set of variables that is found when a plateau of AUC is reached.

Other scores to predict severity and mortality

We performed a comparison with several multivariate scores of COVID severity or death. The COVID-GRAM score was the only multimodal score we considered that also includes information from CT scan [START_REF] Liang | Development and Validation of a Clinical Risk Score to Predict the Occurrence of Critical Illness in Hospitalized Patients With COVID-19[END_REF] . When computing COVID-GRAM score, we assume that patients were not unconscious at admission and did not have hemoptysis as a symptom because these two information were missing from our dataset. The other scores we considered are based on clinical variables and possibly biological variables. They include the CALL (severity) score with clinical and biological information [START_REF] Ji | Prediction for Progression Risk in Patients with COVID-19 Pneumonia: the CALL Score[END_REF] as well as two other scores (the Yan et al. model for mortality prediction and the Colombi et al. model for severity prediction) that include clinical and biological information [START_REF] Yan | An interpretable mortality prediction model for COVID-19 patients[END_REF][START_REF] Colombi | Well-aerated Lung on Admitting Chest CT to Predict Adverse Outcome in COVID-19 Pneumonia[END_REF] . In order to compute the Yan et al. score, we considered the same features as the ones used by the authors and reproduced their training of an XGBoost model with a single tree and a maximum depth of 2 [START_REF] Yan | An interpretable mortality prediction model for COVID-19 patients[END_REF] . We also considered the MIT Covid Analytics as a risk score for mortality ( https://www.covidanalytics.io/mortality_calculator) and the CURB65 score developed to predict mortality for community-acquired pneumonia 66 .

Figure 1 :

 1 Figure 1 : Axial chest CT scans and segmentation results COVID-19 radiology patterns, as provided by the model AI-segment , for 3 patients with COVID-19. Green/transparent: sane lung; blue: GGO; yellow : crazy paving; red: consolidation. (Top) 67-year-old woman with diffuse distribution, and multiple large regions of subpleural GGO with consolidation to the right and left lower lobe. Estimated disease extent by AI: 69%/47% (right/left). Radiologist report: critical stage of COVID-19 (stage 5). (Middle) 56-year-old man, with diffuse distribution and multiple large regions of subpleural GGO with superimposed intralobular and interlobular septal thickening (crazy paving). Estimated disease extent by AI: 51%/68% (right/left). Radiologist report: severe stage of COVID-19 (stage 4). (Bottom) 70-year-old woman, with minimal impairment, and multiple small regions of subpleural GGO with consolidation to the right lower lobe. Estimated disease extent 13%/7% (left/right). Radiologist report: moderate stage of COVID-19 (stage 2).

Figure 2 :

 2 Figure 2: Receiver operating characteristic (ROC) curves for the models that predict severity. Models were evaluated on two distinct validation sets consisting of 150 patients from KB (left panels) and 135 patients from IGR (right panels). The model RR denotes the model based on the variables of the radiologist report, the model C & B denotes the model based on clinical and biological data only, and the prefix Tri stands for Trimodal when clinical and biological data were included in addition to CT-scan data. AI-segment and AI-severity denote two models based on deep learning variables extracted from CT-scans.

Figure 3 :

 3 Figure 3 : AUC values of the different models for the three distinct outcomes. The C & B (bimodal model with clinical and biological information), Tri AI-severity, Tri AI-segment (trimodal models with deep learning to extract information from CT scans) and ScanCov 6-variable trimodal model were trained on 646 patients from KB. These models were trained using the severity outcome defined as an oxygen flow rate of 15 L/min or higher, the need for mechanical ventilation, or death. When evaluating these 4 models on the alternative outcomes, models were not trained again. Results are reported on the validation set from KB (150 patients) and the external validation set from IGR (135 patients). Error bars represent the 95% confidence intervals.

