Dr Florian Kollert
email: florian.kollert@uniklinik-freiburg.de

MD Carolin Müller

Andrea Tippelt

Rudolf Jorres

PhD; Dominic Heidinger

MD Corina Probst

MD Michael Pfeifer

MD Stephan Budweiser

Rudolf A Jörres

ANAEMIA IN CHRONIC RESPIRATORY FAILURE

Keywords: Respiratory failure, anaemia, prognostic factors, COPD, restrictive disease

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.

What is already known about this topic?

Anaemia is highly prevalent in COPD and associated with increased long-term mortality. In contrast, the prevalence of anaemia has not yet been tested in other severe, non-inflammatory respiratory diseases.

What does this article add?

The prevalence of anaemia was high in COPD but also in other severe respiratory diseases, even after exclusion of relevant co-morbidities. These findings suggest that anaemia is a common phenomenon in patients with severe chronic respiratory disease, which has a multifactorial origin and is not only explained by systemic inflammation.

INTRODUCTION

Anaemia of chronic disease (ACD) is one of the most frequent forms of anaemia which is often observed in patients with infections, cancer and chronic inflammatory or autoimmune diseases. The underlying mechanisms are complex, including dysregulation in iron homeostasis and erythropoietin production, impaired proliferation of erythroid progenitor cells and reduced life span of red blood cells. Moreover, ACD often is superimposed by malnutrition, bleeding, renal failure and effects of medication or interventions [START_REF] Weiss | Anaemia of chronic disease[END_REF]. In patients with chronic renal failure, congestive heart failure, or malignant diseases, anaemia has been shown to be associated with impaired quality of life and prognosis [START_REF] Ezekowitz | Anaemia is common in heart failure and is associated with poor outcomes: insights from a cohort of 12 065 patients with new-onset heart failure[END_REF][START_REF] Littlewood | The impact of haemoglobin levels on treatment outcomes in patients with cancer[END_REF][START_REF] Ma | Hematocrit level and associated mortality in hemodialysis patients[END_REF].

A retrospective analysis of patients with chronic obstructive pulmonary disease (COPD) receiving long-term oxygen therapy (LTOT) has revealed that anaemia is also common in severe COPD, being linked to morbidity and survival [START_REF] Chambellan | Prognostic value of the hematocrit in patients with severe COPD receiving long-term oxygen therapy[END_REF]. Moreover, a prospective study of stable COPD patients with a wide range of airflow limitation reported haemoglobin levels of <13 g/dl in 17% of patients, whereby anaemia acted as a risk factor for dyspnoea, functional capacity and mortality [START_REF] Cote | Haemoglobin level and its clinical impact in a cohort of patients with COPD[END_REF]. However, a limitation of these investigations appeared to be that co-morbidities relevant for anaemia were not excluded. Thus COPD is associated with many co-morbidities [START_REF] Barnes | Systemic manifestations and comorbidities of COPD[END_REF], not only renal failure [START_REF] Incalzi | Chronic renal failure: a neglected comorbidity of COPD[END_REF], which could substantially contribute to anaemia. In addition, the clinical significance and pathogenesis of anaemia in COPD are still under discussion. Erythropoietin resistance secondary to systemic inflammation has been proposed as a contributor [START_REF] John | Prevalence of anaemia in chronic obstructive pulmonary disease: comparison to other chronic diseases[END_REF], but a number of other mechanisms, such as malnutrition or oxidative stress, may also play a role in severe forms of the disease [START_REF] Similowski | The potential impact of anaemia of chronic disease in COPD[END_REF], as well as medication, such as theophylline [START_REF] Tsantes | Theophylline treatment may adversely affect the anoxia-induced erythropoietic response without suppressing erythropoietin production[END_REF].

Based on these considerations we aimed to assess the prevalence of anaemia in a large group of patients with severe respiratory diseases of different aetiologies, to compare this with the prevalence found in COPD and to identify risk factors linked to anaemia. All patients were of comparable clinical state with regard to the fact that they received home mechanical

METHODS

Study population

Patients who were discharged with HMV due to CRF from the Donaustauf Hospital, Centre for Pneumology, University of Regensburg, between April 1992 and March 2007 were identified from a data base. Since January 2002 data entry was performed prospectively. The underlying disorders were classified as obstructive disorders (OD) (COPD or overlap syndrome) or restrictive disorders (RD) including obesity-hypoventilation syndrome (OHS), thoracic restrictive diseases (TRD), neuromuscular disorders (NMD), and mixed respiratory disease (predominately interstitial lung diseases). The diagnosis of COPD was based on clinical history, symptoms, a ratio of forced expiratory volume in one second (FEV 1 ) to inspiratory vital capacity (VC) of <70%, and FEV 1 being <50%predicted. In case of FEV 1 >50% (and FEV 1 /VC <70%) and in the presence of chronic hypercapnia, patients were classified as "overlap syndrome" (OL) [START_REF] Weitzenblum | Overlap syndrome: obstructive sleep apnea in patients with chronic obstructive pulmonary disease[END_REF]. OHS was defined as obesity (BMI >30 kg/m 2 ) plus daytime hypercapnia (PaCO 2 ≥45 mm Hg) and symptoms of hypoventilation [START_REF]Sleep-related breathing disorders in adults: recommendations for syndrome definition and measurement techniques in clinical research. The Report of an American Academy of Sleep Medicine Task Force[END_REF].

