Anne-Sophie Miclot
email: anne-sophie.miclot@inra.fr

Soizic Guimier

Francois F Delmotte

Mazet I F Fabre

C Couture

Laurent Deliere

Sustainable management of grapevine resistance. Detect the emergence of breakdown, of new diseases and adapt crop systems

Keywords: Observatoire, Vigne, Mildiou, Oïdium, Résistance, Durabilité Monitoring, Grapevine, Downy mildew, Powdery mildew, Resistance, Durability

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

Introduction

Avec un IFT total moyen de 15,3 [START_REF] Agreste | Enquête Pratiques Phytosanitaires en viticulture en 2016 : Nombre de traitements et indicateurs de fréquence de traitement[END_REF], la viticulture présente l'une des plus fortes pressions d'utilisation des produits phytosanitaires. Les fongicides représentent plus de 80% des traitements et ciblent très majoritairement deux maladies aériennes, le mildiou et l'oïdium. La gestion de ces deux bioagresseurs repose donc principalement sur l'utilisation de produits phytosanitaires et dans une moindre mesure sur des leviers d'atténuation et un recours aux produits de biocontrôle.

Si une réduction de l'usage des produits phytosanitaires est possible à moyen terme par une amélioration et une généralisation des leviers actuellement mobilisés, une réduction plus significative ne pourra se faire qu'en déployant des innovations plus « radicales ». L'utilisation de la résistance variétale constitue l'une des pistes car les variétés résistantes au mildiou et à l'oïdium sont actuellement très peu utilisées.

Pourtant, l'introduction du mildiou et de l'oïdium en Europe au 19 e siècle a été à l'origine des premiers travaux utilisant les espèces de Vitis américaines (V. rupestris, V. lincecumi, V. berlandieri…) comme sources de résistance en France. Ces travaux ont permis la création de nombreuses variétés appelées hybrides producteurs directs, résistantes à la fois à l'oïdium, au mildiou et au phylloxéra. Ces hybrides couvraient encore 30% du vignoble français en 1958. Cependant, la mauvaise qualité des vins issus de ces variétés a freiné leur développement et la plantation de ces cépages en AOC sera interdite en 1951 (ICV, 2013). Ces hybrides représentent aujourd'hui moins de 1% de l'encépagement français.

Au cours du 20 e siècle, les recherches ont permis de caractériser d'autres sources de résistance. C'est à partir de la résistance portée par Vitis rotundifolia (résistance totale à l'oïdium et très élevée au mildiou) que l'INRA a développé à partir de 1974, un programme de création variétale [START_REF] Bouquet | Vitis x Muscadinia hybridization: A new way in grape breeding for disease resistance in France[END_REF]. Ce programme a abouti après 25 ans de travaux à une série de génotypes monogéniques appelés « Bouquet ». Chaque génotype portant un gène conférant une résistance partielle au mildiou (Rpv1 ; [START_REF] Merdinoglu | Genetic analysis of downy mildew resistance derived from Muscadinia rotundifolia[END_REF] et un gène conférant une résistance totale à l'oïdium (Run 1, [START_REF] Pauquet | Establishment of a local map of AFLP markers around the powdery mildew resistance gene Run1 in grapevine and assessment of their usefulness for marker assisted selection[END_REF]. En 2000, l'INRA s'est engagé dans un nouveau projet de sélection visant à créer des variétés cumulant deux à trois sources de résistance afin de proposer des variétés possédant une résistance potentiellement plus durable [START_REF] Schneider | ResDur, le programme Inra de création de variétés de vignes de cuve résistantes aux maladies cryptogamiques et de bonne qualité oenologique[END_REF]. Ce programme appelé « Resdur » a déjà permis l'inscription de quatre variétés résistantes en France (Delière et al., 2017), plusieurs autres variétés sont attendues dans les années à venir. D'autres variétés résistantes européennes sont également classées en France, il s'agit principalement de variétés Allemandes, Suisses et Italiennes. En parallèle, les variétés issues du programme ResDur sont utilisées comme géniteurs dans le cadre de programmes de sélections conduits par différentes interprofessions. L'objectif est de proposer des variétés résistantes adaptées à différents types de vins. Ainsi, de très nombreuses variétés résistantes seront mises à disposition des viticulteurs dans les trente prochaines années. Ce déploiement sera facilité par différentes évolutions de la réglementation : instauration du classement temporaire permettant au viticulteur d'expérimenter une nouvelle variété tout en vendant le vin obtenu ; possibilité d'intégrer de nouveaux cépages dans les AOP et les IGP.

Les premiers travaux montrent que l'utilisation de variétés résistantes au mildiou et à l'oïdium permet une réduction de l'usage des produits phytosanitaires de plus de 80% (Guimier et al., in press). Néanmoins, ce déploiement de nouvelles variétés résistantes à large échelle soulève de nouvelles questions. Si la problématique du potentiel qualitatif des vins issus de ces variétés reste centrale celle de la durabilité des résistances déployées constitue également un enjeu majeur. En effet, si certaines résistances restent efficaces de nombreuses années (citons la résistance au phylloxéra, introduite grâce à des porte-greffes américains à la fin du 19 e siècle) d'autres perdent plus ou moins rapidement leur efficacité et des contournements de gènes ont été observés dans de nombreuses interactions plantes pathogènes. Un exemple édifiant est le gène de résistance Rlm1 au phoma du colza, (causé par le champignon Leptosphaeria maculans) qui a été contourné en 3 ans seulement en France [START_REF] Rouxel | Phylogenetic and experimental evidence for host-specialized cryptic species in a biotrophic oomycete[END_REF]. Toutes plantes et maladies confondues, dans la moitié des cas avérés montrent des pertes d'efficacité, elles ont lieu dans les six premières années [START_REF] Mcdonald | Pathogen population genetics, evolutionary potential, and durable resistance[END_REF]. Pour la viticulture cet enjeu est particulièrement important car peu de facteurs de résistances ont été identifiés, 14 facteurs de résistance au mildiou (nommés Rpv) et 11 à l'oïdium (nommés Run ou Ren) [START_REF] Merdinoglu | Breeding for durable resistance to downy and powdery mildew in grapevine[END_REF], et encore moins sont utilisés dans les programmes de sélection actuels. Ils constituent un patrimoine fragile, leur efficacité et donc leur utilité étant soumises aux risques d'évolution des populations de pathogènes. De plus l'oïdium et le mildiou de la vigne présentent un fort potentiel évolutif car ils combinent plusieurs caractéristiques favorisant leur adaptation (production d'une grande quantité de spores, bonnes capacités de dispersion, grande taille de population en Europe du fait des conditions climatiques favorables et de l'utilisation quasi exclusive de cépages sensibles). D'un point de vue plus général, il convient de réfléchir à l'intégration de ces nouvelles variétés dans les systèmes de culture existants et d'identifier les itinéraires techniques les plus adaptés à leur conduite. En effet, leur utilisation va modifier en profondeur non seulement les objectifs mais aussi les méthodes de protection. Ces itinéraires techniques devront à la fois compléter l'efficacité partielle des gènes de résistance (notamment pour le mildiou), garantir leur durabilité tout en maîtrisant les maladies et ravageurs non ciblés par la résistance.

Pour répondre à ces enjeux, l'INRA et l'IFV ont créé un dispositif original à l'échelle nationale : l'Observatoire national du déploiement des Cépages Résistants (OsCaR).

Les objectifs de cet observatoire sont (i) d'organiser la surveillance collective du déploiement afin d'anticiper les risques liés à l'évolution des populations de mildiou et d'oïdium et à l'émergence de nouvelles problématiques sanitaires et (ii) d'organiser le partage d'expériences sur le comportement des cépages résistants dans différents systèmes de culture pour aider les viticulteurs à construire ces nouveaux itinéraires techniques.

Matériels et méthodes

Le dispositif

L'observatoire a été créé en 2017. Il s'agit d'un dispositif partenarial qui s'appuie sur les viticulteurs et les structures professionnelles qui souhaitent expérimenter les variétés résistantes en conditions de production. Toute parcelle plantée avec une variété résistante au mildiou et à l'oïdium en classement temporaire ou définitif peut rejoindre le réseau. Il s'agit donc d'un dispositif ouvert et l'intégration se fait principalement sur la base du volontariat. Seules les variétés résistantes INRA en classement temporaire sont obligatoirement incluses dans le dispositif lors de la plantation.

