Dr Pierre Jésus
email: p.jesus@wanadoo.fr

Marin Benoit

Philippe Fayemendy

Marie Nicol

Géraldine Lautrette

Huguette Sourisseau

Pierre-Marie Preux

Philippe Couratier

Jean-Claude Desport

Resting energy expenditure equations in Amyotrophic Lateral Sclerosis, creation of an ALS-specific equation

Keywords: Amyotrophic lateral sclerosis, resting energy expenditure, predictive formula, indirect calorimetry, new formula amyotrophic lateral sclerosis ALSFRS: amyotrophic lateral sclerosis functional rating scale ALSFRS-R: amyotrophic lateral sclerosis functional rating scale-revised BIA: bioelectric impedance analysis interquartile range; Mifflin: Mifflin St. Jeor

Introduction: Resting energy expenditure (REE) formulas for healthy people (HP) are used to calculate REE (cREE) in amyotrophic lateral sclerosis (ALS) patients. In 50-60% of ALS cases an increase of measured REE (mREE) in indirect calometry (IC) compared to cREE is found. The aims here were (i) to assess the accuracy of cREE assessed using 11 formulas as compared to mREE and (ii) to create (if necessary) a specific cREE formula for ALS patients. Method: 315 Patients followed in the ALS expert center of Limoges between 1996 and 2014 were included. mREE assessed with IC and cREE calculated with 11 predictive formulas (Harris Benedict (HB) 1919, HB 1984, WSchofield, De Lorenzo, Johnstone, Mifflin, WHO/FAO, Owen, Fleisch, Wang and Rosenbaum) were determined at the time of diagnosis. Fat free mass (FFM) and fat mass (FM) were measured with impedancemetry. A Bland and Altman analysis was carried out. The percentage of accurate prediction ± 10% of mREE, and intraclass correlation coefficients (ICC) were calculated. Using a derivation sample, a new REE formula was created using multiple linear regression according to sex, age, FFM and FM. Accuracy of this formula was assessed in a validation sample.

Results: ICC ranged between 0.60 and 0.71 (moderate agreement), and percentage of accurate prediction between 27.3% and 57.5%. Underestimation was found from 31.7% to 71.4% of cases. According to these unsatisfactory results we created an ALS-specific formula in a derivation sample (130 patients). ICC and percentage of accurate prediction increased in a validation sample (143 patients) to 0.85 (very good agreement) and 65.0% respectively, with 17.5% underestimation. Conclusion: REE formulas for HP underestimate REE in ALS patients compared to mREE.

Our new ALS-specific formula produced better results than formulas for HP. This formula can be used to estimate REE in ALS patients if IC is not accessible.

Introduction

Amyotrophic lateral sclerosis (ALS) is a rare neurodegenerative disease affecting motor neurons, age at diagnosis is 65-70 years (1-4) and its incidence is stable at around 2/ 100 000 person years in Western populations [START_REF] Marin | Variation in worldwide incidence of amyotrophic lateral sclerosis: a meta-analysis[END_REF]. The prognosis is severe, with a median survival in Europe of 25 to 30 months from onset [START_REF] Marin | Clinical and demographic factors and outcome of amyotrophic lateral sclerosis in relation to population ancestral origin[END_REF].

ALS patients are at risk of malnutrition in the short and medium term (9-55% according to the literature) [START_REF] Marin | Alteration of nutritional status at diagnosis is a prognostic factor for survival of amyotrophic lateral sclerosis patients[END_REF][START_REF] Desport | Nutritional status is a prognostic factor for survival in ALS patients[END_REF][START_REF] Genton | Nutritional state, energy intakes and energy expenditure of amyotrophic lateral sclerosis (ALS) patients[END_REF]. Causes may include increased resting energy expenditure (REE) [START_REF] Genton | Nutritional state, energy intakes and energy expenditure of amyotrophic lateral sclerosis (ALS) patients[END_REF][START_REF] Muscaritoli | Nutritional and metabolic support in patients with amyotrophic lateral sclerosis[END_REF][START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Marin | Troubles nutritionnels lors de la sclérose latérale amyotrophique (SLA)[END_REF][START_REF] Ngo | Body mass index and dietary intervention: implications for prognosis of amyotrophic lateral sclerosis[END_REF] which if not compensated by diet, may cause weight loss. REE may be measured (mREE) with indirect calorimetry (IC) [START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Funalot | High metabolic level in patients with familial amyotrophic lateral sclerosis[END_REF][START_REF] Kasarskis | Nutritional status of patients with amyotrophic lateral sclerosis: relation to the proximity of death[END_REF][START_REF] Vaisman | Do patients with amyotrophic lateral sclerosis (ALS) have increased energy needs?[END_REF][START_REF] Sherman | Standard Equations Are Not Accurate in Assessing Resting Energy Expenditure in Patients With Amyotrophic Lateral Sclerosis[END_REF],but because of the low availability of this highcost apparatus, and the length of time necessary for each measurement (≥20 min), predictive formulas have been developed to provide calculated REE (cREE). The most widely used is Harris and Benedict 1919 (HB1919) [START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Funalot | High metabolic level in patients with familial amyotrophic lateral sclerosis[END_REF][START_REF] Kasarskis | Nutritional status of patients with amyotrophic lateral sclerosis: relation to the proximity of death[END_REF][START_REF] Sherman | Standard Equations Are Not Accurate in Assessing Resting Energy Expenditure in Patients With Amyotrophic Lateral Sclerosis[END_REF]. The Mifflin St. Jeor (Mifflin) formula is also used [START_REF] Kasarskis | Estimating daily energy expenditure in individuals with amyotrophic lateral sclerosis[END_REF][START_REF] Lee | Association between estimated total daily energy expenditure and stage of amyotrophic lateral sclerosis[END_REF]. The difference between mREE and cREE allows for the definition of energy metabolism disorder. A difference between mREE and cREE of more than 10% defines hypermetabolism, which is found in 50-60% of ALS patients [START_REF] Genton | Nutritional state, energy intakes and energy expenditure of amyotrophic lateral sclerosis (ALS) patients[END_REF][START_REF] Muscaritoli | Nutritional and metabolic support in patients with amyotrophic lateral sclerosis[END_REF][START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF]Prise en charge des personnes atteintes de SLA-Texte des recommandations version longue[END_REF]. REE may increase from +10 to +20% in these patients. For Sherman et al., HB 1919 is not valid when used to predict REE in ALS patients [START_REF] Sherman | Standard Equations Are Not Accurate in Assessing Resting Energy Expenditure in Patients With Amyotrophic Lateral Sclerosis[END_REF]. Kasarskis et al. and Shimizu et al. recently created total energy expenditure (TEE) formulas for ALS patients using HB1919 and Mifflin formulas for REE prediction. These REE formulas were constructed for healthy people [START_REF] Jésus | Validity of predictive equations for resting energy expenditure according to the body mass index in a population of 1726 patients followed in a Nutrition Unit[END_REF].

Currently, no REE formulas are validated for ALS patients.

The objectives here were, in ALS patients: (i) to assess the accuracy of cREE calculated with 11 predictive formulas, commonly used in healthy patients (HB 1919, HB 1984, World Schofield (WSchofield), De Lorenzo, Johnstone, Mifflin) [START_REF] Jésus | Validity of predictive equations for resting energy expenditure according to the body mass index in a population of 1726 patients followed in a Nutrition Unit[END_REF] and used in ALS studies (HB 1919, world health organization / food and agriculture organization of the United Nations (WHO/FAO), Owen, Fleisch, Wang, Rosenbaum, Mifflin) [START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Kasarskis | Estimating daily energy expenditure in individuals with amyotrophic lateral sclerosis[END_REF][START_REF] Siirala | Predictive equations overestimate the resting energy expenditure in amyotrophic lateral sclerosis patients who are dependent on invasive ventilation support[END_REF] as compared to mREE assessed using IC, and; (ii) to create, if necessary a REE formula adapted to ALS patients and suitable for use in clinical practice without IC.

Methods

ALS patients followed in the ALS expert center in Limoges (France) from November 1996 to November 2014 with nutritional, neurological and respiratory assessments were included. The assessments were performed after diagnosis and then regularly until the patient died.

Nutritional assessment included the use of indirect calorimetry to measure REE.

