Clément Desjardins

Frédéric Caux

Bertrand Degos

Djallel Benzohra

Astrid De Liège

Gérôme Bohelay

Michel Longy

Chloé Béreaux

Dr Béatrice Garcin
email: beatrice.garcin@aphp.fr

Impaired social cognition and fine dexterity in patients with Cowden syndrome associated with germline PTEN variants

Keywords: Cowden Syndrome, Social Cognition, PTEN, Germline mutation, Neuropsychology, Genetics, Dexterity

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

INTRODUCTION:

Cowden syndrome (CS, MIM 158350) is a rare autosomal dominant inherited tumor predisposition syndrome, [START_REF] Uppal | Cowden disease: a review: Cowden disease[END_REF] originally named and described by Lloyd and Dennis in 1963 after a patient with multiple hamartomas, fibrocystic breast disease and neurological abnormalities [START_REF] Lloyd | Cowden's Disease: A Possible New Symptom Complex with Multiple System Involvement[END_REF] even if some clinical descriptions without giving rise to the individualization of the entity have been previously

published. [START_REF] Costello | A case for diagnosis (keratosis follicularis?)[END_REF][START_REF] Witten | A CASE FOR DIAGNOSIS-VERRUCAE PLANAE-ADENOMA SEBACEUM-EPIDERMODYSPLASIA VERRUCIFORMIS[END_REF][START_REF] Brownstein | Cowden's disease: a cutaneous marker of breast cancer[END_REF] CS is related to germline variants of PTEN (Phosphatase and TENsin homolog), a tumor suppressor gene with a documented role in the development of both hereditary and sporadic malignancies.

Several syndromes are associated with germline variants of PTEN, including CS, [START_REF] Zbuk | Cancer phenomics: RET and PTEN as illustrative models[END_REF] and are grouped under the umbrella term « PTEN hamartoma tumor syndrome » (PHTS).

CS is characterized by an increased risk of developing numerous cancers particularly female breast cancer, thyroid cancer, melanoma, endometrial cancer and renal cancer. [START_REF] Bubien | High cumulative risks of cancer in patients with PTEN hamartoma tumour syndrome[END_REF] It is associated with macrocephaly and autism spectrum disorders (ASD). [START_REF] Hobert | Biochemical screening and PTEN mutation analysis in individuals with autism spectrum disorders and macrocephaly[END_REF] Encephalic abnormalities, notably Lhermitte-Duclos disease (hamartoma of the cerebellum), described as pathognomonic of CS in adult, are frequently encountered. Various neuroimaging abnormalities are reported in CS such as meningiomas, multiple venous anomalies, but also white matter abnormalities, prominent perivascular spaces and cortical malformations. [START_REF] Dhamija | Neuroimaging abnormalities in patients with Cowden syndrome: Retrospective single-center study[END_REF] There are several genetic variants, mainly nonsense, missense, splice site and frameshift, affecting all exons of the gene. [START_REF] Yehia | The Clinical Spectrum of PTEN Mutations[END_REF] In our practice of reference center for rare genetic skin diseases, we observed during CS patients' visits, that their behavior was often slightly maladapted to social norms and conventions (see Supplementary Material S1 for clinical vignettes). For example, during his first consultation, a patient with CS asked if the medical doctor could subsidize his wedding. However, most of these patients are professionally well inserted. Thus, current data in the literature suggesting a link between ASD in which social cognition is majorly impaired and germline PTEN variant, [START_REF] Fernández | Neural Circuits for Social Cognition: Implications for Autism[END_REF] as well as our clinical observation both suggest a link between impaired social cognition and CS. To date, no study has specifically assessed social cognition in CS.

These behaviors can be interpreted as social impairs and thus be linked to impaired social cognition.

Social cognition refers to the various cognitive processes that are involved in our interpersonal relationships and that make these relationships adequate and adapted to social norms. [START_REF] Frith | Social cognition[END_REF] There are different approaches of social cognition, and others define social cognition as socially contextualized cognition. [START_REF] Smith | Contextualizing person perception: distributed social cognition[END_REF] Social cognition performances correlate with other cognitive processes notably executive functions [START_REF] Ziv | Social cognition in schizophrenia: cognitive and affective factors[END_REF] and language in its semantic component. [START_REF] Apperly | Studies of adults can inform accounts of theory of mind development[END_REF] As most cognitive domains, it also correlates with mood, social cognition being affected in depressive syndromes. [16] To date, only one study has focused on the cognitive functioning of adult patients with CS. [START_REF] Busch | Cognitive characteristics of PTEN hamartoma tumor syndromes[END_REF] This study did not evaluate social cognition, but it highlighted an extremely variable intellectual functioning, and an impairment of working memory, executive functions, and fine dexterity. which was suggestive of frontal lobe damage or dysfunction. However, in this study, there were no systematic brain imaging to search for brain lesions which are commonly reported in CS, and no specific evaluation of social cognition. Executive function disorders have also been observed in children with PTEN variant.

Fine dexterity can be defined as the ability to coordinate accurately and rapidly hand and finger movements in an adaptive manner, such as required for fine control in grasping and manipulation of small objects. [START_REF] Makofske | Manual Dexterity[END_REF] It is acquired through repetition and experience in motor learning. [START_REF] Poirier | Dexterity as a valid measure of hand function[END_REF] Fine dexterity overlaps with other cognitive functions notably motor control, limb-kinetic praxis and ideomotor praxis. [START_REF] Vanbellingen | Impaired finger dexterity in Parkinson's disease is associated with praxis function[END_REF][START_REF] Leiguarda | Limb apraxias: higher-order disorders of sensorimotor integration[END_REF] Additionally, several studies have shown an association between fine dexterity and various cognitive domains, notably executive function, in healthy individuals as well as in Alzheimer's disease and parkinsonian patients. [START_REF] De Paula | Impairment of fine motor dexterity in mild cognitive impairment and Alzheimer's disease dementia: association with activities of daily living[END_REF][START_REF] Menon | Motor Speed Matters! Cognitive Profile of Parkinson's Disease Patients With and Without Deficits in Motor Speed[END_REF] More specifically, fine dexterity was mainly associated with flexibility, fluency and problem solving. [START_REF] Vanbellingen | Impaired finger dexterity in Parkinson's disease is associated with praxis function[END_REF][START_REF] Menon | Motor Speed Matters! Cognitive Profile of Parkinson's Disease Patients With and Without Deficits in Motor Speed[END_REF] In clinical practice, dexterity can be evaluated by various tests including the Nine Hole Peg Test (9-HPT) [START_REF] Mathiowetz | Adult norms for the nine hole peg test of finger dexterity[END_REF] which has been previously used in Parkinson's Disease [START_REF] Earhart | The 9-hole PEG test of upper extremity function: average values, test-retest reliability, and factors contributing to performance in people with Parkinson disease[END_REF] or Multiple Sclerosis. [START_REF] Feys | Multiple Sclerosis Outcome Assessments Consortium. The Nine-Hole Peg Test as a manual dexterity performance measure for multiple sclerosis[END_REF] Most manual dexterity tests are timed and require a certain level of accuracy. [START_REF] Berger | Task specificity of finger dexterity tests[END_REF] The aim of the study was to assess social cognition and fine dexterity in CS by means of a neuropsychological assessment. In this aim, we analyzed 15 patients with PTEN variants in order to determine whether the inappropriate behaviors we observed in CS patients relate to impaired social cognition. All patients underwent an extensive neuropsychological assessment, and a brain MRI to verify whether the putative social cognition impairment would be associated with brain lesions and/or other cognitive impairment and/or fine dexterity impairment. Because of previous reports of executive dysfunctions in CS, we proposed a slightly more detailed assessment of executive functions than other cognitive functions. The secondary aim was to assess whether social cognition impairment correlates with impaired mood, dysexecutive syndrome, or language impairment and to search for a correlation between social cognition impairment and cerebral abnormalities on brain MRI.

MATERIAL AND METHODS:

Patients

All CS patients seen by a dermatologist (FC) in the department of Dermatology at Avicenne Hospital (Bobigny, France), whether they had expressed a cognitive complaint or not, have been granted neurological examination, neuropsychological testing, and brain MRI, as part of the follow-up for CS.

Patients seen between July 2018 and February 2020 and fulfilling the following inclusion criteria were included: (i) clinical manifestations of Cowden syndrome; (ii) definite germline PTEN variants; (iii) age greater than 18 years. The non-inclusion criterion was a refusal to perform the neuropsychological tests or the brain MRI. We also excluded patients who had a severe comorbidity requiring urgent care. All the data were obtained from the records of patients. Oral consent was obtained from all participants and written consent was obtained for genetic analysis. The current study obtained the authorization of the Local Ethics Committee of Avicenne Hospital (CLEA-2019-92).

Demographic and clinical information such as gender, age, and history of benign or malignant tumors of skin, breast, thyroid, gastrointestinal tract, and central nervous system were collected.