Les parcelles intégrant le dispositif doivent avoir une surface minimale de 0,2 ha. Aucune contrainte n'est fixée en termes d'itinéraire technique et de mode de conduite. L'objectif est d'avoir au sein de l'observatoire une diversité de situations agro-climatiques et de systèmes de culture la plus large possible.

L'observatoire est piloté par une équipe d'animation responsable des différentes activités du réseau (coordination, formation, gestion et analyse des données, surveillance des populations de pathogènes), appuyée par un Comité de Pilotage pluridisciplinaire. Les données de terrain sont collectées selon un protocole standardisé, par les partenaires (viticulteurs, caves coopératives, organismes de développement).

Les données collectées

Des données concernant les caractéristiques de l'exploitation et de la parcelle (localisation, superficie, année de plantation, porte-greffe…) sont collectées lors de l'intégration des parcelles dans le dispositif. Innovations Agronomiques 77 (2019),192021222324252627282930Annuellement, des données de pratiques culturales et de comportement des variétés sont collectées sur le terrain :

-L'estimation des dates de débourrement, floraison, véraison et de maturité, -Des suivis des dynamiques épidémiques des bioagresseurs à 5 périodes de l'année : préfloraison, floraison, fermeture de la grappe, véraison et récolte. Ces suivis concernent les bioagresseurs ciblés par la résistance (mildiou, oïdium) mais également le black rot, l'anthracnose, l'érinose et le phylloxéra. L'estimation de la présence de bioagresseurs est qualitative ; l'observation se fait le long d'un parcours prédéfini. La fréquence de ceps touchés, la fréquence d'organes touchés et l'intensité globale des symptômes sont évaluées sur feuilles et sur grappes pour chaque bioagresseur grâce à une grille de notation (Tableau 1) allant de 0 à 5.

Résultats

Le réseau

En 2018, le réseau est constitué de 69 parcelles plantées sur 35 sites répartis dans 7 régions viticoles françaises : Alsace (n=2), Beaujolais (n=2), Bordeaux/Sud-Ouest (n=19), Charentes-Cognac (n=3), Languedoc (n=32), Provence (n=3), Rhône (n=8) (Figure 1).

La majorité des parcelles constituant le réseau en 2018 sont jeunes et ne sont pas encore en production (Figure 2). Plus de la moitié des parcelles a été plantée en 2017 et 2018 et seulement 30% avaient atteint la troisième feuille en 2018.

Vingt-trois variétés résistantes sont représentées dans l'observatoire en 2018 (Figure 3). Soixante-deux pourcents des parcelles sont plantées avec des variétés issues programmes de sélection INRA (38% de variétés Bouquet et 24% de variétés RESDUR) et 38% des parcelles sont plantées avec des variétés issues des programmes de sélection étrangers.

Pratiques phytosanitaires

L'IFT fongicide du réseau OsCaR est égal à 1.2 en 2017 et à 1.6 en 2018 (Figure 5). Cela représente une réduction de 90% en 2017 et 87% en 2018 par rapport à l'IFT fongicide de la référence nationale Agreste 2016.

Zoom sur les variétés INRA

Les variétés INRA totalement résistantes à l'oïdium grâce au gène Run1 ne présentaient aucun symptôme d'oïdium en 2017 et 2018.

En ce qui concerne le mildiou, les variétés INRA portent une résistance partielle. En 2017, une seule parcelle présentait des symptômes de mildiou sur feuilles à une intensité inférieure à 1%. En 2018, 38% des parcelles étaient touchées sur feuilles et sur grappes à une intensité inférieure à 5%.

Quant au black rot non ciblé par la résistance, seule une parcelle en 2017 a été touchée sur feuilles à une intensité inférieure à 1%. En 2018, des symptômes de black rot ont été observés sur feuilles sur 23% des parcelles et sur grappes sur 10% des parcelles à des intensités inférieures à 1%.

Prélèvements des isolats de mildiou

En 2018, deux périodes d'échantillonnage d'isolats de mildiou ont eu lieu (Figure 7). Une première a été réalisée aux mois de juin et juillet, elle a permis de mettre en collection 606 isolats de mildiou : 142 isolats issus de variétés Bouquet, 78 isolats issus de variétés Resdur, 128 isolats issus de variétés étrangères et 258 isolats issus de variétés sensibles prélevés à environ 1 km des parcelles résistantes. La deuxième session d'échantillonnage a été réalisée au mois de septembre, elle a permis de mettre en collection 1103 isolats de mildiou : 158 isolats issus de variétés Bouquet, 303 isolats issus de variétés Resdur, 236 isolats issus de variétés étrangères et 406 isolats issus de variétés sensibles.

Discussion et perspectives

En permettant d'appréhender en temps réel l'évolution de l'efficacité des résistances déployées et d'identifier rapidement voire d'anticiper l'évolution des populations d'agents pathogènes ciblés par la résistance, cet observatoire constitue d'abord un dispositif d'alerte. La problématique de la durabilité des résistances est particulièrement importante en viticulture du fait du caractère « pérenne » de la culture, du faible nombre de gènes de résistance introgressés dans les variétés actuellement déployées et surtout des évolutions de populations déjà identifiées. En effet, le premier cas d'érosion de la résistance de la vigne au mildiou a été décrit sur la variété Bianca [START_REF] Peressotti | Breakdown of resistance to grapevine downy mildew upon limited deployment of a resistant variety[END_REF] et plus récemment, avec les variétés Bronner, Prior et Regent [START_REF] Delmotte | Rapid and multiregional adaptation to host partial resistance in a plant pathogenic oomycete: Evidence from European populations of Plasmopara viticola, the causal agent of grapevine downy mildew[END_REF][START_REF] Delmas | Adaptation of a plant pathogen to partial host resistance: selection for greater aggressiveness in grapevine downy mildew[END_REF]. En Innovations Agronomiques 77 ( 2019), 19-30

Amérique du Nord, des infections d'oïdium ont été observées sur des plantes porteuses du gène Run1 conférant une résistance totale à l'oïdium (Feechan et al., 2013[START_REF] Feechan | Strategies for RUN1 deployment using RUN2 and REN2 to manage grapevine powdery mildew informed by studies of race specificity[END_REF]. Les observations réalisées dans le cadre de l'observatoire durant les deux premières années n'ont mis en évidence aucune érosion ou contournement de la résistance des variétés déployées. En dépit de cette forte baisse de l'usage des fongicides, l'ensemble des bio-agresseurs est resté dans la majorité des cas bien contrôlé.

Compte-tenu du fort potentiel adaptatif du mildiou et de l'oïdium de la vigne des méthodes complémentaires de protection doivent être mis en oeuvre pour maximiser la durabilité des résistances et la préservation de la ressource limitée que constituent les gènes de résistance. Ainsi, un nombre de traitements phytosanitaires minimum associé à des méthodes prophylactiques peut permettre de diminuer la taille des populations de pathogènes et donc le risque de contournement de la résistance (Mc Donald et Linde, 2002). Ces stratégies doivent aussi permettre la maitrise des bio-agresseurs non contrôlés par la résistance. Cette question des stratégies de protection complémentaires à appliquer est importante et nécessite d'être documentée. En effet, il n'existe actuellement que peu de connaissances sur les dynamiques épidémiques du mildiou et de l'oïdium sur les variétés résistantes. Les modèles et les règles de décisions pour décider du moment optimal de traitement ont été développés pour des variétés sensibles et ne prennent pas en compte la durabilité des résistances. Les données collectées au sein de l'Observatoire doivent ainsi permettre de contribuer à la co-construction de ces stratégies de protection complémentaires. D'un point de vue global ce dispositif permettra de mieux connaître les performances des différentes variétés en fonction des contextes agro-climatiques et des différents systèmes de culture mis en oeuvre.

Mais l'Observatoire a également pour ambition d'être un outil au service de la recherche. En constituant une base de données historiques sur les premiers déploiements des résistances variétales en France couplée à une collection d'agents pathogènes, il se pose comme support pour aborder les différentes problématiques et questions de recherche liées au déploiement des variétés résistantes au vignoble. La base de données constituée est reliée à la plateforme de prévisions des risques d'épidémie Epicure développée par l'IFV [START_REF] Raynal | Spray only if necessary: point on the IFV modeling phytosanitary risk works applied on vineyard protection[END_REF] et utilisée dans le cadre de la surveillance biologique du territoire.