Inclusion criteria:

We included patients with ALS diagnosed according to Airlie House criteria (definite, probable, or laboratory-supported probable and possible) [START_REF] Brooks | El Escorial revisited: revised criteria for the diagnosis of amyotrophic lateral sclerosis[END_REF] and treated with riluzole.

Patients could also have had ALS associated with frontotemporal dementia. The respiratory quotient (RQ) of patients by indirect calorimetry (IC) was required to be between 0.7 and 0.87 [START_REF] Ferrannini | The theoretical bases of indirect calorimetry: A review[END_REF]. IC and the other nutritional assessments had to have been performed within 1.5 months, and IC had to be performed no more than 12 months after diagnosis.

Data collection:

The data were extracted prospectively from the CleanWEB TM Their height (in m) was measured using a SECA ® gauge recording to 0.2 cm (Vogel & Halke, Hamburg, Germany) in an upright position or using the Chumlea formulas for people over 60 years who could not be verticalized [START_REF] Chumlea | Estimating stature from knee height for persons 60 to 90 years of age[END_REF]. BMI (in kg / m 2 ) was calculated using the formula: BMI (kg / m 2 ) = weight (kg) / height * height (m 2 ). The triceps skinfold (TSF) was obtained from the average of three measurements on each side with a Harpenden caliper (Baty International, Burgess Hill, UK) according to the usual modalities [START_REF] Frisancho | New norms of upper limb fat and muscle areas for assessment of nutritional status[END_REF]. Fat free mass (FFM in kg) and fat mass (FM in kg) were calculated with the validated formula for ALS patients using weight, TSF and total body impedance at 50 kHz in bioelectric impedance analysis (BIA) Analycor ® (Eugédia, Chambly, France) in supine position after 5 min of rest [START_REF] Desport | Validation of bioelectrical impedance analysis in patients with amyotrophic lateral sclerosis[END_REF]. The impedancemetry also allowed for measurement of the phase angle (PA) marker of cellular function [START_REF] Desport | Phase angle is a prognostic factor for survival in amyotrophic lateral sclerosis[END_REF]. Measured REE (mREE in kcal / 24h) by IC was obtained with the Quark RMR ® with canopy (Cosmed, Rome, Italy) after a calibration of the instrument (± 0.02% on measures of expired volumes of CO2 and inspired volumes of O2) [START_REF] Ferrannini | The theoretical bases of indirect calorimetry: A review[END_REF]. It was performed in the morning after 12 hours of fasting, in a supine position and at rest. The patient was not physically active before the IC, and did not sleep during the exam or hyperventilate. The cREE was calculated (cREE in kcal / 24h) according to eleven predictive formulas (HB 1919, HB 1984, WSchofield, De Lorenzo, Johnstone, Mifflin, WHO/FAO, Owen, Fleisch, Wang and Rosenbaum) (Table 1). Formulas with results in kj (WSchofield, De Lorenzo and Johnstone) were converted into kcal by multiplying by 0.2388. The REE variation (bias in %) was calculated according to the formula: cREE (kcal / 24h) -mREE (kcal / 24h) / mREE (kcal / 24h) * 100. The thresholds of accurate prediction of cREE compared to mREE is of ± 10%.

Overestimation was > 10% of measured value and underestimation was < 10% of measured value [START_REF] Jésus | Validity of predictive equations for resting energy expenditure according to the body mass index in a population of 1726 patients followed in a Nutrition Unit[END_REF].

Statistical analysis:

Statistical analysis was performed using SAS ® software v9.3 (SAS Institute, Cary, North Carolina, USA) and GraphPad Prism 6.0 (GraphPad Software Inc, La Jolla, CA, USA). The threshold of significance for all statistical analyses was p <0.05. We complied with the STROBE statement [START_REF] Cohen | 2015 guidelines for reporting diagnostic accuracy studies: explanation and elaboration[END_REF]. Quantitative variables were expressed with the median (interquartile range [IQR]) or mean± standard deviation (SD). Qualitative variables were expressed in frequency and percentage. Normality of quantitative variables was studied using the Shapiro-Wilk test. Quantitative variables were compared using non-parametric Mann-Whitney test, and qualitative variables were compared using Chi2.

Agreement between mREE and cREE

The REE variation (bias in %) was calculated according to the formula: cREE (kcal / 24h) -mREE (kcal / 24h) / mREE (kcal / 24h) * 100. The threshold of accurate prediction of cREE compared to mREE was ± 10%. Overestimation is > 10% of measured value and underestimation is < 10% of measured value [START_REF] Bland | Comparing methods of measurement: why plotting difference against standard method is misleading[END_REF]. The percentage of prediction between the 95% limit of agreement (±2 SD) and the error risk were computed. The mean percentage difference between cREE and mREE (bias in kcal / 24h and %) was calculated.

Formula derivation and validation

The entire sample was split at random into a derivation and a validation subsample. The construction of the formula for REE in ALS patients was based on the following steps using the derivation sample : (i) detection and elimination of outliers, decision based on the Cook's D influence statistics (threshold 4/n); (ii) simple linear regression analysis considering mREE as the dependent variable and the following independent variables : age, sex, height, weight, independent variables those with a p-value <0.20 in the simple regression, the first model was simplified step by step, confounders were checked at each step; (iv) check of the linear nature of the relation between dependent and independent variables; (v) evaluation of the normality (using Shapiro-Wilk test and Kernel and qq plot graphs) and homoscedastisticy (White test = 0.42) of the residuals of the final model; (vi) check for any misspecification of the final model (vii) check for multicollinearity among independent variables included in the final model, (viii) check for interaction between independent variables. Based on the coefficient of the multiple linear regression, REE was estimated in the validation sample. Assessment of the agreement between mREE and REE estimated by our equation was based on the above mentioned strategy.

Results

Study sample

From November 1996 to November 2014, 405 ALS patients had IC. Ninety patients were excluded: 35 for a RQ < 0.7 or > 0.87; 30 because the time lag between IC and nutritional assessment was over 1.5 months; and 25 because the delay between diagnosis and IC was over 12 months. The flowchart of patients included and not included is shown in Figure 1.

The 315 included patients had a median age at diagnosis of 65.9 years (56.5 -73.7), with a sex ratio of 1.0. The median delay between diagnosis and nutritional assessment was 4.3 months (2.2 -6.6). The median mREE with IC was of 1503 kcal /24h (1290 -1698). The nutritional, and neurological characteristics of the patients included are presented in Table 2.

cREE accuracy

The results of cREE prediction with the 11 REE formulas in the entire sample (n=315) are presented in Table 3. The analysis found moderate agreement between mREE and cREE, with an ICC range between 0.60 (-0.07 -0.84) and 0.71 (0.54 -0.81).

Figure 2 shows the Bland and Altman plots for the 11 formulas. With a threshold of ± 10% difference between mREE and cREE, the proportion of accurate prediction ranged between 27.3% and 57.5%. An underestimation of REE (REE variation < 10%) was found in 31.7% to 71.4% of cases.

ALS-specific REE formula derivation and validation

Given these results (high percentage of underestimation of REE formula in ALS patients) we attempted to create a new formula. Some patients were excluded from the derivation and validation subsamples due to lack of BIA measurement and others were excluded from the derivation because they had been detected as outliers (hence their inclusion was not desirable). Both subsamples displayed a high level of comparability only with BMI, which was slightly higher in the derivation sample compared to the validation sample: 24.8 kg/m 2 (22.3 -27.7) vs. 23.6 kg/m 2 (21.8 -26.5), respectively (p = 0.047) (Table 2).

After the simple linear regression analysis, age, sex, height, weight, FM, FFM and PA assessed using BIA were considered to enter the first multiple linear regression model (pvalues <0.0001 for all these variables, except for FM: p = 0.0014). After a step by step simplification of the model, age, sex, FM and FFM were retained in the final model (p-values <0.0001 for all these variables, except for age: p = 0.004). The graphical evaluation of the linear nature of the relation between the dependent and the independent variables was satisfactory. The residuals of the model were considered as normally distributed (Shapiro Wilk test p = 0.58, satisfactory Kernel and qq plot graphs) and with a constant error variance (White test p = 0.42). The model was shown to be correctly specified, there was no multicollinearity or interaction between dependent variables. In the validation sample, our formula was compared to the 11 other REE formulas (Table 4) and to mREE; results were the same as for the entire sample. The ICC between mREE and REE estimated using our formula was 0.85 (0.79 -0.89) (i.e. very good agreement) (Table 3).

