Philippe Decq
email: philippe.decq@aphp.fr

Nathalie Gault

Mathias Balndeau

Tristan Kerdraon

Miassa Berkal

Amine El Helou

Bernard Dusfour

Jean-Claude Peyrin

Mathias Blandeau

Amine Elhelou

Long-term consequences of recurrent sports concussion

Keywords: Concussion, Rugby, Depression, Cognitive disorder, Headache

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

Introduction

According to the American Congress of Rehabilitation Medicine, mild traumatic brain injury is defined as Ba traumatically-induced physiologic disruption of brain function including: any period of loss of consciousness <30 min; any loss of memory <24 h; any alteration in mental state at the time of the accident; and focal neurological deficits that may or may not be transient [START_REF]ACRM: Mild Traumatic Brain Injury Committee (1993) Definition of mild traumatic brain injury[END_REF]. The term Bconcussion^is generally used in the context of sports. The most recent international consensus conference on concussion in sport [START_REF] Mccrory | Consensus statement on concussion in sport: the 4th International Conference on Concussion in Sport held in Zurich, November 2012[END_REF] established a definition of concussion that reflects the complexity of an apparently Bbenign^phenomenon that can be briefly described as sudden, transient brain dysfunction following a direct or transmitted blow to the head, which remains one of the most difficult forms of sports injury to diagnose, evaluate and manage, as no clinical or complementary diagnostic test is currently available to reliably and immediately confirm the diagnosis [START_REF] Aubry | Concussion in Sport Group (2002) Summary and agreement statement of the First International Conference on Concussion in Sport, Vienna 2001. Recommendations for the improvement of safety and health of athletes who may suffer concussive injuries[END_REF][START_REF] Mccrory | Summary and agreement statement of the 2nd International Conference on Concussion in Sport, Prague[END_REF][START_REF] Mccrory | Consensus statement on concussion in sport-the Third International Conference on Concussion in Sport held in Zurich, November 2008[END_REF][START_REF] Mccrory | Consensus statement on concussion in sport: the 4th International Conference on Concussion in Sport held in Zurich, November 2012[END_REF].

The incidence of concussion in sport varies according to the type of sport, but is higher for so-called collision sports, such as American football or ice hockey [START_REF] Gessel | Concussions among United States high school and collegiate athletes[END_REF][START_REF] Hootman | Epidemiology of collegiate injuries for 15 sports: summary and recommendations for injury prevention initiatives[END_REF][START_REF] Lincoln | Trends in concussion incidence in high school sports: a prospective 11-year study[END_REF]35]. The Center for Disease Control and Prevention has estimated that about 135,000 patients with sports concussion attend emergency departments each year in the USA [START_REF] Laker | Epidemiology of concussion and mild traumatic brain injury[END_REF]. The incidence of concussion during rugby matches ranges from 4.1 to 8 concussions per 1,000 player-hours [START_REF] Hollis | Compliance with return-to-play regulations following concussion in Australian schoolboy and community rugby union players[END_REF][START_REF] Kemp | The epidemiology of head injuries in English professional rugby union[END_REF]. Only one study has recorded the number of head impacts (linear accelerations >10 G) observed during rugby matches and reported a mean of 564 ± 618 impacts per player over the season and a mean of 95 ± 133 impacts per player per match [START_REF] King | Instrumented mouthguard acceleration analyses for head impacts in amateur rugby union players over a season of matches[END_REF].

Head impacts, some of which are responsible for clinical concussions, therefore appear to be an inevitable aspect of this type of sport without any apparent sequelae, leading these accidents to be generally considered benign. Only 5 to 10% of players with concussion have persistent symptoms more than 10 days after the event, which usually completely resolve over a period of several weeks [START_REF] Makdissi | Natural history of concussion in sport: markers of severity and implications for management[END_REF]. However, the critical issue is to determine whether repeated concussions can be partly or completely responsible for longer term neurological disorders, such as:

