Karen Ritchie

Isabelle Jaussent
email: isabelle.jaussent@inserm.fr

Robert Stewart

Anne-Marie Dupuy

Philippe Courtet

Alain Malafosse

Marie-Laure Ancelin

ADVERSE CHILDHOOD ENVIRONMENT AND LATE-LIFE COGNITIVE FUNCTIONING

Keywords: elderly, child abuse, cognition, ApoE, gene-environment interaction

INTRODUCTION

Childhood maltreatment has been observed to induce both structural and functional brain changes, notably reduced development of the hippocampus and amygdala, and abnormal fronto-temporal electrical activity [START_REF] Teicher | Developmental neurobiology of childhood stress and trauma[END_REF][START_REF] Teicher | The neurobiological consequences of early stress and childhood maltreatment[END_REF]. Not surprisingly these changes have a significant detrimental effect on cognitive functioning. Clinical studies show that children subject to abuse without neurological injury show deficits of central executive functioning, memory, attention, visuospatial ability, language and motor speed, in some cases also accompanied by significant cerebral atrophy [START_REF] Prasad | Cognitive and neuroimaging findings in physically abused preschoolers[END_REF][START_REF] Savitz | Genotype and childhood sexual trauma moderate neurocognitive performance: a possible role for brain-derived neurotrophic factor and apolipoprotein E variants[END_REF][START_REF] Pears | Developmental, cognitive, and neuropsychological functioning in preschool-aged foster children: associations with prior maltreatment and placement history[END_REF][START_REF] Nolin | Using neuropsychological profiles to classify neglected children with or without physical abuse[END_REF][START_REF] Porter | Neurobehavioral sequelae of child sexual abuse[END_REF]. Abuse has also been associated with lower IQ [START_REF] Koenen | Domestic violence is associated with environmental suppression of IQ in young children[END_REF][START_REF] Nolin | Using neuropsychological profiles to classify neglected children with or without physical abuse[END_REF]. While the greatest cognitive deficits are observed in cases of physical abuse with neglect, neglect alone has been associated with cognitive deficits in attention, response set and visual-motor integration, and conversely greater capacity for problem solving and abstraction [START_REF] Nolin | Using neuropsychological profiles to classify neglected children with or without physical abuse[END_REF][START_REF] Pears | Developmental, cognitive, and neuropsychological functioning in preschool-aged foster children: associations with prior maltreatment and placement history[END_REF]. There is furthermore some early evidence from a study of childhood abuse and cognition in bipolar disorder of a gene-environment interaction implicating genes known to exert a neurotrophic effect in response to cellular injury [START_REF] Savitz | Genotype and childhood sexual trauma moderate neurocognitive performance: a possible role for brain-derived neurotrophic factor and apolipoprotein E variants[END_REF] notably Apolipoprotein E (ApoE), which has also been linked to late-life cognitive functioning and dementia [START_REF] Blacker | Neuropsychological measures in normal individuals that predict subsequent cognitive decline[END_REF][START_REF] Caselli | Cognitive domain decline in healthy apolipoprotein E epsilon4 homozygotes before the diagnosis of mild cognitive impairment[END_REF]. Polymorphisms on the ApoE gene are believed to influence capacity for compensatory neurite outgrowth and synaptogenesis following neuronal injury [START_REF] Poirier | Apolipoprotein E in CNS models of CNS injury and in Alzheimer's disease[END_REF] and may thus modulate the neurobiological impact of environmental trauma.

There is some evidence for the persistence of the cognitive consequences of child abuse into adulthood. Several small clinical studies of women with a history of physical and sexual abuse reported disorders of vigilance, memory and mathematical ability compared to controls [START_REF] Navalta | Effects of childhood sexual abuse on neuropsychological function in college women[END_REF][START_REF] Bremner | Deficits in short-term memory in adult survivors of childhood abuse[END_REF][START_REF] Bremner | Deficits in verbal declarative memory function in women with childhood sexual abuse-related posttraumatic stress disorder[END_REF] but with no impact on IQ.

Although Stein et al. found no significant impairment on a verbal and visual recall task in 22 adult women subject to childhood sexual abuse [START_REF] Stein | Memory functioning in adult women traumatized by childhood sexual abuse[END_REF], they did observe significantly reduced left-side hippocampal volume [START_REF] Stein | Hippocampal volume in women victimized by childhood sexual abuse[END_REF]. Little is known, however, about the longer-term impact of abuse-related brain changes, and in particular whether they may constitute a significant risk factor for cognitive disorder in old age. While adverse life events occurring in old age have been related to poorer cognitive performance, the impact of more distal trauma, notably those occurring at critical stages of brain development, has yet to be explored.

This study aimed to examine the relationship between childhood trauma and late-life cognitive performance in an elderly general population, taking into account proximal risk factors for poor cognitive performance, and interaction with ApoE genotype. We considered the possibility that childhood abuse would engender damage to developing cortical structures which would persist into adulthood and we hypothesised that it would be associated with lower late-life cognitive functioning when neuronal resources are again challenged. The prospective study design allowed us to compare both levels of cognitive functioning and decline over a four-year period. We further hypothesized that the extent of cognitive compromise will be modified by genetically determined capacity for neuronal repair.

METHODS

Sample

Community dwelling persons, 65 years and over, were recruited by random selection from the fifteen electoral roles of the Montpellier district between March 1999 and February 2001 as part of the ESPRIT study of late-life psychiatric disorder [START_REF] Ritchie | Prevalence of DSM-IV psychiatric disorder in the French elderly population[END_REF]. Participants were given a base-line examination and re-examined on two further occasions at two-yearly intervals. At follow-up the neurological, cognitive and psychiatric examinations were repeated and medication use and incident illness were recorded. The present analyses have been carried out on participants who completed the child abuse questionnaire, who did not have dementia at base-line or follow-up (due to doubts about the reliability of the information given about childhood events) and for whom information was available on all potential confounding variables (1282 of 1580 subjects). Ethical approval for the study was obtained from the National Ethics Committee.

Measures

Participants were asked to attend a half-day examination by a neurologist and a centre interviewer (nurse or psychologist) at the Neurology Hospital. Disabled subjects unable to come to the study centre were interviewed in their homes. The following procedures were carried out:

A standardized health interview covering present state of health, individual and family medical history, and medication use (subjects were asked to bring their medication to the centre). Recent exposure to adverse life events in the past year was assessed using the Gospel Oak questionnaire [START_REF] Harwood | The prevalence of diagnoses, impairments, disabilities and handicaps in a population of elderly people living in a defined geographical area: the Gospel Oak project[END_REF]. Detailed medical questionnaires were used to obtain information on history of vascular disease (including angina pectoris, arrhythmia, lower limb arteritis, heart failure, myocardial infarction, stroke), other chronic illnesses (asthma, diabetes defined as fasting glucose≥7.2mmol/l or reported treatment, hypercholesterolemia defined as total cholesterol ≥6.2mmol/l or reported treatment, hypertension defined as resting blood pressure ≥160/95mm Hg or treatment, and thyroid disorders). Participants with chronic diseases were classified as having one, or two or more, of these illnesses.

A standardized neurological examination based on ICD-10 criteria [START_REF] Who | International Classification of Diseases[END_REF] was carried out to detect neurological and cardiovascular co-morbidity, including measures of sitting and standing blood pressure.

A standardized psychiatric interview to record life-time and current DSM-IV Axis I psychiatric disorder; the Mini International Neuropsychiatric Interview (MINI) [START_REF] Lecrubier | The Mini International Neuropsychiatric Interview (MINI), a short diagnostic interview: reliability and validity according to the CIDI[END_REF] (French version 5.00) previously validated within the general population setting.

Positive cases were reviewed by a panel of psychiatrists. The Center for Epidemiologic Studies-Depression Scale (CES-D) [START_REF] Radloff | The CES-D scale: a self-report depression scale for research in the general population[END_REF] was used to detect high levels of depressive symptomatology.

Childhood environment A self-administered checklist based on a review of existing instruments covering 25 adverse and 8 protective factors (expressed as categorized variables, yes/no) was given to subjects for completion in the third wave of the study (four years after recruitment) as described previously [START_REF] Ritchie | Association of adverse childhood environment and 5-HTTLPR genotype with late-life depression[END_REF] Adverse factors (traumatic events) included physical, verbal and sexual abuse, conflict at home, mental cruelty, neglect, mental disorder in parents, excessive sharing of parental problems, separation, illness, poverty, mistreatment at school, separation, war and natural catastrophe. Protective factors included maternal and paternal affection, availability of an adult friend, impression of having had a happy childhood or a normal education, parents perceived as doing their best, feeling happy at school, having been raised by both parents.

Cognitive functioning. The Benton's Visual Retention Test assessed visual memory [START_REF] Benton | Manuel pour l'application du test de rétention visuelle[END_REF], the Trail Making Test B (TMTB) assessed executive function respectively [START_REF] Reitan | Validity of the Trail Making Test as an indicator of organic brain damage[END_REF], the Isaacs' Set Test measured verbal fluency [START_REF] Isaacs B Kennie | The Set test as an aid to the detection of dementia in old people[END_REF] and the 5-word test of Dubois examined immediate and delayed verbal memory [START_REF] Dubois | L'épreuve des cinq mots[END_REF]. The National Adult Reading Test (NART) [START_REF] Blair Jr Spreen | Predicting premorbid IQ: a revision of the National Adult Reading Test[END_REF] was used as a marker of IQ and was administrated as baseline.