Figure 3 shows the Bland and Altman plots for the 11 formulas and our new formula in the validation sample. With the threshold of ± 10% of mREE, the percentage of accurate prediction was 65% (-347.7 to 304.4 kcal / 24h) with only 17.5% underestimation. Accurate prediction was significantly higher with our formula than eight of the other 11 formulas used, 45.5%, 49.7%, 49.0%, 51.7%, 34.3%, 26.6%, 30.1% and 43.4% for HB 1919, HB 1984, WSchofield, De Lorenzo, Johnstone, Mifflin, Wang and Rosenbaum, respectively (p = 0.0009, p = 0.0085, p = 0.006, p = 0.023, p < 0.0001, p < 0.0001, p < 0.0001 and p = 0.0002 respectively). However, though lower than our formulas, accurate prediction was not significantly different with WHO/FAO, Owen and Fleisch (55.2%, p = 0.09, 56.6%, p = 0.15 and 55.9%, p = 0.12, respectively). Underestimation was significantly lower with our formula (17.5%) than the 11 formulas used 51.0%, 46.2%, 45.5%, 44.8%, 62.9%, 71.3%, 34.3%, 33.6%, 39.9%, 66.6%, and 50.3% for HB 1919, HB 1984, WSchofield, De Lorenzo, Johnstone, Mifflin, WHO/FAO, Owen, Fleisch, Wang and Rosenbaum, respectively (p < 0.0001, p < 0.0001, p < 0.0001, p < 0.0001, p < 0.0001, p < 0.0001, p = 0.001, p = 0.002, p < 0.0001, p < 0.0001 and p < 0.0001, respectively).

Discussion

This study is the first to consider the accuracy of 11 REE formulas in a large sample of ALS patients (n=315), with the creation of an ALS-specific REE formula which was validated in an independent subsample. Assessment of the level of REE in ALS patients is important as it helps to better match the diet to the metabolic disorders present in ALS. This allows to better adapt energy intake in case of hypermetabolism, which is found in 50-60% during this disease according to HB 1919 to predict cREE [START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF]. If this adjustment is not made, patients are exposed to weight loss and accelerated development of undernutrition, which is an important risk factor for death in ALS [START_REF] Marin | Alteration of nutritional status at diagnosis is a prognostic factor for survival of amyotrophic lateral sclerosis patients[END_REF][START_REF] Marin | Population-Based Evidence that Survival in Amyotrophic Lateral Sclerosis Is Related to Weight Loss at Diagnosis[END_REF][START_REF] Desport | Nutritional status is a prognostic factor for survival in ALS patients[END_REF]. In addition, better food intake could allow increased FM, which is a positively associated with survival (1). The reference measurement method for REE, indirect calorimetry, is often unavailable in clinical practice due to lack of equipment. Even if it is possible, it is still time consuming. For these reasons, reliable predictive formulas are important. HB 1919 formulas are frequently used to assess energy need in various diseases including ALS [START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Sherman | Standard Equations Are Not Accurate in Assessing Resting Energy Expenditure in Patients With Amyotrophic Lateral Sclerosis[END_REF][START_REF] Kasarskis | Estimating daily energy expenditure in individuals with amyotrophic lateral sclerosis[END_REF][START_REF] Siirala | Predictive equations overestimate the resting energy expenditure in amyotrophic lateral sclerosis patients who are dependent on invasive ventilation support[END_REF][START_REF] Shimizu | The measurement and estimation of total energy expenditure in Japanese patients with ALS: a doubly labelled water method study[END_REF][START_REF] Takemura | Energy metabolism and nutritional status in hospitalized patients with lung cancer[END_REF][START_REF] Oliveira | Comparison of resting energy equations and total energy expenditure in haemodialysis patients and body composition measured by multi-frequency bioimpedance[END_REF][START_REF] Kruizenga | Predicting resting energy expenditure in underweight, normal weight, overweight, and obese adult hospital patients[END_REF]. Sherman et al. alone performed, in 2004, a Bland and Altman analysis to compare HB 1919 formulas with mREE in IC in a small sample of 34 ALS patients with and without ventilation [START_REF] Sherman | Standard Equations Are Not Accurate in Assessing Resting Energy Expenditure in Patients With Amyotrophic Lateral Sclerosis[END_REF]. HB 1919 are not adapted to predict REE of ALS patient. Other studies published focused on mREE and cREE are presented in Table 5.

In our study we found a mREE in IC of 1514 ± 283 kcal / 24h in agreement with the literature [START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Vaisman | Do patients with amyotrophic lateral sclerosis (ALS) have increased energy needs?[END_REF][START_REF] Kasarskis | Estimating daily energy expenditure in individuals with amyotrophic lateral sclerosis[END_REF]. Sherman et al. reported slightly lower results in 16 non-ventilated patients [START_REF] Sherman | Standard Equations Are Not Accurate in Assessing Resting Energy Expenditure in Patients With Amyotrophic Lateral Sclerosis[END_REF]. This discrepancy may be due to differences in the IC apparatus used. Our study shows that, in a large population of ALS patients, the 11 predictive formulas used are not adapted to ALS patients. The main problem with these formulas is underestimation of the energy requirement in 31.7% to 71.4% of patients, with a real risk of inadequate energy intake, which can lead to weight loss and undernutrition. Reasons for this maladjustment are probably diverse. The main issue is the absence of validation of these REE formulas in ALS patients with alteration of the body composition. Indeed, ALS, patients lose FFM and increase their FM [START_REF] Marin | Alteration of nutritional status at diagnosis is a prognostic factor for survival of amyotrophic lateral sclerosis patients[END_REF][START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF]. In addition, the numbers of ALS patients to whom these equations were applied were sometimes low, and patient characteristics may be very different [START_REF] Funalot | High metabolic level in patients with familial amyotrophic lateral sclerosis[END_REF][START_REF] Vaisman | Do patients with amyotrophic lateral sclerosis (ALS) have increased energy needs?[END_REF][START_REF] Sherman | Standard Equations Are Not Accurate in Assessing Resting Energy Expenditure in Patients With Amyotrophic Lateral Sclerosis[END_REF]. Given these difficulties, we created a new formula that allows for better prediction and less underestimation of REE in ALS patients. This formula integrates body composition data (FFM and FM) obtained with impedancemetry according to a validated method which is easy, fast and noninvasive for ALS patients [START_REF] Desport | Validation of bioelectrical impedance analysis in patients with amyotrophic lateral sclerosis[END_REF]. Moreover, body composition is a better reflection of nutritional status than weight and height used in several REE predictive formula. REE is therefore related to FFM.

The recent ESPEN guidelines for ALS, propose to use HB 1919 equations to assess energy needs in the absence of IC [START_REF] Burgos | ESPEN guideline clinical nutrition in neurology[END_REF]. But because of the poor agreement of HB 1919 formulas in ALS, an ALS-specific formula seems necessary. In absence of IC, this new formula could be used easily in clinical practice to diagnose hypermetabolism at onset of the disease and to adapt energy needs in ALS during follow up.

However, there are several limitations to our study. Although the ALS referral center follows 88.2% of ALS patients in our region, this population is not totally representative of patients in the region and country [START_REF] Marin | Population-based epidemiology of amyotrophic lateral sclerosis (ALS) in an ageing Europe -the French register of ALS in Limousin (FRALim register)[END_REF]. There is therefore a selection bias. Moreover, it would be desirable to validate the new formula in a sample of ALS patients from another center and in a population-based setting if possible. This new formula found a poor REE prediction for 35% of patients, suggesting that other elements determining REE of ALS patients were not taken into account (R 2 of the model was 76%). These remain to be discovered [START_REF] Ioannides | Anthropometric measures are not accurate predictors of fat mass in ALS[END_REF], as it is known that neither the intensity of the fasciculations, smoking, nor any inflammatory or infectious condition is implicated [START_REF] Desport | Hypermetabolism in ALS: Correlations with Clinical and Paraclinical Parameters[END_REF][START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Ioannides | Anthropometric measures are not accurate predictors of fat mass in ALS[END_REF]. Cortical hyperexcitability could be related to metabolic dysfunction in ALS and could increase glucose metabolism in the brains of ALS patients [START_REF] Cistaro | Brain hypermetabolism in amyotrophic lateral sclerosis: a FDG PET study in ALS of spinal and bulbar onset[END_REF][START_REF] Buhour | Voxel-based mapping of grey matter volume and glucose metabolism profiles in amyotrophic lateral sclerosis[END_REF]. However, there is currently no recognised link between REE in indirect calorimetry and brain hypermetabolism. It is therefore difficult to integrate this parameter into a REE predictive formula used in daily practice. We did not calculate the sample size a priori but verified that the power was sufficient given the size of the study. For example, the linear regression used for formula derivation was at least of 80% even considering an independent variable that would be weakly correlated to the dependent variable (r=0.25, e.g.).

