Paulina Listewnik

Mikhael Bechelany

Małgorzata Szczerska

Microsphere Structure Application for Supercapacitor In Situ Temperature Monitoring

Keywords: fiber-optic microstructure, fiber-optic microsphere, supercapacitor, fiber-optic sensor, temperature monitoring

Constant, real-time temperature monitoring of the supercapacitors for efficient energy usage is in high demand and seems to be crucial for further development of those elements. A fiberoptic sensor can be an effective optoelectronic device dedicated for in-situ temperature monitoring of supercapacitors. In this work, the application of the fiber-optic microstrucutre with thin zinc oxide (ZnO) coating fabricated in the atomic layer deposition process (ALD) applied as a temperature sensor is reported. Such a structure was integrated with supercapacitors and used for the temperature measurements. Described sensors are built with the utility of the standard optical telecommunication fibers. The inner temperature of the supercapacitor was investigated in the range extending from 30°C to 90°C with a resolution equal to 5°C. The sensitivity of temperature measurement is about 109.6 nW/°C. The fitting of the sensor was achieved with a correlation coefficient R 2 = 0.97.

Introduction

Supercapacitors are designed as devices able to store substantially more amounts of energy than electrolytic capacitors [START_REF] Frackowiak | Carbon materials for supercapacitor application[END_REF]. Their many advantages, including high-power density, cyclic stability and durability, make supercapacitors highly sought-after storage devices, whether for standalone or hybrid applications [START_REF] Raza | Recent advancements in supercapacitor technology[END_REF][START_REF] Zhang | A review of supercapacitor modeling, estimation, and applications: A control/management perspective[END_REF].

Increasing demand for portable energy sources, supercapacitors are gaining more and more interest. Therefore, the possibilities of advancements of this technology are constantly investigated and new solutions are developed [START_REF] Wu | Flexible micro-supercapacitor based on in-situ assembled graphene on metal template at room temperature[END_REF][START_REF] Naoi | Nanohybrid Supercapacitor[END_REF][START_REF] Zuo | Battery-Supercapacitor Hybrid Devices: Recent Progress and Future Prospects[END_REF][START_REF] Najib | Current progress achieved in novel materials for supercapacitor electrodes: mini review Nanoscale[END_REF]. Learning about the inner workings of every device leads to gaining understanding of the processes occurring inside the device, which in turn allows to enhance their performance.

Real-time monitoring of the supercapacitor's internal temperature ensures efficient operation of the device. Temperature exceeding beyond the expected range is a good indicator of a faulty device. Whereas some changes can be undone, most are irreversible and contribute to the degradation of the device. Exceeding a limit beyond operating temperature can cause destabilization of electrolyte, which leads to further damage of supercapacitors. The electrolyte is a crucial component of any electrochemical electric cells, including supercapacitors [START_REF] Frackowiak | Redox-active electrolyte for supercapacitor application Faraday Discuss[END_REF][START_REF] Wu | A simple and high-effective electrolyte mediated with pphenylenediamine for supercapacitor[END_REF][START_REF] Liu | Self-Recovering Tough Gel Electrolyte with Adjustable Supercapacitor Performance[END_REF]. Their purpose is to transfer charge between electrodes during electrochemical processes [START_REF] Pal | Electrolyte selection for supercapacitive devices: a critical review[END_REF]. Parameters of the supercapacitors, such as power density, longevity, chargingdischarging rates are largely dependent on their state, balance and conformity [START_REF] Deng | Electrolyte-Dependent Supercapacitor Performance on Nitrogen-Doped Porous Bio-Carbon from Gelatin[END_REF]. Overheating can cause the emergence of chemical reactions between the electrolyte and the electrodes, and chemical decomposition which in turn impedes its performance, e.g., accelerate its aging, slow down charging cycles and speed up discharging cycles, distortion or even a rupture of the device [START_REF] Yang | Effects of Aging and Temperature on Supercapacitor Charge Capacity[END_REF][START_REF] Yang | Effects of Aging and Temperature on Supercapacitor Peukert Constant[END_REF][START_REF] Zheng | Study on effects of applied current and voltage on the ageing of supercapacitors[END_REF]. On the other hand, extreme low-temperature performance is also damaging the deviceit can cause increased charge transfer resistance or deteriorate electrodes and their contact with electrolyte [START_REF] Xiong | Influence of Temperature on Supercapacitor Performance Thermal Effects in Supercapacitors SpringerBriefs in Applied Sciences and Technology[END_REF][START_REF] Ruiz | Ionic liquidsolvent mixtures as supercapacitor electrolytes for extreme temperature operation[END_REF].

Many factors can influence temperature distribution within the device, including elements of which supercapacitors are composed (electrode materials [START_REF] Tan | Graphene for supercapacitor applications[END_REF][START_REF] Zhang | Graphene-based materials as supercapacitor electrodes[END_REF][START_REF] Snook | Conducting-polymerbased supercapacitor devices and electrodes[END_REF][START_REF] Choudhary | Asymmetric Supercapacitor Electrodes and Devices[END_REF], charge storage mechanism [START_REF] Salanne | Efficient storage mechanisms for building better supercapacitors[END_REF][START_REF] Ray | Study on charge storage mechanism in working electrodes fabricated by solgel derived spinel NiMn2O4 nanoparticles for supercapacitor application[END_REF], electrolyte) as well as its intended application or mode of operation [START_REF] Raza | Recent advancements in supercapacitor technology[END_REF][START_REF] Yu | Supercapacitor electrode materials: nanostructures from 0 to 3 dimensions Energy[END_REF]. However, in-situ monitoring of the device can often provide a better comprehension of the conditions occurring inside.

The distribution of the temperature in the pouch cells is widely studied to estimate the best construction of the device and to improve its efficiency. Starting with modelling and creating new algorithms as it is presented by Zhang et al. in [START_REF] Zhang | Electrochemical-electrical-thermal modeling of a pouch-type lithium ion battery: An application to optimize temperature distribution[END_REF] or by Wu et al. in [START_REF] Wu | Thermal Design for the Pouch-Type Large-Format Lithium-Ion Batteries: I. Thermo-Electrical Modeling and Origins of Temperature Non-Uniformity[END_REF]. The pouch cells are then investigated in experimental settings, using whether contactless methods like infrared thermography [START_REF] Goutam | Threedimensional electro-thermal model of li-ion pouch cell: Analysis and comparison of cell design factors and model assumptions[END_REF][START_REF] Rani | Comparative study of surface temperature of lithium-ion polymer cells at different discharging rates by infrared thermography and thermocouple[END_REF] or more direct methods such as measurements by thermocouples [START_REF] Martiny | Development of an All Kapton-Based Thin-Film Thermocouple Matrix for In Situ Temperature Measurement in a Lithium Ion Pouch[END_REF][START_REF] Mutyala | In-situ temperature measurement in lithium ion battery by transferable flexible thin film thermocouples[END_REF] and interferometric sensors [START_REF] Ghannoum | Fiber optic monitoring of lithium-ion batteries: A novel tool to understand the lithiation of batteries[END_REF][START_REF] Hedman | Fibre Optic Sensor for Characterisation of Lithium-Ion Batteries[END_REF]. However, none of the presented solutions provides additional information about the correct operation of the sensor at all times. To investigate the changes occurring in the supercapacitors, a fiber-optic sensors functionalized with a ZnO coating, similar to those presented in [START_REF] Brice | Whispering gallery mode resonators covered by a ZnO nanolayer[END_REF] and [START_REF] Myndrul | Photoluminescence label-free immunosensor for the detection of Aflatoxin B1 using polyacrylonitrile/zinc oxide nanofibers[END_REF], can be utilized.

In this paper, an in-situ measurement of the temperature of the supercapacitor is presented. To accomplish it, a microsphere-based fiber-optic sensor with a 200 nm ZnO ALD coating was embedded in the device. With the use of the presented sensor, it is possible to simultaneously monitor the internal temperature of the supercapacitor and the integrity of the sensor head structure in real-time, therefore avoiding uncertainties resulting from faulty sensors. The research presented in this paper is an incremental advancement of a similar type of sensor. The application presented herein is unique due to the use of fiber optics for precise temperature measurement of supercapacitors, which is important because other methods cause variations in the electromagnetic field and disrupt the operation of the supercapacitors. In presented research ZnO coating is used as a sensing medium itself. And what we used is the dependence of the optical parameters on temperature. Furthermore, we use unusual for ALD technique thickness, which is very thick -200 nm. Previously, dependence of the changing of the refractive index on the intensity of the reflected signal was measured using similar technique [START_REF] Listewnik | Preparation and Characterization of Microsphere ZnO ALD Coating Dedicated for the Fiber-Optic Refractive Index Sensor Nanomaterials[END_REF][START_REF] Hirsch | ZnO coated fiber optic microsphere sensor for the enhanced refractive index sensing[END_REF]. Furthermore, a validation of the microsphere-based temperature sensor is presented in [START_REF] Listewnik | ZnO ALD-Coated Microsphere-Based Sensors for Temperature Measurements[END_REF].

Materials and Methods

The microsphere-based fiber-optic sensor with a 200 nm ZnO ALD coating was embedded inside the supercapacitor, in a manner to prevent disruption of its operation. The supercapacitors utilized in this research, their construction and parameters are described elsewhere [START_REF] Bogdanowicz | Enhanced Charge Storage Mechanism and Long-Term Cycling Stability in Diamondized Titania Nanocomposite Supercapacitors Operating in Aqueous Electrolytes[END_REF]. The sensor was placed between the electrode and the foil forming the cover of the device. The location of the sensor inside the supercapacitor is presented in the schematic of the device's cross-section (Fig. 1.). The microsphere structure of the sensor was made at the tip of a standard telecommunication optical fiber (SMF-28, Thorlabs Inc., Newton, NJ, USA), using a fusion splicer (FSU975, Ericsson, Sweden). The obtained microsphere of the diameter of 245 µm was formed during the three-step pull process. The image of the microstructure, obtained under a microscope (CX31, Olympus, Japan) is presented in Figure 2. The sensor was used to observe changes in an optical spectrum while increasing the temperature of the device, and subsequent temperature growth of the electrolyte of which the investigated supercapacitors are composed. The device was tested in the temperature range of 30-90°C because of the aqueous properties of the used electrolyte (1 M K2SO4). While increasing the temperature, the electrolyte can change its properties, e.g., refractive index. More thorough research regarding refractive index sensing is presented in [START_REF] Listewnik | Preparation and Characterization of Microsphere ZnO ALD Coating Dedicated for the Fiber-Optic Refractive Index Sensor Nanomaterials[END_REF][START_REF] Hirsch | ZnO coated fiber optic microsphere sensor for the enhanced refractive index sensing[END_REF].