-Depressive disorders: Recent studies in a population of retired American football players (mean age: 53.8 ± 13.4 years, mean duration of professional career: 6.6 ± 3.6 years) have retrospectively revealed a statistical association between the number of reported concussions and frequency of depressive episodes, although the global frequency of depressive disorders reported in this population is comparable to that observed in the general population [START_REF] Gonzalez | The epidemiology of major depression and ethnicity in the United States[END_REF]. Retired sportsmen who report one or two episodes of concussion appear to be exposed to a 1.5-fold higher risk of depression than sportsmen with no history of concussion. The risk of depression is increased threefold in sportsmen reporting three or more concussions during their career [START_REF] Guskiewicz | Recurrent concussion and risk of depression in retired professional football players[END_REF]. -Headache: Headache is frequent after concussion and constitutes one of the key symptoms of the diagnosis of post-concussion syndrome [START_REF] Carney | Concussion guidelines step 1: systematic review of prevalent indicators[END_REF][START_REF] Merritt | Injury-related predictors of symptom severity following sports-related concussion[END_REF]. Chronic posttraumatic headache is defined as secondary headache in the International Classification of Headache Disorders (ICHD-2) [START_REF]Headache Classification Committee of the International Headache (2013) The International Classification of Headache Disorders, 3rd edition[END_REF]. Its incidence is poorly defined, and its pathophysiology and potential link with the development of neurodegenerative disease remain controversial [START_REF] Seifert | Sports concussion and associated post-traumatic headache[END_REF]. -Mild cognitive disorder: The same type of retrospective survey conducted among 513 retired American football players showed that 35% of them presented an SF-36

Mental Component Summary (MCS) score compatible with possible mild cognitive disorder, and the degree of cognitive impairment increased with the number of reported concussions [START_REF] Guskiewicz | Association between recurrent concussion and late-life cognitive impairment in retired professional football players[END_REF], but this group of sportsmen was not compared with a control group. -Neurodegenerative disease: A history of serious head injury has been identified for many years as a risk factor for the development of neurodegenerative disease, especially in epidemiological studies of Alzheimer's disease [START_REF] Mortimer | Head trauma as a risk factor for Alzheimer's disease: a collaborative re-analysis of case-control studies. EURODEM Risk Factors Research Group[END_REF]. Regarding concussion, a study of causes of death in a population of 3,439 American football players who had played between 1959 and 1988 revealed an excess mortality due to Alzheimer's disease (standardized mortality ratio SMR = 3.86), amyotrophic lateral sclerosis (SMR = 4.31) and Parkinson's disease (SMR 1.69) compared to the general population [START_REF] Lehman | Neurodegenerative causes of death among retired National Football League players[END_REF]. However, it should be stressed that in this study, the overall mortality was very low compared to that of the general population (SMR = 0.53). Finally, chronic post-traumatic encephalopathy (CTE) has been described for a long time in boxers, for the first time by H. Martland in 1928, although the term was published for the first time only in 1947 by Critchley [START_REF] Critchley | Punch-drunk syndromes: the chronic traumatic encephalopathy of boxers. Hommage à Clovis Vincent[END_REF]. Recently, a number of clinical cases and autopsy series have been published concerning sports other than boxing, particularly American football, reopening the debate on the causal relationship between CTE and recurrent concussion [START_REF] Cantu | Chronic traumatic encephalopathy in the National Football League[END_REF][START_REF] Mckee | TDP-43 proteinopathy and motor neuron disease in chronic traumatic encephalopathy[END_REF][START_REF] Omalu | Chronic traumatic encephalopathy in a National Football League player[END_REF][START_REF] Omalu | Chronic traumatic encephalopathy in a national football league player: part II[END_REF].

In the absence of prospective epidemiological studies able to establish an indirect or direct relationship between recurrent concussion and these disorders, there are many unresolved controversies that need to be considered very cautiously [START_REF] Mccrory | What is the evidence for chronic concussion-related changes in retired athletes: behavioural, pathological and clinical outcomes?[END_REF]. Although American football is a sport derived from rugby, to our knowledge no studies have yet been published on the possibility of long-term neurological disorders secondary to rugby injuries.

The purpose of this study was to compare a population of retired rugby players with a population of other retired sportsmen in terms of the prevalence of depressive disorders, mild cognitive disorders and headache and to study the link between scores evaluating these disorders and the number of reported concussions.

Material and methods

Design

We conducted a cross-sectional study comparing exposure to recurrent concussion in sports and the incidence of depressive disorders, mild cognitive disorders, fluency disorders and headache.

Study populations

This study included retired, French mother tongue, high-level sportsmen, aged 45 to 65 years, who had played sports for at least 10 years and had reached the national or international championship level between 1985 and 1990, divided into two groups:

Rugby (exposed) group Composed of retired rugby players who had reached the first division championship level in France between 1985 and 1990: 1,491 rugby players who had played for 24 clubs were identified from game sheets; 1,047 sportsmen (RRPs) were contacted. Finally, 524 were invited by letter to participate, and 239 (response rate: 46%) agreed to participate in the study. This group was considered to be exposed to a risk of recurrent concussion.

