Yvon Billon

Philippe Ganier

Régis Janvier

Francis Le Gouevec

Nadine Mézière

Jean-Noël Thibault

Keywords: amino acids, glucose, inflammation, pig, protein turnover, residual feed intake

INTRODUCTION

Residual feed intake (RFI) is a criterion used to select pigs for feed efficiency [START_REF] Gilbert | Genetic parameters for residual feed intake in growing pigs, with emphasis on genetic relationships with carcass and meat quality traits[END_REF]. Briefly, for a similar production level, a high-RFI animal eats more than predicted by its BW gain and body composition and thus uses nutrients less efficiently than a low-RFI animal. Compared with high-RFI pigs, low-RFI pigs have reduced heat production due to reduced daily feed intake (Young et al., 2011), physical Metabolic response to an inflammatory challenge in pigs divergently selected for residual feed intake 1 E. Merlot,* † 2 H. Gilbert, ‡ § and N. Le Floc'h,* † *INRA, UMR1348 PEGASE, F-35590 Saint-Gilles, France; †Agrocampus Ouest, UMR1348 PEGASE, F-35000 Rennes, France; ‡INRA, UMR444 Laboratoire de Génétique Cellulaire, F-31326 Castanet-Tolosan, France; §INRA, UMR1313 Génétique Animale et Biologie Intégrative, F-78352 Jouy-en-Josas, France ABSTRACT: Selection for residual feed intake (RFI), which is used to select animals for feed efficiency, also influences nutrient partitioning between growth and maintenance functions. This study was designed to investigate if selection for reduced RFI can alter the trade-off between growth and immunity and contributes to differences in metabolic responses to an inflammatory challenge. Piglets from 2 lines divergently selected on RFI (low: RFI -, n = 10, and high: RFI + , n = 11) were challenged at 55 d of age (on d 0) with complete Freund's adjuvant (CFA) to induce a noninfectious pneumonia. Plasma haptoglobin and nutrient concentrations (in fasted state and 2 h after feeding) were determined from d -1 to d 7, and tissue protein metabolism was determined on d 8. Haptoglobin concentrations were greater from d 1 to d 7 relative to d -1 (P < 0.01). Feed intake was less on d 1 than on the other days (P < 0.001), as was total AA plasma concentrations at fasted state (P < 0.05). Fasted concentrations of His (P = 0.06) and Trp (P = 0.05) tended to be less, those of Val were less (P < 0.05), and fed concentrations of Lys were increased (P < 0.05) on d 7 compared to d -1. Uremia was less on d 7 than on d -1 at fasted state (P < 0.05), whereas it did not vary at fed state (P > 0.1). Fasted glucose and insulin plasma concentrations were stable across days (P > 0.1). In the fed state and in only RFI + pigs, glucose concentration was greater on d 1 than on d 3, 5, and 7 (P < 0.05). Total AA, Gln, Ile, Leu, Pro (P < 0.05), and hydroxyproline (P = 0.07) were less in RFI -than RFI + pigs at fed state, whereas Ala and Gly were less in RFI -pigs at fasted and fed states (P < 0.05). Citrulline (P < 0.05) and Met (P < 0.01) concentrations were greater in RFI -than RFI + pigs in the fasted state, whereas Asp was greater in RFI - pigs in both fasted and fed states (P < 0.05). On d 8, liver and LM protein synthesis tended to be lower (P = 0.07 and 0.09, respectively) and liver calpain activity was greater (P = 0.07) in RFI -than RFI + pigs. Liver and LM proteasome did not differ between lines (P > 0.1). The metabolic differences between lines were not associated with differences in feed intake, ADG between d -1 and d 8, and haptoglobin concentration (P > 0.1). Thus, it seems that that, using different metabolic strategies, both lines coped similarly with the CFA challenge. Contrary to our hypothesis, this experiment showed, in young pigs, no advantage of RFI + animals in response to an inflammatory challenge.

activity [START_REF] Meunier-Salaun | Divergent selection for residual feed intake in group-housed growing pigs: Characteristics of physical and behavioural activity according to line and sex[END_REF], and basal metabolic rate [START_REF] Barea | Energy utilization in pigs selected for high and low residual feed intake[END_REF], indicating that selection for RFI influences the nutrient partitioning between production and maintenance functions. Although required for economic reasons, there are concerns that this altered trade-off could increase susceptibility to stressors and diseases because of an inadequate reallocation of nutrients to nonproductive functions when needed.

In particular, immune activation imposes decreased resource acquisition due to sickness-induced anorexia [START_REF] Pastorelli | Meta-analysis of feed intake and growth responses of growing pigs after a sanitary challenge[END_REF] and additional nutritional requirements to cover a greater protein synthesis in immune and hepatic compartments (Iseri and Klasing, 2013, in chickens) and energy expenditure for the fever and oxidative responses (Benhariz et al., 1997, in children). Whether highly efficient pigs display an impaired immunity and resistance to diseases has not been clearly established until now [START_REF] Clapperton | Associations of acute phase protein levels with growth performance and with selection for growth performance in Large White pigs[END_REF][START_REF] Doeschl-Wilson | Clinical and pathological responses of pigs from two genetically diverse commercial lines to porcine reproductive and respiratory syndrome virus infection[END_REF][START_REF] Dunkelberger | Response of pigs divergently selected for residual feed intake to experimental infection with the PRRS virus[END_REF].

This study was designed to investigate if energy and protein metabolism would be more affected by inflammation in low-RFI pigs than in high-RFI pigs. Piglets obtained from lines divergently selected for RFI were challenged with complete Freund's adjuvant (CFA), known to induce a noninfectious lung inflammation and substantial changes in AA metabolism [START_REF] Melchior | Chronic lung inflammation affects plasma amino acid concentrations in pigs[END_REF]. To assess the metabolic response to inflammation, plasma nutrient concentrations were measured during the 7 following days, and tissue protein metabolism was measured on the eighth day.

MATERIALS AND METHODS

The care and use of animals were performed in accordance with the guidelines of the French Ministry of Agriculture and Fisheries for animal research. The scientific and technical staffs obtained an agreement from the French veterinary services to conduct animal research. The protocol was approved by the local ethical committee (CREEA Bretagne, n°b-2009-NLF-02).

Animal and Experimental Design

Purebred French Large White female pigs were produced in the course of a divergent selection experiment on RFI in the INRA experimental facilities (GenESI, Le Magneraud and Rouillé, France). The selection program, started at INRA in 2000, was previously described [START_REF] Gilbert | Genetic parameters for residual feed intake in growing pigs, with emphasis on genetic relationships with carcass and meat quality traits[END_REF][START_REF] Naou | Metabolic changes and tissue responses to selection on residual feed intake in growing pigs[END_REF]. Briefly, daily feed intake (DFI) and ADG from 35 to 95 kg were recorded for male candidates for selection together with back fat thickness at 95 kg (UBT). An RFI selection index was computed as a linear combination of those traits to account for nutritional growth requirement as follows: RFI = DFI -(1.24 × ADG) -(31.9 × UBT), in which RFI, DFI, and ADG are measured in grams per day and UBT is measured in millimeters. In the present study, pigs from the seventh and eighth generations (G7 and G8) were considered. Sibs bred in the selection farm showed significant line differences for DFI (the contrasts between estimated breeding values in the low RFI [RFI -] and high RFI [RFI + ] pigs were -242 and -266 g/d in G7 and G8, respectively), feed conversion ratio (-0.28 and -0.31 in G7 and G8, respectively), and RFI (-141 and -153 g/d in G7 and G8, respectively, i.e., -3.28 and -3.56 genetic standard deviations of the trait). Additionally, significant line differences were found for lean meat content of the carcass (+2.9 and +3.1% in G7 and G8, respectively).

The trial was performed in 2 successive replicates 3 mo apart using a total of 21 pigs. At weaning (28 d of age), female piglets from the high-RFI (n = 6 and 5 in replicates 1 and 2, respectively) and low-RFI (n = 5 per replicate) lines were transferred from the selection herd to the experimental facilities of INRA PEGASE (Saint-Gilles, France). They were kept in individual cages (1.2 × 0.7 m stainless-steel cages, providing visual contact with each other) in a room maintained at 26°C. Piglets from the RFI -(more efficient line) and RFI + (less efficient line) groups were chosen so that several litters per line were represented (7 RFI -and 8 RFI + sows) and their BW (8.7 ± 0.9 and 9.0 ± 1.1 kg, respectively, and statistically not different) was representative of the average weaning BW in their contemporary group.