Figure 4 :

 4 Figure 4: KM curves for the high risk individuals and the ones with low or medium risk according to the ScanCov score. The threshold to assign individuals into a high risk group was the ⅔-quantile of the ScanCov scores computed for patients of the KB training set. Kaplan-Meier curves were obtained for individuals of the KB validation set (left panel) and IGR validation set (right panel). P-values for the log-rank test were equal to 2.90e-07 (KB) and 5.38e-08 (IGR). The two terciles used to determine threshold values for low, medium and high risk groups were equal to 0.144, and 0.369.

  variables, Table 1 and Supp Fig 2): age (Odds Ratio [OR] KB 1.66 (1.41-1.96), OR IGR 1.35 (0.92-1.98), P Stouffer = 5.25e-10), sex (OR KB 1.95 (1.41-2.69), OR IGR 1.07 (0.51-2.23), P Stouffer = 5.75e-05), hypertension (OR KB 1.84 (1.35-2.51), OR IGR 1.11 (0.51-2.42), P Stouffer = 1.11e-04), chronic kidney disease (OR KB 2.51 (1.62-3.89), OR IGR 16.59 (1.93-142.84), P Stouffer = 6.71e-06), respiratory rate (OR KB 1.34 (1.13-1.59), OR IGR 3.37 (1.28-8.86), P Stouffer = 2.14e-04), oxygen saturation (OR KB 0.38 (0.31-0.47), OR IGR 0.35 (0.20-0.63), P Stouffer = 2.91e-21), diastolic pressure (OR KB 0.70 (0.59-0.83), OR IGR 0.75 (0.51-1.11), P Stouffer = 1.35e-05), CRP (OR KB 1.47 (1.25-1.72), OR IGR 1.48 (1.03-2.14), P Stouffer = 4.48e-07), LDH (OR KB 2.05 (1.65-2.54), OR IGR 2.36 (1.32-4.21), P Stouffer = 6.05e-12), polynuclear neutrophil (OR KB 1.36 (1.13-1.60), OR IGR 1.15 (0.80-1.64), P Stouffer = 1.29e-04), and urea (OR KB 1.70 (1.43-2.01), OR IGR 2.19 (1.36-3.52), P Stouffer = 9.17e-11).

  Inclusion criteria were(1) date of admission at hospital (from the 12th of February to the 20th of March at Kremin Bicêtre and from the 2nd of March to the 24th of April at Institut Gustave Roussy) and (2) a positive diagnosis of COVID-19. Patients were considered positive either because of a positive RT-PCR (real-time fluorescence polymerase chain reaction) based on nasal or lower respiratory tract specimens or a CT scan with a typical appearance of COVID-19 as defined by the ACR criteria for negative RT-PCR patients[START_REF] Simpson | Radiological Society of North America Expert Consensus Statement on Reporting Chest CT Findings Related to COVID-19[END_REF] . Children and pregnant women were excluded from the study.The clinical and laboratory data were obtained from detailed medical records, cleaned and formatted retrospectively by 10 radiologists with 3 to 20 years of experience (5 radiologists at GR and 5 at KB). Data include demographic variables: age and sex, variables from the clinical examination include: body weight and height, body mass index, heart rate, body temperature, oxygen saturation, blood pressure, respiratory rate, and a list of symptoms including cough, sputum, chest pain, muscle pain, abdominal pain or diarrhoea, and dyspnea. Health and medical history data include presence or absence of comorbidities (systemic hypertension, diabetes mellitus, asthma, heart disease, emphysema, immunodeficiency) and smoker status. Laboratory data include conjugated alanine, bilirubin, total bilirubin, creatine kinase, CRP, ferritin, haemoglobin, LDH, leucocytes, lymphocyte, monocyte, platelet, polynuclear neutrophil, and urea.

CT scan acquisition CT scan data were available for 980 patients representing a total of 506,341 images (517 slices per patient on average). Summary statistics for the clinical, biological, and CT scan data are provided in Table

1

. Three different models of CT scanners were used : two General Electric CT scanners (Discovery CT750 HD and Optima 660 GE Medical Systems, Milwaukee, USA) and a Siemens CT scanner (Somatom Drive; Siemens Medical Solutions,

Acknowledgements

We would like to thank J.-Y. Berthou, H. Berry, and Ph. Gesnouin from Inria and M. He, R. Patel, G. Rouzaud, B. Schmauch, J. Du Terrail from Owkin and F Lion from Gustave Roussy for their support.

