Anne-Claire Binter

Ana M Mora

Joseph M Baker

Jennifer L Bruno

Katherine Kogut

Stephen Rauch

Allan L Reiss

Brenda Eskenazi

PhD Sharon K Sagiv
email: sagiv@berkeley.edu

Exposure to DDT and DDE and functional neuroimaging in adolescents from the CHAMACOS cohort

Keywords: Cohort studies, neuroimaging, pesticide exposure

Background: Epidemiological studies suggest that exposure to p,p'-dichloro-diphenyl-trichloroethane (p,p'-DDT) is associated with poorer cognitive function in children and adolescents, but the neural mechanisms underlying this association remain unclear.

Objective: We investigated associations of prenatal and childhood exposure to p,p'-DDT and its metabolite p,p '-dichloro-diphenyl-dichloroethylene (p,p'-DDE) with cortical activation in adolescents using functional near-infrared spectroscopy (fNIRS).

Methods: We administered fNIRS to 95 adolescents from the Center for the Health Assessment of Mothers and Children of Salinas (CHAMACOS) aged 15-17 years. We assessed cortical activity in the frontal, temporal, and parietal brain regions while participants completed tasks of executive function, language comprehension, and social cognition. We measured serum p,p'-DDT and -DDE concentrations at age 9 years and then estimated exposure-outcome associations using linear regression models adjusted for sociodemographic characteristics. In secondary analyses, we back-extrapolated prenatal concentrations using prediction models and examined their association with cortical activation.

Results: Median (P25-P75) p,p'-DDT and -DDE concentrations in childhood were 1.4 (1-2.3) and 141.5 (75.0-281.3) ng/g lipid, respectively. We found that childhood exposure to p,p'-DDT and -DDE was associated with altered patterns of brain activation during tasks of cognition and executive functions. For example, we observed increased activity in the left frontal lobe during a language comprehension task (β per 10 ng/g lipid increase of serum p,p'-DDE at age 9 years=3.4; 95% CI: 0.0, 6.9 in the left inferior frontal lobe; and β=4.2; 95% CI: 0.9, 7.5 in the left superior frontal lobe). We found no sex differences in the associations of childhood p,p'-DDT and -DDE concentrations with neural activity. Associations between prenatal p,p'-DDT and p,p'-DDE concentrations and brain activity were similar to those observed for child p,p'-DDT and -DDE concentrations.

Conclusions: Childhood p,p'-DDT and -DDE exposure may impact cortical brain activation, which could be an underlying mechanism for its previously reported associations with poorer cognitive function.

Highlights

 Dichloro-diphenyl-trichloroethane (DDT) is a persistent organochlorine pesticide.

 p,p'-DD/E were measured in child serum at 9 years and back-extrapolated during pregnancy.

 Functional near-infrared spectroscopy was performed in 95 children aged 15-17 years.

 p,p'-DDT/E concentrations were associated with altered patterns of cortical activation.

 Most associations were found for language comprehension and executive function tasks.

Introduction

Dichloro-diphenyl-trichloroethane (DDT), an organochlorine pesticide, is one of the 12 pesticides recommended by the World Health Organization (WHO) to combat malaria (World Health Organization (WHO) 2011). Although DDT use was banned in the U.S. in 1972, it was used in Mexico until 2000 and continues to be used under the Stockholm Convention for public health vector control in several countries worldwide (United Nations Environment Programme 2017). DDT persists in the environment for 2-15 years (ATSDR (Agency for Toxic Substances and Disease Registry) 2019) and has a half-life of more than 4 years in the human body. It is metabolized into 1,1′-dichloro-2,2'-bis(p-chlorophenyl)ethylene (p,p'-DDE) and other minor breakdown products (ATSDR (Agency for Toxic Substances and Disease Registry) 2019). Human exposure to p,p'-DDT and -DDE can occur by consumption of contaminated fish, vegetables grown in contaminated soil, or food imported from countries that use DDT, or by drift from nearby applications [START_REF] Byard | DDT, Chlordane, Toxaphene and PCB Residues in Newport Bay and Watershed: Assessment of Hazard to Wildlife and Human Health[END_REF][START_REF] Schafer | Persistent toxic chemicals in the US food supply[END_REF].

Early life exposure to low levels of p,p'-DDT and -DDE is of concern due to the sensitivity of the developing brain and other organ systems to environmental stressors [START_REF] Eskenazi | In utero exposure to dichlorodiphenyltrichloroethane (DDT) and dichlorodiphenyldichloroethylene (DDE) and neurodevelopment among young Mexican American children[END_REF][START_REF] Eskenazi | Prenatal Exposure to DDT and Pyrethroids for Malaria Control and Child Neurodevelopment: The VHEMBE Cohort, South Africa[END_REF][START_REF] Grandjean | Developmental neurotoxicity of industrial chemicals[END_REF][START_REF] Rice | Critical periods of vulnerability for the developing nervous system: evidence from humans and animal models[END_REF]. p,p'-DDT can cross the placenta and expose the fetus during pregnancy (Saxena et al. 1981) and, as a highly lipophilic compound, has been frequently detected in breastmilk (Sala et al. 2001).

Epidemiological studies indicate that prenatal p,p'-DDT and -DDE exposure may have adverse effects on child neurodevelopment [START_REF] Jurewicz | Chemical exposure early in life and the neurodevelopment of children--an overview of current epidemiological evidence[END_REF]). Studies have shown that higher p,p'-DDE concentrations in maternal serum during pregnancy or cord serum were associated with poorer cognitive function, including poorer quantitative, and verbal skills, poorer spatial orientation and memory [START_REF] Ogaz-González | Maternal dietary intake of polyunsaturated fatty acids modifies association between prenatal DDT exposure and child neurodevelopment: A cohort study[END_REF][START_REF] Osorio-Valencia | Prenatal p,p'-DDE exposure and establishment of lateralization and spatial orientation in Mexican preschooler[END_REF][START_REF] Torres-Sánchez | Prenatal p,p´-DDE Exposure and Neurodevelopment among Children 3.5-5 Years of Age[END_REF], poorer executive function and working memory [START_REF] Ribas-Fitó | In Utero Exposure to Background Concentrations of DDT and Cognitive Functioning among Preschoolers[END_REF]) and higher odds of attention deficit and hyperactivity disorder (ADHD)-related behaviors [START_REF] Sagiv | Prenatal organochlorine exposure and behaviors associated with attention deficit hyperactivity disorder in school-aged children[END_REF][START_REF] Sagiv | Neuropsychological Measures of Attention and Impulse Control among 8-Year-Old Children Exposed Prenatally to Organochlorines[END_REF]. In the Center for the Health Assessment of Mothers and Children of Salinas (CHAMACOS) cohort, in which the current cohort is set, maternal serum p,p'-DDE concentrations measured during pregnancy were associated with delayed processing speed in 7-year-old children, particularly among girls [START_REF] Gaspar | Prenatal DDT and DDE exposure and child IQ in the CHAMACOS cohort[END_REF]. In contrast, several cohort studies from Mexico, South Africa, Greece, the U.S., and the Netherlands observed null associations between prenatal p,p'-DDT exposure and neurodevelopmental outcomes assessed at various ages from infancy to adolescence [START_REF] Bahena-Medina | Neonatal neurodevelopment and prenatal exposure to dichlorodiphenyldichloroethylene (DDE): A cohort study in Mexico[END_REF][START_REF] Berghuis | Developmental neurotoxicity of persistent organic pollutants: an update on childhood outcome[END_REF][START_REF] Eskenazi | Prenatal Exposure to DDT and Pyrethroids for Malaria Control and Child Neurodevelopment: The VHEMBE Cohort, South Africa[END_REF][START_REF] Jusko | In-utero exposure to dichlorodiphenyltrichloroethane and cognitive development among infants and school-aged children[END_REF][START_REF] Kyriklaki | Prenatal exposure to persistent organic pollutants in association with offspring neuropsychological development at 4years of age: The Rhea mother-child cohort, Crete, Greece[END_REF].