The supercapacitors were investigated using an interferometric setup consisting of a broad band light source with a central wavelength of 1310 ±10 nm (SLD-1310-18-W, FiberLabs Inc., Fujimi) which generates an optical signal. The experimental setup used for measurements of the supercapacitor's inner temperature is presented in Fig. 3. The signal is propagated through the optical coupler (G657A, CELLCO, Kobylanka, Poland) to the microspherebased fiber-optic sensor where the phenomenon of interference is incited. The signal is reflected off the two boundaries from which the sensor is built. Firstly, a part of the signal reflects on the boundary between the inner sphere, made of the core of the fiber, and the outer sphere, made of the cladding of the fiber, while the rest is transmitted through and reaches the boundary between the outer sphere and the measured medium, on which it is also reflected. The two waves superpose, resulting in an interference effect. The placement of the sensor in the supercapacitor as well as its operation principle is presented in Fig. The obtained signal is gathered by the Optical Spectrum Analyzer (OSA, Ando AQ6319, Yokohama, Japan). The data is then processed. The response time of the sensor is dependent on multiple factors, e.g., the type of utilized detector. The utilized OSA allows to read the data every 3 s. Preliminary measurements to determine the proper operation of the sensor and the results are presented in [START_REF] Listewnik | ZnO ALD-Coated Microsphere-Based Sensors for Temperature Measurements[END_REF].

Throughout the measurements, the temperature of investigated supercapacitors was also verified by a thermal camera (i7, FLIR, Wilsonville, OR, USA) to ensure uniform distribution of the temperature. Images obtained from this test are presented in Fig. 5. The emissivity of the thermal camera was set to Ɛ=0.6 during the measurements due to the fact that the supercapacitor has been enclosed in a triplex foil which reflectance value was taken into consideration during the measurements. The camera was set to measure the highest temperature inside the selected area and it is determined by the marker. Obtained measurement is presented in the top left corner of each image.

Results and discussion

This section discusses the data acquired during measurements performed in the experimental setup. All measurements were performed at least 5 minutes after stabilization of the temperature, which was controlled by observation through a thermal camera, while the supercapacitor's state of charge was at about 80%. Fig. 6 shows the changes in the spectrum while the temperature was growing in the set range. As can be observed, the intensity of the reflected signal is increasing with the rise of temperature while the envelope retains similar. Moreover, the interference signal ensures that the sensor is not damaged. To maintain the clarity of the graph, only selected spectra were plotted. The dependence of the peak intensity of the reflected signal on the temperature is presented in Fig. 7. Peak intensity increases according to the second-order polynomial fit. By including polynomial regression in Fig. 7, a match between obtained data and theoretical fitting can be estimated. R 2 coefficient, which equals 0.97, exhibits a close fit of both plots. Based on the obtained data, the sensitivity of the sensor was calculated to be 109.6 nW/°C. Even though the sensitivity in the temperature range of 30-65°C is visibly lower (57 nW/°C), this behavior is repeatable throughout multiple measurement series, therefore it serves during the monitoring of the internal temperature as a sensing mechanism. Having reference spectral characteristics of the healthy device, any deviation from the known will be noticeable indicating either warning or critical state.

Performed investigation shows that by embedding a microsphere-based fiber-optic sensor, the internal temperature of supercapacitors can be monitored. The obtained interferometric signal remains present, therefore indicating proper operation of the device. Upon the sensor sustaining the damage, the interference within the signal ceases. Furthermore, based on polynomial regression, the behavior of the characteristics can be estimated. Substantial deviation of the characteristic from the reference indicates that the investigated supercapacitor became defective. The information allows taking the steps to preserve the device.

Conclusions

In this paper, the application of the microsphere-based fiber-optic sensor for in-situ monitoring of the temperature of the supercapacitor was examined. Because of a growing need for more efficient energy, it is necessary to thoroughly explore the processes occurring in the devices. The knowledge allows to optimize, find new solutions and improve current technology. The presented sensor was embedded inside the supercapacitor with aqueous electrolyte. During the operation of the device, we were able to investigate the in-situ temperature of the supercapacitor in a range of 30-90°C, with a resolution of 5°C, by observing changing optical spectrum. The intensity of the reflected signal increased, with the rise of the temperature and the presence of the interference indicated the integrity of the sensor, which in turn allowed to ensure the accuracy of the measurements. Based on the obtained data, the sensitivity of the sensor was calculated and it equals 109.6 nW/°C for the measured range. Thermal imaging was also performed to verify the accuracy of the measured temperature. The presented approach of internal temperature monitoring is ready to be used for application in the supercapacitors. Unlike other methods, it allows to constantly control the validity of performed measurements which is especially important in the devices and conditions where the inspection of the system operation and its components may not be feasible or easily reachable.

Figure 1 .

 1 Figure 1. Placement of the microsphere-based fiber-optic sensor embedded in the supercapacitor in schematic crosssection where: 1covers, 2 -electrodes, 3separator, 4microsphere-based fiber-optic sensor.

Figure 2 .

 2 Figure 2. A microscope image of the microstructure used for supercapacitor in situ temperature measurement.

Figure 3 .

 3 Figure 3. Measurement setup where: 1broadband light source, 2 -Optical Spectrum Analyzer, 3optical coupler, 4 hot plate, 5investigated supercapacitor, 6thermal camera.

  4. When the temperature changes the optical parameters of the ZnO cladding such as refractive index change what influences the reflection coefficient of the second boundary and influences the phase differences between interfering beams.

Figure 4 .

 4 Figure 4. Operation principle of the in-situ fiber-optic sensor temperature monitoring.

Figure. 5 .

 5 Figure. 5. Images of the supercapacitor with the in-situ fiber-optic temperature sensor obtained by a thermal camera for the lowest a) 30°C and highest b) 89.8°C value of investigated temperature range.

Figure 6 .

 6 Figure 6. Changes in the intensity of the reflected signal with rising temperature.

Figure 7 .

 7 Figure 7. Reflected signal peak intensity dependence in the changing temperature.Peak intensity increases according to the second-order polynomial fit. By including polynomial regression in Fig.7, a match between obtained data and theoretical fitting can be estimated. R 2 coefficient, which equals 0.97, exhibits a close fit of both plots. Based on the obtained data, the sensitivity of the sensor was calculated to be 109.6 nW/°C. Even though the sensitivity in the temperature range of 30-65°C is visibly lower (57 nW/°C), this behavior is repeatable throughout multiple measurement series, therefore it serves during the

Data Availability Statement: 10.34808/pnwz-7035. Conflicts of Interest: The authors declare no conflict of interest.

Informed Consent Statement: Not applicable.


Marie Fabre

Directeur De

Professeur Dereure
email: dereure@chu--montpellier.fr

Président Oliver Jury

Oliver Assesseurs

Professeur Meunier

Laurent Docteur

Lamoureux Anouck

Annee Universitaire

Bernard Albat

Michel Brunel

Claude Humeau

Maurice Navarro

Yves Allieu

Bernard Canaud

Claude Jaffiol

Henri Navratil

Robert Alric

Paul--André Chaptal

Charles Janbon

Jacques Othoniel

Bernard Arnaud

Albert--Jean Ciurana

François Janbon

Michel Pages

Gérard Asencio

Jacques Clot

Daniel Jarry

Claude Peguret

Jacques Astruc

Pierre Costa

Jacques Jourdan

Jacques Pelissier

Charles Aussilloux

Françoise D'athis

Bernard Klein

Pierre Petit

Michel Averous

Jacques Demaille

François Laffargue

Régis Pouget

Guy Ayral

Bernard Descomps

Jean Gabriel Lallemant

Christian Prefaut

Jean--Marc Davy

Jean--Pierre Dedet

Jean Ribstein

Jean--Jacques Eledjam

Jean--François Schved

Robert Grolleau Raoux

Charles Sultan

Bernard Guerrier

Jacques Touchon

Bernard Guillot

Alain Uziel

Olivier Jonquet

Michel Annee Voisin

Universitaire

Dominique Pujol Prat

Annee Rémy

Universitaire 2021--2022

Pierre Alric

Eric Baccino

Jean--Paul Beregi

Hubert Blain

Pierre Boulot

François Canovas

Xavier Capdevila

Michel Chammas

Pascal Colson

Valérie Costes

Jérôme Cottalorda

Philippe Coubes

Philippe Courtet

Louis Crampette

Jean Paul Cristol

Catherine Cyteval

L A De

Jean Emmanuel Coussaye

Benoît De Wazieres

Eric Delaporte

Pascal Demoly

Jacques Domergue

Hugues Duffau

Jean Eliaou

Fabre François

Michel Jean

Samir Hamamah

Christian Herisson

Samir Jaber

Claude Jeandel

Christian Jorgensen

Michel Koenig

Pierre Olivier Kotzki

Pierre Labauge

Isabelle Laffont

Jean--Yves Lefrant

Sylvain Lehmann

Serge Lumbroso

Denis Mariano--Goulart

Jacques Mercier

Laurent Meunier

Michel Mondain

Denis Pageaux Morin

Philippe Georges

Pascal Pujol

Isabelle Quere

Eric Renard

Jacques Reynes

Jacques Ripart

Philippe Rouanet

Albert Sotto

Patrice Vande Taourel

Philippe Perre

Hélène Vernhet

Marc Ychou

Pu Ph De

Patricia Assenat

Éric Avignon

Antoine Azria

David Baghdadli

Amaria Blanc

Pierre Borie

Frédéric Bourdin

Arnaud Cambonie

Gilles Camu

William Captier

Guillaume Cartron

Guillaume Cayla

Guillaume Chanques

Gérald Corbeau

Pierre Coulet

Bertrand Cuvillon

Philippe Dadure

Christophe Dauvilliers

Yves De Tayrac

Renaud De Vos

Marie Hélène

Béatrice

Mes Amis Gérard

Martine Nicole

Christian Michèle

Stéphan, Martin Alex Hugo

Fabre Marie

MD Dereure Olivier

Olivier Dereure

DOCTEUR EN MEDECINE Présentée et soutenue publiquement Par

Keywords: melanoma, CNS metastases, tritherapy, targeted therapy, immunotherapy 8 melanoma, CNS metastases, tritherapy, targeted therapy, immunotherapy

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Sommaire

INTRODUCTION

The risk of developing central nervous system (CNS) metastases is particularly high in melanoma compared to other malignancies with postmortem studies demonstrating the presence of CNS secondary lesions in up to 55--75% of patients with advanced disease [START_REF] Amer | Malignant melanoma and central nervous system metastases.Incidence, diagnosis, treatment and survival[END_REF][START_REF] Bullard | Central Nervous System Metastases in Malignant Melanoma[END_REF].