Conclusion

When REE formulas for healthy people are used in ALS patients, they provide an accurate prediction of REE (± 10% of mREE) in less than 58% of cases, with a high level of underestimation up to 71% of cases. These formulas are not adapted to predict REE in ALS patients, and their use can lead to underestimation of energy need with weight loss and malnutrition, which are important prognosis factors in ALS. The creation of an ALS-specific REE formula using body composition allows prediction of REE in 65% of cases with only 17.5% underestimation. Agreement between mREE and estimated REE using the formula was very good (0.85). This formula can therefore be used to predict REE in clinical practice in ALS patients if indirect calorimetry is not available. Validation in another independent sample of ALS patients is required.

  database of the ALS expert center, which has been validated by the Commission Nationale de l'Informatique et des Libertés (CNIL; No. 1244525). Patients gave given informed consent for data collection. The ClinicalTrial registration number is NCT03378375. Nutritional assessments: General data collected were: sex, date of diagnosis, date of calorimetry. Nutritional assessment was carried out in the nutrition unit after diagnosis in the Nutrition Unit. Patients were weighed (to 0.1 kg) in underwear using a SECA ® electronic balance (Vogel & Halke, Hamburg, Germany) in an upright position or on a SECA ® weighing chair if they could not stand upright. Usual weight 6 months before onset of symptoms was collected allowing the calculation of the percentage of initial weight loss relative to the usual weight.

  The formula based on the coefficient of the model from the derivation sample (130 patients) appeared as follows: cREE (kcal/24h) = 901.34 -(5.82 * age [years]) + (15.65 * FFM [kg]) + (8.88 * FM [kg]) +145.21 if men. The R-square of the model was 76%.

  requirements and the body cell mass. Am J Clin Nutr. 1984;40(1):168-82. 40. Johnstone AM, Rance KA, Murison SD, Duncan JS, Speakman JR. Additional anthropometric measures may improve the predictability of basal metabolic rate in adult subjects. Eur J Clin Nutr. 2006;60(12):1437-44. 41. Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr. 1990;51(2):241-7.

Figure 1 :

 1 Figure 1: Flowchart of patients with ALS included in the study.

Figure 2 :Figure 3 :

 23 Figure 2: Bland and Altman graphics between calculated resting energy expenditure with the

Figure 1 :

 1 Figure 1: Flowchart of patients with ALS included in the study.

Figure 2 :Figure 3 :

 23 Figure 2: Bland and Altman graphics between calculated resting energy expenditure with the 11 formulas and measured resting energy

Harris& 5 - 35 -

 535 Benedict 1919 (38) -Male: (Weight (kg) * 13.7516) + (Height (cm) * 5.0033) -(Age (years) * 6.755) + 66.473 -Female: (Weight (kg) * 9.5634) + (Height (cm) * 1.8496) -(Age (years) * 4.6756) + 655.0955 Harris & Benedict 1984 (39) -Male: (Weight (kg) * 13.397) + (Height (cm) * 4.799) -(Age (years) * 5.677) + 88.362 -Female: (Weight (kg) * 9.247) + (Height (cm) * 3.098) -(Age (years) * 4.33) + 477.593 World Schofield(20) -Male of 18 -30 years: (0.063 * Weight (kg)) + 2.896 -Male of 30 -60 years: (0.048 * Weight (kg)) + 3.653 -Male > 60 years: (0.049 * Weight (kg)) + 2.459 -Female of 18 -30 years: (0.062 * Weight (kg)) + 2.036 -Female of 30 -60 years: (0.034 * Weight (kg)) + 3.538 -Female > 60 years: (0.038 * Weight (kg)) + 2.755 De Lorenzo(20) -Male: (53.284 * Weight (kg)) + (20.957 * Height (cm)) -(23.859 * Age (years)) + 487 -Female: (46.322 * Weight (kg)) + (15.744 * Height (cm)) -(16.66 * Age (years)) + 944 Johnstone (40) (90.2 * FFM (kg)) + (31.6 * FM (kg)) -(12.2 * Age (years)) + 1613 Mifflin St. Jeor (41) -Male: (9.99 * Weight (kg)) + (6.2 * Height (cm)) -(4.92 * Age (years)) + Female: (9.99 * Weight (kg)) + (6.2 * Height (cm)) -(4.92 * Age (years)) -161 WHO/FAO (17) -Male of 18 -30 years: (15.4 * Weight (kg)) -(27 * Height (cm)) + 717 -Male of 31 -60 years: (11.3 * Weight (kg)) + (16 * Height (cm)) + 901 -Male of > 60 years: (8.8 * Weight (kg)) + (1128 * Height (cm)) -1071 -Female of 18 -30 years: (13.3 * Weight (kg)) + (334 * Height (cm)) + Female of 31 -60 years: (8.7 * Weight (kg)) -(25 * Height (cm)) + 865 -Female of > 60 years: (9.2 * Weight (kg)) + (637 * Height (cm)) -302 Owen (17) -Male: 879 + 10.2 * Weight (kg) -Female: 795 + 7.18 * Weight (kg) Fleisch (17) -Male: 24 * BSA * (38 -0.073 * (Age (years) -20)) -Female: 24 * BSA * (35.5 -0.064 * (Age (years) -20)) Wang (17) 24.6 * FFM (kg) +175 Rosenbaum (17) (17.2 * FFM (kg)) + (10.5 * FM (kg)) + 375 New formula 901.34 -(5.82 * Age (years)) + (15.65 * FFM  (kg)) + (8.88 * FM  (kg)) + 145.21 if men BSA: body surface area = 0.007184 * (Height (cm) 0.725 ) * (Weight (kg) 0.425 ); FFM: fat-free mass; FM: fat mass; WHO/FAO: world health organization / food and agriculture organization of the United Nations.  body composition measured in bioelectrical impedancemetry with Desport et al. validated formula (26).

Table 1 :

 1 Resting energy expenditure formulas tested and new formula constructed.

Table 2 :

 2 Nutritional characteristics of included patients.

	Criteria	Entire sample	MD	Derivation	sample	(to	Validation sample (to test	p
		Median (IQR) ; n (%)		construct REE formula)		REE formula)
		n = 315		Median (IQR) ; n (%)		Median (IQR) ; n (%)
				n = 130			n = 143
	Age at diagnosis (years)	65.9 (56.5 -73.7)	0	66.1 (56.5 -73.9)		65.3 (56.4-72.3)	0.48
	Age at calorimetry (years)	66.6 (56.9-74.1)	0	66.7 (56.9 -74.3)		66.2 (57.0 -73.5)	0.47
	% male	161 (51.1)	0	65 (50.0)			72 (50.3)	0.95
	ALSFRS-R (points)	40 (35 -43)	24	36 (33 -40)			34 (31 -41)	0.23
	Weight (kg)	65.0 (57.3 -74.7)	0	64.3 (57.3 -74.4)		65.0 (58.0 -73.6)	0.91
	BMI (kg / m 2 )	24.2 (22.0 -27.6)	0	24.8 (22.3 -27.7)		23.6 (21.8 -26.5)	0.047
	FFM (kg)	44.4 (36.9 -51.9)	28	42.7 (36.2 -51.9)		44.8 (37.1 -51.5)	0.63
	FM (kg)	20.7 (15.2 -25.4)	28	21.0 (17.0 -25.5)		19.9 (13.9-24.6)	0.17
	PA (°)	3.0 (2.4 -3.7)	31	3.0 (2.4 -3.6)			3.0 (2.4 -3.7)	0.88
	mREE (kcal / 24h)	1503 (1290 -1698)	0	1455 (1266 -1683)		1503 (1320 -1678)	0.39
	cREE HB1919 (kcal / 24h)	1327 (1190 -1497)	0	1293 (1182 -1480)		1327 (1190 -1495)	0.58

Table 3 :

 3 Prediction of calculated resting energy expenditure with the 11 formulas compared to measured resting energy expenditure in the entire sample (n=315).