Other sports (control) group Composed of other retired sportsmen (ORSs) registered on Bhigh-level^lists between 1985 and 1990: 1,164 sportsmen were identified by the French Ministry of Sports. Eighteen of the 41 sports federations to which these sportsmen belonged agreed to participate in the study representing 637 sportsmen; 455 were invited by letter to participate (71%), and 138 (response rate: 30%) agreed to participate in the study. This group was considered to be exposed to a lower risk of recurrent concussion.

Study procedure

We conducted a two-phase study First, a self-administered questionnaire was sent to the subjects with an invitation to make a telephone appointment for the second step of the study. When the subject agreed to participate, he returned the completed questionnaire indicating sociodemographic and lifestyle data, comorbidities and the history of reported concussion.

Second, a telephone conversation was conducted by an interviewer specifically devoted to this survey, with the use of validated questionnaires to explore depressive disorders (PHQ-9 score) [START_REF] Kroenke | The PHQ-9: validity of a brief depression severity measure[END_REF][START_REF] Martin | Validity of the Brief Patient Health Questionnaire Mood Scale (PHQ-9) in the general population[END_REF], mild cognitive disorders (F-TICS-m score) [START_REF] Cook | The use of the Modified Telephone Interview for Cognitive Status (TICS-M) in the detection of amnestic mild cognitive impairment[END_REF][START_REF] Lacoste | Adaptation française d'un outil d'évaluation par téléphone des troubles mnésiques: le French Telephone Interview for Cognitive Status Modified F-TICS-m)[END_REF][START_REF] Vercambre | Validation study of a French version of the modified telephone interview for cognitive status (F-TICS-m) in elderly women[END_REF], fluency disorders (Isaacs Set Test) [START_REF] Thomas Antérion | Apport de l'épreuve d'évocation lexicale du Set Test dans le dépistage de la maladie d'Alzheimer[END_REF] and headache severity (HIT-6 score) [START_REF] Martin | The Short-Form Headache Impact Test (HIT-6) was psychometrically equivalent in nine languages[END_REF][START_REF] Yang | Validation of the Headache Impact Test (HIT-6) across episodic and chronic migraine[END_REF].

The PHQ-9 score was further categorized as follows: minimal depressive disorder (PHQ-9: 0 to 4), mild depressive disorder (PHQ-9: 5 to 9), moderate depressive disorder (PHQ-9: 10 to 14), moderately severe depressive disorder (PHQ-9 15 to 19) and severe depressive disorder (PHQ-9: 20 to 27). A PHQ-9 score >9 was considered to be compatible with major depressive disorder [START_REF] Kroenke | The PHQ-9: validity of a brief depression severity measure[END_REF][START_REF] Zuithoff | The Patient Health Questionnaire-9 for detection of major depressive disorder in primary care: consequences of current thresholds in a crosssectional study[END_REF].

A TICS-m score ≤30 was considered to be compatible with mild cognitive disorder [START_REF] Cook | The use of the Modified Telephone Interview for Cognitive Status (TICS-M) in the detection of amnestic mild cognitive impairment[END_REF].

The severity of the headache and its impact on daily life were further categorized as follows: little or no impact on daily life (HIT-6 ≤49), some impact on daily life (HIT-6: 50 to 55), substantial impact on daily life (HIT-6: 56 to 59) and severe impact on daily life (HIT-6 ≥60) [START_REF] Yang | Validation of the Headache Impact Test (HIT-6) across episodic and chronic migraine[END_REF]. An HIT-6 score ≥50 was subsequently considered to be compatible with disabling headache.

Ethics

Subjects provided their consent to participate in the study. The study obtained a positive opinion from the institutional review board (CEERB PARIS NORD no. 14-048) and authorization from the French data protection authorities (CCTIRS no. 13-096 and CNIL no. 913132).

Statistical analysis

Qualitative variables are expressed as the number and percentage. Quantitative variables are expressed as median and interquartile range as well as mean and standard deviation.

Associations between the number of reported concussions and the PHQ-9, TICS-m, HIT-6 and Isaacs scores were studied successively by univariate linear regression models.

Multivariate analyses were then conducted to adjust for the sport group and factors that were associated with the scores in univariate analyses with a p-value < 0.20 as well as clinically relevant ones. The results are reported in the form of unadjusted and adjusted regression coefficients with their 95% confidence interval.