Innovations Agronomiques 77 ( 2019), 19-30 29

Du fait de la dynamique de déploiement des variétés résistantes dans le vignoble français, cet observatoire reste un outil récent, majoritairement composé de jeunes parcelles pas encore productives. L'intégration de nouvelles parcelles et les suivis sur plusieurs années seront nécessaires pour produire des données pertinentes par rapport aux objectifs fixés. Ainsi, ce dispositif doit donc continuer à être ouvert et avoir la capacité à intégrer le plus grand nombre possible de réseau expérimentaux conduits par les organismes professionnels.

Figure 1 :

 1 Figure 1 : Les 35 sites participant au réseau OSCAR en 2018. Les sites sont numérotés. Les régions viticoles sont représentées en gris.

Figure 2 :

 2 Figure 2 : Répartition des 69 parcelles du réseau en 2018 en fonction de leur année de plantation.

Figure 3 :

 3 Figure 3 : Caractéristiques (facteurs de résistance et obtenteurs) et localisation des variétés suivies par l'observatoire en 2018. Répartition du nombre de parcelles par variété.

Figure 4 :

 4 Figure 4 : Représentation de la pression parasitaire locale pour le mildiou, l'oïdium et le black rot en 2017 et en 2018.

Figure 5 :

 5 Figure 5 : Indice de fréquence de traitement fongicide sur les parcelles du réseau OSCAR en 2017 (n=30) et 2018 (n=32) et la référence nationale 2016[START_REF] Agreste | Enquête Pratiques Phytosanitaires en viticulture en 2016 : Nombre de traitements et indicateurs de fréquence de traitement[END_REF]. L'écart type entre les parcelles apparait sur le graphique.

Figure 6 :

 6 Figure 6 : Fréquence et intensité d'attaque du black rot, du mildiou et de l'oïdium sur les feuilles et les grappes des parcelles du réseau à la véraison 2017 (a,b,c,d) et 2018 (e,f,g,h). Fréquence de ceps touchés sur feuilles (a et e) et sur grappes (c et g). Intensité globale des symptômes sur feuilles (b et f) et sur grappes (d et h). La fréquence et l'intensité sont classées en 5 classes. Les histogrammes représentent le pourcentage de parcelles par classe (en 2017, n=30 parcelles sur feuilles et n=28 parcelles sur grappes ; en 2018 n=21 parcelles sur feuilles et sur grappes).

Figure 7 :

 7 Figure 7 : Répartition du nombre de parcelles et d'isolats de mildiou prélevés en fonction du bassin de production. Les isolats de mildiou sont répartis en fonction du type de variétés résistantes dont ils sont issus. Première session de collecte au mois de juin/juillet (a). Deuxième session de collecte au mois de septembre (b).

  Des isolats de mildiou sont prélevés au vignoble à la fois sur des variétés résistantes et sur des variétés sensibles de V. vinifera. Les isolats collectés sur plantes sensibles n'ayant jamais été confrontés à la résistance variétale, constituent une population de référence pour mesurer l'augmentation d'agressivité potentielle des populations de mildiou. Les isolats sont conservés sous azote liquide. A périodes régulières des tests d'agressivité sont réalisés au laboratoire d'après la méthodologie standardisée décrite par[START_REF] Delmas | Adaptation of a plant pathogen to partial host resistance: selection for greater aggressiveness in grapevine downy mildew[END_REF] Des populations d'isolats prélevés sur des variétés résistantes et des variétés sensibles sont inoculées sur des variétés résistantes et sensibles. Après incubation, différents paramètres du cycle d'infection sont évalués : temps de latence, dynamique de sporulation, quantité de sporanges émis par unité de surface foliaire.

	Tableau 1 : Grille de notation utilisée pour la notation des bioagresseurs
	Fréquence de ceps touchés	Fréquence d'organes touchés	Intensité globale des symptômes
	5 -Présence généralisée (> 80%)	5 -Très élevée (> 50%)	5 -Dégâts très importants (> 50%)
	4 -Présence très importante (50 -80%) 4 -Elevée (10 -50%)	4 -Dégâts importants (10% -50%)
	3 -Présence importante (25 -50%)	3 -Moyenne (5 -10%)	3 -Dégâts significatifs (5 -10%)
	2 -Présence régulière (5 -25%)	2 -Faible (1 -5%)	2 -Facilement visibles (1 -5%)
	1 -Rares (< 5%)	1 -Cas isolés (< 1%)	1 -Traces (< 1%)
	0 -Nulle	0 -Nulle	0 -Nulle

-L'estimation de la pression parasitaire locale (sur cépages sensibles) est réalisée selon une grille de notation allant de 0 (nulle à très faible) à 3 (forte à très forte), -Le port de la vigne, la facilité de palissage, la fragilité des rameaux ainsi que la compacité des grappes sont également évalués à l'aide d'une échelle qualitative, -A la récolte, des informations sur le rendement et la facilité à la récolte mécanique sont également recueillies, -Les données relatives à l'itinéraire technique concernent principalement les traitements phytosanitaires (date, produit, dose, cibles et règle de décision associée). La quantité de fongicides utilisée est exprimée par l'indice de fréquence de traitement (IFT) calculé grâce à l'atelier de calcul de l'IFT du Ministère de l'Agriculture et de l'Alimentation https://alim.agriculture.gouv.fr/ift/.

L'ensemble des données est saisi sur une interface web et stocké dans une base de données dédiée.

1.3 Monitoring de l'évolution de l'agressivité des agents pathogènes

  Aucun symptôme d'oïdium n'a été détecté sur les variétés INRA porteuses du gène Run1 conférant une résistance totale. Concernant le mildiou, les variétés possèdent des résistances partielles à cet oomycète et des symptômes sont apparus sur les parcelles du réseau en 2017 et de façon plus marquée en 2018 du fait de la forte pression du mildiou. Si des fréquences de symptômes ont pu être parfois importantes en 2018, les intensités d'attaques étaient toujours faibles, n'entraînant pas de pertes de récolte significatives. Ces observations de terrain seront complétées en 2019 par un suivi au laboratoire de l'agressivité des populations de mildiou prélevées au vignoble en 2018. Ces suivis seront réitérés régulièrement afin de mesurer les dynamiques d'évolution de cette agressivité.La réduction importante de l'usage des fongicides permise par la résistance variétale au mildiou et à l'oïdium peut cependant favoriser la réémergence de maladies habituellement contrôlées par les traitements ciblant le mildiou et l'oïdium. Des maladies et ravageurs dits « secondaires » telles que le black rot, l'anthracnose, l'érinose et le phylloxera ont en effet été observées sur les parcelles du réseau. Néanmoins, les évaluations réalisées à la véraison 2017 et 2018 ont montré que ces maladies n'ont pas eu d'impact sur les parcelles hormis ponctuellement pour le black rot (2 parcelles du réseau en 2018).Au-delà de la surveillance, l'Observatoire constitue également un dispositif d'acquisition de connaissances sur les systèmes de culture mobilisant des variétés résistantes au mildiou et à l'oïdium. Les données recueillies aux cours de ces deux premières années ont ainsi confirmé le fort potentiel de ces variétés pour réduire l'usage des produits phytosanitaires au sein des exploitations viticoles. En effet, une réduction de 90% de l'IFT fongicide par rapport aux références a pu être observée en 2017. Cette réduction s'est confirmée en 2018 malgré la forte pression parasitaire du mildiou et du black rot.

Innovations Agronomiques 77 (2019), 19-30


Student Member, IEEE Matthias Hesse
email: hesse@i3s.unice.fr

Student Member, IEEE Marko Mailand
email: marko.mailand@ieee.org

Senior Member, IEEE, Luc Deneire Member, IEEE Hans-Joachim Jentschel
email: hans-joachim.jentschel@tu-dresden.de

Jérôme Lebrun
email: lebrun@i3s.unice.fr

L Deneire
email: deneire@i3s.unice.fr

Semi-Blind Cancellation of IQ-Imbalances

Keywords:

The technical realization of modern wireless receivers yields significant interfering IQ-imbalances, which have to be compensated digitally. To cancel these IQ-imbalances, we propose an algorithm using iterative blind source separation (IBSS) as well as information about the modulation scheme used (hence the term semi-blind). The novelty of our approach lies in the fact that we match the nonlinearity involved in the IBSS algorithm to the probability density function of the source signals. Moreover, we use approximations of the ideal non-linearity to achieve low computational complexity. For severe IQ-mismatch, the algorithm leads to 0.2 dB insertion loss in an AWGN channel and with 16-QAM modulation.

s(t) -sin(2πf c t + ϕ Q ) cos(2πf c t + ϕ I ) h LP (t) h LP (t) A/D A/D DSP g I g Q r Q (t) r I (t) y Q (t)
y I (t)

Fig. 1. Block diagram of a zero-IF receiver with imbalances of phase (ϕ I , ϕ Q ) and amplitude (g I , g Q ) in I-and Q-path

II. SYSTEM MODEL

In this section, we describe the two main parts of our model. Each part on its own, is well known in the corresponding field of research.

