Philippe Connes

Didier Bouix

Guillaume Py

Corinne Caillaud

Pascale Kippelen

Jean-Fre ´déric Brun

Alain Varray

Christian Prefaut

Jacques Mercier

Does exercise-induced hypoxemia modify lactate influx into erythrocytes and hemorheological parameters in athletes?

This study investigated 1) red blood cells (RBC) rigidity and 2) lactate influxes into RBCs in endurance-trained athletes with and without exercise-induced hypoxemia (EIH). Nine EIH and six non-EIH subjects performed a submaximal steady-state exercise on a cycloergometer at 60% of maximal aerobic power for 10 min, followed by 15 min at 85% of maximal aerobic power. At rest and at the end of exercise, arterialized blood was sampled for analysis of arterialized pressure in oxygen, and venous blood was drawn for analysis of plasma lactate concentrations and hemorheological parameters. Lactate influxes into RBCs were measured at three labeled [U-14 C]lactate concentrations (1.6, 8.1, and 41 mM) on venous blood sampled at rest. The EIH subjects had higher maximal oxygen uptake than non-EIH (P Ͻ 0.05). Total lactate influx was significantly higher in RBCs from EIH compared with non-EIH subjects at 8.1 mM (1,498.1 Ϯ 87.8 vs. 1,035.9 Ϯ 114.8 nmol ⅐ ml Ϫ1 ⅐ min Ϫ1 ; P Ͻ 0.05) and 41 mM (2,562.0 Ϯ 145.0 vs. 1,618.1 Ϯ 149.4 nmol ⅐ ml Ϫ1 ⅐ min Ϫ1 ; P Ͻ 0.01). Monocarboxylate transporter-1-mediated lactate influx was also higher in EIH at 8.1 mM (P Ͻ 0.05) and 41 mM (P Ͻ 0.01). The drop in arterial oxygen partial pressure was negatively correlated with total lactate influx measured at 8.1 mM (r ϭ Ϫ0.82, P Ͻ 0.05) and 41 mM (r ϭ Ϫ0.84, P Ͻ 0.05) in the two groups together. Plasma lactate concentrations and hemorheological data were similar in the two groups at rest and at the end of exercise. The results showed higher monocarboxylate transporter-1-mediated lactate influx in the EIH subjects and suggested that EIH could modify lactate influx into erythrocyte. However, higher lactate influx in EIH subjects was not accompanied by an increase in RBC rigidity.

monocarboxylate transporter; endurance; lactate metabolism; hypoxemia; hemorheology TRANSPORT OF LACTATE ACROSS the erythrocyte membrane proceeds by three distinct pathways (9): 1) nonionic diffusion of the undissociated acid; 2) an inorganic anion-exchange system, often referred to as the band 3 system; and 3) a monocarboxylate-specific carrier mechanism [START_REF] Poole | Transport of lactate and other monocarboxylates across mammalian plasma membranes[END_REF]. Juel et al. [START_REF] Juel | Human skeletal muscle and erythrocyte proteins involved in acid-base homeostasis: adaptations to chronic hypoxia[END_REF] recently showed that monocarboxylate transporter-1 (MCT-1) and band 3 expressions were increased with chronic hypoxia exposure, suggesting that these proteins may be upregulated by hypoxia.

The functional significance of the hypoxia-induced changes is likely an increase of lactate and H ϩ fluxes from plasma to erythrocyte. During sea-level exercise, some endurance-trained athletes experience arterial hypoxemia [exercise-induced hypoxemia (EIH)] that can be defined as a decrease in both oxygen arterial partial pressure (Pa O 2 ) and arterial hemoglobin saturation during exercise [START_REF] Dempsey | Exercise-induced arterial hypoxaemia in healthy human subjects at sea level[END_REF]. Miyachi and Katayama (21) have reported repeated episodes of EIH during training sessions when endurance athletes performed very intense exercise, a result suggesting that athletes develop frequent episodes of mild hypoxemia during training. One can thus think that repeated mild hypoxemia stimulus may lead to increased expression or activity of band 3 and MCT-1 proteins on the red blood cell (RBC) membranes. An increase in lactate and H ϩ fluxes into RBCs during exercise may also alter the deformability of these cells, because lactate uptake by RBCs increases their rigidity [START_REF] Smith | Lactate/H ϩ uptake by red blood cells during exercise alters their physical properties[END_REF]. These changes in RBC deformability could, in turn, alter blood rheological properties and then participate to EIH. Several studies have suggested that blood viscosity and its determinants, i.e., RBC rigidity and Hct, could be involved in pulmonary diffusion impairment [START_REF] Connes | Is hemoglobin desaturation related to blood viscosity in athletes during exercise?[END_REF][START_REF] Weiss | Effects of pentoxifylline on hemorheologic alterations induced by incremental treadmill exercise in thoroughbreds[END_REF]. First, pulmonary diffusing capacity is widely affected by RBC deformability. When deformability is artificially reduced by chemical treatment, diffusion capacity may decrease by 20% [START_REF] Betticher | Effect of RBC shape and deformability on pulmonary O2 diffusing capacity and resistance to flow in rabbit lungs[END_REF]. Second, high blood viscosity or RBC rigidity causes higher mechanical stress on the blood-gas barrier and may result in membrane disruptions. Aguilaniu et al. [START_REF] Aguilaniu | Effects of indomethacin and polyunsaturated fatty acid diet on exerciseinduced hypoxaemia in master athletes[END_REF] showed that 6 wk of a polyunsaturated fatty acid (PUFA) diet led to an upward shift in Pa O 2 in master athletes. PUFA regimens are known to improve RBC deformability and to reduce blood viscosity [START_REF] Guezennec | Influence of polyunsaturated fatty acid diet on the hemorrheological response to physical exercise in hypoxia[END_REF]; however, hemorheological measurements were not performed in this study [START_REF] Aguilaniu | Effects of indomethacin and polyunsaturated fatty acid diet on exerciseinduced hypoxaemia in master athletes[END_REF].