Diagnosis of dementia. A preliminary diagnosis and classification of dementia at each follow-

up was made by the study clinical investigators, according to DSM-IV revised criteria [START_REF] Apa | Diagnostic and Statistical Manual of Mental Disorders (DSM-IV)[END_REF] and was further validated by a national panel of neurologists independently of the investigators.

Blood samples were taken at base-line to establish ApoE genotype [START_REF] Dufouil | APOE genotype, cholesterol level, lipid-lowering treatment, and dementia: the Three-City Study[END_REF].

Statistical Analysis

Two-tailed chi-squared tests were used to determine which of the baseline characteristics were significantly associated with poor performance on each of the cognitive tasks.

Univariate logistic regression analyses adjusted for age, sex, and educational level were used to determine if childhood events were significantly associated with cognitive impairment (cross-sectional analysis) or cognitive decline (longitudinal analysis). Adjustment on baseline cognitive score was also performed for the analysis of cognitive decline. Multivariate adjusted logistic regression included covariates that were associated with poor cognitive performance (p≤0.10). Cognitive impairment was defined as being in the lowest quartile of the baseline cognitive score for the Isaacs, Benton and Dubois tests and in the highest quartile for TMTB.

Cognitive decline was defined as being in the lowest quartile of the maximal difference between baseline score and either follow-up.

We tested the hypothesis that ApoE genotype might modify the relationship between cognitive impairment or decline and childhood events using a logistic regression model. We therefore stratified our analysis by ApoE genotype and then added the interaction term to the full model and tested for its significance using Wald's  2 test given by the logistic regression model. The distribution of ApoE was tested by  2 for Hardy-Weinberg equilibrium.

Significance level was set at p<0.05. The statistical analysis was carried out using SAS software (version9.1).

RESULTS

Ninety one percent of participants experienced at least one adverse childhood event and of these 14.7 % reported at least one traumatic childhood event (physical, verbal or sexual abuse, neglect, excessive punishment, humiliation). Comparing this latter group to subjects without a severe event, who also recalled their childhood as being generally happy, no significant difference was found in relation to NART scores. Twenty nine percent of subjects who experienced traumatic events were classified as having Mild Cognitive Disorder according to commonly accepted criteria [START_REF] Petersen | Current concepts in mild cognitive impairment[END_REF] compared to 24% of subjects with happy childhood, although this difference did not reach statistical significance. The principal sociodemographic and clinical characteristics of the population are given in Table 1. As expected a significant relationship was found on all cognitive tests with age, education and IQ. Reporting recent life events was not associated with modified performance on any cognitive test.

Chronic disorder and sex were associated with cognitive performance on all tasks except the Benton. Performance on the Isaac test was also marginally associated with depression, the Benton test with depression and marginally with widowhood, TMTB with widowhood, ApoE4, and depression.

The association between individual childhood events, both protective and adverse, and latelife cognitive performance was then examined in relation to each test adjusting for potential confounders. Significant associations are given in Table 2. On the Isaacs test, sharing of parental problems with the children in the family (OR=1.68; 95%CI=1.18-2.38, p=0.004) and parental loss (OR=1.43; 95%CI=1.03-2.00, p=0.035) were found to constitute significant risk factors for poor performance in later-life. Being sent to a foster home (OR=2.23; 95%CI=0.96-5.15, p=0.062) or having been mistreated by schoolmates (OR=2.27; 95%CI=0.98-5.29, p=0.057) are marginally risk factors for poor performance on the Benton test. Parents being perceived as having done their best in relation to their children tends to be a protective factor for performance on both the Dubois (OR=0.63; 95% CI =0.38-1.04, p=0.074) and TMTB (OR=0.61; 95%CI=0.36-1.02, p=0.062), with perceptions of a happy childhood also being associated with better scores on the TMTB (OR=0.64, 95%CI=0.41-1.00, p=0.051). Reporting a normal education was also associated with better scores on the Benton (OR= 0.60; 95%CI=0.34-1.05, p=0.072) and TMTB (OR=0.56; 95%CI=0.33-0.94, p=0.029). Experiencing physical, mental or sexual abuse was associated with a lower risk of cognitive impairment on the Isaacs test, however small numbers make separate analyses for each type of traumatic event unreliable. Having had a mother suffering from mental problems was associated with a lower risk of cognitive impairment on the Dubois (OR=0.61; 95%CI=0.39-0.95, p=0.035) and Benton tests (OR=0.60; 95%CI=0.36-1.01, p=0.056).

The distribution of ApoE did not deviate from Hardy-Weinberg equilibrium ( 2 =1.21, df=5, p=0.94). Gene-event interactions were found between happy childhood and ApoE polymorphisms (Wald  2 =2.92, df=1, p=0.087) on the TMTB. Elderly persons without an ApoE 4 allele who reported a happy childhood had significantly better scores on the TMTB (OR=0.55; 95%CI=0.34-0.88; p=0.014) than 4 allele carriers (OR=4.39; 95%CI=0.51-37.52; p=0.18). A sex interaction effect with loss of a parent during childhood was also found (Wald  2 =5.23, df=1, p=0.022); women, but not men having low scores on the Isaacs test if they had lost a parent during childhood (OR=1.95; 95%CI=1.25-3.06; p=0.003).

Changes in cognitive scores were examined over time in order to observe the relationship between childhood abuse and rate of cognitive decline. Performance at baseline was subtracted from that of either follow-up visit two or four years later. Most of the negative effects observed in cross-sectional analyses were also found longitudinally, notably the association between sharing of adult problems with children and decline on the Isaacs (OR=1.46; 95%CI=1.01-2.09; p=0.043) and Benton tests (OR=1.54; 95%CI= 1.09-2.17; p=0.014) (data not shown). Some of the positive effects were also observed in the longitudinal analysis, notably having had a mother suffering from mental problems being associated with lower decline on the Benton (OR=0.69; 95%CI=0.46-1.02; p=0.065), and reporting a happy childhood (OR=0.56, 95%CI=0.35-0.89, p=0.014), and parents being perceived as having done their best (OR=0.63; 95%CI=0.37-1.08; p=0.090) being associated with lower decline on the TMTB. Severe abuse (sexual or physical abuse or excessive physical punishment) was also observed in association with decline on the Benton (OR=0.55; 95%CI=0.30-0.99, p=0.048), although numbers are small for sexual abuse. Some additional associations were found, such as a effect on the Dubois task for subjects with a father suffering from mental disorder (OR=0.55; 95%CI=0.32-0.96; p=0.034), a decline on the Isaacs test related to experience of verbal abuse (OR=1.75; 95%CI=1.02-2.99; p=0.041), and a decline on the TMTB associated with fathers having alcohol problems (OR=2.69; 95%CI=1.66-4.36; p<0.0001) and conflict at home (OR=1.47, 95%CI=1.03-2.09, p=0.033).

DISCUSSION

In this large population study of community-dwelling elderly we found 13% of this cohort reporting severe childhood abuse and neglect. Unlike studies of abused children we found no difference in IQ scores between severely abused and non-abused elderly. The removal of subjects from the study with a diagnosis of dementia may, however, have introduced a bias given that low IQ is a risk factor for dementia. After adjusting for multiple competing causes of poor cognitive functioning, childhood mistreatment appeared nonetheless to have some residual adverse effects on late-life cognitive performance, however this was related mostly to general long-term conditions of child-rearing (parents overly sharing their problems and being sent to a foster home or chronic difficulties with schoolmates) rather than to specific traumatic events. There were, however, very few reported cases of sexual and severe physical abuse in our sample (n=26, 2.0%), precluding adequate exploration of these events which have been the central focus of studies with children. Under-reporting of sexual abuse in this elderly cohort is also likely.

Contrary to studies of children where childhood maltreatment has been associated with significant dysfunction in all areas of cognitive functioning, in this older population the effects appear to be less marked and limited to some traumatic events; excessive sharing of parental problems or, for women, early parental loss, being sent to a foster home or being mistreated by schoolmates. There are a number of possible reasons for this; the effects of abuse may decrease over time, abused children may have higher mortality, be more likely to be institutionalized, have recall bias or be more likely to not participate in adult studies of psychiatric disorder. As suggested above, the removal of subjects with dementia, who are more likely to have hippocampal damage and an ApoE4 allele may have significantly reduced the strength of associations between childhood events and cognitive disorder. Our analyses may also have over-adjusted and thus precluded the demonstration of an intermediary effect, with childhood abuse giving rise to greater vulnerability for other disorders such as cardioand cerebro-vascular disease and depression, which in turn heighten risk for poor cognitive function in late-life. This would be coherent with recent studies based on longitudinal birth cohort data which suggest inflammation to be a developmental mediator linking childhood experience with pathologies such as depression, cardiac pathologies and neurological disorder [START_REF] Danese | Elevated inflammation levels in depressed adults with a history of childhood maltreatment[END_REF][START_REF] Danese | Childhood maltreatment predicts adult inflammation in a life-course study[END_REF].