Neurological examination

All participants had a clinical evaluation by a neurologist (BG or ADL). A systematic interview was performed for each patient to collect personal and family history (notably neurological and psychiatric history), neurological development (dyslexia, psychomotor retardation, and educational difficulties), cognitive complaint and lifestyle (notably education duration and occupation). Neurological examination was carried out in search of focal signs or impairment of cognitive functions (memory, instrumental and executive). Among instrumental functions, praxis was assessed during physical examination of limb-kinetic, ideomotor and ideational praxis. Cranial perimeter was systematically measured; macrocephaly was defined as a cranial perimeter greater than 58 cm for female and 60 cm for male, according to Pilarski et al. [START_REF] Pilarski | Cowden syndrome and the PTEN hamartoma tumor syndrome: systematic review and revised diagnostic criteria[END_REF]

Neuropsychological testing

All participants underwent a systematic and standardized neuropsychological assessment, conducted by a qualified neuropsychologist (CB).

It included an evaluation of the two core aspects of social cognition: theory of mind and facial emotions recognition. The cognitive theory of mind was assessed by the TOM-15 [START_REF] Desgranges | TOM-15 : Une épreuve de fausses croyances pour évaluer la théorie de l'esprit cognitive[END_REF] and the modified and reduced version of the Faux-Pas test, [START_REF] Baron-Cohen | Recognition of faux pas by normally developing children and children with Asperger syndrome or high-functioning autism[END_REF] which are components of the mini Social and Emotional Assessment (MINI-SEA). [START_REF] Bertoux | Neural correlates of the mini-SEA (Social cognition and Emotional Assessment) in behavioral variant frontotemporal dementia[END_REF] They assess mentalizing abilities through two different goldstandard paradigms. TOM-15 relies on false-beliefs understanding, and the modified Faux-Pas test relies on both mentalizing and social contexts understanding. Facial emotions recognition was assessed with Ekman faces test, which is a reduced version of the Pictures of Facial Affect (POFA) test [START_REF] Ekman | Pictures of Facial Affect[END_REF] and which is also a component of the MINI-SEA. Dexterity was assessed by the 9-HPT. [START_REF] Mathiowetz | Adult norms for the nine hole peg test of finger dexterity[END_REF] Neuropsychological testing included Raven's progressive matrices (PM-38) to assess inductive reasoning capacity, [START_REF] Raven | �ber die Potenz von Gastrulaektoderm nach 24st�ndigem Verweilen im �usseren Blatt der dorsalen Urmundlippe[END_REF] which is a component of global intellectual functioning. It included an assessment of executive functions with Trail Making Test (TMT-A and B) and verbal fluencies for mental flexibility, [START_REF] Godefroy | Groupe de Réflexion sur l'Evaluation des Fonctions Exécutives Study Group. Dysexecutive syndrome: diagnostic criteria and validation study[END_REF] Stroop for mental inhibition, [START_REF] Godefroy | Groupe de Réflexion sur l'Evaluation des Fonctions Exécutives Study Group. Dysexecutive syndrome: diagnostic criteria and validation study[END_REF] and memory of WAIS-IV numbers for working memory. [START_REF] Suwartono | Development and Reliability of the Indonesian Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV)[END_REF] Language was assessed with a 40 drawings naming test (DENO-40). A psycho-affective assessment was performed with the Apathy Scale [START_REF] Starkstein | Reliability, validity, and clinical correlates of apathy in Parkinson's disease[END_REF] and the HADS Depression and Anxiety Scales. [START_REF] Zigmond | The Hospital Anxiety and Depression Scale[END_REF] All tests were interpreted using age-corrected and, when appropriate, educationally corrected standards according to the recommendations of published textbooks (Supplemental material S1). Since all tests were interpreted in the context of age, and/or education, and/or gender that varied across patients we described the results as normal or impaired according to normative data. Results were considered as impaired when the Z-score value was below -1.65.

Brain MRI

All study participants underwent a brain MRI to search for brain abnormalities and tumors associated with CS.

The imaging protocol was developed based on the most frequently described brain abnormalities in CS patients [START_REF] Dhamija | Neuroimaging abnormalities in patients with Cowden syndrome: Retrospective single-center study[END_REF]. It included the following imaging sequences: diffusion and Apparent Diffusion

Genetics analyses

The variant search was carried out on blood DNA by next-generation sequencing according to an Illumina technique on a Myseq device after exon capture of a genes panel including PTEN (Agilent SureSelect Target enrichment kit). The detected variants were confirmed by Sanger sequencing on two independent samples. Interpretation of sequence variants was performed using the criteria of the American College of Medical Genetics and the Association for Molecular Pathology (ACMG/AMP). [START_REF] Richards | Standards and guidelines for the interpretation of sequence variants: a joint consensus recommendation of the American College of Medical Genetics and Genomics and the Association for Molecular Pathology[END_REF]

Statistics

We performed statistical analyses to compare patients' characteristics and neuropsychological results according to the different types of PTEN variants. We also carried statistical analyses to search for correlation between cognitive tests and demographic characteristics. These analyses can be found as Supplementary Material S2.

We used non-parametric tests given the small size of the population sample. We performed Kruskal-Wallis (Chi2) tests followed by Mann Whitney (U) tests to compare patients' characteristics and neuropsychological results according to the different types of PTEN variants (nonsense, missense, splice site and frameshift) found in our population.

We performed Mann Whitney (U) tests to compare quantitative data between two groups and Spearman (Rho) correlations analyses to search for correlations between quantitative data. The degree of significance p was set at 0.05, after correction for multiple comparisons by Bonferroni method. All statistics were performed using SPSS IBM v24 software.

Results are expressed as mean ± standard deviation (SD).

RESULTS: Population description

A total of 16 patients were assessed between July 2018 and February 2020. One patient was excluded because of a psychiatric disorder requiring emergency hospitalization. Data of 15 patients from 13 families were analyzed (Table 1).

Mean age was 43.3 ± 14.4 years old (range: 18 to 67 years) with a mean education duration of 12.7 ± 2.6 years (range: 8 to 17 years). The sex ratio was nine women and six men (9:6).

Genetic features

All patients had an identified germline PTEN mutation. Variant types included 6 non-sense (40%), 3 missense (20%), 5 frameshift (33.3%) and 1 splice site (6.6%). These are truncating mutations (all but missense) responsible for a loss of function of PTEN in most of cases and missense mutations in three cases classified as probably pathogenic (class 4) according to the ACMG/AMP criteria. The identified variants are summarized in Table 2.

Patient

Clinical features

The two most frequent benign tumors in this cohort were skin tumors (n=15; 100%) with gingival papillomatosis in 10 patients (66.7%), and thyroid tumors (n=13; 86.7%) with thyroid nodules in 8 patients (53%). The most frequent malignant tumor was adenocarcinoma of the breast in 5 patients (33.3%). Macrocephaly was present in 14 out of 15 patients (93.3%) and mean cranial perimeter was 61.9 ± 1.96 cm, (range: 58-64 cm).

One patient had a history of neurosurgery for a brain tumor during childhood (oligodendroglioma; patient 4), and two patients (13.3%) had a neurodevelopmental abnormality: a proven confirmed autistic spectrum disorder (ASD) associated with a delay in language acquisition for one patient (patient 10), a delay in writing and reading learning for the other patient (patient 15). Diagnosis of ASD was confirmed by a multidisciplinary examination, including a specialized psychiatrist, psychologist and neuropsychologist and following the diagnosis criteria of the DSM-5. [START_REF]Diagnostic and Statistical Manual of Mental Disorders[END_REF] In addition, 3 patients (20%) had a history of focal epileptic seizure.

Three patients had a psychiatric history (20%), dominated by depressive syndrome (n=2) and anxiety disorder (n=1).

Neuropsychological testing

Three of the 15 patients (20%) expressed a cognitive complaint before the neuropsychological testing. These complaints were about attention (1 patient) and memory (2 patients).

All patients presented at least one pathological score at the neuropsychological assessment ( Overall inductive reasoning, assessed with the PM-38, was preserved in all but one patient (Patient 10 who suffered from ASD).

Social cognition

Five patients (33.3%) were impaired at the TOM-15, which assesses false-beliefs understanding.

These five patients were not able to move away from their own beliefs to put themselves in someone else's shoes. Nine patients (60%) had a pathological modified Faux-Pas test, which assesses mentalizing and social contexts understanding. These nine patients judged social missteps to be intentional or did not understand or perceive social missteps. Eleven patients (73%) were impaired on facial emotion recognition test. More precisely, fear (n=13; 86.6%), anger (n=9; 60%) and sadness (n=8; 53.3%) were the least recognized emotions. On the contrary, all participants identified joy and neutral emotions.

New French norms of the mini-SEA that take into account age and education have been published

after the end of the study. [START_REF] Quesque | Validation de la mini-SEA dans une population française variée : données de référence pour la pratique clinique[END_REF] Using these new norms showed slightly different results, with ten patients (instead of 9) having abnormal modified Faux-Pas test scores and five patients (instead of 11) having abnormal facial emotion recognition scores.

Executive functions

Regarding flexibility assessment, two patients had a pathological score (13.3%) at the TMT-B and at the TMT-B-A, 4 patients (26.7%) were impaired at semantic verbal fluency with animals and 2 patients (13.3%) at verbal fluency with the letter "P".

Four patients had a pathological score (26.7%) at the interference part of the Stroop test, which assesses cognitive inhibition. Four patients (26.7%) had a pathological score at the digit span subscore of the WAIS IV, which assesses working memory.