Selection criteria

Only patients with complete blood count data prior to initiation of HMV were included. Based on the fact that intensive care or endotracheal intubation is associated with repeated blood withdrawal or blood loss due to interventions, we also excluded all patients who had undergone invasive ventilation before initiation of HMV. It has been shown, that the prevalence of renal anaemia in patients with an estimated glomerular filtration rate (eGFR) between 30 and 60 ml/min/1.73m² is low [START_REF] Clase | Relationship between glomerular filtration rate and the prevalence of metabolic abnormalities: results from the Third National Health and Nutrition Examination Survey (NHANES III)[END_REF], thus only patients with eGFR <30 ml/min/1.73 m² were excluded. Further exclusion criteria were known malignancies/haematological disorders within the last 5 years, surgeries, interventions, accidents or haemorrhage within the last 3 months; additional chronic inflammatory, infectious or autoimmune diseases; previous gastrointestinal resection that could evoke malabsorption; substitution of iron, folate or vitamin B 12 ; preceding withdrawal of blood due to polyglobulia or blood transfusion.

Measurements

All data were assessed at the beginning of the hospital stay. Routine blood parameters including haemoglobin (Hb), haematocrit (Hk), leukocyte number, C-reactive protein (CRP), creatinine and total protein (if available) were documented upon admission. Patients were classified as anaemic (Hb<12 g/dl in females, Hb<13 g/dl in males) [START_REF]Nutritional anaemias. Report of a WHO scientific group[END_REF] or normal. BMI was calculated as weight(kg)/height(m) 2 . Glomerular filtration rate was estimated by the "Modification of Diet in Renal Disease (MDRD)" study equation, as this formula is known to be more accurate especially in older and obese patients than the Cockroft-Gault equation [START_REF] Stevens | Assessing kidney function--measured and estimated glomerular filtration rate[END_REF].

Chronic renal failure was defined by an eGFR <60 ml/min/1.73 m². Daytime capillary blood gas values (pH, arterial oxygen pressure (PaO 2 ), arterial carbon dioxide pressure (PaCO 2 ), base excess (BE)) were determined prior to HMV therapy from the hyperaemic earlobe. Only values acquired without additional oxygen supplementation were used. Spirometry and bodyplethysmography were performed according to guidelines of the American Thoracic Society (ATS) / European Respiratory Society (ERS) [START_REF] Miller | Standardisation of spirometry[END_REF] using ERS reference values [START_REF] Quanjer | Lung volumes and forced ventilatory flows. Report Working Party Standardization of Lung Function Tests, European Community for Steel and Coal. Official Statement of the European Respiratory Society[END_REF]. Co-morbidities, such as coronary heart disease, left heart failure, cardiac arrhythmias, arterial hypertension and diabetes mellitus, as well as concomitant medication, such as inhaled bronchodilators, theophylline or anti-hypertensive medication, were documented. The presence of acute infection, such as pneumonia or lower urinary tract infection, was derived from clinical findings and/or CRP levels >20mg/dl.

Statistical analysis

The results are shown as median and quartiles. For the comparison of groups, the Mann-Whitney U-test or t-test was used in case of continuous variables, and Fisher's exact test for categorical variables. Parameters which were significant different between anaemic and non-

RESULTS

Study population

Within the study period 966 patients were discharged with HMV. In total, 939 patients showed appropriate laboratory data prior to initiation of HMV. The exclusion of patients with co-morbidities possibly contributing to anaemia (Figure 1) resulted in a study population of 595 patients aged from 21 to 84 years. OD (n=326; 54.8%) comprised severe COPD (n=304) and overlap syndrome (n=22). RD (n=269; 45.2%) comprised OHS (n=120), TRD (n=80), NMD (n=48) and other respiratory disease (n=21) (Table 1).

Prevalence of anaemia in different chronic respiratory diseases

The overall prevalence (n=595) of anaemia was 13.3% (n=79), without significant difference between OD (14.7%) and RD (11.5%) (p=0.276), or between COPD (15.1%) and RD (11.5%) (p=0.221). However, the prevalence of anaemia was significantly different between TRD (6.3%) and COPD (15.1%) (p=0.041), NMD (20.8%) and TRD (6.3%) (p=0.021) and OD (14.7%) and TRD (6.3%) (p=0.043). In contrast, the prevalence did not show significant differences between overlap syndrome (9.1%), OHS (10.8%) and other respiratory diseases (14.3%) (Figure 2). Only in OD the prevalence of anaemia differed between females and males (7.9% versus 17.3%; p=0.035), whereas no such differences occurred in the total group (p=0.081) or in patients with RD (p=1.0) (Figure 3).

Characteristics of patients with anaemia in chronic respiratory diseases

Patients with OD and anaemia showed higher age (p=0.003), pH (p=0.014) and arterial oxygen pressure (PaO 2 ) (p=0.012), lower BMI (p=0.011) and total protein (p=0.012), and higher rates of male sex (p=0.035) coronary heart disease (p=0.01), cardiac arrhythmia (p=0.014) and diabetes mellitus (p=0.003) in comparison to non-anaemic patients with OD. Moreover, anaemic patients with OD showed less intake of theophylline (p<0.001). In anaemic patients with RD, there were higher age (p=0.008), pH (p=0.011) and lower leukocyte numbers (p=0.006) as compared to non-anaemic patients with RD (Table 2).