Studies of childhood p,p'-DDT and p,p'-DDE exposure and neurodevelopment are sparse. The few studies that have examined associations found that postnatal p,p'-DDE exposure was associated with higher risk of conduct disorder and hyperactivity [START_REF] Rosenquist | Prenatal and Postnatal PCB-153 and p,p′-DDE Exposures and Behavior Scores at 5-9 Years of Age among Children in Greenland and Ukraine[END_REF], slower response speed [START_REF] Forns | Longitudinal association between early life socio-environmental factors and attention function at the age 11 years[END_REF], and poorer cognitive and motor function [START_REF] Gladen | Effects of perinatal polychlorinated biphenyls and dichlorodiphenyl dichloroethene on later development[END_REF]. A Norwegian study of 13-year-old children reported that exposure to p,p'-DDT during the first two years of life was associated with lower odds of ADHD [START_REF] Lenters | Early-life exposure to persistent organic pollutants (OCPs, PBDEs, PCBs, PFASs) and attention-deficit/hyperactivity disorder: A multipollutant analysis of a Norwegian birth cohort[END_REF].

These previous epidemiological studies have examined neurodevelopment using neuropsychological assessment tools or scales completed by parents; identification of the neural mechanisms underlying associations with p,p'-DDT and -DDE remains limited, however. In this study, we aimed to examine the association of prenatal and childhood p,p'-DDT and -DDE exposure with cortical brain activation, assessed using fNIRS while completing tasks of executive function, language comprehension, and social cognition, in a subset of 95 adolescent CHAMACOS participants.

Methods

Study Population

In the present study, we included youth enrolled in the CHAMACOS cohort when they were 9 years old (n=305; 2009-2011; henceforth referred to as CHAM2). Participants are Mexican-origin families living in the agricultural Salinas Valley community in Monterey County, California. We recruited families for CHAM2 using the following criteria: children born between 2000-2002; Spanish-or English-speaking mothers; mothers who were at least 18 years of age at CHAM2 child delivery; mothers who were eligible to receive state-supported medical coverage during pregnancy and received prenatal care; and mother-child pairs residing in the Salinas Valley from pregnancy until the time of recruitment. CHAM2 children were demographically similar to the children included prenatally in the original CHAMACOS cohort [START_REF] Gaspar | Prenatal DDT and DDE exposure and child IQ in the CHAMACOS cohort[END_REF]. From the CHAM2 children, 288 (94%) attended the 14-year-old follow-up visit (2014)(2015)(2016). In 2017, we invited (by phone or inperson) a subset of these 288 youth to participate in this preliminary fNIRS study. Our target recruitment sample size was between 80 and 100 youth. Reasons for non-participation were loss to follow-up, including moving of town; refusal to participate (n=7) and youth was in house arrest (n=2). This resulted in 95 youth who participated in this preliminary fNIRS study.

Parents provided written permission and youth (aged 15-17 years) provided written assent to participate. The Office for the Protection of Human Subjects at the University of California Berkeley approved the study.

DDT and DDE exposure assessment

Child p,p'-DDT, and -DDE concentrations were directly measured in blood samples collected in CHAM2 participants at age 9 years (one child was missing a sample). Chemical analyses were conducted at the Centers for Disease Control and Prevention (CDC) using gas chromatography-high resolution mass spectrometry (Sjödin et al. 2004). p,p'-DDT and -DDE levels were based on a serum-lipid concentration (nanograms per gram lipid). Total lipid concentrations were estimated using the method described by [START_REF] Phillips | Chlorinated hydrocarbon levels in human serum: effects of fasting and feeding[END_REF]) and based on serum levels of triglycerides and total cholesterol measured using standard enzymatic methods (Roche Chemicals, Indianapolis, IN).

Maternal p,p'-DDT and -DDE concentrations during pregnancy (henceforth referred to as prenatal p,p'-DDT and -DDE concentrations) were predicted from the p,p'-DDT and -DDE concentrations measured in venous blood samples collected from CHAM2 mothers and/or children when they were recruited (9 years after birth).

We used additional health and lifestyle data (i.e., maternal weight before pregnancy, maternal pregnancy weight gain, parity, and breastfeeding), collected by questionnaire [START_REF] Gaspar | Prenatal DDT and DDE exposure and child IQ in the CHAMACOS cohort[END_REF][START_REF] Verner | Increasing Sample Size in Prospective Birth Cohorts: Back-Extrapolating Prenatal Levels of Persistent Organic Pollutants in Newly Enrolled Children[END_REF].

Prediction models were built with a weighted Super Learner algorithm, using data from a subsample of study participants recruited during pregnancy (1999)(2000); henceforth referred to as CHAM1) who had measured p,p'-DDT and -DDE concentrations during pregnancy (in mothers) and at 9 years of age (in mothers and/or children) [START_REF] Bradman | Factors predicting organochlorine pesticide levels in pregnant Latina women living in a United States agricultural area[END_REF][START_REF] Gaspar | Prenatal DDT and DDE exposure and child IQ in the CHAMACOS cohort[END_REF][START_REF] Verner | Increasing Sample Size in Prospective Birth Cohorts: Back-Extrapolating Prenatal Levels of Persistent Organic Pollutants in Newly Enrolled Children[END_REF].

Child and prenatal p,p'-DDT and -DDE concentrations were transformed on a log10. p,p'-DDT and -DDE concentrations of all samples measured during childhood were above the limit of detection.

Functional neuroimaging data collection

We measured cortical neural activation using fNIRS, synchronized with a computerized neurobehavioral test battery, to monitor hemodynamic changes during specific stimuli and engaging tasks [START_REF] Cui | Functional near infrared spectroscopy (NIRS) signal improvement based on negative correlation between oxygenated and deoxygenated hemoglobin dynamics[END_REF][START_REF] Sagiv | Prenatal exposure to organophosphate pesticides and functional neuroimaging in adolescents living in proximity to pesticide application[END_REF]. We selected cognitive tasks and cortical regions of interest based on previous epidemiological studies of prenatal organophosphate pesticide exposures [START_REF] Sagiv | Prenatal exposure to organophosphate pesticides and functional neuroimaging in adolescents living in proximity to pesticide application[END_REF]) and previous neuroimaging studies in children [START_REF] Rauh | Brain anomalies in children exposed prenatally to a common organophosphate pesticide[END_REF]). Details about cognitive tasks, fNIRS acquisition and processing were published previously [START_REF] Sagiv | Prenatal exposure to organophosphate pesticides and functional neuroimaging in adolescents living in proximity to pesticide application[END_REF] and are provided as Supplementary Material.

In brief, participants engaged in a total of six tasks, including four tasks that assess attention and executive function (i.e., attention and response inhibition with the Go/No-Go task, working memory with the Sternberg working memory and the visuospatial N-back tasks, and cognitive flexibility with the Wisconsin Card Sorting task (WCST)); the Dynamic Social Gestures task that assesses social cognition, and the Pyramid and Palm Trees task that assesses language comprehension with. In the Go/No-Go, the participant was asked to press a button when seeing any letter but 'X' (i.e., go trials), and withhold otherwise (i.e., no-go trials). For the Sternberg working memory task, the participant viewed a string of 7-8 letters and then was asked if a presented "target" letter occurred in the previous letters. In the visuospatial N-back, the letter "O" was presented on the screen in a 3x3 matrix, and the participant was asked whether the letter was presented at the same location in the previous trial (1-back) or two trials previous (2-back). In the WCST, the participant was asked to match cards based on an unstated rule (shape, number, or color). For the Dynamic Social Gestures task, the participant viewed video clips portraying social gestures (e.g., friendly wave) and nonsocial gestures (e.g., looking at a book) and was asked to press when the dot on the screen turned red (a device to ensure that the participant was attending to the video clip). In the Pyramids and Palm Trees task, the participant was asked to decide which of two words was semantically related to a stimulus word. To avoid bias associated with test fatigue, task presentations were randomized across two testing sessions, except the Go/No-Go, which was always presented at the end of one of the two sessions.

While study participants completed the six cognitive tasks, we collected hemodynamic activity data (i.e., oxygenated hemoglobin (HbO) and deoxygenated hemoglobin (HbR)), from 36 detector channels positioned on the scalp. We then estimated brain activation for each task with a generalized linear model (GLM) approach using trial onsets, duration of each condition, and HbO hemodynamic activity [START_REF] Plichta | Model-based analysis of rapid event-related functional near-infrared spectroscopy (NIRS) data: A parametric validation study[END_REF].