Two weeks after weaning (10 kg BW), pigs were fasted overnight, and a jugular catheter was inserted under general anesthesia, using a premedication with 15 mg/kg of ketamine injected intramuscularly (Imalgène 1000, Merial, Lyon, France), followed by inhalation of sevofluorane (Sevoflurane, Baxter, Maurepas, France) using a facemask. After surgery, antibiotics (0.5 mg/mL ampicillin; Coophavet, Ancenis, France) were administrated intramuscularly. The catheters were flushed daily with 10 mL of sterile saline solution containing 2.5 mL of heparin (5,000 U/mL). Twelve days after (at 55 ± 2 d of age and 14.90 ± 0.02 kg BW), pigs were fasted overnight, and a lung inflammation was induced according to the procedure described by Le [START_REF] Floc'h | Dietary tryptophan helps to preserve tryptophan homeostasis in pigs suffering from lung inflammation[END_REF] modified as follows. An emulsion composed of 3 mL of CFA and 7 mL of saline was intravenously injected between 0800 and 0900 h on 2 consecutive days (approximately 2/3 on the first day [d 0] and 1/3 on the second day [d 1]) to avoid mortality. As described by [START_REF] Edwards | Complete Freund's adjuvant-induced pneumonia in swine-A model of interstitial lung-disease[END_REF], CFA injection in the jugular vein induced interstitial pneumonia. The experimental period started the day before the injection of CFA (d -1) and ended on d 8.

Pigs were fed a standard starter diet for the first 10 d after weaning and then a weaner diet until the end of the trial (Table 1). During the experimental period, pigs had free access to water. They were fed twice a day (at 0900 and 1500 h), except on d 0, when they were fed only at 1500 h, and individual feed consumption was recorded daily. The feed was removed from the trough at 1700 h the day before each blood sampling to ensure that blood was sampled after an overnight fasting. Rectal temperature was recorded with digital electronic thermometers (Vetarvor, Ingwiller, France) at 0900 and 1600 h from d -1 to d 3. Pigs were weighed weekly.

Blood and Tissue Sampling

Blood (5 mL) was collected before (0730 h) and 2 h after the morning meal on the day before (d -1) and 1, 3, 5, and 7 d after the challenge (d 1 to 7). Blood was collected into heparin (100 units per tube, Sanofi-Aventis, France) and dry tubes; plasma and sera were centrifuged (4°C, 2,500 × g, 15 min), aliquoted, and kept at -20°C until analysis.

All pigs were killed 8 d after the challenge. Before slaughter and 2 h after the morning meal, each pig was injected with a flooding dose of valine (20% 15 N valine and 80% of unlabeled valine) to measure tissue protein synthesis rate [START_REF] Jamin | Accelerated growth rate induced by neonatal high-protein milk formula is not supported by increased tissue protein synthesis in low-birth-weight piglets[END_REF]. Blood (2 mL) was collected in heparinized ice-cooled tubes just before and 7 and 14 min after the injection. Blood was centrifuged (4°C, 2,500 x g, 15 min), and plasma was stored at -20°C until analysis. Fifteen minutes after the valine injection, piglets were euthanized with a lethal dose of T61 injected intravenously (Intervet, Beaucouzé, France) and exsanguinated. Lungs were inspected to observe their general aspects, texture, and lesions. Samples of liver and LM were immediately collected, frozen in liquid nitrogen, and stored at -80°C.

Plasma Haptoglobin and Nutrients

Plasma haptoglobin was determined in samples collected at fasted state by a colorimetric assay (phase haptoglobin assay T801, Tridelta Development Ltd., Maynooth, Ireland). Plasma glucose, urea, insulin, and AA concentrations were determined on blood samples collected every 2 d, before and 2 h after the morning meal. Plasma glucose and urea were determined in duplicate using commercial kits (Biomerieux, Craponne, France) and a Konelab 20i device (Thermo Fisher Scientific, Courtaboeuf, France). Plasma concentrations of insulin were measured using a RIA kit (INSULIN-CT, CisBio Bioassays, Codolet, France). The intra-assay CV were below 5%.

Plasma AA concentrations were determined using an ultra HPLC system (Waters Acquity Ultra Performance LC system, Waters, Guyancourt, France) coupled to an Acquity tunable UV detector and a mass detector (SQD detector) to identify the few coeluting chromatographic peaks. The column was a MassTrak AAA column (2.1 × 150 mm). Amino acid derivatization was performed using an AccQ•Tag Ultra derivatization (MassTrak AAA Waters, Milford, MA). The Empower 2chromatography software (Waters corporation, Milford, MA, USA) was used for instrument control and data acquisition.

Tissue Protein Metabolism

Activities of the proteasome, the key enzyme of the ubiquitin-dependent proteolysis, and of calpains (µ-calpain and m-calpain) involved in Ca 2+ -dependent proteolysis were assayed in the LM and the liver as described by [START_REF] Naou | Metabolic changes and tissue responses to selection on residual feed intake in growing pigs[END_REF].

Tissue protein synthesis rate was determined in liver and LM. Plasma free valine enrichment (S A ) was 1 Premix provided the following amount of vitamins and minerals per kilogram of diets (as-fed basis): the starter diet = vitamin A, 15,000 IU; vitamin D3, 3000 IU; vitamin E, 40 IU; iron sulfate, 104 mg; copper sulfate, 20 mg; zinc oxide, 99 mg; manganese oxide, 40 mg; carbonate cobalt, 2 mg; sodium selenium, 0.3 mg; and calcium iodate, 1 mg; the weaner diet = vitamin A, 10,000 IU; vitamin D 3 , 2,000 IU; vitamin E, 20 mg; iron sulfate,104 mg; copper sulfate, 20 mg; zinc oxide, 99 mg; manganese oxide, 40 mg; carbonate cobalt, 1 mg; Se as sodium selenium, 0.3 mg; and calcium iodate, 0.6 mg.

2 Myo-inositol-hexakisphosphate-phosphohydrolase3.1.3.8, Natuphos (BASF, Limburgerhof, Germany).

determined by gas chromatography coupled with a mass spectrometer (Agilent Technology, Santa Clara, CA) after derivatization with N-tert-butyldimethylsilyl N-methyl-trifluoroacetamide. Protein-bound valine enrichment (S B ) was measured by gas chromatography coupled to an isotopic ratio mass spectrometer (Isochrom, Fisons Instruments, Manchester, UK) after derivatization with ethyl chloroformate. The fractional protein synthesis rate (KS, %/d), corresponding to the percentage of proteins newly synthesized per day, was calculated as follows: KS = (S B × 100)/(S A × t), where S B represents plasma enrichment, S A is the tissue protein enrichment, and t is the time elapsed between the injection of valine and animal bleeding.

Statistical Analysis

The experimental unit was the piglet. Growth performance and tissue metabolic activities were analyzed by ANOVA using the MIXED procedure of SAS (SAS Inst. Inc., Cary, NC), with line (RFI + or RFI -) and replicate (first or second replicate) as fixed effects. Plasma metabolite concentrations, BW, and feed intake were analyzed as time-repeated measures with the MIXED procedure (SAS) using the effects of day (d -1, 1, 3, 5, and 7), replicate, and line as main effects, as well as the corresponding interactions. The adequate covariance structure was selected as that minimizing Akaike's information criterion and Schwarz's Bayesian criterion for each model. Fasted and fed plasma nutrient concentrations were analyzed separately. When line, day, or interaction effects were significant (P < 0.05), differences between RFI + and RFI-or between days were tested by a Bonferroni test and considered as significant for P < 0.05. However, values with 0.1 < P < 0.05 were considered as trends and are discussed.

RESULTS

Feed Intake and Growth Performance

Feed consumption was influenced by the day effect (P < 0.001). It was lower on d 0 relative to all other days (P < 0.001) and greater on d 7 than on d -1, 1, 2, and 4 (P < 0.01; Fig. 1A). Both lines of pigs had similar BW on d -1 (15.0 ± 0.2 vs. 14.8 ± 0.02 kg), ADFI (697 and ± 25 g/d for RFI -pigs and 665 ± 24 g/d for RFI + pigs), ADG (455 ± 34 g/d for RFI-pigs and 470 ± 33 g/d for RFI + pigs), and feed consumption from d -1 to d 8 (P > 0.1). There was no line × day interaction for those variables (P > 0.1). At slaughter, the relative weights of liver (30 ± 2 g/kg BW) and lung (17 ± 3 g/kg BW) did not differ between the 2 lines (P > 0.1).

Indicators of Inflammation

Immediately after the first administration of CFA, all pigs became lethargic and exhibited an increased respiration rate as previously described [START_REF] Melchior | Chronic lung inflammation affects plasma amino acid concentrations in pigs[END_REF][START_REF] Melchior | Is tryptophan catabolism increased under indoleamine 2,3 dioxygenase activity during chronic lung inflammation in pigs?[END_REF][START_REF] Floc'h | Dietary tryptophan helps to preserve tryptophan homeostasis in pigs suffering from lung inflammation[END_REF]. Pigs developed a febrile response (40.7°C and 40.1°C ± 0.1°C at 1600 h on d 0 and 1, respectively, vs. 39.5°C ± 0.1°C on d -1; P < 0.01). After 2 d, the clinical signs and rectal temperature decreased (39.4°C and39.5°C ± 0.1°C on d 2 and 3 at 1600 h, respectively), and piglets seemed to recover.