Stepwise multivariate regression analysis of all patients, including OD versus RD as binary variable, revealed that age (p=0.012), pH (p=0.002) and PaO 2 (p=0.006) but not the disease category were independently associated with anaemia. In OD only pH (p=0.011) and PaO 2 (p=0.013) were independently associated with anaemia, while in RD leukocyte number (p=0.035) and pH (p<0.001) were independent predictors of anaemia (Table 3).

DISCUSSION

This study demonstrates that anaemia, a treatable condition, is highly prevalent in patients with CRF irrespective of the underlying disease. Anaemia was associated with age, nutritional indices and blood gas indices. In view of the heterogeneity of the study population these results suggest, that not only systemic inflammation, but also conditions associated with respiratory failure itself, contributes to the development of anaemia in respiratory diseases.

Anaemia is known to be a common feature in COPD. When defining anaemia via haemoglobin levels, prevalence rates between 13% (Hb<13 g/dl) [START_REF] Cartwright | The anaemia of chronic disorders[END_REF] and 17% (Hb<13.5 g/dl for male, Hb<12.0 g/dl for female) have been reported [START_REF] Cote | Haemoglobin level and its clinical impact in a cohort of patients with COPD[END_REF]. In line with this our data show a prevalence of 15.1% in COPD, if anaemia was defined based on WHO criteria (Hb<12 g/dl for females and Hb<13 g/dl for males) [START_REF]Nutritional anaemias. Report of a WHO scientific group[END_REF]. Remarkably, this percentage did not vary much when patients with overlap syndrome were included (14.9%). Using the same definition for anaemia, a prevalence of 23.1% has been found in a population of 312 hospitalised COPD patients [START_REF] John | Prevalence of anaemia in chronic obstructive pulmonary disease: comparison to other chronic diseases[END_REF]. In severe COPD (n=80) the prevalence of anaemia (13.9%) was similar to our results, while it was higher in less severe disease [START_REF] John | Prevalence of anaemia in chronic obstructive pulmonary disease: comparison to other chronic diseases[END_REF]. Possibly, hypoxemia which often is present in more severe forms of the disease and which is known as stimulus for erythropoesis acts against the development of anaemia. This might may also explain why a lower prevalence of anaemia was found in patients with COPD who were candidates for LTOT (12.6% in men, 8.2% in women), apart from the fact that in this study haematocrit had been used as criterion (<39% in men, <36% in women) [START_REF] Chambellan | Prognostic value of the hematocrit in patients with severe COPD receiving long-term oxygen therapy[END_REF]. As in the present investigation, the prevalence of anaemia reported in this study was also higher in males with COPD.

To the best of our knowledge, the prevalence of anaemia in patients with CRF due to other respiratory diseases than COPD has not been systematically studied so far. Our data reveal that in severe restrictive disease anaemia is nearly equally frequent, as the overall prevalence in non-COPD was 11.5% and not significantly different from that in OD or prevalence was found in patients with NMD (20.8%) and "other respiratory diseases" (14.3%; predominantly interstitial lung disease), whereas patients with TRD showed the lowest prevalence (6.3%). In COPD anaemia reflects prognosis [START_REF] Celli | The body-mass index, airflow obstruction, dyspnoea, and exercise capacity index in chronic obstructive pulmonary disease[END_REF]. Correspondingly, in non-COPD patients anaemia also appears to be inversely related to long-term survival, as this is known to be best in patients with CRF due to TRD and often worse in patients with lung fibrosis or NMD such as amyotrophic lateral sclerosis. In view of this it is surprising, that also in patients with OHS anaemia was observed in a considerable number of patients.

The current study was not designed to elucidate causative mechanisms regarding anemia. Phenomenologically, anaemic patients with OD showed higher age, lower BMI and total protein, and a higher rate of relevant co-morbidities. Among these, diabetes mellitus could be causal for anaemia [START_REF] Singh | Erythropoietic stress and anaemia in diabetes mellitus[END_REF] and the development of coronary heart disease and cardiac arrhythmias probably favoured by it.

ACD is a frequent phenomenon in patients with acute or chronic immune activation [START_REF] Cartwright | The anaemia of chronic disorders[END_REF]. Interleukin-1, interleukin-6, tumor necrosis factor-α and interferon-γ are involved in the underlying mechanism [START_REF] Weiss | Anaemia of chronic disease[END_REF]. These cytokines also take part in the pathogenesis of COPD [START_REF] Barnes | The cytokine network in chronic obstructive pulmonary disease[END_REF] and therefore could contribute to the development of anaemia in COPD (5;10;23). In addition, an imbalance between the erythropoietin-stimulating effect of hypoxia and inflammationinduced erythropoietin resistance resulting in anaemia has been proposed in COPD [START_REF] Similowski | The potential impact of anaemia of chronic disease in COPD[END_REF]. Our finding, that anaemia is present in severe respiratory disease largely irrespective of the underlying disorder suggests that inflammation probably is not the major driver of anaemia. Thus, anaemia was also prevalent in disorders such as NMD, TRD or OHS, which are commonly considered as non-inflammatory.

Among the mechanisms evoking anaemia in CRF, malnutrition probably plays a major role. Actually, haematocrit has been found to be positively correlated with BMI [START_REF] Chambellan | Prognostic value of the hematocrit in patients with severe COPD receiving long-term oxygen therapy[END_REF].

Correspondingly, in our study patients with OD and anaemia presented with lower BMI and This was confirmed in an additional analysis excluding OHS patients (data not shown).