Dexterity

Fourteen patients had a pathological score with the dominant hand at first trial (93.3%) and ten had a pathological score with the non-dominant hand (66.7%). Performances were slightly improved at second try, with 8 pathological scores with the dominant hand (53.3%) and 8 pathological scores with the non-dominant hand (53.3%).

Language

Only one patient had a naming disorder on the DENO-40 scale (6.7%).

Mood

Nine patients (60%) had a pathological score on the HADS anxiety scale and three (20%) on the HADS depression scale. Three patients (20%) had a pathological score at the Apathy scale.

Statistical analyses (Supplementary Material S2)

Statistical analyses showed no genotype-phenotype correlations: results in social cognition tests, dexterity, as well as the whole neuropsychological assessment were not different according to the type of germline PTEN variants or according to the nature of variants (truncating versus nontruncating). Additionally, there was no correlation between any cognitive scores, dexterity and/or demographic characteristics.

Statistical analyses

Neuropsychological testing according to the type of mutation

There were no significant differences in TOM-15 results (Chi2 = 4.216, p = 0.239), Faux-Pas score (Chi2 = 1.206, p = 0.752) and recognition of facial emotions (Chi2 = 4.156, p = 0.245) according to the type of PTEN variant. Furthermore, there was no significant difference between results of social cognition tests according to the presence of truncating or non-truncating PTEN variants (TOM-15: U = 6.00, p = 0.087; Faux-pas: U = 12.00, p = 0.421; facial emotion recognition: U = 9.00, p = 0.217).

Neuropsychological testing according to demographical and psychological parameters.

Performance at the Raven progressive matrices (PM-38) correlated negatively with HADS depression score (Rho = -0.638, p = 0.010), HADS anxiety score (Rho = -0.546, p = 0.035) and the apathy scale (Rho = -0.553, p = 0.033). There was a significant negative correlation between the Faux-Pas score and the HADS depression score (Rho = -0.544, p = 0.036). Education duration also negatively correlated with anxiety (Rho = -0.566, p = 0.028).

There was no correlation between scores on the HADS anxiety scale and scores of social cognition tests (TOM-15: Rho = -0,449, p = 0,093; Faux-Pas score: Rho = 0,035, p = 0,903; facial emotion recognition: Rho = 0,249, p = 0,371) and no correlation between scores on tests exploring executive functions and scores of social cognition tests (Supplemental material S1).

Additionally, neuropsychological tests did not differ according to gender, age, or cranial perimeter.

Nor did they differ according to the presence of a memory complaint, nor according to the presence of a cerebellar abnormality (Supplemental material S1).

MRI (Supplementary Material S3)

Thirteen patients (86.7%) had at least one brain abnormality, when dilatation of Virchow-Robin spaces was considered abnormal. The most frequent abnormality was the presence of dilated perivascular spaces (PVS) or Virchow-Robin present in 13 patients (86.7%). Eight patients (53.3%) presented developmental venous anomalies and 5 (33.3%) had periventricular and semi-oval centers nonspecific leukopathy, which rated at 2 on the Fazekas scale, corresponding to moderate impairment. In addition, 7 patients out of the 15 (46.7%) had various cerebellar abnormalities and among them, 2 patients (13.3%) presented a Lhermitte-Duclos disease.

The other observed abnormalities were meningioma (n=3; 20%), microbleeds (n=3; 20%), ptosis of the cerebellar tonsils (n=4; 26.7%) and cavernoma (n=2; 13.3%).

Main MRI findings are presented in Figure 1.

DISCUSSION:

We examined social cognition in patients with CS and PTEN variants using a standardized neuropsychological assessment and showed impaired social cognition especially in facial emotion recognition and affective theory of mind. Fine dexterity was impaired in almost all patients. All patients underwent a clinical neurological evaluation and a standardized brain MRI, which showed various brain abnormalities.

This study has several limitations. First, the size of our patient group was small since CS is a rare disorder, with estimated prevalence of 1:200.000. [START_REF] Nelen | Novel PTEN mutations in patients with Cowden disease: absence of clear genotype-phenotype correlations[END_REF] However, the results were clear-cut showing that the majority of patients were impaired on at least one of the social cognition tests. This suggests a strong link between social cognition impairment and germline PTEN variants. Secondly, there might have been a selection bias because participation was based on willingness and the most affected patients may have refused to take the tests. The cognitive assessment was systematically proposed to all patients during a follow-up dermatological consultation whether they had expressed a cognitive complaint or not, to limit this bias as much as possible. Thirdly, the tests used for social cognition assessment may be partly outdated, notably regarding the Ekman's faces. This test, developed by Ekman and Friesen in 1976, was one of the first tools available for the evaluation of facial emotion recognition. It only takes primary emotions into account and therefore does not provide information on the patient's ability to perceive more complex emotional states. Thirdly, we showed here a significant impairment of social cognition by comparing the test results to validated norms, but controlled studies with age, gender and pathological context-matched controls group would be necessary to confirm these results. Finally, patients had significant anxiety and depressive symptoms on the HADS scale, which may confound and distort the results of neuropsychological tests and thus be responsible for a confusion bias. However, we found no correlation between HADS scores and social cognition scores.

The majority (73%) of patients were impaired on facial emotion recognition. Fear was the most affected emotion, followed by anger and sadness. On the contrary, joy and neutral emotions were relatively preserved. Ekman faces test analyses primary emotions. Thus, impairment on this test may indicate a non-subtle impairment of primary emotions, which may have significant impact on daily activities. However, these results should be interpreted with caution, since an additional analysis in the light of the latest published norms showed less significant results with only 5 patients having impaired scores on facial emotion recognition.

Regarding the theory of mind assessment, we found that the modified and reduced version of the Faux-Pas test, assessing social context understanding, was abnormal in the majority of patients (60%), while the TOM-15 scores, assessing false-beliefs understanding, were relatively preserved in most patients. The different degree of impairment between these two tests might be explained by several factors such as more possibilities for subjective interpretation, higher variance in the responses and the greater differential importance of socials norms in the modified Faux-Pas test that in the TOM-15.

The different degree of impairment between the two components of the theory of mind might be explained by their possible functional independence. Impairment of the cognitive theory of mind might relate to diffuse lesions of the lateral prefrontal cortex while impairment of the affective theory of mind would relate to lesions of the orbito-medial prefrontal cortex and the fronto-striatal limbic system. The predominant impairment of negative emotions, particularly fear, can be compared to other pathological situations, notably in patients with behavioral variant Fronto-Temporal Dementia (bv-FTD). Indeed, the deficit in the treatment of negative-valued emotions (sadness, fear, anger, disgust) in bv-FTD, is usually attributed to lesions of the orbito-medial prefrontal cortex and the amygdala. Our results suggest a possible involvement of the orbito-medial prefrontal cortex and the amygdala (anteromedial region of the temporal lobe): notably because the recognition of negative emotions and the theory of affective mind rely on both structures. There was no brain anomaly detected to explain social cognition impairment, but microstructural and molecular modifications may be involved. At a molecular level, it has been recently shown that synaptic actions of PTEN in mice's amygdala interferes with their social behavior : decrease in activity at synapses was associated with less sociability whereas an increase in activity was associated with increased social behavior. [START_REF] Sánchez-Puelles | PTEN Activity Defines an Axis for Plasticity at Cortico-Amygdala Synapses and Influences Social Behavior[END_REF] In parallel, the cerebellum might be involved in the social cognition impairment of our patients. Several arguments support this hypothesis. First, almost half of the patients had a cerebellar abnormality on brain MRI and all but one had an impaired dexterity that was compatible with cerebellar dysfunction. Second, there is a demonstrated link between germinal PTEN variants and the existence of structural abnormalities of the cerebellum (Lhermitte-Duclos disease). Third, it has been shown that the cerebellum plays an important role in social cognition by assisting in learning and understanding social actions and by supporting optimal predictors about social interactions. [START_REF] Van Overwalle | -01155-1 abnormalities in individuals with germline heterozygous PTEN mutations and autism[END_REF] Social cognition testing was not different in patients with cerebellar abnormalities when compared to patients without cerebellar abnormalities. However, microstructural changes undetected by brain MRI might be involved. Further studies, including functional MRI, will be necessary to determine the anatomical correlates of social cognition impairment of CS patients.

Statistical analyses showed no genotype-phenotype correlations: results in social cognition tests as well as the whole neuropsychological assessment were not different according to the type of germline PTEN variants or according to the nature of variants (truncating versus non-truncating variants). However, this analysis should be interpreted cautiously because of the small size of the subgroups tested. Previous mutation analyses of patients with PHTS have shown an overrepresentation of missense type mutations in patients with a proven ASD,[44] but other authors showed no phenotype-genotype correlation. [START_REF] Waite | Protean PTEN: Form and Function[END_REF] This highlights the complexity of the genotypephenotype relationship, the need for a better understanding of the natural history of PHTS via longitudinal studies and suggests the existence of inter-and intra-individual variability factors.

Only a small proportion of CS patients had altered cognitive inhibition, flexibility, lexical fluency and/or working memory. In a previous study, the authors described an impairment of executive functions in CS. [START_REF] Busch | Cognitive characteristics of PTEN hamartoma tumor syndromes[END_REF] In this study, four tests were proposed to assess executive functions. Although results were under the normative mean at the group level, only 13-26% of the 25 participants were impaired in these tests when impairment is defined by a Z-score of -1.65. These figures are strictly comparable to 13 to 26% of participants in the current study. A previous study showed an impairment of all of these executive functions in 25 CS patients. This discrepancy may be explained by a lack of statistical power of our study due to a smaller sample size. Alternatively, the high number of tests used in Busch's study might have led to false positive results due to multiple comparisons.