On the other hand we found that positive childhood environment (having experienced a happy childhood, feeling that parents did their best, having had a normal education) to be strong promoting factors in relation to adult cognitive performance, notably on central executive functioning. While negative childhood factors and health has received a great deal of attention, this is the first study to our knowledge to report the long-term impact of positive childhood environment, both on cognitive performance and decline across time. Elderly persons who have experienced a childhood characterized by parents appearing to do their best by the children, and who generally recall this as a happy period, have improved scores on tests of central executive functioning, verbal recall and retrieval even after adjustment for multiple health variables.

Interestingly we observed a lower risk of cognitive dysfunction associated with physical and sexual abuse, however, numbers in the latter group were too small (n=26) for us to be able to examine the impact of individual events..We also observed a reduction in risk for cognitive dysfunction in persons having a parent suffering from a mental disorder. These observations suggest a possible resilience effect, with adverse events leading in some persons to decreased vulnerability to cognitive impairment. Children neglected but without physical abuse have been shown in a previous study to have a greater capacity for problem solving, abstraction, and planning than non-abused children [START_REF] Nolin | Using neuropsychological profiles to classify neglected children with or without physical abuse[END_REF]. In young foster children, the number of maltreatment types has been observed to be positively associated with capacity for everyday functioning [START_REF] Pears | Developmental, cognitive, and neuropsychological functioning in preschool-aged foster children: associations with prior maltreatment and placement history[END_REF]. On the other hand, adults who have suffered severe abuse with long term cognitive consequences may also refuse to take part in research studies. Our data also suggest above all that aggregate scores of traumatic events are less informative than estimates of individual traumatic events, since individual life events may have both a positive and a negative effect, which cancel each other out when using the sum score of events.

We only observed one gene-environment interaction effect for persons having reported a happy childhood who were more likely to have better performance in later life on the Trail test if they were not carriers of an ApoE 4 allele. It is difficult to interpret this result, and we conclude only that ApoE 4 carriers are at increased risk for life-time lower cognitive performance, but that unlike non-4 carreirs, their performance is not improved by positive early environmental conditions.

Prospective follow-up of changes in cognitive performance over a four-year period suggested that experience of verbal abuse was associated with greater decline in verbal retrieval skills, and that having had a father with alcohol problems or experiencing conflict at home was associated with increased decline in executive functioning. These data also confirmed some associations already observed on cognitive impairment at base-line, notably sharing of parental problems with children having a significant negative effect on verbal retrieval. We also observed that a positive early environment characterized by a happy childhood is associated with lower decline in executive functioning. On the other hand having a father or mother suffering from a mental disorder is also associated with better performance on both visual and verbal memory over the follow-up period. The association of some environmental factors not only with lower cognitive performance, but also with increased decline over time, argues in favour of a persistent underlying biological vulnerability as has been suggested in previous neurophysiological studies of abused children.

The results of the present study support and extend observations in children with severe trauma suggesting a link between severe stress and alterations in brain structures and brain functions [START_REF] Teicher | The neurobiological consequences of early stress and childhood maltreatment[END_REF][START_REF] Nolin | Using neuropsychological profiles to classify neglected children with or without physical abuse[END_REF]. The fact that these alterations persist in the elderly also supports the hypothesis that early severe stress and maltreatment initiates a cascade of neurobiological events that have the potential for producing enduring changes in brain development, which may occur on multiple levels, from neurohumoral (especially the hypothalamic-pituitary-adrenal axis) to structural and functional.

CONCLUSION

Our general conclusion is that only some aspects of childhood adversity continue to have a negative effect on later-life cognitive functioning. They are moreover associated with general environmental conditions (fostering and over-sharing of parental problems, problems with schoolmates, loss of a parent for women and paternal alcohol problems) rather than with traumatic events such as physical and sexual abuse, humiliation and neglect, although verbal abuse is observed to be associated with increased rates of decline on a verbal retrieval task.

The impact is less than that observed in children and younger adults, possibly due to a weakening of the effect of trauma over time, neuronal compensatory processes, or mortality effects. Our results may, however, have under-estimated the true association due to sampling (elderly persons who have experienced abuse may be under-represented) or recall bias (underreporting of severe abuse), the exclusion of persons with dementia who have both hippocampal damage and a higher likelihood of an ApoE 4 allele.

While this large population study was able to control for many competing causes of cognitive dysfunction, notably illness, there may have been over-adjustment, thus precluding the examination of intermediary pathologies, notably depression, cardiac disorders and neuropathologies which may constitute a link between childhood environment and late-life cognitive functioning. Of particular interest are the apparent cognition-promoting effects of a positive early environment, which appear to persist into old age. Future studies are needed with more in-depth clinical examination of childhood experiences both to validate true cases of abuse and to ensure that control groups used in the analyses are not contaminated by falsenegative reports. Such studies should also take into account the possible intermediary role of chronic illness.

Table 1 .

 1 Relationship between sociodemographic, and clinical characteristics and cognitive tests.

			ISAACS			Benton			Dubois		TMTB
		>42	42		11	<11		>8	8		< 110	110
		N=954	N=328		N=1057	N=225		N=942	N=340		N=958	N=324
		%	%	P-value %	%	P-value %	%	P-value %	%	P-value
	Gender, women	60.59	51.22	0.003 57.99	59.11	0.76	61.78 48.24 <0.0001 55.95 64.81 0.005
	Age Group (years)
	<70	40.78	33.54	0.005 40.11	33.33	0.07	41.30 32.35 0.001 41.86 30.25 <0.0001
	[70-75[	33.54	31.10		33.21	31.56		32.48 34.12		34.13 29.32
	[75-80[	18.13	23.17		18.54	23.56		19.11 20.29		17.85 24.07
	 80	7.55	12.20		8.14	11.56		7.11 13.24		6.16 16.36
	Marital Status, widowed	19.29	20.43	0.65	18.64	24.00	0.07	18.90 21.47 0.31	17.12 26.85 0.0001
	Education
	High	29.87	16.77 <0.0001 28.19	18.67 <0.0001 27.81 22.94 0.001 30.58 14.51 <0.0001
	Medium-High	26.73	16.16		25.64	16.44		24.42 22.94		24.74 21.91
	Medium-Low	29.04	35.06		30.18	32.44		31.53 27.94		30.90 29.63
	Low	14.36	32.01		15.99	32.44		16.24 26.18		13.78 33.95
	Chronic diseases
	0	29.45	25.30	0.029 28.86	26.22	0.60	29.83 24.41 0.012 30.06 23.46	0.021
	1	40.04	36.28		39.17	38.67		39.92 36.76		39.25 38.58
	 2	30.50	38.41		31.98	35.11		30.25 38.82		30.69 37.96
	Recent life events
	0	42.77	39.94	0.30	42.10	41.78	0.77	42.14 41.76 0.70	42.28 41.36	0.15
	1	35.43	34.15		34.72	36.89		35.56 33.82		36.12 32.10
	2	21.80	25.91		23.18	21.33		22.29 24.41		21.61 26.54
	APOE 4	19.81	16.46	0.18	19.30	17.33	0.49	19.43 17.65 0.47	20.35 14.81	0.030
	CESDT16 or antidepressant intake 26.10	31.10	0.08	26.02	33.78	0.02	27.81 26.18 0.56	25.47 33.02	0.008
	NART Score 18	20.75	42.38 <0.0001 22.61	43.56 <0.0001 23.14 35.00 <0.0001 19.83 45.37 <0.0001

Table 2

 2 Significant associations (odds ratios, confidence intervals and significance levels) between specific childhood events and performance on cognitive tests adjusted by potential confounders A -Effects on verbal fluency and on visual memory

		Isaacs 1				Benton 2
	> 42	 42			 11	<11
	N=954	N=328			N=1057	N=225
	%	%	OR [95 %CI]	p-value	%	%	OR [95 %CI]	p-value

1 Adjusted by gender, age, education and chronic diseases 2 Adjusted by gender, age, education, CESDT16 or antidepressant intake, chronic diseases and ApoE 4

Adjusted by gender, age, education, CESDT16 or antidepressant intake and chronic diseases

Adjusted by gender, age, education, CESDT16 or antidepressant intake and widowed

ACKNOWLEDGMENTS

The ESPRIT project is financed by the regional government of Languedoc-Roussillon, the Agence Nationale de Recherche (ANR) Project 07 LVIE 004, and an unconditional grant from Novartis.

Key Points

 In our community-dwelling sample 91 % of elderly people reported havingexperienced at least one adverse childhood event, of which 14.7 % reported severe physical, mental or sexual abuse.

 Childhood adversity does not appear to be associated with a general lowering of cognitive functioning, but rather poorer performance in specific areas.

 While moderate childhood adversity is observed to continue to have a negative effect on cognitive performance in later-life ,some more severe events appear to have the opposite effect suggestive of a resilience mechanism possibly linked to improved problem-solving capacity. Positive early environment continues to have cognitionpromoting effects even in old age.

 Estimates of individual traumatic events will be more informative than aggregate scores of traumatic events, since individual life events may have both a positive and a negative effect, which cancel each other out when using the sum score of events.

