Présentée Pour L'

Obtention Du

Titre De

Docteur En

Médecine Diplôme D'état

Mathilde Ulliel Roche

Thèse Soutenue

E N Visioconference

M Le Professeur

Pierre Bouzat

M Le Docteur

Stéphane Doutreleau

François Esteve

Paul Robach

Samuel Verges

CARDIAC REMODELLING IN THE HIGHEST CITY IN THE WORLD : EFFECTS OF ALTITUDE AND CHRONIC MOUNTAIN SICKNESS THÈSE

AVERTISSEMENT

Ce document est le fruit d'un long travail approuvé par le jury de soutenance.

La propriété intellectuelle du document reste entièrement celle du ou des auteurs. Les utilisateurs doivent respecter le droit d'auteur selon la législation en vigueur, et sont soumis aux règles habituelles du bon usage, comme pour les publications sur papier : respect des travaux originaux, citation, interdiction du pillage intellectuel, etc.

Il est mis à disposition de toute personne intéressée par l'intermédiaire de l'archive ouverte DUMAS (Dépôt Universitaire de Mémoires Après Soutenance).

Si vous désirez contacter son ou ses auteurs, nous vous invitons à consulter en ligne les annuaires de l'ordre des médecins, des pharmaciens et des sagesfemmes.

Contact à la Bibliothèque universitaire de Médecine Pharmacie de Grenoble : bump-theses@univ-grenoble-alpes.fr

REMERCIEMENTS

Membres du jury :

A monsieur le Professeur Pierre BOUZAT, pour m'avoir permis de réaliser ce Master 2 et de vivre cette incroyable aventure. Et pour les belles expériences que nous avons partagées au bloc des urgences et au déchocage. Des patients et des prises en charge (succès et échecs, on ne peut pas faire des miracles !) que je garderai bien en tête.

A monsieur le Docteur Stéphane DOUTRELEAU, un immense Merci pour tout. Pour ton accueil chaleureux et bienveillant à HP2. Toujours de bonne humeur, c'est un réel plaisir de travailler à tes côtés ! Merci aussi pour le chocolat à la Rinconada ! Et Merci beaucoup pour le partage et la réalisation de ce bel article. La cardiologie c'est passionnant, je pense avoir beaucoup appris en creusant ce sujet. Et en anesthésieréanimation, rien de plus important que le coeur et l'hémodynamique ! A monsieur le Docteur Samuel VERGES, un grand Merci également, pour m'avoir intégré dans votre superbe équipe. Pour m'avoir donné la chance de participer à Expédition 5300, qui était une expérience unique et très enrichissante, sur tous les plans. C'est une chance inouïe d'avoir pu partager tous ces bons moments avec vous. Merci pour ta motivation sans faille (notamment pour inclure des sujets !), je suivrai de près tous vos prochains projets.

A monsieur le Professeur François ESTEVE, de me faire le plaisir de participer à ce jury. C'était une chance de t'avoir auprès de nous lors de cette expédition, de partager tes expériences professionnelles et personnelles, mais aussi ta vision des choses.

A monsieur le Docteur Paul ROBACH, Merci d'avoir accepté de participer à ce jury. C'était un plaisir de participer à l'un de tes projets, toujours dans la joie et la bonne humeur.

Merci à mes parents, pour m'avoir offert une si belle enfance à la montagne, pour m'avoir transmis l'amour de la nature et du sport : du ski de piste au ski de fond (une pensée pour Champagny-le-Haut!), en passant par la randonnée et le tennis à 2 mains (qui surprendra toujours!). Pour m'avoir permis de découvrir la musique, le violoncelle, le piano, la guitare. Pour continuer de nous gâter avec tous vos bons petits plats. Pour m'avoir toujours tant soutenue durant ces longues études. Merci infiniment, je vous dois beaucoup.

Merci à mon frère Ivan, d'être le meilleur des grands frères. Pour avoir inventé la fête des petites soeurs, pour notre complicité, tous ces moments partagés : de la danse au foot dans le couloir! Tu as toujours pris soin de moi. Pour ces sorties magiques de ski et toutes celles à venir. A Maud, pour ta bonne humeur et ta simplicité. A nos futures sessions de ski et de kitesurf en Suisse ! Merci à ma soeur Fabienne, de prendre soin de moi depuis ma plus tendre enfance ! Malgré la différence d'âge, nous avons créé un lien fort et c'est un toujours un plaisir de t'avoir près de moi (même s'il est vrai que… quelques fois tu radotes !).

Merci à Manon, ma nièce adorée, ma négra, d'être comme une petite soeur pour moi. Pour tous ces souvenirs à la Chavonnerie que nous n'oublierons jamais toi et moi ! Pour ton humour décapant, ton rire, tes imitations, ta véritable joie de vivre. Tu sais mieux que quiconque à quel point il faut profiter la vie, et on ne peut que t'admirer pour ta force et ton courage.

Merci au reste de la famille, les Ulliel et les Roche, parce que vous êtes uniques ! A mes grands-parents, que je n'oublie pas.

Merci à la famille Alloin, pour m'avoir toujours si bien accueillie. Jean-Ga, entres autres pour m'avoir dépannée plus d'une fois ! Françoise, pour ton énergie, ta bonne humeur, tes conseils pratico-pratiques et tous tes merveilleux petits plats ! Lucas, Clémence, Eliott, Mathias pour votre incroyable gentillesse et votre joie de vivre. Sans oublier tes efforts Eliott pour sauver nos plantes ! Merci à Marie, Claire, Laurence et Jean-François, pour m'avoir apporté tant de choses durant ces années à Villarlurin. Comme une deuxième famille, vous m'avez fait découvrir la simplicité et le bonheur de la vie en montagne, aux Prés derniers, la via ferrata, la pêche dans les rivières, le chewing-gum de miel, la mousse sous les bolets que j'aime tant... Tant de souvenirs avec vous ! Vous avez toujours été là pour moi, et même si je ne suis plus souvent là, je n'oublie rien de tout ça. A ma petite Ophélie, qui promet d'être une sacré savoyarde !

Merci à mes copains d'enfance :

A Elodie, mon amie de toujours. Tu m'as tant apporté durant toutes ces années. Début de l'aventure dans ce bon vieux collège ! Puis le lycée version Option Sport, de chouettes années, entre ski de rando et spéléo. Et enfin les études à Grenoble, nos premières soirées médecine, ta rapide reconversion dans le droit qui t'a si bien réussie. Une pensée pour tous nos 31 ensemble (y'a eu quelques ratés !), tous nos fous rires et nos pleurs (si peu !), nos virées de folies (de Barcelone à Londres !). A ma Rose que j'aime tant, un bonheur de te voir grandir. A Quentin, pour prendre si bien soin d'elles (et si bien soin de nous!).

A Cindy, ma p'tite fouine. Toi non plus je ne veux plus te lâcher depuis le collège ! A nos virées en scooter (j'adoooore !), notre premier trail à Pralo (et pas le dernier !), toutes nos soirées (et pas des moindres !). Merci d'être toujours égale à toi-même, avec ton rire que j'aime tant, ta simplicité et ton humour. A Eva, une vraie Combaz. A Nico, super trailer, qui égaye toujours nos fins de soirées ! A Nicolas, mon fouino, tu garderas toujours une place spéciale dans mon coeur. Tellement de souvenirs avec toi, de l'école primaire (ouii, j'avais plus d'images !) à la fac, on en a vécu des choses ! En souvenir de toutes nos parties de foot, ces journées à la gouille, au ski, les campings, nos soirées HIMYM, la découverte de Guitar Hero, sans oublier Metallica à la guitare électrique. Merci pour tous ces bons moments, je n'oublie rien.

A Flo, mon couz d'amour, on ne se voit plus assez, mais tu restes une personne exceptionnelle qui m'a beaucoup apporté.

A tous les amis du collège (ma choup's et les autres !) et du lycée (spéciale dédicace pour l'Option Sport !).

Aux copains de Villarlurin : Dadou, Thomas, Loïc, Doudou, Cédric, Vincent, Guilllaume, Alexis, Adeline, Valentine, Karine, Kévin, JC…. Parce qu'on en a fait des choses ensemble ! Du foot (beaucoup !), du ski (bien trop de snow park !), mais aussi des jeux dans le village des après-midis entières, des campings, de la moto, des cabanes… Tellement de bons souvenirs !

Merci aux copains de l'externat, et en particulier…

A Marjo, mon ex-voisine de palier. Pour ta gentillesse (tu as osé me passer un cours d'HBDD en P1, je m'en rappellerai toujours !), ton humour, notre amour pour la bouffe (malheureusement !) et tout le reste. A Olivier et Amandine, je les aime forcément ! A Laurence et Clémence, pour toutes nos soirées, virées en montagnes, à Bologne. Que de bons souvenirs. Sans oublier Mickael et Robin ! A Sarah, je me souviens encore de notre rencontre en Première année ! Toujours tellement sympa. Et puis un concours de passé, quelques années d'externat, un deuxième concours et nous voilà toujours rassemblées. Déjà 12ans… on a dû changer et pourtant, notre amitié est intacte et je compte bien la préserver. Une belle pensée pour Ayden et Loris.

Merci aux copains de l'internat :

A Virgile, parce que cet internat n'aurait pas été le même sans toi ! Tant de bons moments partagés depuis notre rencontre à Thonon : 6 mois de coloc de folies dans la superbe baraque, beaucoup de ski, beaucoup de sport, pas mal de soirées (toujours les derniers !), 6 autres mois de coloc, la folle mais merveilleuse idée du chalet à la montagne (il n'y a que toi pour proposer ça ! Et sans doute que moi pour accepter ça !), les vacances au surf, tous tes délicieux petits plats avec plein de fromage, les soirées tisanes… Bref, merci d'avoir toujours été là pour moi, avec ton sourire et ton entrain. Ne change pas.

A Cédricou, pour nos parties de tennis endiablées, nos stages de réa ensemble, les Airbnb du DU d'écho, les virées de kite-surf… Toujours un petit bonheur.

A Martin, pour ton petit grain de folie (ouiiii) qui fait du bien au quotidien.

A Mélanie, pour ton accent que j'adore, nos debriefs qui détendent, tes coups de gueule qui me font rire (je dois l'avouer !), ton pep's, A Mariette, pour ce merveilleux semestre à Annecy, pour ta bonne humeur légendaire, pour ton sourire et ta voix qu'on aime tant. A Yohan, mon roccoyoyo, quelle fierté de t'avoir tout appris (ahah), pour nos conversations scandaleuses, pour cette belle amitié, A Anne-Gaelle, pour ta joie de vivre, ta motivation sans faille pour faire du sport, ton pain faitmaison. A Zoé, pour m'avoir supportée en tant qu'interne séniorisée ! Sans oublier tous les autres, sans exception : Jojo, Rémi, Sarah, Thibaut, JB, Paul, Cécile, Elo, Manue, Pierre, Felix, Sam, Valentin, Bart, Solange, Sophie, … A la superbe équipe de Thonon : Vivi, Charles, Pierre, Alex, Valentin, Marie, Nadège (et les +1 !) pour cet inoubliable semestre passé à vos côtés, début d'une belle amitié. Nos week-ends oenologiques à travers la France restent des moments incontournables et j'espère que nous perpétuerons cette excellente tradition ! A mes copains chirurgiens (parce que je vous aime bien !) : Manu, Benoit, Guigui, Nico, les neurochir (pour votre aide si précieuse en garde ! Julien, Arnaud, Florian et les autres), et j'en passe ! A Marjorie, ma cardiologue préférée, Aux copains du M2 (Marine, Christophe, Arnaud, Maxime, Calypso…), pour ces bons moments partagés, en cours, aux bars comme en montagne ! Merci à tous les autres copains de Grenoble et d'ailleurs, compagnons de montagnes, de voyages. Et en particulier à Maeva, ma copine de colo devenue ma copine de toujours. Enormément de beaux souvenirs avec toi, tu es fabuleuse ! Et j'ai envie de dire… Que les actes.