In this setting, fatality classically occurs in almost 95% of patients with a median survival of less than 1 year despite treatments [START_REF] Bullard | Central Nervous System Metastases in Malignant Melanoma[END_REF]. Even though the recent development of innovative systemic treatments including targeted therapies (TT) combining BRAF and MEK inhibitors in BRAF--mutated melanoma along with immune checkpoint inhibitors (ICI, mainly anti--PD1 +/-- anti--CTLA4 agents) for both BRAF--mutated and wild type melanomas significantly improved response rate (ORR), progression free survival (PFS) and overall survival (OS) in advanced melanoma [START_REF] Tawbi | Combined Nivolumab and Ipilimumab in Melanoma Metastatic to the Brain[END_REF][START_REF] Long | Combination nivolumab and ipilimumab or nivolumab alone in melanoma brain metastases: a multicentre randomised phase 2 study[END_REF][START_REF] Rulli | The impact of targeted therapies and immunotherapy in melanoma brain metastases: A systematic review and meta--analysis[END_REF][START_REF] Holbrook | Intracranial antitumor activity with encorafenib plus binimetinib in patients with melanoma brain metastases: A case series[END_REF][START_REF] Rishi | Current Treatment of Melanoma Brain Metastasis[END_REF][START_REF] Gutzmer | Melanoma brain metastases -Interdisciplinary management recommendations 2020[END_REF][START_REF] Makawita | Nonsurgical Management of Melanoma Brain Metastasis: Current Therapeutics, Challenges, and Strategies for Progress[END_REF], the outcome of patients with advanced melanoma and CNS metastases has been improved but remains overall poor compared to extra--cranial disease especially if clinical symptoms are present. In these patients the median overall survival may reach 15 to 17.5 months (9-13), therefore significantly longer than historical data but still reduced compared with patients with no CNS secondary lesions. On another hand, emerging preclinical and clinical studies suggested a possible synergic action between TT and anti--PD1 immunotherapies especially in BRAF mutated patients [START_REF] Blank | Combination of targeted therapy and immunotherapy in melanoma[END_REF] with BRAF inhibition appearing to elicit intra--tumoral T cell infiltration supporting the rational for a combined approach with immunotherapy. Of note recent reports indeed showed that such a triplet therapy may confer both longer PFS and response duration in advanced melanoma free of brain metastasis [START_REF] Ribas | Combined BRAF and MEK inhibition with PD--1 blockade immunotherapy in BRAF--mutant melanoma[END_REF][START_REF] Ascierto | Dabrafenib, trametinib and pembrolizumab or placebo in BRAF--mutant melanoma[END_REF][START_REF] Ferrucci | KEYNOTE--022 part 3: a randomized, double--blind, phase 2 study of pembrolizumab, dabrafenib, and trametinib in BRAF --mutant melanoma[END_REF][START_REF] Gutzmer | Atezolizumab, vemurafenib, and cobimetinib as first--line treatment for unresectable advanced BRAFV600 mutation--positive melanoma (IMspire150): primary analysis of the randomised, double--blind, placebo--controlled, phase 3 trial[END_REF][START_REF] Dummer | Combined PD--1, BRAF and MEK inhibition in advanced BRAF--mutant melanoma: safety run--in and biomarker cohorts of COMBI--i[END_REF] while some promising results were also obtained in patients with CNS metastases whether or not refractory to a first line immunotherapy [START_REF] Burton | Safety and efficacy of TRIplet combination of nivolumab (N) with dabrafenib (D) and trametinib (T) [TRIDeNT] in patients (pts) with BRAF--mutated metastatic melanoma (MM): A single center phase II study[END_REF][START_REF] Dummer | Atezolizumab, vemurafenib, and cobimetinib in patients with melanoma with CNS metastases (TRICOTEL): a multicentre, open--label, single--arm, phase 2 study[END_REF].

To expand these data in a real--life setting, the clinical and imaging response to a second--line triple therapy combining BRAFi, MEKi and anti PD1 agent in a cohort of patients with BRAF--mutated melanoma displaying CNS relapse after a first--line combined targeted therapy were retrospectively analyzed in a series of patients from a single center.

PATIENTS and METHODS

Overall Study Design

This study was designed as a monocenter retrospective analysis based on patients treated and followed in a third--level referral center (department of Dermatology, University of Montpellier France) from January 2017 to January 2022.

Patients

Inclusion criteria were defined as follows: patients at least 18 years old ; stage IV melanoma (with or without CNS metastasis at initial stage IV diagnosis) ; presence of BRAF V600E/K mutation ; CNS metastases (tentorial, infra tentorial and/or leptomeningeal involvement) occurring or progressing (if initially present) during follow up despite combined BRAFi/MEKi targeted therapy and leading to the addition of an anti PD1 agent in an attempt to optimize therapeutic efficiency (at least one antiPD1 perfusion administered).

Objectives

The primary objective was to investigate the intra--and extra--CNS clinical and/or morphological response rates to a combined anti--PD1/dual targeted anti--BRAF/anti--MEK therapy implemented after CNS disease progression despite prior anti--BRAF/anti--MEK therapy.

The secondary objectives were 1) to compare the clinical and morphological responses of CNS metastases whether or not a local treatment (surgery and/or radiotherapy) was added to medical treatment upon progression 2) to describe PFS and OS in the study population 3) to describe the median time intervals and interquartile range (IQ 25/75) between stage IV diagnosis and CNS progression and between initiation of dual anti--BRAF/anti--MEK targeted therapy and CNS progression 4) to compare the responses of CNS and non CNS targets to the triplet combination 5) to evaluate safety of the triple anti--PD1/ anti--BRAF anti--MEK therapy.

Evaluation procedures and criteria of judgment

The characteristics of the study population are detailed in Table 1. To address the primary objective clinical evaluation was performed on a monthly basis and clinical response was defined by improved neurological symptoms if they were present upon triplet therapy implementation. Morphological evaluation was based on RECIST 1.1 or EORTC criteria applied to extra--CNS (if applicable) and intra--CNS lesions as assessed by 3-or 4--level CT scan and/or CNS MRI performed at 3--month intervals or at shorter time interval, depending on the clinical setting.

Statistics

For quantitative variables mean values and range, standard deviations and 95% confidence intervals (estimated by normal approximation) and/or median values and interquartile range (IQ 25/75) were calculated. Qualitative variables including response rates were expressed by absolute numbers and percentages. Exact Fisher test was applied to compare responses observed with and without local intra cranial treatment.

RESULTS

Patients and treatments

17 patients fulfilling inclusion criteria and having received at least one infusion of anti--PD1 agent in addition to dual TT were retained for final analysis. The median age was 62 years (range 47--69) with 76.47% of male patients (n=13). The main clinical/histopathological pattern of primary tumor was SSM and the trunk (52.94%, n=12) with a median Breslow of 2.50 mm (range 1.20--3.88).

The mean and median time intervals between primitive melanoma diagnosis and CNS progression were respectively 48.18 (± 48.67) and 37.00 (15.00--60.00) months vs. 7.59 (± 10,60) and 4.0 (0.00--9.00) months between stage IV melanoma diagnosis and CNS progression. The mean and median time to CNS progression after targeted therapy initiation was 5.71 (± 10.98) and 3.00 (--1.00--8.00) months.

Two patients (7.5%) had received a prior treatment with anti--PD1 before implementation of the dual TT: Nivolumab (included in CA045--001 study, one infusion in one patient) or Pembrolizumab (included in the EORTC study, several infusions in one patient).

In all cases CNS lesions were supra tentorial brain metastases (100%, n=17), associated with infra tentorial (29.41% n=5) or leptomeningeal (11.76% n=2) involvement. 70.59% had three or more brain metastases at first evaluation (n=12), and 76.47% displayed more than ten brain metastases at final assessment (n=13). Interestingly, no neurological symptoms were observed in more than half of the patients (52.94%, n=9) upon initial diagnostic of CNS evolution The mean value of LDH at first CNS progression was 316.77 UI/L (± 256.29). Almost two third (11/17, 64.71%) of patients also received a local therapy of one or more CNS metastases in addition to systemic treatment: neurosurgery, gamma--knife radiosurgery or both ± additional stereotaxic radiotherapy (SRT), whole brain radiotherapy (WBRT), or adjuvant radiotherapy (ART), as assessed in figure 1.

Figure 1. Additional intra cranial local therapy [NOM DE CATÉGORIE] (n=[VALEUR]) [NOM DE CATÉGORIE] (n=[VALEUR]) [NOM DE CATÉGORIE] (n=1) [NOM DE CATÉGORIE] (n=[VALEUR]) [NOM DE CATÉGORIE] (n=[VALEUR]) [NOM DE CATÉGORIE] (n=[VALEUR]) [NOM DE CATÉGORIE] (n=[VALEUR]) [NOM DE CATÉGORIE] (n=[VALEUR]) [NOM DE CATÉGORIE] (n=[VALEUR])

Patients' outcome (see also fig. 2) After a mean and median duration of 2.24 (range 0.5--9 months ± 2.43) and 1.58 (0.60--3.76) months of triplet therapy respectively, a morphological response was observed in only 1/17 patient who was clinically asymptomatic with less than 3 CNS lesions at initial progression and who benefited of radiosurgery in addition to medical treatment.