CONFLICT OF INTEREST

All authors report no competing interests.


Dr Anna M Foss
email: anna.foss@lshtm.ac.uk

Peter Vickerman

Philippe Mayaud

MD MSc Helen A Weiss

M Ramesh

Sushena Reza-Paul

MBBS Reynold Washington

James Blanchard

PhD Stephen Moses

MD Catherine M Lowndes

Mmath Phd

Philippe Dphil

Mayaud

M D Mbbs

PhD Michel Alary

PhD Charlotte H Watts

Modelling the interactions between Herpes simplex virus type-2 (HSV-2) and HIV: implications for the HIV

Keywords: HIV, Herpes simplex virus type-2, mathematical modelling, India, female sex work

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

Figures and Tables count

The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an exclusive licence (or non exclusive for government employees) on a worldwide basis to the BMJ Publishing Group Ltd to permit this article (if accepted) to be published in STI and any other BMJPGL products and sub-licences such use and exploit all subsidiary rights, as set out in our licence http://group.bmj.com/products/journals/instructions-for-authors/licence-forms

KEY MESSAGES

1. This is the first model exploring the role of HSV-2 in a concentrated HIV epidemic within an Asian setting.

2. The modelling suggests that HSV-2 plays an important role in the transmission and acquisition of HIV in Mysore, mostly through asymptomatic HSV-2 shedding.

3. Even in the best-case scenario, HSV-2 suppressive therapy is unlikely to reduce HIV transmission or acquisition by >50%, as aimed for in recent trials. 4. Modelling analyses can help guide trial design for expected power and sample size calculations, and retrospectively inform the interpretation of trial results.

ABSTRACT Background

The role of HSV-2 in the HIV epidemic, and the potential impact of HSV-2 suppressive therapy, have been previously explored only within the context of sub-Saharan Africa.

In this analysis, modelling is used to estimate: (1) the contribution of herpes simplex virus type-2 (HSV-2) to HIV transmission from clients to female sex workers (FSWs) in a Southern Indian setting; and (2) the maximum potential impact of 'perfect' HSV-2 suppressive therapy on HIV incidence.

Methods

A dynamic HSV-2/HIV model was developed, parameterised and fitted to Mysore data.

The model estimated the attributable fractions (AFs) of HIV infections due to HSV-2.

Multivariate sensitivity analyses and regression analyses were conducted.

Results

The model suggests that 36% (95% CI: 22-62%) of FSW HIV infections were due to HSV-2, mostly through HSV-2 asymptomatic shedding. Even if HSV-2 suppressive therapy could eliminate the effect of HSV-2 on HIV infectivity among all coinfected clients, only 15% (95% CI: 3-41%) of HIV infections among FSWs would have been averted. 36% (95% CI: 18-61%) of HIV infections among HSV-2-infected FSWs could have been averted if suppressive therapy reduced their risk of HIV acquisition to that of the HSV-2-uninfected FSWs.

INTRODUCTION

Herpes simplex virus type-2 (HSV-2) is highly prevalent in regions with high HIV prevalence and among groups at high risk of HIV. [START_REF] Smith | Age-specific prevalence of infection with herpes simplex virus types 2 and 1: a global review[END_REF][START_REF] Weiss | Epidemiology of herpes simplex virus type 2 infection in the developing world[END_REF] These associations are partly due to both infections being sexually transmitted, but several lines of biological evidence support bidirectional synergistic interactions between the two viruses. [START_REF] Celum | Genital herpes and human immunodeficiency virus: double trouble[END_REF][START_REF] Corey | The Effects of Herpes Simplex Virus-2 on HIV-1 Acquisition and Transmission: A Review of Two Overlapping Epidemics[END_REF][START_REF] Van De Perre | Herpes simplex virus and HIV-1: deciphering viral synergy[END_REF] In HIVuninfected individuals, HSV-2 infection increases susceptibility to HIV through clinical and subclinical recurrences which disrupt the genital epithelium and increase the density of HIV target cells in the genital submucosa. [START_REF] Van De Perre | Herpes simplex virus and HIV-1: deciphering viral synergy[END_REF][START_REF] Rebbapragada | Negative mucosal synergy between Herpes simplex type 2 and HIV in the female genital tract[END_REF][START_REF] Zhu | Virus-specific CD8+ T cells accumulate near sensory nerve endings in genital skin during subclinical HSV-2 reactivation[END_REF] In accord with this evidence, a systematic meta-analysis of longitudinal studies of the effect of HSV-2 on HIV acquisition showed that, after adjusting for confounding by age and at least one measure of sexual behaviour, 38-60% of new HIV infections may be attributable to prevalent HSV-2 infection in women and 8-49% in men, in the general populations reviewed. [START_REF] Freeman | Herpes simplex virus 2 infection increases HIV acquisition in men and women: systematic review and meta-analysis of longitudinal studies[END_REF] In HIV-infected individuals, co-infection with HSV-2 may increase HIV infectivity by upregulating the replication of HIV through different interactions, potentially resulting in increased rates of HIV transmission from these coinfected individuals. [START_REF] Van De Perre | Herpes simplex virus and HIV-1: deciphering viral synergy[END_REF] In fact, several cross-sectional studies have observed increased HIV genital shedding and plasma viral loads in the presence of HSV genital shedding or clinical recurrences. [START_REF] Augenbraun | Increased Genital Shedding of Herpes Simplex Virus Type 2 in HIV-Seropositive Women[END_REF][START_REF] Mbopi-Keou | Interactions between herpes simplex virus type 2 and human immunodeficiency virus type 1 infection in African women: opportunities for intervention[END_REF][START_REF] Mcclelland | Association between cervical shedding of herpes simplex virus and HIV-1[END_REF][START_REF] Legoff | Cervicovaginal HIV-1 and herpes simplex virus type 2 shedding during genital ulcer disease episodes[END_REF] However, two recent randomised controlled trials evaluating the impact of HSV-2 suppressive therapy (HSVST) on HIV acquisition have shown that acyclovir 400mg twice daily had no significant effect on HIV incidence. [START_REF] Celum | Effect of aciclovir on HIV-1 acquisition in herpes simplex virus 2 seropositive women and men who have sex with men: a randomised, double-blind, placebo-controlled trial[END_REF][START_REF] Watson-Jones | Effect of herpes simplex suppression on incidence of HIV among women in Tanzania[END_REF] These disappointing results may be related to the lack of effectiveness of the intervention, or the possibility that, although the treatment reduced the HSV-2 virus, it did not cause a reduction in the density of cells which enhance susceptibility to HIV in HSV-2 infected individuals. 7 13- 16 In contrast, results of randomised controlled trials conducted among dually infected individuals have suggested that HSV-2 enhances HIV infectivity through demonstrating that HSVST reduces HIV shedding, [START_REF] Baeten | Herpes Simplex Virus (HSV)-Suppressive Therapy Decreases Plasma and Genital HIV-1 Levels in HSV-2/HIV-1[END_REF][START_REF] Delany | Impact of HSV-2 suppressive therapy on genital and plasma HIV-1 RNA in HIV-1 and HSV-2-seropositive women not taking ART: a randomized, placebo-controlled trial in Johannesburg[END_REF][START_REF] Dunne | Suppressive acyclovir therapy reduces HIV cervicovaginal shedding in HIV-and HSV-2-infected women, Chiang Rai, Thailand[END_REF][START_REF] Nagot | Reduction of HIV-1 RNA levels with therapy to suppress herpes simplex virus[END_REF][START_REF] Paz-Bailey | Improvement in healing and reduction in HIV shedding with episodic acyclovir therapy as part of syndromic management among men: a randomized, controlled trial[END_REF][START_REF] Zuckerman | Herpes simplex virus (HSV) suppression with valacyclovir reduces rectal and blood plasma HIV-1 levels in HIV-1/HSV-2-seropositive men: a randomized, double-blind, placebo-controlled crossover trial[END_REF] although perhaps not sufficiently to actually reduce HIV transmission from coinfected individuals [START_REF] Celum | Acyclovir and transmission of HIV-1 from persons infected with HIV-1 and HSV-2[END_REF] .

Lastly, HSV-2 may also accelerate HIV disease progression by increasing HIV plasma viral load, [START_REF] Hennessey | AIDS onset at high CD4+ cell levels is associated with high HIV load[END_REF] and HIV could potentially increase HSV-2 infectivity through increased genital shedding of HSV-2 among coinfected individuals. 10 25 The latest trial results support this hypothesis since HSVST used by those coinfected significantly reduced HIV disease progression. [START_REF] Lingappa | Daily aciclovir for HIV-1 disease progression in people dually infected with HIV-1 and herpes simplex virus type 2: a randomised placebo-controlled trial[END_REF] Only four models (albeit applied to several different research questions) have incorporated both HSV-2 and HIV, and their interactions. [START_REF] Abu-Raddad | Genital herpes has played a more important role than any other sexually transmitted infection in driving HIV prevalence in Africa[END_REF][START_REF] Baggaley | Estimating the public health impact of the effect of herpes simplex virus suppressive therapy on plasma HIV-1 viral load[END_REF][START_REF] Blower | Calculating the contribution of herpes simplex virus type 2 epidemics to increasing HIV incidence: treatment implications[END_REF][START_REF] Freeman | Population-level effect of potential HSV2 prophylactic vaccines on HIV incidence in sub-Saharan Africa[END_REF][31][32][33][34] We build on these African and US focussed analyses, and our previous work 35 , by using a model to explore the contribution of HSV-2 to HIV transmission for a female sex worker (FSW) population in Southern India, where the HIV epidemic is concentrated among high-risk groups. The relative importance of symptomatic versus asymptomatic HSV-2 genital shedding is explored. The implications of the findings for the maximum potential impact of HSVST are discussed.