A. Mixture Model

The received signal

s(t) = Re{d(t) exp(j2πf c t)} + n(t) (1)
= Re{d(t)} cos(2πf c t) -Im{d(t)} sin(2πf c t) + n(t)

is split by the zero-IF receiver into the orthogonal I-component r I (t) and Q-component r Q (t) by multiplying with cos(2πf c t) and -sin(2πf c t), respectively. In this ideal case, the I-path contains the real part of the transmitted symbol Re{d(t)} = d I (t), some high frequency (HF) components and noise n(t), the Q-path includes the imaginary part Im{d(t)} = d Q (t), HF components and also some noise n(t). The HF components are removed by a low pass filter h LP (t) being assumed to be ideal.

The imperfection of the local oscillators (LO) yields phase errors (denoted as ϕ I for the I-path and ϕ Q for the Q-path (Figure 1)) which are assumed to be time invariant. Due to this maladjustment, the Q-component is interfered by the I-signal and vice versa. Furthermore, due to production imperfections, the mismatches in the circuitry cause amplitude imbalances. We model these as an imbalance in gain g I and g Q (Figure 1) which is also assumed to be invariant in time. Having defined these impairments, we are able to compute the disturbed I-and Q-signal by

r I (t) = g I cos(ϕ I )d I (t) -g I sin(ϕ I )d Q (t) r Q (t) = -g Q sin(ϕ Q )d I (t) + g Q cos(ϕ Q )d Q (t). (2)
A common assumption in the literature is that ϕ I is zero and ϕ Q is only the phase difference between I-and Q-path. That means that the I-path is perfectly synchronised. In this paper, we don't make this assumption. Simulations in section IV show that small synchronisation errors are also compensated.

We define an observation vector #ř (t) = r

I (t) r Q (t) T , a source vector #ď (t) = d I (t) d Q (t)
T and a mixing matrix

H = h 11 h 12 h 21 h 22 = g I cos(ϕ I ) -g I sin(ϕ I ) -g Q sin(ϕ Q ) g Q cos(ϕ Q ) . (3)
The mixture model is now given by

#ř (t) = H #ď (t) + #ň (t). (4)
The task of the BSS algorithm is to estimate the separation matrix W * = H -1 such that the separated vector #y (t) =

y I (t) y Q (t) T fulfills #y (t) = W * #ř (t) = W * H #ď (t) = #ď (t)
when noise is neglected. Whenever W * H = I, where I is a 2 × 2 identity matrix, the IQ-imbalances are cancelled.

B. Separation System

The iterative inversion (II) [START_REF] Cruces | An iterative inversion approach to blind source separation[END_REF], [START_REF] Cruces | Una visión unificada de los algoritmos de separatión ciega de fuentes[END_REF] is an optimization algorithm with a maximum likelihood (ML) criterion [START_REF] Cardoso | Infomax and maximum likelihood for source separation[END_REF] (or equivalently, the mutual information criterion [START_REF] Pham | Blind separation of mixture of independent sources through a quasi-maximum likelihood approach[END_REF] and the INFOMAX criterion [START_REF] Bell | An information-maximization approach to blind separation and blind deconvolution[END_REF]). The purpose of these criteria is to restore the statistical independence of the source signals. Therewith the data sent over the I-and Q-path have to be statistically independent.

The optimization of all three criteria Ψ results in the condition for independence:

∂Ψ ∂W W=W * = R ψ( #y ) #x -W -T W=W * = 0 (5)
which have to be fulfilled for the separation solution W * where R ψ( #y ) #x = E{ψ( #y ) #x T } is a correlation matrix and E{•} denotes the expectation operator. The score function [START_REF] Babaie-Zadeh | Differential of the mutual information[END_REF] ψ( #y ) acts component-wise and is given by

ψ( #y ) = -d ln p dQ (y Q )/dy Q -d ln p dI (y I )/dy I T = -p ′ dQ (y Q )/p dQ (y Q ) -p ′ dI (y I )/p dI (y I ) T (6)
where p di (y i ) is the estimated pdf of the source signal d i and p ′ di (y i ) is its first derivation.

In [START_REF] Cruces | An iterative inversion approach to blind source separation[END_REF], equation ( 5) is solved numerically with a quasi-Newton algorithm. This algorithm approaches the separation solution W * iteratively as

W (n+1) = W (n) -µ (n) R (n) f ( #y )g( #y ) -I W (n) . (7)
The correlation matrix R f ( #y )g( #y ) with two arbitrary non-linear functions replaces the exact correlation matrix R ψ( #y ) #y because ψ( #y ) is unknown if the separation is completely blind. However, in communication systems the modulation is usually known in advance and therewith the pdf of the source. This a-priori knowledge can be used to determine ψ( #y ) (section III)

and there is no need to approximate ψ( #y ) by f ( #y ). Following this idea and according to [START_REF] Amari | Blind source separation-semiparametric statistical approach[END_REF], the optimal function g( #y ) is simply #y .

In [START_REF] Cruces | An iterative inversion approach to blind source separation[END_REF], two methods are proposed for estimating R

(n) ψ( #y ) #y . The first one uses a single sample to estimate the correlation. This requires the least calculation effort and causes no additional delay. But, due to the bad estimation performance, the convergence behavior is degraded. The second technique averages the correlation by using a long fixed block (assuming stationarity and ergodicity), which leads to better estimation performance, at the cost of computational complexity and additional delay. In our approach, the delay and complexity are kept at a minimum by using a sliding window block of size L, enabling very small delay and low complexity by resorting to an adaptive implementation. Moreover, the block size L can be adjusted to optimize performance.

R (n) ψ( #y ) #y ≈ 1 L L l=0 ψ( #y [nL + l]) #y T [nL + l]. (8)
Finally, the convergence characteristics of the iterative inversion algorithm [START_REF] Mailand | Blind iq-imbalance compensation using iterative inversion for arbitrary direct conversion receivers[END_REF] are determined by the step size

µ (n) = η 1 + η R (n) f ( #y )g( #y ) (9)
It is defined in a way that prevents the estimation of the separation matrix W from crossing any discontinuities. This way, the convergence of the algorithm is assured (if 0 < η < 1) (convergence to a stationary point, which is not guaranteed to be a separation solution). For analyzing the quality of separation, we use the performance index (PI) [START_REF] Cichocki | Adaptive Blind Signal and Image Processing[END_REF]:

P I (n) = N i=1   N j=1 |G (n) ij | 2 max l {|G (n) il | 2 } -1   . . . + N j=1   N i=1 |G (n) ij | 2 max l {|G (n) lj | 2 } -1   (10)
whereas G = WH is the transfer function of the whole system. The performance index provides the quadradic distance between the transfer function and closest permutation of the unity matrix.

III. NON-LINEARITIES

In this section we propose three non-linearities ψ( #y ) that depend on the sources pdfs (like suggested by equation ( 6)), leading to a semi-blind approach (i.e. using more a-priori information). To obtain the semi-blind source separation we have to specify the pdf-dependent non-linearities suited to digital communication signals. Therefore we assume that the widespread M 2 quadrature amplitude modulation (QAM) is used, which corresponds to the use of M pulse amplitude modulation (PAM) in I-and Q-path. The discrete pdf of a PAM signal d i is described by a sum of shifted and scaled Dirac impulses :

p di (y i ) = 1 M M m=1 δ (y i -k(2m -M -1)) , (11)
with M being the number of different amplitudes and

k = M/2 M/2 n=1 2n -1 (12)
as the half distance between two adjacent Dirac impulses. With this definition, unit variance of the source signals is guaranteed. Thus, it is not necessary to rescale the separated signals. The investigations of ( 6) and [START_REF] Cruces | An iterative inversion approach to blind source separation[END_REF] show that the denominator of ψ(y i )

is zero for most of the values of y i . To avoid the non-defined expressions, the Dirac function is approximated by a Gaussian or a Cauchy distribution.