Plasma haptoglobin concentration was greater from d 1 to d 7 than on d -1 (P < 0.01; Fig. 1B), and the 2 lines did not differ (P > 0.1). At slaughter, on d 8, lungs of piglets presented clear signs of inflammation characterized by the presence of small inflammatory foci in the parenchyma, as already reported [START_REF] Melchior | Chronic lung inflammation affects plasma amino acid concentrations in pigs[END_REF].

Plasma Glucose, Insulin, and Urea

Plasma variables were measured every 2 d from d -1 to d 7. There was no effect of day (P > 0.1) on concentrations of glucose measured in fasted conditions and 2 h after feeding (Fig. 1C), insulin (21 ± 9 and 57 ± 30 µIU/mL before and 2 h after feeding, respectively), and glucose:insulin ratio (52 ± 15 and 25 ± 16 µmol/ mIU before and 2 h after feeding, respectively). Plasma uremia was influenced by day in fasted state (P < 0.05), with lower concentrations on d 7 than on d 1 (P < 0.05), whereas it did not vary in the fed state (Fig. 1D).

The 2 lines did not differ for fasted glucose, fasted and postprandial insulin, and urea concentrations (P > 0.1). There was a day × line interaction for postprandial glucose concentration (P < 0.05), which did not differ across days in RFI -pigs but was greater on d 1 than on d 3, 5, and 7 in RFI + pigs (P < 0.05).

Plasma AA Concentrations

Total AA concentration was lower on d 1 relative to the other days in the fasted state (P < 0.05) and to d 3 and 7 in the fed state (P < 0.05; Table 2). Among individual AA, concentrations of Ala, Asp, Gln, Glu, Gly, and Leu displayed a pattern comparable to total AA. The examples of Gln, Gly, and Asp are provided in Fig. 2A to 2C. The temporal patterns for Asn, Ile, hydroxyproline (Hypro), Pro, and Ser were also quite similar to those for total AA. For Asn, the concentration measured on d 1 was lower than that on d 5 in the fasted state (P < 0.05). For Ile and Pro, d 1 concentrations were lower than those on d 3 and 5 in the fasted state (P < 0.01) and d 3 and 7 in the fed state (Ile: P = 0.07 and P < 0.01, respectively; Pro: P < 0.01). Hydroxyproline concentration was stable across days in the fasted state (P > 0.1) but lower on d 1 than on d 3 and 7 in the fed state (P < 0.05). Serine concentrations were lower on d 1 than on d 5 in the fasted state (P < 0.5) but stable across days in the fed state (P > 0.1). On d 7, Ala (P < 0.01) and Glu (P < 0.01) concentrations in the fed state were greater than on d -1 (P < 0.05), whereas for other AA in Table 2, concentrations in fed and fasted states were comparable to the d -1 prechallenge concentrations (P > 0.1).

Some AA concentrations varied differently from total AA across days (Table 3). For His, Trp, and Val, the day effect was significant (Val, P < 0.01; Fig. 2D) or tended to be significant (His and Trp, P < 0.1; Table 3) in the fasted state but not in the fed state (P > 0.1). Overall, the concentrations decreased across days and were lower on d 7 than on d -1 (P < 0.05 for Trp and Val, P = 0.06 for His). In contrast, in the fed state, Lys concentrations were greater on d 7 than on d -1 (P < 0.05; Fig. 2E), and Thr tended to be influenced by the day effect in the same direction (P = 0.06), whereas their fasted state concentrations did not vary across days (P > 0.1).

Plasma total AA concentrations did not differ between RFI -and RFI + in the fasted state (P > 0.1), whereas they were lower in RFI -pigs than in RFI + pigs in the fed state regardless of the day (P < 0.05; 1 Least squares means calculated from the concentrations (nmol/mL) measured every second day from d -1 to d 7 after 1 night fasting (fasted state) and 2 h after the daily meal (fed state).

2 For the listed AA, the temporal patterns showed decreased concentrations on d 1 in both fasted and fed states, with significantly reduced concentrations on d 1 than on d -1, 5, or 7, except for Asn, hydroxyproline (Hypro), and Ser. Serine and Hypro concentrations were decreased on d 1 in only fasted and fed states, respectively. Asparagine differences between days were not significant, although visually the temporal pattern was close to those of the other AA in this table.

Table 2). The RFI -pigs displayed lower concentrations than RFI + pigs in both fasted and fed states for Ala and Gly (P < 0.05, Fig. 2B) and in only the fed state for Gln (Fig. 2A), Pro, Ile, Leu (P < 0.05), and Hypro (P = 0.07; Table 2). In contrast, concentrations were greater in RFI -than RFI + pigs in both fasted and fed states for Asp and Glu (fasted state: P < 0.05 for both AA, fed state: P < 0.05 and P = 0.08, respectively; Table 2 and Fig. 2C) and in only the fasted state for citrulline (Cit) and Met (P < 0.05 and 0.01 respec-tively; Table 3 and Fig. 2F). Other AA concentrations did not differ among lines (P > 0.1).

The day × line interaction was significant for postprandial concentrations of several AA (Ile, Leu, Cit, Met; P < 0.05). The concentrations of Ile and Leu varied across days for RFI -but not RFI + pigs. In RFI - pigs, concentrations increased across days: Ile concentration was greater on d 7 than on d -1 and 1 (P < 0.05; Fig. 2F), and those of Leu were greater on d 3 and 7 than on d 1 (P < 0.05 and P = 0.07).

Tissue Protein Metabolism

Liver and LM protein synthesis tended to be greater (P = 0.07 and 0.09, respectively; Table 4) and liver calpain activity tended to be lower (P = 0.07) in RFI - pigs than in RFI + pigs. Liver and LM proteasome activities did not differ between lines (P > 0.1).

DISCUSSION

A CFA administration was used to generate granulomatous pulmonary lesions and mimic the perturbations resulting from an infection by living respiratory pathogens [START_REF] Edwards | Complete Freund's adjuvant-induced pneumonia in swine-A model of interstitial lung-disease[END_REF]. In pigs, this model is known to induce, within the first 2 d, a febrile response and a reduction in feed intake [START_REF] Melchior | Chronic lung inflammation affects plasma amino acid concentrations in pigs[END_REF], followed by an increase of the plasma concentration of acute phase proteins such as haptoglobin, pig major acute phase protein, and C-reactive protein [START_REF] Melchior | Chronic lung inflammation affects plasma amino acid concentrations in pigs[END_REF][START_REF] Kampman-Van De Hoek | Induced lung inflammation and dietary protein supply affect nitrogen retention and amino acid metabolism in growing pigs[END_REF]. Finally, within 1 wk, a chronic inflammatory response develops, characterized by a consistently elevated haptoglobin concentration and long-term alterations in blood AA concentrations and metabolism [START_REF] Melchior | Chronic lung inflammation affects plasma amino acid concentrations in pigs[END_REF][START_REF] Kampman-Van De Hoek | Induced lung inflammation and dietary protein supply affect nitrogen retention and amino acid metabolism in growing pigs[END_REF]. In the present study, the development of the inflammatory response was confirmed by the febrile response on d 0 and 1, the transient drop in feed intake on d 0, alterations in blood AA concentrations on d 1 that lasted until d 7 for some AA, and a greater haptoglobin concentration from the day after CFA injection until the end of the experimental period. The high relative weight of the lungs on d 8 is also a characteristic of this inflammatory model, as reported in a previous study using CFA in piglets [START_REF] Melchior | Is tryptophan catabolism increased under indoleamine 2,3 dioxygenase activity during chronic lung inflammation in pigs?[END_REF].

Transient Alteration of Plasma Glucose Metabolism in RFI+ Pigs

Inflammatory states are associated with alterations of glucose metabolism. Inflammatory cytokines such as tumor necrosis factor-α and the macrophage migration inhibitory factor increase glucose uptake and glycolysis in adipose [START_REF] Porter | Effects of TNF-α on glucose metabolism and lipolysis in adipose tissue and isolated fat-cell preparations[END_REF], muscle [START_REF] Zentella | Cachectin/TNFmediated lactate production in cultured myocytes is linked to activation of a futile substrate cycle[END_REF], and immune [START_REF] Dietl | Lactic acid and acidification inhibit TNF secretion and glycolysis of Human monocytes[END_REF] cells in vitro and stimulate gluconeogenesis in hepatocytes [START_REF] Blumberg | Tumor-necrosis-factor-alpha stimulates gluconeogenesis from alanine in-vivo[END_REF]. Accordingly, in growing pigs injected with bacterial endotoxin, an increased glucose uptake by muscle and viscera is observed, with a concomitant increase in hepatic gluconeogenesis [START_REF] Bruins | Aspects of organ protein, amino acid and glucose metabolism in a porcine model of hypermetabolic sepsis[END_REF] and active transport of glucose at the ileal level [START_REF] Rakhshandeh | Effect of immune system stimulation and divergent selection for residual feed intake on digestive capacity of the small intestine in growing pigs[END_REF]. In the same way, in growing pigs, lower pre-and postprandial glucose concentrations can be observed during a 1 Least squares means calculated from the concentrations measured every second day from d -1 to d 7 after 1 night fasting (fasted state) and 2 h after the daily meal (fed state).