Malnutrition, especially vitamin deficiency, is however also reflected in measures beyond BMI and total protein. It occurs frequently in NMD, such as duchenne muscular dystrophia [START_REF] Davidson | A review of nutrition in Duchenne muscular dystrophy[END_REF], due to dysphagia and/or dyspnoea and needs to be treated by gastrostomy tube feeding [START_REF] Birnkrant | Noninvasive ventilation during gastrostomy tube placement in patients with severe duchenne muscular dystrophy: case reports and review of the literature[END_REF]. Similarly, in anorexia nervosa, anaemia is common, and weight loss is associated with the disappearance of hematopoietic cells and an increased fat fraction in bone marrow [START_REF] Abella | Bone marrow changes in anorexia nervosa are correlated with the amount of weight loss and not with other clinical findings[END_REF].

This may be associated with lower leukocyte numbers, as in anaemic patients with RD in our study. Anaemia is also frequent in the elderly and often of unknown cause [START_REF] Guralnik | Prevalence of anaemia in persons 65 years and older in the United States: evidence for a high rate of unexplained anaemia[END_REF].

Correspondingly, age was also associated with lower haemoglobin in the present study, in line with previous results in COPD (5;6). Taken together, these data suggest that anaemia in these patients is of multifactorial origin.

Dyspnoea is a known symptom in anaemia. We found a higher PaO 2 and pH, and a lower PaCO 2 in anaemic patients. Among these, PaO 2 and pH were independently associated with anaemia in OD, both of them possibly based on hyperventilation. Anaemia in COPD is linked to morbidity and mortality (5;6), and anaemic patients with COPD and respiratory failure might benefit from blood transfusion (28;29). In patients with heart failure exercise capacity improves after rising haemoglobin level [START_REF] Mancini | Effect of erythropoietin on exercise capacity in patients with moderate to severe chronic heart failure[END_REF]. Thus, in addition to worsening tissue oxygenation, anaemia could increase the work of breathing and thereby contribute to the impairment of the nutritional status and prognosis in CRF.

Our study is limited by its partially retrospective design, which hampers the causative interpretation. Moreover, there might have been potential confounders of anaemia which became evident only at a later time and were not detected in our retrospective data analysis. Not only patients with stable disease were included. It appeared, however, that acute infection was not associated with a higher prevalence of anaemia. Another limitation is the lack of a control group. An age-matched control cohort is difficult to define and was not

  ) due to chronic respiratory failure (CRF). To reduce the bias by confounders, patients with known causes for anaemia were strictly excluded from the analysis.

  patients, and disease category (OD versus RD) as binary variable, were evaluated by multivariate regression analyses to identify independent factors. A p-value <0.05 was considered statistically significant. Calculations were performed using PASW statistics 17.0 (Chicago, IL, USA).

  protein. However, neither BMI nor total protein was associated with anaemia in RD.

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Selection of study population. Definition of abbreviations: NIV=non-invasive ventilation; eGFR=estimated glomular filtration rate. 168x122mm (300 x 300 DPI)

Table 1 .

 1 Patients' characteristics (n=595) with either obstructive or restrictive diseases.

	TABLES

Table 2 .