In the present study, we hypothesized that EIH subjects have 1) a higher capacity for lactate influx in RBCs and 2) a reduced RBC deformability and increased blood viscosity during exercise. To test this hypothesis, we compared RBC lactate influx characteristics at rest in subjects with and without EIH, and we studied the hemorheological profiles at rest and at the end of a submaximal exercise bout.

MATERIALS AND METHODS

Subjects

Fifteen male endurance-trained subjects (runners, cyclists, and triathletes) were assigned to one of two groups (EIH or non-EIH) by Address for reprint requests and other correspondence: J. Mercier, UPRES EA 701 "Physiologie des Interactions," Service Central de Physiologie Ho ˆpital Arnaud de Villeneuve, 34295 Montpellier, France (E-mail: j-mercier @chu-montpellier.fr).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. assessing the decrease in oxyhemoglobin saturation [oxyhemoglobin saturation measured by pulse oximetry (SpO 2 )], during a first exercise test. A minimum drop of 3-4% in Sp O 2 for at least the last three steps of an incremental exercise test is required to conclude that the drop is significant [START_REF] Prefaut | Exercise-induced arterial hypoxaemia in athletes: a review[END_REF]. ⌬SpO 2 was calculated as the difference between SpO 2 measured at rest and during the last step of the incremental exercise. Group assignment was also confirmed by the decrease in PaO 2 , i.e., ⌬Pa O 2 , measured during a subsequent submaximal test. Nine subjects with EIH were included in the EIH group (24 Ϯ 1 yr, 73.4 Ϯ 2.2 kg, 180 Ϯ 3 cm, ⌬PaO 2 ϭ Ϫ12.40 Ϯ 1.17 Torr, ⌬SpO 2 ϭ Ϫ4.9 Ϯ 1.1), and six subjects without EIH were assigned to the non-EIH group (26 Ϯ 2 yr, 72.7 Ϯ 2.2 kg, 182 Ϯ 2 cm, ⌬PaO 2 ϭ Ϫ2.50 Ϯ 1.50 Torr, ⌬Sp O 2 ϭ Ϫ1.9 Ϯ 0.4).

The major exclusion criteria were tobacco use and muscle, joint, and cardiorespiratory diseases.

Experimental Protocol and Procedures

The local ethics committee approved the study, and each subject gave informed, written consent to participate. The subjects performed two exercise tests on a cycle ergometer (Ergoline type) separated by 1 wk. The first one was a progressive and maximal exercise test to determine the maximal cardiorespiratory parameters and ⌬SpO 2 . The second was a submaximal steady-state exercise test. Arterialized blood was sampled at rest and at the end of exercise for analysis of PaO 2 , and venous blood was sampled at the same times for analysis of plasma lactate concentrations ([Lac]) and hemorheological parameters. Lactate influxes into RBCs were measured on blood sampled at rest.

Exercise tests. The incremental maximal exercise test began with a 3-min warm-up at 60 W. Pedaling speed remained constant (Ͼ70 rpm) throughout testing, and the load was increased by 30 W every minute until maximal oxygen uptake (V ˙O2 max) was reached. Oxygen uptake (V ˙O2) was considered maximal if at least three of the following criteria were met: 1) a respiratory exchange ratio of Ͼ1.10; 2) attainment of age-predicted maximal heart rate [210 Ϫ (0.65 ϫ age) Ϯ 10%]; 3) an increase in V ˙O2 lower than 100 ml with the last increase in work rate; and 4) an inability to maintain the required pedaling frequency (70 rpm), despite maximum effort and verbal encouragement. A 5-min recovery period was then respected with 2 min of pedaling and 3 min at rest.

One week later, each subject performed a submaximal steady-state exercise based on the maximal intensity determined during the first test. Before exercise, a catheter was inserted into the antecubital vein of the nondominant arm. Venous blood samples were drawn at rest and at the end of exercise (i.e., during the last seconds of the test). After recording of cardiac, ventilatory, and gas exchange data for 5 min at rest, the test began with a 10-min warm-up at 60% of V ˙O2 max followed by 15 min at 85% of V ˙O2 max. The recovery period consisted of 5 min of pedaling at low intensity.

V ˙O2, CO2 output, and ventilation were continuously measured at rest and during exercise and recovery by using a breath-by-breath automated exercise metabolic system (Vmax 229, Sensor Medics). A 12-lead electrocardiogram (Hellige, Marquette Medical Systems) was monitored continuously.

Sp O 2 and PaO 2 . Before measurements, the ear lobe was systematically cleaned with alcohol and rubbed with a vasodilator cream (Finalgon, Boehringer Ingelheim, Barcelona, Spain). During the first exercise test, Sp O 2 was measured by using a noninvasive pulse oximetry method (Satlite Trans, Helsinki, Finland). The ear oximeter has been proven both valid and reliable for measuring significant falls in Sp O 2 during exercise [START_REF] Poppius | A new ear oximeter for assessment of exercise-induced arterial desaturation in patients with pulmonary diseases[END_REF][START_REF] Rebuck | The accuracy and response characteristics of a simplified ear oximeter[END_REF].

Pa O 2 was determined by using the blood-gas method. Blood was collected at the subject's ear and analyzed immediately (IL Meter 1306, Milan, Italy). We considered a Pa O 2 decrease of at least 8 Torr as significant for EIH, in agreement with the study performed by Anselme et al. [START_REF] Anselme | Histamine and exercise-induced hypoxemia in highly trained athletes[END_REF].