2 Ascending arrows indicate increasing (or tending to increase) concentrations between d -1 and d 7, and descending arrows indicate decreasing (or tending to decrease) concentrations between d -1 and d 7.

3 Cit = citrulline, Orn =ornithine. respiratory infectious challenge compared with those of healthy control pigs [START_REF] Floc'h | Effect of feed restriction on performance and postprandial nutrient metabolism in pigs co-infected with Mycoplasma hyopneumoniae and swine influenza virus[END_REF], and a dramatic drop of glucose concentration occurs during endotoxic shock [START_REF] Leininger | Physiological response to acute endotoxemia in swine: Effect of genotype on energy metabolites and leptin[END_REF]. In the present experiment, fasted glucose concentrations were unchanged throughout the experimental period, showing that fasted glucose homeostasis was not altered. However, the postprandial glucose level, assumed to reflect the fate of dietary glucose, was transiently greater in RFI + pigs on d 1, although the feed intakes of RFI + and RFI -pigs were similar. This greater postprandial glucose concentration in RFI + pigs compared with RFI -pigs might reflect a transiently decreased uptake of dietary glucose for reconstitution of the glycogen pool in both the liver and the muscle even though the glucose:insulin concentration ratio did not vary and an alteration in insulin sensitivity cannot be attested. In that way, greater glycogen content was reported in the muscle and the liver of RFI -healthy pigs than that of RFI + pigs slaughtered at market weight [START_REF] Lefaucheur | Muscle characteristics and meat quality traits are affected by divergent selection on residual feed intake in pigs[END_REF]. Conversely, [START_REF] Montagne | Difference in short-term responses to a highfiber diet in pigs divergently selected for residual feed intake[END_REF] reported that the increase in glucose concentration after meal ingestion was more pronounced in the RFI -line than in the RFI + line, suggesting that the effect on glucose metabolism discussed in the present experiment was specifically related to different responses of the lines to inflammation.

A Moderate Influence of Inflammation on Whole Body Protein Metabolism

During severe inflammation, the decrease in protein anabolism [START_REF] Jahoor | Chronic protein undernutrition and an acute inflammatory stimulus elicit different protein kinetic responses in plasma but not in muscle of piglets[END_REF][START_REF] Daiwen | Influences of lipopolysaccharide-induced immune challenge on performance and whole-body protein turnover in weanling pigs[END_REF] together with the increase in protein catabolism [START_REF] Bruins | Aspects of organ protein, amino acid and glucose metabolism in a porcine model of hypermetabolic sepsis[END_REF] of skeletal muscle results in an enhancement of the release of AA by the muscle into the blood. However, if this release is compensated by an immediate catabolism and utilization for the synthesis of immune proteins, plasma AA concentrations can remain unchanged. Plasma Hypro and urea can be used as markers to evaluate muscle protein and AA catabolism, respectively. Hydroxyproline is formed by the hydroxylation of Pro in proteins. Because Pro and Hypro represent approximately one-third of AA in collagen and Hypro cannot be recycled into Pro for protein synthesis [START_REF] Phang | Proline metabolism and microenvironmental stress[END_REF], its blood concentration is assumed to reflect muscle collagen catabolism. Plasma urea is produced by catabolism of AA, coming mainly from body protein breakdown in the fasted state, to which is added the degradation of AA from dietary proteins by the liver in the fed state.

In the present study, muscle protein degradation was probably very moderate, as indicated by the lack of plasma urea and Hypro increases in the days after CFA. Furthermore, animals had a positive BW gain, showing that the CFA challenge did not stop muscle protein accretion. However, because Lys is used mainly for protein synthesis, the regular increase in the concentration of Lys in the fed state from d -1 to d 7 might indicate a reduction of N body retention, as reported by [START_REF] Kampman-Van De Hoek | Induced lung inflammation and dietary protein supply affect nitrogen retention and amino acid metabolism in growing pigs[END_REF]. A lower uremia was also observed in a previous study using piglets coinfected by a mycoplasma and influenza virus [START_REF] Floc'h | Effect of feed restriction on performance and postprandial nutrient metabolism in pigs co-infected with Mycoplasma hyopneumoniae and swine influenza virus[END_REF]. We hypothesized that AA released by protein catabolism might be recycled into new proteins more effectively by the organism during the inflammatory challenge for acute phase protein synthesis, for instance, thus preserving AA from catabolism. Alternatively, we cannot exclude that the reduced feed intake caused by inflammation may have limited urea synthesis, which is mainly influenced by protein intake [START_REF] Zervas | Effects of dietary protein and oathull fiber on nitrogen excretion patterns and postprandial plasma urea profiles in grower pigs[END_REF].

A Greater Muscle Protein Catabolism in RFI+ than RFI-Pigs

In the present experiment, LM protein turnover was investigated after 8 d of CFA-induced inflammation. The tendency for greater protein synthesis and lower protein degradation (calpain activity) in the muscle of RFI -pigs suggested greater muscle protein accretion in RFI -pigs. This was also in agreement with their tendency for lower Hypro concentrations across the experiment, at least in the fed state. This did not result in a greater growth in RFI -pigs, probably because 7 d is too short a period to evaluate a global growth response. These results might reflect either a constitutive difference in muscle protein metabolism between the 2 lines or a difference appearing in only the inflammatory state. The first hypothesis is in agreement with results from a different selection experiment, where unchallenged RFI -gilts displayed reduced protein degradation in LM compared with RFI + gilts, although protein synthesis was unaffected [START_REF] Cruzen | Evidence of decreased muscle protein turnover in gilts selected for low residual feed intake[END_REF]. However, young pigs from this selection scheme did not differ for LM protein synthesis and activity of proteolytic enzymes when measured in healthy conditions [START_REF] Naou | Metabolic changes and tissue responses to selection on residual feed intake in growing pigs[END_REF]. Thus, the observation of differences in protein turnover in the muscle of RFI -and RFI + pigs in the present study 8 d after CFA administration supports the hypothesis that selection for low RFI favored the preservation of muscular protein accretion specifically during inflammation. This was also suggested in a different selection experiment using a porcine reproductive and respiratory syndrome virus infection challenge, where the slowing down of growth measured during a 28-d period following infection was less in RFI -pigs than in RFI + piglets [START_REF] Dunkelberger | Response of pigs divergently selected for residual feed intake to experimental infection with the PRRS virus[END_REF].

Alteration of Plasma AA Concentrations by the CFA Challenge

Both RFI -and RFI + pigs displayed a drop in the plasma concentrations of total AA on d 1 in both the fasted and fed states, probably because of the transient anorexia caused by CFA injection on d 0, generating a lower availability of those AA on d 1 in the fasted state and thus rapid uptake for immediate use when supplied by dietary proteins in the postprandial state. Most nonessential AA followed this pattern (Ala, Asn, Asp, Gln, Glu, Gly, Pro, Ser). It cannot be excluded for these AA that the effect of anorexia was combined with an increased specific use for the acute inflammatory response. For example, in a previous experiment CFA-treated piglets displayed lower concentrations of Gln, Gly, and Pro compared with pair-fed control pigs during the first 48 hours after CFA in both the fed and fasted states, and Ala, Asn, and Ser were decreased in the fed state [START_REF] Melchior | Chronic lung inflammation affects plasma amino acid concentrations in pigs[END_REF]. This indicated that anorexia caused by CFA injection cannot be the only explanation for their decreased concentrations, which were therefore supposed to reflect an increased utilization of those AA for immune-specific purposes. Alanine, Asp, Gln, Gly, and Ser plasma concentrations were also reported to be lower after bacterial challenges [START_REF] Yoo | Glutamine supplementation maintains intramuscular glutamine concentrations and normalizes lymphocyte function in infected early weaned pigs[END_REF][START_REF] Jonasson | Blood concentrations of amino acids, glucose and lactate during experimental swine dysentery[END_REF].