Potential confounders

We collected sociodemographic and lifestyle data during in-person maternal interviews conducted at several follow-up visits between enrollment and the child's age 14 year visit. We identified potential confounders for our regression models a priori using a causal model framework (see Supplementary Material, Figure S1). We adjusted for maternal education at delivery (<6th grade, 7-12th grade, completed high school or more), parity (nulliparous, one child, at least 2 children), breastfeeding duration (<1 month, 1-6 months, 6-12 months, more than 12 months), child age at assessment (years), and child sex (boy, girl).

Statistical analysis

We grouped channels into 15 functional localization clusters across both brain hemispheres based on proximity to allow for anatomical variation of task-responsive brain regions across participants (Figure 1).

Clusters were located as follows: 1=left inferior frontal pole (channels 1, 3, 5); 2=left superior frontal pole (channels 2, 6); 3=left Broca's/Brodmann areas 44 and 45 (channels 4, 7); 4=left dorsolateral prefrontal cortex (channels 10,11); 5=left Broca's/Brodmann areas 44 and 6 (channels 8, 12); 6=left superior/inferior temporal gyrus/postcentral gyrus (channels 9, 13); 7=left inferior parietal lobule (channels 14, 15, 17) (channels 32, 36). As in previous work [START_REF] Sagiv | Prenatal exposure to organophosphate pesticides and functional neuroimaging in adolescents living in proximity to pesticide application[END_REF], we employed a functional localization procedure in which we chose the channel with the greatest contrast value within each cluster to represent activation for that cluster [START_REF] Baker | Evaluation of smartphone interactions on drivers' brain function and vehicle control in an immersive simulated environment[END_REF][START_REF] Hosseini | Neural, physiological, and behavioral correlates of visuomotor cognitive load[END_REF].

In our main analyses, we examined associations (β and 95% confidence interval (CI)) of log10 child p,p'-DDT and --DDE concentrations with cortical brain activity using linear regression models adjusting for potential confounders. β coefficients were contrasted between the task of interest and its corresponding control condition to capture the brain activation specific to task demands. Contrast conditions were: "No-Go vs. Go" for the Go/No-Go task, "maintenance/encoding vs. recall" for the Sternberg working memory task, "2-back vs. 1-back vs. control" for the N-back, "card sort vs. exact match" for the WCST, "social vs. non-social gestures" for the Dynamic Social Gesture task, and "semantic meaning vs. size" for the Pyramids and Palm Trees task), Each β coefficient indicates the direction (positive/negative) and the intensity, for the sign and the magnitude, respectively, of blood oxygen level-dependent change (i.e., brain activity) that occurs during each condition. Assumptions of linear regression models were met. Technical problems with data collection (i.e., task presentation and/or recording) and preprocessing (i.e., correlations between HbO and HbR concentrations, poor signal-to-noise ratio, and/or low signal quality) led to some exclusions. Missing values varied across tasks and localization clusters (Supplementary Material, Table S1). To correct for multiple testing, we controlled for type I error using the Benjamini-Hochberg FDR at <0.05. We examined sex-specific effects by including an interaction term between childhood p,p'-DDT or -DDE concentrations and sex in our linear regression models and computing sex-specific effect estimates. In sensitivity analyses, we adjusted linear regression models for enrichment in the home with the Home Observation for the Measurement of the Environment-Short Form (HOME) score, administered at age 10.5 [START_REF] Bradley | The HOME Inventory and family demographics[END_REF].

In secondary analyses, we examined associations of log10 prenatal p,p'-DDT and -DDE concentrations with cortical brain activity. In addition, we examined associations of childhood and prenatal p,p'-DDT and -DDE concentrations with task performance (i.e., errors, accuracy, and reaction time). Performance indicators varied across tasks. We also built a composite performance score for each task by subtracting response latency from accuracy, following standardization (Collignon et al. 2010). We did not investigate task performance for Dynamic Social Gestures because the performance aspect of this task (i.e., pressing a button when seeing a red dot) was to ensure participation in the task and was not a test of social cognition.

Results

Study population

As shown in Table 1, youth included in the present study had a median (P25-P75) age of 15.8 (15.5-16.1) years and 7.4% were left-handed. Most of their mothers were born in Mexico (89.5%) and did not graduate from high school (70.6%). We did not observe differences in sociodemographic characteristics between fNIRS participants and non-participants, except that mothers of participants were older at delivery (46.3% were age 30+ y at delivery) than mothers of non-participants (24.7%) (see Supplementary Material, Table S2).

Median (P25-P75) serum p,p'-DDT and -DDE concentrations in childhood were 1.4 (1-2.3) and 141.5 (75.0-281.3) ng/g lipid, respectively (Table 2). Median back-extrapolated prenatal serum p,p'-DDT and -DDE concentrations were 14.4 (9.8-82.0) and 522.1 (324.3-1770.7) ng/g lipid, respectively. Both childhood and prenatal serum p,p'-DDT and -DDE concentrations were highly variable (Table 2). For example, childhood p,p'-DDE concentrations ranged from 32 to 14,000 ng/g lipid. Correlations between childhood and prenatal p,p'-DDT and -DDE concentrations were moderate to high (r=0.64 between childhood p,p'-DDT and -DDE; r=0.81 between prenatal p,p'-DDT and -DDE; Table 2).

Childhood DDT/DDE and cortical activation

We found associations of childhood p,p'-DDT and -DDE concentrations with increased cortical activition during a language comprehension task (Pyramid and Palm Trees) in the left inferior frontal lobe (cluster 1: βDDT=3.2; 95% CI: -0.7, 7.0; and βDDE=3.4; 95% CI: 0.0, 6.9) and in the left superior frontal lobe (cluster 2: βDDT=3.1; 95% CI: -0.6, 6.8; and βDDE=4.2; 95% CI: 0.9, 7.5) (Figure 2-A). We also found associations of childhood p,p'-DDT and -DDE concentrations with altered patterns of activation during the tasks of working memory (Sternberg and N-back) (Figures 2-B and2-C). Like in the language comprehension task, childhood p,p'-DDE concentrations were associated with increased activation in the left inferior frontal lobe during the Sternberg working memory task (cluster 1: βDDE= 4.8; 95% CI: 0.5, 9.0) and the visuospatial N-back task (cluster 1: βDDE=3.7; 95% CI: -0.3; 7.7). We also observed associations of childhood p,p'-DDT and -DDE concentrations with increased activation in the right frontal cortex and the right inferior parietal lobe, but only for the Sternberg test (cluster 11: βDDT=3.0; 95% CI: -1.9, 7.9; and βDDE=5.1; 95% CI: 0.7, 9.5, cluster 12: βDDT=5.1; 95% CI: 0.6, 9.6; and βDDE=4.3; 95% CI: 0.3, 8.3, and cluster 14: βDDT=3.5; 95% CI: -1.4, 8.4; and βDDE=4.6; 95% CI: 0.3, 8.9). During the WCST task, childhood p,p'-DDE concentrations were associated with a slight increase in activation in the left inferior parietal lobe (cluster 7: βDDE=4.1; 95% CI: -0.1, 8.4) (Figure 2-D). We found null associations of childhood p,p'-DDT and -DDE concentrations with cortical brain activation during the Go/No-Go task and the Dynamic Social Gestures task (Figure 2-E and 2-F). Notably, no estimates remained statistically significant after adjusting for multiple comparisons (FDR-corrected p-value <0.05).

Associations remained the same when further adjusting for HOME score (see Supplementary Material, Table S3). When we stratified childhood p,p'-DDT and -DDE concentrations and brain activation associations by child sex, we found no notable sex differences for any of the six tasks (see Supplementary Material, Figure S2). In addition, we found null associations of childhood p,p'-DDT and -DDE concentrations with task performance (see Supplementary Material, Table S4).

Prenatal DDT/DDE and cortical activity

Overall, associations of estimated p,p'-prenatal DDT and -DDE concentrations with brain activity were similar to those observed for childhood p,p'-DDT and -DDE concentrations (Supplementary Material, Figure S3). Some associations were attenuated and were not statistically significant (e.g., associations in the right frontal cortex and the right inferior parietal lobe during the Sternberg task: cluster 11: β DDE=2.7; 95% CI: -1.4, 6.7, cluster 12: βDDE=2.1; 95% CI: -1.5, 5.8, and cluster 14: βDDE=2.6; 95% CI: -1.2, 6.5). We observed additional associations between prenatal p,p'-DDE concentrations and increased cortical activity in the right temporal cortex during the Dynamic social gestures task (cluster 13: βDDE=1.9; 95% CI: 0.3, 3.5), and in the right superior parietal lobe during the visuospatial N-back task (cluster 15: βDDE = 3.2; 95% CI: 0.2, 6.0), but decreased cortical activity in the left superior parietal lobe during the Go/No-Go task (cluster 8: βDDE=-3.7; 95% CI: -6.4, -1.1). No associations were statistically significant after correcting for multiple testing (FDRcorrected p-value <0.05).