Hemorheology. Seven milliliters of venous blood were collected in Vacutainer tubes (Becton Dickinson) containing EDTA as the anticoagulant for the hemorheological measurements. Hct was measured by the micromethod after blood microcentrifugation. Measurements of blood viscosity and plasma viscosity were performed with a falling ball viscometer (MT 90 Medicatest, Saint Benoit, France) [START_REF] Doffin | Blood viscosity measurements in both extensional and shear flow by a falling ball viscometer[END_REF]. The coefficient of variation for this method ranged from 0.6 to 0.8% [START_REF] Fons | Evaluation of blood viscosity at high shear rate with a falling ball viscometer[END_REF]. Plasma was obtained via centrifugation at 2,000 g and 4°C for 5 min (Jouan, Saint Nazaire, France). The index of RBC rigidity (Tk) was calculated according to the equation of Dintenfass [START_REF] Dintenfass | Red cell rigidity, Tk, and filtration[END_REF]:

b ϭ p͓1 Ϫ ͑Tk ⅐ Hct͔͒ Ϫ2.5
where b is blood viscosity (mPa/s), p is plasma viscosity (mPa/s), and Hct is in percent.

Plasma [Lac]. Venous blood (5 ml) was sampled in heparinized tubes (Becton Dickinson). Plasma was obtained via centrifugation at 2,000 g and 4°C for 5 min in a refrigerated centrifuge (Jouan). Plasma was then isolated and frozen at Ϫ80°C until assay. Plasma [Lac] was determined by using an enzymatic method (Roche Diagnostics kit, Mannheim, Germany).

RBC lactate transport. For lactate influx into RBCs, 5 ml of venous blood were collected at rest in heparin tubes (heparin, 0.2 U/ml), stored in ice, and prepared before lactate influx measurements.

The techniques for RBC preparation and lactate influx measurement were modified from previously published methods [START_REF] Skelton | Lactate influx into red blood cells from trained and untrained human subjects[END_REF][START_REF] Skelton | Lactate influx into red blood cells of athletic and nonathletic species[END_REF]. The initial Hct (pre-Hct) was determined for all blood samples. One-half (2.5 ml) of each blood sample was transferred to a 50-ml conical tube, depleted of lactate, and washed by using the following procedure. First, the RBCs were isolated by centrifugation at room temperature (25°C, 15 min, 2,000 g). Plasma and buffy coat were removed by aspiration. Thirty volumes of chloride buffer [150 mM NaCl and 10 mM sodium tricine, pH 8.0, at 37°C, osmolality ϳ315 mosmol/ kgH 2O, volume (ml) ϭ 30 ϫ 2.5 ϫ pre-Hct] were added to the pellet, which was mixed by inversion and incubated in a water bath for 30 min at 37°C to ensure complete removal of endogenous lactate [START_REF] Deuticke | Monocarboxylate transport in red blood cells: kinetics and chemical modification[END_REF][START_REF] Skelton | Lactate influx into red blood cells from trained and untrained human subjects[END_REF][START_REF] Skelton | Lactate influx into red blood cells of athletic and nonathletic species[END_REF]. After incubation, the RBCs were sedimented at room temperature (25°C, 10 min, 2,000 g), and the supernatant was removed by aspiration. The cell pellet was then washed twice with chloride buffer and suspended in a volume of HEPES buffer (90 mM NaCl, 50 mM HEPES, pH 7.4, 37°C, osmolality ϳ267 mosmol/kgH 2O) equivalent to a 30% Hct level (packed cell volume) to obtain the stock cell suspension for influx measurements. This suspension was divided into two tubes, each containing 1 ml. One of the two tubes contained no lactate transport blockers. The second tube contained 1 mM of p-chloromercuribenzenesulfonic acid (PCMBS), which is known to inhibit the monocarboxylate-specific carrier at this concentration [START_REF] Skelton | Lactate influx into red blood cells from trained and untrained human subjects[END_REF][START_REF] Skelton | Lactate influx into red blood cells of athletic and nonathletic species[END_REF]. The tubes were then incubated in a water bath for an additional 30 min at 37°C. Part of the stock cell suspension was used for Hct determination (post-Hct).

All samples for lactate influx measurements were run in triplicate. At time t ϭ 0, a 25-l sample of stock cell suspension was added to a 13 ϫ 100-mm test tube containing 75 l of HEPES influx buffer at 37°C. The HEPES influx buffer contained L-[U- 14 C]lactate (sodium salt, specific activity 50 Ci/mmol) at three [Lac] values of 2, 10, and 50 mM. The HEPES influx buffer was adjusted to pH 7.4. Because of dilution with the stock cell solution, the actual [Lac] values were 1.6, 8.1, and 41 mM. The cells were exposed to the influx buffer and mixed at 37°C for 20 s [START_REF] Skelton | Lactate influx into red blood cells from trained and untrained human subjects[END_REF][START_REF] Skelton | Lactate influx into red blood cells of athletic and nonathletic species[END_REF]. At that time, 5 ml of an ice-cold stop solution [150 mM NaCl, 10 mM sodium-2-(N-morpholino)ethanesulfonic acid, pH 6.5] were then added to each test tube to stop influx. The sample was spun for 15 min at 2,000 g and 4°C, and the supernatant was removed by aspiration. Control blanks were run in duplicate at the three [Lac] values for both total and MCT-1-mediated lactate influxes, to correct for any residual extracellular radioactivity and for any transmembrane lactate exchange that might have occurred, despite ice-cold stop solution. An additional wash phase was conducted by adding 5 ml of stop solution to each sample. The cells were spun again, and the supernatant was removed. The RBC pellet was lysed and deproteinized with 0.5 ml of 4.2% perchloric acid followed by centrifugation of the sample for 15 min (2,000 g) at 4°C. A 0.4-ml sample was then placed into scintillation vials containing 5 ml of aqueous counting fluid and counted in a liquid scintillation counter (Tri-Carb Liquid Scintillation Analyzer, model 2200).

Total lactate influx into the RBCs was determined at the three [Lac] values (1.6, 8.1, and 41 mM). For this determination, neither the stock cell solution nor the HEPES influx buffer contained any lactate transport blocker. Influx into PCMBS-treated RBCs was measured at the same three concentrations of lactate. Because PCMBS treatment inhibits the monocarboxylate pathways, influx into the PCMBStreated RBCs was the sum of lactate transport by the band 3 pathway and nonionic diffusion. Therefore, total lactate influx minus influx into the PCMBS-treated cells represents the MCT-1-mediated lactate influx. Control blanks radioactivity was subtracted from the radioactivity measured in samples.