	6

Table 4 :

 4 Prediction of calculated resting energy expenditure with the 11 formulas and the constructed formula compared to measured resting energy expenditure in the validation sample (n = 143). : comparison cREE CF vs other cREE formulas p <0.05 CI: confidence interval; C-M: calculated REE minus measured REE; HB: Harris & Benedict; ICC: intraclass correlation coefficients; IQR: interquartile range; Mifflin: Mifflin St. Jeor; PA: phase angle; REE: resting energy expenditure; cREE: calculated resting energy expenditure; SD: standard deviation; WHO/FAO: world health organization / food and agriculture organization of the United Nations; WSchofield: World

	REE	Bias	95% limits of agreement

*

Table 5 :

 5 Studies on patients with amyotrophic lateral sclerosis with measured and calculated resting energy expenditure and bias.

	First autor /	Number of patients Age (years)	Weight (kg)	FFM (kg)	Height (cm)	mREE (kcal / 24h)	cREE (kcal / 24h)	Bias (%)
	years		Mean ± SD	Mean ± SD	Mean ± SD	Mean ± SD or	Mean ± SD or	Mean ± SD or median (IQR)	Mean ± SD
			or median	or median		median (IQR)	median (IQR)		or median
			(IQR)	(IQR)					(IQR)
	Sherman et	Ventilated: 18	67.2 ± 3.2	70.6 ± 15.6	-	172.0 ± 10.0	1654.9 ± 362.9	HB 1919: 1461.0 ± -	-10.1 ± 17.6
	al. / 2004	Non ventilated: 16	56.2 ± 14.5	76.2 ± 26.6	-	169.6 ± 10.8	1340.8 ± 471.6	HB 1919: 1505.0 ± -	18.6 ± 24.9
	(16)6)
	Desport et al.	168	-	64.5 ± 13.9	43.8 ± 10.7*	162.5 ± -	1521.9 ± 307.5	HB 1919: 1334.0 ± 234.7	-12.3 ± -#
	/ 2005 (9)9)
	Bouteloup et	61	64.3 ± 9.9	-	43.8 ± 11.6*	-	1449.0 ± 300.7	HB 1919: 1315.5 ± 242.2	-9.2± -#
	al. / 2009
	(10)0)
	Siirala et al. /	Ventilated: 5	55 (50 -76) 83 (58 -98)	-	177 (155 -192) 1060 (960 -1480)	HB 1919: 1580 (1190 -	49.1 (-) #
	2010(21)4)							2020)	56.2 (-) #

Acknowledgements:

We thank the Mr Francis William for the translation of the manuscript.

Authors' contributions:

PJ, PC, JCD and BM designed the research; PJ, PF, HS, GL, PC and JCD conducted the research; PJ, PF, MN, GL, PC and JCD provided essential materials (databases); PJ and BM performed statistical analysis; PJ, PF, PMP, PC, JCD, BM wrote the paper; PJ and BM had primary responsibility for the final content. All authors read and approved the final manuscript.

Conflict of Interest (COI) Statement:

Authors had no financial or personal relationships with companies or organizations sponsoring the research at the time it was carried out.

Source of support: none

# Bias not calculated in the study, a posteriori calculation with mean or median cREE and mREE. FFM: fat-free mass (*: in bioimpedance analysis); HB:


D Franco

E López

F Vargas

Hélène Ageorges

Tribological performance at high temperatures of alumina coatings applied by plasma spraying process onto a refractory material

Keywords:

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

INTRODUCTION

Atmospheric Plasma Sprayed (APS) alumina coatings show good performance against abrasive, corrosive and erosive wear at extreme conditions of temperature, oxidation and pressure [START_REF] Rong | Comparative tribological study of plasma sprayed alumina and alumina-yttria under severe conditions[END_REF][START_REF] Manojkumar | Sliding wear behaviour of alumina coatings prepared from mechanically milled powders[END_REF][START_REF] Yang | Study on erosion-wear behavior and mechanism of plasma-sprayed alumina-based coatings by a novel slurry injection method[END_REF]. This is the reason why they have been widely used in applications of high exigency such as automotive, aeronautic and primary industry [START_REF] Tingaud | Microstructure and tribological behavior of suspension plasma sprayed Al 2 O 3 and Al 2 O 3 -YSZ composite coatings Microstructure and tribological behavior of suspension plasma sprayed Al 2 O 3 and Al 2 O 3 -YSZ composite coatings[END_REF][START_REF] Bolelli | Plasma-sprayed graded ceramic coatings on refractory materials for improved chemical resistance[END_REF][START_REF] Bartuli | Thermal spraying to coat traditional ceramic substrates: Case studies[END_REF]. Specifically, alumina coatings are commonly used for wear resistance due to their high hardness at room temperature [START_REF] Singh | A study on sliding and erosive wear behaviour of atmospheric plasma sprayed conventional and nanostructured alumina coatings[END_REF]. However, the hardness of alumina materials decreases at high temperatures as a result of micro-structural slips activated by the temperature and developed with the applied stresses [START_REF] Sánchez-González | Temperature dependence of mechanical properties of alumina up to the onset of creep[END_REF], which is more accentuated by the presence of other oxides [9], which in turn could affect the tribological performance of alumina coatings exposed at high temperature.

Glass and cement industries use refractories subjected to extreme conditions of wear (sliding, abrasion, erosion, etc.) at high temperatures (>1000 °C), which require the employment of expensive electro-melted Al 2 O 3 refractories [START_REF] Guzmán | Corrosion-erosion wear of refractory bricks in glass furnaces[END_REF]. In order to decrease the wear of the materials involved with a lower cost, different solutions have been proposed [START_REF] Bolelli | Plasma-sprayed graded ceramic coatings on refractory materials for improved chemical resistance[END_REF][START_REF] Bartuli | Thermal spraying to coat traditional ceramic substrates: Case studies[END_REF][START_REF] Khattab | Alumina-Zircon refractory materials for lining of the basin of glass furnaces: Effect of processing technique and TiO 2 addition[END_REF][START_REF] Liang | Dynamic slag/refractory interaction of lightweight Al 2 O 3 -MgO castable for refining ladle[END_REF][START_REF] Seifert | New Techniques for the Determination of Refractory Material Properties at High Temperatures[END_REF][START_REF] Bolelli | Plasma-sprayed glass-ceramic coatings on ceramic tiles: microstructure, chemical resistance and mechanical properties[END_REF]. Among these, thermally sprayed coatings could be an alternative solution to protect the cheap pressed & sintered refractories against tribological failures produced at high temperature. Previous studies have indicated that plasma sprayed ceramic coatings have been manufactured onto pressed & sintering refractory substrates, increasing their useful life when they are exposed to corrosive environments at high temperature and increasing the wear resistance of substrates at room temperature [START_REF] Bolelli | Plasma-sprayed graded ceramic coatings on refractory materials for improved chemical resistance[END_REF][START_REF] Bartuli | Thermal spraying to coat traditional ceramic substrates: Case studies[END_REF][START_REF] Bolelli | Plasma-sprayed glass-ceramic coatings on ceramic tiles: microstructure, chemical resistance and mechanical properties[END_REF].

The tribological performance of polycrystalline α-Al 2 O 3 bulk materials has been studied indicating that until ≈ 800 ºC, the wear is produced by brittle deformation [START_REF] Woydt | High temperature tribology of ceramics[END_REF][START_REF] Yust | Observations on the sliding wear of ceramics[END_REF][START_REF] Dong | Tribological characteristics of α-alumina at elevated temperatures[END_REF]. This last one is developed when the speed and the load applied on the material overcome its mechanical resistance, generating detachment of large and sharp particles, which acts as a third body resulting in high wear rate [START_REF] Holmberg | Tribology of engineered surfaces[END_REF][START_REF] Stachowiak | Wear of non-metallic materials[END_REF]. On the other hand, at higher temperatures, a plastic flux is produced in the material and then, little rounded particles are detached from the surface, producing a protective layer, which reduces the wear rate of the material and is known as ductile deformation [START_REF] Dong | Tribological characteristics of α-alumina at elevated temperatures[END_REF][START_REF] Holmberg | Tribology of engineered surfaces[END_REF][START_REF] Stachowiak | Wear of non-metallic materials[END_REF].