A. Gaussian approximation based non-linearity

The limit of a Gaussian distribution for the variance at zero is the Dirac function. For a = √ 2σ the pdf of the M -PAM source is approximated by

p di (y i ) ≈ 1 a √ π M m=1 exp - y i -k(2m -M -1) a 2 . ( 13
)
With this approximation, we obtain a non-linearity which is defined for any y i . Namely,

ψ G (y i ) = M m=1 2(yi-k(2m-M-1)) a 2 exp -(yi-k(2m-M-1)) 2 a 2 M m=1 exp -(yi-k(2m-M-1)) 2 a 2 . ( 14
)
Figure 2(a) shows the Gaussian non-linearity for different a. For decreasing a the slope of the non-linearity increases and vice versa. Steep non-linearities lead to convergence problems, on the other hand less steep non-linearities denote a relatively large a which is equivalent to a poorly approximated Dirac function. An optimized slope can be determined by red investigating the PI, depending on the parameter a and η, with simulations. The optimization result is shown in Figure 3.

B. Cauchy approximation based non-linearity

Alike the Gaussian distribution, the limit of the Cauchy distribution for a going to zero is the Dirac function, too. With the Cauchy distribution we get an approximated pdf as follows:

p di (y i ) ≈ 1 π M m=1 a a 2 + (y i -k(2m -M -1)) 2 . ( 15
)
The resulting approximation is used to calculate the Cauchy non-linearity:

ψ C (y i ) = - M m=1 2(yi-k(2m-M-1)) (a 2 +(yi-k(2m-M-1)) 2 ) 2 M m=1 1 a 2 +(yi-k(2m-M-1)) 2 . ( 16
)
The Cauchy non-linearity is depicted in Figure 2(b). As for to the Gaussian non-linearity, the slope is optimized by computer simulations and the resulting optimized a-η-ratio is shown in Figure 3.

C. Simplified Cauchy non-linearity

The two proposed non-linearities are precise but require a large computational effort. To alleviate this, we propose a sinusoidal approximation of the Cauchy non-linearity (indeed, a linear approximation of the Gaussian non-linearity would lead only to decorrelation and not statistical independence). The period of the sine wave is determined by the distance between two PAM symbols. A whole oscillation has the length of 2k with zeros at the positions of the PAM symbols. The amplitude is fitted to the Cauchy non-linearity with a = 0.1 which is given in Table I for different constellations. Due to the importance of the correct slope, a scaling factor a ′ = -A/10a corresponding to the other non-linearities is introduced. Thereby the amplitudes of the Cauchy and the simplified Cauchy non-linearity match for a = 0.1. For the outer areas, linear functions are employed. We finally obtain the simplified Cauchy non-linearity expressed by:

ψ SC (y i ) =          a ′ 2 (y i + k(M -0.5) + 2) y i < -k(M -0.5) a ′ sin π d y i otherwise a ′ 2 (y i -k(M -0.5) -2) y i > k(M -0.5) (17)
by scaling and shifting the linear functions. As for the previous non-linearities, the scaling a is optimized by simulations (Figure 3).

Non-linearities for modulations with discrete points in their constellation diagram can be constructed similarly. For modulations like CPM or FSK the modeling of the pdf will have to be derived via a different approach.

IV. SIMULATIONS

In this section we evaluate the bit error rate (BER) of a zero-IF receiver combined with the proposed separation algorithm and the convergence characteristics of the separation algorithms. The analysis is carried out by Matlab simulations. To classify the performance of the proposed non-linearities, we compare them with the EASI algorithm [START_REF] Valkama | Advanced methods for i/q imbalance compensation in communication receivers[END_REF], [START_REF] Cardoso | Equivariant adaptive source separation[END_REF] and three conventional non-linearities:

• Mutual Information (MI) non-linearity [START_REF] Amari | A new learning algorithm for blind source separation[END_REF];

ψ MI (y i ) = 3 4 y 11 i + 25 4 y 9 i -14 3 y 7 i -47 4 y 5 i + 29 4 y 3 i , • Cubic non-linearity [START_REF] Cruces | An iterative inversion approach to blind source separation[END_REF]; ψ CU (y i ) = y 3 i and • Hyperbolic non-linearity [START_REF] Girolami | An alternative perspective on adaptive independent component analysis algorithms[END_REF]; ψ H (y i ) = y i -tanh(y i ). We investigate the behavior of these algorithms under the effect of additive white Gaussian noise (AWGN) within baseband.

A Gray coded 16-QAM signal which consists of two 4-PAM signals is used for the simulations. The phase and gain error are assumed to be random variables which are uniformly distributed between ±5 • and ±7.5%, respectively (which is a rather severe IQ mismatch). The BER of each algorithm is the result of 50 Monte Carlo runs over these two random variables. Next, the step size η is 0.01 for all six II algorithms. Therewith, we get (Fig. 3) the values of the slope a, namely, 0.17 for the Cauchy and Gaussian non-linearity and 0.11 for the simplified Cauchy non-linearity. The step size of the EASI algorithm is fixed to 0.001 such that the BER of the EASI algorithm and the II algorithm are almost equal. The batch length L is 40.

Figure 4 shows the resulting BER for typical signal to noise ratios (SNR -E S /N 0 ). The lower bold line is the BER of 16-QAM receiver without IQ-imbalances. Reaching this BER means complete cancellation of the IQ-imbalances. The upper bold line is the BER which is obtained with an inaccurate receiver and without cancellation of the IQ-imbalances. The gap between the two curves becomes more significant when the SNR is high due to the fact that the IQ-imbalances are then more dominant. We obtain almost the same result for all seven algorithms as intended by the choice of the step size η. Only the iterative inversion algorithm with the MI non-linearity is sensitive to very low noise. In this case the BER is even worse than the uncancelled signal which is the result of converging to an incorrect separation matrix. Furthermore, the BER degrades with growing step size η. A second property of a BSS-algorithm is the convergence time. To analyze the convergence behavior we use the performance index from equation [START_REF] Cardoso | Equivariant adaptive source separation[END_REF]. The convergence time increases at low SNR and decreases with growing step size η. Hence, the step size can be used to get a tradeoff between BER behavior and convergence time.

The convergence behavior of the algorithm is shown in Figure 5, where we performed 50 Monte Carlo simulations for a SNR of 12dB, a phase error of ϕ I = 6 • , ϕ Q = 3 • and an amplitude error g I = 1.05, g Q = 0.98. The semi-blind algorithms outperforms the EASI algorithm and the other three non-linearities. Figure 5(a) illustrates the convergence of the II algorithm with the three pdf dependent non-linearities ψ C , ψ G , ψ SC . The initial PI is shown as a dashed line. The zone of convergence can hardly be seen because only around 5 iterations are needed to reach a stable state. Figure 5(b), in contrast, shows the convergence properties of the EASI algorithm and the pdf independent non-linearities ψ MI , ψ CU , ψ H . The convergence of the algorithm based on pdf dependent non-linearities is much better than with the non-dependent non-linearities. This is a major advantage of our approach. Indeed, a short convergence time is needed in burst-mode communications, where the IQ-imbalance has to be corrected from the first symbols. To reduce the computational complexity, the separation matrix may be computed only at the start of the burst, under the assumption of slow IQ-imbalance evolution with time.

V. CONCLUSIONS

In this paper, a new semi-blind source separation algorithm for the cancellation of IQ-imbalances in zero IF-receiver has been introduced. The algorithm is based on an existing iterative inversion blind source separation algorithm, but uses the knowledge of the modulation to significantly enhance its performance.

Compared to the original algorithm, the semi-blind approach performs similarly to the blind one in steady-state. The main advantage of the semi-blind approach is its convergence time, which is very short and makes it suitable in bursty communications. Moreover, similarly to the blind algorithm, no additional bandwidth is necessary which makes the system attractive from the spectral point of view.

This paper considers only IQ-imbalance cancellation for zero-IF receiver but the proposed method is also applicable to low-IF receiver or other receiver architectures based on separate IQ-down-conversion. It is also possible to extend the algorithm to convolutive imbalances caused by the equivalent low pass filter (baseband) transfer function in I-and Q-paths.

Fig. 2 .

 2 Fig. 2. Different approximations of pdf dependent non-linearities to separate 4-PAM signals with unity energy.

Fig. 3 .

 3 Fig. 3. Optimization result for the slope a as a function of step size η.

Fig. 4 .

 4 Fig. 4. BER comparison of receiver with pdf dependent (ψ G ,ψ C ,ψ SC ) and pdf independent II algorithms (ψ M I ,ψ CU ,ψ H ), with EASI algorithm, without separation (noSep) and without IQ-imbalances (noMix) .

Fig. 5 .

 5 Fig. 5. Comparison of the mean convergence behavior for a phase error ϕ I = 6 • , ϕ Q = 3 • and a amplitude error g I = 1.05, g Q = 0.98.