The percentage of contribution from the MCT-1 pathway was calculated by dividing MCT-1-mediated lactate influx by the corresponding total lactate influx. Lactate influx was calculated in nanomoles of lactate per milliliter of cells (erythrocyte) per minute: the 25 l of stock solution were multiplied by its Hct fraction (0.30) to obtain a packed cell volume. Total lactate influxes into RBCs and MCT-1mediated lactate influxes were determined.

Statistical Analysis

Values are presented as means Ϯ SE. Subject characteristics and V ˙O2 max values were compared between groups by using an unpaired Student's t-test. Lactate influxes into RBCs were compared with a two-way ANOVA with repeated measures: two groups (EIH subjects and non-EIH subjects) ϫ three [Lac] values (1.6, 8.1, and 41 mM). The relationships between the drop in Pa O 2 (⌬PaO 2 ) and the total lactate influx values and between V ˙O2 max and the total lactate influx values were evaluated for each subject by using a Pearson correlation. Hemorheological parameters and plasma [Lac] were compared by using a two-way ANOVA: two groups ϫ sample time (at rest or at the end of submaximal exercise). Pairwise contrasts were used when necessary to determine where the significant differences occurred. The level of significance was set at ␣ ϭ 0.05.

RESULTS

V ˙O2 max

V ˙O2 max was significantly higher in the EIH subjects (65.33 Ϯ 2.09 ml⅐kg Ϫ1 ⅐min Ϫ1 ) compared with the non-EIH subjects (60.27 Ϯ 0.85 ml ⅐kg Ϫ1 ⅐min Ϫ1 ) (P Ͻ 0.05).

Hemorheological Parameters

The values of the hemorheological parameters were identical in the two groups at rest (Table 1). During exercise, blood viscosity, plasma viscosity, and Hct increased significantly in both groups (P Ͻ 0.001) and reached similar values. Neither a group nor an exercise effect was observed for RBC rigidity.

Plasma [Lac]

Plasma [Lac] values were similar for both groups at rest: 2.15 Ϯ 0.11 and 2.32 Ϯ 0.19 mM for EIH and non-EIH subjects, respectively. At the end of submaximal exercise, the plasma [Lac] was also identical in the two groups: 4.88 Ϯ 1.12 and 5.32 Ϯ 1.34 mM for EIH and non-EIH subjects, respectively.

Lactate Influx into RBCs

Total lactate influxes into RBCs are illustrated in Fig. 1. At 1.6 mM [Lac], no difference between groups was observed. Total lactate influx was greater in the EIH subjects at 8.1 mM (P Ͻ 0.05) and 41 mM [Lac] (P Ͻ 0.001) compared with the other group. MCT-1-mediated lactate influx was higher in the EIH subjects at 8.1 mM (P Ͻ 0.05) and 41 mM [Lac] (P Ͻ 0.001; Fig. 2).

The fractional contribution of MCT-1 to total lactate influx decreased with external [Lac] (Table 2).

Relationships between ⌬Pa O 2 and total lactate influx values. We found no relationship between ⌬Pa O 2 and total lactate influx measured at 1.6 mM (Fig. 3A). Negative correlations were found between ⌬Pa O 2 and total lactate influx measured at 8.1 mM (r ϭ Ϫ0.82, P Ͻ 0.05, Fig. 3B) and between ⌬Pa O 2 and total lactate influx at 41 mM (r ϭ Ϫ0.84, P Ͻ 0.05, Fig. 3C).

Relationships between V ˙O2 max and total lactate influx values. We found no significant correlation between V ˙O2 max and any of the total lactate influx values.

DISCUSSION

This study mainly showed that, in the resting condition, total and MCT-1-mediated lactate influxes into RBCs were higher in the EIH subjects at 8.1 and 41 mM [Lac]. In addition, there was a strong correlation between ⌬Pa O 2 and total lactate influx. The hemorheological profile was the same in the two groups at rest and at the end of exercise. These results suggest that EIH can modify lactate fluxes into RBC without any significant change in cell deformability.

Lactate Influx

We have observed higher total lactate influx into the RBCs from EIH subjects at moderate (8.1 mM) and high [Lac] (41 mM) than in the other group. We are mindful that the use of another [Lac], as done by Skelton et al. [START_REF] Skelton | Lactate influx into red blood cells from trained and untrained human subjects[END_REF], closer to the physiological range would have reinforced our results. From Figs. 1 and2, we can reasonably think that the use of a [Lac] around 16 mM would have given similar results, i.e., higher total or MCT-1-mediated lactate influx in EIH subjects. The results obtained at the tested concentrations showed in EIH subjects an increased influx via MCT-1, the major pathway of lactate influx into RBCs [START_REF] Skelton | Lactate influx into red blood cells from trained and untrained human subjects[END_REF]. This could be related to the greater aerobic physical fitness in EIH subject. Indeed, Skelton et al. [START_REF] Skelton | Lactate influx into red blood cells of athletic and nonathletic species[END_REF] showed that the lactate influx via MCT-1 was faster in RBC obtained from animals with high-oxidative capacity (dogs and horses) than from animals with low-oxidative capacity (goats and cattle). However, in the present study, we did not find any significant relationship between V ˙O2 max and total lactate influx. Lactate uptake by RBCs may, nevertheless, play a role in enhancing physical performance. The accumulation of lactate and hydrogen ions in muscle during exercise may inhibit muscular function and cause fatigue [START_REF] Fitts | Cellular mechanisms of muscle fatigue[END_REF][START_REF] Hogan | Increased [lactate] in working dog muscle reduces tension development independent of pH[END_REF]. High-RBC uptake of these ions could help in establishing a gradient between plasma and interstitial fluid [START_REF] Deuticke | Monocarboxylate transport in erythrocytes[END_REF][START_REF] Roth | The sarcolemmal lactate transporter: transmembrane determinants of lactate flux[END_REF]. Transport of these metabolites away from the exercising muscles into the blood would reduce the potential for muscle acidosis and delay the onset of fatigue.