Sequential imaging evaluation at 3 and 6 months showed progressive CNS metastases volume regression and no subsequent CNS progression during the 8--month follow up. A delayed morphological control was observed in another initially asymptomatic patient with more than 10 infra and supra tentorial CNS metastases, with volumetric progression at 3 months followed by a stabilization at 6 months and for 8 additional months upon morphological evaluation with no neurological symptoms occurrence during follow up. The triplet therapy was maintained for 9 months until the antiPD1 agent had to be discontinued owing to grade IV joint toxicity and CNS metastasis remained subsequently controlled by iterative radiosurgery sessions until the end of follow up. He was last evaluated in December 2021, 27 months after CNS metastases morphological manifestations.

Conversely, no clinical and/or morphological response (when imaging data are available) nor disease control were observed for the 15 other patients of whom 2 received a third-line treatment by fotemustine.

No statistically significant difference was observed regarding clinical and morphological response rate whether or not an additional local treatment was implemented (Fisher test, p=1) but the number of events was low.

Overall, mean and median clinical PFS, after triplet therapy was started, were 2.59 (± 5.98) and 0,00 (0, 00--2,00) months respectively while morphological PFS were 0.82 (± 2.35) and 0.00 (0.00--0.00) months. Mean and median OS were respectively 4.12 (± 5.55) and 2.43 (2.00--4.68) months after triplet implementation while overall mean and median OS after initial stage IV diagnosis were 23.19 (± 18.36) and 14.1 (11.54--31.30) months respectively. We used Kaplan and Meier curves to assess median survivals from stage IV melanoma diagnosis (months) and from triplet association (days). (fig 3 and4)

Safety data

Less than 30% of the patients experienced adverse effects under triplet therapy (29.4%, n=5), mostly rated grade 2 (23.53%, n=4) and none of them displayed auto immunity background. Only one patient had to stop the antiPD1 agent owing to grade 4 joint toxicity. Liver toxicity was reported in one patient (grade 2) and the treatment was not discontinued.

DISCUSSION

CNS is a major site of relapse and treatment failure in advanced melanoma even when extra--cranial disease is well controlled, and a predominant cause of death (1,2).

Additionally, CNS metastases are excluded from most clinical trials especially from registration RCT and therefore remain a major therapeutic issue.

BRAF--mutant melanomas frequently metastasize to CNS, with 58% of patients with CNS secondary lesions harboring BRAF mutation [START_REF] Jakob | NRAS mutation status is an independent prognostic factor in metastatic melanoma[END_REF] a data possibly at least partially related to lower BRAF inhibitor levels in CSF compared to plasma as it has been demonstrated in mice [START_REF] Mittapalli | Mechanisms Limiting Distribution of the Threonine--Protein Kinase B--RaF V600E Inhibitor Dabrafenib to the Brain: Implications for the Treatment of Melanoma Brain Metastases[END_REF]. Additionally and despite promising results, overall median response duration of CNS metastases was shorter than for non--CNS sites (6.5 months vs. 10.2 months) with Dabrafenib/Trametinib combo in COMBI--MB phase II trial [START_REF] Holbrook | Intracranial antitumor activity with encorafenib plus binimetinib in patients with melanoma brain metastases: A case series[END_REF][START_REF] Davies | Dabrafenib plus trametinib in patients with BRAFV600--mutant melanoma brain metastases (COMBI--MB): a multicentre, multicohort, open--label, phase 2 trial[END_REF]. On another hand activated T cells can cross blood brain barrier and significant responses have been obtained in this setting with monotherapies using antiPD1 agents and especially with double antiPD1--antiCTLA4 immunotherapy [START_REF] Long | Combination nivolumab and ipilimumab or nivolumab alone in melanoma brain metastases: a multicentre randomised phase 2 study[END_REF][START_REF] Wolchok | Long--Term Outcomes With Nivolumab Plus Ipilimumab or Nivolumab Alone Versus Ipilimumab in Patients With Advanced Melanoma[END_REF][START_REF] Tawbi | Long--term outcomes of patients with active melanoma brain metastases treated with combination nivolumab plus ipilimumab (CheckMate 204): final results of an open--label, multicentre, phase 2 study[END_REF]. A long--term control may be obtained with combined immunotherapy in up to 55% of patients with asymptomatic melanoma brain metastases along with long--term PFS and OS compared to mono--immunotherapy and combined targeted therapy despite similar intracranial response rate between combined targeted therapy and combined immunotherapy [START_REF] Tawbi | Long--term outcomes of patients with active melanoma brain metastases treated with combination nivolumab plus ipilimumab (CheckMate 204): final results of an open--label, multicentre, phase 2 study[END_REF].

The addition of immunotherapy to dual targeted therapy may elicit a synergistic effect since it has been established that the inhibition of BRAF and MEK has an immune-modulating effect, enhancing anti--tumor immunity and tumor infiltration by CD8+ T cells and leading to favorable changes in the tumor microenvironment [START_REF] Pelster | Combined targeted therapy and immunotherapy in melanoma: a review of the impact on the tumor microenvironment and outcomes of early clinical trials[END_REF][START_REF] Abate--Daga | The biology and therapeutic management of melanoma brain metastases[END_REF]. On another hand, brutal discontinuation of targeted therapies in such patients may be followed by a rapid and potentially lethal progression of CNS metastasis. Finally extra--CNS lesions are still responding in most patients at the time of CNS progression [START_REF] Makawita | Nonsurgical Management of Melanoma Brain Metastasis: Current Therapeutics, Challenges, and Strategies for Progress[END_REF]. For all these reasons, maintenance of TT when using a second--line mono--immunotherapy after CNS progression seems justified. Phase III studies [START_REF] Ferrucci | KEYNOTE--022 part 3: a randomized, double--blind, phase 2 study of pembrolizumab, dabrafenib, and trametinib in BRAF --mutant melanoma[END_REF][START_REF] Gutzmer | Atezolizumab, vemurafenib, and cobimetinib as first--line treatment for unresectable advanced BRAFV600 mutation--positive melanoma (IMspire150): primary analysis of the randomised, double--blind, placebo--controlled, phase 3 trial[END_REF] on stage IV melanoma, CNS metastases excluded, reported longer PFS with triplet therapy than doublet therapy. Only three triplet therapy studies included CNS metastases, and even though promising results were reported, final results did not discriminate between extra and intra--CNS metastases response in two of them [START_REF] Dummer | Combined PD--1, BRAF and MEK inhibition in advanced BRAF--mutant melanoma: safety run--in and biomarker cohorts of COMBI--i[END_REF][START_REF] Burton | Safety and efficacy of TRIplet combination of nivolumab (N) with dabrafenib (D) and trametinib (T) [TRIDeNT] in patients (pts) with BRAF--mutated metastatic melanoma (MM): A single center phase II study[END_REF].

To our knowledge, our survey is the only study to date investigating tritherapy efficacy in a "rescue" setting after primary or secondary CNS progression upon combined TT. With only 2/17 patients achieving a response or a stabilization and despite a good tolerance the results are overall disappointing by comparison with studies investigating first--line combined TT/antiPD1 strategies such as TRIDeNT or COMBI--i which showed an ORR of 89% and 78% respectively (all metastases combined), and the most recent first line triplet therapy which reported an intra cranial objective response rate of 42% [START_REF] Dummer | Atezolizumab, vemurafenib, and cobimetinib in patients with melanoma with CNS metastases (TRICOTEL): a multicentre, open--label, single--arm, phase 2 study[END_REF].

(fig 6)

However it is important to point out that these studies did not include symptomatic CNS metastases in TRIDeNT study, nor CNS relapses after 1 st line TT in both study [START_REF] Dummer | Combined PD--1, BRAF and MEK inhibition in advanced BRAF--mutant melanoma: safety run--in and biomarker cohorts of COMBI--i[END_REF][START_REF] Burton | Safety and efficacy of TRIplet combination of nivolumab (N) with dabrafenib (D) and trametinib (T) [TRIDeNT] in patients (pts) with BRAF--mutated metastatic melanoma (MM): A single center phase II study[END_REF].

Overall and rather surprisingly, the combination with local treatment of CNS lesions did not result in any additional significant efficacy in this series while this strategy using surgery, gamma--knife or SRT, whether combined with IT or TT, has been repeatedly reported to obtain better clinical outcome, better local control and better OS in patients with CNS metastases compared to systemic treatment alone [START_REF] Tawbi | Treatment patterns and clinical outcomes for patients with melanoma and central nervous system metastases: A real--world study[END_REF][START_REF] Gaudy--Marqueste | Survival of melanoma patients treated with targeted therapy and immunotherapy after systematic upfront control of brain metastases by radiosurgery[END_REF][START_REF] Hadi | Stereotactic radiosurgery combined with targeted/ immunotherapy in patients with melanoma brain metastasis[END_REF][START_REF] Dalmasso | Intracranial Treatment in Melanoma Patients with Brain Metastasis Is Associated with Improved Survival in the Era of Immunotherapy and Anti--BRAF Therapy[END_REF][START_REF] Amaral | Combined immunotherapy with nivolumab and ipilimumab with and without local therapy in patients with melanoma brain metastasis: a DeCOG* study in 380 patients[END_REF][START_REF] Hassel | Evaluation of radio--immunotherapy sequence on immunological responses and clinical outcomes in patients with melanoma brain metastases (ELEKTRA)[END_REF][START_REF] Rhun | Response assessment and outcome of combining immunotherapy and radiosurgery for brain metastasis from malignant melanoma[END_REF][START_REF] Khan | Efficacy of BRAF Inhibitors in Combination With Stereotactic Radiosurgery for the Treatment of Melanoma Brain Metastases: A Systematic Review and Meta--Analysis[END_REF]. Immediate intracranial local treatment should always be considered in symptomatic CNS metastases, regardless of the ongoing systemic treatment, whereas it can theoretically be delayed in asymptomatic patients with secondary implementation in case of progression despite systemic treatment or if the patient becomes symptomatic even though it is likely more efficient when applied early. SRT is also recommended after surgery and for patients with 4

or less CNS metastases. WBRT is rarely recommended and should be individually discussed [START_REF] Keilholz | ESMO consensus conference recommendations on the management of metastatic melanoma: under the auspices of the ESMO Guidelines Committee[END_REF][START_REF] Vogelbaum | Treatment for Brain Metastases: ASCO--SNO--ASTRO Guideline[END_REF].