Merci à toute cette formidable équipe d'Expédition 5300 :

Axel pour ton travail de dingue sur ce projet, ta motivation légendaire et ta bienveillance pendant toute cette expédition, Tom pour tes photos et vidéos époustouflantes mais aussi pour ta folle présence aux soirées, Emeric parce qu'on est une team toi et moi, « Mathilde tu peux m'aider ?» Yann pour ton entrain, ta curiosité, pour ces bonnes soirées, Elisa pour nos quelques fous rires à la Rinconada, Laura, pour ta gentillesse et ta persévérance, Julien, pour cette rigueur dont tu fais preuve, pour ces challenges pendant cette expédition, Aurélien, pour ton sourire qui fait toujours plaisir, Connor, pour cette belle moustache et cet accent à couper au couteau (hum, sorry ?) Ivan, pour ton aide précieuse durant tout ce projet qui serait impossible sans toi. Stéphane, Samuel et François, encore un immense merci à tous les 3 ! C'était un plaisir de découvrir avec vous cet univers de la Recherche et de la Médecine du Sport ! Merci aux participants de cette étude qui ont énormément de courage pour vivre dans des conditions si difficiles. Cela m'a beaucoup apporté, de passer ces quelques jours à leurs côtés, de quoi relativiser… J'espère que la recherche continuera à progresser, pour comprendre et apprendre à mieux les soigner.

Merci aux étudiants de Puno qui nous ont été d'une grande aide !

Merci à toute l'équipe de l'Unité Sports et Pathologies de l'Hôpital Sud et du laboratoire HP2, pour votre accueil chaleureux dans votre unité ! C'était un plaisir ! Et en particulier à Sébastien, pour ta gentillesse et le partage de votre beau bureau !

Merci à toutes les équipes médicales et paramédicales qui m'ont formée :

A l'équipe de Thonon, pour ce premier stage d'internat qui restera gravé dans ma mémoire ! Une équipe d'infirmiers exceptionnelle (Jean-Yves, Rocco, Jérémy, Sandra, Mathieu, Antho, Vincent, Coco…). En souvenir des repos de garde au ski, des batailles d'eau au self, de mon petit Jean-Yves et ses plans ABCD mais surtout D, sans oublier la descente du Mont Grange sur les avant-bras (c'est comme si c'était hier !), le grand Paradis, et accessoirement… pour l'apprentissage de l'anesthésie ! Parce qu'il y a eu beaucoup de premières fois à vos côtés (Premières intubations, ALR, VVC, PA, péridurales, Midlines…), merci de m'avoir fait découvrir et aimer ce beau métier.

Aux équipes du CHU : en réanimation neurochirurgicale (mon premier stage de réa et mes premières gardes séniorisées, une chouette équipe !), en RPC, en anesthésie pédiatrique, viscérale, thoracique (merci Luis et Martine, pour tous vos petits trucs !), au BU-déchocage (avec quelques très beaux cas à garder dans les annales !). Merci pour ce dernier stage d'interne séniorisée à l'HCE (un bonheur de travailler à vos côtés !).

A la clinique générale d'Annecy : une superbe équipe (anesthésistes, chirurgiens, infirmiers !), travaillant dans une bonne ambiance, où j'ai appris à piquer des blocs comme jamais ! Je vais devoir revenir vous voir ! Aux équipes d'Annecy, en chirurgie cardiaque, au bloc général et en réanimation : quel plaisir d'apprendre l'anesthésie et la réanimation à vos côtés ! Je suis heureuse de pouvoir bientôt vous retrouver.

Et enfin, Merci à Quentin, l'amour de ma vie, pour m'avoir tant soutenue du Début à la Fin de ces longues études… Ça en fait des années à me supporter ! Tellement de bons moments partagés aux 4 coins du monde. Merci pour m'avoir toujours suivie, pour ton amour au quotidien, ton aide si précieuse, ton calme et ta sérénité, mais aussi ta générosité, ton intelligence et ton honnêteté. Une page se tourne et une nouvelle s'ouvre… J'ai hâte de poursuivre cette magnifique histoire.

ABSTRACT

Background: Despite unique adaptations to chronic hypoxic exposure, Andeans highlanders frequently develop a maladaptive syndrome, termed chronic mountain sickness (CMS), characterised by a combination of hypoxaemia, excessive erythrocytosis and various nonspecific symptoms. The aim of this study was to evaluate cardiac remodelling and pulmonary circulation at rest and during exercise in healthy lowlanders and highlanders, and in CMS patients living in the highest city in the world (La Rinconada, 5,100 m, Peru).

Methods: 98 males were evaluated: 18 healthy lowlanders, 23 healthy highlanders living at 3,800 m, and 55 highlanders living at 5,100 m, among which 17 were asymptomatic (no CMS), 14 reported mild CMS and 24 reported moderate-severe CMS. Cardiac remodelling was quantified by rest echocardiography. Pulmonary artery pressure (PAP) and pulmonary vascular resistance (TVR) were measured at rest and during submaximal cycling exercise. Total blood volume and haemoglobin mass were determined using the carbon monoxide rebreathing technique.

Results: Heart remodelling, predominantly of the right heart, together with an elevation of resting PAP and an impairment in systolic function progressively occurred with the increase in altitude of residency. The left heart exhibited a progressive concentric remodelling with diastolic dysfunction but without systolic dysfunction. Those modifications were emphasised in moderatesevere CMS patients at 5,100 m. Mean PAP was higher both at rest and during exercise in healthy highlanders at 5,100 m albeit without significant difference in TVR. On another hand, the moderate-severe CMS subjects had a higher TVR at rest and a larger increase in mPAP during exercise. The right heart remodelling was significantly correlated with resting and exercise mPAP, total blood volume and arterial oxygenation.

INTRODUCTION

The populations in the Andes in South America live at various altitudes ranging from sea level (e.g. Lima, the capital of Peru) to >4,000 m. In Peru, about one third of the population lives at high-altitude (>3,500 m) and experiences low oxygenation secondary to hypobaric hypoxia, resulting in alveolar hypoxia and chronic hypoxaemia. La Rinconada, in Peru, is the highest city in the world (5,100 -5,300 m) [START_REF] West | Physiological Effects of Chronic Hypoxia[END_REF], where around 70,000 inhabitants (2016 census, INEI-Peru) are living. This is a unique population permanently exposed to severe hypoxia and extreme living conditions which has so far never been investigated from a pathophysiological point of view [START_REF] Hancco | Excessive Erythrocytosis and Chronic Mountain Sickness in Dwellers of the Highest City in the World[END_REF].

To optimize oxygen delivery to the tissues, adaptive mechanisms have been developed by several high-altitude populations around the world. For instance, Andeans dwellers tend to display polycythaemia with an increase in haemoglobin concentration ([Hb]) and secondary hypervolemia [START_REF] Oberholzer | Re-evaluation of excessive erythrocytosis in diagnosing chronic mountain sickness in men from the world's highest city[END_REF][START_REF] Stembridge | The overlooked significance of plasma volume for successful adaptation to high altitude in Sherpa and Andean natives[END_REF]. Tibetans, who have a longer history of high-altitude residence, show lower [Hb] and seem better adapted to chronic hypoxia than Andeans dwellers [START_REF] Moore | Human genetic adaptation to high altitude[END_REF][START_REF] Beall | Tibetan and Andean patterns of adaptation to high-altitude hypoxia[END_REF]. One significant difference between those two specific populations is that Andeans develop more frequently signs of maladaptation to chronic hypoxia, a syndrome known as chronic mountain sickness (CMS) [START_REF] Villafuerte | Chronic Mountain Sickness: Clinical Aspects, Etiology, Management, and Treatment[END_REF]. This syndrome is diagnosed in patients based on the presence of excessive erythrocytosis ([Hb] ≥21g•dL -1 for males and ≥19 g•dL -1 for females) associated with a range of nonspecific clinical symptoms [START_REF] Leon-Velarde | Consensus statement on chronic and subacute high altitude diseases[END_REF]. Relative hypoventilation as well as specific hormonal, cellular and genetic factors may promote CMS [START_REF] Villafuerte | Chronic Mountain Sickness: Clinical Aspects, Etiology, Management, and Treatment[END_REF][START_REF] Bermudez | Increased hypoxic proliferative response and gene expression in erythroid progenitor cells of Andean highlanders with chronic mountain sickness[END_REF][START_REF] Leon-Velarde | Respiratory control in residents at high altitude: physiology and pathophysiology[END_REF][START_REF] Zhou | Whole-genome sequencing uncovers the genetic basis of chronic mountain sickness in Andean highlanders[END_REF] but the exact mechanisms underlying the occurrence and the severity of CMS still remain to be elucidated.

The heart remodels at high-altitude, with important anatomical and functional changes, in response to a large variety of stimuli including mainly rest and exercise-induced variations in loading conditions [START_REF] Penaloza | The heart and pulmonary circulation at high altitudes: healthy highlanders and chronic mountain sickness[END_REF]. In highlanders permanently exposed to chronic hypoxia, this remodelling is probably a combination of different mechanisms including reduced blood oxygen level, pulmonary and systemic arterial pressure changes, haemorheological variations (i.e. increased haematocrit and blood viscosity) [START_REF] Stauffer | Blood viscosity and its determinants in the highest city in the world[END_REF] and increase in total blood volume. The respective role of these different mechanisms regarding heart anatomical and functional changes remains however to be clarified.

The most important modifications reported in highlanders concern the right ventricle (RV) with a combination of hypertrophy and dilatation in response to higher rest and exercise pulmonary artery pressure (PAP) and vascular resistance leading to a decrease in RV systolic function [START_REF] Penaloza | The heart and pulmonary circulation at high altitudes: healthy highlanders and chronic mountain sickness[END_REF][START_REF] Brito | Long-Term Intermittent Work at High Altitude: Right Heart Functional and Morphological Status and Associated Cardiometabolic Factors[END_REF][START_REF] Maignan | Pulmonary pressure and cardiac function in chronic mountain sickness patients[END_REF][START_REF] Pratali | RV contractility and exercise-induced pulmonary hypertension in chronic mountain sickness: a stress echocardiographic and tissue Doppler imaging study[END_REF]. The left heart remodelling is less pronounced in chronic hypoxia with normal rest and exercise systolic left ventricle (LV) function [START_REF] Maignan | Pulmonary pressure and cardiac function in chronic mountain sickness patients[END_REF][START_REF] Pratali | RV contractility and exercise-induced pulmonary hypertension in chronic mountain sickness: a stress echocardiographic and tissue Doppler imaging study[END_REF], but since most studies focused on the right heart, further evaluations of the left heart in highlanders are required. Furthermore, while the highest population of highlanders studied so far resides at 4,540 m (Morococha, Peru) [START_REF] Leon-Velarde | Chronic mountain sickness and the heart[END_REF], whether highlanders exposed to even more severe chronic hypoxia exhibit further cardiac remodelling remains to be explored. All these anatomic and functional modifications have been reported to be more marked in CMS patients compared to their healthy counterparts [START_REF] Maignan | Pulmonary pressure and cardiac function in chronic mountain sickness patients[END_REF][START_REF] Pratali | RV contractility and exercise-induced pulmonary hypertension in chronic mountain sickness: a stress echocardiographic and tissue Doppler imaging study[END_REF][START_REF] Naeije | Pulmonary hypertension and the right ventricle in hypoxia[END_REF][START_REF] Pratali | Exercise induces rapid interstitial lung water accumulation in patients with chronic mountain sickness[END_REF][START_REF] Groepenhoff | Exercise pathophysiology in patients with chronic mountain sickness[END_REF][START_REF] Dedobbeleer | Left ventricular adaptation to high altitude: speckle tracking echocardiography in lowlanders, healthy highlanders and highlanders with chronic mountain sickness[END_REF][START_REF] Soria | Pulmonary arterial pressure at rest and during exercise in chronic mountain sickness: a meta-analysis[END_REF]. While these studies mostly involved severe CMS patients, it needs to be clarified whether patients with the more frequent mild CMS phenotype also exhibit a significant heart remodelling.