Most of our patients (93%) had an impaired fine dexterity predominant on the dominant hand or on both hands. This impairment tended to improve at second try. Dexterity assessed by the 9-HPT test was impaired in almost all patients. Processing speed might also be involved in this test and a decreased processing speed may induce altered score at the 9-HPT. However, The TMT-A, which is a test that highly relies on processing speed, was not altered in our patient group. Moreover, the 9-HPT is supposed to assess dexterity more than speed because the test consists of grasping small sticks and inserting them into holes. This requires a certain precision and therefore good fine motor skills. Surprisingly, none of the patients presented any complaint concerning dexterity and no abnormality was observed on clinical neurological examination, in particular no cerebellar syndrome and no apraxia. Thus, the significance of this impairment from a neuroanatomical and pathophysiological point of view remains unclear. Indeed, it could be linked to a pure motor disorder, to a cerebellar dysfunction, to a cognitive slowness and/or to a praxis disorder. The improvement during the second trial would be in favor of a praxis disorder but this improvement is not present in all patients. A similar impairment of fine dexterity has been described previously in CS patients. [START_REF] Busch | Cognitive characteristics of PTEN hamartoma tumor syndromes[END_REF] It might be considered as an endophenotype of PTEN variants, and further studies will help to determine the relation between PTEN variants, dexterity and the cerebral and cerebellar bases of this dexterity impairment in CS.

All but one patient had a normal score at the inductive reasoning task, suggesting that intellectual functioning, defined as the ability to obtain and use knowledge in adaptive situations, was preserved in most patients, as described previously. [START_REF] Busch | Cognitive characteristics of PTEN hamartoma tumor syndromes[END_REF] It is consistent with the normal professional integration of CS patients. Furthermore, there was a significant negative correlation between anxiety, depressive features, apathy and inductive reasoning task. Although some authors have shown the negative impact of anxiety and depressive symptoms over intellectual functioning, other have shown that the higher an individual's Intellectual Quotient (IQ), the higher the risk of developing psychiatric comorbidities.

ASD is part of the clinical symptoms of CS, [START_REF] Pilarski | Cowden syndrome and the PTEN hamartoma tumor syndrome: systematic review and revised diagnostic criteria[END_REF] and may relate to PTEN variants.

[44] PTEN variant seams to lead to a particular cognitive phenotype in patients diagnosed with ASD (PTEN-ASD). A recent study has shown that pediatric population PTEN-ASD had a distinct neurobehavioral phenotype compared to PTEN variant without ASD and to idiopathic ASD: in PTEN-ASD, cognitive deficits are more severe and appears to involve several domains such as executive functions, language and intellectual functioning. [START_REF] Busch | Neurobehavioral phenotype of autism spectrum disorder associated with germline heterozygous mutations in PTEN[END_REF] As social cognition is the most impaired cognitive function in ASD, [START_REF] Fernández | Neural Circuits for Social Cognition: Implications for Autism[END_REF] similar mechanisms might be involved in our CS patient group. In the present study, the patient who was diagnosed with ASD (patient 10) belongs to the same family and carries the same variant as patient 9, emphasizing the intra-familial variability of expression for PTEN variants, specifically in the constitution of the autistic phenotype. This observation highlights the need for additional factors associated with PTEN variants in the genesis of ASD, which may involve modifier genes. However, the precise pathophysiological involvement of the PTEN variants in ASD remains unclear. Anomalies in the hippocampal and cerebellar structures have been reported in CS patients with ASD, [START_REF] Rademacher | PTEN in Autism and Neurodevelopmental Disorders[END_REF] including neuronal hyperproliferation, migration and lamination defect, anomalies of synaptic plasticity and axonal myelination, but further studies will be necessary to determine whether similar mechanisms are involved in patients presenting with minor social cognition impairment such as our patient population.

Analysis of cerebral MRI scans revealed various abnormalities in our patients, similar to what has been previously reported for CS. [START_REF] Dhamija | Neuroimaging abnormalities in patients with Cowden syndrome: Retrospective single-center study[END_REF] The most frequent brain anomaly was the dilated Virchow-Robin spaces. This lesion is common in the general population (50-100% of patients after the age of 60 years depending on the measurement scales) [START_REF] Laveskog | Perivascular Spaces in Old Age: Assessment, Distribution, and Correlation with White Matter Hyperintensities[END_REF] and it is found in many neurological pathologies such as small vessel disease. [START_REF] Brown | Understanding the role of the perivascular space in cerebral small vessel disease[END_REF] According to recent data, it does not appear to be associated with cognitive decline or increased risk of cognitive impairment, [START_REF] Cs | Enlarged perivascular spaces and cognition: A meta-analysis of 5 population-based studies[END_REF] although this is still debated. It is questionable whether there is a link between this abnormality and impaired social cognition, especially as our patients had a mean age of 43.3 years, whereas dilated Virchow-Robin spaces are usually reported in older populations with a significant increase of prevalence after the age of 65 years. Finally, most of our patients had developmental venous anomalies, in line with previous studies showing that CS had more central nervous system vascular abnormalities such as venous angiomas and cavernous angiomas. [START_REF] Lok | Brain magnetic resonance imaging in patients with Cowden syndrome[END_REF] In conclusion, fine motor dexterity impairment was observed in almost all patients, and social cognition impairment was observed in 73% of the 15 CS patients included in this study. Social cognition impairment might explain some of the awkward behaviors of these patients. Impairment in facial emotion recognition and social context understanding could lead to a shift in social relations and could explain the discomfort of clinicians during consultations. In view of these results, it seems important to recognize the social cognition disability of patients suffering from CS, as it may have important functional implications for patients and their relatives. This study also raises the question of a specific treatment of social cognition impairment.

Although not yet validated, specific rehabilitation approaches may be proposed notably with cognitive remediation and social skills training. [START_REF] Kurtz | Comprehensive treatments for social cognitive deficits in schizophrenia: A critical review and effect-size analysis of controlled studies[END_REF][START_REF] Bon | Cognition sociale et autisme : bénéfices de l'entraînement aux habiletés sociales chez des adolescents présentant un trouble du spectre de l'autisme[END_REF] Recognition of disability, development of specific treatments and rehabilitation for social cognition might improve the quality of life of patients with CS. Finally, this study relied on a small number of patients, and further controlled studies will be necessary to confirm these results.

  Coefficient (ADC), Susceptibility Weighted Imaging (SWI), 3-dimensional Fluid Attenuated Inversion Recovery (3-d FLAIR), time-of-flight (TOF), 3-dimensional Brain Volume T1-weighted (BRAVO) and gadolinium injection with Time Resolved Imaging of Contrast KineticS (TRICKS) and Fast Spoiled Gradient-echo (3d FSGPR).

Fig 1 .

 1 Fig 1. Main associated MRI findings involved in the 15 Cowden syndrome patients. (A) Axial T2

Table 1 . Demographical features. DVA: Developmental Venous Anomaly, CP: Cranial Perimeter, GI: Gastrointestinal SD: Standard Deviation. Patients with macrocephaly are marked with °.

 1

		Gender	Age	Occupation	CP (cm)	Education	Cognitive	Neurological	Neurodev.	Tumoral history
			(range in			(years)	complaint	history	Disorder
			years)
	Patient 1	M	45-50	Computer	63°	14	No	No	No	Gingival papillomatosis, thyroid nodule,
				scientist						melanoma
	Patient 2	M	50-55	Teacher	65°	17	No	No	No	Gingival papillomatosis, GI polyposis,
										thyroid nodule
	Patient 3	F	65-70	Child care	58°	10	No	No	No	Breast adenocarcinoma, acrokeratoses,
				assistant						thyroid nodule
	Patient 4	M	35-40	Employee	61°	15	No	Focal epilepsy	No	Oligodendroglioma, gingival papillomatosis,
										thyroid nodule
	Patient 5	F	30-35	Caregiver	62°	11	Yes	No	No	Breast adenocarcinoma, gingival
										papillomatosis, thyroid nodule
	Patient 6	M	30-35	Human	62°	15	No	No	No	Acrokeratoses, thyroid nodule
				resources
	Patient 7	F	50-55	Secretary	60°	14	No	No	No	Meningioma, gingival papillomatosis,
										thyroid nodule
	Patient 8	F	45-50	Public official	59°	15	No	No	No	Breast adenocarcinoma, acrokeratoses,
										thyroid nodule
	Patient 9	F	45-50	Specialized	59.5°	12	Yes	Focal epilepsy	No	Thyroid nodule, acrokeratoses
				Helper in pre-
				school
	Patient 10	M	15-20	Student	59.6	10	No	No	Yes (language,	Arnold-Chiari, acrokeratoses, thyroid
									motor)	nodule
	Patient 11	M	20-25	Automobile	64°	12	No	No	No	Cerebellar DVA, gingival papillomatosis
				inspector
	Patient 12	F	25-30	Dog handler	60°	12	No	No	No	Meningioma, gingival papillomatosis,
										thyroid nodule
	Patient 13	F	55-60	Director of	61°	16	No	Focal epilepsy	No	Gingival papillomatosis, breast
				company						adenocarcinoma, thyroid nodule
	Patient 14	F	40-45	Public official	62°	14	No	No	No	Gingival papillomatosis, breast
										adenocarcinoma, thyroid nodule
	Patient 15	F	45-50	Public official	62°	8	Yes	No	Yes (language)	GI polyposis, papillary thyroid carcinoma
	Mean (SD)	6M/9F	43.3		61.9	12.7 (2.6)
			(14.4)		(1.96)

Table 2 -List of the PTEN variants involved in the 15 Cowden syndrome patients. Patient with proven autistic spectrum disorder is marked with °.