Our study was limited by its retrospective design, the restricted number of patients, and the absence of morphological evaluation in 40% of the patients due to a rapidly unfavorable evolution.

To conclude, triplet therapy combining immunotherapy and BRAF/MEK inhibitors after CNS progression during dual targeted therapy resulted in significant morphological response in only very few patients and can be viewed as an overall ineffective strategy in most cases in this real--life survey and second--line double immunotherapy might be a preferable option. Conversely, the interest of second--line triplet TT/antiPD1 therapy in case of morphological and/or clinical primary or secondary CNS progression after first--line double immunotherapy remains to be investigated. [START_REF] Wang | First line immunotherapy extends brain metastasis free survival, improves overall survival, and reduces the incidence of brain metastasis in patients with advanced melanoma[END_REF].

  découverte, Pierre merci pour tes bons plans et ton amour du partage, Mathias merci pour ton mental exemplaire, Teresa et vos théories sur la vie, et surtout pour le giraffon, Bertrand ton rire moqueur qui cache bien ta bienveillance, et ta couleur, Philippine et ton banoffi qui nous a fait revivre, Richard ton talent d'acteur et d'orateur, ta musicalité, et ta passion, Arthy aux milles facettes, caméléon parisien, toujours dispo pour des retrouvailles poissonnières ! Merci à tous les copains montpelliérains, Le premier semestre, les vrais, le covid aura eu du bon de nous rapprocher : Chloé merci pour Frantz, Johnny, et le bleu de travail, Marie merci pour ta passion, Laura pour les pauses yoga, Justine merci pour ton rire et ta force d'arriver à tous nous réunir, Suheda merci pour tes recettes miracles et tes coloriages, Laurine pour ta motivation et ta gourmandise, merci Olga pour les croquetas et ta force d'esprit inspirante, merci Dadou pour la rigolade, et Marion pour ta bienveillante maternelle. Merci Nicolas pour tes attentions et ta générosité et Romain pour ton épicurisme partagé ! Merci à Laëticia et Marie Sophie, toujours partantes pour tout à mes côtés ! Et Chris et Charlotte pour vos bons plans et votre goût des bonnes choses. Merci Alex pour les virées bateaux, les week--end ski et les afterwork et merci à Héloïse et Mathilde pour toujours être de la partie ! Merci à tous mes colocs perpignanais : Ségolène pour ta sagesse et ta gentillesse, Aurélia pour ton énergie et ta joie de vivre, Noé pour tes théories sur le monde et ta convivialité et Jeanne pour ta douceur et ta sérénité. Merci à ceux qui m'ont supporté en stage : Benjamin ta sagesse et tes commérages, Mehdi ta cool attitude et ton goût de la vie, Agathe ton hyperactivité et ta jovialité, Selma ton perfectionniste et ta gentillesse, Marine ta bonne humeur et tes bons conseils et puis merci à Laurène pour ton travail appliqué et ta bienveillance maternelle, et Mathilde la fashion tornade, merci ton rire et ton râlage. J'ai beaucoup appris de vous ! Merci à ma famille de dermatologues, A ceux qui m'ont beaucoup appris, Quentin merci pour ta rigueur et ta bienveillance, Emilie pour m'avoir transmis tes connaissances et ta passion, Laura pour tes bons conseils sur la dermato et sur la vie, et Blanche pour ta détermination et ta volonté de bien faire. Manon merci pour ton assistance en chirurgie, et of course pour l'urban du mercredi, Dorian merci pour tes conseils au 1 er semestre et tes apéros posés, Aude merci pour ton énergie et tes milles histoires, Rémy merci pour ta curiosité et ta folie des grandeurs. Merci Leo Paul pour ta gentillesse, ton humilité et tes connaissances. Merci Maéva et Sophie pour votre force de caractère exemplaire et vos conseils pour l'après. Merci Charlotte pour ton énergie et ta rigueur et Margaux pour ton sourire et ta curiosité. Merci Berin pour ton grain de folie et ton goût de la vie, Louise pour ta bonne humeur, Ariane pour ta justesse d'esprit et Marianne pour ta douceur et ta grande aide ! Merci Eva pour ta vivacité et Angèle, Célia et Valentine pour votre brin de fraicheur ! Un grand merci à ma seule et unique co--interne Marie que j'admire pour son mental d'acier, sa curiosité et son apprentissage constant, son optimisme pour la vie, son altruisme et sa générosité, et merci Thibaut pour ta gentillesse et ta joie de vivre.

  and tolerance of triple BRAF inhibitor/MEK inhibitor/anti--PD1 combined therapy in patients with melanoma central nervous system metastases occurring during first--line BRAFinh / MEKinh therapy

  The triplet therapy was mostly introduced after both clinical and morphological CNS progression (58.82%, n=10), less frequently owing to CNS progression only identified on imaging follow--up with no clinical symptom (41.18%, n=7). It mainly consisted of an association of Nivolumab (88.24%, n=15) to prior Dabrafenib/Tametinib therapy (70.59%, n=12), less frequently of Nivolumab associated with Encorafenib/Binimetinib (n=4), Pembrolizumab associated with Dabrafenib/Trametinib therapy (n=2), and Nivolumab associated with Vemurafenib/Cobimetinib (n=1).

Figure 1 .

 1 Figure 1. Additional intra cranial local therapy

Figure 3 .

 3 Figure 3. Kaplan Meier curve -Median survival from stage IV melanoma diagnosis (months)

Figure 4 .

 4 Figure 4. Kaplan Meier curve -Median survival from triplet therapy initiation (days)

Figure 5 .

 5 Figure 5. Summary of triplet therapy studies

UNIVERSITAIRE 2021--2022 PERSONNEL ENSEIGNANT Maitre de Conférences de Universités --Praticiens Hospitaliers MCU -PH Hors classe -Echelons exceptionnels

	Hélène BLAYAC Jean Pierre FREREBEAU Philippe MARTY ANE Charles SANY Jacques BLOTMAN Francis GALIFER René Benoît MATHIEU--DAUDE Pierre SEGNARBIEUX François BONNEL François GODLEWSKI Guilhem MEYNADIER Jean SENAC Jean--Paul BOURGEOIS Jean--Marie GRASSET Daniel MICHEL François--Bernard SERRE Arlette BOUSQUET Jean GUILHOU Jean--Jacques MION Charles SOLASSOL Claude BRUEL Jean Michel GUITER Pierre MION Henri TOUITOU Isabelle BUREAU Jean--Paul HEDON berbard MIRO Luis VIDAL Jacques HERTAULT Jean VISIER Jean Pierre PERSONNEL ENSEIGNANT -Professeurs Emérites ANNEE UNIVERSITAIRE 2021--2022 ARTUS Jean--Claude LANDAIS Paul ZANCA Michel BASTIEN Patrick LARREY Dominique PUJOL Joseph BLANC François BONAFE Alain MARES Pierre BOULENGER Jean--Philippe MAUDELONDE Thierry BOURREL Gérard MAURY Michèle MESSNER Patrick CLAUSTRES Mireille MILLAT Bertrand COMBE Bernard MONNIER Louis DAURES Jean--Pierre MOURAD Georges DEMARIA Roland DEREURE Olivier DROUPY Stéphane DUCROS Anne DUPEYRON Arnaud FESLER Pierre GARREL 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Stéphane MEROUEH Fadi SEGURET Fabienne CHEVALLIER--MICHAUD Josyane GINIES Patrick MOSER Camille SOUKSI MEDIONI Isabelle BATTISTELLA Pascal COLIN Olivier GRECO Frédéric MOUSTY Eve STOEBNER DELBARRE Anne BAUCHET Luc CONEJERO Ismael GUEDJ Anne Marie MOUTERDE Gaël TEOT Luc BELL Ariane CONSEIL Mathieu GROSSIN Delphine PANSARD Nicole THIRION Marina BENEZECH Jean--Pierre CORBEAU Catherine GUYON Gaël BERNARD Nathalie COUDRAY Sarah HENRY Vincent PEYRON Pierre--Antoine VERNES Eric BERTCHANSKY Ivan CRANSAC Fréderic JAMMET Patrick PICARD Eric VIALA Maurice BIBOULET Philippe CUNTZ Danielle JEDRYKA François PICOT Marie Christine VINCENT Laure BIRON--ANDREANI Christine DARDALHON Brigitte JREIGE Riad PIERONI Laurence WAGNER Laurent BLANC Brigitte DAVID Aurore KINNE Mélanie POQUET Hélène Xavier LABORDE Caroline PUPIER Florence BLATIERE Véronique DEBIEN Blaise LACAMBRE Mathieu QUANTIN Xavier BOBBIA Xavier DELPONT Marion LANG Philippe RAFFARD Laurence BOGE Gudrun DENIS Hélène LAZERGES Cyril RAPIDO Francesca BOURRAIN Jean Luc DEVILLE de PERIERE Gilles LE GUILLOU Cédric RIBRAULT Alice BOUYABRINE Hassan DI CASTRI Alberto LEGLISE Marie Suzanne RICHAUD--MOREL Un grand merci à mon président et directeur de thèse Monsieur le Brigitte Un grand merci à mon jury, Professeur
	LE QUELLEC Alain MULLER Laurent ROULET Agnès	BRINGER Jacques QUANTIN Xavier FITENI Frédéric	DAUZAT Michel HAYOT Maurice CHEVALLIER Thierry