Moreover, on d 7, some AA were not back to the basal concentrations observed on d -1 in both the fasted (His, Trp, Val) and fed (Ala, Glu, and, in the RFI -line, Ile and Leu) states, indicating that the CFA challenge induced long-lasting alterations in AA metabolism. Among them, His, Trp, and Val displayed (or tended to display) a continuous decline in their fasted concentrations over time. The drop in Trp concentration was to a lesser extent and was observed only in the fasted state, in contrast to the decrease previously observed [START_REF] Melchior | Chronic lung inflammation affects plasma amino acid concentrations in pigs[END_REF][START_REF] Floc'h | Dietary tryptophan helps to preserve tryptophan homeostasis in pigs suffering from lung inflammation[END_REF]. The differences between these studies might be due to the greater Trp content in the diet used in the present experiment (0.35% vs. 0.29%, DM basis) since the response in plasma Trp to inflammation depends on the quantity of dietary Trp [START_REF] Floc'h | Dietary tryptophan helps to preserve tryptophan homeostasis in pigs suffering from lung inflammation[END_REF]. Other infectious challenges, like Escherichia coli or influenza mycoplasma coinfection, were reported to decrease Trp, His, and Val plasma concentrations in the fasted state [START_REF] Yoo | Glutamine supplementation maintains intramuscular glutamine concentrations and normalizes lymphocyte function in infected early weaned pigs[END_REF] or only His [START_REF] Floc'h | Effect of feed restriction on performance and postprandial nutrient metabolism in pigs co-infected with Mycoplasma hyopneumoniae and swine influenza virus[END_REF]. Because His, Trp, and Val are glucogenic, as well as ketogenic in the case of Trp, this may reflect an increase of their use by the liver for energetic purpose. Besides its utilization as a precursor of energy, Trp has been reported to be specifically degraded into kynurenine during a CFA challenge [START_REF] Melchior | Is tryptophan catabolism increased under indoleamine 2,3 dioxygenase activity during chronic lung inflammation in pigs?[END_REF] by the activation of the indoleamine 2,3-dioxygenase pathway. Interestingly, in Le Floc'h et al. ( 2008), Val concentrations were unaffected by the CFA challenge, and His concentrations were increased. In a recent study us-ing labeled AA infusion, a lower Val turnover rate was even observed in CFA pigs [START_REF] Kampman-Van De Hoek | Induced lung inflammation and dietary protein supply affect nitrogen retention and amino acid metabolism in growing pigs[END_REF], suggesting that Val catabolism and/or utilization for protein synthesis were reduced by inflammation. The singular response of plasma Val and His across studies might reveal their sublimiting dietary supply concentrations in a chronic inflammatory situation.

Line Differences in the Metabolism of Some Specific AA Interestingly, RFI -pigs had lower concentrations of total AA from d -1 to d 7 in the fed state (mainly because of lower concentrations of Ala, Gln, Gly, Leu, Ile, and Pro), suggesting a faster and greater uptake of AA after the meal for immediate use than in RFI + pigs. This greater uptake might support their greater rate of proteosynthesis, a greater use of AA for hepatic gluconeogenesis, or, in the case of Gln, a greater use as energetic fuel in activated immune cells in RFI -pigs [START_REF] Newsholme | Why is l-glutamine metabolism important to cells of the immune system in health, postinjury, surgery or infection?[END_REF]. However, because there was no day × line interaction, it might be that these differences were not specific to the inflammatory state but a constant difference between lines.

In inflammatory states, muscles increase their release of Ala into the blood, which is then used in the liver for gluconeogenesis [START_REF] Bruins | Aspects of organ protein, amino acid and glucose metabolism in a porcine model of hypermetabolic sepsis[END_REF]. In RFI + pigs, Ala concentration was greater in both the fed and fasted states, suggesting that RFI + pigs might have a greater muscular production of Ala to supply the glucose-Ala cycle (Cahill cycle) than RFI -pigs. Moreover, Ile and Leu are 2 major donors of the amino group for Ala synthesis in the muscle. Contrary to what was observed in RFI -pigs, in which Ile and Leu postprandial concentrations increased in comparison to prechallenge concentrations, Ile and Leu postprandial use in RFI + pigs was maintained across days. This contrasting temporal evolution after CFA administration suggests that the differential use of the Cahill cycle between the 2 lines might be even greater after the CFA challenge than in a basal healthy state. Such results may be associated with the greater glucose postprandial concentration reported in RFI + pigs on d 1 after the CFA challenge. A greater Cahill cycle activity in RFI + pigs should lead to increased liver production of Glu and Asp, which are acceptors of the amino group from Ala to form pyruvate then glucose in the liver. Thus, the lower concentrations of Glu and Asp in RFI + pigs in comparison to RFI -pigs is a limitation to our hypothesis.

Conclusion

The present study confirmed that the inflammation induced by CFA administration can lead to alterations in AA metabolism lasting for at least 7 d. The data suggested selection for low RFI favored the preservation of muscle protein accretion during inflammation. The selection on RFI might have also favored preferences for different energetic pathways in RFI+ and RFI-lines: to generate energy, the glucose-Ala cycle might be greater in RFI + pigs than RFI -pigs, reducing their need for other gluconeogenic AA, whereas RFI -pigs would use more other AA for gluconeogenesis and Gln as energetic substrates. Whether these differences between the 2 lines are permanent or specific to inflammatory states needs to be clarified. Nevertheless, these metabolic differences were not associated with fever, haptoglobin, and growth differences, suggesting that both lines coped similarly with the CFA challenge. Contrary to our hypothesis, this experiment showed, in young pigs, no advantage of RFI + animals in response to an inflammatory challenge.

LITERATURE CITED

Figure 1 .

 1 Figure 1. (A) Feed intake, (B) haptoglobin concentration, and (C) glucose and (D) urea concentrations in fasted and fed states in piglets divergently selected on low or high residual feed intake (RFI -and RFI + ) and treated with complete Freund's adjuvant on d 0. The presented data are least squares means ± SE. The day (D), line (L), and their interaction (D × L) effects are indicated on the charts when significant (*P < 0.05; **P < 0.01; ***P < 0.01). For glucose, means of RFI + pigs without a common superscript differ (P < 0.05).

Figure 2 .

 2 Figure 2. Plasma concentrations of (A) glutamine, (B) glycine, (C) asparagine, (D) valine, (E) lysine, and (F) methionine in fasted and fed conditions in piglets divergently selected on low or high residual feed intake (RFI -and RFI + ) and treated with complete Freund adjuvant on d 0. The presented data are least squares means ± SE. The day (D), line (L), and their interaction (D × L) effects are indicated on the charts when significant (*P < 0.05; **P < 0.01; ***P < 0.01).

Table 1 .

 1 Ingredients and chemical composition of diets (as-fed basis)

	Item	Starter	Weaner
	Ingredient, %
	Wheat	-	23.2
	Corn	-	25.0
	Barley	45.7	22.6
	Dried whey	20.0	-
	Soybean meal	17.5	24.3
	Lactose	8.0	-
	Vegetable (corn) oil	2.3	0.45
	Calcium carbonate	1.5	0.97
	Monocalcium phosphate	0.68	-
	Dicalcium phosphate	-	1.1
	Sodium chloride	-	0.40
	Vitamin-mineral premix 1	0.50	0.50
	l-Lysine HCL	0.38	0.7
	dl-Methionine	0.23	0.18
	l-Threonine	0.15	0.15
	l-Tryptophan	0.35	0.35
	3-Phytase 2	0.24	0.01
	Chemical composition
	CP, %	19.0	18.6
	Digestible lysine, %	1.25	1.14
	NE, kJ/g	10.6	9.4

Table 2 .

 2 Plasma concentrations (nmol/mL) of AA that were transiently decreased following treatment with complete Freund adjuvant, measured in low and high residual feed intake pigs (RFI -and RFI + lines)

							P-value
		Nutritional						Line ×
	Item	status	RFI -1 RFI +1 SEM	Line	Day 2	day
	Total AA Fasted 4,225 4,346	110	0.45	<0.0001 0.48
		Fed	5,600 6,339	219	0.03	<0.001	0.28
	Ala	Fasted	534	593	19	0.03	<0.0001 0.72
		Fed	712	818	36	0.05	0.0002 0.35
	Asn	Fasted	77	68	4	0.15	0.015	0.84
		Fed	139	154	9	0.25	0.01	0.19
	Asp	Fasted	20	16	1	0.0004 <0.0001 0.34
		Fed	26	22	1	0.02	<0.0001 0.92
	Gln	Fasted	641	644	23	0.92	<0.0001 0.47
		Fed	726	792	20	0.03	<0.0001 0.68
	Glu	Fasted	250	194	15	0.01	<0.001	0.25
		Fed	303	256	18	0.08	<0.001	0.45
	Gly	Fasted	962 1143	46	0.01	<0.0001 0.34
		Fed	925 1111	57	0.03	0.0007 0.29
	Hypro	Fasted	102	106	5	0.55	0.25	0.77
		Fed	97	112	5	0.07	0.004	0.78
	Ile	Fasted	132	133	4	0.87	0.0001 0.68
		Fed	172	197	6	0.005	0.0009 0.03
	Leu	Fasted	147	141	5	0.44	0.0002 0.70
		Fed	198	223	8	0.03	0.0007 0.04
	Pro	Fasted	245	254	8	0.45	<0.0001 0.60
		Fed	217	255	17	0.02	<0.0001 0.31
	Ser	Fasted	175	193	11	0.26	0.03	0.21
		Fed	217	255	16	0.11	0.09	0.46

Table 3 .