Recently, Juel et al. [START_REF] Juel | Human skeletal muscle and erythrocyte proteins involved in acid-base homeostasis: adaptations to chronic hypoxia[END_REF] found that band 3 and MCT-1 expressions on RBC membranes from humans were increased after 2 and 8 wk of hypoxia exposure. RBC MCT-1 and band 3 contents increased dramatically (ϩ330 and ϩ150%, respec-Fig. 3. Relationships between change in oxygen arterial partial pressure (⌬PaO 2 ) and total lactate influx at 1.6 mM (A; n ϭ 15), 8.1 mM (B; n ϭ 14), and 41 mM (C; n ϭ 15). Significant relationships were found between ⌬PaO 2 and lactate influx at 8.1 mM (r ϭ Ϫ0.82, P Ͻ 0.05) and between ⌬PaO 2 and lactate influx at 41 mM (r ϭ Ϫ0.84, P Ͻ 0.05). tively) after 2 wk. These data suggest that the proteins involved in RBC lactate transport can be upregulated by hypoxia. In our study, the subjects exhibiting hypoxemia during exercise had the higher RBC lactate transport activity. These subjects trained regularly, sometimes twice a day, and it is possible that they experienced repeated hypoxemic events that had led to changes in RBC lactate transport activity. We found significant relationships between the drop in Pa O 2 and the total lactate uptake values measured at 8.1 and 41 mM, i.e., the two [Lac] values at which differences in total lactate uptake were noted between EIH and non-EIH. Although this finding indicates no causality, this correlation strengthens the argument that the enhanced lactate influx is more related to EIH than to V ˙O2 max . Overall, these results suggest that hypoxemia (induced by either exercise or environmental condition) could be a strong stimulus for lactate transport into RBCs by acting on either the expression of the proteins involved or their activity. The underlying physiological mechanism is still unknown but may be related to erythropoietin (Epo) secretion. In a recent study [START_REF] Connes | Injections of recombinant human erythropoietin increases lactate influx into erythrocytes[END_REF], our laboratory showed that 4 wk of treatment with recombinant human Epo led to a significant increase in RBC lactate influx in human subjects. A potential role for Epo in MCT-1 expression might also explain why Juel et al. [START_REF] Juel | Human skeletal muscle and erythrocyte proteins involved in acid-base homeostasis: adaptations to chronic hypoxia[END_REF] found an increase in MCT-1 expression on RBC membrane but did not find such a change in muscle samples. Indeed, to our knowledge, there is no Epo receptor in mature human muscular cells.

Hemorheological Measurements

Blood viscosity was assessed by using a falling ball viscometer, the MT 90 Medicatest. This method was shown to be valid for the assessment of both plasma and blood viscosities in humans [START_REF] Doffin | Blood viscosity measurements in both extensional and shear flow by a falling ball viscometer[END_REF][START_REF] Fons | Evaluation of blood viscosity at high shear rate with a falling ball viscometer[END_REF]. Moreover, Doffin et al. [START_REF] Doffin | Blood viscosity measurements in both extensional and shear flow by a falling ball viscometer[END_REF] specifically demonstrated that the MT 90 viscometer measures with a shear rate of 1,000 s Ϫ1 . Based on the Dintenfass equation, it was thus possible to calculate Tk in our study because this Tk becomes more specific as the shear rate rises [START_REF] Dintenfass | Red cell rigidity, Tk, and filtration[END_REF]. Blood viscosity depends on several parameters, including plasma viscosity, Hct, and RBC rigidity [START_REF] Dintenfass | Red cell rigidity, Tk, and filtration[END_REF][START_REF] Quemada | Rheology of concentrated disperse systems. II. A model of non newtonian shear viscosity in steady flows[END_REF]. In our study, the hemorheological parameters involved in blood viscosity regulation had increased to the same value in both groups at the end of exercise, and thus blood viscosity also showed the same increase. This increase in plasma viscosity during exercise could be related to a rise in plasma protein concentration. For example, Vandewalle et al. [START_REF] Vandewalle | Blood viscosity after a 1-h submaximal exercise with and without drinking[END_REF] observed higher plasma concentrations of ␣ 1 -globulins, ␣ 2 -globulins, ␤-globulins, and ␥-globulins at the end of a moderate exercise.

Several factors could be responsible for the change in Hct during exercise, including fluid shift, water loss, and RBCs released from the spleen [START_REF] Isbister | Physiology and pathophysiology of blood volume regulation[END_REF][START_REF] Laub | Spleen emptying and venous hematocrit in humans during exercise[END_REF][START_REF] Ploutz-Snyder | Resistance exercise-induced fluid shifts: change in active muscle size and plasma volume[END_REF][START_REF] Stephenson | Plasma volume during heat stress and exercise in women[END_REF], but we did not determine the relative contribution of each factor in this study.

RBC rigidity did not change with exercise in either group. Usually, RBC deformability decreases with exercise [START_REF] Bouix | Relationships among body composition, hemorheology and exercise performance in rugby men[END_REF][START_REF] Signorelli | Hemorheological changes during exercise][END_REF]. The increased plasma [Lac] and decreased pH that occur during exercise lead to water loss by RBCs (osmotic process), which, in turn, results in greater rigidity [START_REF] Lipovac | Influence of lactate on the insulin action on red blood cell filterability[END_REF][START_REF] Smith | Lactate/H ϩ uptake by red blood cells during exercise alters their physical properties[END_REF]. In our study, however, the rise in plasma [Lac] during exercise was slight in all subjects, which can explain the lack of RBC rigidity change. The subjects exhibiting EIH had higher RBC lactate transport activity at 8.1 and 41 mM [Lac], but, in vivo, the plasma [Lac] reached lower values during exercise (Ͻ6 mM at the end of exercise). These results could also explain the lack of RBC rigidity difference between the two groups at the end of exercise.