Therefore, our study aimed to investigate the effect of the altitude of residency (from sea level up to 5,100 m in the city of La Rinconada) and CMS severity at 5,100 m, on both heart remodelling and pulmonary haemodynamic at rest and during exercise. We hypothesized that right and left heart remodelling and PAP will increase i) with the altitude of residency, reaching extreme values in La Rinconada and ii) with the severity of CMS in dwellers from La Rinconada.

MATERIALS AND METHODS

Study population

The study population consisted of 98 male Andeans: 18 healthy lowlanders living at sea level (Lima, Peru), 23 healthy highlanders permanently living at 3,800 m (Puno, Peru), and 55 highlanders permanently living at 5,100 -5,300 m (La Rinconada, Peru), among whom 17 were asymptomatic (CMS score ≤5; CMS-), 14 reported mild CMS (CMS score 6-10) and 24 reported moderate to severe CMS (CMS score >10) symptoms. All highlanders at 3,800 m had a CMS score ≤5. All the highlanders were Andean natives (mostly of Quechua ancestry) from high altitude (≥3,800 m). Based on clinical interviews and examinations, subjects with a medical history of diabetes, respiratory and cardiovascular diseases were excluded. None of the lowlanders at sea level were acclimatized to high-altitude at the time of the tests (i.e. no sojourn above 2,000 m over the past 3 months) and none of the highlanders reported a prolonged stay at low altitude (more than 5 days below 3,500 m) over the past 3 months. At 5,100 m, all highlanders were working in gold mine facilities. All participants were informed about the procedures and gave their written informed consent prior to participating in this study. The study was approved by the ethics committee of Universidad Nacional Mayor de San Marcos (CIEI-2019-002) and performed according to the Declaration of Helsinki.

Experimental protocol

This study is part of a larger research programme (Expedition 5300) investigating the pathophysiological consequences of living permanently in the highest city in the world [START_REF] Enserink | Hypoxia city[END_REF].

Measurements were made under identical experimental settings in the cities of Lima, Puno and La Rinconada.

Clinical measurements

An initial clinical examination was performed by a Peruvian doctor (IH). Medical history of current and past medical issues, cardiovascular diseases, tobacco, alcohol and drug uses was obtained. Diagnostic and severity of CMS were evaluated using the "Qinghai score" based on excessive erythrocytosis (EE) ([Hb] ≥ 21g•dL -1 ) and the following signs and symptoms [START_REF] Leon-Velarde | Consensus statement on chronic and subacute high altitude diseases[END_REF]:

Rest echocardiography

Images were obtained by the same trained operator (SD) using a portable ultrasound system (Vivid-IQ Portable Cardiac Ultrasound, GE Healthcare, Little Chalfont, UK), with a 1 to 3-Mhz cardiac transducer. Recordings were stored for offline analysis (EchoPac system, GE Healthcare, Little Chalfont, UK). Reported values represent the mean of three cycles in the left lateral position. A complete evaluation of both right and left cavities dimensions was carried according to the guidelines of the European Association and American Society of Echocardiography [START_REF] Lang | Recommendations for cardiac chamber quantification by echocardiography in adults: an update from the American Society of Echocardiography and the European Association of Cardiovascular Imaging[END_REF][START_REF] Rudski | Guidelines for the echocardiographic assessment of the right heart in adults: a report from the American Society of Echocardiography endorsed by the European Association of Echocardiography, a registered branch of the European Society of Cardiology, and the Canadian Society of Echocardiography[END_REF] and indexed to the body surface area (BSA). The LV systolic function was assessed by LV ejection fraction (EF, Simpson's method) and LV global longitudinal strain (GLS), calculated in an 18-segments model from the apical 4-chamber view. LV mass was calculated using the linear method and indexed to BSA (g•m -2 ) and relative wall thickness (RWT) was used to describe the LV remodelling. To assess left diastolic function, peak velocities of transmitral early (E) and late (A) velocities were measured and the E/A ratio was calculated. The ratio of peak velocity of early mitral inflow to mitral annular early diastolic peak velocity (E/E') was used as an index of left ventricular filling. A LV diastolic dysfunction was defined as an abnormal E/A profile (Grade I to IV). Cardiac output (CO, L•min -1 ) was calculated by measuring the diameter of the LV outflow tract, the aortic time-velocity integral (TVIao) and the heart rate (HR).

The RV systolic function was assessed by measuring the RV fractional area change (RVFAC), the systolic tricuspid annular velocity (S') in Doppler tissue imaging and the RV strain of the free wall (3 segments), from an apical 4-chamber view [START_REF] Rudski | Guidelines for the echocardiographic assessment of the right heart in adults: a report from the American Society of Echocardiography endorsed by the European Association of Echocardiography, a registered branch of the European Society of Cardiology, and the Canadian Society of Echocardiography[END_REF]. To assess RV diastolic function, peak velocities of tricuspid early (Et) and late (At) velocities were measured using pulsed-wave Doppler at the end of a normal expiration; an Et/At ratio < 0.8 was used as an index of abnormal RV filling. Systolic PAP (sPAP) was estimated from the trans-tricuspid gradient calculated from the maximal velocity of tricuspid regurgitation (TR), using the simplified Bernoulli equation.

Mean PAP (mPAP) was also calculated as mPAP = 0.61 × sPAP + 2 (mmHg) [START_REF] Chemla | New formula for predicting mean pulmonary artery pressure using systolic pulmonary artery pressure[END_REF]. Total pulmonary vascular resistance (TVR) was estimated by the mPAP/CO ratio (in WU).

Left and right atrial end-diastolic volumes (LA and RA) were obtained using the biplane arealength formula from an apical 4-chamber view and indexed to the BSA (mL•m -2 ).

Exercise stress echocardiography

The exercise echocardiography was performed in an upright position on a cycle ergometer (SpeedBike BC 4620, Lima, Peru). HR and SpO2 were continuously recorded at rest and during two 5-min constant-load exercise stages. After 2 minutes of rest, the intensity was adjusted to reach 55% and 70% of the SL (HRmax pred SL) and HA (HRmax pred HA) predicted maximum HR, calculated as follows:

HRmax pred SL = 210 -0.65 × age HRmax pred HA = HRmax pred SL -0.0024 × altitude (m) + 0.73 [START_REF] Mourot | Limitation of Maximal Heart Rate in Hypoxia: Mechanisms and Clinical Importance[END_REF].

At rest and during the last minute of each stage, measurements of TVI aortic and TR velocity were performed for the calculation of CO and mPAP, respectively. The relationships between mPAP and CO were compared between groups. Since haematocrit and blood viscosity increase with altitude, measured TVR was converted to TVR at a haematocrit of 45% as follows: TVR45% = TVR/e (2(measured haematocrit -45%)) [START_REF] Vanderpool | Hematocrit-corrected Pulmonary Vascular Resistance[END_REF].

24h Holter ECG monitoring

All participants underwent 24-h Holter ECG monitoring (Vista, Novacor, Rueil-Malmaison, France). Holter ECG recordings were exported and manually scanned to remove artefacts before being analysed with the HolterSoft software (HolterSoft Ulitma, Novacor). The number of premature atrial and ventricular complexes (PAC and PVC, respectively) were quantified (number/hour) and a significant arrhythmia was defined as PAC or PVC > 30/h [START_REF] Bikkina | Prognostic implications of asymptomatic ventricular arrhythmias: the Framingham Heart Study[END_REF].

Haemoglobin mass and blood volume measurement

Total haemoglobin mass (Hbmass) and intravascular volumes were measured in a supine position, using the CO rebreathing technique [START_REF] Burge | Determination of hemoglobin mass and blood volume with CO: evaluation and application of a method[END_REF] with an automated system (OpCO; Detalo Health, Denmark) as previously published [START_REF] Oberholzer | Re-evaluation of excessive erythrocytosis in diagnosing chronic mountain sickness in men from the world's highest city[END_REF]. Two mL of whole blood from an antecubital vein was sampled and analysed immediately in quadruplicates for 1) percent carboxyhaemoglobin (%HbCO) and [Hb] (ABL80 OSM; Radiometer, Denmark) and 2) haematocrit (Ht) with the microcentrifuge method (1 min at 13,500 RPM). The participant was then connected to the OpCO system and breathed 100% O2 for 4 min, before being switched to the rebreathing circuit.

A bolus dose of 1.5 ml•kg -1 body weight of 99.997% chemically pure CO (Praxair, USA) was administered to the rebreathing circuit. O2 was supplied automatically into this circuit. The participant rebreathed the O2-CO gas mixture for 10 min before a second blood sample was obtained analysed in quadruplicates for %HbCO. The remaining CO volume in the rebreathing circuit was determined as previously specified and was subtracted from the applied CO dose. For the calculation of Hbmass, the absorbed CO dose and the changes in %HbCO from before to after rebreathing were used. Total blood volume, red blood cell volume and plasma volume were derived from Hbmass, [Hb], and Ht.

Statistical analysis

Variables were described by using means and standard deviation for quantitative variables and frequency and percentage for qualitative variables. After confirmation of the non-normality of the distributions using the Shapiro-Wilk test, comparison between groups were performed by using a non-parametric Kruskall Wallis test with Bonferroni correction for multiple tests. A multivariable linear regression was performed for each significant parameter with adjustment on age. Pearson correlations were used to assess correlations between CV parameters (RV end diastolic area, RA volume, SpO2, mPAP, Ht, Hbmass and the total blood volume). Finally, to assess the impact of altitude and CMS on pulmonary haemodynamics (mPAP and TVR) during exercise, mixed linear models for repeated measures with a patient random effect were used.

Statistical analyses were performed by using SAS V9.4 software (SAS Institute Inc., Cary, NC, USA). A p-value threshold of 0.05 was considered significant.

Table 1. Clinical and haematological characteristics in lowlanders and highlanders without or with chronic mountain sickness.

Data are mean ± SD. BMI, body mass index; [Hb], haemoglobin concentration; SpO2, pulse oxygen saturation; CMS, chronic mountain sickness; BP, blood pressure; Hbmass, haemoglobin mass; PAC and PVC: premature atrial and ventricular complexes. The first three columns represent the effect of altitude of residency in healthy subjects: *p<0.01 different from Lima; @ p<0.01 different from Puno. The three last columns represent the effect of CMS in dwellers from La Rinconada: # p<0.01 different from no CMS; £ p<0.01 different from Mild CMS.

Lowlanders

Comparison in healthy individuals according to altitude of residency

As expected, mPAP and TVR were higher in highlanders compared to lowlanders (table 2), the difference disappearing when TVR was corrected for a Ht of 45%.

With the increase in altitude of residency, a progressive dilatation of the right heart occurred, the remodelling concerning mainly the RA volume, which was 54% larger in highlanders at 5,100 m than in lowlanders. The RV end diastolic area was larger in highlanders at 5,100 m. RA volume, but not RV end diastolic area, was significantly correlated with SpO2 (r=-0.33; p=0.02), mPAP (r=0.38; p=0.01), Ht (r=0.61; p<0.0001), Hbmass (r=0.65; p<0.001) and the total blood volume (r=0.54; p<0.001).