 3 Plasma concentrations of AA (nmol/mL) that showed differences from total AA temporal patterns after treatment with complete Freund adjuvant, measured in low and high residual feed intake pigs (RFI - and RFI + lines)

		Nutritional				P-value
	Item	status	RFI -1 RFI +1 SEM	Line Time 2 Line × time
	Arg	Fasted	32	51	7	0.11 0.11	0.75
		Fed	168	187	16	0.39 0.59	0.05
	Cit 3	Fasted	61	50	3	0.02 0.07	0.93
		Fed	79	69	4	0.09 0.11	0.02
	His	Fasted	36	33	3	0.41 0.06 (↓)	0.45
		Fed	65	73	4	0.21 0.75	0.19
	Lys	Fasted	55	60	10	0.72 0.16	0.13
		Fed	263	326	27	0.11 0.03 (↑)	0.59
	Met	Fasted	36	28	2	0.008 0.44	0.90
		Fed	67	69	4	0.63 0.03	0.007
	Orn 3	Fasted	61	51	4	0.15 0.32	0.82
		Fed	110	114	6	0.63 0.30	0.17
	Phe	Fasted	76	71	3	0.29 0.11	0.45
		Fed	124	135	4	0.08 0.44	0.21
	Thr	Fasted	113	106	10	0.65 0.34	0.58
		Fed	217	260	18	0.10 0.06	0.18
	Trp	Fasted	35	29	2	0.10 0.05 (↓)	0.74
		Fed	64	68	4	0.49 0.54	0.28
	Tyr	Fasted	50	44	4	0.21 0.31	0.92
		Fed	93	103	7	0.32 0.36	0.05
	Val	Fasted	147	136	10	0.46 0.01 (↓)	0.86
		Fed	225	251	14	0.22 0.64	0.12

Table 4 .

 4 Rate of protein synthesis (K s ) and specific activities of key enzymes involved in protein degradation in tissues of piglets divergently selected on low or high residual feed intake (RFI -and RFI + ), measured 8 d after the complete Freund adjuvant challenge

	Item	RFI -1	RFI +1	SEM	P-value
	N	10	11
	LM
	K s , %/d	8.9	8.2	0.3	0.07
	Proteasome 2	1,692	2,265	386	0.15
	Calpains 2	1,663	2,534	456	0.07
	Liver
	K s , %/d	85.9	76.9	5.2	0.09
	Proteasome 2 170,414	153,094	10609	0.12
	Calpains 2	130,255	121,422	13571	0.52

The presented data are least squares means calculated by SAS (SAS Inst. Inc., Cary, NC).

Activities are expressed as mRFU•min-1•mg-1 protein expressed as mRFU/min/mg protein. RFU = relative fluorescent unit.

Marie Rekiba) for their technical help. This work was funded by the INRA PHASE division, the INRA GA division, and a grant from the French National Research Agency (ANR-08-GENM038 PIG_FEED Project).


Kwassi H Degue

Denis Efimov

Jerome Le Ny

Interval Observer-based Feedback Control for Rehabilitation in Tremor

Tremor, one of the most common health disorders, is defined as a chronic movement disorder. To reduce tremor in patients, the design of stabilizing techniques is critical. For this purpose, we consider an uncertain continuoustime linear time-varying oscillator model of tremor in this article. We design a state feedback control for deep brain stimulation technique by considering the practical case in which only sets of admissible values are given for the nominal values of the stimulation amplitude, the time-varying tremor's angular frequency and the tremor measurement noise. First, we estimate state signal bounds that include the true unknown value of the state. Next, we design a stabilizing control input based on the estimated bounds. The stability of the controlled system is verified using linear matrix inequalities (LMIs). We demonstrate the methodology's performance in numerical simulations.

I. INTRODUCTION

Tremor, which is an involuntary, approximately sinusoidal movement and roughly rhythmic, is one of the most common types of movement disorders [START_REF] Tarsy | Handbook of essential tremor and other tremor disorders[END_REF]. Indeed, 6.38 to 7.63 million people were living with Essential Tremor in the USA in 2014 [START_REF] Louis | How many people in theUSA have Essential Tremor? Deriving a population estimate based on epidemiological data[END_REF]. Tremor has impacts on sundry parts of the body, but the hands are the most affected. It is not a life-threatening disease, but it usually seriously lessens the patients' quality of life, since they are not able to execute simple daily tasks such as opening a door or drinking a glass of water [START_REF] Padilha Lanari | On the use of FES to attenuate tremor by modulating joint impedance[END_REF].

An effective therapy for pathological tremor is Deep Brain Stimulation (DBS) [START_REF] Perozzo | Deep brain stimulation of the subthalamic nucleus in Parkinson's disease: comparison of preand postoperative neuropsychological evaluation[END_REF]- [START_REF] Ostrem | Treatment of dystonia with deep brain stimulation[END_REF]. Namely, in Parkinson disease patients, one surgically implants electrodes in the basal ganglia, commonly in the subthalamic nucleus, to generate electric-pulse stimulation of multifarious neurons [START_REF]Modulation of human time processing by subthalamic deep brain stimulation[END_REF], [START_REF]Reversing cognitive-motor impairments in parkinson's disease patients using a computational modelling approach to deep brain stimulation programming[END_REF]. Some characteristics of the high-frequency electronic pulse-train that is applied to the brain are pulse- kwassi-holali.degue,jerome.le-ny@polymtl.ca D. Efimov is with Inria, Univ. Lille, CNRS, UMR 9189 -CRIStAL, F-59000 Lille, France and ITMO University, 197101 Saint Petersburg, Russia. Denis.Efimov@inria.fr width, amplitude and frequency. Over the last decade, advanced techniques of controlled DBS have been proposed to decrease tremor in patients [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF]- [START_REF] Rouhollahi | Controllability and observability analysis of basal ganglia model and feedback linearisation control[END_REF]. Feedback control techniques have been proposed in [START_REF] Rouhollahi | Designing a robust backstepping controller for rehabilitation in parkinson's disease: a simulation study[END_REF]- [START_REF] Rouhollahi | Controllability and observability analysis of basal ganglia model and feedback linearisation control[END_REF] by assuming that one can measure the perfect value of the tremor, which constitutes a drawback since real measurements are usually corrupted by noise. An output feedback control technique has been developed in [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF] by assuming that an estimation of the perfect value of the stimulation amplitude is possible, which can be a limitation in many cases. Indeed, it has been shown that an estimation of such a perfect value can be highly inaccurate in several cases [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF]. In addition, [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF] assumes noiseless outputs in their model, i.e., they assume that the noise in the tremor signal is totally removed by means of a band-pass filter. Nevertheless, for example by using a second-order Butterworth filter from 3 to 10 Hz in case of tremor [START_REF] Giuffrida | Clinically deployable Kinesia technology for automated tremor assessment[END_REF], [START_REF] Mera | Kinematic optimization of deep brain stimulation across multiple motor symptoms in parkinson's disease[END_REF], only noisy measurements are usually available. Moreover, they propose a static output feedback controller, which does not include an observer. When considering dynamic systems, a state feedback control technique has better performances than a static output feedback controller. Furthermore, when one has to handle the presence of exogenous disturbances or uncertain parameters, whose values are only known to belong to an interval or polytope, all the aforementioned methodologies that are proposed in the existing literature (based on point-wise estimation) cannot be applied. The use of methodologies based on interval estimators [START_REF] Mazenc | Asymptotically stable interval observers for planar systems with complex poles[END_REF]- [START_REF] Efimov | Interval state observer for nonlinear time-varying systems[END_REF] instead of point-wise observers can address such problems.

The contribution of this article consists in designing for the first time a stabilizing state feedback control based on an interval observer methodology to reduce tremor in patients. We consider an uncertain continuous-time linear time-varying oscillator model of tremor, with four types of uncertainty: the initial condition, the nominal value of the stimulation amplitude, the time-varying tremor's angular frequency and the measurement noise. For these parameters, we assume that the exact values are not available, only bounds are given. Following [START_REF] Efimov | Control of nonlinear and LPV systems: interval observer-based framework[END_REF], [START_REF] Degue | Stabilization of linear impulsive systems under dwell-time constraints: Interval observerbased framework[END_REF], first, we evaluate the state signal bounds, assuming that the control signal is given. Next, we use these bounds to design a stabilizing control law for the observer's system. The stabilization of the state bounds around a vicinity of zero implies the same property for the state due to the inclusion relation. Note that only noiseless systems have been considered in [START_REF] Efimov | Control of nonlinear and LPV systems: interval observer-based framework[END_REF] when applying such a methodology. Furthermore, we consider a stabilizing control design in this article, in contrast to [START_REF] Degue | Estimation and outbreak detection with interval observers for uncertain discrete-time SEIR epidemic models[END_REF]- [START_REF] Chebotarev | Interval observers for continuous-time LPV systems with L 1 /L 2 performance[END_REF] that has studied only observer design problems.

We present the problem statement in Section II. Then, we rewrite the model as a linear parameter-varying (LPV) system and review some results on the theory of interval estimation and on positive systems in Section III. We apply these results to design state signal bounds and a stabilizing control input in the rest of Section III. Finally, we illustrate the performance of our methodology by presenting numerical simulations to reduce the tremor of a Parkinson's disease patient.