METHODS

Dynamic deterministic models of HSV-2 and HIV were coupled to simulate the transmission of HIV and HSV-2 among FSWs and their clients. The HSV-2 model is described elsewhere, 35 and includes separate compartments for initial infection (which may be symptomatic or asymptomatic), the long 'latent' phase with infectious asymptomatic shedding, and periodic short recurrences of infectious symptoms. The HIV model incorporates the initial short phase of high viral load, followed by the long asymptomatic phase in which viral load is low. This coupled model was programmed in C and solved numerically. Further details are supplied in the supplemental online appendix.

The FSWs were modelled as a cohort, with the HSV-2, HIV and coinfection prevalences being modelled dynamically over the duration of sex work, whereas the client prevalences were assumed to remain constant over the short timeframe of five years considered. Clients were assumed to randomly contact FSWs regardless of the duration for which each had sold/bought sex.

Enhanced transmission of HIV or HSV-2 in the presence of the other infection was modelled through the use of 'direct cofactors' that directly increase the probability of transmission during each (penile-vaginal) sex act. Additionally, among coinfected individuals, the symptomatic recurrence rate, proportion shedding asymptomatically, and rate of progression to AIDS were all assumed to be increased compared with those singly infected. The effect of other STIs facilitating HIV transmission was included as a constant cofactor.

Steps in analysis

Parameterisation

The parameter definitions and values used are shown in Table S1 in the supplemental online appendix, along with further details about the parameterisation process.

The model was parameterised and fitted using detailed behavioural and epidemiological data from FSWs in Mysore, Karnataka, and data on clients from Mysore when available, or elsewhere in Karnataka or other Indian states otherwise. [36][37]

Uncertainty analysis and model fitting

First the model input parameter ranges were developed, distributions defined and correlations set (Table S1 in the online appendix). Latin Hypercube Sampling (LHS) was then used to randomly sample 10,000 parameter sets from these uncertainty ranges.

Those simulations that were rejected in our previous analysis, 35 are discarded here also, along with those predicting too low a prevalence at the start of sex work, leaving 7,536 simulations.

Any simulation that lay within the 95% confidence intervals (CIs) of the HSV-2, HIV and HSV-2/HIV coinfection prevalence data among FSWs, by duration of sex work up to five years, was accepted as a model fit. 'Least chi-squared' error was used to identify the best-fit. However, in addition to using prevalence data among FSWs, the mean values for the HSV-2 and HIV prevalence among the small number of men reporting visiting FSWs (42) in the unpublished general population survey from Mysore were also used to identify the best-fit.

Calculating attributable fractions

To investigate the contribution HSV-2 makes to HIV incidence, the model estimates of annual HIV incidence among FSWs after one to five years of sex work were compared with and without specific interaction cofactors included, for each model fit. These incidence values were used to calculate the attributable fraction (AF) of a specific interaction cofactor for increasing HIV transmission by using the following formula:

(1) (Incidence with interaction) -(Incidence without interaction) (Incidence with interaction) AF = .

An average AF was calculated after weighting the AFs at each year of sex work by the proportion having worked in sex work for each equivalent duration. Confidence bounds were estimated by calculating the AFs for all the model fits and reporting the range spanned by 95% of the fits.

The model fits were also used to estimate the maximum potential impact that a hypothetical 'perfect' HSVST could have on HIV transmission in this FSW population, where 'perfect' refers here to completely removing the effect of HSV-2 on either HIV infectivity or HIV acquisition.

Sensitivity analysis

Multivariate sensitivity analysis using the best-fit simulation was used to identify which interaction inputs have the greatest effect on the predictions and to investigate the robustness of the model predictions to key assumptions. Each interaction model input was given the same relative uncertainty bounds (±20%), and 10,000 parameter sets were randomly sampled within these bounds using LHS. For each parameter set, the model was used to produce estimates of the percentage of incident HIV due to HSV-2. The relative importance of each non-correlated interaction parameter for the model prediction of the AFs was assessed using multilinear regression.

RESULTS

Selecting the best-fit and description of fits and correlations S1 in the online appendix. The best-fit predicted an HSV-2 prevalence of 20% and HIV prevalence of 6% among clients (data estimates were 19% and 5%, respectively).

[INSERT Figure 1]

Attributable fractions

The AFs of all interaction effects of HSV-2 for HIV transmission among FSW are shown in Table 1, averaged over the first five years of sex work.

[ Mysore are due to HSV-2, with the frequent infectious shedding of HSV-2 in the absence of symptoms contributing much more to HIV incidence than the less frequent recurrences of infectious symptoms (AF: 32.4% versus 3.0%).

If HSVST reduces the HIV infectivity of all coinfected clients to the same level as singly HIV-infected clients, then the model projects that 14.6% (95% CI: 3.3-41.2%) of HIV infections among FSWs would have been averted.

If an average cofactor is calculated that quantifies the overall effect of HSV-2 on HIV infectivity among coinfected individuals (see supplemental online appendix for details and figures), then Figure S2a suggests the impact projections are highly correlated to this average cofactor (linear regression R 2 =0.880). Indeed, if HSV-2 increases HIV infectivity 3-fold (up from 1.9-fold in the best-fit) then the linear regression implies that the maximum impact of 'perfect' HSVST for the coinfected clients would be a 34% decrease in HIV incidence in the FSWs. However, if this cofactor is between 1.25 and 1.43, coinciding with the shedding data from the trials 17-20 22-23 , and what their translated effect 39 means for the average cofactor, then the regression suggests 7-10% of HIV infections could have been averted. This projection is in close agreement with the Partners in Prevention trial results of an 8% reduction in HIV incidence. [START_REF] Celum | Acyclovir and transmission of HIV-1 from persons infected with HIV-1 and HSV-2[END_REF] If instead it is assumed that HSVST used by all FSWs singly infected with HSV-2 reduces their risk of acquiring HIV to that of the HSV-2-uninfected FSWs, the model projects that 36.0% (95% CI: 17.6-60.8%) of HIV infections among HSV-2-infected FSW could have been averted.

Again, if an average multiplicative cofactor for the effect of HSV-2 on increasing susceptibility to HIV among individuals singly-infected with HSV-2, is calculated in a similar way to that described above, then Figure S2b shows the impact projections are highly correlated to this average cofactor (linear regression R 2 =0.774). If HSV-2 increases a FSW's susceptibility to HIV 5-fold (up from 3.6-fold in the best-fit) then the linear regression implies that the maximum impact of 'perfect' suppressive treatment for the HSV-2-infected FSWs would be a 55% decrease in HIV incidence among these FSWs. A lower average cofactor of 2, results in a lower impact estimate of 24%.

Sensitivity analysis

Table 2 shows that the AFs for HIV incidence change by at most 8% in relative terms for a 20% relative change in the interaction input parameters. The AFs are most sensitive to changes in the direct cofactors, i.e. those that increase the probability of HIV transmission per sex act in the presence of HSV-2. Other regression coefficients are very small. Table 2 presents the results when the largest cofactors from each correlated pair are entered into the multilinear regression.

[INSERT Table 2]

DISCUSSION

The limitations of the HSV-2 model have been discussed previously, 35 mainly that the model does not allow for sexual behaviour differences during symptomatic versus asymptomatic shedding.

Since the focus of this study is on the biological interactions between HIV and HSV-2, sexual behaviour among FSWs is assumed to be homogeneous (and similarly for clients), and HSV-2 is the only STI that is modelled dynamically. Non-commercial partnerships of FSWs and clients, or transmission to the general population are ignored, as is the population of men who have sex with men. Using the model as a cohort model, due to lack of data on clients, limited the use of the interaction parameters, potentially leading to underestimates in the attributable fractions.

The model suggests that approximately 36% of HIV infections among FSWs in Mysore are due to HSV-2. Similarly, another modelling analysis, by Abu-Raddad et al. (2008), predicted that 35% of HIV infections in Kisumu, Kenya, were attributable to HSV-2. [START_REF] Abu-Raddad | Genital herpes has played a more important role than any other sexually transmitted infection in driving HIV prevalence in Africa[END_REF] Freeman et al. (2007), also used African data in a modelling analysis which found that the population attributable fraction of HIV due to HSV-2 increases with the maturity of the epidemic. 40 Our model findings emphasise the greater contribution to the HIV epidemic of HSV-2 shedding in the absence of symptoms, than in the presence of symptoms. This is biologically plausible since, although symptomatic recurrences may be more important per shedding episode, 41 asymptomatic shedding is much more frequent 42 .