RV systolic function was modified in highlanders at 5,100 m, with a significant reduction in both the free wall longitudinal strain and S' velocity when compared to lowlanders, even when controlling for age. The RV strain value was significantly correlated with SpO2 (r=0.60; p<0.001), mPAP (r=-0.33; p=0.03), Ht (r=-0.52; p<0.001), Hbmass (r=-0.55; p<0.001) and the total blood volume (r=-0.52; p<0.001).

Although RV diastolic pattern remained normal without any sign of dysfunction in all subjects, the trans-tricuspid filling pattern decreased in highlanders at 5,100 m because of a lower Et velocity, but this difference was not significant anymore when controlling for age. The Et/At ratio was significantly correlated with SpO2 (r=0.60; p<0.001), Ht (r=-0.34; p=0.006), Hbmass (r=-0.52; p<0.001) and the total blood volume (r=-0.56; p<0.001).

Comparison in highlanders at 5,100 m according to CMS severity

No significant difference was found between CMS groups among highlanders at 5,100 m for mPAP and TVR. Moderate-severe CMS subjects showed a larger dilatation of both the RV end diastolic area and the RA volume (+12% and +53%, respectively) when compared to subjects without CMS. Both parameters were significantly correlated with mPAP (r=0.50 and r=0.47, respectively; both p<0.001). RV systolic and diastolic functions were similar between CMS groups.

Left heart remodelling and function (table 3)

Comparison in healthy individuals according to altitude of residency

With the increase in altitude of residency, a progressive concentric remodelling of the left ventricle was observed, together with an increase in wall thickness and a parallel decrease in the LV diameter and volume, resulting in a significant increase in the RWT in highlanders at 5,100 m. RWT was not correlated with mean systemic arterial pressure (p>0.05), but was significantly correlated with SpO2 (r=-0.39; p=0.006), Ht (r=0.46; p=0.004), Hbmass (r=0.44; p=0.002) and the total blood volume (r=0.32; p=0.002).

All parameters of systolic LV function (EF and global LV longitudinal strain) did not differ significantly between altitudes, but a modification of the LV diastolic pattern was observed in highlanders at 5,100 m with a significant decrease in the mitral E/A ratio. The prevalence of LV diastolic dysfunction, with a grade I mitral pattern, was higher in highlanders at 5,100 m, even when controlling for age. E/A ratio was significantly correlated with SpO2 (r=0.50; p<0.001), Hbmass (r=-0.65; p<0.001) and the total blood volume (r=-0.58; p<0.001).

Comparison in highlanders at 5,100 m according to CMS severity

The remodelling of the LV in highlanders at 5,100 m was more pronounced in moderate-severe CMS subjects with a higher RWT. The RWT was significantly correlated with SpO2 only (r=-0.44; p=0.001). Both LV systolic function and LV filling pattern did not differ between highlanders with or without CMS.

The resting CO, systemic vascular resistance and the LV filling pressure were within the normal range without any effect of the altitude of residency and the CMS status.

E/A ratio 1.6 ± 0.3 1.5 ± 0.4 1.1 ± 0.3 @ 1.1 ± 0.4 1.1 ± 0.3 Diastolic dysfunction, n (%) 0 (0) 2 (10) 6 (35.3)* 5 (35.7) 8 (33.3)
E/E' ratio 5.1 ± 1 4.9 ± 0.9 4.8 ± 0.9 5.2 ± 1.1 5 ± 1

SVR (WU)

15.1 ± 3.8 18.9 ± 5.4 17.5 ± 4.9 17.4 ± 4.3 17 ± 3.8

Pulmonary haemodynamic during exercise (table 4 and figures 1 and 2)

All subjects performed the exercise test without any complication. SpO2 decreased significantly during exercise in highlanders (-5% to -7% from rest to load 2 at 3,800 m and 5,100 m, respectively). Tricuspid regurgitation during exercise could be analysed in 8 lowlanders, 10 highlanders at 3,800 m, 10, 6, and 13 highlanders at 5,100 m without CMS, with mild CMS and with moderate-severe CMS, respectively.

Comparison in healthy individuals according to altitude of residency

Figure 1 shows the evolution of both mPAP and TVR during exercise. Mean PAP increased significantly from rest to 70% of the maximal theoretical heart rate at all altitudes. The mPAP was systematically higher in highlanders at 5,100 m compared to lowlanders (figure 1A). When considering the pressure-flow relationship using the mPAP/CO ratio (figure 2), all data points except one from the highlanders during exercise were above the upper limits of either mPAP (30 mmHg) or TVR (3 UW) (figure 2A).

Comparison in highlanders at 5,100 m according to CMS severity

Mean PAP values did not differ between CMS groups at rest but the moderate-severe CMS subjects had a significant higher increase in mPAP throughout the exercise (figure 1C). TVR decreased significantly with exercise and no significant difference was seen between highlanders at 5,100 m, except for the resting values (figure 1D). The correction of TVR for a haematocrit of 45% normalised the mean TVR value below 3 WU during exercise in all CMS groups. Both RA volume and RV EDA were significantly correlated with resting and exercise mPAP values (r=0.4 and 0.43 for RA volume and r=0.47 and r=0.48 for the RV EDA at 55% and 70% of the maximal theoretical heart rate, respectively; p<0.001).

The mPAP/CO relationship (figure 2B) showed that TVR and mPAP values are always above the value of 3 WU or the limit of 30 mmHg, respectively. In comparison to lowlanders and healthy highlanders, a large dispersion of the individual points was observed in highlanders at 5,100 m with CMS (figure 2). In the present study lowlanders and highlanders showed similar patterns of exercise-induced changes in pulmonary haemodynamics but mPAP was higher in highlanders at 5,100 m. The values of mPAP in our study are higher (45±8 mmHg) than those reported in a recent metaanalysis (32 mmHg) [START_REF] Soria | Pulmonary arterial pressure at rest and during exercise in chronic mountain sickness: a meta-analysis[END_REF]. However, the latter analyse only included measurements performed at a lower altitude (3,600 m) and during a lighter exercise intensity (50 W). In an invasive study conducted at 4,540 m in young subjects [START_REF] Banchero | Pulmonary pressure, cardiac output, and arterial oxygen saturation during exercise at high altitude and at sea level[END_REF], the mean mPAP value at the end of a supine bicycle exercise was 60±3 mmHg and the TVR was 5.1±0.3 WU. The difference with our results could be explained by a lighter exercise in our study, as attested by lower heart rate and cardiac output, and possibly by the lack of precision in echocardiographic measurements. Since there is a relationship between blood viscosity and haematocrit, we investigated this effect by correcting the TVR with a normal haematocrit of 45% [START_REF] Vanderpool | Hematocrit-corrected Pulmonary Vascular Resistance[END_REF]. We found that the corrected TVR values were similar between groups, regardless the altitude or the CMS status, at rest and during exercise.

This suggests that high haematocrit plays an important role in the upward shift of the mPAP/CO relationship with altitude (figure 2A). We can also hypothesise that in Andeans permanently living in a hypoxic environment, the higher mPAP/CO relationships is explained not only by vascular remodelling and smaller vascular distensibility [START_REF] Penaloza | The heart and pulmonary circulation at high altitudes: healthy highlanders and chronic mountain sickness[END_REF][START_REF] Grimminger | Thin Air Resulting in High Pressure: Mountain Sickness and Hypoxia-Induced Pulmonary Hypertension[END_REF] but also by the large increase in haematocrit and blood viscosity as recently reported [START_REF] Stauffer | Blood viscosity and its determinants in the highest city in the world[END_REF].

Pulmonary haemodynamic at rest and during exercise in CMS patients

Moderate-severe CMS patients in La Rinconada had a similar mPAP and a slightly higher TVR value at rest than healthy individuals. During exercise, moderate-severe CMS patients showed a larger increase in mPAP and no significant difference in TVR. This is contrasting with several previous studies reporting an exaggerated response to chronic hypoxia in highlanders with CMS both at rest [START_REF] Soria | Pulmonary arterial pressure at rest and during exercise in chronic mountain sickness: a meta-analysis[END_REF][START_REF] Naeije | Pulmonary hypertension and chronic mountain sickness[END_REF][START_REF] Penaloza | Chronic cor pulmonale due to loss of altitude acclimatization (chronic mountain sickness)[END_REF] and during exercise [START_REF] Pratali | RV contractility and exercise-induced pulmonary hypertension in chronic mountain sickness: a stress echocardiographic and tissue Doppler imaging study[END_REF][START_REF] Pratali | Exercise induces rapid interstitial lung water accumulation in patients with chronic mountain sickness[END_REF][START_REF] Groepenhoff | Exercise pathophysiology in patients with chronic mountain sickness[END_REF][START_REF] Stuber | Exaggerated pulmonary hypertension during mild exercise in chronic mountain sickness[END_REF], with higher mean mPAP and pulmonary vascular resistance when compared to their healthy counterparts. However, most of the studies compared only moderate to severe CMS patients living at a maximal altitude of 4,540 m to healthy highlanders and the results of these studies are often heterogeneous. For example, in a small invasive study conducted in 10 CMS patients in Morococha (4,540 m), the resting mean mPAP was 47 mmHg but with a range from 31 to 85 mmHg and the mean TVR was 7.8 WU ranging from 3.8 to 13 WU [START_REF] Penaloza | Chronic cor pulmonale due to loss of altitude acclimatization (chronic mountain sickness)[END_REF]. Such heterogeneity was also evident in the present study when considering the mPAP/CO relationships with a more important dispersion of the points in CMS subjects than in healthy highlanders (figure 2). This important variability in the individual responses of highlanders with CMS already observed in previous studies [START_REF] Groepenhoff | Exercise pathophysiology in patients with chronic mountain sickness[END_REF][START_REF] Soria | Pulmonary arterial pressure at rest and during exercise in chronic mountain sickness: a meta-analysis[END_REF] underlines the wide spectrum of pulmonary haemodynamic responses among those patients, and suggests that the CMS diagnostic may encompass various patient phenotypes.

Prevalence of pulmonary hypertension

Because of the parabolic relationship between altitude and PAP, the definition of high-altitude pulmonary hypertension (HAPH) is difficult and still debated [START_REF] Simonneau | Haemodynamic definitions and updated clinical classification of pulmonary hypertension[END_REF][START_REF] Naeije | Pulmonary hypertension at high altitude[END_REF]. The seal-level maximal value of 25 mmHg is probably not suitable at very high altitude [START_REF] Simonneau | Haemodynamic definitions and updated clinical classification of pulmonary hypertension[END_REF] explaining that the proposed cut-off value for HAPH is higher, with mPAP >30 mmHg in highlanders without EE [START_REF] Leon-Velarde | Consensus statement on chronic and subacute high altitude diseases[END_REF]. In our study, by using the maximal value of 30 mmHg for normal mPAP and adding the criteria of pulmonary vascular resistance ≥3 WU as suggested in the updated haemodynamic definition of pulmonary hypertension [START_REF] Simonneau | Haemodynamic definitions and updated clinical classification of pulmonary hypertension[END_REF], the prevalence of HAPH was 22.2% and 30.7% at 3,800 m and 5,100 m, respectively. Because the consensus definition of HAPH explicitly states that excessive erythrocytosis should be absent, while all highlanders at 5,100 m except 4, had an [Hb] >21g•dL - 1 , we intentionally omitted this notion which is obviously questionable as a mandatory criterion for HAPH. Altogether, even if the studied population is quite small and the mPAP measured indirectly by echocardiography, these prevalence are in line with others [START_REF] Naeije | Pulmonary hypertension at high altitude[END_REF][START_REF] Soria | Pulmonary artery pressure and arterial oxygen saturation in people living at high or low altitude: systematic review and meta-analysis[END_REF]. Our results highlight that PH prevalence is low even at extremely high altitude but also underlines that the definition should be reconsidered to include the impact of the altitude of residency.