TABLE I MAXIMUM

 I AMPLITUDE A OF THE CAUCHY NON-LINEARITY FOR M-PAM

	M	4	8	16	64
	A 9.43 7.46 3.33 0.363

The work of M. Hesse is supported by the EU by a Marie-Curie Fellowship (EST-SIGNAL program : http://est-signal.i3s.unice.fr) under contract No MEST-CT-2005-021175.


Claudio Vergari
email: c.vergari@gmail.com

Isabelle Courtois

Eric Ebermeyer

Raphael Pietton

Houssam Bouloussa

Raphael Vialle

Wafa Skalli

Head to pelvis alignment of adolescent idiopathic scoliosis patients both in and out of brace

Keywords: AIS, Bracing, Brace effect, Sagittal balance, Compensation

Purpose To determine the short-term effect of bracing of adolescent idiopathic scoliotic (AIS) patients on the relationships between spinopelvic parameters related to balance, by comparing their in and out-of-brace geometry and versus healthy subjects. Methods Forty-two AIS patients (Cobb angle 29° ± 12°, ranging from 16° to 61°) with a prescription of orthotic treatment were included retrospectively and prospectively. They all underwent biplanar radiography and 3D reconstruction of the spine and pelvis before bracing as well as less than 9 months after bracing. Eighty-three age-matched healthy adolescents were also included as control group and underwent biplanar radiography and 3D reconstruction. Results Sacral slope was higher in AIS than healthy patients (p = 0.005). Bracing induced large changes of pelvic tilt (between -9° and 9°), although patients' sagittal spinopelvic alignment tended to remain within the normality corridors defined by the healthy patients. Patients had flatter backs compared to healthy subjects and bracing further reduced their spinal curves. The head tended to remain above the pelvis in-brace. Conclusion Analysis of sagittal alignment from head to pelvis showed that bracing further flattened the patients' backs and induced large compensating reorientations of the pelvis. Sagittal balance should be included in the planning and evaluation of brace treatment, since it could play a role in its outcome.

Graphical abstract

These slides can be retrieved under Electronic Supplementary Material.

Key points

[AIS; bracing; brace effect; sagittal balance; compensation] 1. Adolescent idiopathic scoliosis is a deformity of the trunk, which can induce alterations of patient's balance alignment 2. Effect of bracing on sagittal alignment is often limited to the spine, and it does not include the head and the pelvis.

3. The aim of this study was to characterize the patient's global alignment in and out of brace, from head to pelvis, using biplanar X-rays and 3D-reconstruction methods.

Introduction

Scoliosis is a complex deformity of the trunk in the three planes of space. Its most prominent characteristic is a deviation of the spinal curve in the coronal plane, which is usually quantified by the Cobb angle, together with a flattening of the sagittal spinal curve and vertebral rotations in the transverse plane. Currently, the attention is shifting from a 2D characterisation of the deformity through the Cobb angle, towards a global 3D analysis of the patient, including their alignment. This should ideally include the spinal chain of balance from the head to the "pelvic vertebra" and, in some cases, the lower limbs [START_REF] Dubousset | Definition of adolescent idiopathic scoliosispathogenesis of idiopathic scoliosis[END_REF].

Patients tend to compensate any alteration of the balance in order to keep the head upon the pelvis and a horizontal gaze: the compensation is obtained by altering the spinal alignment and, for congruity, pelvis orientation [START_REF] Huec | Sagittal balance and spinepelvis relation: a French speciality?[END_REF]. When spinal flexibility is reduced or pelvic reorientation does not suffice to keep the head upon the pelvis, such as in elderly patients, lower limbs are the last link of the compensatory chain that can help them maintain their balance [START_REF] Barrey | Compensatory mechanisms contributing to keep the sagittal balance of the spine[END_REF].

Analysis of spinopelvic parameters and their mutual relationships have been thoroughly characterized in healthy adolescents [START_REF] Vedantam | Comparison of standing sagittal spinal alignment in asymptomatic adolescents and adults[END_REF] and adults [START_REF] Huec | Normative values for the spine shape parameters using 3D standing analysis from a database of 268 asymptomatic Caucasian and Japanese subjects[END_REF][START_REF] Schwab | Sagittal plane considerations and the pelvis in the adult patient[END_REF][START_REF] Legaye | Sagittal plane alignment of the spine and gravity a radiological and clinical evaluation[END_REF][START_REF] Vaz | Sagittal morphology and equilibrium of pelvis and spine[END_REF][START_REF] Vialle | Radiographic Analysis of the Sagittal Alignment and Balance of the Spine in Asymptomatic Subjects[END_REF]. In particular, the interest of patient balance is recognized for spinal surgery [START_REF] Lafage | Spino-pelvic parameters after surgery can be predicted: a preliminary formula and validation of standing alignment[END_REF][START_REF] Roussouly | Pre-and postoperative sagittal balance in idiopathic scoliosis: a comparison over the ages of two cohorts of 132 adolescents and 52 adults[END_REF], which is the final recourse to correct progressive scoliotic patients for whom the non-operative treatment failed. Postsurgery malalignment can be a source of pain and disability, and it can lead to severe mechanical consequences such as proximal junctional failure or adjacent disc degeneration [START_REF] Alzakri | Global sagittal alignment and proximal junctional kyphosis in adolescent idiopathic scoliosis[END_REF][START_REF] Glassman | The impact of positive sagittal balance in adult spinal deformity[END_REF][START_REF] Lazennec | Sagittal alignment in lumbosacral fusion: relations between radiological parameters and pain[END_REF][START_REF] Kumar | Correlation between sagittal plane changes and adjacent segment degeneration following lumbar spine fusion[END_REF].

Adolescent idiopathic scoliosis (AIS) is the most common form of the pathology, with risk of progression especially during the pubertal growth spurt. The most common conservative treatment for progressive moderate to severe curves is bracing, which aims to stop or slow down the progression to avoid surgery. Just like the assessment of scoliosis severity, evaluation of brace effect on the spinal alignment of AIS patients is often only focused on Cobb angle correction. Thanks to relatively recent technical advancements in 3D imaging of scoliosis in clinical routine [START_REF] Dubousset | A new 2D and 3D imaging approach to musculoskeletal physiology and pathology with low-dose radiation and the standing position: the EOS system[END_REF], three-dimensional parameters started being included in the analysis of bracing [START_REF] Courvoisier | 3D analysis of brace treatment in idiopathic scoliosis[END_REF][START_REF] Lebel | Three dimensional analysis of brace biomechanical efficacy for patients with AIS[END_REF][START_REF] Clin | Comparison of the biomechanical 3D efficiency of different brace designs for the treatment of scoliosis using a finite element model[END_REF]. This shows that bracing can have limited effects on the 3D deformity: it can leave the thoracic kyphosis and axial rotations unchanged or even worsened in up to 80% of cases [START_REF] Courvoisier | 3D analysis of brace treatment in idiopathic scoliosis[END_REF]. This shows how the correction mechanisms of braces are still not completely understood. Several factors account for this: the complex shape of the deformity, the difficulty of planning and implementing an effective correction strategy, but also the compensating mechanisms that are usually not accounted for when planning a brace.

To our knowledge, no study analysed the effects of bracing on the relationships between spinopelvic parameters, rather than on the parameters themselves. The hypothesis of this work is that such analysis could clarify how bracing acts on the deformity and give an insight on the compensation mechanisms of young AIS patients.

Materials and methods

Subjects

Forty-two patients (27 girls and 15 boys, average age 13 ± 2, average Cobb angle 29° ± 12°, ranging from 16° to 61°) diagnosed with progressive AIS were included retrospectively and prospectively from 2 clinical centres. Patients were treated if they presented a Risser sign ≤ 2, Cobb angle ≥ 25° [START_REF] Negrini | SOSORT guidelines: orthopaedic and rehabilitation treatment of idiopathic scoliosis during growth[END_REF] or an increase of more than 5° in 6 months paired with a worsening of the clinical appearance with hump increase [START_REF] Lonstein | The prediction of curve progression in untreated idiopathic scoliosis during growth[END_REF]. Twenty-three patients had thoracic curves (apex in T1-T11), nine were thoracolumbar (apex in T12-L1) and ten were lumbar (apex in L2-L5). All patients were at their first prescription of treatment; 30 patients wore thoracic lumbar sacral orthosis (TLSO) and 12 night-time braces. All patients underwent biplanar radiographs (EOS system, EOS Imaging, Paris, France) in free-standing position at treatment decision (pre-brace) and in-brace. In-brace acquisition was performed on average 3 ± 2 months after pre-brace x-ray (ranging between same day and 9 months).