Data Availability

The dataset of patients hospitalized at Kremlin-Bicêtre (KB) and Institut Gustave Roussy (IGR) are stored on a server at Institut Gustave Roussy (IGR). The data are available from the first author upon request subject to ethical review.

Code Availability

Code to execute all the models presented in this article, including ScanCov score, AI-segment and AI-severity is available online on a public github repository.

Author Contributions

N.L., S.A., E.C.,P.H.,R.M.,N.L.,P.T., E.B.,M.S., A.S., F.C.,S.J., M.S., I.B., J.D.,JC.P., H.T.,E.P.,G.W., T.C., F.B.,MF.B.,M.B conceived the idea of this paper N.L., S.A., E.C., H.G.,P.H., M.D., S.S., O.M., MP.T., JP.L.,R.M.,N.L.,P.T., E.B.,G.G, C.B.,S.J., F.G.,N.T.,Y.L., T.D., K.G., A.N., M.T., S.V., M.S., I.B., Y.B, E.P., M.A., J.D.,F.B., A.G.,J.D.,JC.P., H.T.,E.P.,G.W., T.C., F.B.,MF.B.,M.B participated to the acquisition and treatment of data N.L., S.A., E.C.,P.H.,R.M.,N.L.,P.T., E.B.,S.J., M.S., P.J., I.B., J.D.,JC.P.,H.T.,E.P.,G.W., T.C., MF.B.,M.B.implemented the analysis N.L., S.A., E.C.,P.H.,R.M.,N.L.,P.T., E.B.,S.J., M.S., I.B., J.D.,JC.P., H.T.,E.P.,G.W., T.C., MF.B.,M.B.contributed to the writing of the manuscript

Competing Interests statement

The authors declare the following competing interests: Supp Fig. 7: Receiver operating characteristic (ROC) curves of the models that predict severity. Models were evaluated on two distinct validation sets consisting of 150 patients from KB (left panels) and 137 patients from IGR (right panels). ROC curves were obtained using the severity outcome defined as an oxygen flow rate of 15 L/min or higher, the need for mechanical ventilation, or death.

GGO

Crazy paving Consolidation

Accuracy (1% thresh.) 0.7951 0.7684 0.6167 F1 Score (1% thresh.) 0.8848 0.6452 0.7473 Accuracy (2% thresh.) 0.7876 0.7692 0.6667 F1 Score (2% thresh.) 0.8800 0.6182 0.7848 Supp Table 1: Detection accuracy and F1 scores of AI-segment when considering the radiologist report as ground truth . The binary decision used to compute the score is "presence or not of a lesion type" . Accuracy and F1 score are averaged over the IGR validation set . We compared, for each patient of the IGR validation set, detection obtained using AI -segment to the information provided in the standardized radiologist report. When using AI-segment , a lesion type is considered as present when its relative volume w.r.t. the full volume of both lung, is above a certain threshold indicated into parenthesis in the 1st column of the table.

Variable

Center Odds ratio (95%lower -95% upper)

P-value P-value Stouffer


B G Giraud
email: bertrand.giraud@cea.fr

Scalar nature of the nuclear density functional

Because of the rotational invariance of the nuclear Hamiltonian, there exists a density functional (DF) for nuclei that depends only on two scalar densities. Practical calculations boil down to radial, one-dimensional ones.

Let Z, N, A ≡ Z +N be the proton, neutron and mass numbers, respectively. The nuclear Hamiltonian H is known to be invariant under rotations. Therefore, besides Z and N, nuclear ground states (GSs) carry good quantum numbers, J and M, for the total angular momentum and its z-component. Two cases occur : either J = 0, hence the GS is not degenerate and its density is isotropic, or J > 0, hence one sees a trivial degeneracy for a magnetic multiplet of GSs, the densities of which, non isotropic, contain multipole components [1] [2] up to order 2J, with the same monopole for all members of the multiplet.