Our analysis suggests that HSVST, used by either FSWs singly-infected with HSV-2 or clients coinfected with HIV and HSV-2, may reduce HIV incidence among FSWs, but not to any great extent (by 36% or 15%, respectively). These findings are in close For the main analysis, the values used for the cofactor effect of HSV-2 on susceptibility to HIV were calculated from reviews and pre-HSVST trial data (e.g. see references 7, 42 and 47 in the online appendix). [START_REF] Corey | The Effects of Herpes Simplex Virus-2 on HIV-1 Acquisition and Transmission: A Review of Two Overlapping Epidemics[END_REF] These cofactor values remain valid, despite the lack of significant impact observed in the HSVST trial of HIV acquisition [START_REF] Celum | Effect of aciclovir on HIV-1 acquisition in herpes simplex virus 2 seropositive women and men who have sex with men: a randomised, double-blind, placebo-controlled trial[END_REF][START_REF] Watson-Jones | Effect of herpes simplex suppression on incidence of HIV among women in Tanzania[END_REF] , since the trial results do not negate the good biological plausibility and observational data that HSV-2 increases HIV susceptibility. 3-6 8 43-44 The disappointing results from the HIV acquisition trials compared to the successful HIV shedding trials could be due to many reasons, including factors relating to the drug choice, dosage strategy and adherence levels [START_REF] Celum | Effect of aciclovir on HIV-1 acquisition in herpes simplex virus 2 seropositive women and men who have sex with men: a randomised, double-blind, placebo-controlled trial[END_REF][START_REF] Watson-Jones | Effect of herpes simplex suppression on incidence of HIV among women in Tanzania[END_REF] , different effects of the drug in coinfected individuals versus those singly infected with HSV-2 [START_REF] Lisco | Acyclovir is activated into a HIV-1 reverse transcriptase inhibitor in herpesvirus-infected human tissues[END_REF][START_REF] Stapleton | Coinfection alters the playing field: herpesviruses induce acyclovir to inhibit HIV[END_REF] , and/or the possible persistence of activated CD8+ T cells which enhance susceptibility to HIV in HSV-2 infected individuals but are not shut down by HSVST [START_REF] Zhu | Virus-specific CD8+ T cells accumulate near sensory nerve endings in genital skin during subclinical HSV-2 reactivation[END_REF] .

Observing an impact of HSVST in a trial setting may also be difficult because of limited statistical power. The Partners in Prevention trial was powered to detect a 50% decrease in HIV incidence, [START_REF] Celum | Acyclovir and transmission of HIV-1 from persons infected with HIV-1 and HSV-2[END_REF] yet our modelling suggests that this would have required HSV-2 to increase the per sex act HIV infectivity, among those coinfected, at least 4-fold. The HIV acquisition trials were powered at a similar level and our results suggest that an effect of HSVST would only have been observed if HSV-2 increased HIV susceptibility more than 4.5-fold. For these reasons, it is plausible that the trials observed no impact of HSVST on HIV incidence simply because the interaction between these viruses is not large enough to enable a significant impact to be observed for the statistical power set in the trials. The model strongly supports this premise for the impact of HSVST on HIV transmission (more so than acquisition), since even the upper bound on the modelpredicted decrease in HIV incidence is 41% in this case, which is below the 50% that the trials were powered for. The broader scientific literature suggests that the values of these cofactors are likely to be lower than what the model suggests is required to observe a statistically significant impact in these trials (e.g. see references 7, 28, 42, 47, 58-59, 61-65 in the online appendix). 45 The Partners in Prevention trial results also support these model findings since the upper bound on the impact estimate was 40%, [START_REF] Celum | Acyclovir and transmission of HIV-1 from persons infected with HIV-1 and HSV-2[END_REF] implying that there may have been a small impact of acyclovir which could not achieve the statistical significance required in the trial. Any imperfections in the effect of HSVST or adherence issues in a trial would require even higher cofactors in order to observe a statistical significant result.

Given this, the modelling analyses suggest that, although HSV-2 may play an important role in both concentrated and generalised HIV epidemics, this interaction is likely too weak to warrant the promotion of HSVST specifically for HIV prevention, given the lack of effect noted in the trials. However, HSVST in an important intervention for those who are infected with HSV-2, and may offer broader benefits since it has been demonstrated in a trial to delay progression to AIDS among those coinfected. [START_REF] Lingappa | Daily aciclovir for HIV-1 disease progression in people dually infected with HIV-1 and herpes simplex virus type 2: a randomised placebo-controlled trial[END_REF] It also remains possible that HSVST could have a weak effect on reducing HIV acquisition or transmission by less than 50%. Larger trials may be able to observe a weak effect of HSVST on HIV incidence but the importance of conducting such a trial would need to be weighed alongside the costs and relevance of identifying a low impact product.

Conclusions

This is the first model that has been used to explore the importance of HSV-2 to a concentrated HIV epidemic in an Asian setting. The modelling suggests that HSV-2 plays a critical role in the transmission and acquisition of HIV in Mysore, and that this may be mostly due to infectious shedding of HSV-2 in the absence of symptoms.

Given the successful trial of once-daily valacyclovir to reduce the risk of transmission of genital herpes 46 , continuous suppressive treatment of HSV-2 could be an effective strategy among FSWs and their clients in India, for reducing the transmission of HSV-2.

Over time, the HIV epidemic may be curtailed indirectly through the use of HSV-2 suppressive therapy, since a lower prevalence of HSV-2 could result in fewer HIV infections.

Increasing the potency of current HSV-2 antiviral drugs may help in further reducing HSV-2 incidence. However, the model suggests that even in the best case scenario, in which HSV-2 suppressive therapy completely removes the effect of HSV-2 on either HIV infectivity or HIV acquisition, this hypothetical 'perfect' therapy is unlikely to lead to a 50% reduction in HIV incidence, because of the limited strength of the interaction effect between HSV-2 and HIV.

Modelling analyses such as these should be repeated or adapted and used to explore the potential impact of other HIV/STI prevention interventions, helping to guide trial design for expected power and sample size calculations, and to retrospectively inform the interpretation of trial results.

  Figures and Tables count: 2 figures (labelled 1a and 1b) and 2 tables (labelled 1 and 2)

  Data came mostly from two unpublished surveys undertaken amongst FSWs (2004) and the general population (2005-6) in Mysore by the Karnataka Health Promotion Trust (KHPT), collected within the monitoring and evaluation of Avahan, the Bill and Melinda Gates Foundation funded India AIDS Initiative. The study was approved by the Ethics Review Boards of St Johns Medical College, Bangalore, India, Centre hospitalier affilié universitaire de Québec, Canada, and the University of Manitoba, Canada. The cohort model was fitted to HIV, HSV-2 and coinfection prevalences among FSWs by duration of sex work.

Four hundred and one of the 7 ,Figure 1 .

 71 Figure 1. The input values used in the best-fit are given in TableS1in the online

  agreement with White et al. (2008) for a concentrated African epidemic 34 and Baggaley et al. (2009) for two generalised HIV epidemics in sub-Saharan Africa 28 .

Figure 1 :Figure

 1 Figure 1: A comparison of the model best-fit with HSV-2 and HIV prevalence and

Table 1 ]

 1 INSERT Table 1 suggests that 35.5% (95% CI: 22.2-62.5%) of HIV infections among FSWs in

ACKNOWLEDGEMENTS

Support for this research was provided by the Bill & Melinda Gates Foundation (BMGF) through Avahan, its India AIDS Initiative (grant no. 33978), and the Department for International Development (DFID) funded Knowledge Programme on HIV/AIDS and STI and the Research Programme Consortium for Research and Capacity Building in Sexual and Reproductive Health and HIV in Developing Countries of the LSHTM. Michel Alary is a National Researcher of the Fonds de la Recherche en Santé du Québec (grant no. 8722). The views expressed herein are those of the authors and do not necessarily reflect the official policy or position of LSHTM, the BMGF/ Avahan or DFID. The Mysore data were collected as part of the monitoring and evaluation of the multisite HIV prevention intervention funded by the BMGF.

Many thanks go to the Karnataka Health Promotion Trust (KHPT) and St John's

Research Institute, Bangalore, India, and the University of Manitoba, Canada, for providing and helping interpret the Indian data. We especially thank Ashodaya Samithi, the local sex workers organisation, who agreed to the use of the data for modelling. We would also like to thank other colleagues involved in the HSV-2 therapy trials, and also Geoff Garnett at Imperial College, London, and Sevgi Aral at the US Centers for Disease Control, for their helpful input into this work.

AUTHOR CONTRIBUTIONS

AMF developed, programmed, parameterised and fit the model, conducted the modelling analyses, and wrote the manuscript (incorporating comments from coauthors). PTV input into the model development, parameterisation and fitting, and helped to guide the analyses, interpret the results and write the manuscript. PM participated in the planning of the project and analyses, helped interpret the findings and relate to other HSV-2/HIV research, and provided substantive edits and comments on drafts of the manuscript. HAW helped interpret the findings and relate to other HSV-2/HIV research, and provided substantive edits and comments on drafts of the manuscript. BMR, SR-P and RW were involved in the Mysore behavioural and epidemiological data collection and analysis required for model input and fitting parameters. JB, SM and CML helped contextualise the data collected and interpret for modelling. SM, CML and MA coordinated the data collection and analysis. CHW helped guide the analyses, interpret the findings, and provided substantive edits and comments on drafts of the manuscript.