The tribological performance of these materials could be related to the microstructure, the phases and their mechanical properties, and in plasma sprayed coatings, these properties are usually different to those in bulk materials due to the fast heating and quenching during the manufacturing of coatings.

The goal of this work is to evaluate the tribological behavior at different temperatures of two thermally sprayed Al 2 O 3 coatings, with different structures and phase compositions, comparing the results with those obtained from both, an electro-melted Al 2 O 3 bulk refractory used as reference, and a conventional pressed & sintered silico-aluminous refractory used as substrate, which were tested under the same conditions that the coatings.

The first comparison is justified because the literature about wear performance of thermally sprayed Al 2 O 3 coatings for temperatures as high as those used in this work is poor, and therefore, only there is available information about Al 2 O 3 bulk materials. And the second comparison aims to determine the potential application of the Al 2 O 3 coatings as a possible way to protect the cheap pressed & sintered refractories, to replace the expensive electro-melted ones subjected to extreme abrasive conditions, but without structural requirements, commonly used in high exigency applications such as: glass, cement and other primary industries.

Wear tests were performed using a ball-on-disk test under dry sliding conditions from room temperature until 1000 °C, and changes in crystalline phases, porosity, micro-hardness, Young's modulus and fracture toughness experienced by the materials due to their heating during tribological tests were also evaluated.

MATERIALS AND METHODS

A Sulzer-Metco PTF4 TM plasma torch was used to spray the alumina coatings according to the parameters listed in Table 1. Two different Al 2 O 3 feedstock powders were used, the first one was constituted by submicrometric agglomerated particles, and the second one was constituted by fused & crushed particles. The substrate was a commercial pressed & sintered silico-aluminous refractory brick, which was cut in shape of discs 25 mm in diameter and 7 mm in height. The arithmetic average of the surface roughness (Ra) was 12 ± 1.1 µm for the substrates, and for this reason, it was not necessary to apply a jet of abrasive particles to give them greater roughness. Therefore, only an air jet 6 bar of pressure was applied to remove particles detached from the surface.

The chemical composition and the crystallographic phases of the feedstock powders, as well as of both, the silico-aluminous refractory used as substrate and the electro-melted alumina refractory used as reference were determined using a Thermo Fisher SCIENTIFIC ARL TM OPTIM'X Wavelength-Dispersive X-Ray Fluorescence (WD-XRF) spectrometer and a Bruker D8 ADVANCE X-Ray Cu Kα 1 radiation (DRX) Diffractometer respectively, using the Rietveld method for the quantification of the phases. The particle size distribution of feedstock powders was determined with a Horiba PARTICA LA-950V2 Laser Diffraction (LD) equipment. The shape of the particles, the cross sections, the surface of both coatings and the refractories, as well as the wear tracks were analyzed by Scanning Electronic Microscopy (SEM) using a JEOL JSM IT-300 LV equipment. The cross sections and surfaces of the coatings, as well as the refractories were grinded and polished according to the ASTM E1920 standard [START_REF] Astm E | Standard Guide for Metallographic Preparation of Thermal Sprayed Coatings[END_REF] in order to obtain an arithmetic average roughness (Ra) lower than 0.2 µm. The porosity was measured on the cross sections of the coatings and refractories from images taken by SEM according the indications of the ASTM E2109 standard [START_REF] Astm E | Standard Test Methods for Determining Area Percentage Porosity in Thermal Sprayed Coatings[END_REF] and using Image J software. Mechanical properties before and after the wear tests of all samples were determined from indentations carried out on the polished surface using a Shimadzu HMV-G 20 equipment, according with the ASTM C-1327 [START_REF] Astm C- | Standard Test Method for Vickers Indentation Hardness of Advanced Ceramics[END_REF] and ASTM E-384 [START_REF]Standard Test Method for Microindentation Hardness of Materials[END_REF] standards. The Vickers micro-hardness, the Young's modulus and the fracture toughness from the Anstis model were calculated according to the Eq. ( The wear tests were performed at 25, 500, 750 and 1000 ºC with a ball-on-disk tribometer, under a dry sliding contact, without eliminating the formed debris. The wear test conditions are shown in Table 2 following some of recommendations of ASTM G-99 standard [START_REF] Astm G | Standard Test Method for Wear Testing with a Pin-on-Disk Apparatus[END_REF].

Then, the physical features of the wear tracks on the samples and the morphology of the debris produced in the wear tests were analyzed by SEM using the same equipment aforementioned, equipped with an Energy Dispersive Scanning (EDS) with an Oxford

Instruments SDD X-MaxN 80 detector, which was used to determine the chemical elemental composition of these debris. Finally, the wear rate was calculated from the profile curves of wear tracks measured on the samples using a Surtronic S125 profilometer, as well the Eq. ( 4).

%& = ' ( 1000 ) *

Eq. ( 4)

Where %& is the wear rate [mm 3 /N.m], ' ( is the wear track cross section area [µm 2 ], is the applied normal load [N] and ) * is the total cycle number.

After tribological tests, the porosity, the crystalline phases, the micro-hardness, the Young's modulus and the fracture toughness of all samples (coatings and refractories) were evaluated again with the same equipments, standards and equations aforementioned, in order to compare the values with those obtained before the wear tests. Each measured property was determined before and after the wear tests over 3 samples, 10 times over each sample, guaranteeing statistical reproducibility and repeatability for all measurements respectively.

RESULTS AND DISCUSSION

The chemical composition, the particle size distribution and the crystallographic phases of the feedstock powders used to manufacture the coatings are shown in Table 3. The 4) characteristic of electro-melting processes of manufacturing.

The surface analysis of as-sprayed Al 2 O 3 coatings (Figures 3 a-b) evidenced the continuous stacking of micrometrical splats typical of thermal sprayed coatings, indicating that these layers seal the pores of the silico-aluminous refractory. Additionally, on the surface coating sprayed from the agglomerated powder feedstock, sub-micrometrical particles were identified into some splats. (Figure 3 a). Furthermore, the cross-section analysis (Figures 3 c-d) allowed to establish that the thickness of both coatings was similar, 370 ± 20 µm for the coating sprayed from the agglomerated powder feedstock and 355 ± 20 µm for that made from the fused & crushed powder feedstock. Concerning the porosity (Table 5), it is possible to see that the values before and after the wear tests for all materials and all temperatures evaluated are statistically the same (all p-values are > 0.05), evidencing that there were no sintering processes.

The XRD results indicated that in both alumina coatings, α-Al 2 O 3 , γ-Al 2 O 3 [START_REF] Murray | Suspension High Velocity Oxy-Fuel (SHVOF) -Sprayed Alumina Coatings: Microstructure, Nanoindentation and Wear[END_REF][START_REF] Di Girolamo | Microstructure and mechanical properties of plasma sprayed alumina-based coatings[END_REF][START_REF] Tesar | Development of suspension plasma sprayed alumina coatings with high enthalpy plasma torch[END_REF][START_REF] Sabiruddin | Analysis of phase transformation in plasma sprayed alumina coatings using Rietveld refinement[END_REF] and amorphous phase were the predominant phases (Figure 4 a-b, Table 6). In the electromelted Al 2 O 3 reference refractory used as reference, α-Al 2 O 3 was the main phase (Figure 4 c, Table 6). In the uncoated silico-aluminous refractory used as substrate, mullite and silica phases were prevalent (Figure 4 d, Table 6). It is important to notice that after the spraying process for both Al 2 O 3 coatings, the α-Al 2 O 3 from the powder feedstock became mainly in γ-Al 2 O 3 in the as-sprayed coatings. This behavior is due to the initial features of feedstock powders (Table 3) and the spraying parameters (Table 1) as it was previously mentioned by other authors [START_REF] Di Girolamo | Microstructure and mechanical properties of plasma sprayed alumina-based coatings[END_REF][START_REF] Tesar | Development of suspension plasma sprayed alumina coatings with high enthalpy plasma torch[END_REF][START_REF] Sabiruddin | Analysis of phase transformation in plasma sprayed alumina coatings using Rietveld refinement[END_REF]. Concerning the mechanical properties (Table 7), the micro-indentation results allowed establishing that the micro-hardness of the alumina coatings manufactured from the agglomerated powder feedstock is slightly lower than that of the alumina coating manufactured from the fused & crushed powder feedstock. For both coatings, the values of micro-hardness before and after the wear tests performed at 25, 500 and 750ºC are statistically the same (p-values are > 0.05). While at 1000ºC, there are differences statistically significant (p-value are < 0.05), due to these hardness significantly increased after their heating at 1000 °C during the wear tests (Table 7), which, could be related with the increasing in the α-Al 2 O 3 level produced (Table 6, Figure 4 a-b) [START_REF] Tingaud | Microstructure and tribological behavior of suspension plasma sprayed Al 2 O 3 and Al 2 O 3 -YSZ composite coatings Microstructure and tribological behavior of suspension plasma sprayed Al 2 O 3 and Al 2 O 3 -YSZ composite coatings[END_REF][START_REF] Singh | A study on sliding and erosive wear behaviour of atmospheric plasma sprayed conventional and nanostructured alumina coatings[END_REF][START_REF] Heintze | Preparation and structures of plasma-sprayed γ-and α-A1 2 O 3 coatings[END_REF].