In any case, the ensemble density operator for the GS(s) of a given nucleus,

B ZN = (2J + 1) -1 M |ZN JM ZN JM |, (1)
is a scalar under rotations. In any case also, the GS energy obtains by,

E ZN = Tr B ZN H. (2)
Every spherical harmonic function, except a monopole, integrates out to zero. Therefore, only the monopole components of the proton and neutron densities contribute to the density normalizations which identify a nucleus,

∞ 0 r 2 dr ρ p0 (r) = Z, ∞ 0 r 2 dr ρ n0 (r) = N, (3)
the position r being here taken as a scalar rather than a vector. In the following, for conciseness, we omit the subscript 0 and often denote ρ the pair {ρ p , ρ n }.

Consider the "density constrained search" [START_REF] Levy | Proc. Natl. Acad. Sci[END_REF] [4] for a minimal energy,

Inf ρ→{Z,N } ( Inf B→ρ Tr B H ) + ∞ 0 r 2 dr [ u p (r) ρ p (r) + u n (r) ρ n (r) ] , (4) 1
where it is understood that the many-body density operator B is restricted to be a scalar under rotations. Also u p and u n are scalar. With two distinct densities ρ p , ρ n , two potentials are needed to represent the external potential used by the Hohenberg-Kohn [5] theorem as a functional Lagrange multiplier to constrain the density. Notice that now we do not put subscripts Z, N to B, because the normalizations, Eqs. [START_REF] Levy | Proc. Natl. Acad. Sci[END_REF], are implemented at the stage of the "outer" minimization. At the "inner" stage, N and Z do not need to be integers. This inner minimization, Inf B→ρ , defines a density functional,

F [ρ] ≡ Inf B→ρ Tr B H, (5)
and, in that sector defined by the additional constraints, Eqs. ( 3), with now Z and N physical integers, the GS energy of a nucleus results from,

E ZN = Inf ρ F [ρ], ∞ 0 r 2 dr ρ p (r) = Z, ∞ 0 r 2 dr ρ n (r) = N. (6)
It seems, therefore, that Eqs. ( 5) and ( 6) provide the basis of a fulfledged nuclear DF theory (DFT) in radial space, a symmetrized theory à la Görling [6]. However, one must first remove an ambiguity in the definition of the degree of freedom r and the associated density ρ(r). For A nucleons, the simplest set of degrees of freedom are the single nucleon coordinates r 1 , r 2 , ... r A and the simplest definition of the density consists in integrating out all of them but one,

ρ( r) = A d r 1 d r 2 ... d r A-1 |Ψ( r 1 , r 2 , ..., r A-1 , r)| 2 . ( 7
)
But, as discussed by [7], it is more physical to use a density σ r -R , measured from the center-of-mass (CM) coordinate R = ( r 1 + ... + r A )/A of the nucleus, rather than the density ρ( r), defined in the laboratory frame. Since H is also translation invariant, the wave function for A nucleons is rather an "internal" one, ψ int ( ξ 1 , ..., ξ A-1 ), of (A -1) Jacobi coordinates only,

ξ 1 = r 2 -r 1 , ξ 2 = r 3 -( r 2 + r 1 )/2, ... , ξ A-1 = r A -( r A-1 + r A-2 + ... + r 1 )/(A -1) . It turns out that the last Jacobi coordinate is proportional to r A -R, namely, ξ A-1 = A A-1 ( r A -R).
Except for trivial scaling factors, the "internal" density appears naturally to be,

σ( ξ) = A d ξ 1 d ξ 2 ... d ξ A-2 |ψ int ( ξ 1 , ξ 2 , ..., ξ A-2 , ξ)| 2 . ( 8
)
Strictly speaking, what we called F [ρ] should rather be a functional of σ. Unfortunately, there is no need to stress that calculations with Jacobi coordinates are much more complicated than calculations in the laboratory frame. The solution found in [8] to link internal density σ and laboratory density ρ consists in trapping the CM by a harmonic potential. The Hamiltonian becomes,