Eighty-three healthy adolescents and young adults (58 girls, 25 boys, mean age 14 ± 3 years, ranging between 9 and 21 years) were also included as control group. They all underwent biplanar radiography. The study was performed after approval of the ethical committee (CPP 6001 Ile de France V and local hospital committee).

Data processing and analysis

Validated methods were employed to reconstruct the 3D geometry of the spine and pelvis for each biplanar X-ray [START_REF] Humbert | 3D reconstruction of the spine from biplanar X-rays using parametric models based on transversal and longitudinal inferences[END_REF]. In addition, the odontoid process (OD) and the bicoxo-femoral axis were digitized in both radiographs (Fig. 1). An anatomical coordinate system was calculated for each patient, with its origin placed at the centre of the bicoxo-femoral axis (HA). The coronal plane was considered vertical and passing through the two acetabula, the sagittal plane was vertical and at 90° from the coronal plane, while the transverse plane was horizontal.

Clinical parameters were calculated in the patient coordinate system from the 3D reconstruction: pelvic incidence (PI), pelvic tilt (PT), sacral slope (SS), L1-S1 lumbar lordosis (LL), T1-T12 thoracic kyphosis (TK). In addition, the angle between the vertical and the line that connects OD to HA was measured in the sagittal and coronal planes (Fig. 1, [START_REF] Amabile | A new quasi-invariant parameter characterizing the postural alignment of young asymptomatic adults[END_REF]).

Vialle et al. and Schwab et al. Previously reported several significant relationships between pelvic and spinal parameters in healthy subjects [START_REF] Schwab | Sagittal plane considerations and the pelvis in the adult patient[END_REF][START_REF] Vialle | Radiographic Analysis of the Sagittal Alignment and Balance of the Spine in Asymptomatic Subjects[END_REF] (SS vs. PI, PT vs. PI, LL vs. PI, LL vs. a linear combination of PT, PI and TK). For each of these relationships, a confidence ellipse was built [START_REF] Coe | Fisher matrices and confidence ellipses: a quick-start guide and software[END_REF] using the data from the previous work to represent the distribution of the different parameters in the healthy population and compare it with the present data on healthy subjects and AIS patients.

Statistics

Non-parametric tests were selected because not all variables passed normality tests (Lilliefors' test). Differences between pre-brace and in-brace parameters were analysed with paired Wilcoxon signed rank test, while comparisons with healthy controls using Kruskal Wallis test and Tukey-Kramer post-hoc analysis. Correlations were quantified with Spearman's rank test. Slopes and intercepts of the linear regression were compared between groups using rank transform analysis of covariance (ANCOVA) [START_REF] Conover | Analysis of covariance using the rank transformation[END_REF]. Analyses were performed with Matlab 2016b (The Mathworks, Natick, MA, USA).

Results

Age and sex distributions were not significantly different between healthy and AIS subjects (p > 0.05). Table 1 reports the clinical parameters for the healthy subjects and the AIS patients before and in brace. Curve topology had no significant impact on brace effect (p > 0.05, Kruskal-Wallis test).

Pelvis

Figure 2 shows the relationship between PI and SS in each group, compared to the normal distribution published by Vialle et al. [START_REF] Vialle | Radiographic Analysis of the Sagittal Alignment and Balance of the Spine in Asymptomatic Subjects[END_REF]. It can be noted that the data for pre-brace and in-brace patients appears shifted upwards relative to the normal ellipse; indeed, SS was higher in AIS patients prebrace than healthy subjects (p = 0.005). PT and linear regressions did not differ between groups (p > 0.05).

Figure 3 shows the relationship between PI and PT in each group. Again, regression parameters did not statistically vary between groups. PT was lower in AIS patients than healthy subjects, but the difference was not significant, nor was brace effect significant (p = 0.37, Table 1). Nevertheless, PT change due to bracing ranged from -9° to 9°; in other words, while the average PT did not change between prebrace and in-brace, large PT variations took place. Further analysis showed that all patients (but one) who had a pelvic tilt lower than 5° increased their pelvic tilt when in-brace, while 64% of the patients who had pelvic tilt higher than 5° decreased it (Fig. 4).

Spinal alignment

Figure 5 shows the relationship between PI and LL; the intercept of the linear regression for healthy subjects was significantly higher than in the other groups (p < 0.001), while the slope was lower but not significantly. In other words, for a given SS, AIS patients tended to have flatter lordotic spines (because LL values are negative). Moreover, AIS patients further decreased their lordosis when in brace (p = 0.04, Table 1). The change in LL was significantly correlated to the change in PT (Spearman's rho = 0.48, p= 0.001). T1-T12 kyphosis was significantly higher in healthy patients that in pre-brace and in-brace (Table 1). Figure 6 shows a multilinear relationship between LL vs a combination of PT, PI and TK, as previously described by Vialle et al. [START_REF] Vialle | Radiographic Analysis of the Sagittal Alignment and Balance of the Spine in Asymptomatic Subjects[END_REF]. This relationship, which includes the thoracolumbar spine and pelvis, was similar between groups, even if LL and TK showed differences.

Odontoid process. Figure 7 reports OD-HA sagittal and coronal angle in the three groups. Both sagittal and coronal angles tended to increase from healthy to pre-brace and to in-brace, although differences between groups were not significant. Similarly to brace-induced changes in PT, changes in sagittal OD-HA were not statistically significant but they ranged between -6° and + 6°. Again, changes depended on the pre-brace angle (Fig. 4).

Fig. 3 Relationship between pelvic incidence and pelvic tilt in healthy subjects, pre-brace and in-brace scoliotic patients. Dashed lines represent linear regressions (equations and correlation coef-ficients are reported in each panel) while shaded areas represent the 95% confidence ellipse of healthy subjects from Vialle et al. [START_REF] Vialle | Radiographic Analysis of the Sagittal Alignment and Balance of the Spine in Asymptomatic Subjects[END_REF] Fig. 4 Difference between in-brace and pre-brace pelvic tilt and OD-HA sagittal angle relative to pre-brace values. All patients but one who had a pelvic tilt lower than 5° increased their pelvic tilt when in-brace, while 64% of the patients who had pelvic tilt higher than 5° decreased it. Similarly, all patients but one who had sagittal OD-HA lower than -3° increased their OD-HA in brace, while 61% of the patients who had OD-HA higher than -3° decreased it

Discussion

This work focused on the analysis of spinopelvic alignment in AIS patients at decision of conservative treatment and in-brace, compared to healthy subjects. Only the immediate effects of bracing were analysed, 3 months after the last out-of-brace biplanar radiography. While short-term effect cannot be used to determine brace efficacy for the longterm outcome, several studies suggest that the two are correlated, thus confirming the interest in analysing immediate brace effects [START_REF] Negrini | SOSORT guidelines: orthopaedic and rehabilitation treatment of idiopathic scoliosis during growth[END_REF][START_REF] Zaina | Correlation between in-brace radiographic correction and short time brace results[END_REF][START_REF] Clin | Correlation between immediate in-brace correction and biomechanical effectiveness of brace treatment in adolescent idiopathic scoliosis[END_REF]. The originality of this work lies in the analysis of the relationship between parameters, compared to those obtained in healthy patients, in addition to the range and distribution of each single parameter. This approach allows an insight into the strategy to maintain balance of AIS patients relative to healthy subjects, and how this strategy could be affected by bracing.

While the analysis was mainly focused on sagittal plane parameters, these were calculated from a 3D model. This allows correction of projection biases; for instance, if the patient was not perfectly aligned with the lateral plane of the radiographic device, their pelvic parameters would still be calculated in the anatomical sagittal plane rather than in the radiographic plane. The 3D geometry of the spine is also accounted for when calculating sagittal parameters, which Fig. 6 Relationship between L1-S1 lordosis, Pelvic tilt (PT), pelvic incidence (PI) and T1-T1 thoracic kyphosis (TK) in healthy subjects, pre-brace and in-brace scoliotic patients. Dashed lines represent lin-ear regressions (correlation coefficients and p-values are reported in each panel) while shaded areas represent the 95% confidence ellipse of healthy subjects from Vialle et al. [START_REF] Vialle | Radiographic Analysis of the Sagittal Alignment and Balance of the Spine in Asymptomatic Subjects[END_REF] are classically measured in 2D, since they can be measured using the 3D orientation of the vertebral endplates.