Statistical analysis was performed with R software, version 2.12.0 (The R Foundation for Statistical Computing).

Results

Results of the self-administered questionnaire

General description of the population

The study population comprised 377 retired sportsmen whose general characteristics are presented according to sport group in Table 1. The ORSs participated in various disciplines (athletics, badminton, canoeing, horseback riding, rock climbing, fencing, golf, weightlifting, swimming, paragliding, pelota, skiing, squash, table tennis, archery, triathlon, sailing and gliding). One hundred thirty-three (56%) of the sportsmen were forwards and 106 (44%) were backs.

Morphometric data show that RRPs had a significantly higher BMI than other retired sportsmen

Lifestyle and medical history

Daily alcohol consumption was reported more frequently by other retired sportsmen than RRPs (31% versus 20%), but more RRPs reported heavy drinking (5 glasses a day) than ORSs (88% versus 71%). RRPs more frequently reported impaired exercise capacity than ORSs (12% versus 5%) and a poorer perceived state of health (9% reported an excellent state of health versus 18%).

History of reported concussion

RRPs reported significantly more concussions than other retired sportsmen. The severity of reported concussions was comparable between the two groups in terms of loss of consciousness and loss of memory. Finally, 18% of RRPs and

Results of the telephone survey

Factors associated with the PHQ-9 score

The distribution of the PHQ-9 score is reported in Table 2 and Figs. 1 and2.

We showed that the median PHQ-9 score was higher in RRPs than other retired sportsmen, and a higher proportion of RRPs reported major depressive disorders (PHQ-9 score >9) than ORSs (p = 0.04).

Concussions and PHQ-9 score

The PHQ-9 score increased with the number of reported concussions regardless of the type of sport performed (Table 3, Fig. 3).

This trend was found to be significant after adjustment in multivariate analysis. History of depressive episodes and perceived state of health were factors independently associated with the PHQ-9 score: subjects with a history of depressive episodes reported higher PHQ-9 scores than those without a history of depressive episodes; similarly, subjects with a less favorable perceived state of health reported higher PHQ-9 scores than others (Table 4).

Factors associated with the TICS-m score

The distribution of the TICS-m score is reported in Table 2 and in Figs. 4 and5.

We showed that the median TICS-m score was lower in RRPs than ORSs (p = 0.007), and more mild cognitive disorders (TICS-m score ≤30) were observed in RRPs compared to ORSs (p = 0.005).

Concussion regardless of the type of sport and detection of mild cognitive disorders

The median TICS-m score seemed to be lower if concussions were reported (Table 5).

After adjustment, smoking and higher education were factors independently associated with a higher TICS-m score, while the sport group and age were factors independently associated with a lower TICS-m score. No association was observed between the TICS-m score and number of reported concussions (Table 6).

Study of verbal fluency disorders

Overall, no significant difference in verbal fluency was observed between the two groups of retired sportsmen (Table 2). In univariate analysis, neither the number of reported concussions nor the group of retired sportsmen was associated with a modification of the total Isaacs score.

Factors associated with the HIT-6 score

The distribution of the HIT-6 score is reported in Table 2 and Figs. 6 and7.

The median HIT-6 score was higher in the group of RRPs than in the group of ORSs (p = 0.084), with a similar proportion of subjects with disabling headache with an impact on daily life in the two groups (Table 2).

Concussion and the HIT-6 score

The HIT-6 score increased with the number of reported concussions (Table 7 and Fig. 8). NB: Interpretation of estimates: an estimate >0 indicates that the factor is associated with a higher PHQ-9 score; inversely, an estimate <0 indicates that the factor is associated with a lower PHQ-9 score This trend was found to be significant after adjustment on multivariate analysis (Table 8). A history of depression was also a factor independently associated with a higher HIT-6 score.

Discussion

This retrospective study conducted in 2014 in a population of retired, top-level sportsmen around the age of 50 years who had played competitive sport between 1985 and 1990 shows that:

RRPs reported more concussions per player and more recurrent concussions than ORSs.

A higher rate of major depressive disorder (defined by a PHQ-9 >9) was observed in RRPs compared to ORSs. A statistically significant association was observed between the PHQ-9 score and number of reported concussions.

A higher rate of mild cognitive disorder (defined by a TICS-m score ≤30) was observed in RRPs compared to ORSs, but no statistically significant association was observed between the TICS-m score and number of reported concussions.