Cardiac remodelling with chronic hypoxia

Right heart (altitude effect)

With increasing altitude of residency, we found a progressive increase in RV area and in RA volume and this remodelling was associated with resting and exercise mPAP levels but also with total blood volume and Hbmass, two major responses to chronic hypoxic exposure to 5,100 m.

The histological pulmonary vascular remodelling, together with a higher haematocrit, explains the higher PAP level and consequently the higher stress on the thin-wall of the RV [START_REF] Gerche | Disproportionate exercise load and remodeling of the athlete's right ventricle[END_REF] and in turn the higher resting and exercise myocardial work [START_REF] Banchero | Pulmonary pressure, cardiac output, and arterial oxygen saturation during exercise at high altitude and at sea level[END_REF], two of the main factors explaining the changes in right heart dimension [START_REF] Naeije | Pulmonary hypertension and the right ventricle in hypoxia[END_REF]. During daily life, the repetitive increase in RV afterload (pulmonary artery pressures) and preload (blood volume expansion) likely leads to RV remodelling. The lack of RV dilatation in Sherpas living above 3,000 m [START_REF] Stembridge | Ventricular structure, function, and mechanics at high altitude: chronic remodeling in Sherpa vs. short-term lowlander adaptation[END_REF] together with the minimal hypoxic pulmonary hypertension at rest and during exercise in this specific population [START_REF] Groves | Minimal hypoxic pulmonary hypertension in normal Tibetans at 3,658 m[END_REF] support this hypothesis. RA volume was more impacted than RV in our study. To our knowledge, such a specific dilatation has never been described but some studies previously reported larger RA in healthy miners working between 4,400 and 4,800 m [START_REF] Brito | Long-Term Intermittent Work at High Altitude: Right Heart Functional and Morphological Status and Associated Cardiometabolic Factors[END_REF] and in highlanders living permanently at 4,000 m (La Paz, Bolivia) [START_REF] Huez | Echocardiographic and tissue Doppler imaging of cardiac adaptation to high altitude in native highlanders versus acclimatized lowlanders[END_REF]. As for the RV, those changes were likely related to both haemodynamic and hemorheological changes induced by altitude.

This anatomical remodelling was accompanied by significant modifications in RV function.

First, we found a decrease in resting RV systolic function. While RVFAC were normal, we observed decreases in the systolic annular tricuspid velocity (S' wave) and in the free wall RV strain in highlanders at 5,100 m. This is in line with other studies reporting a preserved RV function in acute hypoxia [START_REF] Huez | Right and left ventricular adaptation to hypoxia: a tissue Doppler imaging study[END_REF] but a decrease of RV systolic function parameters (S' wave and strain) in healthy highlanders [START_REF] Dedobbeleer | Left ventricular adaptation to high altitude: speckle tracking echocardiography in lowlanders, healthy highlanders and highlanders with chronic mountain sickness[END_REF][START_REF] Stembridge | Ventricular structure, function, and mechanics at high altitude: chronic remodeling in Sherpa vs. short-term lowlander adaptation[END_REF][START_REF] Stembridge | Short-term adaptation and chronic cardiac remodelling to high altitude in lowlander natives and Himalayan Sherpa[END_REF]. We also found a RV decrease in E/A ratio with altitude as already reported both in acute and chronic hypoxia [START_REF] Huez | Echocardiographic and tissue Doppler imaging of cardiac adaptation to high altitude in native highlanders versus acclimatized lowlanders[END_REF] without any resting diastolic dysfunction.

Right heart (CMS effect)

The moderate-severe CMS highlanders at 5,100 m had the most important dilatation of the right cavities. This extreme remodelling can probably be induced by the higher exercise-induced increase in PAP and the higher haematocrit and blood viscosity. The modifications in systolic and diastolic functions were similar in healthy and CMS highlanders and similar to previous observations [START_REF] Pratali | RV contractility and exercise-induced pulmonary hypertension in chronic mountain sickness: a stress echocardiographic and tissue Doppler imaging study[END_REF]. We did not explore the RV systolic function during exercise but in moderatesevere CMS highlanders, the RV cardiac reserve is known to be reduced compared to healthy highlanders [START_REF] Pratali | RV contractility and exercise-induced pulmonary hypertension in chronic mountain sickness: a stress echocardiographic and tissue Doppler imaging study[END_REF]. Moreover, there was no difference in the E/A ratio between the CMS patients, while RA progressively dilated, strengthening the idea that the RA remodelling is not due to diastolic dysfunction. While we did not find any relationship with the duration of stay in La Rinconada (results not shown), the important dilatation of the right ventricle and atria in the more severe CMS patients, together with the observed exercise RV systolic dysfunction, could represent a long-term response to a chronic increase in right afterload [START_REF] Naeije | Pulmonary hypertension and the right ventricle in hypoxia[END_REF] in some individuals living permanently at extreme altitude and could probably precede the progression towards right heart failure.

Left heart (altitude effect)

The anatomic left heart remodelling was less important than the modifications of the right side.

LV diameter and volume decreased with altitude while the thickness of the wall increased, resulting in a significant increase in the RWT ratio. LV ejection fraction, global LV longitudinal strain and cardiac output were normal, confirming preserved LV contractility in people living permanently at the extreme altitude of La Rinconada. These results are similar to those published in highlanders of similar age living permanently at 4,350 m (Cerro de Pasco, Peru) with a smaller LV volume, and a normal systolic function as determined by EF and GLS [START_REF] Dedobbeleer | Left ventricular adaptation to high altitude: speckle tracking echocardiography in lowlanders, healthy highlanders and highlanders with chronic mountain sickness[END_REF]. However, the authors reported a normal LV diastolic function whereas we found a significant decrease in E/A ratio, exclusively because of lower E velocities (early filling), suggesting a modification in the LV filling. When precisely characterising the mitral pattern, we found an abnormal relaxation (grade I) in 6 healthy highlanders (35.3 %) at 5,100 m. This suggests that in relatively young healthy people living at very high-altitude, a diastolic dysfunction could appear. The reasons for such abnormalities are not clear. Although these highlanders were significantly older in our study when compared to the 11 people with a normal mitral pattern (50±1 and 36±2 years, respectively; p<0.001), this is a relatively intriguing observation in middle-aged people with the same normal mean systemic arterial pressure (90±6 and 87±3 mmHg, respectively; p>0.05) and without known cardiovascular diseases. A recent study in mice suggested that an increase in RV afterload could result in biomechanical and transcriptional changes in both the RV and the LV, with LV fibrosis [START_REF] Kheyfets | The left ventricle undergoes biomechanical and gene expression changes in response to increased right ventricular pressure overload[END_REF]. The chronic elevation of the RV afterload in highlanders residing at 5,100 m could possibly explain the LV diastolic dysfunction but this mechanism has to be confirmed in humans.

Left heart (CMS effect)

In moderate-severe CMS patients we found a more important change in LV geometry with a thicker LV, resulting in a higher RWT ratio without significant differences in both systolic and diastolic functions and without any increase in the prevalence of diastolic dysfunction. This LV phenotype was similar to previous data in highlanders with the same severity of CMS [START_REF] Maignan | Pulmonary pressure and cardiac function in chronic mountain sickness patients[END_REF][START_REF] Dedobbeleer | Left ventricular adaptation to high altitude: speckle tracking echocardiography in lowlanders, healthy highlanders and highlanders with chronic mountain sickness[END_REF].

The origin of this LV phenotype in the more severe CMS patients is not clear. It could be associated with higher haematocrit and blood viscosity [START_REF] Stauffer | Blood viscosity and its determinants in the highest city in the world[END_REF]. Similarly to others [START_REF] Maignan | Pulmonary pressure and cardiac function in chronic mountain sickness patients[END_REF][START_REF] Dedobbeleer | Left ventricular adaptation to high altitude: speckle tracking echocardiography in lowlanders, healthy highlanders and highlanders with chronic mountain sickness[END_REF], we did not find any changes in LA volume, neither with altitude, nor with CMS. As for the right cavities and despite the absence of relationship with the duration of stay in La Rinconada, we suggest that in chronic severe hypoxia, a progressive thickening of the LV with abnormal relaxation occurs, possibly reflecting a long-term evolution of a chronic modification in myocardial histology with a more fibrotic pattern.

Interestingly, and despite the progressive remodelling of the heart, no significant auricular or ventricular arrhythmia were recorded, confirming that highlanders, with or without CMS, are not overexposed to arrhythmias [START_REF] Busch | Global REACH: Assessment of Brady-Arrhythmias in Andeans and Lowlanders During Apnea at 4330 m[END_REF].

Funding. The Expedition 5300 altitude research programme was supported by the Grenoble Alpes University foundation, the "Fonds de dotation AGIR pour les maladies chroniques" and the French National Research Agency (ANR-12-TECS-0010) in the framework of the ''Investissements d'avenir'' program (ANR-15-IDEX-02).

Conclusions:

  In the highest city in the world, healthy dwellers exhibit right heart dilatation in response to a chronically increased afterload and a left ventricle concentric remodelling with diastolic dysfunction. Those modifications are accentuated in moderate-severe CMS subjects and may enhance the risk of heart failure.

  breathlessness and palpitations, sleep disturbance, cyanosis, veins dilatation, paraesthesia, headache, and tinnitus. A score between 0 and 3 was attributed for each item, 0 indicating the absence of the symptom, 1 indicating mild symptoms, 2 moderate symptoms and 3 severe symptoms. The [Hb] was also scored by 0 or 3 points, 0 if the [Hb] was < 21 g•dL -1 and 3 if the [Hb] was ≥ 21g•dL -1 . Haemoglobin concentration was measured in situ with a HemoCue system (HemoCue®Hb201+, HemoCue AB, Ängelholm, Sweden) and haematocrit (Ht) by microcentrifugation (Hemata STAT -II, Separation Technology Inc., Sandford, USA). Pulsed oxygen saturation (SpO2) (OxiMax N65, Medtronic, Dublin, Ireland) and blood pressure (Digital Blood Pressure Monitor, A&D Medical, Sydney, Australia) were measured after at least 5 min of sitting. A 12-lead electrocardiogram (ECG) was performed in supine position (ECG Colson Cardi-12, Limay, France).

Figure 1 .

 1 Figure 1. Mean pulmonary artery pressure (mPAP, panels A and C) and total pulmonary resistance (TVR, panels B and D) at rest and during exercise (55 and 70% of the maximal theoretical heart rate value). Panels A and B provide comparisons in healthy individuals according to altitude of residency (lowlanders in black, highlanders at 3,800 m in grey and highlanders at 5,100 m in white). Panels C and D provide comparisons in highlanders at 5,100 m according to CMS severity (no CMS in white, mild CMS in hatched black and moderate-severe CMS in hatched grey). All parameters were significantly modified with the exercise intensity. * Different from lowlanders (p<0.01), £ different from no CMS (p<0.01); # different from mild CMS (p<0.01). Error bars are SEM.

Figure 2 .

 2 Figure 2. Relationship between cardiac output and mean pulmonary artery pressure during moderate to intense exercise (70%predicted maximum heart rate). Panel A: altitude effect between lowlanders (black points), highlanders at 3,800 m (grey points) and highlanders at 5,100 m (white points). Panel B: CMS effect in highlanders at 5,100 m between subjects with no CMS (white points), with mild CMS (black points) and with moderate-severe CMS (grey points). mPAP, mean pulmonary artery pressure; CO, cardiac output; TVR, total vascular resistance. The plain line represents the upper limit of 3 UW of TVR and the dotted line the upper limit of 30 mmHg of mPAP.

table 2 )

 2 Mean PAP could not be assessed (no recordable tricuspid insufficiency) in 12 out of 98 subjects (12%), i.e. in 3 lowlanders, 2 highlanders at 3,800 m and 7 highlanders at 5,100 m.