 2

		Exon	cDNA	Protein	Consequence Pathogenicity
			(NM_000314.8)
	Patient 1	Exon 2	c.103A>G	p.(Met35Val)	missense	Class
	Patient 2	Exon 5	c.388C>T	p.(Arg130*)	nonsense	Class
	Patient 3	Exon 5	c.463T>A	p.(Tyr155Asn)	missense	Class
	Patient 4	Exon 7	c.675 T>A	p.(Tyr225*)	nonsense	Class
	Patient 5	Exon 5	c.352dupC	p.(His118Profs*8)	frameshift	Class
	Patient 6	Exon 7	c.733C>T	p.(Gln245*)	nonsense	Class
	Patient 7	Exon 7	c.722_723dupTT	p.(Glu242Leufs*15) frameshift	Class
	Patient 8	Exon 5	c.477G>T	p.(Arg159Ser)	missense	Class
	Patient 9	Exon 8	c.955_958delTACT p.(Thr319*)	nonsense	Class
	Patient 10° Exon 8	c.955_958delTACT p.(Thr319*)	nonsense	Class
	Patient 11 Exon 5	c.352dupC	p.(His118Profs*8)	frameshift	Class
	Patient 12 Exon 1	c.48T>A	p.(Tyr16*)	nonsense	Class
	Patient 13 Intron 7	c.801+1delG		splice	Class
	Patient 14 Exon 8	c.820 delT	p.(Trp274Glyfs*2)	frameshift	Class
	Patient 15 Exon 7	c.659dupT	p.(Val222Glyfs*21) frameshift	Class

Table 3

 3 ).

		PM-38 (max. 55)	TMT-A (seconds)	TMT-B (seconds)	TMT B-A (seconds)	*Stroop Interference	Faux-Pas (/15)	Emotion Recognition (/15)	TOM-15 (0-15)	9-HPT DH (seconds) 1 2	9-HPT NDH (seconds) 1 2	HADS > 8) anxiety (0-21, abnormal	HADS > 8) depression (0-21, abnormal
	Patient 1	41		99	65	34	12.4	13.7	13	28°	19	26	26	9	4
	Patient 2	46		55	38	98°	9°'	10.7°'	14	27,9°	22	26,2	20,8	6	5
	Patient 3	35		121	81	NC°	10.9°'	11.1°	14	23,5°	20,7	23,6	24,2	11°	10°
	Patient 4	45		151°	111°	107°	8.2°'	8.1°'	13	30,5°	25°	31,2°	29°	2	5
	Patient 5	51		134°	93°	43	9.4°'	13.3	14	24,4°	19,8°	31,8°	23,3	5	2
	Patient 6	47		58	36	36	13.1	12	13	23,4°	18,7	26,4°	19,2	5	2
	Patient 7	54		42	24	49	13.1	9.4°'	13	21,7°	19,7	19	17,3	8	5
	Patient 8	50		80	54	71	11.2'	12.9	14	23,9°	20,9°	23,4° 21,03	9°	4
	Patient 9	44		65	35	58	13.1	9.4°'	11	23,7°	19,6	19,5	19,2	11°	4
	Patient 10	31°		104	69	49	5.2°'	10.3°'	6°	26,9° 26,06° 25,31° 27,8°	9°	7
	Patient 11	48		65	38	51	15	13.7	11°	26,63° 20,9°	23,7°	20,5	10°	3
	Patient 12	42		85	56	73	8.2°'	12°	13	25,7°	22,2°	23,5° 21,5°	8	4
	Patient 13	47		83	51	NC°	10.9°'	11.1°	9°	26°	26,4°	27,5° 32,5°	7	5
	Patient 14	36		60	23	44	8.2°'	11.5°	3°	23,8°	20,8	25°	22,7°	12°	11°
	Patient 15	34		82	63	52	8.2°'	12°	9°	19,2	20,9	18,6	18,3	15°	11°
	Mean	43.4	29.8	85.6	55.8	58.8	12.1	11.4	13.3	25.0	21.5	24.7	22.9	8.5	5.5

Table 3 -Results of neuropsychological assessment. Abnormal results (according to age-appropriate standards) are highlighted in bold and with °. Abnormal results according to recent French norms of MINI-SEA[40] are marked with '.*This score corresponds to the score obtained on the third part of Stroop test. DH: Dominant Hand, NDH: Non Dominant Hand, NC: Not Completed.

 3

Frazier TW, Embacher R, Tilot AK, Koenig K, Mester J, Eng C. Molecular and phenotypic

ACKNOWLEDGMENTS

We thank the patients who contributed to this study. No sponsorship was obtained for this study.

DATA AVAILABILITY STATEMENT

All the data supporting in Table 1, 2, 3 and Figure 1 are publicly available.

DISCLOSURE

The authors declare no conflicts of interest.

ETHICS DECLARATION

We conducted a retrospective study, which complied with the Declaration of Helsinki. French law requires neither ethics committee approval nor informed consent for studies of retrospective data.

However, all data were anonymized and compiled as required by the Commission Nationale de l'Informatique et des Libertés (the French data protection authority).

The current study obtained the authorization of the Local Ethics Committee of Avicenne Hospital (CLEA-2019-92). Oral consent was obtained from all participants.


Christophe Ars

Joseph Gauthier
email: joseph.gauthier@univ-fcomte.fr

Nicolas Florsch

Underground ancient mine work ventilation modeling

Keywords: Mining archaeology, Ventilation system, Numerical modelling, Computational fluid dynamics

come

Introduction

Mining activities have long been -and still are -an essential source of wealth for sovereign states and principalities. The extraction of raw materials, in particular those presenting strategic values through their industrial use or for minting money, has always involved considerable investments. Access to and successful extraction of mines allow a state to position itself among its neighbors as on a global scale. From the 5 th century BC Laurion mines in Greece to the modern-time mines of Potosi, those who hold rich minerals hold the wealth and that's that.

Visiting an underground set up dating from before the invention of explosives immediately immerses the researcher in the extraordinary scale of money and man-time investments dedicated to this activity. Although less visible than pyramids, the underground work, once added up, is beyond understanding: there are hundreds of kilometers of galleries, carved with a hammer and an iron gad or by the use of fire-setting.

Although the extraction itself is the main and certainly the most visible part of the investment, dewatering and ventilation come second only in terms of expenditure. The latter aspects must be taken into account before even thinking about ore dressing and metallurgical transformations that follow after the mining work. However, these workstations are not always present, depending on the possibilities the field offers, and can often be bypassed or in any case facilitated in mountainous areas.

Ventilation, along with dewatering, is a major concern in mining. Sufficient fresh air must be provided for the miners who work in the galleries that are sometimes confined and far from the surface. Nowadays, complex mechanical ventilation systems (and, thanks to electric fans, forced ventilation) respond to this demand but the question remains open for the mines of Antiquity and the Middle Ages when men did not benefit from these technologies.

A distinction must be made between mountainous and lowland areas. In the mountains, the miner tries to establish openings at different altitudes as soon as possible (Grandemange, 1988) or to use false ceiling systems [START_REF] Florsch | Etude quantitative de l'aérage d'une galerie de mine du XVI e siècle[END_REF]. When such installations are not implemented (in particular at the start of drilling), air renewal is not naturally ensured beyond fifty meters in a gallery, as has been shown by [START_REF] Florsch | Sur l'aérage naturel des anciennes galeries de mines en zone montagneuse : expérimentation et modélisation[END_REF].

In the plains, where galleries are systematically located at a lower altitude than the surface itself, the use of wind traps was frequent, as evidenced by various sources (starting with those of [START_REF] Agricola | De Re Metallica[END_REF]. The problem is most critical in summer: the cool air stagnates in underground works. This cold air is also denser. Artificial ventilation may also be established by using multiple wells. A fire at the base of such a shaft creates an ascending air flow and thus allows for fresh air to be sucked in through the other shafts. This very probably explains the particular geometry seen, for example, in the Carolingian mining sector of Melle in western France [START_REF] Téreygeol | À la main ou au feu : les choix techniques pour l'extraction des minerais argentifères » in Du monde franc aux califats omeyyade et abbasside : extraction et produits des mines d'argent de Melle et de Jabali[END_REF][START_REF] Bonnamour | Ouvrage d'assistance et espace minier en contexte mellois : fouille préventive du site du Prieuré (Saint-Martin-Les-Melle, 79)[END_REF].