A statistically significant association was observed between the HIT-6 score used for the detection of chronic headache and the number of reported concussions.

An important recruitment bias

Finding the names and contact information of subjects who ended their sporting career several decades previously is difficult. Sports club files are often fragmented and not updated. Some clubs may even have disappeared. The most reliable source remains retired player associations, but they only comprise former players who are still actively involved in rugby and the life of their former club. Contact with retired players is based more on word of mouth than reliable databases. A large proportion of players identified on game sheets cannot be contacted because they have changed region or even country or because they are now ill or even dead. Therefore, the study population is composed of players with better scores for the various factors studied inasmuch as they have maintained an effective network of social relations. It could be speculated that any abnormality detected in this population would be underestimated compared to the overall population, but probably not overestimated. This type of bias related to the selection of a healthier population has been extensively described in epidemiological studies [START_REF] Rothman | Incidence and risk factors for concussion in high school athletes, North Carolina, 1996-1999[END_REF].

Choice of telephone interview

The recruitment difficulty was compounded by the difficulty of ensuring good quality neurological assessment for subjects living in various regions all over France and still working, allowing them little time to participate in a study that would require global evaluation of their cognition, which could last several hours. It was therefore decided to conduct this assessment by self-administered questionnaire and telephone interview. A similar methodology was used in the study by Guskiewicz on retired American football players [START_REF] Guskiewicz | Recurrent concussion and risk of depression in retired professional football players[END_REF]. The scores and scales used during the telephone interview are validated tools for the detection of depressive disorders, mild cognitive disorders and headache in the general population, with a global duration not exceeding 30 min, a duration compatible with the time that these retired players would be likely to devote to the survey.

The declarative nature of concussion: memorization bias

Another possible bias of the study is related to the declarative nature of concussions. These events were long considered a Bnormal^part of rugby and have been largely under-evaluated and under-declared even up until very recently [START_REF] Torres | Sportsrelated concussion: Anonymous survey of a collegiate cohort[END_REF]. Furthermore, the only events retrospectively identified as concussion were usually those causing loss of consciousness, which represent only 15% of documented concussions [START_REF] Decq | Professional rugby and head injury (Concussions): Guidelines for their management in France[END_REF]. Finally, these events are often accompanied by amnesia, which does not facilitate recall by the subjects concerned, particularly many Fig. 8 Boxplot representing the distribution of the number of reported concussions according to the presence of disabling headache years later. The number of reported concussions in this study is therefore probably largely underestimated.

Other confounding factors

Other confounding factors were probably not collected. In order to minimize this bias, it was decided to compare RRPs with ORSs with little or no exposure to a risk of recurrent concussion, but who had achieved a comparable level of competitive sports during the same period and who had been submitted to the same environment (diet, smoking, drinking, doping temptation, etc.). It must be remembered that concussions can occur regardless of the sport considered, but that the main characteristic of contact sports is the possibility of repeated concussions, which can also occur in the context of other sports but much less frequently. Together with the type of sport (contact or non-contact sport), recurrent concussion is probably also related to individual high-risk behavior, which is another confounding factor that was not taken into account in the present study.

Conclusion

This study showed that RRPs reported a significantly greater number of concussions and recurrent concussions than ORSs.

Their results on the PHQ-9 score, used to detect depressive disorders, and the TICS-m score, used to detect mild cognitive disorders, were also significantly different. A statistically significant association was observed between the PHQ-9 score and number of reported concussions regardless of the type of sport performed, but no such association was observed for the TICS-m score. Finally, a statistically significant association was also observed between the HIT-6 score and the number of reported concussions. These results confirm some of the results reported in American football players. However, no increased incidence of clinically significant episodes of depression or cognitive decline was observed in this population of retired sportsmen compared to the general population. Due to the numerous biases of this study design, these results need to be confirmed, ideally by means of larger scale prospective studies.