EIH

We investigated blood rheology to clarify its relationship with EIH. Because the measurements were performed at a high-shear rate, we were able to hypothesize about the effects of blood rheological properties in small vessels like the capillaries, even though the blood was drawn from the antecubital vein. At a high-shear rate, blood viscosity depends primarily on erythrocyte rigidity and then on plasma viscosity and Hct, whereas, at a low-shear rate, blood viscosity depends mostly on aggregation properties and Hct.

Previous studies have suggested a potential role of RBC rigidity in pulmonary hemodynamics and pulmonary diffusion limitation. Weiss et al. [START_REF] Weiss | Effects of pentoxifylline on hemorheologic alterations induced by incremental treadmill exercise in thoroughbreds[END_REF] perfused pony lungs with pentoxifylline-treated RBCs, which are known to be very deformable. They observed a 27% decrease in filtration pressure, resulting in a 10% decrease in pulmonary arterial pressure. In master athletes, Aguilaniu et al. [START_REF] Aguilaniu | Effects of indomethacin and polyunsaturated fatty acid diet on exerciseinduced hypoxaemia in master athletes[END_REF][START_REF] Aguilaniu | Exercise-induced hypoxaemia in master athletes: effects of a polyunsaturated fatty acid diet[END_REF] observed a decrease in EIH severity after a PUFA diet. Because a PUFA diet is known to improve RBC deformability, a potential contribution of blood parameters to EIH genesis cannot be excluded. In our study, it seems that hemorheology did not contribute to EIH during the submaximal exercise performed at 85% V ˙O2 max , because no difference between groups was noted for any of the hemorheological parameters. Nevertheless, blood viscosity may contribute to EIH during very intense exercise, i.e., Ͼ90% V ˙O2 max , because we observed a greater increase in blood viscosity in the endurance-trained subjects with EIH compared with those without EIH during a progressive and maximal exercise [START_REF] Connes | Is hemoglobin desaturation related to blood viscosity in athletes during exercise?[END_REF].

In conclusion, higher total lactate transport activity and greater MCT-1-mediated lactate influx were found in the RBCs from the EIH subjects, but erythrocyte deformability and blood viscosity were similar in the two groups of endurance-trained subjects. We suggest that the higher lactate influx into RBCs may be more closely related to hypoxemia than to aerobic capacity. Further studies are needed to identify the underlying physiological process.

Fig. 1 .

 1 Fig. 1. Total lactate influx into red blood cells (RBCs) from 2 groups at different lactate concentration ([Lac]) values. Values at 8.1 and 41 mM were higher in exercise-induced hypoxemia (EIH) subjects. Values are means Ϯ SE. *P Ͻ 0.05; †P Ͻ 0.001.

Fig. 2 .

 2 Fig. 2. Lactate influx via the monocarboxylate pathway in RBCs from EIH and non-EIH subjects. Values are means Ϯ SE. Monocarboxylate transporter-1 (MCT-1)-mediated lactate influx was higher in EIH subjects at 8.1 mM (*P Ͻ 0.05) and 41 mM ( †P Ͻ 0.001).

Table 1 .

 1 Hemorheological parameters at rest and at the end of submaximal exercise in EIH and non-EIH subjects

		EIH Subjects	Non-EIH Subjects
			End of		End of
		Rest	exercise	Rest	exercise
	b, mPa/s	3.31Ϯ0.13	3.83Ϯ0.17*	3.11Ϯ0.11	3.61Ϯ0.15*
	p, mPa/s	1.37Ϯ0.01	1.46Ϯ0.01*	1.33Ϯ0.01	1.44Ϯ0.01*
	Hct, %	42.1Ϯ0.8	45.9Ϯ0.9*	42.7Ϯ0.4	46.0Ϯ0.9*
	Tk	0.69Ϯ0.02	0.69Ϯ0.01	0.68Ϯ0.01	0.68Ϯ0.01

Values are means Ϯ SE. EIH, exercise-induced hypoxemia; b, blood viscosity; p, plasma viscosity; Hct, hematocrit; Tk, red blood cell rigidity coefficient. *Significantly different between rest and the end of exercise (P Ͻ 0.001).

Table 2 .

 2 FractionalValues are means Ϯ SE. No significant difference was observed between groups at any concentration.

		contribution (%) of the
	monocarboxylate transporter-1 pathway to total
	lactate influx at three lactate concentrations
		1.6 mM	8.1 mM	41 mM
	EIH subjects, %	89.7Ϯ0.6	92.5Ϯ1.4	80.8Ϯ4.6
	Non-EIH subjects, %	93.8Ϯ3.7	88.0Ϯ0.8	70.2Ϯ3.2

ACKNOWLEDGMENTS

The authors express their sincere gratitude to all of the athletes who participated in the present study. We are also grateful to the staffs from the Laboratoire de Physiologie des Interactions (Hopital Arnaud de Villeneuve, Montpellier, France) and Service de Me ´decine Nucle ´aire (Hopital Lapeyronie, Montpellier, France) for their vital contribution. We thank C. Carmeni for help in writing the English manuscript.


Didier Fraix-Burnet
email: didier.fraix-burnet@univ-grenoble-alpes.fr

Tanuka Chattopadhyay

Mauro D'onofrio

Paula Marziani

Saptarshi Mondal

Multivariate and phylogenetic analyses of galaxies

Investigating the formation and evolution of galaxies is becoming a complicated process with the increased availability of huge databases as a result of instrumental improvements. In this poster we present preliminary results on two statistical studies using multivariate partitioning and cladistic analyses to find homogeneous groups and their evolutionary relationships.

NYU Value-Added Galaxy Catalog (VAGC)

We have carried out a multivariate classification of 362 923 galaxies from the VAGC Catalogue (Blanton et al 2005). Independent Component Analysis is used to determine a set of derived independent variables as linear combinations of the various 49 observed parameters. A K-means cluster analysis is applied on the independent components and the optimum number of homogeneous groups is found to be ten. A cladistic analysis * is performed on these ten groups using the median values of the 49 parameters.