Existing literature has already dealt with the matter of ventilation in galleries and shafts. An unprocessed issue is definitely challenging for mining archaeologists. The ventilation of the various kinds of stopes, especially those relative to the veins that have been excavated and where the miners were digging, is such an issue. These areas most often follow geological fracturing, developing narrow vertical to sub-vertical void volumes. They can extend over several dozens of meters in two directions with perpendicular thicknesses of a few decimeters to several meters. These underground work areas can be far from the mine's entrance, and drilling at another altitude only to create a natural air flow is most often complicated and costly, at least at the beginning. In that case, the issue of ventilation for air renewal is crucial. The only solution is to provide the mine with a system for conveying fresh air to the bottom, and/or for evacuating stale air.

Here we study the functioning of a ventilation system in complex mining volumes of the excavated vein zone type such as we meet in the Vosges mountains.

From the discovery of a ventilation duct to the exploration of an ancient mine ventilation system

The discovery of a metallic seal and a wooden ducting artifact in the Giro mine at Sainte-Marie-aux-Mines (Alsace, France) motivated us to begin this study.

A horizontal duct discovered at Sainte-Marie-aux-Mines

The Giro mine is located in the heart of the Altenberg, which is a mining sector continuously exploited since the end of the Carolingian period to the Thirty Years War [START_REF] Gauthier | The Alsatian Altenberg: a seven-hundred-year laboratory for silver metallurgy[END_REF]. The district, and this claim in particular, are primarily mineralised in galena, then in gray copper, embedded in a gangue of quartz and siderite. The vein system is surrounded by gneisses with various lithologies. Giro mine has been very recently explored for the first time thanks to an archaeological excavation program since its rediscovery in 2016. Observing the digging directions and intersections of galleries lead to the identification of three phases of exploitation, for which currently no absolute date can be given. One can nonetheless attribute the first phase to the central Middle Ages (10 th -12 th centuries), the second to the 15 th -16 th centuries, and the last to the 17 th -18 th centuries [START_REF] Gauthier | La mine Giro, massif de l'Altenberg, Sainte-Marie-aux-Mines[END_REF]. The area where the remains of a wooden duct were found corresponds to a gallery along a vein mainly exploited during the 15 th -16 th centuries (figure 1). The original entrance to this gallery is still unknown since colluvions has halted current progression (it is nowadays accessed via a modern gallery from below). Stopes were dug upwards and downwards from the gallery. All the underground networks related to this 15 th -16 th c. phase of activity were dug with hand tools. No trace of fire-setting has been observed. The issue of smoke does not have to be taken in consideration. The excavation of the area located between the entrance and the first descending stope permitted to discover the remains of a wooden pipe lying on the gallery floor. The remains of this facility consist of a streak of decomposed wood punctuated by metal rings found still in place. The pipe can be followed for over 22.5 m. Eight iron pipe sealing joints were discovered. The interval between two connecting pieces stays constant (3.05 m) except upon turning a corner. The fittings are then positioned closer to each other to adapt the curvature of the pipe to the gallery. The duct ends upon reaching a filled shaft that communicates with a lower stope. It is reached by following another decline that leads into the gallery about thirty meters from said shaft.

The discovered fittings have the shape of iron rings with an approximate internal diameter of 7-8 cm. (figure 2). The diameter cannot be measured accurately due to the state of alteration of the artifacts. The ring is about 4 cm wide, and has two stops around its outer periphery, in between which there is a 1 cm wide. We can link these artifacts to those represented on one of the engravings in book 6 of De Re Metallica. The component was used to join the different parts of the pipe by forcing the wood onto each side until it reached the stopes. This system seals the connecting pipes. However, the graphical representation of the seal in Agricola concerns the hydraulics system, and more particularly a sealing of a pump body. Its diameter is larger, while the diameter of the pipe found in the Giro mine would not allow it to be used for water drainage. It might also be noted that Agricola never represents a pipe used for nearly horizontal drainage, but always open channels. Equipping a gallery with a pipe when water can naturally flow on its floor would not make sense either. The remains found thus correspond to a duct intended to transport air. How such a system was set up on the floor of a gallery is explained and shown a few pages later, still in book 6 of De Re Metallica (figure 3). We therefore propose to interpret the presence of this pipe as evidence of a system for conveying fresh air from the outside to the lower stopes and galleries. It therefore had to be connected to a gear located at the mine's entrance, such as the bellows depicted in the engraving of the Saxon doctor's book. To validate this hypothesis of forced ventilation actuated by external bellows, it would be best to reconstruct this system. Since this is not possible physically, numerical simulation of the air flow in the mine can be used to test and validate different assumptions. This approach resembles experimental archaeology but in a context where life-size experimentation would be very difficult to carry out. The numerical simulation approach is a computational substitute for reality.

Numerical model implementation

In the same way that the benchmark reproduces a device or a process to check its own effectivness, one must build a numerical model that represents the mine and its ventilation system. It is based on a simplified geometry of the gallery and includes five miners working there.

Model geometry

Modeling involves a simplified representation of the mine from a geometric point of view. It would in fact be impossible to simulate the air flow taking into account the reality of the mine down to the smallest roughness of the wall. Taking into account wall asperities would have the same effect as changing slightly the widths of the stope, and would not lead to significant changes in the modelling. However, the model retains the general geometrical features that influence the air flow, and obtained results are reliable in terms of scientific conclusions.

The model involves several parts:

1) The underground route which is shown in figure 4 is made up of a 60 m long and 2 m high gallery, a vertical extraction site 20 m wide and 20 m high as well as a decline of about 10 m long. The width of the gallery and of the site is considered constant and equal to 1 m.

Halfway in the gallery is a first shaft to access the stope. This shaft is considered closed in the mine's model and is only used to supply fresh air from outside. The end of the wooden ventilation pipe is modeled with an internal diameter of 6 cm, extrapolated based on the fitting found during the excavations. This pipe constitutes one of the air inlets of the model. At the end of the gallery is a decline through which the air circulating and rising from the stope is evacuated. At the outlet, the gallery makes a turn, which differs from the real access to the gallery but facilitates the numerical simulation of the natural convection flow by simplifying the outlet pressure condition and limiting reverse flows. This numerical setup does not disturb the resolution of the flow in the rest of the study area because reverse flows at the outlet are determined by the flow dynamics in the stope. 2) In order to simulate the production of heat and CO 2 in the gallery, one must also model the miners at work. There are five miners modeled and each one is represented by a vertical cylinder 1.5 m high and 0.4 m in diameter. The dimensions of this simplified representation permit a heat exchange surface close to that of a real human. For each miner, a second horizontal cylinder, which is 6 cm in diameter, represents the nose and mouth in order to model the miners' breathing. These horizontal cylinders are five more inlets in the model.

3) Although a minimum of scaffolding may have existed to ease the miners' mobility within the mine, it could also have played a central role in ventilation by channeling the air flow. Hence, numerical simulation must allow for the testing of several gallery layouts: with and without ventilation, but also with and without scaffolding. The chicane shaped scaffolding, which is shown on figure 5, is designed to facilitate the movement of miners and ventilation in the stope. The height between scaffolding floors is 3 m and the width of the circulation spaces at the ends of the scaffolding is 1.5 m. In the model, the scaffolding is considered airtight. When there is scaffolding in the stope, the five miners are randomly placed on the different floors.

Model mesh

Meshing the mine consists in dividing its geometry into elementary volumes small enough to be able to approximate the equations of fluid mechanics in a system of appropriate matrix equations. The aim is to find a compromise between elementary volumes small enough to correctly represent the flow and a limited number of elementary volumes for the given geometry to ensure computational efficiency.

For the two models, whether there is scaffolding or not, the characteristics of the mesh are the same. Most of the mesh is based on cubic volumes of approximately 5 cm per side. The mesh is refined around the miners to match the geometry, with elementary volumes of about 8 mm per side. Along the walls, a layer of thinner volumes is applied to take the friction of the flow into account. The mesh cells' height on the walls of the mine is about 1.5 cm and 2 mm on the surface of the miners. The mesh and its refined areas are illustrated in figure 6 and its characteristics are summarized in table 1. The mesh is generated using blockMesh and snappyHexMesh utilities from the openFoam toolbox.

Boundary conditions

Once the computational domain is defined and meshed, one more step to undertake in order to solve fluid mechanics equations is to specify initial and boundary conditions. The initial conditions serve as a starting point for the simulation. As for the boundary conditions, they set physical quantities on the domain's borders. There are different kinds of boundary conditions:

• on the mine walls, the temperature is imposed and the flow velocity is zero;

• at the air inlets (the miners' mouths and the exit of the pipe), an air flow is imposed;

• at the gallery outlet, a pressure is imposed.

The boundary conditions are necessary for solving the equations but modifying them also allows to study several ventilation hypotheses. Let us simulate four possible cases of gallery ventilation:

• case 1: without scaffolding, the ventilation being ensured by natural convection and the miners' breath

• case 2: without scaffolding, the ventilation being forced with an inlet air flow from the pipe;

• case 3: with scaffolding, the ventilation being ensured by natural convection and the miners' breath;

• case 4: with scaffolding, the ventilation being forced by an air flow inlet from the pipe.

Case 1: heat and breathing of the miners

In this first case, the air flow is caused by two phenomena: a) the natural convection due to the dissipation of heat by the miners at work and b) the miners' breathing. Each miner is considered to dissipate 200 W of heat while working and his breathing corresponds to an air flow of 15 l/min (0.25 l/s). In both cases, this is approximately twice the heat dissipation and respiratory ventilation of a human at rest [START_REF] Florsch | Sur l'aérage naturel des anciennes galeries de mines en zone montagneuse : expérimentation et modélisation[END_REF].