Particularly, for both coatings the quantities of α-Al 2 O 3 detected are obtained by two ways:

1) Keeping the corundum phase of powder feedstock during thermal spraying process and 2) Promoting the formation of more corundum phase during the wear tests. The first way is explained through the presence of un-melted particles into the coating, which allow keeping the initial features of the alumina powders. Regarding the second way, the high temperature of wear tests (1000ºC), the longtime during pre-heating (≈ 2 h), the wear tests (≈ 2 h) and the cooling (≈ 2 h) of the coatings into the furnace allow to produce the thermodynamic conditions that promote the formation of α-Al 2 O 3 phase [START_REF] Chráska | Alumina-base plasma-sprayed materials part I: Phase stability of alumina and alumina-chromia[END_REF][START_REF] Souza Santos | Standard Transition Aluminas[END_REF] as it is shown in Table 6 and Figure 4 a-b.

In the same way, the electro-melted Al 2 O 3 refractory used as reference showed that the hardness after wear test at 1000 °C, is slightly higher than the hardness before the test (pvalue < 0.05) (Table 7). This result could be attributed to the percentage decrease of m-ZrO 2 and amorphous secondary phases during the heating carried out for tribological test (Figure 4 c, Table 6). The m-ZrO 2 phase is a polymorph of ZrO 2 with low density and in general with low mechanical [START_REF] He | Effects of a second phase on the tribological properties of A1 2 O 2 and ZrO 2 ceramics[END_REF][START_REF] Liang | Structural, mechanical and thermodynamic properties of ZrO 2 polymorphs by first-principles calculation[END_REF][START_REF] Zhang | First principles study of structural and thermodynamic properties of zirconia[END_REF] and tribological properties. Regarding the silicoaluminous refractory used as substrate, although the levels of mullite phase increased and the amorphous phase decreased during wear test carried out at 1000 °C (Figure 4 d, Table 6), the hardness and fracture toughness values decreased (Table 7). This could be due to cohesive failures producing in highly porous materials due to their heating.

Some of the Young's modulus and the fracture toughness values measured before and after the wear tests carried out for all materials, presented change statistically significantly, however these may not be relevant to their tribological performance. particles which join forming small as island-shaped layers, that in some cases plug the wear tracks produced by the detachment. On the other hand, in the both coatings tested at 1000 ºC (Figure 5c) a continuous layer was formed on the wear track, consisting of fine particles, on which was observed a plastic flow.

X. Dong et al. [START_REF] Dong | Tribological characteristics of α-alumina at elevated temperatures[END_REF] previously studied the change in the tribological mechanism of bulk α-Al 2 O 3 as a function of temperature. They indicated that the wear was low at the beginning of the tests, with temperatures below 200 ºC and applying a normal contact stress greater than 260 MPa at 1.4 mm/s. This was due to the effect of the environmental humidity.

Whereas, from this temperature and up to 800 ºC, the wear suffered by the material was severe due to the fracture of the material in the zone of contact with the counter-body.

Finally, from this last temperature, the wear rate had become moderate again due to the formation of a protective layer. The normal stress applied at the beginning of the tribological tests carried out in this work was 210 MPa, however, there is a similarity in the morphological characteristics observed in the wear tracks of the samples tested at 25 °C (plastic flow), at 500 °C and 750 ºC (cracks and fractures), as well as, at 1000 ºC (formation of a protective layer), with those reported by X. Dong, et al. [START_REF] Dong | Tribological characteristics of α-alumina at elevated temperatures[END_REF]. Therefore, the wear stages developed in both Al 2 O 3 coatings are similar to those established by this researcher for bulk α-Al 2 O 3 materials, despite the fact that the stress applied was lower.

This can be related to the higher sliding speed of the ball on the coating (10 cm/s) compared to that of the bulk material (1.4 mm/s), as well as the predominant presence of the γ-Al 2 O 3 phase in the coatings compared to predominant presence of the α-Al 2 O 3 phase in the bulk material. It is important to notice that the hardness of γ-Al 2 O 3 is lower than that of α-Al 2 O 3 [START_REF] Aruna | Effect of critical plasma spray parameters on the microstructure, microhardness and wear and corrosion resistance of plasma sprayed alumina coatings[END_REF].

G. W. Stachowiak, et al. [START_REF] Stachowiak | Wear of non-metallic materials[END_REF] have studied the tribological behavior developed in ceramic materials from applied wear conditions (mainly speed and load) by the sliding contact with a counter-body also ceramic. They found that if the material was able to withstand the stress mechanically applied through the counter body, wear by ductile deformation through plastic flow in the track was produced. While in the case of the material did not have sufficient mechanical strength to withstand the stresses, the wear was produced by brittle deformation. In consequence, cracks and an excessive detachment of the particles were produced. In accordance with that established by W. Stachowiak, et al. [START_REF] Stachowiak | Wear of non-metallic materials[END_REF], both types of coatings studied exhibited wear by ductile deformation when they have been tested at 25 °C and 1000 ºC. But, when they were tested at 500 °C and 750 ºC, the tribological behavior is governed by brittle deformation with higher wear rates due to excessive detachment of the particles.

Despite the fact that the sliding speed (0.1 m/s) and the applied load (5 N) were the same for all tests, a transition from ductile to brittle deformation was detected in the samples evaluated at 25 °C and 500 ºC. This result is mainly related the gradual decrease in hardness experienced by alumina as a function of the increase in temperature as previously described [START_REF] Sánchez-González | Temperature dependence of mechanical properties of alumina up to the onset of creep[END_REF][9], promoting the detachment of particles. This behavior is more severe in the samples tested at 750 ºC, plugging the wear track. The gradual increase of the particles detachment with the temperature has favored the formation of a continuous layer which has protected the wear track of the tested samples at 1000 ºC, producing in this case, a wear transition from brittle to ductile deformation, in which it has been again observed plastic flow (Figure 5 c). It has been previously reported that the presence of wear debris in the friction track can reduce the contact stresses on the surface of coatings, modifying the tribological conditions and therefore the wear resistance [START_REF] Fischer | Genesis and role of wear debris in sliding wear of ceramics[END_REF]. Additionally, the increase in α-Al 2 O 3 detected after the wear tests carried out at 1000 ºC (Figure 4a-b, Table 4), may have had a contribution in the wear transition from fragile to ductile deformation, thanks to the fact that this phase is the hardest of the alumina materials.

Concerning the wear track of the electro-melted Al 2 O 3 refractory used as reference, it was detected the same change aforementioned from ductile to fragile for returning to ductile deformation again when the temperature increased (Figure 6). A bigger quantity of debris was detected despite the fact that the tests conditions applied were the same than those for the coatings. this could be due to the low fracture toughness of this material (Table 7), increasing the wear rate compared to the coatings. For its part, the pressed & sintered silico-aluminous refractory used as substrate showed wear by brittle deformation in all cases (Figure 7). This is due to the low mechanical properties of this material shown in Table 7.