BPT diagrams: a more refined classification K7 and K9 have no AGN, hence are pure star forming galaxies; K3 seems to be mainly composed of LINERs; K2 and K6 are clearly intermediate between star forming galaxies and AGNs; K1, K4, K5, K6 and K10 appear as a mixture of star forming and mainly LINERs galaxies; the very small group K8 is quite peculiar with two peaks, one in the pure star forming region, the other one in the pure AGN zone.

Colour-magnitude diagram: bimodality revisited K1 to K6 clearly belong to the red branch; K7 to K9 are on the blue branch; K10 is in a region often called the green valley; K2 and K4 seem to include also a part of this green valley; K8 appears peculiar, with a very blue part, and some galaxies from the red branch.

An evolutionary path in the colour-magnitude diagram

The tree, built in a 49-D parameter space, provides an objective evolutionary path when projected on the 2-D colour-magnitude diagram.

The tree globally goes from the blue to the red sequences, and shows a clear evolution within each of them.

Our multivariate analysis yields groups of galaxies that could not be identified with 2-D diagnostic diagrams. For instance, groups K1 to K6 belong to the red branch, but most contain mixtures of LINERs, AGNs and star forming galaxies.

WIde-field Nearby Galaxy-clusters Survey (WINGS) Catalogue

We have applied a hierarchical clustering method followed by a cladistic analysis * . We use a sample of 1991 galaxies from the WINGS survey (Fasano et al 2006) which are mostly quiescent or host modest star formation activity and low-luminosity AGNs. 1494 galaxies are members of nearby clusters, while 497 are field galaxies at higher redshifts for purpose of comparison. We use eleven parameters: B-V, logRe, surface brightness, Hβ, D4000, Mass, Sersic index n, Hα+NII, Gband, Mg and Na.

An evolutionary sequence

We here show the most parsimonious unrooted tree given by the cladistic algorithm on the 300 "pre-groups" found by hierarchical clustering.

The nine groups shown in colour are the larger ones with more than 30 galaxies.

Multivariate properties of nine groups

The boxplots show the quantiles for several parameters for each of the nine main groups defined on the tree above.

The colour progression from blue to red grossly matches several trends (B-V, Gband, D4000...). Some parameters are more erratic (logRe, SFR, Mass...). Groups 1, 2, 3 and 8 have roughly the same number of cluster and field galaxies. Groups 4, 5, 6, and 9 are mainly composed of cluster members.

Evolution in the colour-magnitude diagram

The tree is here projected onto the 2-D colour-magnitude diagram. The coloured squares are the median values. The density contours show that the distributions are generally not symmetric at all. Despite the different bands, the global projection of the tree is somewhat similar to the one for the VAGC sample in this poster.

This multivariate and phylogenetic study shows that the evolution of galaxies is not driven by only one parameter, like mass or luminosity.

Conclusion

The multivariate unsupervised classification analyses reveal groups which are often mixtures of traditional empirical classes based on only a few properties. These groups depict a more realistic picture of galaxy diversity and complexity than simple eye-based classifications. Phylogenetic tools like cladistics establish the optimal evolutionary paths of galaxies from the data themselves. The inferred evolutionary scenario is thus more objective and complete.


Nonlocal damage formulation with evolving internal length: the Eikonal nonlocal approach G. Rastiello 1 , C. Giry 2 , F. Gatuingt 2 , R. Desmorat 2 1 CEA Saclay, DEN, DANS, DM2S, SEMT, Seismic Mechanics Laboratory, France giuseppe.rastiello@cea.fr 2 LMT-Cachan/ENS-Cachan/CNRS/Université Paris Saclay giry@lmt-cachan.fr, gatuingt@lmt-cachan.fr, desmorat@lmt-cachan.fr Integral non-local (INL) formulations [START_REF] Bazant | Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress[END_REF] are often used to regularize continuum damage models in the presence of strain softening laws. In numerical computations the introduction of an internal length allows for avoiding pathological mesh sensitivities. Some questions concerning the identification of the internal length, its possible evolution during damage process and the need for special treatments of non-locality operators near boundaries (e.g. edges, cracks) are however still open. A physical request is that material points separated by a crack or a highly damaged zone should not interact (despite what is done in standard non-local integral theories). This can be obtained by allowing non-local interactions to evolve depending on mechanical fields (e.g. damage [START_REF] Pijaudier-Cabot | Non-local damage model with evolving internal length[END_REF], stress [START_REF] Giry | Stress based nonlocal damage model[END_REF], etc.).

Different formulations where proposed in the literature for this purpose. In particular, based on the analogy between wave and information propagation within an elastic damaged medium, Desmorat et al. [START_REF] Desmorat | Nonlocal models with damagedependent interactions moti-vated by internal time[END_REF] proposed to reformulate the classic non-local averaging procedure in terms of the ratio of the time needed for an elastic wave to propagate between two material points and the corresponding time in undamaged conditions. Using such an approach in two-and three-dimensional contexts may however reveal complex. As no general analytical solutions for the wave propagation equation through the heterogeneous medium are available, time-consuming numerical solution procedures are indeed needed.

Based on the Wentzel-Kramers-Brillouin (WKB) approximation for high-frequency wave propagation in a damaged medium, the Eikonal non-local (ENL) formulation provides a novel interpretation of damage dependent non-local interactions both in isotropic and anisotropic contexts. From a mathematical point of view, interaction distances are now computed as the viscosity solution of a time-independent Eikonal equation with a damage dependent isotropic/anisotropic Riemannian metric. From a differential geometry viewpoint, this leads to consider that damage induces a curvature of the Riemannian space in which interaction distances are computed. Geodesic interaction distances determined in the curved space are used to compute non-local variables driving damage evolution, thus preserving the general theoretical framework of INL theories. This allows modeling non-local interactions that gradually vanish in damaged zones, leading to a progressive transition from diffuse damage to fracture.