Competing Interest: None declared.

TABLES AND FIGURES


Benoit ; Grosdidier
email: grosdidi@univ-metz.fr

Es Driss

Abdellatif Ben Sbihi

Jean-Georges Abdellah

Gasser

D Es Sbihi

A Ben Abdellah

J G Gasser

Structure of liquid bismuth calculated from pseudo-potentials and molecular dynamics

Keywords: atomic structure, liquid metals, molecular dynamic simulations user supplied): bismuth, pseudo potential mc.manuscriptcentral liquid metal, bismuth, atomic structure, pseudo-potentials, molecular dynamics

  L'archive ouverte pluridisciplinaire

Introduction

The bismuth-lead alloy is used as coolant in nuclear reactors [1]. The knowledge of the physical properties of this heavy metal is thus essential for this technology [2,3]. In this paper we propose a new approach, never used to our knowledge, which allows modelling correctly the structure of liquid bismuth. The structure factor has been calculated by several authors [4,5] who have some difficulties to explain simultaneously the position and the amplitude of the first peak and the large q scattering vector oscillatory behaviour. The pseudo-potential formalism [START_REF] Harrison | Pseudopotentials in the Theory of Metals[END_REF][START_REF] Animalu | [END_REF][8][9] for bismuth has been used by Hafner [5]. Their results, regarding the peaks positions, are quite satisfactory but discrepancies appear on their amplitudes. We used two pseudo-potentials. The local Ashcroft Empty Core Potential (ECP) [8] even used by Hafner and Heine [10] and the local Optimized Model Potential (OMP) proposed by Shaw [9], but never used to our knowledge for structure calculations. The form factors and the effective potentials are calculated with the Ichimaru-Utsumi [11] dielectric screening function. With these ECP and OMP local pseudo-potentials it is necessary to choose the relevant parameter. Often these parameters are fitted from the experimental data such as the electrical resistivity. This choice is not the best one because the resistivity is a scalar and is written as an integral in the Ziman formula [12]. Several compensations may appear in this integral. The fit of the parameters on the experimental structure is more pertinent; indeed the agreement of the two functions must be achieved in a large range. We wished to consider the Density Of States (DOS) data measured by Indlekofer [13] and those calculated by Hafner and Jank [5] which are displayed in figure 1. They show that there is a wide gap between the s and the p bands. In other words the valence 5 for bismuth must be replaced by valence 3 which is physically coherent with DOS data. On the other hand, according to Tamaki et al. [14], the effective ionic radius of Bi ion in liquid Bi-Zn alloys is estimated to be 1.23 Å which is very close to that of Bi 3+ ion (1.20 Å ) and very different from that of Bi 5+ ion (0.74 Å ). The best agreement is obtained on the transport electronic properties of liquid Cu-Bi alloys by Khalouk et al. using three conduction electrons [15].

We took into account these experimental results in order to carry out our structure calculations. To our knowledge, there is no pseudo-potential of which the parameters for bismuth have been calculated with valence 3. We have been led to determine ourselves these The structure calculation was performed by molecular dynamics (MD) on a 4000 particles NVT system. Our calculated pair correlation functions and structure factors are compared to the experimental ones (Waseda [START_REF] Waseda | The Structure of Non-Crystalline Materials[END_REF]). The paper is written as following. In the second and theoretical part we present briefly the calculation of the ion-ion effective potential from ECP and OMP pseudo-potentials and the numerical code which calculates the structure from these effective potentials. The results are presented and discussed in the third part. We show firstly that it is impossible to model the structure of liquid bismuth with both three and five conduction electrons from Ashcroft ECP pseudo-potential. The results are improved with OMP and five conduction electrons but do not fit on the experimental data. We finally show the very good agreement between the experimental structure factor and the calculated one for liquid bismuth with OMP using three conduction electrons. We also discuss the coherence with the electronic transport properties such as the resistivity. Then we conclude.

Theory and theoretical tools

A. Effective potential

The local pseudo-potential theory and the definition of the ingredients are given in the references [START_REF] Harrison | Pseudopotentials in the Theory of Metals[END_REF][START_REF] Animalu | [END_REF][8][9]. The expression of the ion-ion effective potential ) (r V calculated from the pseudo-potential is given by:

        - = ∫ ∞ 0 2 ) sin( ) ( 2 1 ) ( dq q qr q F r Z r V N π , ( 1
)
where Z is the chemical valence. The quantity r is the inter-ionic distance. The normalized energy wave number characteristic ) (q F N in reciprocal space, is defined from the Fourier transform of the local electron-ion model potential ) ( 0 q w : is the local field correction. This correction becomes more important when the electronic density increases. A lot of expressions for the local field correction have been developed in the literature. In this work, we shall choose the Ichimaru-Utsumi [11] (IU) expression considered as one of the best. We use the local pseudo-potential, whose expression in the real space is:

        - -         Ω = ) ( 1 1 ) ( 1 1 ) ( 4 ) ( 2 0 2 2 0 q q G q w Z q q F N ε π , (2)
     < - < = C C R r r Z R r A r w ) ( 0 , (3)
where C R is the core radius whose value can be fitted on physical properties such as the resistivity [START_REF] Bath | [END_REF]. The parameter A is equal to zero for the Ashcroft [START_REF] Harrison | Pseudopotentials in the Theory of Metals[END_REF] Empty Core Potential (ECP) or is related to the core radius C R by the optimization condition, for the local Shaw [9] Optimized Model Potential (OMP) (

C R Ze A 2 - =
). The Fourier transform

) ( 0 q w of ) ( 0 r w is expressed as: ) ( ) cos( 4 ) ( 0 2 0 0 q w qR q Z q w ECP C = Ω - = π (ECP) , (4)
) ( ) sin( 4 ) ( 0 2 0 0 q w qR qR q Z q w OMP C C = Ω - = π (OMP) .
(

) 5
In order to have the same node of the ) ( 0 q w ECP and ) ( 0 q w OMP form factors, the condition

ECP C OMP C R R 2 =
must be achieved. Equations ( 1), ( 2), (3) (4) and (5) show that the chemical valence Z plays a determinant role in the expression of the effective potential.

B. Molecular dynamics

The structure is calculated by a simulation code. This code uses the standard Verlet [18] algorithm and processes in NVT ensemble.

⋅

and the number of iterations after thermalisation is equal to 40000 . The code computes the pair correlation function ) (r g for each configuration and gives the its mean value. The static structure factor ) (q S is simply obtained from the pair correlation function

Results and discussion

For each run temperature the bismuth density is calculated using Lucas [START_REF] Lucas | Techniques de l'Ingénieur, Traité des Matériaux Métalliques[END_REF] compilation of density as a function of temperature under the form:

) ( M T T b a d - - =
where M T is the melting temperature of the metal. The calculated density values for the three temperatures 300, 550 and 800°C are respectively 0.02890, 0.02795 and ( )

3 0.02700 / Å atom .
We first calculate the four effective potentials for liquid bismuth, for both values

( 3 = Z and 5 = Z
) of the number of conduction electrons using ECP and OMP local pseudo-potentials.

The same node 0 q of the form factor has been used for ECP and OMP for each valence. This induces the relation 2

OM P ECP R R =
. The effective potentials are presented in figure 2. We observe that with 5 conduction electrons the effective potentials obtained from ECP and OMP are attractive and oscillate normally. Those calculated with ECP are deeper than those calculated with OMP. When we use the valence 3, the position of the hard part of the effective potentials decreases and a shoulder (OMP) or a pre well (ECP) appears. For the potential obtained by ECP the pre well is deeper than T k B . We shall see that it leads to the system solidification. We calculated the bismuth structure using ECP pseudo-potential and The minimum depth is comparable to T k B and its position is pushed to a r value near Å 38 . 4 . Two peaks with nearly the same height appear in its corresponding pair correlation function, the first at Å 75 . 2 near the shoulder of the potential at Å 13 .

3

, the second at Å 12 . 4 near the first minimum of the potential at Å 38 . 4 . Figure 4 show well that, with valence 5, it . We concluded that it is impossible to reproduce the structure of liquid bismuth from ECP pseudo-potential for the two values 5 and 3 of the valence.

We now use the local Shaw potential which has the advantage of having no discontinuity. We first present our results with valence 5. Figure 5 The minimum is much lower than T k B . This result hinders the possibility of adjusting the amplitudes of the calculated main peaks on the experimental curves. This appears clearly, on the pair correlation functions (figure 6) and on the corresponding structure factors (figure 7).

The OMP potential with valence 5 allows obtaining a satisfactory result on the different peaks positions. The amplitudes of the main peaks of the pair correlation functions are lower than the experimental ones, while the structure factors are higher than the experimental one. With We present in figure 8.a the effective potential of bismuth at 300 °C obtained with

Å 174 . 1 = OMP R
using the OMP and 3 conduction electrons. Its shape is similar to those achieved by Dzugutov-Dahlborg [4] and Hafner-Jank [5]. We observe a shoulder on the effective potential, which characterises the repulsive nature, checked by the low experimental ) of the coordination number [START_REF] Waseda | The Structure of Non-Crystalline Materials[END_REF]. In figure 9.a, we plot the experimental and calculated pair correlation functions. A very good agreement is obtained. In figure 10.a, we display the experimental and calculated structure factors. Here again the agreement is excellent in the position, the height of the main peak and in the oscillations, but we cannot reproduce the experimental hump located on the right side of the main peak.