Results were compared with 95% confidence ellipses calculated on the data reported by Vialle et al. on a population of healthy subjects aged from 20 to 70 years old [START_REF] Vialle | Radiographic Analysis of the Sagittal Alignment and Balance of the Spine in Asymptomatic Subjects[END_REF]. Since the age range in the present study was limited to adolescents, it was necessary to include a population of healthy adolescents to determine if the previously published spinopelvic relationships remained valid. Figures 3,4, 5 and 6 show that this is the case; only PI appeared smaller in this study (45.3° ± 9.8° against 54.7 ° ± 10.6° in Vialle et al.). This could be expected, since PI tends to increase with age.

The advantage of comparing patient clinical parameters with 95% confidence ellipses based on healthy subjects, is that ellipses simultaneously represent the distribution of data in two dimensions, the slope of the relationship between parameters and the correlation coefficient of the underlying linear regression (represented by the transversal diameter of the ellipse). In other words, there is an immediate comparison with the linear regression between parameters of healthy patients and with the parameters' confidence intervals.

Spinal sagittal alignment was further flattened by bracing: kyphosis was lower in AIS than in healthy subjects, as expected, but it was further reduced by bracing. Lordosis was also reduced by bracing, thus worsening the characteristic scoliotic "flat back", confirming previous 3D analyses of brace effect [START_REF] Courvoisier | 3D analysis of brace treatment in idiopathic scoliosis[END_REF]. The general consensus is that bracing should aim at restoring a normal 3D geometry of the trunk, without neglecting the transverse and sagittal planes. These were included in the SOSORT guidelines for scoliosis treatment [START_REF] Coe | Fisher matrices and confidence ellipses: a quick-start guide and software[END_REF][START_REF] Conover | Analysis of covariance using the rank transformation[END_REF]. Nevertheless, brace is still often prescribed only using a coronal x-ray, thus neglecting the 3D configuration. Figure 6 shows a multilinear relationship representing a global spino-pelvic alignment, since it includes PT, PI, TK and LL. Even though TK and LL differences were present between groups (for instance, in TK and LL, Table 1), this graph remains within the confidence ellipse for the three groups, suggesting that global sagittal alignment remained balanced even after the loss of kyphosis and lordosis.

Bracing had variable effect on PT, with some patients increasing and other decreasing it (Fig. 4), and the change in PT was significantly correlated to the change in LL (p = 0.001). Thus, patients who flattened their LL in brace, compensated by increase their PT (pelvic retroversion). This is expected, but a non-negligible portion of patients (N = 10) actually decreased their PT while also decreasing LL. Figure 8 and Online Resource 1 show such a case; this patient had a high pre-brace PT (13°, 85th percentile), but her head was posterior relative to her acetabula (OD-HA = -5°). Her strategy to compensate the sagittal straightening of her spine was to pivot her whole trunk forward around her pelvic acetabula, resulting in a forward shift of the head, which actually brought the head close to the vertical of the acetabula (in-brace OD HA = 1.3°).

As shown by the description of this compensation mechanism, the inclusion of the head in the analysis of brace effect is an original aspect of this work. OD is just below the head's centre of mass [START_REF] Vital | Anatomical bases of the study of the constraints to which the cervical spine is subject in the sagittal plane a study of the center of gravity of the head[END_REF], and it has the advantage over the auditory meatuses of being easily recognizable in frontal and lateral radiographs. It is commonly accepted that all subjects tend to maintain the head upon the pelvis and a horizontal gaze, with minimal expenditure of energy [START_REF] Huec | Sagittal balance and spinepelvis relation: a French speciality?[END_REF][START_REF] Dubousset | Reflections of an orthopaedic surgeon on patient care and research into the condition of scoliosis[END_REF]. This is because the head has a non-negligible weight which is applied to the relatively small cervical spine; a small displacement of the head could induce higher muscular forces to counterbalance large moments on the cervical vertebrae and discs. Indeed, recent studies showed that the OD-HA angles are almost constant in asymptomatic subjects, whether young or elderly [START_REF] Amabile | Invariance of headpelvis alignment and compensatory mechanisms for asymptomatic adults older than 49 years[END_REF].

This result was confirmed in AIS patients, who showed the same variability of sagittal OD-HA (SD: 2.8°, Fig. 7) as healthy subjects in the present work (SD: 2.4°) and in the previous study from Amabile et al. (SD: 2°). Bracing did not affect variability (SD: 2.5), and the same applied for the coronal angle, which presented even lower variability (less than 2° in all groups). Nevertheless, AIS patients in-brace showed a small forward shift of the head relative to healthy subjects (-1.3° sagittal OD-HA against -2.5°, respectively), corresponding to a 1 cm displacement. This could be due to the reduced kyphosis which were compensated by a forward shift of the body inclination.

Lower limbs were not included in the analysis of sagittal balance, but it is generally accepted that they mostly intervene in compensation mechanisms of elderly subjects, who present less spinal and pelvic mobility, or adolescents with high-grade spondylolisthesis. A further limitation of this study is that the cohort was not sufficiently large to perform a sub-analysis concerning the different effects of night-time Fig. 7 OD-HA angle in the coronal and sagittal planes for the three groups. Differences between groups were not significant and TLSO braces, although this was beyond the scope of this work. Finally, patients were recruited from only two centres, and therefore results should be generalized with care. Type and quality of bracing depends on the orthotist's experience, and different centres could have different approaches to brace manufacturing: a larger multi-centric cohort could increase result variability.

Quantitative analysis of the sagittal plane is important in bracing, because its correction could play a role in treatment outcome. For instance, it was previously suggested that negative pre-brace pelvic tilt could be indicative of curve progression [START_REF] Guo | Pelvic tilt and trunk inclination: new predictive factors in curve progression during the Milwaukee bracing for adolescent idiopathic scoliosis[END_REF]. In the present study, brace-induced changes of PT and OD-HA depended on the out-of-brace values. Patients who had low out-of-brace PT tended to increase them proportionally, and vice-versa; the same principle applied to the position of the head (Fig. 4). In other words, patients tended to normalise their pelvic orientation and the position of the head above the pelvis. This observation gives an insight on the compensation strategy actuated by the patient, although this strategy remains a complex combination of neuromuscular activity, dynamic adaptation, proprioception and biomechanics, which cannot be summed up in simplified rules than will be true for all patients.

Conclusion

Bracing enabled a significant correction of Cobb angle, but analysis of sagittal alignment from head to pelvis showed that it further flattened the patients' backs. This resulted in large compensating reorientations of the pelvis to keep the congruity with spinal alignment and to keep maintain the head upon the pelvis. Sagittal balance should be included in the planning and evaluation of bracing treatment. Indeed, its systematic measurement could play a role in treatment outcome and, considering the present analysis, help improve brace action on the sagittal deformity.

Fig. 1

 1 Fig. 1 Biplanar radiographs of an adolescent idiopathic scoliotic patient (a) and 3D reconstruction of the pelvis, spine and C2 odontoid process (OD) in frontal (b), sagittal (c), top (d) and 3D views. Panel B reports the coronal projection of the OD-HA angle and panel C the

Table 1 Fig. 2

 12 Fig. 2 Relationship between pelvic incidence and sacral slope in healthy subjects, pre-brace and in-brace scoliotic patients. Dashed lines represent linear regressions (equations and correlation coef-

Fig. 5

 5 Fig. 5 Relationship between pelvic incidence and L1-L5 lumbar lordosis in healthy subjects, pre-brace and in-brace scoliotic patients. Dashed lines represent linear regressions (equations and correlation

Acknowledgements

The authors are grateful to the BiomecAM chair

program on subject-specific musculoskeletal modelling (with the Fig. 8 Biplanar radiographies of a patient before a and in brace b. Green lines show the interacetabular axis and the vertical line from its midpoint. This patient, who had a pelvic incidence of 37°, significantly flattened her lumbar lordosis in brace (from -52° to -39°) while reducing her pelvic tilt (from 13° to 7°). 3D reconstruction of the pelvis c-d) shows the forward shift of the sacral plate in brace d, i.e. the pelvic anteversion support of ParisTech and Yves Cotrel Foundations, Société Générale, Covea and Proteor) and to the DHU MAMUTH for funding. We are also grateful to Ms Fay Manning for her technical support.

Compliance with ethical standards

Conflict of interest Wafa Skalli holds patents related to the EOS system and associated 3D reconstruction methods, with no personal financial benefit (royalties rewarded for research and education). Raphael Vialle received consulting fees from EOS Imaging unrelated to this study.

Affiliations