The mine gallery walls are set to 10 °C. The pressure at the outlet is equal to one atmospheric pressure of 101325 Pa.

Case 2: forced ventilation

In the second case, forced ventilation from the pipe is added to the natural convection and breathing of the miners. Let us consider a constant ventilation flow of 13 l/s. This flow corresponds to bellow flow values measured in experimental archaeology (Gauthier and al., 2019). A constant flow also means that the ventilation is continuous. A double bellow system is required, which is equipment frequently shown in De Re Metallica, in particular on the engravings relating to ventilation.

Cases 3 and 4: scaffolding

The third and fourth cases aim to test the impact of the scaffolding on the ventilation. The modifications made concern the geometry of the domain described above. The boundary conditions of the flow, pressure and temperature are the same as in case 1 and case 2 respectively.

Numerical methods for solving fluid mechanic's equations

The criterion to assess the breathability of the air within the mine is the CO 2 concentration. In order to simplify the simulations and to improve computational efficiency, flow and CO 2 concentration simulations are segregated. First, a stationary simulation solves the flow of the natural convection due to the heat emanating from the miners. Then, a non-stationary simulation predicts how the CO 2 spreads over time. These simulations are performed with the Computational Fluid Dynamics (CFD) software OpenFOAM v. 6. (https://www.openfoam. org ).

Flow simulation

Natural convection flow simulations are performed using the buoyantSimpleFoam solver from the OpenFOAM toolbox that solves the following continuity, momentum and energy equations [START_REF] Kim | Simulation of a conjugate heat transfer using a preCICE coupling library[END_REF].

Continuity equation:

∇⋅(ρ u)=0
where u and ρ are the velocity vector and density.

Momentum equations:

∇⋅(ρ uu)=-∇ p +ρ g+ ∇⋅(2μ eff D(u))-∇ ( 2 3 μ eff (∇⋅u))
where p, g, μ eff and D(u) are the static pressure, gravitational acceleration, effective viscosity and rate of the strain tensor, (with μ eff =μ+μ t and

D(u)= 1 2 (∇ u+( ∇ u) T ) ).
Energy equation:

∇⋅(ρ uh)+ ∂ ρ K ∂t + ∇⋅(ρu K )- ∂ p ∂ t =∇⋅(α eff ∇ h)+ρu⋅g
where K and α eff are the kinetic energy and effective thermal diffusivity.

The boundary conditions associated to these equations are given in the table below.

Domain location Momentum equations Energy equation

Pipe inlet Fixed velocity value Fixed temperature value

Miners inlet Fixed velocity value Fixed temperature value

Mine outlet Fixed pressure value Fixed temperature value

Mine walls

No slip Fixed temperature value

Miners

No slip Fixed heat flux value

The flow can be laminar or turbulent and it can be predicted thanks to Reynolds number (Re) and Rayleigh number (Ra) that compare convection forces and viscous forces of the flow for forced convection flow and natural convection flow respectively.

R e= ρ UD h μ Ra= ρβ Δ T l 3 g μ λ
where D h , β, ΔT, l, λ are hydraulic diameter of the pipe, thermal expansion coefficient of air, temperature gradient between the miners and the mine, miner's average height and thermal conductivity of air.

The forced air flow coming from the pipe has a Reynolds number close to 18000 and the flow due to the miner's heat has a Rayleigh number about 10 10 . Thus, both flows are turbulent.

To account for turbulence, the flow's simulation is based on « Reynolds-averaged Navier-Stokes (RANS) » equations. The turbulence is represented by the Reynolds Tensor, solved with the k-ε model derived from a hypothesis of eddy viscosity.

The limitations of these models for natural convection flows are well known [START_REF] Hanjalić | One-Point Closure Models for Buoyancy-Driven Turbulent Flows[END_REF]. However, their versatility and settings convenience, when dealing with a variety of applications, make RANS equations a suitable choice for a first quantitative approach of ventilation problems within medieval mines. Analytical calculations of orders of magnitude for velocity and temperature provide a way to ensure first-order validity of the solution.

The RANS equations are then transformed into a linear system using the Finite Volume Method (FVM) applied to the computational domain mesh. The matrix-form equations are then solved through an iterative process, a variation of the SIMPLE algorithm adapted for buoyancy-driven flows.

CO2 concentration simulation

Simulations of CO2 dispersion are performed using scalarTransportFoam solver that solves a transport equation of a passive scalar through a fixed velocity field. Here the passive scalar is CO 2 concentration.

∂C ∂ t + ∇⋅(UC )-∇ 2 ( D C C)=0
where C, D C are the CO 2 concentration and diffusion coefficients divided by the fluid density.

The boundary conditions for this equation are given in the table below.

Domain location Transport equation

Pipe inlet Null concentration value

Miners inlet Fixed concentration value

Mine outlet Null concentration gradient value

Mine walls

Null concentration gradient value

Miners

Null concentration gradient value

During the second simulation step, only the CO 2 transport equation is solved based on the fixed flow field from the first simulation. The stationary flow field does not take into account the inherent oscillations of large eddies but provides an average solution allowing to calculate the CO 2 dispersion.

First, we simulate the air flow and the coupled heat transfers of mixed convection, coupling phenomena of natural convection and forced convection. The simulation is stationary, that is to say that the iterative calculation converges towards a stable solution over time. From this solution, we can then extract and analyze the flow structure and the heat transfers at work in the mine.

To achieve a steady flow field, 20,000 iterations are performed. The calculation is parallelized over the 12 threads (6 cores) of an Intel Core i7-6800K processor and lasts around 13.5 hours.

Velocities of the natural convection flow

Heat produced by miners at work causes the air around them to heat up. The difference in density between the hot air around the miners and the cold air in the rest of the stope causes an upward flow of air by natural convection. Numerical simulation makes it possible to estimate the velocity of this flow at any point in the calculation domain. The velocity of the upward flow of natural convection is around 0.7 m/s in the absence of scaffolding, as shown on figure 7. The velocity is slightly lower when there is scaffolding because it constrains the upward flow.

Heat transfers and validation of the natural convection flow

When considering natural convection, the air flow and heat transfers are strongly coupled. The temperature then provides a criterion for validating the resolution of the flow in comparison with theoretical calculations. Under ideal natural convection conditions (an object heating up in an infinite space filled with an ideal gas), it is possible to estimate the ascending flow velocity from the temperature and the geometry of the object [START_REF] Lismonde | Aérologie des systèmes karstiques[END_REF].

Based on these considerations, we have the following equation:

V ≈ √ g L Δ T
T with g : gravity acceleration L : object height ΔT/T : relative difference of temperature between surrounding and the object By reversing this relationship, the average temperature of the heating object can be estimated from the velocity of the flow. Here the velocity of the upward flow is 0.7 m/s, which corresponds to an average miner surface temperature of 20 °C. Figure 8 shows that the average surface temperature of the miners, computed by the simulation, is around 24 °C without scaffolding and around 29 °C with scaffolding. These temperatures are higher than the estimate of 20 °C valid for ideal natural convection. The walls of the stope and the scaffolding limit the development of natural convection cells and reduce the flow velocity for a given temperature gradient. Nevertheless, the simulation results are still quite close to the theoretical estimates.

Flow structure

Due to the natural convection, the spreading of the CO 2 exhaled by the miners depends on the velocity of the flow, but also on its structure. A linear air flow in a pipe leads to the transport of matter in a direction whereas a rotational flow can translate an exchange of momentum without exchange of matter. To analyze the structure of a flow, it is useful to represent the velocity field on a logarithmic scale. In order to compare the flow from one case to another, a similar scale is used for all simulations and the corresponding figures 9, 10, 11 and 12. In short, the addition of ventilation does little to disrupt the flow structure in the stope but establishes a flow continuity between the eddies from the site to the exit of the gallery. This phenomenon is verified with and without the scaffolding.

Simulations of CO 2 concentration

Simulations of the CO 2 concentration are non-stationary simulations. The aim here is to simulate CO 2 spreading in the mine over 24 hours. The velocity fields from previous simulations serve as "matrices" for propagation by advection or diffusion.

The time-step of the simulation is set to 10 s which means that 8,640 time-steps are solved. The calculation, equally parallelized over the 12 threads (6 cores) of an Intel Core I7-6800K processor lasts around 2.5 hours.

Geometry, mesh and boundary conditions

The geometries and meshes used are the same as for the previous simulations. Specific boundary conditions define the CO 2 concentration of the flows entering the computational domain. Air exhaled by miners has a CO 2 concentration of 5 % while the air from the ventilation duct has a CO 2 concentration equal to zero.