We found null associations for prenatal p,p'-DDT and -DDE concentrations and task performance except for the WCST for which both prenatal p,p'-DDT and -DDE concentrations were associated with longer response latencies (βDDT=0.32, 95% CI: 0.06, 0.58; and βDDE=0.36, 95% CI: 0.02, 0.70) (see Supplementary Material, Table S4).

Discussion

We used fNIRS to investigate the relationship of p,p'-DDT and -DDE exposure measured at 9 years of age with brain function in adolescence. We found altered patterns of cortical activation during tasks of language comprehension and executive function in association with both childhood serum p,p'-DDT and -DDE concentrations. We observed similar associations with estimated prenatal serum p,p'-DDT and -DDE concentrations.

Childhood p,p'-DDT and -DDE concentrations were associated with increased brain activity in the frontal lobe during the Pyramid and Palm Trees Test, a language comprehension task. Prenatal p,p'-DDT and -DDE concentrations showed similar associations. The frontal lobes of the brain are involved in decision-making and planning processes [START_REF] Ogawa | Abnormal cortical activation during silent reading in adolescents with autism spectrum disorder[END_REF]); our findings suggest that higher exposure may be associated with the need to recruit more neural resources to respond to the task. Although no previous studies has investigated p,p'-DDT or -DDE in relation to brain activity, a study of 400 British girls found that prenatal p,p'-DDT concentrations were associated with poorer verbal comprehension scores at 38 months, though the opposite associations were found at 15 months [START_REF] Jeddy | Prenatal exposure to organochlorine pesticides and early childhood communication development in British girls[END_REF]. Serum p,p'-DDT concentrations in the mothers of these girls (median DDT of 11.4 ng/g lipids) were similar to those measured in our study at 9 years of age, and p,p'-DDE concentrations were considerably lower (median p,p'-DDE of 309.5 ng/g lipids).

This study did not investigate postnatal exposure to p,p'-DDT.

In the present study, we found increased brain activition in the left prefrontal area during both working memory tasks (i.e., visuospatial N-Back and Sternberg tasks) in children with higher prenatal and childhood p,p'-DDE exposure. Our results are consistent with those of a Spanish population-based birth cohort (Menorca, Spain, n=326), which found that cord serum p,p'-DDT concentrations were associated with poorer executive function, working memory scores, and memory skills at age 4 years [START_REF] Ribas-Fitó | In Utero Exposure to Background Concentrations of DDT and Cognitive Functioning among Preschoolers[END_REF].

Similarly, higher p,p'-DDE concentrations measured in maternal serum collected during the third trimester of pregnancy were associated with reduced memory scores at ages 42, 48, 54, and 60 months in a Morelos cohort (Mexico, n=203) [START_REF] Ogaz-González | Maternal dietary intake of polyunsaturated fatty acids modifies association between prenatal DDT exposure and child neurodevelopment: A cohort study[END_REF][START_REF] Osorio-Valencia | Prenatal p,p'-DDE exposure and establishment of lateralization and spatial orientation in Mexican preschooler[END_REF][START_REF] Torres-Sánchez | Prenatal p,p´-DDE Exposure and Neurodevelopment among Children 3.5-5 Years of Age[END_REF]). These findings suggest that exposure to p,p'-DDT and -DDE during early life may be associated with poorer working memory in childhood and that the prefrontal cortex may be a target of p,p'-DDT and p,p'-DDE exposure.

We observed that childhood p,p'-DDE concentrations were linked with an increase in brain activition in the left parietal lobe during a cognitive flexibility task (WCST). The parietal cortex is known to be involved in selective attention [START_REF] Behrmann | Parietal cortex and attention[END_REF][START_REF] Salo | Brain activity associated with selective attention, divided attention and distraction[END_REF]). In addition, higher prenatal p,p'-DDE exposure was associated with increased response latency during this task. This is consistent with a Spanish study that reported associations of cord serum p,p'-DDE concentrations with slower reaction time on a continuous performance test [START_REF] Forns | Longitudinal association between early life socio-environmental factors and attention function at the age 11 years[END_REF]).

We did not find sex-specific differences for childhood p,p'-DDT and '-DDE exposure on brain function, but previous studies indicate that girls may be more prone to adverse effects. In Spain, cord serum DDT concentrations were associated with worse verbal, memory, quantitative, and perceptual-performance skills at age 4 years, particularly among girls [START_REF] Ribas-Fitó | In Utero Exposure to Background Concentrations of DDT and Cognitive Functioning among Preschoolers[END_REF]). In the CHAMACOS study, [START_REF] Gaspar | Prenatal DDT and DDE exposure and child IQ in the CHAMACOS cohort[END_REF] found stronger associations between prenatal p,p'-DDT concentrations and delayed processing speed among girls at age 7 years. Our statistical power to detect sex-specific effects may have been limited by our small sample size (n=95).

Although previous epidemiological studies have reported associations of p,p'-DDT and -DDE exposure with impaired executive function, memory, and cognition [START_REF] Ogaz-González | Maternal dietary intake of polyunsaturated fatty acids modifies association between prenatal DDT exposure and child neurodevelopment: A cohort study[END_REF][START_REF] Osorio-Valencia | Prenatal p,p'-DDE exposure and establishment of lateralization and spatial orientation in Mexican preschooler[END_REF][START_REF] Ribas-Fitó | In Utero Exposure to Background Concentrations of DDT and Cognitive Functioning among Preschoolers[END_REF][START_REF] Torres-Sánchez | Prenatal p,p´-DDE Exposure and Neurodevelopment among Children 3.5-5 Years of Age[END_REF], in our study, we did not observe associations of p,p'-DDT and -DDE exposure with task performance. The absence of these associations may suggest that children exposed to p,p'-DDT and -DDE during pregnancy or childhood may present compensatory brain mechanisms to prevent cognitive troubles. On the other hand, we cannot ignore the possibility that our tasks, adapted for an fNIRS assessment, may have been insufficiently challenging and sensitive to detect associations of p,p'-DDT and -DDE exposure with task performance. Furthermore, we reported low correlations between task performances and cortical activity in all our tasks, suggesting that cortical activity alone cannot be considered as a predictor of cognitive performances. While outside of the scope of the current study, future studies with larger sample sizes should address the relationship between brain activity and cognition [START_REF] Marek | Reproducible brainwide association studies require thousands of individuals[END_REF].

The human brain matures into adulthood and windows of vulnerability are not limited to in utero development [START_REF] Rice | Critical periods of vulnerability for the developing nervous system: evidence from humans and animal models[END_REF]. By assessing both prenatal and childhood exposure to p,p'-DDT and -DDE in our study, we considered a broader developmental window. DDT has more than a 4-year half-life in humans (ATSDR (Agency for Toxic Substances and Disease Registry) 2019), so we expect that the p,p'-DDT and -DDE concentrations that we measured in children at 9 years of age reflect their exposure up until that age. In addition, the use of biomarkers enabled us to account for all sources of DDT and DDE exposure (i.e., residential and dietary). In contrast to previous epidemiological studies that have used neuropsychological tests to investigate the effects of exposures to environmental contaminants, we used fNIRS to examine subtle effects of prenatal and childhood p,p'-DDT and -DDE exposure on cortical neural activity.