 2 Characteristics of anaemic versus non-anaemic patients (n=595).

	Variable	Obstructive disease	P value §	Restrictive disease	P value §
		Anaemic	Non-Anemic		Anemic	Non-Anemic
	N (%)	48 (14.7 %)	278 (85.3 %)		31 (11.5 %)	238 (88.5 %)
	Sex (F/M)	7/41	82/196	0.035	15/16	115/123	1.000
	Age (years)	70.40 (62.6; 73.9)	65.6 (58.6; 70.8)	0.003	65.7 (59.5; 71.4)	60.1 (49.1; 67.5)	0.008
	BMI (kg/m²)	24.4 (20.9; 29.8)	28.6 (22.5; 33.9)	0.011	33.7 (25.7; 43.4)	35.0 (25.6; 43.1)	0.813
	Previous LTOT (n/%)	22/45.8	127/45.7	1.000	7/22.6	44/18.5	0.626
	Laboratory parameters
	Haemoglobin (g/dl)	11.9 (10.9; 12.5)	14.8 (13.7; 16.2)	<0.001	11.5 (10.8; 12.0)	15.1 (13.7; 16.6)	<0.001
	Haematocrit (%)	36.0 (33.3; 38.0)	45.0 (42.0; 50.0)	<0.001	35.0 (32.0; 37.0)	46.0 (41.0; 52.0)	<0.001
	Leucocytes (10³/ml)	9.4 (7.7; 11.9)	9.3 (7.5; 11.7)	0.873	6.6 (5.3; 8.4)	7.8 (6.6; 9.5)	0.006
	CRP (mg/dl)	8.7 (3.5; 39.7)	7.5 (4.5; 21.7)	0.851	6.1 (4.5; 33.9)	5.2 (4.5; 15.0)	0.433
	Creatinine (mg/dl)	0.9 (0.7; 1.1)	0.9 (0.8; 1.1)	0.780	0.9 (0.7; 1.0)	0.8 (0.7; 1.0)	0.284
	eGFR (ml/min/1.73 m²)	86.2 (63.8; 117.1)	87.1 (69.7; 102.0)	0.975	88.6 (57.8; 105.8)	91.8 (69.9; 116.1)	0.234
	Total protein (g/dl)	6.4 (5.8; 6.7)	6.6 (6.2; 7.1)	0.012	6.3 (6.0; 7.0)	6.7 (6.3; 7.2)	0.132
	Functional parameters
	VC (%predicted)	49.0 (36.4; 58.9)	53.1 (45.0; 61.8)	0.050	55.6 (41.7; 67.4)	53.9 (37.4; 67.5)	0.544
	FEV 1 (%predicted)	29.5 (22.6; 40.7)	31.0 (23.8; 40.4)	0.527	51.3 (42.8; 58.5)	49.2 (34.3; 64.1)	0.469
	Blood gas values without
	oxygen supply
	pH	7.45 (7.40; 7.49)	7.41 (7.38; 7.44)	0.014	7.45 (7.41; 7.46)	7.41 (7.39; 7.44)	0.011
	PaO2 (mmHg)	54.5 (46.0; 63.3)	48.0 (42.0; 55.0)	0.012	57.0 (49.0; 66.8)	52.0 (45.5; 60.0)	0.056
	PaCO2 (mmHg)	48.5 (40.8; 56.5)	53.0 (48.0; 58.0)	0.090	48.0 (39.8; 53.8)	50.0 (46.0; 56.0)	0.057
	BE (mmol/l)	7.2 (4.2; 16.5)	7.6 (4.7; 10.2)	0.951	5.9 (2.9; 10.6)	6.4 (4.3; 9.0)	0.597
	Co-morbidities
	Chronic renal failure # (n/%)	10/20.8	37/13.3	0.183	9/29.0	35/14.7	0.066
	Coronary heart disease (n/%)	14/29.2	38/13.7	0.010	5/16.1	14/5.9	0.053
	Left heart failure (n/%)	6/12.5	50/18.0	0.414	3/9.7	19/8.0	0.727
	Cardiac arrhythmias (n/%)	13/27.1	35/12.6	0.014	4/12.9	20/8.4	0.498
	Arterial hypertension (n/%)	21/43.8	119/42.8	1.000	21/67.7	118/49.6	0.084
	Diabetes mellitus (n/%)	20/41.7	59/21.2	0.003	9/29.0	57/23.9	0.513
	Acute infection (n/%)	17/35.4	73/26.3	0.221	10/32.3	49/20.6	0.165
	Medication
	Anticholinergic agents (n/%)	39/81.3	228/82.0	0.842	9/29.0	58/24.4	0.659
	β 2 -Sympathometics (n/%)	45/93.8	250/89.9	0.594	9/29.0	84/35.3	0.552
	Steroids (inhalative) (n/%)	29/60.4	186/66.9	0.411	6/19.4	52/21.8	1.000
	Steroids (systemic) (n/%)	31/64.6	166/59.7	0.632	4/12.9	43/18.1	0.619
	Theophylline (n/%)	14/29.2	158/56.8	<0.001	5/16.1	63/26.5	0.274
	ACE-blockers (n/%)	19/39.6	120/43.2	0.752	13/41.9	105/44.1	0.850
	Angiotensin-II-blockers (n/%)	3/6.3	17/6.1	1.000	4/12.9	16/6.7	0.264
	Βeta-blockers (n/%)	6/12.5	21/7.6	0.258	10/32.3	41/17.2	0.053
	Calcium-antagonists (n/%)	10/20.8	42/15.1	0.392	5/16.1	47/19.7	0.810
	Digitalis (n/%)	11/22.9	54/19.4	0.561	4/12.9	33/13.9	1.000
	Diuretics (n/%)	45/93.8	223/80.2	0.024	25/80.6	182/76.5	0.821

Table 3 .

 3 Stepwise binary logistic multivariate regression analysis for the presence of anaemia

	A. All patients with CRF
	Independent variable	Odds ratio (95% CI)	P value
	Age (years)	0.954 (0.920-0.990)	0.012
	pH	<0.001 (<0.001-0.006)	0.002
	PaO 2 (mmHg)	0.957 (0.927-0.987)	0.006
	B. Patients with OD
	Independent variable	Odds ratio (95% CI)	P value
	pH	<0.001 (<0.001-0.041)	0.011
	PaO 2 (mmHg)	0.931 (0.879-0.985)	0.013
	C. Patients with RD
	Independent variable	Odds ratio (95% CI)	P value
	Leukocyte number (10³/µl)	1.306 (1.019-1.674)	0.035
	PaO 2 (mmHg)	<0.001 (0.001-0.098)	0.020

Page 24 of 24 International Journal of Clinical Practice International Journal of Clinical Practice

AUTHORS CONTRIBUTIONS

F.K. participated in study design, statistical evaluation and data interpretation and wrote the manuscript. C.M. and A.T. collected the data, helped in statistical evaluation and data interpretation. R.A.J. helped in statistical evaluation of the data, their interpretation and participated in writing the manuscript. D.H. participated in study design and critical revision of the manuscript. C.P. helped in critical revision of the manuscript and data interpretation. M.P. participated in data interpretation and the initiation of the study, enabled the realization and supervised its performance. S.B. initiated the study, helped writing the manuscript and participated in statistical evaluation, study design and data interpretation.