DEREURE qui a fait preuve d'une grande réactivité, disponibilité et

	bienveillance dans l'encadrement de ma thèse. Merci de m'avoir si bien
	accompagnée et conseillée dans l'élaboration de ce travail. Toujours présent
	pour partager vos connaissances mais aussi pour défendre vos internes.
	Veuillez trouver ici l'expression de mon profond respect et de mon
	admiration.
	Merci à mon Jury, Monsieur le Professeur MEUNIER avec qui j'ai eu le
	plaisir de partager la coordination des internes. Votre présence dans mon jury
	est un immense honneur et je vous en remercie. Merci pour vos bons conseils
	et votre diplomatie. Soyez assuré de ma plus grande considération et
	gratitude.
	Et merci à mon Jury, le Docteur LAMOUREUX que j'admire pour son
	dévouement au travail, sa volonté de bien faire, son humanité et sa rigueur.
	Merci pour ton enseignement, tant sur le plan théorique que sur le plan
	relationnel médecin--patient. C'est un grand honneur de te compter parmi mon
	jury.
	Merci à tous

les médecins qui m'ont appris le métier de dermatologue, Merci à Monsieur le Professeur BESSIS pour son enseignement de la dermatologie inflammatoire et pédiatrique, et à Monsieur le Professeur STOEBNER pour avoir guidé mes premières consultations. Merci au Docteur DU THANH et au Docteur GIRARD avec

	qui j'ai eu la chance de
	travailler. Elles ont toujours été très disponibles pour superviser ma pratique. Elles m'ont
	appris la dermatologie dans son intégralité mais aussi à s'avoir s'adapter à chaque patient.
	Merci au Docteur LESAGE pour son altruisme et son art de la dermoscopie, et au Docteur
	MARQUE pour sa quiétude et son apprentissage soigné.
	Merci au Docteur PALLURE pour sa vivacité, sa gentillesse, et son humanité.
	Merci au Docteur AUGIAS de m'avoir initié au monde du libéral auquel j'aspire, merci pour
	ta patience et ta pédagogie ludique, et merci au Docteur OVTCHINIKOFF pour ses milles
	astuces et sa confiance.
	Merci à tout(e)s

les IDE, AS, et secrétaires des services

  de dermatologies des CHU de Montpellier, de Nîmes et de Perpignan, ce fut un plaisir de travailler avec vous et de progresser à vos côtés. Merci à tous mes proches et amis,

Table 1 .

 1 Population caracteristics Table 1. a)General Descriptive analysis

	Variable	Modalities	N (%)
	Sex	W	4 (23.53)
		M	13 (76.47)
	Melanoma localization (group)	Member	1 (5.88)
		Mucosal	1 (5.88)
		No primitif found	1 (5.88)
		Trunk	9 (52.94)
		Head and neck	5 (29.41)
	Exact melanoma localization	Missing	1 (5.88)
		Abdominal	1 (5.88)
		Cervical	2 (11.76)
		Back	3 (17.65)
		Right side	1 (5.88)
		Left side	1 (5.88)
		Left calf	1 (5.88)
		Left para sternal	1 (5.88)
		Left inferior palpebra	1 (5.88)
		Pinna of the ear	1 (5.88)
		Left pectoral	1 (5.88)
		Left scapula	1 (5.88)
		Left maxilar sinus	1 (5.88)
		Vertex	1 (5.88)
	Type of melanoma	Missing	2 (11.76)
		Dubreuil	1 (5.88)
		Mucosal	1 (5.88)
		Nodular	3 (17.65)
		Not found	1 (5.88)
		SSM	9 (52.94)
	Ulceration	Missing	7 (41.18)
		No	5 (29.41)
		Yes	5 (29.41)
	Auto--immune anteriorities	No	17 (100.00)
		Yes	0.00 (0.00)

Table 1 .

 1 b)General Qualitative analysis

			Mean
	Variable	N		Median (Q25;Q75)	[Min;Max]
			(± standard deviation)
	Age	17	58.12 (± 14.70)	62.00 (47.00;69.00)	[27.00;81.00]
	Breslow (mm)	13	2.81 (± 2.14)	2.50 (1.20;3.88)	[0.60;8.00]
	LDH	13	316.77 (± 256.29)	251.00 (182.00;323.00)	[130.00;1118.00]
	Duration of triplet	17	2.24 (± 2.43)	1.58 (0.60 ; 3.76)	[0.50;8.00]
	therapy (months)

Table 2 .

 2

		First outcome results
			n	% (IC95%)
	ICM
	Clinical response	No	15	88.24 (63.56--98.54)
		Yes	2	11.76 (1.46--36.44)
	ICM
	Morphological	No	9	52.94 (55.50--99.75)
	response	Yes	1	5.88 (0.25--44.50)
		Missing	7
	ECM
	Clinical response	No	6	35.29 (14.21--61.67)
		Yes	11	64.71 (38.33 --85.79)
	ECM
	Morphological	No	6	35.29 (29.93--92.51)
	response	Yes	3	17.65 (7.49--70.07)
		Missing	8
			17 patients
	2 ICM clinical		15 ICM clinical
	responses		progressions
	1 ICM morphological	1 ICM morphological	7 ICM morphological	8 ICM morphological
	response	progression	evaluations missing	progressions
	no ECM associated	ECM morphological response		1 ECM morphological response	5 ECM morphological progressions
					2 ECM
				morphological
				evaluations missing

Figure 2 : Patients' outcome during follow--up. ICM: intra cranial metastases, ECM: extra cranial metastases

Table 3 .

 3 Secondary outcomes --Comparison of clinical and morphological responses whether intra cerebral local treatment was added to the triplet therapy or not

				CNS metastases local
				treatment
			Total Population	No	Yes
	Variable	Modalities	n (%col)	n (%col)	n (%col)	Test	p
	ICM clinical response	No	15 (88.24) 6 (100.00) 9 (81.82) FISHER 0.51
		Yes	2 (11.76)	0 (0.00)	2 (18.18)
		N	17	6 (100.00) 11 (100.00)
	ICM morphological response	No	9 (90.00)	2 (100.00) 7 (87.50) FISHER 1.00
		Yes	1 (10.00)	0 (0.00)	1 (12.50)
		N	10	3 (100.00) 7 (100.00)
	ECM clinical response	No	6 (35.29)	2 (33.33)	4 (36.36) FISHER 1.00
		Yes	11 (64.71)	4 (66.67)	7 (63.64)
		N	17	6 (100.00) 11 (100.00)
	ECM morphological response	No	6 (66.67)	3 (100.00) 3 (50.00) FISHER 0.46
		Yes	3 (33.33)	0 (0.00)	3 (50.00)
		N	9	3 (100.00) 6 (100.00)

Table 4 .

 4 Secondary outcomes -PFS and OS

		Mean
	Variable		Median (Q25 ; Q75)	[Min ; Max]
		(± standard deviation)
	Duration of triplet therapy (months)	2.24 (± 2.43)	1.58 (0.60 ; 3.76)	[0.50 ; 8.00]
	Clinical progression
	free survival	2.59 (± 5.98)	0.00 (0.00 ; 2.00)	[0.00 ; 24.00]
	(months)
	Morphological
	progression free	0.82 (± 2.35)	0.00 (0.00 ; 0.00)	[0.00 ; 8.00]
	survival (months)
	Overall Survival since
	triplet therapy	123.75 (± 166.63)	73.00 (30.00 ; 156.00) [15.00 ; 730.00]
	initiation (days)
	Overall Survival since stage IV melanoma	23.19 (± 18.36)	14.01 (11.54 ; 31.30)	[7.00 ; 66.00]
	diagnosis (months)

Table 5 .

 5 Secondary outcomes -Median duration before CNS metastases progression

		Mean
	Variable		Median (Q25;Q75)	[Min;Max]
		(± standard deviation)
	Time (months)
	between melanoma diagnosis and first	48,18 (± 48.67)	37,00 (15.00 ; 60.00)	[0.00 ; 194.00]
	CNS metastases
	Time (months)
	between stage IV melanoma diagnosis and first CNS	7,59 (± 10.60)	4,00 (00.00 ; 9.00)	[0.00 ; 38.00]
	metastases
	Time (months)
	between doubled targeted therapy introduction and	5.71 (± 10.98)	3.00 (--1.00 ; 8.00)	[--8.00 ; 35.00]
	first CNS metastases

Table 6 .

 6 Immune Adverse effects

	variable	modalités	N (%)
	Immune adverse effect	No	12 (70.59)
		Yes	5 (29.41)
		TOTAL	17
	Type of immune adverse effect	Hepatic cytolysis	1 (20.00)
		Dermatitis	1 (20.00)
		Dysthyroïdism	2 (40.00)
		Rheumatoid arthritis 1 (20.00)
		TOTAL	5
	Immune toxicity grade (CTCAE)	2	4 (80.00)
		4	1 (20.00)
		TOTAL	5

Remerciements

CNS metastases number at triplet therapy initiation

Je donnerai mes soins gratuits à l'indigent et n'exigerai jamais un salaire au--dessus de mon travail. Admise dans l'intérieur des maisons, mes yeux ne verront pas ce qui s'y passe, ma langue taira les secrets qui me seront confiés, et mon état ne servira pas à corrompre les moeurs, ni à favoriser le crime. Respectueuse et reconnaissante envers mes Maîtres, je rendrai à

leurs enfants l'instruction que j'ai reçue de leurs pères. Que les hommes m'accordent leur estime si je suis fidèle à mes promesses. Que je sois couverte d'opprobre et méprisée de mes confrères si j'y manque.

ABSTRACT Background and purpose: Even though new systemic therapies significantly improved objective response rate (ORR), progression free survival (PFS) along with overall survival (OS) in advanced melanoma, the outcome in patient with melanoma CNS metastases remains poor, especially when symptomatic. We aimed to investigate the intra--CNS clinical and/or morphological response rates of patients with stage IV BRAF--mutated melanoma to a combined anti--PD1/dual targeted anti--BRAF/anti--MEK therapy implemented after CNS disease progression despite prior anti--BRAF anti--MEK therapy.

Methods: A monocenter retrospective analysis was conducted from January 2017 to January 2022. The response was defined by a steady of improved statue. Clinical evaluation was monthly performed and morphological evaluation resulted of imaging comparison every 3 months, at minimum.