We also faced several limitations. First, fNIRS evaluates neural activity indirectly by measuring hemodynamic changes at the cortical surface. We were not able to investigate the possible associations between p,p'-DDT and -DDE concentrations and hemodynamic changes in subcortical regions. Second, our sample size (N=95) is small for an epidemiological study on environmental toxicants and may have resulted in a lack of statistical power to detect subtle associations. Further studies should conduct population-based neuroimaging studies in larger sample sizes to confirm the effects of p,p'-DDT and -DDE on the brain. Third, associations in our primary analyses were no longer statistically significant after FDR correction for multiple comparisons. This is likely due to our small sample size and the conservative approach of the FDR correction; however, we cannot rule out the possibility that the associations that we found in our main analyses were due to chance and should be interpreted with caution. Lastly, prenatal p,p'-DDT and -DDE concentrations were estimated using a prediction model based on p,p'-DDT and -DDE concentrations measured in venous blood samples collected from CHAM2 mothers and/or children when they were recruited (9 years after birth) and additional questionnaire data. However, as observed in CHAM1 participants (who had both measured maternal p,p'-DDT and -DDE concentrations during pregnancy and repeated p,p'-DDT and -DDE measures in either the mother or child when the child was 9 years old), our models were strongly predictive of prenatal p,p'-DDT and -DDE concentrations (R2s ranged from 0.86 to 0.97) [START_REF] Verner | Increasing Sample Size in Prospective Birth Cohorts: Back-Extrapolating Prenatal Levels of Persistent Organic Pollutants in Newly Enrolled Children[END_REF].

Conclusions

In a Mexican American population-based cohort, we found associations of childhood exposure to p,p'-DDT and -DDE with alteration in cortical brain activation in adolescents while they completed language and executive tasks. Previous epidemiological studies have shown that exposure to DDT during vulnerable windows of brain development may alter cognitive function using neuropsychological tests. This study suggests that DDT and DDE exposure may have persistent adverse effects on the brain and confirms the added value of neuroimaging techniques for increasing knowledge about the possible mechanisms through which environmental toxicants exert their effects.

Table 1 .

 1 Characteristics of participants with fNIRS data from the CHAMACOS cohort (Salinas Valley, California) (n=95).

	Characteristics

Table 2 .

 2 Serum DDT and DDE concentrations (ng/g lipid) in the CHAMACOS cohort(Salinas Valley, California, from 2009) (n=95). : 25 th percentile, P50: 50 th percentile, P75: 75 th percentile. a Prenatal DDT and DDE concentrations were predicted using p,p'-DDT and -DDE concentrations measured in venous blood samples collected from CHAM2 mothers and/or children when they were recruited (9 years after birth) and using additional questionnaire data (i.e., maternal pre-pregnancy weight, maternal pregnancy weight gain, maternal parity, and breastfeeding history). Figure 1. fNIRS channel (n=36) placement and localization clusters (n=15) in the CHAMACOS study, enrolled in 2009 in Salinas Valley, California.Red circles represent a channel (source and detector pair). Yellow circles are localization clusters based on proximity of channels and anatomy: 1=left inferior frontal pole; 2=left superior frontal pole; 3=left Broca's/Brodmann areas 44 and 45; 4=left dorsolateral prefrontal cortex; 5=left Broca's/Brodmann areas 44 and 6; 6=left superior/inferior temporal gyrus/postcentral gyrus; 7=left inferior parietal lobule; 8=left superior parietal lobule; 9=right inferior frontal pole; 10=right Broca's/Brodmann areas 44 and 45; 11=right superior frontal pole/dorsolateral prefrontal cortex; 12=right premotor/somatosensory cortex; 13=right posterior superior/middle temporal sulcus; 14=right inferior parietal lobule; 15=right superior parietal lobule. Adjusted associations (β (95% CI)) for a 10-fold increase in childhood p,p'-DDT and -DDE concentrations and fNIRS brain activation by task in the CHAMACOS cohort (Salinas Valley, California) (n=95).Adjusted for maternal education at delivery (<6th grade, 7-12th grade, completed high school or more), parity (nulliparous, one child, at least 2 children), duration of breastfeeding (<1 month, 1-6 months, 6-12 months, more than 12 months), age of child at assessment (continuous variable), and child's sex. Clusters: 1=left inferior frontal pole; 2=left superior frontal pole; 3=left Broca's/Brodmann areas 44 and 45; 4=left dorsolateral prefrontal cortex; 5=left Broca's/Brodmann areas 44 and 6; 6=left superior/inferior temporal gyrus/postcentral gyrus; 7=left inferior parietal lobule; 8=left superior parietal lobule; 9=right inferior frontal pole; 10=right Broca's/Brodmann areas 44 and 45; 11=right superior frontal pole/dorsolateral prefrontal cortex; 12=right premotor/somatosensory cortex; 13=right posterior superior/middle temporal sulcus; 14=right inferior parietal lobule; 15=right superior parietal lobule.

		N	Range (min-max)	P25	P50	P75		Correlation (spearman rho)
							Childhood	Prenatal
							p,p'-DDT p,p'-DDE p,p'-DDT p,p'-DDE
	Childhood
	p,p'-DDT	94	0-665	1	1.4	2.3	1	0.64	0.54	0.63
	p,p'-DDE	94	31.8-14000	75.0	141.5	281.3		1	0.60	0.57
	Prenatal a
	p,p'-DDT	95	2.6-6371.1	9.8	14.4	82.0			1	0.81
	p,p'-DDE	95	127.4-29090.8	324.3	522.1	1770.7				1

P25

Acknowledgments

We gratefully acknowledge the CHAMACOS laboratory and field staff, students, community partners, participants, and families. This work was supported by NIH grants UG3 OD023356, P01 ES009605, R01 ES015572, T32 MH019908, and K99 HD092883; grants RD 83171001 and RD 83451301 from the US Environmental Protection Agency (EPA); the Stanford Maternal and Child Health Institute; and a gift from the Kelvin Foundation. The Fondation de France and the EHESP French School of Public Health provided a grant to the first author.


Florent Autrusseau Lten

Rafic Nader
email: rafic.nader@univ-nantes.fr

Anass Nouri
email: anass.nouri@uit.ac.ma

Vincent L'allinec
email: vincent.lallinec@chu-angers.fr

Romain Bourcier
email: romain.bourcier@univ-nantes.fr

Toward a 3D Arterial Tree Bifurcation Model for Intra-Cranial Aneurysm Detection and Segmentation

Keywords:

An accurate detection of intracranial aneurysms is of paramount importance for a timely diagnosis and a possible treatment. Indeed, intracranial aneurysms (ICA) need to be detected at an early stage, and their evolution must be closely monitored before any treatment becomes hazardous. Numerous methods have been proposed to detect ICA either on Digital Subtraction Angiography (DSA) on Computed Tomography Angiography (CTA), or Magnetic Resonance Angiography (MRA) Time-Of-Flight (TOF) modalities. In the present study, we are particularly interested in the saccular ICA occurring onto the vascular tree's bifurcations, and we specifically focus our research on MRA-TOF acquisitions. We propose a synthetic model of both the artery bifurcation and the aneurysm itself. We are able to very accurately model some vasculature bifurcations as they are represented on TOF acquisitions. Their geometrical disposition, the various background noises and the aneurysm's shapes and positions are rigorously reproduced. The purpose of this approach is to alleviate the burden of a ground-truth manual segmentation commonly required when using deep-learning for object detection or semantic segmentation. Our model is highly configurable and intends to produce vast datasets used to feed a Convolutional Neural Network (CNN) for the automatic detection and segmentation of the saccular ICAs. In this preliminary study we only intend to propose a model for 3D aneurysm-bearing bifurcations. Evidently, a thorough evaluation of the model's accuracy is conducted. A preliminary experiment was conducted on a reduced dataset in order to assess the applicability of our bifurcation model. In future works, we will enhance the bifurcation model and propose an in-depth evaluation via Deep Learning methods.