D T Nguyen

Ph C Voisin

C Roussignol

Jean-Sébastien Roquelet

Guillaume Lauret

Cassabois

Ph Roussignol

C Roquelet

J S Lauret

G Cassabois

Elastic exciton-exciton scattering in photoexcited carbon nanotubes

Keywords: numbers: 78.67.Ch, 71.35.-y, 78.47.nd

come

Single wall carbon nanotubes (SWNTs) are rolled graphene sheets with nanometric radial quantum confinement, and the translation invariance along the tube axis makes them a reference one-dimensional (1D) system [START_REF] Saito | Physical properties of carbon nanotubes[END_REF]. The one-dimensionality of carriers in SWNTs results in strong Coulomb interactions. The first striking signature is the non-perturbative binding of an electronhole pair into an exciton due to the attractive Coulomb potential [START_REF] Perebeinos | [END_REF]. The excitonic binding energy is found to be approximately one third of the single-particle gap [3,4] and it opens the way for carbon-based optoelectronic devices operating at room-temperature [5][6][7]. Such a phenomenology resembles the binding of Frenkel excitons in organic materials. In these compounds, exciton-exciton collisions are known to control the population relaxation through an efficient exciton-exciton annihilation (EEA). This Auger process is one type of collisions where one exciton recombines and gives its energy to the second one, that is promoted to a high-energy state, resonant with the continuum of electron-hole pairs (Fig. 1). This nonradiative recombination pathway plays a key role in the population relaxation of Frenkel excitons in organic materials, especially J-aggregates [8] and conjugated polymers [9]. On the contrary, for Wannier excitons in inorganic bulk semiconductors or quantum wells [START_REF] Shah | Ultrafast spectroscopy of semiconductors and semiconductor nanostructures[END_REF], manybody effects first manifest as elastic exciton-exciton scattering (EES) that redistributes the population within exciton bands (Fig. 1) and leads to self-broadening of the excitonic transition. In the prospect of applications, the understanding and the control of the excitonic nonlinearities appears as a central issue for the development of optoelectronic devices, such as lasers, switches or quantum light sources [5][6][7][8][9][START_REF] Shah | Ultrafast spectroscopy of semiconductors and semiconductor nanostructures[END_REF].

In SWNTs, several time-resolved experiments have shown evidence for efficient EEA that drives the population dynamics even at low exciton density [START_REF] Wang | [END_REF]12]. This observation supports the analogy with organic materials and further raises the question of the excitonic decoherence in SWNTs. In organic compounds, the decoherence induced by exciton-exciton collisions comes from the population relaxation due to EEA, whereas in inorganic systems it consists in pure dephasing by EES (the pure dephasing being usually characterized by the T 2 time given by 1/T 2 = 1/2T 1 + 1/T 2 where T 1 and T 2 are the population and coherence relaxation times, respectively). In inorganic semiconductors, the EEA process also affects the relaxation dynamics but at very high excitation densities. On the contrary, the lack of evidence for EES in organic materials is in very high contrast to inorganic semiconductors, as pointed out in Ref. [13]. Here, we show that the collision-induced broadening of excitons in carbon nanotubes is controlled by EES as for Wannier excitons in inorganic semiconductors, while the population relaxation is driven by EEA as for Frenkel excitons in organic materials. Our measurements are performed by means of an original technique of spectral hole-burning spectroscopy, that allows us to explore the exciton decoherence over three decades of excitation density. We observe that the collision-induced broadening is not limited by EEA and we demonstrate that the major contribution consists in pure dephasing by EES. Our interpretation is supported by theoretical calculations of the excitonic nonlinearities in SWNTs, and a quantitative agreement with our experimental results is obtained by calculation of EES based on a nonequilibrium formalism within the second Born approximation.

We have studied SWNTs synthetized by laser ablation of a doped graphite target and purified by ultrasonic and chemical treatment [14]. Semiconducting SWNTs contribute to the optical absorption by inhomogeneously broadened lines centered at 0.75 and 1.3 eV, respectively [14]. Metallic SWNTs absorb at higher energies around 1.9 eV [14]. Our work is focused on the fundamental excitonic transition in semiconducting SWNTs absorbing around 0.75 eV (Fig. 2, inset). In the prospect of evidencing the intrinsic properties of 1D excitons, we have tried to suppress the influence of external non-radiative relaxation processes as much as possible. Therefore, the SWNTs are first isolated by the micelle-wrapping technique [15,16] which allows the observation of a bright photoluminescence signal, as shown by the bottom curve in the inset of Fig. 2. The individual SWNTs are further embedded in a gelatin matrix following the procedure described in Ref. [17], in order to perform measurements at cryogenic temperatures thus minimizing the contribution of exciton-phonon dephasing.

Nonlinear spectral hole-burning experiments were performed around 0.8 eV (λ∼1.55 µm) [18]. Our study under cw-excitation differs from previous nonlinear optical measurements which focused on the ultrafast coherent nonlinear response and its specific aspects in the context of 1D excitons in SWNTs [19]. In our spectrallyresolved pump-probe differential transmission measurements, a narrow pump laser centered at 0.8 eV (indicated by the vertical arrow in the inset of Fig. 2) partially saturates the absorption of the SWNTs that are in resonance. The corresponding sub-ensemble of SWNTs reduces the overall absorption of the sample in a spectral window determined by the homogeneous linewidth Γ. The photoinduced bleaching of the SWNTs sample is detected by recording the change of transmission of a tunable probe laser. A typical spectrum of the pump-induced differential transmission ∆T /T of the probe laser is displayed in Fig. 2. The nonlinear signal exhibits a pronounced bleaching with an amplitude of 3×10 -4 and a full width at half maximum (FWHM) of 6 meV, that is attributed to the excitonic hole-burning signal of the SWNTs. This component is superimposed on a negative signal, which corresponds to a residual non-resonant photo-absorption that is also detected at very large detuning with the pump laser.