Results


Taha Yassine
email: taha.yassine@b-com.com

Luc Le Magoarou
email: luc.lemagoarou@b-com.com

Stéphane Paquelet
email: stephane.paquelet@b-com.com

Matthieu Crussière
email: matthieu.crussiere@insa-rennes.fr

Leveraging triplet loss and nonlinear dimensionality reduction for on-the-fly channel charting

Keywords: channel charting, triplet network, dimensionality reduction, MIMO signal processing, machine learning

Channel charting is an unsupervised learning method that aims at mapping wireless channels to a so-called chart, preserving as much as possible spatial neighborhoods. In this paper, a model-based deep learning approach to this problem is proposed. It builds on a physically motivated distance measure to structure and initialize a neural network that is subsequently trained using a triplet loss function. The proposed structure exhibits a low number of parameters and clever initialization leads to fast training. These two features make the proposed approach amenable to on-the-fly channel charting. The method is empirically assessed on realistic synthetic channels, yielding encouraging results.

I. INTRODUCTION

Signal processing has greatly benefited from the recent advent of machine learning and the growth of computing power. Deep learning in particular has been widely used in a plethora of domains and only a few are left untouched. In wireless communication, neural networks have been exploited to solve many classical problems ranging from physical layer tasks like channel estimation [2], [START_REF] Yassine | mpNet: variable depth unfolded neural network for massive MIMO channel estimation[END_REF] and symbol decoding [START_REF] Samuel | Deep mimo detection[END_REF] to higher level tasks like end-to-end learning of the transmit and receive chains [START_REF] Timothy | An introduction to deep learning for the physical layer[END_REF]. Another prominent example of deep learning application in wireless systems is user localization where the objective is to determine the physical locations of user equipments (UEs) solely based on their uplink channel measurements by a multi-antenna base station (BS) [START_REF] Wen | A survey on 5G massive MIMO localization[END_REF]. Standard deep learning models require a dataset of channel measurements and their corresponding transmit locations to perform supervised learning.

Recently, channel charting has been proposed as an unsupervised alternative to user positioning where a charting function (or encoder) is learned in order to project highdimensional channel vectors into a low dimensional space (a chart) that resembles the geometrical space of UEs' locations. The challenge consists in providing a map without a priori location knowledge, only using channel measurements. Related work. Channel charting was first introduced in [START_REF] Studer | Channel charting: Locating users within the radio environment using channel state information[END_REF]. The approach therein builds on projecting precomputed channel features into a low-dimensional space using manifold learning techniques such as Sammon's mapping and autoencoders. Thereafter, a number of channel charting approaches building on the same ideas have been proposed. In [START_REF] Huang | Improving channel charting with representation-constrained autoencoders[END_REF], autoencoders are used together with representation constraints as a way of injecting prior knowledge to further guide the learning process. In [START_REF] Lei | Siamese neural networks for wireless positioning and channel charting[END_REF], the Sammon's mapping-based approach is reframed as a neural network model in a siamese configuration. In [START_REF] Ferrand | Triplet-based wireless channel charting: Architecture and experiments[END_REF], channel charting is performed using triplet networks. In order to train the model, a database of channel vector triplets is constructed based on travel information of UEs. Similarly, [START_REF] Rappaport | Improving channel charting using a split triplet loss and an inertial regularizer[END_REF] explores the use of triplet networks for channel charting where an improved triplet loss is introduced in order to further distill prior information. Finally, [12] proposes to use a distance measure that better preserves relative channel distances along with another manifold learning algorithm, namely Isomap [START_REF] Tenenbaum | A global geometric framework for nonlinear dimensionality reduction[END_REF], in order to map the channel observations to their low-dimensional representations. It is also worth mentioning the work in [START_REF] Le | Similarity-based prediction for channel mapping and user positioning[END_REF] where a neural network with a particular structure tackles the task of user positioning. The model is implicitly based on the adapted distance measure of [12] and benefits from a smart initialization. However, the training in [START_REF] Le | Similarity-based prediction for channel mapping and user positioning[END_REF] is done in a supervised fashion. Contributions. Building on earlier work [START_REF] Ferrand | Triplet-based wireless channel charting: Architecture and experiments[END_REF], [12], [START_REF] Le | Similarity-based prediction for channel mapping and user positioning[END_REF], a hybrid approach to channel charting is explored. A model-based neural network [START_REF] Shlezinger | Model-based deep learning[END_REF] with few parameters is structured as in [START_REF] Le | Similarity-based prediction for channel mapping and user positioning[END_REF], allowing a smart initialization of its weights based on the adapted distance measure of [12] jointly exploited with Isomap. The network is then trained using a triplet loss as in [START_REF] Ferrand | Triplet-based wireless channel charting: Architecture and experiments[END_REF]. Performance is evaluated on a dataset of synthetic realistic channels using classical manifold learning metrics.

The idea behind the smart initialization is to exploit as much prior information as possible in order to put the model in the best configuration prior to any optimization. This initialization naturally arises from the structure imposed on the network. Training is expected to gradually lead the network to configurations yielding even better results. To do so, the triplet loss relies on the way the channels are collected, bringing another source of information into the mix. The expected result is a reduction in the computational cost of both training and inference when compared to existing models, in an attempt to compute channel charts on the fly.

II. PROBLEM FORMULATION

Channel charting falls within the realm of machine learning in general, and dimensionality reduction in particular. It aims at projecting high-dimensional channel observations into a low-dimensional space, typically of 2 or 3 dimensions, in order to learn a channel chart. In fact, physical channel models indicate that channel observations are subject to the manifold hypothesis [START_REF] Peyré | Manifold models for signals and images[END_REF], meaning that although their original space is of high dimension, they are in reality governed by a small set of parameters. Those parameters are directly related to the spatial locations where the corresponding signals originate from [START_REF] Le | Similarity-based prediction for channel mapping and user positioning[END_REF]. In this sense, a successfully learned chart is a map between channel measurements and low-dimensional representations that preserves the local geometry of the original transmit locations.

We consider a BS equipped with an antenna array of N r antennas, and one or more single antenna UEs placed on a map and sending signals to the BS on S evenly spaced subcarriers and a central frequency f c . We denote h i ∈ C M the ith transmitted uplink channel vector, with M = N r × S, and p i ∈ R D the corresponding transmit location, where D corresponds to the number of retained spatial dimension (2 or 3 typically). A database {h i } N i=1 of N channel vectors is constructed through the collection of channel observations from different locations. Channel charting aims at learning a function F that takes as input the channel vectors h i and produces low-dimensional representations denoted z i .

F : C M → R D h i → F(h i ) = z i .
Note that the learned representations {z i } N i=1 are not necessarily of same dimension as the UE locations, but are typically chosen to be two-dimensional.

III. HYBRID TRIPLET NETWORK

In order to conceive a model capable of learning the function F, we rely on deep learning methods for what they offer in terms of capacity and fast adaptation to data. In particular, we adopt the philosophy of model-based deep learning [START_REF] Shlezinger | Model-based deep learning[END_REF] where neural network structures are guided by physical principles yielding hybrid models more capable than generic multilayer perceptrons (MLPs) for a given task. The same philosophy has already been applied to channel estimation in an earlier work [START_REF] Yassine | mpNet: variable depth unfolded neural network for massive MIMO channel estimation[END_REF].

A. Distance measure

The first step in our approach is to compute the distance matrix of the collected channel vectors. The adopted distance measure needs to correctly reflect the local spatial neighborhoods of channel observations. The traditional Euclidean distance is inadequate to the task because of its unusual behavior in high-dimensional spaces [START_REF] Charu | On the surprising behavior of distance metrics in high dimensional space[END_REF]. A more adequate distance measure is the one introduced in [12]. It is defined as follows:

d (h i , h j ) 2 = 2 -2 |h H i h j | h i 2 h j 2 . (1)
Based on the plane wave physical model, this distance measure removes the sensitivity of channel vectors to the fast variations of the global phase, making it reliable and suitable for retrieval of local neighborhoods. In addition, a normalization factor is introduced to mitigate the detrimental effect of signal intensity. This distance proved useful for channel charting [12] and user positioning [START_REF] Le | Similarity-based prediction for channel mapping and user positioning[END_REF].

B. Hybrid encoder

Now that a distance measure has been defined, one could use a generic manifold learning algorithm to project the channel vectors into the low-dimensional space. For instance, [12] relies on Isomap to obtain the channel chart. However, this approach suffers from two main issues:

(1) Manifold learning algorithms like Isomap are incapable of directly performing out-of-sample projections, meaning that projecting new unseen samples would require recomputing the projection for the whole dataset which is very inefficient and cumbersome. (2) These methods depend on the accuracy of the distance measure and are prone to errors due to its approximative nature. To fix the first issue, we propose the following strategy (summarized in algorithm 1) that resembles the one introduced in [START_REF] Le | Similarity-based prediction for channel mapping and user positioning[END_REF]. We begin by selecting a small subset of N init collected channel observations that we organize in a matrix D ∈ C M ×Ninit as column vectors. The more representative it is of the data distribution the better. We then compute its distance matrix using (1) and feed it to Isomap to produce an initial channel chart Z according to the method proposed in [12]. For a given new observation h that we would like to project, we compute the modulus of its correlation to each one of the channel vectors in D. We keep the k largest elements of the obtained vector using the hard thresholding nonlinear operator denoted HT k (.). We normalize the result using an l 1 -norm so that the vector elements sum up to 1. Finally, we multiply the normalized vector by the matrix Z which amounts to performing a weighted average of the projections of the k most correlated channel vectors to the input vector h.

Algorithm 1 Proposed encoder

Input: Subset of channel vectors D, corresponding initial channel chart Z, channel h to locate on the chart 1: Correlation: a ← D H h 2: Modulus: b ← |a| 3: Hard thresholding: c ← HT k (b) 4: Normalization: d ← c/ c 1 5: Weighted sum: z ← Zd Output: z = F(h)
This strategy makes it possible to project individual channel observations independently of the rest of the dataset. Besides being initialized from a small dataset in conjunction with Isomap, it comprises two matrix multiplications separated by nonlinear operations which makes it easily laid out as a neural network as depicted in Fig. 1.

The second issue is mitigated with the help of training and is tackled in the next section. Indeed, the weight matrices D and Z will be allowed to vary during the training in order to optimize the whole model.