In this contribution, the numerical properties of the ENL regularization technique are investigated. Non-local interactions in 2D damaged domains are illustrated by some ex-amples first. Attention is focused on "artificially" damaged domains, in order to put into evidence some key features of the Eikonal Non-Local formulation. A non-intrusive (or less intrusive as possible) numerical formulation [START_REF] Rastiello | Strain localization from a Eikonal Non-Local (ENL) Continuum Damage model with evolving internal length[END_REF] for modeling damage dependent nonlocal interactions within mechanical computations is presented then. It is obtained by coupling Fast-Marching [START_REF] Sethian | A fast marching level set method for monotonically advancing fronts[END_REF] algorithms for computing interaction distances and a standard Finite Element (FE) procedure for solving the quasi-static equilibrium equations. Geodesic distances computed between Gauss points define the kernel of weighting function considered in integral non-local regularization method. Several numerical results of quasi-static simulations involving the failure of quasi-brittle materials in isotropic media are presented. This allows for showing the capabilities of the ENL formulation in properly modeling a progressive transition from damage to fracture (i.e., strain localization) and the regularization capabilities of the proposed approach. The problem of how adapt/enhance the numerical ENL framework for properly treating nonlocal interactions near free-boundaries is addressed then. Finally, a method for estimating discrete quantities (i.e. cracking) from continuous field is exposed. This technic, based on the post-treatment of the strain field, allows to investigate the capacity of ENL formulation to describe the strain localization at failure.

It should be noted that, although the method is illustrated with a simple isotropic damage model, the formulation proposed is however general. The extension to anisotropic contexts is also possible without major modifications. In this latter case, the only difference will concern the use of a Fast-Marching algorithm that now should be capable of dealing with anisotropic Riemannian metric fields.


R Akiki

C Giry

F Gatuingt

CRACKING ANALYSIS OF FIBRE REINFORCED STRUCTURES SUBJECT TO DYNAMIC LOADING

The fracture process of a prismatic notched beam subjected to a dynamic loading was investigated numerically. Two different approaches for post-treating the finite element analysis performed at the structural scale were tested. First results of the predictions of crack location and opening for the two approaches at different loading steps are presented and compared to the experimental data.

Introduction

The analysis and prediction of the degradation process and cracking of fiber-reinforced concrete structures with numerical models is an important issue in the field of civil engineering. Continuum damage mechanics succeed in predicting the strongly non-linear behaviour of such structures. However, in order to obtain precise quantative information about cracks like spacing and openings, the macroscopic model fails. The objective of this research is to extract local information such as cracking using two post-treatment methods of a global finite element analysis.

Methods & Results

First, a global non-linear finite element analysis of the whole structure is performed. This analysis reveals the zones of degradation that are to be reanalyzed via a local analysis using two post-treatment methods. The displacement fields obtained from the FE analysis are compared to the experimental data provided from the post-processing of the actual test (more details in [START_REF] Akiki | Modeling and simulation for an optimized design of a dynamic bending test[END_REF]) in order to ensure the concordance of the results on the global scale (Figure 1). . The first method combines a topological search method used to locate cracks developed by Bottoni [START_REF] Bottoni | Topological search of the crack pattern from a continuum mechanical computation[END_REF] and a continuous/discontinuous approach used to compute the crack opening initially proposed by Dufour [START_REF] Dufour | Estimation of crack opening from a two-dimensional continuum-based finite element computation[END_REF]. It consists in comparing the computed strain fields , with the analytical one derived from the displacement profile described as a strong discontinuity. Both strain fields are regularized using a Gaussian function. The crack opening can then be adjusted so as to reduce the gap between the regularized strain field and the regularized strong discontinuity strain field .

The second method is a non-intrusive reanalysis at the local scale performed with a discrete model in order to extract fine information about crack opening. A region of interest (ROI) corresponding to the damaged area obtained from the global analysis is defined. Then, the loading steps corresponding to the steps of reanalysis are determined, where boundary conditions are extracted from the continuous displacement field and applied on the non-free surfaces of the ROI. The material is described with a discrete element approach based on an assembly of polyhedral particles linked by Euler-Bernoulli beams with brittle behaviour. Further details concerning the discrete model used at the local scale can be found in [START_REF] Oliver-Leblond | Non-intrusive global/local analysis for the study of fine cracking[END_REF]. First results concerning the crack pattern and opening obtained by both methods are shown in Figure 2.

Conclusions

This contribution aims to determine crack opening of a notched fiber-reinforced concrete beam subjected to a dynamic one-point bending test with the use of finite element analysis performed at the structural scale followed by two post-treatment methods. The first one consists in a topological search method used to locate cracks and then the crack opening is computed by comparing the regularized strain field obtained numerically and the analytical one derived from the strong discontinuity representative of a discrete crack. The second is a global/local method which introduces a discrete mechanical model at the finer scale to obtain crack properties using the finite element displacement field as boundary conditions. These two approaches are compared in terms of crack opening prediction and seem to give promising first results. Further studies are ongoing in order to improve the methods and confirm these results.

Figure 1 .

 1 Figure 1. Displacement fields resulting (a)from the global FE analysis and (b)fromexperimental test using DIC[START_REF] Tomicevc | Mechanics-aided digital image correlation[END_REF]. The first method combines a topological search method used to locate cracks developed by Bottoni[START_REF] Bottoni | Topological search of the crack pattern from a continuum mechanical computation[END_REF] and a continuous/discontinuous approach used to compute the crack opening initially proposed by Dufour[START_REF] Dufour | Estimation of crack opening from a two-dimensional continuum-based finite element computation[END_REF]. It consists in comparing the computed strain fields , with the analytical one derived from the displacement profile described as a strong discontinuity. Both strain fields are regularized using a Gaussian function. The crack opening can then be adjusted so as to reduce the gap between the regularized strain field and the regularized strong discontinuity strain field .

Figure 2 .

 2 Crack field at the last step of the computation: (a) topological search and crack opening estimation and (b) global/local method.

Corresponding author E-mail address: akiki@lmt.ens-cachan.fr (R.Akiki)

Acknowledgements

The authors would like to acknowledge the financial support of AREVA.