The analysis of absorption saturation measurements obeys different rules depending on the fermionic or bosonic statistics of the elementary excitation of the system. In the case of excitonic transitions, the saturation of absorption is not due to a redistribution of an electronic population among the ground and excited states as in atomic systems, but to a change of the oscillator strength f and homogeneous linewidth Γ of the excitonic transition on raising the exciton density, as described in Ref. [20]. When analyzing our measurements as a function of pump power (see details of the technical aspects in the supplemental material [21]), we take advantage of the different signatures of collision-induced broadening (∆Γ) and oscillator strength renormalization (∆f ) to disentangle these two components and extract their contribution to the nonlinear response (Fig. 2, green and blue dashed lines). The result of our data analysis is summarized in Fig. 3(a) where we display the relative variations of the homogeneous linewidth ∆Γ/Γ (full circles) and oscillator strength -∆f /f (open squares) as a function of the pump power. Although both components are required to fit the width and amplitude of our differential transmission signal (Fig. 2), we find that ∆Γ/Γ provides the major nonlinearity, thus leading to a good relative precision in its estimation but to a larger uncertainty for the minor contribution of -∆f /f , as seen in Fig. 3(a). In the prospect of the quantitative interpretation of exciton dephasing in SWNTs, we finally stress that the recording of both collision-induced broadening and oscillator strength renormalization appears to be a fundamental feature for extracting the relative contributions of EEA and EES, which are at the heart of this paper. We have developped a theoretical model (described below) that leads to a global quantitative interpretation of our measurements with the exciton Bohr radius a B as the only free parameter. Its estimation is strongly constrained by the simultaneous comparison of -∆f /f and ∆Γ/Γ with our theoretical predictions, and we find a B =5±2 nm (Fig. 3(a)). This value is consistent with the calculation of the Bohr radius for SWNTs with a diameter of 1.2 nm (i.e. an excitonic transition around 0.8 eV) inside a micelle structure [START_REF] Perebeinos | [END_REF]22,23]. In fact, our study reveals the original phenomenology of 1D excitons in SWNTs, where the exciton Bohr radius is of the order of magnitude of the nanotube diameter. This results in physical properties usually separately observed in inorganic and organic materials, as detailed below.

In the framework of the model developped by Schmitt-Rink et al. for excitonic nonlinearities in 2D quantum wells [20], we first discuss the analysis of the oscillator strength renormalization by using the expression ∆f f = -n ns , which is valid for small perturbation (n n s ), where n is the exciton density, and n s the saturation density. The exciton density n is fixed by the characteristic parameters of the population relaxation in SWNTs. Its estimation for a given pump power is a key factor and requires a careful analysis (see supplemental material [21]). The saturation density n s is fixed by two mechanisms, which are both related to the exclusion principle: phase space filling corresponding to the conduction and valence band filling under generation of excitons, and exciton wave-function renormalization due to the screening of the electron-hole interaction in the presence of other carriers [20]. Let us arbitrarily define the Mott density n M by 1/πa 2 B and 1/2a B for 2D and 1D excitons respectively, with a B the exciton Bohr radius. In 2D quantum wells, Schmitt-Rink et al. showed that 1/n s =(C P SF + C EW R )/n M where C P SF =32/7 and C EW R ∼3.94 are the numerical coefficients associated to phase space filling and exciton wave-function renormalization, respectively. We have extended the theoretical treatment of Ref. [20] to the case of 1D excitons. We find C P SF =3/2 and C EW R =1/4, thus showing that there is no dramatic dimensional effect on these coefficients, and that phase space filling predominates when increasing the confinement.

The variations of ∆Γ/Γ with pump power characterize the effect of collision-induced broadening (we checked that there is no thermal effect due to the pump). The first striking feature is the sublinearity of the collision-induced broadening as a function of the excitation density, as illustrated by the linear-linear plot of ∆Γ in Fig. 3(b). Under the assumption [21] of a linear dependence of the collision-induced broadening on the exciton density, our data indicate that the stationary exciton density does not depend linearly on the pump fluence (so that ∆f /f is also sublinear with the pump power). This phenomenology is the manifestation of the interband Auger process of EEA depicted in Fig. 1. Several groups have brought evidence by means of time-resolved experiments that this mechanism controls the relaxation dynamics of the exciton population in SWNTs [START_REF] Wang | [END_REF]12]. In our measurements performed under cw-excitation, EEA results in a sublinear variation of the stationary exciton density with the pump power [21]. The predominance of EEA in the population relaxation is in fact not specific to excitons in SWNTs and is a general trend for Frenkel excitons in conjugated polymers or J-aggregates [8,9].