C. Triplet loss

The main advantage of using neural networks is the ability to train and improve their performance through gradient descent with backpropagation [START_REF] Goodfellow | Deep Learning[END_REF]Chapter 6]. The main idea is to calculate a loss function that quantifies the error of the network's output and to iteratively "move" its weights in the opposite direction of the gradient of this loss function as to minimize it. In a supervised learning setting, this loss function takes as input both the output of the model and the target value that is ought to be achieved, hence the need of a training dataset of target values. However, in the context of channel charting, the objective is to rely solely on the channel observations themselves. As a consequence, it is necessary to make use of unsupervised learning methods. In particular, contrastive learning has been used extensively for various tasks [START_REF] Jaiswal | A survey on contrastive self-supervised learning[END_REF]. Simply put, it aims at hybrid_cc-eps-converted-to.pdf teaching the network which samples are similar and which are different with the help of a specifically designed loss function L. Triplet networks (Fig. 2) are an implementation of this framework where triplets of three samples each are constructed and fed to a neural network. A single triplet comprises an anchor sample h, a close sample h + and a far sample h -. The network produces their corresponding projections into the channel chart z, z + and z -respectively. The loss function is defined as

L(z, z + , z -) = max(0, d + -d -+ m), (2)
where

d + = z -z + 2 , d -= z -z - 2
and m is a margin parameter. In essence, minimizing L amounts to maximizing the difference between d + and d -by pulling the close sample closer and pushing the far sample farther until the difference is greater that m and therefore L = 0.

Instead of using a generic MLP as in [START_REF] Ferrand | Triplet-based wireless channel charting: Architecture and experiments[END_REF], we propose to use the hybrid encoder presented in Section III-B initialized with a small subset of channel observations following the proposed strategy. The parameters (i.e. weights) of the network θ = {D, Z} are then optimized through the training of the encoder in the triplet configuration. The learned charting function is denoted F θ .

It is important to note that constructing triplets obviously requires knowledge of positive and negative samples for a given anchor sample. In the unsupervised setting, this knowledge has to come from the dataset of inputs itself. Section IV-B describes how channel triplets are extracted from such a dataset.

IV. EXPERIMENTS A. DeepMIMO channels

To assess the performance of the proposed method, we rely on synthetic data generated from the DeepMIMO "O1" outdoor ray-tracing scenario [START_REF] Alkhateeb | DeepMIMO: A generic deep learning dataset for millimeter wave and massive MIMO applications[END_REF]. A total of N = 5910 channels are generated and their transmit locations are geographically triplet_cc-eps-converted-to.pdf distributed along a path representing the route of a pedestrian (Fig. 3). The pedestrian starts their journey at the lower rightmost point of the path and navigates counterclockwise. The pedestrian walks at a speed of v = 1.4 m/s. The sampling rate f s is set at 7 samples/s which means that consecutive samples are separated, on average, by 1.4/7 = 20 cm along the path. In addition, mild noise is added perpendicularly to the direction of travel to better emulate the walking of a real person that would not follow a perfectly straight line.

A single BS (BS 16 in the original scenario) equipped with a UPA of N r = 64 half-wavelength spaced antennas collects the uplink channels at a central frequency of f c = 3.5 GHz, with S = 16 evenly spaced subcarriers spanning a band of 20 MHz. The resulting complex channels are of dimension M = 1024.

B. Triplet dataset construction

Special care should be taken when constructing the triplet dataset as it is a critical component of the model. In the unsupervised setting, mining close and far examples w.r.t each anchor sample can be challenging in the absence of meaningful information to guide the process. However, the time-correlated nature of channel observations can be exploited. In [START_REF] Ferrand | Triplet-based wireless channel charting: Architecture and experiments[END_REF], a timestamp-based approach is used for extracting close and far samples for each anchor sample. Indeed, each channel observation is accompanied by a timestamp corresponding to the exact moment at which it was collected by the BS. It is then legitimate to consider two observations close in time to correspond, with high probability, to transmit locations spatially close to each other. An inner temporal threshold T c can then be set to define an interval around the anchor sample's timestamp; close samples lie inside the interval and far samples outside of Fig. 3: Locations corresponding to a triplet's close (green) and far (red) candidates. The anchor location is where the user is placed. it. In addition, an outer temporal threshold T f can be defined to set the limits of the interval inside of which far samples lie.

The DeepMIMO dataset not providing timestamps, we rely on both the sampling rate and the temporal thresholds to deduce a threshold expressed in terms of the number of preceding and following samples w.r.t. the anchor sample. The inner and outer thresholds are expressed as S c = T c × f s and S f = T f × f s respectively. For example, with f s = 7 samples/s and T c = 100 s, S c amounts to 700 samples, meaning that the 700 preceding samples and the 700 following ones, distributed over a total distance of 2 × v × T c = 280 m, are considered close samples for the triplet construction. The same procedure is used to determine valid far candidates.

Knowing that samples are indexed in the order that their corresponding locations appear on the path, a single triplet (i, j, k), where i, j and k are the indices of the anchor sample, the close sample and the far sample respectively, is constructed so that

i ∈ [0, N -1], j ∼ U [i-Sc,i[∪]i,i+Sc] and k ∼ U [i-S f ,i-Sc[∪]i+Sc,i+S f ] .
Note that we can generate multiple triplets for each anchor sample simply by sampling different close and far samples, allowing us to greatly expend the dataset with no added cost.

C. Results

The evaluation of the method is done based on the contribution of three aspects: initialization, structure and training. An experiment is conducted for each aspect. The base model consists of the hybrid triplet network introduced in sections III-B and III-C. The matrix D is initialized using a subset of N init = 100 channel observations randomly sampled from {h i } N i=1 . The matrix Z is computed using Isomap set to keep 5 neighbors per sample. The hard thresholding nonlinearity HT k is set to pick the k = 5 largest elements. The thresholds are set to T c = 100 s and T f = 290 s, and 5 triplets are generated for each column in D. The margin parameter in the triplet loss is set to m = 1. All models are trained on 70% of the dataset for 30 epochs. Performance of the base model in particular is evaluated over 100 runs with different columns in D each time, as we have observed results of high variance compared to the other configurations. The evaluation is done on the 30% unseen samples. This is in contrast to previous work where performance is evaluated on training data.

First, the base model is compared to a model with the same structure with the difference that the weight matrices are randomly initialized using the well-known Xavier initialization [START_REF] Glorot | Understanding the difficulty of training deep feedforward neural networks[END_REF]. Fig. 4 shows the performance of both models in terms of classical dimensionality reduction metrics, namely trustworthiness (TW) and continuity (CT) (see [12] and references therein for a formal definition). We observe that the smartly initialized model, on average, achieves performance levels comparable to those of the randomly initialized one. However, results vary highly between runs, especially when it comes to TW. This means that choosing the right combination of columns to keep in D is critical and is something to be explored in future work. It is interesting to note that at K = 5%, the CT score begins to degrade for both models. This behavior has to be linked to the thresholds S c and S f imposed during the triplet selection process.

Next, the base model is compared to an MLP composed of 6 hidden layers of sizes 1024, 512, 256, 128, 64 and 2 (output). All layers but the last one are followed by a ReLU nonlinearity. Fig. 4 shows that the base model performs much better both in terms of TW and CT. Another advantage that the base model has over the MLP is the low number of trainable parameters. The MLP has 2 793 600 trainable parameters while the hybrid model only has 409 800 parameters. Therefore, the proposed structure is suitable for applications where computing power and time constraints are critical, which is often the case in wireless communication systems. Indeed, this model may be considered for computing channel charts on the fly to be used by subsequent tasks (e.g. handover). An additional advantage of using light models such as the one presented in this paper is the ability to train the network on the fly (or online) on the continuous stream of collected channel observations to adapt to the changing propagation environment. This aspect is yet to be explored.

Finally, the base model's performance after training is compared to its performance before training. It is clear that the training plays a significant role in improving the results for both TW and CT. Interestingly, the figure clearly shows that CT's variance in particular is reduced after training. Another important observation in favor of the smartly initialized model is that its untrained version still performs better than the trained MLP. In addition, this untrained model naturally performs better than its untrained randomly initialized equivalent (not shown on the figures, near 0.5 for both TW and CT), meaning that less training is required to achieve a desired level of performance when the model is smartly initialized. Fig. 5 shows the learned channel charts of the different models compared to the real physical locations on the path that the UE follows. Colors were added for better understanding of the charts. Although channel chart visualizations are subject to personal interpretation, we can nonetheless observe that local neighborhoods are more or less preserved depending on the model. For example, we observe that the chart learned by the smartly initialized model better preserves the structure of long segments of the path (blue, green, orange, brown and pink points) while points belonging to short segments are more easily mixed with the other points (purple, olive and red points).

V. CONCLUSION AND PERSPECTIVES

In this paper, a triplet hybrid network was proposed for the task of channel charting with the aim of reducing the computation cost, hereby allowing for on-the-fly computation and update in portable devices. The model benefits from smart initialization using a small set of channel observations, an adapted distance measure and a manifold learning algorithm The results are encouraging and show great potential for improvement in future work. First, initialization could be improved by judiciously choosing the channel vectors to keep in the initial subset. Second, the database could be virtually augmented at no cost by constructing multiple triplets for each anchor sample by sampling different close and far samples. However, not all triplets are created equal, and some are more meaningful than others (e.g. ones containing hard-negative samples). Finding a way of selecting the optimal triplets for each sample could help with the training. Finally, extensive hyperparameter tuning could help discover a better configuration of the model.

Fig. 1 :

 1 Fig. 1: Hybrid encoder.

Fig. 2 :

 2 Fig. 2: Triplet network structure. θ is the set of parameters (i.e. weights) that the neural network learns throughout training.

CTFig. 4 :

 4 Fig. 4: Comparison of the models in terms of TW and CT. The K parameter represents the size of the neighborhood considered for computing both metrics. Regarding the smartly initialized model, the lines represent the means over 100 runs, and the shaded regions represent the one-standard deviation bounds. Note that the lines of the smartly initialized model after training and the randomly initialized one overlap.

Fig. 5 :

 5 Fig. 5: Channel charts of the different models compared to the ground-truth locations.

ACKNOWLEDGEMENT

This work has been partly funded by the European Commission through the H2020 project Hexa-X (Grant Agreement no. 101015).