Fig. 1 Fig. 2 Fig. 3

 123 Fig. 1 Distribution of PHQ-9 scores in the two groups of retired sportsmen (the height of the bar represents the number of subjects with the corresponding score)

Fig. 4 Fig. 5

 45 Fig. 4 Distribution of TICS-m scores in the two groups of retired sportsmen (the height of the bar represents the number of subjects with the corresponding score)

Fig. 6 Fig. 7

 67 Fig. 6 Distribution of the HIT-6 score in the two groups of retired sportsmen (the height of the bar represents the number of subjects with the corresponding score)

Table 1

 1

	General characteristics
	of the study population [data are		Other sports	Rugby	p-value
	reported as n (%) unless otherwise		N = 138	N = 239
	specified]
	Age (years) median [IQR]	52 [49-55]	52 [49-55.75]	0.952
	BMI (kg/m 2 ) median [IQR]	24.35 [22.77-26.48]	28.38 [26.12-30.86]	<0.001
	Higher education		84 (61.76)	121 (51.05)	0.045
		Full-time employment	122 (89.05)	204 (86.08)	0.474
	Occupational status	Retired	6 (4.38)	18 (7.59)
		Other	9 (6.56)	15 (6.32)
	Marital status	Marital status (married,	115 (83.33)	200 (83.68)	0.940
		civil union, de facto)
		Other	23 (16.66)	39 (16.31)
	Lifestyle and medical history
	Smoking	Current or former smoker	52 (37.68)	82 (34.31)	0.510
	Alcohol (frequency)	0 to 3 times a month	34 (24.64)	74 (30.96)	0.047
		11 to 4 times a week	61 (44.2)	117 (48.95)
		Daily or almost daily	43 (31.16)	48 (20.08)
	Alcohol (intensity) 5 glasses in 1 day	93 (71.54)	207 (88.09)	<0.001
	Presence of impaired exercise capacity	7 (5.11)	29 (12.18)	0.025
	Reported neurological disease	5 (3.68%)	7 (2.93)	0.763
	Reported chronic disease	14 (10.14)	26 (10.88)	0.824
	Reported depressive episodes	17 (12.32)	30 (12.61)	0.936
	Ongoing antidepressant therapy	4 (2.9)	6 (2.51)	0.999
	Perceived state of health			<0.001
		Poor	2 (1.48)	9 (3.81)
		Good	42 (31.11)	117 (49.58)
		Very good	66 (48.89)	87 (36.86)
		Excellent	25 (18.52)	23 (9.75)
	History of reported concussion
	Total number of reported concussions
	Median [IQR]		0 [0-0]	2 [1-3]	<0.001
	Mean (SD)		0.68 (1.83)	3.1 (5.01)
		None	104 (75.91)	54 (22.69)	<0.001
		1 or 2	21 (15.33)	90 (37.82)
		3 or more	12 (8.76)	94 (39.5)
	Number of reported concussions with loss of consciousness (among subjects who reported at least 1 concussion)
	Median [IQR]		1 [1-3]	1 [ 0 -2]
	Mean (SD)		1.64 (1.39)	1.51 (2.68)
	Number of reported concussions with loss of memory (among subjects who reported at least 1 concussion)
	Median [IQR]		0 [0-1]	0 [0-1]
	Mean (SD)		0.76 (1.15)	0.87 (1.33)

Table 2

 2

	Neuropsychological
	characteristics of the population
	[data are reported as n (%) unless
	otherwise specified]

Table 4

 4 Analysis of factors associated with the PHQ-9 score

	Unadjusted estimate	Adjusted estimate	p

Table 5

 5 Distribution of the TICS-m score according to the number of reported concussions

	Number of reported concussions
	None	1 or 2	3 or more	Total

NB: Interpretation of estimates: an estimate >0 indicates that the factor is associated with a higher TICS-m score; inversely, an estimate <0 indicates that the factor is associated with a lower TICS-m score.

Table 7

 7 Distribution of the HIT-6 score according to the number of reported concussions

			Number of reported concussions
			None	1 or 2	3 or more Total
	HIT-6	Median	36 [36-40] 38 [36-44] 38 [36-46] 36 [36-43]
	score	[IQR]
		Mean	39.53	41.11	41.98	40.71
		(SD)	(6.41)	(7.51)	(7.53)	(7.14)

Acknowledgments We thank Timothée Six for help with the data acquisition.

This work was supported by a grant from the Fédération Française de Rugby (FFR) and the Ligue Nationale de Rugby (LNR) and performed under the auspices of the Comité National Olympique et du Sport Français (CNOSF). There are no competing interests.

Compliance with ethical standards

Funding The Fédération Française de Rugby (FFR) and la Ligue Nationale de Rugby (LNR) provided financial support in the form of research technician funding. The sponsor had no role in the design or conduct of this research.

Conflict of interest All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers' bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript. Drs. Jean-Claude Peyrin and Bernard Dusfour are respectively president of the medical committee of the FFR and of the LNR.