It is an important improvement on earlier calculations which proves that using 3 = Z for liquid bismuth gives a very good pair correlation function and structure factor. We performed the same calculations for liquid bismuth at 550 °C and 800 °C using the same assumptions (OMP and valence three). The results are presented respectively in figure 8.b, 8.c, 9.b, 9.c and 10.b, 10.c.

In order to complete this study, we determined the characteristic parameters of respectively ( ) g r and ( ) S q for the three temperatures. All values are given in Tables 1 and2. Here it is important to refer to the criterion of the classification of the structure of liquid metals due to Waseda [START_REF] Waseda | The Structure of Non-Crystalline Materials[END_REF]. According to this criterion the structure of liquid metals may be classified into three categories, "categories I, II and III". The liquid structure of "category I" such as liquid lead is characterized by the symmetrical first peak of ( ) S q and also by the fact that the ratio 1 2

q q is 1.86 where 1 q and 2 q are, respectively, the positions of the first and second peak of ( ) S q . Waseda [START_REF] Waseda | The Structure of Non-Crystalline Materials[END_REF] showed that the structure of this "category I"' can be well reproduced by the hard sphere structure factor. Also, this ratio, 1.86, keeps its value even at a low packing fraction, η , or at a high temperature. Therefore, the liquid structure of ''category I'' is considered to be rather simple. The asymmetrical first peak is observed for the ( ) S q of "category II" liquid metals such as liquids (Zn, Cd, Hg). A shoulder appears on the rigth side of the first peak of the ( ) S q for "category III" liquid metals. Liquid bismuth can be classified into this "category III". The ratio 1 2 q q of both ''categories II and III'' differs considerably from 1.86. The temperature dependence of this ratio has not yet been investigated for "categorie III", and especially for bismuth. Therefore, the temperature dependence of this ratio, 1 2 q q , was investigated in detail for this liquid metal at three temperature. This ratio is found to remain close to 1.86 even at higher temperatures than the I). This indicates that the deviation from the simple liquid metals is significant for liquid bismuth even at a high temperature.

The characteristic parameters of these ( ) g r 's are given in Table II, in which the first coordination numbers are also shown. The first coordination numbers, which represent the numbers of atoms around the first peak of ( ) g r , were calculated from the fourth method of Waseda's book [START_REF] Waseda | The Structure of Non-Crystalline Materials[END_REF]. The height of the first peak in ( ) II.

g
The choice of the number of p electrons as the number of conduction electrons considerably improves structure factor calculations. These values are consistent with the presence of the gap of the experimental DOS [13]. We check our choice by calculating it electrical resistivity based on the extended Ziman formalism [21]. We start by constructing the muffin potentials necessary to the electrons scattering. The muffin tin potentials building following the method of Mukhopadhyay [22] is explained in reference [23]. We calculate the resistivity for liquid bismuth at 300, 550 and 800°C with the two sets of valencies 5 and 3. All calculations are performed in the frame of the Esposito approach [24] and are clearly explained in the reference [23]. Our results are presented in Table 3 together with experimental values [15] (second column). It appears clearly that, the values calculated with only p conduction electrons are always closer to the experimental resistivities. In every case our assumption improves the resistivity calculation of a factor nearly equal to 2.5.

Conclusion

Calculations of properties of bismuth liquid metals with the Shaw local pseudo-potentials three conduction electrons as valence give good results. The results are improved and better than those obtained earlier by using other local pseudo-potentials [3][4]. This new approach using the local OMP may serve for the study of other properties such as the dynamical r indicate the second peak value of ( ) g r and the corresponding r value.

Table 2: The characteristic parameters of structure factor, ( ) S q , of liquid Bi; ( ) 1 S q and 1 q indicate the first peak value of ( ) S q and the corresponding q value; ( ) 2 S q and 2 q indicate the second peak value of ( ) S q and the corresponding q value. Table 3: Liquid bismuth experimental [15] (second column) and calculated electrical resistivity using 5 conduction electrons (third column) and using 3 conduction electrons (fourth column). 1 Table 1:

FIGURES CAPTIONS

( ) T C ° -1 1 (Å ) q ( ) 1 S q -1 2 (Å ) q ( ) 2 S q 2 1
q q 2 1 ( ) ( ) S q S q 300 2.21

  two local pseudo-potentials (ECP and OMP). The Ashcroft pseudopotential is the simplest and the more known one but it exhibits the disadvantage of presenting discontinuities inducing unphysical oscillations. It is for this reason that we used, for the first time to our knowledge, the Shaw optimised local model pseudo-potential (OMP)[9].

  valence 3, taking into account the existence of the gap, for both values of the core radius The various effective potentials (figure3) and the corresponding pair correlation functions (figure4) are presented. These values of the core radius have been chosen because both of them represent approximately the same height of the first peak of the experimental pair correlation function while the others give the same position of the first peak. Figure3shows in the case of valence 5 that the effective potential calculated for of which the energy depth is much higher than T k B ; the corresponding pair correlation functions (figure4) is tending to a solid like. The effective

  fit the radius parameter ECP R , and to be reasonably near the experimental data. As soon as we adjust the position we lose on the amplitude of the peaks on the pair correlation. In the case of valence 3, the same figures 3 and 4 show that we are not able to reproduce the experimental structure of liquid bismuth. The potential leads to solidification as shown in figure4for the value of the core radius 0is liquid like. The position of the first peak is located at Å

  shows the effective potentials calculated for various values of Shaw core radius OMP R ( 0.95 Å , 1.00 Å and 1.05 Å ). One observes that for 1.00 Å OM P R = and 1.05 Å , the deepest minimum is located directly after the hard part, shifted after the first oscillation of the potential.

  as can be seen in (Table

  r becomes lower with the increase of the temperature for liquid bismuth, as is the case of many other liquid metals. The characteristic behaviour of the pair correlation function ( ) g r for liquid bismuth appears between the first and second peak positions located at 1 g r exhibits a flat shape without deep minimum. Its behaviour is different of that of ''category I'' liquid metals which present clear minimum, such as liquid aluminium or lead… The first coordination number of liquid bismuth decreases monotonously from 9.47 to 8.21 with the increase of temperature from 300 °C to 800 °C, as explicitly shown in Table

Figure 1 .

 1 Figure 1. Indlekofer [13] experimental (full line) and Hafner Jank [5] calculated (dashed line)

Figure 2 .

 2 Figure 2. Liquid bismuth effective potentials calculated at C T °= 300 from ECP and OMP

Figure 3 .

 3 Figure 3. Liquid bismuth effective potentials calculated at C T °= 300 from ECP pseudo-

Figure 4 .

 4 Figure 4. Liquid bismuth Waseda [16] experimental (circle) and computed pair correlation

Figure 5 .

 5 Figure 5. Liquid bismuth effective potentials calculated at C T °= 300 with the valence 5 = Z

Figure 6 .

 6 Figure 6. Liquid bismuth Waseda [16] experimental (circle) and computed pair correlation

Figure 7 .

 7 Figure 7. Liquid bismuth Waseda [16] experimental structure factor (circle) and our

Figure 8 .

 8 Figure 8. Ion-ion effective potential for the liquid metal bismuth ((a): C T Z °= = 300 , 3 , (b):

13 Figure 9 .

 139 Figure 9. Waseda [16] experimental (circle) and computed (full line) pair correlation functions for the liquid metal bismuth ((a): C T Z °= = 300 , 3 , (b) 3, 550 Z T C = = °and (c)

Figure 10 .

 10 Figure 10. Waseda[START_REF] Waseda | The Structure of Non-Crystalline Materials[END_REF] experimental structure factor (circle) and calculated static structure

TABLE CAPTIONS Table 1 .

 CAPTIONS1 The characteristic parameters of radial distribution function,

	( ) g r , of liquid
	bismuth; ( ) 1 g r and 1 r indicate the first peak value of ( ) g r and the corresponding r value;
	( ) 2 g r and 2

Table 2 :

 2

			2.0576	4.16	1.2538	1.88	0.609
	550	2.21	1.8487	4.20	1.1981	1.90	0.648
	800	2.20	1.7130	4.22	1.1595	1.92	0.676

Table 3 :

 3

	Temperature	Experimental	s+p valence	p valence
	( C T °	)	resistivity		Resistivity	Resistivity
			( ρ µ Ω ⋅	cm	)	( ρ µ Ω ⋅	cm	)	( ρ µ Ω ⋅	cm	)
	300		] 15 [				Z	=	5	Z	=	3
			128	.	54		57	.	77	143	.	65
	550		] 15 [				Z	=	5	Z	=	3
			141	.	78		59	.	59	145	.	65
	800		] 15 [				Z	=	5	Z	=	3
			155	.	00		. 70	94	197	.	60

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