The results of wear rate calculated from the track profiles produced in each sample are shown in Table 8. For both types of coatings, their wear rate at 25 ºC was of the same order of magnitude as that measured at 1000 ºC, being lower than that determined at 500 ºC and 750 ºC, this due to the ductile-fragile-ductile transition in the tribological behavior previously explained. In addition, at the different temperatures used, the coating sprayed from the agglomerated powder showed slightly lower wear rates than those manufactured from the fused & crushed powder, as well as, than the electro-melted refractory. This could be related to the superior resistance to crack propagation of this material and the detachment of nanometric particles from un-melted agglomerated grains, in accordance with the results of Y. An, et al. [START_REF] An | Mechanical and tribological properties of nano/micro composite alumina coatings fabricated by atmospheric plasma spraying[END_REF].

Regarding to the electro-melted refractory, although it has a hardness especially higher than that of the alumina coatings, its wear resistance has been lower. This result could be related, on the one hand to the excessive presence of abrasive debris between the surface and the counter-body. These debris have been analyzed by SEM-EDS, evidencing that they are angular and are composed of Al, Si, Zr and O elements from Al 2 O 3 , the SiO 2 and ZrO 2 phases which constitute the refractory, obtaining as a result, a third abrasive body into the system. On the other hand, the presence of SiO 2 and m-ZrO 2 can significantly reduce the high-temperature hardness of alumina-based materials [9, [START_REF] He | Effects of a second phase on the tribological properties of A1 2 O 2 and ZrO 2 ceramics[END_REF][START_REF] Liang | Structural, mechanical and thermodynamic properties of ZrO 2 polymorphs by first-principles calculation[END_REF][START_REF] Zhang | First principles study of structural and thermodynamic properties of zirconia[END_REF].

About the pressed & sintered refractory, it showed higher wear rates than all other materials evaluated, which is basically due to the poor mechanical properties of this material.

In addition, the values of friction coefficient (Table 8) measured during the high temperature tribological tests show a downward trend with respect to the temperature for all samples, which could be related to the detachment of fine particles, resulting in the formation of layers that can be protective at high temperatures. It is important to mention that the values obtained from the coefficient of friction are classic compared to the literature, between 0.7 and 0.9 for the alumina against alumina test [START_REF] Stachowiak | Wear of non-metallic materials[END_REF].

CONCLUSIONS

In this work, the tribological behavior at high temperature was evaluated for two different structures and phase compositions of Al 2 O 3 coatings manufactured by APS onto a pressed and sintered silico-aluminous refractory used as substrate. The results were compared with those from an electro-melted alumina refractory used as reference and they were correlated with the phase compositions, porosities and mechanical properties measured before and after the wear tests. The tests were performed using a ball-on-disk test under dry sliding conditions from room temperature until 1000 °C.

From the results and discussion, it was possible to conclude that the tribological The possible replacement of electro-melted refractories by coated pressed and sintered refractories commonly used in glass and cement industries is only recommended in places subjected to extreme abrasive conditions, but without structural requirements like the combustion ports and the entries of raw materials. --------------------1.0 ± 0.1 Na 2 O --------------------0.3 ± 0.0 CaO --------------------0. --------------------5.3 ± 0.8 c-ZrO 2 --------------------0.5 ± 0.1 Cristobalite 17.9 ± 0.8 -------------------Mullite 45.4 ± 2.4 -------------------Sillimanite 20.8 ± 1.5 -------------------Amorphous 13.6 ± 3.9 2.0 ± 0.

  chemical composition results indicate that mainly Al 2 O 3 constitute these materials, with particle size distributions between ≈ 21 µm and ≈ 64 µm. The main phase in the both feedstock powders was α-Al 2 O 3 and additionally, in the fused & crushed one a low quantity of γ-Al 2 O 3 was also detected. The morphological analysis indicated that the agglomerated powder shows rounded particles constituted by small bonded sub-micrometrical particles (Figure 1 a), evidencing that this powder was manufactured by agglomeration processes, while all particles of the fused & crushed powder were irregular with fracture marks in their surface (Figure 1 b), evidencing that this powder was manufactured by fusing and crushing processes.On the other hand, the chemical analyses carried out to both, the silico-aluminous refractory used as substrate and the electro-melted Al 2 O 3 refractory used as reference are shown in

  From statistical p-values it was established that in Al 2 O 3 coatings the quantity of amorphous phase, α-Al 2 O 3 and γ-Al 2 O 3 has a significant change in samples tribologically tested at 1000ºC (p-values < 0.05). For its part, the mullite and silica phases percentage in the uncoated silico-aluminous refractory change significantly in the specimens tested from 750 ºC. Being of all these, more relevant the increasing of α-Al 2 O 3 , from the decreasing of γ-Al 2 O 3 and amorphous phases produced in alumina coatings tested at 1000 ºC.

The tribological analysis carried

  out to both Al 2 O 3 coatings has evidenced the development of different wear mechanisms as a function of the test temperature. In both samples evaluated at 25 ºC (Figure 5 a), were identified friction marks produced by plastic flow of the asperities in their surface due to sliding contact with the alumina ball. While in those tested at 500 °C and 750 ºC (Figure 5 b) high levels of particle detachments produced by the propagation of cracks in the coatings, were observed, as well as fine and rounded

  behavior of both plasma sprayed Al 2 O 3 coatings was governed by transitions ductile-fragile-ductile similar to those showed by the electro-melted refractory used as reference and those reported by X. Dong, et al.[START_REF] Dong | Tribological characteristics of α-alumina at elevated temperatures[END_REF] for Al 2 O 3 bulk materials.The Al 2 O 3 coatings improved the wear performance of the conventional pressed & sintered silico-aluminous refractory used as substrate, even achieving the wear performance at high temperatures of the electro-melted Al 2 O 3 bulk refractory used as reference, despite le fact that the Al 2 O 3 coatings were mainly constituted by γ-Al 2 O 3 , while the electro-melted refractory was mainly constituted by α-Al 2 O 3 , which indicates that the higher fracture toughness in the coatings contribute to their good wear resistance.

Figure 7 .

 7 Figure 7. Characteristics identified on the surface of pressed and sintered refractory

32

 32

Figure 1 BED

 1 Figure 1

Figure 3 .

 3 Figure 3.

Figure 4 1

 4 Figure 4

Table 4 .

 4 The silico-aluminous refractory is constituted mainly by SiO 2 and Al 2 O 3 , while in the electro-melted one the Al 2 O 3 is the predominant oxide, which is combined with SiO 2 and ZrO 2 . The surface analysis of the silico-aluminous refractory suggests irregular

	grains with low sintering degree and therefore, low density and high porosity, 2.16 to
	2.26 g/cm 3 and 16 to 20% respectively, (Figure 2 a, Table 4) typical of pressing and
	sintering processes of manufacturing. While the structure of the electro-melted Al 2 O 3

Table 2 .

 2 Wear test conditions.

	Counter-body material	Alumina
	Counter-body hardness [GPa]	18.0 ± 0.5
	Counter-body diameter [mm]	6
	Normal load [N]	5
	Linear speed of the sample [m/s]	0.1
	Rotation speed of the sample [rpm]	18,8
	Total number of cycles	20 000
	Total distance of tests [m]	628
	Temperature of tests [°C]	25, 500, 750 and 1000

Table 3 .

 3 Main physical-chemical features of the feedstock powders.

	Properties		Agglomerated OErlikon -Metco 6103 TM	Fused & crushed OErlikon -Metco 6062 TM
		Al 2 O 3	99.9 ± 0.3	97.6 ± 0.3
	Chemical	SiO 2
	composition
	[wt%]

Table 4 .

 4 Main physical-chemical features of the refractories used as substrate and as reference.

	3 ± 0.0

Table 5 .

 5 Porosity measured before and after the wear tests for all materials evaluated.

	5

ACKNOWLEDGEMENTS

The authors are grateful to Departamento Administrativo de Ciencia, Tecnología e Innovación -Colciencias -(Bogotá -Colombia). Convocatoria Doctorado Nacional -647 de 2014 for the Doctoral Fellowship awarded to David Franco and the CODI-Committee of the University of Antioquia for its economic support given to GIPIMME Laboratory in 2018.

TABLES

2.40 ± 0.75 -------------Amorphous

LIST OF FIGURE CAPTIONS