I. INTRODUCTION

Intra-Cranial Aneurysms (ICA) are arterial hernias forming onto the brain vasculature. The formation of the aneurysm is painless, the patient has no way of suspecting the presence of an ICA on its vascular tree. The aneurysm itself does not cause any symptoms whatsoever, nevertheless, it is crucial to detect and monitor the said aneurysms, indeed the risk comes when an ICA ruptures. Effectively, the consequences of the rupture are devastating, it causes bleeding around the brain (subarachnoid hemorrhagic stroke). A ruptured aneurysm is life threatening, and if not causing immediate death, it can provoke some serious brain damage. Mortality rate due to a ruptured aneurysm has been estimated as high as 65%. Moreover, in case of a patient survival, a loss of various brain functions can result from the induced subarachnoid hemorrhage [START_REF] Rava | Assessment of an artificial intelligence algorithm for detection of intracranial hemorrhage[END_REF]. Thus, it is crucial to efficiently detect and monitor the ICA. The preferred imaging modalities used to inspect the vascular tree in search for ICA are the Digital Subtraction Angiography (DSA) or Time-Of-Flight (TOF) Magnetic Resonance Angiography (MRA). DSA provides a very high-quality representation of the vascular tree, and hence of the eventual aneurysms it may hold [START_REF] Stafa | Role of neuroradiology in evaluating cerebral aneurysms[END_REF]. However, the DSA implies the injection of contrast liquid within the blood system and is an invasive imaging. DSA acquisitions benefit from a much better resolution, at the expense of the contrast liquid injection, and moreover, such imagery only displays a single hemisphere of the brain. The vascular tree can very easily be extracted from the DSA volume, as the background noise is significantly weaker than the contrast liquid being imaged. Contrary to the DSA, the MRA-TOF acquisitions are much noisier; apart from the vascular tree, various matters appear on the image: the grey/white matter, the Cerebro-Spinal Fluid (CSF), the ventricle, the corpus callosum, all such portions of the brain exhibit varying radio-opacities, and hence a different grey level onto the resulting acquired volume. Both a DSA and a TOF segmentation are shown on Fig 1; an aneurysm can be observed on each of these acquisitions.

Although the ICA can easily be spotted on the 3D binary segmentations (see inside the red circles), it is a much more tedious and complex task on the original acquisitions. Fig. 1 (bottom row) represents a single slice of the DSA and TOF acquisitions, again the aneurysms are circled in red. Browsing through an entire 3D MRI volume in search for an aneurysm (which sometimes can be rather small) is time consuming and tedious. Of course, one might consider making a diagnosis on the segmented volume, which would be much faster, but unfortunately, although some recent progress on image segmentation (especially thanks to deep learning approaches) leads to better segmentation performances, there is still ample room for improvements. One cannot always fully trust the resulting segmented images, especially when the ICA can occur in hyposignal (e.g. -partially-treated aneurysms for instance). In this work, we are only interested in Unruptured ICAs (UIAs). ICA can present themselves in two different shapes, the fusiform aneurysms are identified by a local swelling of the artery, whereas the saccular aneurysm (also known as berry aneurysms) forms a spherical protrusion. This latter form is predominant in the brain vascular tree, they represent up to 90% of all brain aneurysms. Moreover, such ICA most commonly occur on a specific structure of the vasculature named the "Circle of Willis" [START_REF] Bogunovic | Anatomical labeling of the circle of willis using maximum a posteriori probability estimation[END_REF], [START_REF] Robben | Simultaneous segmentation and anatomical labeling of the cerebral vasculature[END_REF]. Some studies claim that about 85% of the ICAs occur along this particular pattern of the vascular tree [START_REF] Keedy | An overview of intracranial aneurysms[END_REF]. Moreover, the saccular aneurysms most often arise onto a bifurcation of the arterial tree. Indeed, the fluid motion within the arteries presses the blood against the arterial wall, which, if weakened (by a genetic predisposition, or various environmental factors), will entail the aneurysm formation.

The efficient detection and segmentation of unruptured intracranial aneurysms is a matter of great concern, many studies have been devoted to this task throughout the last few decades. The vast majority of the researches being conducted on ICA detection focus on DSA images [START_REF] Jin | Fully automated intracranial aneurysm detection and segmentation from digital subtraction angiography series using an end-to-end spatiotemporal deep neural network[END_REF], [START_REF] Jerman | Computer-aided detection and quantification of intracranial aneurysms[END_REF], fewer works have been devoted to MRA-TOF acquisitions. Furthermore, although ICA detection is a widely studied field [START_REF] Dai | Deep learning for automated cerebral aneurysm detection on computed tomography images[END_REF], the aneurysm segmentation is more marginally investigated [START_REF] Ueda | Deep learning for MR angiography: Automated detection of cerebral aneurysms[END_REF], [START_REF] Timmins | Comparing methods of detecting and segmenting unruptured intracranial aneurysms on TOF-MRAS: The ADAM challenge[END_REF]. Authors in [START_REF] Hu | Automatic detection of intracranial aneurysms in 3D-DSA based on a bayesian optimized filter[END_REF] used a Bayesian optimized filter for the automatic detection of ICA on DSA acquisitions. Quite often, the authors turn to 2D projected images [START_REF] Dai | Deep learning for automated cerebral aneurysm detection on computed tomography images[END_REF], such as Maximum Intensity Projection (MIP) for various tasks of pattern recognition, as such 2D projections offers a better contrast. In [START_REF] Duan | Automatic detection on intracranial aneurysm from digital subtraction angiography with cascade convolutional neural networks[END_REF] a two-stage CNN architecture was used to detect intracranial aneurysms on 2D-DSA images. Deep Learning methods have been employed for aneurysm detection as well. Works in [START_REF] Sichtermann | Deep learning-based detection of intracranial aneurysms in 3D TOF-MRA[END_REF] for instance intended to detect ICAs within MRA-TOF using a CNN. The authors exploited 85 datasets of patients, which represented a total of 115 intracranial aneurysms. They relied on manual annotations of this whole dataset to train their system. It is stated in the paper that 60 examinations were performed on a 3T Siemens scanner, while 12 were performed on a 1.5T Siemens scanner. Similarly, in [START_REF] Shahzad | Fully automated detection and segmentation of intracranial aneurysms in subarachnoid hemorrhage on CTA using deep learning[END_REF], works have been conducted to detect and segment intracranial aneurysms on CT-Angiography, but the aneurysms were to be found in the particular context of aneurysmal subarachnoid hemorrhage, which means that the rupture already took place. However, again, manual segmentations were conducted by neurosurgeons and radiologists on a large panel of patients (68 for training and 185 for the evaluation step). As far as Deep Learning is concerned, manual labeling is most often unavoidable. This indeed, is the problem we expect to tackle using our approach. Effectively the manual annotation of 3D volumes is a rather tedious task, and moreover, if this dataset was constituted of one single acquisition source (e.g. one MRI scanner from a given University hospital), then, the trained neural network might end up being inefficient on different acquisitions (different magnetic field strength, implying a different resolution, background noise or contrast). A challenge has very recently been organized in order to compare some state-of-the-art methods from the literature [START_REF] Timmins | Comparing methods of detecting and segmenting unruptured intracranial aneurysms on TOF-MRAS: The ADAM challenge[END_REF]. A training set was composed of 113 cases, whereas a test set was made of 141 cases, holding respectively 129 and 153 unruptured ICA. Both detection and segmentation tasks were targeted. The authors conclude that "Methods for UIA detection and segmentation are encouraging but require further development before being able to be accurately used to detect, segment and quantify UIAs automatically". We believe that, by providing huge image datasets, it might be possible to increase the detection and segmentation performances. If the CNN could learn on thousands or even tens of thousands of 3D volumes instead of only a few hundreds, significant improvements might be achieved.

The saccular bifurcation aneurysms being predominant onto the cerebral arterial tree, and more particularly onto the tree's bifurcations, this work focuses on this particular disposition. In this study, we aim to propose some means to automatically detect and segment the unruptured saccular intracranial aneurysms on MRA-TOF acquisitions. We propose to build up a full model of both the 3D bifurcation and the aneurysm, in order to train a deep learning network to recognize the ICA. Our approach here is somewhat similar to a previous project we have recently been investigating [START_REF] Chater | Learning from mouse CT-scan brain images to detect MRA-TOF human vasculatures[END_REF]. Nevertheless, the approach presented here is much more advanced, with regard to several aspects: i) in [START_REF] Chater | Learning from mouse CT-scan brain images to detect MRA-TOF human vasculatures[END_REF], a 2D artery dataset was built, whereas here, we aim to tackle not only the artery, but rather the whole bifurcation in 3D; ii) the bifurcation bears an unruptured aneurysm; and iii), the background noise is now characterized and modeled with a much better accuracy. However, it is important to notice that this current work is only devoted to the design of the model itself. We hereby aim to build up the 3D bifurcation along with it's associated aneurysm and also intend to fully evaluate the verisimilitude of the modeled bifurcation (and ICA). Future works will consider adopting Deep Learning for the detection and segmentation tasks. To the best of our knowledge, we propose the very first approach considering the implementation of a full numerical bifurcation model for ICA deep-learning segmentation.