Notation. We denote the real numbers by R, the integers by Z, R + = {τ ∈ R : τ ≥ 0} and Z + = Z ∩ R + . We denote the cones of vectors of dimension n positive, nonnegative, and negative components by

R n >0 , R n + and R n <0 respectively. For a vector x ∈ R n , we denote |x| ∞ := max i∈{1,...,n} |x i |, |x| = |x| 2 := ( k i=1 |x i | 2 ) 1/2
and we denote the induced 2-norm of a matrix A ∈ R n×n by |A|. For a vector-valued signal u : R + → R n , we denote its L ∞ -norm as ||u|| L∞ := ess sup t≥0 |u(t)| ∞ . We denote by L n ∞ the set of signals u with the property ||u|| L∞ < ∞. The n × n identity matrix is denoted I n and the matrix with all elements equal to 0 and dimension p × 1 is denoted 0 p . For two vectors x 1 , x 2 ∈ R n or matrices A 1 , A 2 ∈ R n×n , the relations x 1 ≤ x 2 and A 1 ≤ A 2 are understood elementwise. A matrix A ∈ R n×n is Hurwitz if all its eigenvalues have negative real parts; it is called Metzler if all its elements outside of the main diagonal are nonnegative. The notation P ≺ 0 (P 0) means that the matrix P ∈ R n×n is symmetric and negative (positive) definite.

II. BACKGROUND

One can characterize a DBS signal by several parameters, including but not limited to, frequency ω and stimulation amplitude a that are supplied to a stimulus generator in order to create a stimulus signal [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF]. One applies such a stimulus signal to a particular part of the brain by using an electrode in order to overcome cognitive disorder's motor symptoms. One can quantify the tremor that is caused by a brain disorder in terms of position, velocity and acceleration, by using a sensor that is fixed to a patient's finger [START_REF] Mera | Kinematic optimization of deep brain stimulation across multiple motor symptoms in parkinson's disease[END_REF]. One can attenuate the noise in the tremor signal by using a band-pass filter, for example a secondorder Butterworth filter from 3 to 10 Hz [START_REF] Giuffrida | Clinically deployable Kinesia technology for automated tremor assessment[END_REF], [START_REF] Mera | Kinematic optimization of deep brain stimulation across multiple motor symptoms in parkinson's disease[END_REF]. Further information about the tremor measurement's process can be found in [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF], [START_REF] Mera | Kinematic optimization of deep brain stimulation across multiple motor symptoms in parkinson's disease[END_REF].

The whole process dynamics can be modeled as a simple time-varying oscillator, where DBS parameters are considered as inputs and the filtered tremor signal as the output. Throughout this article, we consider the following continuous-time linear time-varying oscillator model of tremor dynamics [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF], whose design has been inspired by [START_REF] Aqil | Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity[END_REF]

ẋ1 (t) = -ω 2 (t)x 2 (t) + u(t) -a ẋ2 (t) =x 1 (t), (1)
where x := x 1 x 2 T ∈ R 2 is the state vector: x 1 represents the normalized tremor (normalized with the strength of amplitude [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF]) and x 2 is a state variable of the oscillator, u ∈ R stands for the control input, ω ∈ R represents the time-varying tremor's angular frequency and a is the stimulation amplitude's nominal value for which the tremor related to a brain disorder vanishes. The presence of the parameter a in the model ( 1) is appropriate since in case of brain disease such as Parkinson, the tremor of a patient is controlled by DBS after selecting stimulation parameters [START_REF] Haeri | Modeling the Parkinson's tremor and its treatments[END_REF]- [START_REF] Earhart | Effects of thalamic stimulation frequency on intention and postural tremor[END_REF]. As in [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF], we assume that the parameter ω(t) is uncertain but two bounds ω, ω ∈ R + are known such that ω ≤ ω(t) ≤ ω, ∀t ≥ 0. In contrast with [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF], which have assumed that an estimation of the perfect value of the parameter a is possible, we assume in this article that a is unknown but two bounds a, a ∈ R are given such that a ≤ a ≤ a, ∀t ≥ 0. Indeed, it has been proved that an estimation of a perfect value of a can be highly inaccurate in several cases [START_REF] Rehan | Modeling and automatic feedback control of tremor: Adaptive estimation of deep brain stimulation[END_REF]. Furthermore, in contrast to [START_REF] Rouhollahi | Designing a robust backstepping controller for rehabilitation in parkinson's disease: a simulation study[END_REF]- [START_REF] Rouhollahi | Controllability and observability analysis of basal ganglia model and feedback linearisation control[END_REF], where it is assumed that the tremor is measured perfectly, we consider the practical case in which measurements consist of the tremor corrupted by noise as follows

y(t) =x 1 (t) + v(t), (2)
where v ∈ L ∞ represents a measurement noise. We assume that v is unknown but two bounds v, v ∈ R are given such that v ≤ v(t) ≤ v, ∀t ≥ 0. The presence of such a measurement noise is natural since by using a band-pass filter, one has access to a noisy measurement of the tremor signal only.

In this article, we aim at reducing the tremor caused by a brain disorder such that x 1 tracks a vicinity of a desired (healthy) trajectory x d 1 = 0. Hence, the goal of this paper consists in stabilizing system (1) around 0.

III. MAIN RESULTS

Recall that ω(t) is an uncertain parameter that satisfies ω(t) ∈ Θ ⊂ R, where the set Θ is given (Θ = [ω, ω]). By using the structure of the system (1)-( 2), we can rewrite it as follows

ẋ(t) =(A 0 + ∆A(ω(t)))x(t) + Bu(t) -Ba, y t =Cx(t) + v(t), (3)
with

A 0 = 0 1 1 0 , ∆A(ω(t)) = 0 -ω 2 (t) -1 0 0 , B = 1 0 , C = 1 0 .
We treat a as an unknown input. By using the definitions of the parameter ω(t) and the set Θ and using the structure of the system (3), we deduce that the matrix ∆A(ω(t)) is uncertain but there exist two given matrices ∆A, ∆A ∈ R 2×2 <0 such that

∆A ≤ ∆A(ω(t)) ≤ ∆A (4)
for any θ ∈ Θ. Indeed, we get

∆A = 0 -ω 2 -1 0 0 , ∆A = 0 -ω 2 -1 0 0 .
Since, we aim at tracking a desired (healthy) trajectory x d = 0, we solve the problem in two stages. First, we design an interval observer for x(t), i.e., state signal bounds x(t) ≤ x(t) ≤ x(t), ∀t ≥ 0, assuming that the control signal u(t) is given. Next, with the observer gain that is designed a priori, we use the interval observer to design a tracking control law u(t) = f (x(t), x(t)) that implies x → x d , x → x d and keeps the relation x(t) ≤ x(t) ≤ x(t), ∀t ≥ 0. Notice that the tracking of x(t) and x(t) implies the same property for the state x(t) due to the inclusion relation. We assume that the initial condition x(0) is unknown but two bounds x(0), x(0) are given such that x(0) ≤ x(0) ≤ x(0). First, let us review some basic facts from the theory of interval estimation.

A. Preliminaries on interval estimation and positive systems

Given a matrix A ∈ R m×n , define A + = max{0, A}, A -= A + -A (we use the same notation for vectors). Lemma 1. [START_REF] Efimov | Interval estimation for LPV systems applying high order sliding mode techniques[END_REF] Let x ∈ R n be a vector variable with x ≤ x ≤ x for some x, x ∈ R n .

(1) If A ∈ R m×n is a constant matrix, then

A + x -A -x ≤ Ax ≤ A + x -A -x. (5)
(2) If A ∈ R m×n is a matrix variable and A ≤ A ≤ A for some A, A ∈ R m×n , then

A + x + -A + x --A -x + + A -x -≤ Ax (6) ≤ A + x + -A + x --A -x + + A -x -.
Notice that when A, A ∈ R m×n <0 , the inequality (6) simply reads

Ax + -Ax -≤ Ax ≤ Ax + -A x -, (7)
since A = -A -, A + = 0, A = -A -and A + = 0 in such a case. Furthermore, when A ∈ R m×n <0 , the inequality (5) simply becomes

Ax ≤ Ax ≤ Ax, (8)
since A = -A -and A + = 0. Next, consider the following linear time-invariant (LTI) system

ẋ =Ax + Bω(t), ω : R + → R q + , (9)
y =Cx + Dω(t), with x ∈ R n , y ∈ R p and A ∈ R n×n a Metzler matrix. Lemma 2.
[29], [START_REF] Smith | Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems[END_REF] Any solution of the LTI system ( 9) is element-wise nonnegative provided that x(0) ≥ 0 and B ∈ R n×q + . Furthermore, the output solution y(t) is nonnegative if C ∈ R p×n + and D ∈ R p×q + . A dynamical system satisfying all these restrictions is called cooperative (monotone) or nonnegative.