We show now that this similarity between organic materials and the pure carbon-based nanostructures formed by SWNTs breaks down for the coherence relaxation induced by exciton-exciton collisions. In Fig. 3(b) we have displayed in solid blue line ∆Γ EEA , the contribution of EEA to collision-induced broadening given by 2 An where A is the Auger annihilation coefficient defined in Ref. [24]. Since EEA drives the population relaxation, it also induces coherence relaxation but it is not sufficient to account for the excitation power dependence of the spectral broadening. This issue is totally unaddressed in the literature, and the quantitative interpretation of our experimental results presented in Fig. 3 is achieved by taking into account EES. This intraband mechanism corresponds to the exciton-exciton collisions that lead to pure dephasing by quasi-elastic exciton scattering within the fundamental exciton band (Fig. 1). The calculation of the self-broadening due to EES requires the theoretical framework of the second Born approximation which was successfully applied for 3D and 2D excitons [25,26]. This theory is also mandatory in 1D because of the divergence of the exciton density of states at the band edge, reminiscent of Van Hove singularities. In the framework of the regularization procedure of the Coulomb interaction based on a contact potential [24], we find:

∆Γ EES = E b n 2 2 µa B ∫ +∞ -∞ d q|I( q)| 2 2Γ π 1 Λ 2 q 4 + (2Γ ) 2
where Γ =Γ+∆Γ EES with Γ=6 meV the homogeneous linewidth without exciton-exciton interactions, µ the excitonic reduced mass, Λ= 2 /(m e + m h )a 2

B with m e and m h the electron and hole masses equal to 0.1m 0 [START_REF] Saito | Physical properties of carbon nanotubes[END_REF], I( q) the matrix element of fermion-fermion exchange interactions given by 16 ( q 2 +4) 2 -6 ( q 2 +4)( q 2 +1) , and E b the exciton binding energy of 250 meV [START_REF] Perebeinos | [END_REF][3][4].

The competition between EEA and EES is at the heart of the physics governing the collision-induced broadening in SWNTs. The efficiency of these excitonic collision processes is conveniently characterized by the dimensionless parameters ξ EEA and ξ EES , where the collisioninduced broadening is expressed as ∆Γ = E b ξ n nM , with ξ=ξ EEA +ξ EES . The linear dependence of ∆Γ with E b stems from the Coulomb nature of exciton-exciton interactions which impose the typical energy scale of electronic correlations between excitons. Space filling is expressed by the ratio n/n M . The numerical values of ξ EEA and ξ EES depend on the Auger annihilation rate A, exciton binding energy E b and exciton Bohr radius a B (see above). Our fitting procedure consists in analyzing our whole set of data with a B as the only free parameter, other quantities being documented in the literature [21]. The estimation of a B =5±2 nm thus leads to the values ξ EEA =0. 14 While the exciton binding energy E b comprises the modification of the electronic Coulomb correlations, the ξ EES factor contains the information on the density of final states in the scattering process, which is also strongly dimension dependent. From Table 1 where we observe that the ξ EES factors decrease on reducing the exciton dimensionality, we conclude that the strong efficiency of EES in SWNTs arises from the exciton binding energy which is indeed two orders of magnitude larger than for 3D or 2D excitons, and imposes the overall increase of the collision-induced broadening with confinement, since E b ξ EES reaches its highest value in 1D (Table 1).

As far as the interplay between EEA and EES is concerned, an important parameter appears to be the ratio E b /E g where E g is the single-particle energy gap. As pointed out in Ref. [24], the efficiency of EEA scales like E b /E g , and so does ξ EEA , thus explaining the predominance of EEA in strongly bound Frenkel excitons in organic materials. We therefore conclude that SWNTs characterized by an exciton Bohr radius a B =5±2 nm correspond to an intermediate confinement regime between Wannier and Frenkel excitons, at the frontier of inorganic and organic materials.

In summary, we have shown that the collision-induced broadening of excitons in carbon nanotubes is controlled by EES as for Wannier excitons in inorganic semiconductors, while the population relaxation is driven by EEA as for Frenkel excitons in organic materials. Our study reveals the striking hybrid properties of 1D excitons in carbon nanotubes at the crossover of molecular systems and solid-state nanostructures. Our work motivates the exploration of possible scaling laws as a function of the nanotube diameter and the investigation of the limit cases of excitons in nanotubes of very large diameter, corresponding to graphene, and vanishing diameter, such as π-conjugated polymers.

FIG. 1 .

 1 FIG. 1. Exciton energy dispersion and schematic representation of the Auger recombination process of exciton-exciton annihilation (EEA, in blue), and the purely dephasing mechanism of elastic exciton-exciton scattering (EES, in red). The dashed lines delimitate the exciton paths in k-space for EEA and EES.

FIG. 3 .

 3 FIG. 3. (a) Relative variations of the homogeneous linewidth ∆Γ/Γ (full circles), and oscillator strength -∆f /f (open squares), at 10K. Data (symbols) and theoretical fits (solid lines) are plotted as a function of the incident power of the pump laser. The fitting parameter is the exciton Bohr radius aB=5 nm, and the shaded areas correspond to the tolerance of ±2 nm in its estimation. (b) Homogeneous linewidth variations ∆Γ as a function of pump power. Theoretical fits: EEA only (blue line), EEA+EES (red line).

  and ξ EES =0.27.

	d ξEES E b (meV) E b ξEES (meV) Ref.
	3 6.3	4	25	[27]
	2 0.47	8.5	4	[28]
	1 0.27	250	68	this study
	TABLE I. Collision-induced broadening parameters as a func-
	tion of exciton dimensionality d. E b is the exciton binding
	energy, and ξEES a dimensionless parameter.

We thank C. Ciuti and T. Ando for helpful discussions. This work was financially supported by the CNano IdF contract TAIGA and the ANR agency-contract BONAFO.

* e-mail: Guillaume.Cassabois@univ-montp2.fr