This paper is structured as follows. In section II, we will present both the geometrical model (i.e. the topological layout of the arteries, the dark and the bright background areas) and the noise model being employed to generate a background noise being as realistic as possible. Section III is devoted to the presentation of our experimental results. We will first describe how some statistical properties are collected onto human MRI images to be later applied in our model. We provide some examples of the 3D bifurcation model, but most importantly, we show how the 3D U-Net can cope with the segmentation task. We conclude this work in section IV II. METHOD In order to properly feed a neural network, so that it can recognize and locate intracranial aneurysms, we aim to accurately model some three-dimension bifurcations as well as the ICA to be precisely embedded onto the bifurcation. The model will thus need to be composed of three distinct steps, first, the geometry of the three artery branches needs to be built, then, an artificial ICA is generated and fused with the bifurcation and finally, the surrounding noise will also have to be accurately modeled and combined with the synthetic bifurcation.

A. Geometrical model 1) Artery bifurcation:

The composition of the 3D bifurcation is quite straightforward. We build a 60 × 60 × 60 voxels cube, in which we randomly determine 3 points located onto the faces of the cube. We then build three linear segments passing through these 3 points and grouping at the centroid of the cube. This basically forms the skeleton of the bifurcation. The next step consists of bringing some thickness to the three branches. We thus simply convolve the so-obtained 3D skeleton with a binary sphere (of a variable radius). This produces a 3D bifurcation made of three thick linear branches. To make the model more realistic, we need to bring some geometric transformations onto the synthetic arteries. An elastic deformation 1 is thus applied [START_REF] Ronneberger | U-Net: Convolutional networks for biomedical image segmentation[END_REF], [START_REF] Özgün C ¸ic ¸ek | 3D U-Net: Learning dense volumetric segmentation from sparse annotation[END_REF] onto the model, so as to mimic the tortuosity of real-life arteries.

2) Aneurysm model: The synthetic aneurysm is also simply modeled by composing a binary sphere that will be merged onto the binary bifurcation. The ICA will also endure geometric deformations, as in human brains, the ICA commonly 1 The ElasticDeform library was used : https://elasticdeform.readthedocs.io/ exhibit higher level distortions [START_REF] Juchler | Shape irregularity of the intracranial aneurysm lumen exhibits diagnostic value[END_REF], [START_REF] Juchler | Radiomics approach to quantify shape irregularity from crowd-based qualitative assessment of intracranial aneurysms[END_REF]. As for the spatial positioning of the ICA, we seek to place the ICA approximately onto the angle bisector. Thanks to a 3D graph extraction from the vasculature skeleton [START_REF] Nouri | Characterization of 3D bifurcations in micro-scan and MRA-TOF images of cerebral vasculature for prediction of intra-cranial aneurysms[END_REF], we can collect the 3D directional vectors initiated at the bifurcation center and following each of the three arteries (bifurcations' branches).

Let us denote V 1 , V 2 and V 3 the three vectors initiated at a bifurcation center (3D graph node) and tangent to the 3 branches centerlines. If we intend to embed an aneurysm in between branches 1 and 2, we must consider that the blood shall flow from branch 3 (mother branch). Indeed saccular ICA typically occur on the arterial wall opposite to the mother branch, as the blood pressure will be more important on this portion of the bifurcation. V 1 + V 2 being the bisector line for this angle, we want the aneurysm to have a better alignment with branch 3. We thus plan to position the ICA as much as possible on the axis of the mother branch, and hence we compute the orientation that is along the orientation

V 0 = V 1 + V 2 -2 × V 3 .
Once this orientation determined, the distance of the aneurysm along this line must be estimated. We determine the distance D separating the bifurcation center to the aneurysm center (along V 0 ) as shown on Eq. 1.

D = T 2 + r × 2 - θ 12 π × (1 -1/36) , (1)
where θ 12 is the angle formed by the branches #1 and #2, T is the average thickness of the 3 branches and r the aneurysm's radius. We consider that the angles cannot be smaller than 5 • (π/36 rad). This way, the smaller is the angle between the two branches, the further away will the ICA be embedded. On the opposite, for the largest angle configuration (180 • ), the ICA is approximately placed at (T /2 + r) voxels from the bifurcation center, i.e. the aneurysm is tangent to the bifurcation wall.

3) Modeling various radio-opacites: As previously explained, within a MRA-TOF acquisition, several matters appear on the brain image (the grey/white matter, the Cerebro-Spinal Fluid, the ventricle, the corpus callosum, etc.). We thus have to model these different areas, of varying radioopacities. Commonly the arteries are surrounded by the brain fluids and are not directly located within the grey matter. It is thus important to encircle the bifurcations by the darkest background noise. In order to tackle this issue, we generate a distorted version of the segmented artery (binary shape) that will be used as a mask to arrange the darker area within the image. Applying elastic distortions to the artery mask will thus generate a new mask dedicated to the dark background noise.

B. Noise model

Noise in Magnetic Resonance Images (MRI) can be approximated by a Gaussian distributed noise [START_REF] Chaudhari | Noise estimation in single coil MR images[END_REF]. Not only must we properly model the basic statistical properties of the target MRA-TOF (average and variance of the noise) but it is also critical to ensure that the spatial frequency of the modeled noise is a perfect match with the target MRI.

When going through Gaussian blur, the input image I(x, y) is filtered as shown by eq. 2.

O(x, y)

= ∞ i=-∞ ∞ j=-∞ 1 2πσ 2 G e -i 2 +j 2 2σ 2 G I(x + i, y + j) (2)
The Bienaymé's identity states that

V ar n i=1 X i = n i=1 V ar(X i ) + n i,j=1,i =j Cov(X i , X j ) (3)
Thus, the variance of a linear combination is:

V ar n i=1 c i X i = n i=1 c 2 i V ar(X i ) + 2 × n i,j=1,i =j c i c j Cov(X i , X j ) (4)
However, if X i , ..., X n are pairwise independent integrable random variables (Cov(X i , X j ) = 0, ∀(i = j)), which is our assumption in the following, then:

V ar i c i X i = i c 2 i V ar(X i ) (5)
where c i are constants. We consider that the variance of the input image is V ar [I(x + i, y + i)] = σ 2 0 , our goal here is to estimate the variance of the output (filtered) image V ar [O(x, y)] = σ 2 f . Thus,

σ 2 f = σ 2 0 ∞ j=-∞ ∞ i=-∞ 1 2πσ 2 G e -i 2 +j 2 2σ 2 G 2 (6)
For large σ G , the squared Gaussian is smooth and the sum can be approximated as:

σ 2 f ≈ σ 2 0 ∞ -∞ ∞ -∞ 1 2πσ 2 G e -i 2 +j 2 2σ 2 G 2 di.dj = σ 2 0 4πσ 2 G ( 7
)
and thus,

σ f ≈ σ 0 2σ G √ π (8)
In summary, when an image composed of Gaussian noise of standard deviation σ 0 is being filtered by a Gaussian filter of standard deviation σ G , the so-obtained filtered image has a standard deviation of σ f according to the equation 8.

However, for our particular purpose, we intend to determine which Gaussian filter (of standard deviation σ G ) shall be used on the input image so as to obtain a filtered image with a given target statistics (σ f ), and hence σ G ≈ σ 0 /(2σ f √ π). The process starts thus with the generation of a high frequency Gaussian Noise of average set to our target 3D crop. This noise will then be filtered out using a Gaussian filter of standard deviation σ G . The resulting image (of standard deviation σ f ) will thus present strong similarities with the target TOF.

III. EXPERIMENTAL RESULTS

This section is divided into three different parts. We first show how some statistical properties are collected onto target MRA-TOF acquisitions. In the second part, we provide some details on the dataset we have constituted. Finally, the third part is devoted to a full evaluation of the model with regards to different aspects (texture analysis and blur measure).