B. Interval observer design

There exists a matrix L ∈ R 2×1 such that the matrix (A 0 -LC) is Metzler to ensure nonnegativity for the interval observer's errors (for example L = 0 0 T satisfies such a condition due to the structure of the model ( 3) ). Define

α(t) =∆Ax + (t) -∆Ax -(t), α(t) =∆Ax + (t) -∆A x -(t).
By applying Lemma 1, it can be inferred that

α(t) ≤ ∆A(ω(t))x(t) ≤ α(t),∀t ≥ 0. ( 10
)
Since -B ∈ R 2×1 <0 by using the structure of the model (3), one can design an interval estimator for (3) as follows

ẋ(t) =(A 0 -LC)x(t) + α(t) + Bu(t) + Ly(t) -Ba -L + v + L -v, ẋ(t) =(A 0 -LC)x(t) + α(t) + Bu(t) + Ly(t) -Ba + L -v -L + v, (11)
where x ∈ R 2 and x ∈ R 2 stand respectively for the lower and the upper interval estimates for the state x. Notice the nonlinear structure of the interval observer [START_REF]Design of robust adaptive controller and feedback error learning for rehabilitation in parkinson's disease: a simulation study[END_REF] because of the presence of α and α.

Theorem 1. The estimates x(t) and x(t) given by (11) yield the relations

x(t) ≤ x(t) ≤ x(t),∀t ≥ 0, (12)
provided that x(0) ≤ x(0) ≤ x(0).

We skip the proofs of our results due to space limitations. One can compute the observer gain L as solution of a linear program by using [START_REF] Chebotarev | Interval observers for continuous-time LPV systems with L 1 /L 2 performance[END_REF]Theorem 7] to ensure boundedness for the estimation errors e and e. A control algorithm design is required to stabilize x, x and x.

C. Control Design

The idea consists in stabilizing the completely known system (11) instead of (3). Indeed, when x and x converge to the desired trajectory x d , x follows the same property due to [START_REF] Rouhollahi | Controllability and observability analysis of basal ganglia model and feedback linearisation control[END_REF]. First, we can treat the signal y(t) in ( 11) as a state dependent disturbance. Proposition 1. We have

|y(t)| ≤|C|(|x(t)| + |x(t)|) + max{|v|, |v|}, ∀t ≥ 0.
Hence the output y admits a linear upper bound in terms of |x(t)| and |x(t)|. We aim at stabilizing the system (11), i.e., the states x and x, since its stabilization implies the stabilization of the system (3). Next, let us prove that we can rewrite the dynamics (11) as a globally Lipschitz nonlinear system.

Denote ε(t) := x T (t) x T (t) T , and

H = A 0 -LC 0 0 A 0 -LC , ζ = ζ T 1 ζ T 2 T , ζ 1 =(-B) + a -(-B) -a -L + v + L -v, ζ 2 =(-B) + a -(-B) -a + L -v -L + v, φ(ε) = α α .
In the sequel, also define

γ φ = 0 0 -∆A ∆A -∆A ∆A 0 0 .
Corollary 1. One can rewrite the dynamics [START_REF]Design of robust adaptive controller and feedback error learning for rehabilitation in parkinson's disease: a simulation study[END_REF] as follows

ε(t) =Hε(t) + φ(ε(t)) + ζ + B B u(t) + L L y(t) (13)
where φ : R 4 -→ R 4 is a nonlinear function globally Lipschitz at the origin.

Proposition 1 and Corollary 1 ensure uniqueness for the solution of [START_REF]Design of robust adaptive controller and feedback error learning for rehabilitation in parkinson's disease: a simulation study[END_REF]. Then, we need to stabilize the system [START_REF]Design of robust adaptive controller and feedback error learning for rehabilitation in parkinson's disease: a simulation study[END_REF] with respect to Lipschitz nonlinearities. We deduce that we can select the control input as a conventional state linear feedback u(t) =K x(t) + K x(t), ( 14) =Kε(t), with K = K K , where K and K are two feedback gains to be designed. Denote B := B T B T T and L := L T L T T . After substituting ( 14) in ( 13), we get

ε(t) =(H + BK)ε(t) + φ(ε(t)) + ζ(t) + Ly(t). ( 15
)
Theorem 2. If there exist matrices P T = P I 4 ,

J = P -1 , Q T = Q 0, R ∈ R 1×4 and a constant γ > 0 such that Z ≺0, (16)
Z =     W J L I 4 J J 0 0 L T 0 -1 0 I 4 0 0 -γI 4     , W =JH T + R T B T + HJ + BR + (γ φ + 2|C| 2 )J + Q,
then the solutions of the system (3), [START_REF]Design of robust adaptive controller and feedback error learning for rehabilitation in parkinson's disease: a simulation study[END_REF], [START_REF] Mazenc | Asymptotically stable interval observers for planar systems with complex poles[END_REF] with R = KJ asymptotically converge to a vicinity of x d :

lim sup t→+∞ |x(t)| ≤ λ max (J -1 ) λ min (J -1 )λ min (Q) ( √ γ|ζ|+ √ 2 max{|v|, |v|}).
The expression of Z is linear in J, Q and R. Hence, one can solve [START_REF]Interval observers for linear time-invariant systems with disturbances[END_REF] as an LMI with respect to these variables by using standard numerical solvers. The control gain can be deduced as follows K = RJ -1 .

IV. NUMERICAL EXPERIMENTS

We illustrate the performance of the proposed methodology with a simulated example on the tremor of a Parkinson's disease patient under DBS with constant angular frequency ω 2 (t) = 1400, ∀t ≥ 0 and the stimulation amplitude nominal value a = 1 Volt [START_REF] Mera | Kinematic optimization of deep brain stimulation across multiple motor symptoms in parkinson's disease[END_REF]. Consider the following values as bounds for these parameter values: ω 2 = 1300, ω 2 = 500π, a = 0.8 Volt and a = 1.2 Volt. The measurements of the tremor signal are corrupted by a noise sequence v(t) that consists of independent and identically distributed random numbers sampled from a uniform distribution over the interval [-V, V ], with V = 0.1 Volt. The state's initial condition is given by x(0) = 0.5 0.5

T . The measurement of tremor y oscillates from -18.8 Volts to 18.8 Volts (Fig. 1), hence it is required to stabilize the system (3). To design the bounds x, x, we select x(0) = 0.4 0.4 T and x(0) = 0.6 0.6 T .

We compute the observer gain L as solution of a linear program by using [START_REF] Chebotarev | Interval observers for continuous-time LPV systems with L 1 /L 2 performance[END_REF]Theorem 7] to ensure boundedness for the estimation errors e and e. We obtain L = 86963 0

T and the matrix

A 0 -LC = -86963 1 1 0
is Metzler. It can be inferred from the results of the interval estimation (Fig. 2) that the bounds provided by [START_REF]Design of robust adaptive controller and feedback error learning for rehabilitation in parkinson's disease: a simulation study[END_REF] respect the inclusion relation [START_REF] Rouhollahi | Controllability and observability analysis of basal ganglia model and feedback linearisation control[END_REF].

To design the control input u, we solve the linear matrix inequality (16) by using the YALMIP toolbox for Matlab [START_REF] Löfberg | Automatic robust convex programming[END_REF]. Notice the superiority of our control methodology since the control technique that has been proposed in [START_REF] Efimov | Control of nonlinear and LPV systems: interval observer-based framework[END_REF] fails to be applied because these authors have considered only noiseless outputs. The conditions of Theorem 2 are satisfied for the systems (3), [START_REF]Design of robust adaptive controller and feedback error learning for rehabilitation in parkinson's disease: a simulation study[END_REF] and ( 15) with K = -1.33 × 10 5 1.36 × 10 3 , K = -1.33 × 10 5 1.7 × 10 3 .

We see on Fig. 3 that the solution x 1 (the tremor) of the systems (3), ( 11) and ( 15) asymptotically converge to a vicinity of 0 after applying the proposed control methodology, as required.

V. CONCLUSION

We have considered the problem of reducing tremor in patients, in the case in which only sets of admissible values are available for the model's disturbances and uncertainties. We have designed a state feedback control to stabilize estimated bounds of the tremor, which are provided by

Fig. 1 .

 1 Fig. 1. Evolution of the measurement of the tremor when u = 0.

2 Fig. 2 . 1 Fig. 3 .

 2213 Fig.2. Evolution of the actual state and the observed bounds without using control methodology (u = 0).

  This work was supported in part by NSERC under Grant RGPIN-5287-2018 and RGPAS-2018-522686, by the Pierre Arbour Foundation doctoral scholarship, a FRQNT doctoral scholarship, the Government of Russian Federation (Grant 08-08) and the Ministry of Science and Higher Education of Russian Federation (passport of goszadanie no. 2019-0898).

	K. H. Degue and J. Le Ny are with the depart-
	ment	of	Electrical	Engineering,	Polytechnique	Mon-
	treal	and	GERAD,	QC	H3T-1J4,	Montreal,	Canada.

an estimator that we have designed. Due to the inclusion relation, this implies the stabilization of the tremor. The performance of our technique is illustrated through numerical simulations. As a direction for future research, the problem of extending this technique to an uncertain oscillator-based nonlinear tremor model can be considered.