					Highlanders		Highlanders
				Lima	Puno (3 800 m)	La Rinconada (5 100 m)
					Altitude effect
							CMS effect
				No CMS	No CMS	No CMS	Mild CMS	Moderate-severe CMS
	Age (yrs)			31 ± 10	32 ± 12	41 ± 9*	42 ± 9	43 ± 7
	CMS score			1.6 ± 1.9	1.6 ± 2.3	3.9 ± 1.4 @ *	7.9 ± 1.5 #	12.5 ± 1.9 £#
	Duration (years)	of	stay	-	-	13 ± 8	14 ± 10	19 ± 8
	BMI (kg•m -2 )			25.2 ± 4.6	24.5 ± 3.5	25.5 ± 2.1	26.6 ± 3.8	26.2 ± 2.9
	Systolic BP (mmHg)	115 ± 9	115 ± 9	115 ± 12	116 ± 11	118 ± 17
	Diastolic BP (mmHg)	70 ± 9	77 ± 7	79 ± 11	80 ± 8	75 ± 9
	Mean BP (mmHg)		85 ± 8	90 ± 6	88 ± 11	93 ± 7	90 ± 8
	Heart rate (bpm)		71 ± 16	68 ± 8	68 ± 9	65 ± 8	68 ± 10
	SpO2 (%)			98 ± 1	93 ± 3*	84 ± 5 @ *	83 ± 4	81 ± 6
	[Hb] (g•dL -1 )			13.8 ± 1.4	18.7 ± 1.7*	22.1 ± 2.3 @ *	22.2 ± 1.4	23.9 ± 1.5 £#
	Haematocrit (%)		43 ± 5	57 ± 5*	69 ± 7 @ *	70 ± 5	75 ± 5 £#
	Hbmass (g)			744 ± 218	932 ± 246*	1673 ± 440 @ *	1494 ± 419	1823 ± 459
	Blood volume (mL)		5401 ± 1319	4974 ± 1035	7421 ± 1385 @ *	6612 ± 1644	7647 ± 1705

Table 2 .

 2 Echocardiographic data of the right heart in lowlanders and highlanders without or with chronic mountain sickness.

	Data are mean ± SD. RVEDA, right ventricle end diastolic area; RA, right atria; BSA, body surface area; RVFAC, right
	ventricle fractional area change; Et and At, tricuspid early (Et) and late (At) velocities; AT, acceleration time; sPAP and
	mPAP, systolic and mean pulmonary artery pressure, TVR, total pulmonary vascular resistance; TVR45%, total pulmonary

vascular resistance corrected for an haematocrit of 45 %; CMS, chronic mountain sickness. The first three columns represent the effect of altitude of residency in healthy subjects: *p<0.01 different from Lima; @ p<0.01 different from Puno. The three last columns represent the effect of CMS in dwellers from La Rinconada: # p<0.01 different from no CMS; £ p<0.01 different from Mild CMS. All significant differences persist when taking into account age in a multivariate model, both for altitude effect and CMS effect analysis, except for the Et/At ratio.

Table 3 .

 3 Echocardiographic data of the left heart in lowlanders and highlanders without or with chronic mountain sickness.Data are mean ± SD. S, interventricular septum; LV EDD, left ventricle end diastolic diameter; P, left ventricle posterior wall; RWT: relative wall thickness; vol, volume; BSA, body surface area; EF, ejection fraction; CO, cardiac output; CI, cardiac index; SV, stroke volume; E and A, early and late mitral inflow velocities; E', mitral annular early diastolic peak velocity; SVR, systemic vascular resistance; CMS, chronic mountain sickness. The first three columns represent the effect of altitude in healthy subjects: *p<0.01 different from Lima; @ p<0.01 different from Puno. The three last columns represent the effect of CMS in dwellers from La Rinconada: # p<0.01 different from no CMS; £ p<0.01 different from Mild CMS. Significant differences for LV ED diameter and volume and diastolic parameters persist when taking into account age in a multivariate model, both for altitude effect and CMS effect analysis.

		Lowlanders	Highlanders		Highlanders
		Lima (SL)	Puno (3 800m)		La Rinconada (5 100m)
			Altitude effect
					CMS effect
		No CMS	No CMS	No CMS	Mild CMS	Moderate-severe CMS
	S thickness (mm)	10 ± 1	10 ± 2	11 ± 1 @ *	11 ± 1 #	12 ± 1 #£
	LV EDD (mm)	48 ± 4	44 ± 4*	45 ± 3*	47 ± 3	45 ± 4
	P thickness (mm)	10 ± 1	9 ± 1	10 ± 1	10 ± 2	10 ± 1
	RWT	0.40 ± 0.06	0.43 ± 0.07	0.46 ± 0.06*	0.44 ± 0.05	0.50 ± 0.07 #
	LV vol/BSA (mL•m -2 )	60 ± 10	49 ± 8*	53 ± 8*	57 ± 9	52 ± 11
	LA vol/BSA (mL•m -2 )	30 ± 9	26 ± 7	29 ± 5	30 ± 6	31 ± 8
	LV mass/BSA (g•m -2 )	89 ± 13	76 ± 21*	93 ± 26 @	97 ± 21	100 ± 23
	EF (%)	69 ± 7	66 ± 6	65 ± 7	62 ± 5	63 ± 7
	CO (L•min -1 )	5.9 ± 1.3	5 ± 1.1	5.3 ± 1.3	5.4 ± 1.1	5.5 ± 1.1
	SV (mL)	85 ± 17	73 ± 17	78 ± 12	86 ± 16	81 ± 13
	LV longitudinal strain (%)	19.5 ± 1.5	19.4 ± 2	18.4 ± 2.8	17.7 ± 1.8	17.5 ± 1.8
	Peak E (cm•s -1 )	80 ± 14	67 ± 15*	55 ± 10 @ *	54 ± 12	56 ± 12
	Peak A (cm•s -1 )	50 ± 8	46 ± 9	54 ± 15	51 ± 11	51 ± 11

Table 4 .

 4 Exercise responses in lowlanders and highlanders without or with chronic mountain sickness.Data are mean ± SD. HR, heart rate; mPAP, mean pulmonary artery pressure; CO, cardiac output; TVR45%, total pulmonary vascular resistance at a haematocrit of 45%; load 1 and 2, intensities corresponding to 55 and 70% of the theoretical maximal heart rate, respectively (see Materials and Methods section); CMS, chronic mountain sickness. The first three columns represent the effect of altitude in healthy subjects: *p<0.01 different from Lima; @ p<0.01 different from Puno. The three last columns represent the effect of CMS in dwellers from La Rinconada.

		Lowlanders	Highlanders		Highlanders
		Lima	Puno (3 800m)		La Rinconada (5 100m)
			Altitude effect
					CMS effect
		No CMS	No CMS	No CMS	Mild CMS	Moderate-severe CMS
	Rest HR (b•min -1 )	67 ± 7	73 ± 9	70 ± 9	67 ± 9	74 ± 11
	HR load 1 (b•min -1 )	104 ± 7	104 ± 8	98 ± 9	100 ± 6	99 ± 9
	HR load 2 (b•min -1 )	133 ± 7	130 ± 7	122 ± 11* @	122 ± 8	120 ± 10
	Rest SpO2 (%)	98 ± 1	93 ± 3*	84 ± 5* @	83 ± 4	81 ± 6
	SpO2 load 1 (%)	98 ± 1	89 ± 5*	79 ± 5* @	78 ± 7	77 ± 5
	SpO2 load 2 (%)	97 ± 1	88 ± 4*	77 ± 5* @	76 ± 6	74 ± 4
	TVR45% rest (WU)	4.7 ± 1.3	3.6 ± 0.8	3.4 ± 1.1	2.9 ± 0.9	3.7 ± 1.3
	TVR45% load 1 (WU)	3.3 ± 0.8	2.8 ± 0.5	2.6 ± 0.8	2.5 ± 0.5	3.0 ± 1.3
	TVR45% load 2 (WU)	3.0 ± 0.8	2.5 ± 0.5	2.4 ± 0.5	2.3 ± 0.5	2.7 ± 1

Acknowledgements. The authors would like to thank the volunteers for their commitment and time investment in this study. Furthermore, our thanks are extended to the Peruvian medical students who were assisting in the participant recruitment and screening for this study. We also thank GE Healthcare for providing the portable cardiac ultrasound.

RESULTS

Clinical and haematological characteristics (table 1)

Comparison in healthy individuals according to altitude of residency

Highlanders at 5,100 m were older compared to lowlanders but body mass index, arterial blood pressure and HR were similar between groups. As expected, SpO2 decreased significantly with altitude while [Hb], Ht, Hbmass and total blood volume significantly increased. SpO2 showed strong (all p<0.001) negative correlations with Ht (r=-0.81), Hbmass (r=-0.77) and total blood volume (r=-0.58).

Comparison in highlanders at 5,100 m according to CMS severity

In highlanders at 5,100 m, there was no effect of CMS, except for [Hb] and Ht which were significantly higher in the moderate-severe CMS group. The moderate-severe CMS subjects tended to reside in La Rinconada for a longer time (p=0.06).

All resting ECG were normal without sign of pathologic state. Despite PAC and PVC in all lowlanders and highlanders, no significant arrhythmia was detected on the 24-hour Holter ECG recordings whatever the altitude and the CMS status.

DISCUSSION

This study described, for the first time, the pulmonary haemodynamic during exercise and the remodelling of both the right and the left heart in highlanders living permanently at 5,100 m above sea level with or without CMS. The main results are that i) mPAP at rest and during exercise increased with the altitude of residency but did not differ between highlanders with or without CMS, ii) the dilatation and functional remodelling of the right heart was correlated to resting and exercise pulmonary artery pressures, total blood volume and SpO2 while the left heart showed a progressive concentric remodelling pattern with associated diastolic dysfunction, and iii) highlanders at 5,100 m with moderate-severe CMS patients showed the most extensive heart remodelling.

Pulmonary haemodynamic at rest and during exercise in healthy highlanders

In highlanders living permanently at 5,100 m, both mPAP and TVR were higher at rest and during exercise. The resting mean mPAP level of 28±5 mmHg in La Rinconada was similar to the values measured in Morococha (Peru, 4,540 m) [START_REF] Penaloza | Pulmonary hypertension in helathy men born and living at high altitudes[END_REF], the highest altitude where PAP has been invasively determined (about 30 mmHg) [START_REF] Penaloza | Pulmonary hypertension in helathy men born and living at high altitudes[END_REF][START_REF] Banchero | Pulmonary pressure, cardiac output, and arterial oxygen saturation during exercise at high altitude and at sea level[END_REF], but higher than the echocardiographic values measured in Cerro de Pasco (4,350 m; 23-26 mmHg) [START_REF] Groepenhoff | Exercise pathophysiology in patients with chronic mountain sickness[END_REF][START_REF] Dedobbeleer | Left ventricular adaptation to high altitude: speckle tracking echocardiography in lowlanders, healthy highlanders and highlanders with chronic mountain sickness[END_REF]. The parabolic relationship between mPAP and altitude predicts a higher level of about 32-33 mmHg [START_REF] Penaloza | The heart and pulmonary circulation at high altitudes: healthy highlanders and chronic mountain sickness[END_REF] in La Rinconada (5,100 m) but such a difference could probably be explained by the indirect determination and lack of precision of echocardiographic measurements [START_REF] Doutreleau | Pulmonary Vascular Resistance in Patients With Pulmonary Hypertension: Importance of the Quadratic Velocity-Pressure Relationship-Reply[END_REF][START_REF] Naeije | Exercise-induced pulmonary hypertension: physiological basis and methodological concerns[END_REF]. We also found an increase in TVR with altitude with resting values at 5,100 m of 5.5±1.9 WU. Those values are higher than published data determined either by right heart catheterization (4.7 WU; 4,540 m) [START_REF] Banchero | Pulmonary pressure, cardiac output, and arterial oxygen saturation during exercise at high altitude and at sea level[END_REF] or echocardiography (4.9 WU; 4,350 m) [START_REF] Groepenhoff | Exercise pathophysiology in patients with chronic mountain sickness[END_REF]. The higher altitude and the lower oxygenation level in La Rinconada can probably explain this difference.