A. Statistical Modeling of the TOF volumes

In order to efficiently model the 3D bifurcations, and more specifically, the background noise, it is critical to gather some coherent statistics from the target MRI images. For this purpose, we have used Gaussian Mixture Models (GMM) to collect a range of target averages and standard deviations on 13 MRA-TOF volumes. Based on the assumption that a TOF volume contains 4 distinct components, which, ordered by increasing grey level would be: i) the black noisy background, ii) the various fluids, iii) the white/grey matter and iv) the arteries and possibly the fat tissues (if skull stripping methods were not applied). An example of a GMM fit with 4 components is shown on Fig. 2. The fourth component has been partially cut out of the plot, and is barely visible on this scale, as it accounts for the arteries, which represent very few pixels in this TOF slice (inset within the plot). The fat tissues, the meninges along with all unwanted portions or the MRI, such as the eyes, or nasal cavities can be discarded via the use of the Brain Extraction Tool (BET) [START_REF] Smith | Fast robust automated brain extraction[END_REF], indeed, keeping these parts of the image might bias the results. We have thus applied BET prior to collect the statistics of the various background noises. The so-obtained skull-stripped images go through a GMM decomposition, see Eq. 9, where several Gaussian components N (µ i , Σ i ) are each weighted by an independent weight φ i . This allows to gather the target averages and standard deviations of the various image portions we want to model. The collected averages and standard deviations can be observed on Fig. 3. In the following, the background noise representing the grey matter will be modeled according to the properties of the third Gaussian distribution. In this study, in order to limit the number of generated images, the voxel values for the darker portions of the image (ventricle, CSF) have simply be set to two-thirds of the brighter noise. Future works will consider having a better differentiation between those two areas by considering both the second and third GMM. The bifurcation model can now be carried out using these statistical properties to modulate the synthetic noise that will be added up onto the modeled arteries.

p(x) = N i=1 φ i N (x|µ i , Σ i ) (9)

B. Dataset constitution

Overall, the model was used to generate 5 418 bifurcations. For each bifurcation, when its configuration made it possible, we have independently embedded three ICA (one between each pair of branches). In total, 14 073 ICA were thus generated, with arteries diameters in the range [START_REF] Robben | Simultaneous segmentation and anatomical labeling of the cerebral vasculature[END_REF][START_REF] Dai | Deep learning for automated cerebral aneurysm detection on computed tomography images[END_REF], the amplitude (in grey levels) of the arteries were in [220, 290], 3 different parameters were used for the elastic deformations, the target average of the background noise (white matter) was in the interval [50, 110] whereas its standard deviation was in [START_REF] Jerman | Computer-aided detection and quantification of intracranial aneurysms[END_REF][START_REF] Hu | Automatic detection of intracranial aneurysms in 3D-DSA based on a bayesian optimized filter[END_REF]. As previously explained, the darker noise was simply set to 2/3 of the white matter average. Four aneurysms' diameters have been modeled: 2, 4, 6 and 8 voxels (with two different distortion strengths). Table I encompasses the various geometrical and statistical settings being used by the model. During our experiments, we have witnessed a rather realistic rendering of the various matters composing the brain (i.e. CSF, grey/white matter, arteries, etc.) as shown on Fig. 4. Four different ICA are depicted on Figure 5, where we show some modeled 3D aneurysm-bearing bifurcations after a manual segmentation. This Figure shows how realistic is the positioning of the ICA onto the bifurcation. We did encounter a few cases where the aneurysm collar is slightly shifted away from the bifurcation center (see Fig. 5b and 5c for instance), but we believe that such a small shift might not influence much a CNN in its task of ICA detection and segmentation.

C. Evaluation of the bifurcation model

The very first purpose of our bifurcation model being to feed a CNN in order to automatically detect and segments Intra-Cranial Aneurysms, we obviously need to ensure that the model efficiently simulates some true ICAs. The bifurcation model must thus present very strong similarities with the true bifurcations collected from MRA-TOF acquisitions.

In order to assess the verisimilitude of our model, or in other words, its resemblance with the ground-truth, we have constituted a substantial dataset. Out of the full bifurcation dataset, 100 modeled bifurcations were (randomly) extracted from the 14.073 samples and Template Matching [START_REF] Lewis | Fast normalized cross-correlation[END_REF] was used to find the best matches with the MRA-TOF images. A matching 3D normalized correlation is highly unlikely, as the geometry of the images is too complex to efficiently match, and hence, we ran numerous 2D correlations. From the 100 bifurcations models, 10 slices were extracted from each 3D stack, they were correlated (using Template Matching) with 430 slices extracted from each tested TOF volumes (along the x, y and z orientations). Three different TOF were used, making a total of 1.000 modeled slices correlated with 1.290 TOF slices. We have set a matching threshold based on the Normalized Correlation Coefficient (NCC), all patches with a peak correlation such as N CC > 0.75, have been retained as good matches. Overall, the Template Matching allowed to collect more than 50.000 correlated patches. The statistics of the TOFs are closely modeled, as previously shown in section II-B, but for a thorough analysis, we also ran a texture analysis and a blur factor evaluation. The Haralick features [START_REF] Haralick | Statistical and structural approaches to texture[END_REF] were computed to ensure a good match of both textures (model and ground truth), as for the blur factor, both the Variance of the Laplacian and the Tenengrad coefficient [START_REF] Ali | Analysis of blur measure operators for single image blur segmentation[END_REF] were computed. The Figure 6 shows a comparison between the model and three different TOF acquisitions with regard to these three measurements. The distribution of the data is displayed next to the box plot to show the (mis)matching dispersion. Although both the Haralick features and the Variance of the Laplacian seem to accurately match, the Tenengrad coefficient seems to drift a bit away in the Model. Hopefully, this drift might not be strong enough to have an impact on the upcoming use of this dataset for Deep Learning ICA detection. In previous works [START_REF] Chater | Learning from mouse CT-scan brain images to detect MRA-TOF human vasculatures[END_REF], we managed to efficiently train a CNN (Half U-Net) using only modeled arteries, we believe that despite the more sophisticated model presented here (3D artery and ICA), such a training scenario should still be feasible. Moreover, the model might also be used as backup to some ground truth segmentations to train a neural network (acting as augmented data).

In order to evaluate the applicability of our model within a Deep Neural Network, we have set up a 3D U-Net to perform the segmentation of small 3D cropped bifurcations. The network was first trained on 120 modeled bifurcations and provided an average DICE score of 0.8 on a test set composed of 41 images, which is fairly close to the performances achieved in [START_REF] Chater | Learning from mouse CT-scan brain images to detect MRA-TOF human vasculatures[END_REF]. Next, to evaluate the model's suitability as a generator of augmented data, we have first launched the U-Net on 120 ground truth bifurcations, and then, on a set composed of both 40 ground truth and 80 modeled bifurcations. For both scenarios, the average DICE score was equivalent (≈ 0.94).

IV. CONCLUSION

In this work, we have presented a full 3D artery bifurcation model. More precisely, an aneurysm-bearing bifurcation model. Effectively, both the bifurcation and the aneurysm were built in such a way to best model the various features of MRA-TOF acquisitions. Evidently, the geometrical characteristics of the actual MRA bifurcations and ICA were respected. Moreover, the statistical properties of the background noise were collected from a set of target TOF images and accurately modeled. A thorough comparison between some ground-truth MRA volumes and the bifurcation+ICA model was conducted and showed that the resemblance might be sufficient for using a CNN in a ICA detection and segmentation task. Indeed, this work is a preliminary study on the feasibility of designing a fully synthetic artery bifurcation model. Using such a model to train a Deep Learning architecture can be very advantageous. Using such an approach, we avoid resorting to manual annotations on 3D volumes, which is a laborious task, and moreover, such manual annotations would have to be conducted on a very wide variety of MRI scanners for the Neural Network to apprehend the wide variety of image qualities. Using a model such as the one presented in this paper might help to train a CNN for a specific target MRI scanner. One single TOF acquisition is sufficient to gather some statistical properties and generate a vast image dataset that will be used to feed the network. A preliminary experiment was set up in order to evaluate the applicability of our model within a deep learning segmentation / recognition framework, this latter produced very encouraging results.

Fig. 1 .

 1 Fig. 1. 3D segmented stacks, along with a example of 2D slice for DSA (left) and TOF (right) acquisitions.

Fig. 2 .

 2 Fig. 2. One example of a fit with 4 components of a GMM.

Fig. 3 .

 3 Fig. 3. Collected averages and standard deviations out of 13 MRA-TOF acquisitions (GMM with four components).

Fig. 4 .

 4 Fig. 4. A modeled (left column) and a true (right) ICA.

Fig. 5 .

 5 Fig. 5. Some example of modeled ICAs in 3D (after segmentation from the grey-level produced 3D model).

Fig. 6 .

 6 Fig. 6. Evaluation of the model : (a) Haralick features, (b) Variance of the Laplacian and (c), Tenengrad coefficient.

ACKNOWLEDGMENT

This work was partially supported by the French ANR-"WECAN" project.