Ethical approval All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Informed consent Informed consent was obtained from all individual participants included in the study.


G Pont

P Brenner
email: pierre.brenner@astrium.eads.net

P Cinnella
email: paola.cinnella@ensam.eu

J.-C Robinet

High-order hybrid RANS/LES strategy for industrial applications

Introduction

Turbulent flows of industrial interest are often dominated by large turbulent structures. A typical example is provided by launcher base flows, combining one or more extended and interacting separated regions with strong compressibility effects. Such flow features represent a challenge for CFD simulations, since, on the one hand, well established Reynolds-Averaged-Navier-Stokes (RANS) solvers cannot represent such highly unsteady and three-dimensional large scales and, on the other hand, Large Eddy Simulation (LES) approaches remain too expensive for routine production use in industry. In fact, LES methods can lead to inaccurate results if the mesh size and/or the scheme accuracy are not good enough to resolve correctly most of the relevant flow scales. In complex industrial applications, the energy spectrum is often ill defined and changes from one point to another of the simulation, so that it is difficult to warrant a sufficient resolution everywhere, unless extremely fine meshes are used. Mesh resolution requirements become particularly severe if industrial codes based on low order, low resolution discretization schemes are used. In this work we assess a recently developed hybrid RANS/LES strategy, combining a self-adaptive hybrid turbulence model [START_REF] Perot | A self-adapting turbulence model for flow simulation at any mesh resolution[END_REF] and a hybrid high-order finite volume scheme [Pont et al., 2013], for flow around industrial geometries, namely, the Ariane 6 and Ariane 5 space launchers. Increasingly complex geometrical details are included in the simulation and the results are compared with the experimental data available for the average and root mean square (rms) of the longitudinal distribu-tion of the pressure coefficient, which represent a significant quantity of interest for launcher design.

Numerical methodology

The simulations are carried out by using a high-order unstructured finite volume solver. The space discretization scheme uses k-exact reconstructions of the variables over each cell to obtain high-order approximations of the fluxes at cell interfaces. Precisely, the reconstruction process requires approximations of the solution derivatives up to order two, leading to a third-order accurate approximation on generic grids. Derivative approximations are obtained by means of an efficient successive reconstruction technique [START_REF] Haider | Efficient implementation of high order reconstruction in finite volume methods. Finite Volumes for Complex Application VI-Problem & Perspectives[END_REF]]. An exact Riemann solver is then applied to the reconstructed solution at cell interfaces. The resulting numerical scheme is suitable for highly compressible flows since it has good shock capturing capabilities. Nevertheless, it appears to be too dissipative for scale-resolving simulations since it overdamps the vortical structures associated to LES regions of the computational domain. To overcome this difficulty, a hybrid numerical scheme is constructed by locally recentering the third-order scheme in vortex-dominated regions according to a blending function involving Ducros' compressibility/vorticity sensor [Ducros et al., 1999] and a stability criterion involving the grid Reynolds number based on the sum of the local molecular and turbulent viscosity. The fully centered scheme is fourth-order accurate. If the stability criterion is not satisfied, the blending function partly re-centers the scheme while keeping a minimal amount of numerical dissipation to ensure stability. The proposed scheme is referred-to as vortex-centered (VC) scheme. More details can be found in Ref. [Pont et al., 2013]. The proposed strategy has been implemented within FLUSEPA, the unstructured finite-volume solver developed by Airbus Defence & Space (ADS) to calculate compressible, multidimensional, unsteady, viscous and reactive flow over bodies in relative motion. Time integration is carried out by means of the explicit second-order accurate Heun scheme, along with a time-consistent local time stepping technique.

Unresolved turbulence effects on the resolved scales are taken into account by means of a self-adaptive hybrid RANS/LES model, initially developed by Perot and Gadebusch [START_REF] Perot | A self-adapting turbulence model for flow simulation at any mesh resolution[END_REF], based on a modification of the well known kε model. The model is referred-to as PG hereafter. Such a model acts as a subgrid model in well-resolved regions while keeping a classical kε model in underresolved regions, via a sensor based of the local amount of resolved kinetic energy compared to the modeled one. When the amount of resolved kinetic energy is low compared to an indicator of the local grid resolution, the model switches automatically from the RANS to the LES mode. The original model was developed for free turbulence. In order to apply the model to wall-bounded flows, we introduce a shielding function near the wall, similar to that introduced in [Spalart, 2009]. Wall functions are used near the wall [START_REF] Launder | Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc[END_REF] to avoid too severe restrictions on the maximum allowable time step.