H = A i=1 p 2 i 2m + Km 2 A i=1 r i 2 + A i>j=1 v ij + A i>j>k=1 w ijk . ( 9
)
Here v is the usual two-body interaction, and one can also include a threebody interaction w or even the luxury of more-body ones. Except for the trap, Galilean invariance is requested; no density dependence in v, w, ... is allowed. The trap is parametrized by an arbitrary, but fixed constant K, to be chosen for maximum convenience of practical calculations. The term, Km

A i=1 r i 2 ,
can also be written as, Am ω 2 R 2 , with the CM coordinate R = A -1 A i=1 r i and ω = √ KA; the CM frequency depends on the mass number A. The same form also shows that the trap is the sum of a one-body and a two-body operators, representable in second quantization without coefficients depending on A,

K m 2 A i=1 r i 2 = K m 2   A i=1 r 2 i + 2 A i>j=1 r i • r j   . ( 10
)
In each sector specified by integer Z and N, the GS(s) of H factorize(s) as product(s) of a common Gaussian Γ for the CM and internal wave function(s) of the (A -1) Jacobi coordinates,

Ψ( r 1 , ..., r A ) = Γ(R) ψ int ( ξ 1 , ..., ξ A-1 ), Γ(R) = π -3 4 b -3 2 exp - R 2 2b 2 , (11)
with b = [ h/(A m ω) ] 1 2
. The Gaussian is rotation invariant. Its does not perturb the physical quantum numbers J, M when H is substituted for H.

As shown in [8] the link between ρ and σ is a trivial, invertible convolution,

ρ( r) = A 3 (A -1) 3 d R [Γ(R)] 2 σ A A -1 r -R . ( 12
)
This link is the same for any member of a magnetic multiplet. Hence it extends to the scalar densities ρ and σ provided by that kind of ensemble described by Eq. ( 1). The vector coordinates we used temporarily to handle the non isotropic densities of individual members of a magnetic multiplet can be reduced again to scalars. The convolution, ρ = Γ 2 * σ, see Eq. ( 12), actually becomes,

r ρ(r) = 2 π -1 2 A 3 (A -1) 3 b ∞ 0 ds exp - r 2 + s 2 b 2 sinh 2rs b 2 s σ A A -1 s . ( 13
)
Since it is easy to second quantize H and use the laboratory proton and neutron densities, ρ p (r) = Tr B c † pr c pr , ρ n (r) = Tr B c † nr c nr , where, with obvious notations, we have introduced proton and neutron creation and annihilation operators at a scalar position r, traces upon scalar density operators can be calculated in Fock space. Then one only tunes Eqs. (6) into,

E ZN + 1 2 h√ KA = Inf ρ F [ρ], ∞ 0 r 2 dr ρ p (r) = Z , ∞ 0 r 2 dr ρ n (r) = N . ( 14
)
We conclude by claiming that a DFT for nuclei energies (and every other scalar) is available with scalar densities. Practical designs of a nuclear DF, F [ρ] ≡ Inf B→ρ Tr B H, simultaneously valid for doubly even, odd and doubly odd nuclei, can be attempted in the laboratory radial frame.

From a DFT, one expects densities and energies. At the cost of ignoring density multipoles 1 other than monopoles, our approach does provide formally exact energies, in a most simplified, one-dimensional theory. A major problem of nuclear physics is the prediction of exotic nuclei. Our result is of a special interest for the study of the neutron drip line, where neutron halos are notoriously difficult to describe. Dimensional reduction should make it easier to better focus the theory on the design 2 of the functional F , a still formidable problem. Whether the same reduction to "radial pictures" might also simplify the non local [10] versions of the DFT, in particular the quasi-local versions derived from Skyrme force models and labelled "energy density" theories, is likely.

Acknowledgement: A discussion with J. Dobaczewski is gratefully acknowledged.