CONCLUSION


Student Member, IEEE Antonio Bazco-Nogueras

Member, IEEE Paul De Kerret
email: dekerret@eurecom.fr

Fellow, IEEE David Gesbert
email: gesbert@eurecom.fr

Senior Member, IEEE Nicolas Gresset
email: n.gresset@fr.merce.mee.com

Distributed CSIT Does Not Reduce the Generalized DoF of the 2-user MISO Broadcast Channel

Keywords: Generalized Degrees-of-Freedom, Distributed MISO Broadcast Channel, Cooperative Systems, Imperfect CSI

In this letter we analyze the high Signal-to-Noise Ratio (SNR) regime performance of the multi-transmitter MISO Broadcast Channel (BC) with so-called distributed Channel State Information at the Transmitters (CSIT), i.e., where CSIT is made transmitter-dependent. Specifically, we show the unexpected result that it is possible to achieve the same Generalized Degreesof-Freedom (GDoF) independently of whether a channel link estimate is present at one Transmitter (TX), at the other TX, or at both, and regardless of the channel pathloss topology, thanks to a novel transmission scheme. The proposed scheme involves as key ingredient a new precoding scheme coined Sliced Zero-Forcing which efficiently adapts to any distributed CSIT setting.

I. INTRODUCTION

F UTURE wireless networks are expected to be flexible and heterogeneous, with moving or flying base stations, such that the centralization of the signal processing as envisioned in the Cloud Radio Access Network (C-RAN) may not be possible. In such settings, designing an efficient approach to reduce the interference in a decentralized manner becomes necessary.

Several works have focused on such decentralized network deployments, where the TXs are possibly endowed with different CSI, from different perspectives. In [START_REF] Vahid | Two-User Erasure Interference Channels With Local Delayed CSIT[END_REF], the erasure interference channel is studied when each TX has local delayed CSIT, showing that who has which information affects the capacity region. In [START_REF] De Kerret | Enforcing Coordination in Network MIMO with Unequal CSIT[END_REF], a hierarchical CSIT setting is assumed in the broadcast channel, where each TX knows the CSIT used by the TXs with worse CSIT than itself, and a robust hierarchical decentralized precoding scheme is presented which obtains significant gains with respect to the previously known schemes. Other works have focused on centralized settings with heterogeneous or alternating CSIT configurations [START_REF] Lin | Gaussian Broadcast Channels With Intermittent Connectivity and Hybrid State Information at the Transmitter[END_REF].

In this paper, we address the BC with decentralized and nonhierarchical CSIT. This setting models a broad variety of practical deployments where the TXs are not connected with ideal backhaul. To get intuition and analytical results, we consider the high-SNR regime and we consider in particular the Degrees-of-Freedom (DoF) metric, which has already proved instrumental in several key discoveries [START_REF] Cadambe | Interference Alignment and Degrees of Freedom of the K-User Interference Channel[END_REF]. Specifically, the DoF is defined as DoF lim

P →∞ C(P ) log 2 (P ) , (1)
where C(P ) denotes the sum capacity and P the transmission SNR. However, the DoF analysis exhibits some limitations, especially in scenarios with strong pathloss differences. To circumvent this problem, Etkin et al. introduced the GDoF in [START_REF] Etkin | Gaussian Interference Channel Capacity to Within One Bit[END_REF],

where the pathloss topology is taken into account by modeling the relative channel strength of each link as a function of P .

Recently, the GDoF of the MISO BC with imperfect, yet centralized 1 , CSIT has been derived in [START_REF] Davoodi | GDoF Region of the MISO BC: Bridging the Gap between Finite Precision and Perfect CSIT[END_REF]. In that work, the estimate of the link between TX k and RX i has an error decreasing in P -α i,k , where α i,k is the accuracy parameter and P √ P . Extending that model to the so-called Distributed CSIT setting [START_REF] De Kerret | Degrees of Freedom of the Network MIMO Channel with Distributed CSI[END_REF], where the TXs do not access the same CSIT estimates, the estimation error at a TX j for the link TX k-RX i is then modeled as P -α (j) i,k , where the superscript (j) reflects the TX-dependent nature of the CSI quality.

For the 2-user MISO BC, it has been shown in [START_REF] Bazco | Generalized Degrees-of-Freedom of the 2-user case MISO Broadcast Channel with Distributed CSIT[END_REF] that, for the specific case where α

(1) i,k ≥ α (2)
i,k for every i,k, the sum-GDoF solely depends on the CSI quality at the better informed TX. However, in a more realistic scenario, there might not be a notion of "better informed TX" that is valid across all the links.

Our main contribution in this letter is to extend the result of [START_REF] Bazco | Generalized Degrees-of-Freedom of the 2-user case MISO Broadcast Channel with Distributed CSIT[END_REF] from the "better informed TX" case to any CSIT allocation and any pathloss topology of the 2-user case. Specifically, we show that it does not matter whether an estimate of a given channel coefficient is known at one TX, at the other TX, or at both. This is surprising as the result in [START_REF] Bazco | Generalized Degrees-of-Freedom of the 2-user case MISO Broadcast Channel with Distributed CSIT[END_REF] relies on the idea of a (passive) uninformed TX transmitting with fixed coefficients, and an (active) informed TX reducing interference, such that it was believed that this property would not extend to other CSIT configurations. Hence, this work reveals that cooperative settings are much more resilient against CSI mismatches between TXs than commonly thought in the community, what could impact the future design of feedback mechanisms.

Illustrating Example

We introduce in the following a simple example to convey the main intuition of the proposed transmission scheme -called in the following Sliced Zero-Forcing (S-ZF) and described in detail in Section IV-, and in order to illustrate how the CSIT configuration -i.e., what CSI is known with which quality at which TX-affects the GDoF performance. As aforementioned, each TX has its own estimate of the channel between TX k and RX i with an error scaling as P -α (j) i,k. In the following example, we consider the conventional DoF, i.e., that the channel pathloss does not scale as the SNR P . Moreover, the CSIT quality allocation is given for ρ ∈ [0,1] by

TX 1 → α (1) 1,1 = 0.25, α (1) 1,2 = 0.25, α (1) 2,1 = 0.5, α (1) 2,2 = 0.5 , TX 2 → α (2) 1,1 = ρ, α (2)
1,2 = ρ, α

2,1 = 1-ρ, α

2,2 = 1-ρ . Note that as ρ increases, TX 2 becomes better informed about links towards RX 1 and less about links towards RX 2, while TX 1 keeps a fixed estimation quality for each user. In Fig. 1 we show the DoF achieved by the proposed S-ZF scheme as a function of ρ. We compare this DoF with a centralized CSIT setting with CSIT quality α i,k = max(α

(1) i,k ,α (2) i,k ), ∀i,k ∈ {1,2},
whose DoF is computed in [START_REF] Davoodi | GDoF Region of the MISO BC: Bridging the Gap between Finite Precision and Perfect CSIT[END_REF], as well as with conventional Zero-Forcing (ZF) and time-sharing.

Surprisingly, it can be seen that the proposed scheme attains the same DoF as the centralized case, whereas conventional ZF, which is optimal in the centralized CSIT scenario, performs poorly when confronted with CSI discrepancies between the TXs. Note that the only case where the conventional ZF scheme is performing as S-ZF is when ρ = 0.25, due to the fact that both TXs have the same accuracy for the worse user RX 1.

Notations: The exponential equality is denoted as . =, i.e., f (P )

. =P β is equivalent to lim P →∞ log(f (P )) log(P ) =β. The exponential inequalities ≤ and ≥ are defined in the same manner.

II. SYSTEM MODEL

A. Channel Model

We consider single-antenna nodes and we assume that the RXs have perfect CSI. The signal received at RX i is written as

y i h H i x+z i , (2)
where

h H i [h i,1 , h i,2
] denotes the multi-TX channel to RX i and h i,k denotes the fading channel coefficient from TX k to RX i. The term z i ∼ N C (0,1) is the additive Gaussian noise at RX i, and x ∈ C 2×1 is the multi-TX transmitted signal which fulfills the average sum power constraint

E[ x x [t RX1 t RX2 ] s 1 s 2 , (3)
where t RXi denotes the precoder for RX i's symbol s i . Following the GDoF model [START_REF] Etkin | Gaussian Interference Channel Capacity to Within One Bit[END_REF], the channel coefficient is defined as

h i,k P γ i,k -1 g i,k , (4)
where P is the nominal SNR parameter. The parameter γ i,k ∈ [0,1] is the relative channel strength exponent between TX k and RX i. Intuitively, γ i,k = 0 implies that any received signal lies below the noise floor, i.e., that the channel coefficient is negligible in terms of GDoF, while γ i,k = 1 means that the channel coefficient is not significantly attenuated. Finally, the normalized channel parameters g i,k are mutually independent and drawn from a generic (in the sense that any matrix formed by i.i.d. elements according to this distribution will be full rank) continuous distribution with density and independent of P .

B. Distributed CSIT Model

In the distributed CSIT setting, each TX receives a different estimate of the whole multi-user channel [START_REF] De Kerret | Degrees of Freedom of the Network MIMO Channel with Distributed CSI[END_REF]. The channel coefficient estimation at TX j is written as ĥ(j) i,k

P γ i,k -1 ĝ(j) i,k where ĝ(j) i,k g i,k + P -α (j) i,k δ (j) i,k ∀j ∈ {1,2}, (5)
with the estimation noise terms δ (j)

i,k being drawn from a generic continuous distribution with density, independent of P , and independent from TX to TX, and with α (j) i,k ∈ [0,γ i,k ] being the CSIT exponent at TX j used to parametrize the accuracy of the CSIT. Note that α (j) i,k ∈ [0,γ i,k ] because -in terms of GDoFan estimation with α (j) i,k = γ i,k can be intuitively understood as being perfect [START_REF] Davoodi | GDoF Region of the MISO BC: Bridging the Gap between Finite Precision and Perfect CSIT[END_REF]. Conversely, α (j) i,k = 0 is intuitively understood as being useless. The set of CSIT exponents of TX j is denoted by S (j) α {α (j) i,k |i, k ∈ {1, 2}}. Importantly, it is assumed that the TXs have the knowledge of all the long-term statistics, i.e., γ i,k , for all i, k, and both S (1)

α , S (2)
α .

III. MAIN RESULT

We can now state our main result.

α ) is given by GDoF D-CSIT (S (1) α ,

S (2) α ) ≥ GDoF C-CSIT (S max α ), (6)
where GDoF C-CSIT (S max α

) is the GDoF of the centralized CSIT scenario with a single shared estimate of exponents

S max α = α i,k = max α (1) i,k , α (2) i,k i,k ∈ {1,2} . (7)
The GDoF GDoF C-CSIT (S max α ) corresponds to the scenario where both TXs share the best estimate, which is hence a (logically) centralized setting whose GDoF has been derived in [START_REF] Davoodi | GDoF Region of the MISO BC: Bridging the Gap between Finite Precision and Perfect CSIT[END_REF]. Therefore, the achieved GDoF is only limited by the most accurate estimate of each link, no matters which TX has it.