The proposed numerical methodology was assessed against well documented test cases [Pont et al., 2013, Pont et al., 2014]. In particular, simulations of the flow around 2D and axi-symmetric backward facing steps showed that the proposed approach provides satisfactory results by using relatively coarse computational grids compared to similar calculations available in the litterature. 3 Application to the RANS/LES simulation of industrial launcher configurations

Flow around the shrinkage of Ariane 6

We simulate a 1/60 scale of the wind tunnel model of Ariane 6 space launcher, with an angle of attack and yaw angle equal to 0. Simulations are carried out for a Reynolds number, based on the main diameter D of the launcher equal to 9.1 × 10 5 and a Mach number equal to 0.9. Figure 1 shows the composite grids used to discretize the computational domain. The total number of cells is about 15 × 10 6 . The mesh resolution in the wall-normal and longitudinal directions is of approximately 30 and 50 wall units, respectively. An azimuthal step of 2 degrees is used. The calculations are started from a partially converged kε solution. Statistics are collected over a non-dimensional duration T × U ∞ /(Dd) = 200 (with U ∞ the freestream velocity and D and d the diameters upstream and downstream of the shrinkage).

Figure 2 (a) shows the instantaneous Q criterion around the skinkage of the launcher colored by Mach number. In the recirculation area, the heads of Kelvin-Helmholtz vortices are supersonic and induce local compressibility effects. A shock/boundary layer interaction occurs on the fairing of the launcher. The proposed numerical approach accurately captures Kelvin-Helmoltz instabilities while ensuring robustness.

The present results are compared to the experiments available for a slightly different configuration [Kumar, 2002]. In the mean flow, see figure 3

Flow around the Ariane 5 launcher with boosters

The next application is a 1/60 scale model of the Ariane 5 launcher at zero angle of attack. The freestram Mach number is equal to 0.8 and the Reynolds number based on the diameter of the central body is 2 × 10 -6 . The computational mesh, shown in fig. 5 is composed by 20 × 10 6 cells. The y + is about 20 at the beginning of the separated region. The azimuthal resolution equal to 2 degrees. The simulation is initialized with a partly converged RANS solution, and the statistics are collected over a non-dimentional duration T * U ∞ /H equal to 40 after the numerical transient. This is not long enough to fully converge the statistics, so that results heareafter are to be taken with caution. Figure 6 gives an overview of the instantaneous field at the base of the launcher. The Kelvin-Helmholtz instabilities are clearly visible and are triggered without delay. Figure 7 compares present results for the average and rms pressure coefficient with experimental data collected at ADS the recirculation area of the launcher. The overall agreement is reasonably good.

Conclusions

The present work demonstrated the capability of a hybrid high-accurate industrial solver to successfully predict complex launcher configurations to within engineering accuracy, while ensuring the necessary robustness. Using a low-dissipative scheme in conjunction with a hybrid RANS/LES model is found to be crucial for triggering flow instabilities and obtaining correct average and rms wall pressure levels.

Fig. 1

 1 Fig. 1 Details of the overlapping grid around the Ariane 6 shrinkage.

  (a), the predicted reattachment length, normalized with shrinkage height (h = (Dd)/2), is equal to 6.1, the experimental value being 5.8. Finally, figure3(b) shows that the kinetic energy is fully modeled in the attached upstream boundary layer, while in the shear layers and recirculation bubble the modeled kinetic energy is gradually replaced by the resolved one. Figures (a) and (b) shows respectively the evolution of mean pressure and rms pressure coefficients along the shrinkage, versus the longitudinal coordinate normalized by the recirculation length. Both are in good agreement with the experiments. The Strouhal number based on the buffeting frequency, the recirculation length x r and U ∞ is about 0.63, a value close to the experiments and other calculations in the litterature.

Fig. 2 Fig. 3

 23 Fig. 2 Instantaneous Q criterion colored by the Mach number.

Fig. 4

 4 Fig. 4 Distributions of the average (left) and rms (right) pressure coefficient along the shrinkage.

Fig. 5

 5 Fig. 5 Details of the overlapping grid around the Ariane 5 launcher.

Fig. 6

 6 Fig. 6 Instantaneous Q criterion colored by the Mach number.

Fig. 7

 7 Fig. 7 Distributions of the average (left) and rms (right) pressure coefficient along the nozzle.