CO 2 concentration

The CO 2 flow rate is the product of CO 2 concentration and air flow rates exhaled by miners, i.e. 0.0625 l/s for the five miners. After 24 hours, 5.4 m³ of CO 2 entered the 456 m³ volume of the underground model. This corresponds to a theoretical maximum average concentration of 1.18 %. During the simulation, the average concentration of CO 2 is calculated at all times. One can then plot the evolution of this concentration as a function of time, as shown on figure 13 for all four calculated cases. Figure 13 shows the evolution of the average CO 2 concentration over time. In case 1, without scaffolding or forced ventilation, the average CO 2 concentration in the mine reaches 1 % after 24 h, which is very close to the theoretical maximum average concentration calculated above. The constant increase in concentration confirms that only a tiny part of the exhaled CO 2 escapes from the mining site through the gallery. The addition of the scaffolding in the stope for case 3 slightly improves the evacuation of CO 2 but the average concentration remains high and is still increasing after 24 h. The forced ventilation in cases 2 and 4 slows the increase in average concentration which also seems to stabilize.

The CO 2 concentration fields displayed in figure 14 are very homogeneous in the absence of scaffolding since the natural convection causes the mixing of air. However, the average concentration is much higher in case 1 than in case 2 (which includes forced ventilation). In case 1, the spreading of CO 2 relies only on diffusion, while in case 2 convection of CO 2 occurs thanks to the forced ventilation.

In case 1 and 3, flow velocity in the gallery is very low which hinders the evacuation of CO 2 . In case 3, the scaffolding prevents advection by multiplying the number of convection cells and finally causes the stagnation of CO 2 in the lower part of the stope. The CO 2 concentration approaches 2 % on some floors, a local concentration much higher than the average concentration of CO 2 in the whole mine.

Discussion

The concentration of CO 2 in the air is considered dangerous from 1 % up, with a risk of respiratory acidosis [START_REF] Anses | Concentrations de CO 2 dans l'air intérieur et effets sur la santé[END_REF]. The results of the simulations establish that such a concentration average is reached over the entire underground in 24 hours. Analysis of the structure of the flow shows that in the absence of ventilation, there is little exchange of matter between flow eddies and the rest of the air. Natural convection alone does not permit air renewal and keeps stale air confined in the stope.

Stagnation would also cause the accumulation of CO 2 day by day within the underground extraction site. By imagining a two eights work day [START_REF] Agricola | De Re Metallica[END_REF][START_REF] Degermann | Réglement sur les mines du 22 juillet 1527 (Sainte-Marie-aux-Mines)[END_REF], the CO 2 concentration can be extrapolated after one day and a half and is then equivalent to the CO 2 concentration at the end of the simulations for cases 1 and 3.

On the other hand, ventilation ensures a good evacuation of CO 2 , as shown by the analysis of the structure of the flow. The CO 2 is no longer trapped in the convection cells but also spreads by advection from one eddy to another, from the stope to the exit of the gallery. The average concentration of CO 2 stabilizes and capped to a sustainable level.

Regarding the organization of underground works, the results of numerical simulations show that scaffolding and forced ventilation are a valid solution to breathability problems in stopes that do not have two accesses located at different altitudes. It must be said that the scaffolding's first aim is not to enhance ventilation, and it can be noted that the CO 2 rate is low enough in case 2 to enable the miners' work. In any case, scaffolding is usually required to work within a stope. Forced ventilation is needed all the more, and scaffolding must be considered a part of the ventilation system.

The excavation of the Giro mine thus sheds light on the use of forced ventilation thanks to the duct remains found between the entrance and the deep stope, originally used to convey air. These remains are the only evidence for the potential existence of such a system. The traces left by this equipment are usually scarce or lacking. The presence of scaffolding, of which main purpose is to ease both circulation and access of miners in a stope, does not necessarily attest to a ventilation system on its own.

So far archaeologists have not really considered the hypothesis of forced air circulation, let alone its implementation in remote stopes. This can be explained by the numerous traces of false ceiling and ventilation shafts that have been observed, e.g. in Sainte-Marie-aux-Mines. The morphology of a mine is in constant evolution until its abandonment. In many cases, ventilation systems are dropped once a gallery exits at another altitude. Hence, the good conservation of remains of forced ventilation facilities that are no longer necessary during the main exploitation period of the mine is unlikely. In any case, reflections about ventilation must be based on the underground galleries and stopes morphology and their evolution. Unfortunately, the parts of any ancient mine that were most typically concerned by a need of fresh air supply and could provide more evidence of forced ventilation system are under the valley level, and thus flooded.

Conclusion

Numerical simulations show that the CO 2 production of five miners at work can quickly render the air unbreathable in the stope of a mine such as Giro mine. The natural convection produced by the heat dissipation of the miners does not allow the CO 2 to be evacuated. An outdoor ventilation system seems required. A wooden pipe with a diameter corresponding to the metal fitting found during the excavations of the gallery, supplied by a double bellow system, allows sufficient ventilation of the work area. The setting up of scaffolding in the stope facilitates the movement of miners and promotes ventilation.

Numerical simulations of the air flow in the mine gallery and the propagation of the resulting CO 2 provide quantitative elements to assess the quality of the gallery ventilation relative to several hypotheses. This validates technical assumptions derived from archaeological data. In the case of Giro mine, numerical simulation replaces conventional experimentation that is not feasible in the context of experimental archaeology.

Figure 1 :

 1 Figure 1: Projected horizontal plan of a part of the level 610 of the Giro mine, showing the location of duct remains and the ways to the lower stope.

Figure 2 :

 2 Figure 2: (a) De Re Metallica (1556), book 6, fig. 178. The metallic fitting can be seen down left; (b) One of the iron fitting found in the Giro mine; (c) Reconstruction of the fitting connecting two sections of the wooden pipe.

Figure 3 :

 3 Figure 3: De Re Metallica (1556), book 6, fig. 209. The ventilation system consists of one gear located at the mine's entrance connected to a conduct set on the floor and entering the gallery.

Figure 4 :

 4 Figure 4: General view of the computational domain. The domain features a gallery and a stope. Five miners are modeled at the bottom of the stope and are numbered from 1 to 5 along ascending x axis.

Figure 5 :

 5 Figure 5: Symmetry plane of the computational domain including scaffolding. The height between scaffolding floors is 3 m and the width of traffic spaces at the scaffolding ends is 1.5 m. Five miners are placed randomly and numbered from 1 to 5 along the circuit formed by the scaffolding, from bottom to top.

Figure 6 :

 6 Figure 6: Views of the mesh in the symmetry plane of the domain. The mesh is refined around the miners and on the mine walls to correctly predict the convection heat transfers.

Figure 7 :

 7 Figure 7: Velocity field in the symmetry plane of the computational domain. The maximum velocity of the natural convection flow is below 1 m/s while the air flow velocity at the pipe exit is close to 4 m/s. The ventilation flow rate is small compared to the natural convection and does not seem to disturb the flow pattern much. The scaffolding constrains the development of natural convection.

Figure 8 :

 8 Figure 8: Miners' average surface temperatures. Without scaffolding, it appears that miner 3, in the middle, dissipates heat less efficiently. The scaffolding constrains natural convection and stabilizes temperatures. In this case, miner 5 dissipates heat better because the flow has more space above him.

Figure 9 :

 9 Figure 9: Velocity field (log scale) in the symmetry plane for case 1; zoom on velocity vectors. The natural convection creates two main convection cells in the stope. Two secondary elongate eddies appear in the decline and the gallery, showing much lower velocities. The velocity vectors indicated in red highlight the rotational structure of the flow in the gallery. The velocity vectors indicated in blue show the flow discontinuity between two secondary eddies.

Figure 10 :

 10 Figure 10: Velocity field (log scale) in the symmetry plane for case 2; zoom on velocity vectors. The forced ventilation does not disturb the main convection cells much. However, the eddy in the gallery is disturbed by an outflow (red). A flow continuity is established between two secondary eddies (blue).

Figure 11 :

 11 Figure 11: Velocity field (log scale) in the symmetry plane for case 3; zoom on velocity vectors. Natural convection cells develop on each floor with a miner. Again the vector field indicated in blue shows mostly momentum exchanges between eddies. The flow velocity is very small in the gallery (red) which makes it difficult to properly solve the flow field.

Figure 12 :

 12 Figure 12: Velocity field (log scale) in the symmetry plane for case 4; zoom on velocity vectors. The forced ventilation does not disturb the convection cells around miners much. However, a flow continuity is established between two secondary eddies (blue). A fully developed outflow is established in the gallery (red).

Figure 13 :

 13 Figure 13: Average CO2 concentration in the mine. Without forced ventilation, the average CO2 concentration is close to 1 % after a 24 h work shift of the five miners. The forced ventilation stabilizes the CO 2 concentration in the mine below 0.5 %. The stabilization is reached faster in case 4, with scaffolding.

Figure 14 :

 14 Figure 14: CO2 concentration field on the symmetry plane of the domain, after 24 h. The CO2 concentration field is uniform without scaffolding whereas stagnation appears with scaffolding in case 3. The forced ventilation decreases the CO2 concentration inside the mine after 24 h.

Table 1 : The mesh features

 1

Acknowledgments

We sincerely thank the Association Spéléologique pour l'Etude et la Protection des Anciennes Mines (ASEPAM) in Sainte-Marie-aux-Mines, the owners of the mine Brigitta Wolf and Roger Zenner, and the Giro mine excavation team, especially Antonin Hergault, Margaux Herbrich and Paul Winterhalter.

We are grateful to Pauline Florsch for the numerous improvements of the English.

We would like to thank the two reviewers who were of great help in improving the paper.

Funding

ERDF (European Regional Development Funds): Interreg Regio Mineralia DRAC Grand Est (French Ministère de la Culture)