Remark 1. For completeness, we recall the expression for the Centralized CSIT GDoF derived in [START_REF] Davoodi | GDoF Region of the MISO BC: Bridging the Gap between Finite Precision and Perfect CSIT[END_REF]:

GDoF C-CSIT (S max α ) = min(D 1 ,D 2 ), (8)
where

D 1 max(γ 1,2 ,γ 1,1 )+ max(γ 2,1 -γ 1,1 +α 1 , γ 2,2 -γ 1,2 +α 1 ) + D 2 max(γ 2,2 ,γ 2,1 )+ max(γ 1,1 -γ 2,1 +α 2 , γ 1,2 -γ 2,2 +α 2 ) +
with γ i,k being defined in (4) and α 1 and α 2 given by α 1 min(α 1,1 , α 1,2 ), α 2 min(α 2,1 , α 2,2 ). (9) Theorem 1 shows that it is possible to achieve the GDoF of the centralized setting where the best estimate of each link is perfectly shared. It is intuitively expected that the GDoF in this centralized setting is higher than in the decentralized setting considered, i.e., that the inequality in ( 6) is an equality. Indeed, having one TX with less accurate CSI and having inconsistencies between the TXs is not expected to improve the performance. Yet, rigorously proving the information theoretic upper-bound is tedious and requires additional technical assumptions. For the sake of clarity, and as our main contribution is the achievability, we have left the discussion of the converse for future works. Finally, note that this result can be straightforwardly extended to M > 1 antennas at each node.

IV. SLICED ZERO-FORCING PRECODING

We present here the Sliced Zero-Forcing (S-ZF) scheme where, as usual in interference minimizing schemes, the designs of the beamformers towards RX 1 and RX 2 can be decoupled [START_REF] De Kerret | Enforcing Coordination in Network MIMO with Unequal CSIT[END_REF], [START_REF] Davoodi | GDoF Region of the MISO BC: Bridging the Gap between Finite Precision and Perfect CSIT[END_REF]. Consequently, we present in the following the beamformer aimed at RX 1 that minimizes the interference to RX 2, whereas the other beamformer follows by a permutation of the indices. Furthermore, we omit hereinafter any index referring to the intended RX (RX 1). Based on the available CSIT, the S-ZF precoder is designed so that the ZF condition is fulfilled, i.e.,

h H 2 t SZF = h H 2 λt (1) 1 λt (2) 2 = 0, (10) where t (j)
k denotes the precoder coefficient applied at TX k and the super-index (j) means that it is computed locally at TX j on the basis of the local estimate ĥ(j) 2 . Note that one TX does not need to compute/know the coefficient applied at the other TX. λ is a normalization constant chosen to fulfill an average power constraint and is given by

λ P E t (1) 1 t (2) 2 T 2 F -1 (11)
for the constraint E[ t SZF2 2 ] = P . The normalization constant λ only depends on statistical information and is hence known at both TXs. Given that h H 2 is composed of two coefficients, we can distinguish four different regimes depending on which TX has better knowledge of each link. Those four regimes are shown in Table I above. As illustrated in the table, the four regimes are reduced to three by symmetry. For each of these regimes, we will now describe the S-ZF precoding scheme.

TABLE I: CSIT Configuration Regimes

α (1) 2,2 > α (2) 2,2 α (1) 2,2 ≤ α (2) 2,2 α (1) 2,1 > α (2) 2,1

Most-informed TX (TX 1)

Locally Informed TXs

α (1) 2,1 ≤ α (2) 2,1
Non-locally Informed TXs Most-informed TX (TX 2) a) Locally Informed TXs: In this case, each TX has the best estimate of its own channel towards RX 2 (i.e., the interfered user when considering the beamformer aimed at RX 1). The S-ZF precoding coefficient at TX j is then given by 2 t (j) j = (-1) j ĥ(j)

2,j -1 , ∀j ∈ {1,2}. (12)
b) Non-locally Informed TXs: In this case, each TX knows more accurately the channel coefficient from the other TX towards RX 2. Upon defining j (mod 2)+1, the precoding coefficient at TX j is

t (j) j = (-1) j ĥ(j) 2, , ∀j ∈ {1,2}. (13)
c) Most-informed TX: In this last case, there exists one TX that has the best estimate of both coefficients. The S-ZF precoding then matches the AP-ZF scheme presented in [START_REF] Bazco | Generalized Degrees-of-Freedom of the 2-user case MISO Broadcast Channel with Distributed CSIT[END_REF]: The TX with less precise CSIT (e.g., TX j) transmits with a constant precoder t (j) j (-1) j λ while the most-informed TX precodes with

t ( ) = ( -1) ĥ( ) 2, -1 ĥ( ) 2,j . (14)
V. PROOF OF THEOREM 1 Superposition coding schemes have been shown to achieve optimal DoF/GDoF for multiple BC settings with imperfect CSIT [START_REF] De Kerret | Enforcing Coordination in Network MIMO with Unequal CSIT[END_REF], [START_REF] Davoodi | GDoF Region of the MISO BC: Bridging the Gap between Finite Precision and Perfect CSIT[END_REF], [START_REF] Bazco | Generalized Degrees-of-Freedom of the 2-user case MISO Broadcast Channel with Distributed CSIT[END_REF], [START_REF] Piovano | Optimal DoF Region of the K-User MISO BC With Partial CSIT[END_REF]. This commonly used transmission structure always fits the expression

x = t BC s BC +t ZF RX1 s 1 +t ZF RX2 s 2 +t φ s φ . (15)
Depending on the pathloss topology (i.e., the value of γ i,k ) and the CSIT allocation (i.e., the value of α

i,k ), some of those four symbols may be suppressed. In the general scheme, those symbols form a three-layer structure where each layer has a different power scaling. Specifically:

1) Low-power layer: s φ is a non-zero-forced symbol transmitted with power such that it is only received by the intended RX, if the pathloss topology allows for that. 2) Zero-Forcing layer: s i , i ∈ {1,2}, is intended to RX i and canceled at the other RX using ZF-type precoding.

A necessary condition for the optimality of the scheme is that the interference generated by those symbols lies below the noise floor. Therefore, they are transmitted with a power proportional to the accuracy of the CSIT. 3) Full-power layer: s BC is a broadcast symbol transmitted with full power, intended to be decoded at both RXs. In order to perfectly decode every intended symbol, RX i applies successive decoding [START_REF] Bazco | Generalized Degrees-of-Freedom of the 2-user case MISO Broadcast Channel with Distributed CSIT[END_REF] to first decode s BC , then its intended symbol s i and finally s φ , if it is intended to RX i.

Interestingly, the precoders t BC and t φ depend only on the long-term statistical information (α (j) i,k and γ i,k ) and are hence not affected by the instantaneous CSI discrepancies between TXs. This implies that, in order to prove Theorem 1, i.e., that it is possible to achieve the same GDoF as in the centralized setting with α i,k = max(α

(1) i,k , α (2)
i,k ), we only need to show that S-ZF achieves the same level of interference attenuation as ZF in the centralized setting of reference. This is shown for the interference at RX 2 by means of the following lemma, while the same result holds for RX 1 after permutation of indices.

Lemma 1. The Sliced ZF achieves the same interference reduction scaling as the conventional ZF precoder computed from the best estimate of each channel coefficient, i.e.,

E h H 2 t SZF RX1 2 . = P min(γ2,1,γ2,2)-α opt 2 , ( 16
)
when E t SZF RX1 2 2 = P , where we have defined the short-hand notation α opt 2 as

α opt 2 min max j ∈ {1,2} α (j) 2,1 , max j ∈ {1,2} α (j) 2,2 . (17)
Proof. We prove separately each of the regimes of Table I. We need to consider only the first two cases since the result for the Most-Informed TX configuration has been already proved in [START_REF] Bazco | Generalized Degrees-of-Freedom of the 2-user case MISO Broadcast Channel with Distributed CSIT[END_REF]. a) Non-locally Informed TXs: First, it holds from the precoder definition in (13) that t

Then, the interference term satisfies that

E h H 2 t SZF RX1 2 = λ 2 E -h 2,1 ĥ(1) 2,2 +h 2,2 ĥ(2) 2,1 2 (19)
(a) = λ 2 E -h 2,1 h 2,2 -h 2,1 P -α (1) 2,2 +γ2,2-1 δ (1) 2,2 + h 2,2 h 2,1 + h 2,2 P -α (2) 2,1 +γ2,1-1 δ (2) 2,1 2 (20) (b) = λ 2 P γ2,1+γ2,2-2 E P -α (2) 2,1 g 2,2 δ (2) 2,1 -P -α (1) 2,2 g 2,1 δ (1) 2,2 2 (21)
where (a) holds because, by definition, we can rewrite ĥ(j) 2,k as ĥ(j)

2,k h 2,k + P -α (j) 2,k +γ 2,k -1 δ (j) 2,k , (22)
and (b) comes from h 2,k P γ 2,k -1 g 2,k . Focusing on the expectation term in (21), it holds that

E P -α (2) 2,1 g 2,2 δ (2) 2,1 -P -α (1) 2,2 g 2,1 δ (1) 2,2 2 = P -α opt 2 E P α opt 2 -α (2) 2,1 g 2,2 δ (2) 2,1 -P α opt 2 -α (1) 2,2 g 2,1 δ (1) 2,2 2 (23) . = P -α opt 2 , (24)
where (24) follows from using definition α opt 2 = min(α

(1) 2,2 ,α (2)
2,1 ) and because g i,k and δ (j) i,k are independent of P . Including (24) in (21) and substituting λ with (18) yields = λ 2 E -h 2,1 ( ĥ(1) 2,1 ) -1 +h 2,2 ( ĥ(2) 2,2 ) -1 2 (28)

E h H 2 t SZF RX1 2 . = λ 2 P γ2,1+γ2,2-2-α opt 2 (25) . = P min(γ2,1,γ2,2)-α opt 2 . ( 26
= λ 2 E -ĥ(1)

2,1 ĥ(1)

2,1

-1 + P -α (1) 2,1 +γ2,1-1 δ

(1) 2,1 ĥ(1) where (29) follows from h 2,k = ĥ(j) 2,k -P -α (j) 2,k +γ 2,k -1 δ (j) 2,k , (30) comes from substituting ĥ(j) 2,k = P γ 2,k -1 ĝ(j) 2,k , (31) follows from applying the same argument as in ( 23)-(24), and (32) is obtained after substituting λ with its value in (27). This concludes the proof of Lemma 1, and hence Theorem 1 is proven.

VI. CONCLUSION

We have shown that, remarkably, having different CSIT at each TX does not decrease the GDoF of the 2-user MISO Broadcast Channel, in any channel topology. Key to this surprisingly good performance is the adaptation of the role of each TX as a function of the multi-TX multi-user CSIT configuration. An interesting future extension is to analyze how this GDoFbased distributed scheme behaves at finite SNR, where different effects that are hidden in the GDoF analysis may appear. Moreover, extending the result to larger values of K is very challenging, and from preliminary results, it is expected that the surprisingly good performance does not extend well to more users.

Fig. 1 :

 1 Fig. 1: DoF of the illustrative example setting as function of ρ.

Theorem 1 .

 1 In the 2-user MISO BC with distributed CSIT exponents S

2 .

 2 = P γ2,1-1 .Therefore, from the definition of λ we obtain that λ . = P 2-max(γ2,1,γ2,2) .

Centralized refers to a logically centralized setting where all the TXs have access to the same, possibly imperfect, CSI.

2 ] = P . x is generated from the i.i.d. information symbols s i ∼ N C (0,1) as

The precoder can be improved at finite SNR using Regularized ZF. However, regularization is not necessary in terms of GDoF.