Franc ¸ois Simon
email: fsimon05@gmail.com.

Mathieu Beraneck

Interpreting pendred syndrome as a foetal hydrops: Clinical and animal model evidence

Keywords: Menière, pendred, DFNB4, hydrops, mouse

BACKGROUND: Menière disease (MD) and SLC26A4 related deafness (Pendred syndrome (PS) or DFNB4) are two different inner ear disorders which present with fluctuating and progressive hearing loss, which could be a direct consequence of endolymphatic hydrops. OBJECTIVE: To present similarities between both pathologies and explore how the concept of hydrops may be applied to PS/DFNB4. METHODS: Review of the literature on MD, PS/DFNB4 and mouse model of PS/DFNB4. RESULTS: MD and PS/DFNB4 share a number of similarities such as fluctuating and progressive hearing loss, acute episodes with vertigo and tinnitus, MRI and histological evidence of endolymphatic hydrops (although with different underlying mechanisms). MD is usually diagnosed during the fourth decade of life whereas PS/DFNB4 is congenital. The PS/DFNB4 mouse models have shown that biallelic slc26a4 mutations lead to Na + and water retention in the endolymph during the perinatal period, which in turn induces degeneration of the stria vascularis and hearing loss. Crossing clinical/imagery characteristics and animal models, evidence seems to support the hypothesis of PS being a foetal hydrops. CONCLUSIONS: When understanding PS/DFNB4 as a developmental hydrops, treatments used in MD could be repositioned to PS.

Introduction

Menière's disease (MD) and endolymphatic hydrops are both very frequently discussed topics in the literature, although the underlying mechanisms are still poorly understood. First described in 1938 by Hallpike and Cairns [START_REF] Hallpike | Observations on the pathology of Meniere's syndrome[END_REF], endolymphatic hydrops corresponds to a dilated endolymphatic sector within the inner ear, and is considered as a histological basis for MD although it has also been found in other inner ear diseases. In addition, it is still debated whether endolymphatic hydrops is a cause or consequence of MD. Genetics seem to play a role in some sporadic and familial cases but are of a complex and polygenic nature [START_REF] Gallego-Martinez | Genetic architecture of Meniere's disease[END_REF].

SLC26A4 mutations are the cause of two autosomal recessive diseases, which share the same audiometric phenotype of progressive and fluctuating hearing loss (HL): Pendred syndrome (PS), a rare ISSN 0957-4271/$35.00 © 2021 -IOS Press. All rights reserved. syndrome deafness associated with thyroid disorders and DFNB4, an isolated deafness (SLC26A4 related deafness hereinafter referred to as PS/DFNB4).

Recent studies on a mouse model of PS/DFNB4 have shown evidence of endolymphatic hydrops which could draw parallels with the better-known hydrops described in MD patients. Both MD and PS/DFNB4 correspond to internationally defined entities, yet may easily be confused with other types of fluctuating HL of idiopathic origin. Thus, for the sake of clarity, this paper will only discuss clinical presentations of definite MD (as defined by the American Academy of Otolaryngology-Head and Neck Surgery) and PS/DFNB4 with confirmed biallelic SLC26A4 mutations. The objective of this paper is to present similarities between both entities and explore how the concept of hydrops may be applied to PS/DFNB4.

Menière versus Pendred, similarities and differences

MD and PS/DFNB4 are two different inner ear disorders, which share a number of similarities and differences as reported in Table 1.

MD, first described by Prosper Menière in 1861, is the typical clinical example of hydrops. It has a very strict clinical definition, which was recently updated in 2015 [START_REF] Goebel | Equilibrium Committee Amendment to the 1995 AAO-HNS Guidelines for the Definition of Ménière's Disease[END_REF]. Briefly, a patient must present with two or more spontaneous episodes of vertigo, ranging from 20 minutes to 12 hours long, with low to medium frequency sensorineural HL and aural symptoms (tinnitus or aural fullness), which cannot be accounted for by any other vestibular diagnosis. Symptoms which do not exactly correspond to this definition may be linked to endolymphatic hydrops and be considered as probable or possible MD. MD may have very different presentations from one patient to the other, but the key aspect is the fluctuating and progressive HL which spans out over several years. Over time, the HL worsens at all tested frequencies and becomes constant, usually stabilizing between 50 and 70 dB. Symptoms are usually unilateral, but up to half of patients present with bilateral symptoms, and the majority have bilateral electrophysiological or imagery anomalies (regardless of the contralateral ear being symptomatic or not) [START_REF] Huang | Bilateral Meniere's disease assessed by an inner ear test battery[END_REF][START_REF] Morimoto | Endolymphatic hydrops in patients with unilateral and bilateral Meniere's disease[END_REF]. This is an adult's disease, with most cases diagnosed in the fourth or fifth decade of life. Juvenile MD has been described in case reports in the literature, but remains extremely rare and linked to family history of MD [START_REF] Wang | Pediatric Meniere's disease[END_REF]. The most frequent diagnosis in the child is vestibular migraine [START_REF] Wiener-Vacher | Epidemiology of Vestibular Impairments in a Pediatric Population[END_REF], but the clinical symptoms also resemble the rarer PS/DFNB4.

Vaughan Pendred first described Pendred syndrome in 1896, reporting an Irish family with congenital deafness and thyroid goitre. The disease has since then been linked to the SLC26A4 (or PDS) gene which codes for the pendrin protein (Na + independent Cl -/Iodine/HCO3 -exchanger) [START_REF] Everett | Pendred syndrome is caused by mutations in a putative sulphate transporter gene (PDS)[END_REF]. Biallelic recessive mutation can cause DNFB4 isolated deafness or the Pendred syndrome when associated to a goitre (10-20% of cases) and is estimated to be responsible for 5-15% of congenital HL [START_REF] Aimoni | Enlarged vestibular aqueduct: Audiological and genetical features in children and adolescents[END_REF][START_REF] Albert | SLC26A4 gene is frequently involved in nonsyndromic hearing impairment with enlarged vestibular aqueduct in Caucasian populations[END_REF][START_REF] Fang | GJB2 as Well as SLC26A4 Gene Mutations are Prominent Causes for Congenital Deafness[END_REF][START_REF] Li | A mutation in PDS causes non-syndromic recessive deafness[END_REF][START_REF] Miyagawa | Mutation spectrum and genotype-phenotype correlation of hearing loss patients caused by SLC26A4 mutations in the Japanese: a large cohort study[END_REF][START_REF] Suzuki | Clinical characteristics and genotype-phenotype correlation of hearing loss patients with SLC26A4 mutations[END_REF]. The prevalence of SLC26A4 mutations is higher in China (carry rate 2.02% I la population of 2627 new-borns) [START_REF] Fang | GJB2 as Well as SLC26A4 Gene Mutations are Prominent Causes for Congenital Deafness[END_REF]. Clinically, the same triad can be found as in MD, with episodes of fluctuating HL (although not specifically low to medium frequencies), vertigo and tinnitus. An auditory bonegap can be found in low frequencies, probably due to a third-window effect, but may as in some MD patients be due to decreased stapes mobility entailed by excessive endolymphatic pressure [START_REF] Seo | Correlation of vestibular aqueduct size with air-bone gap in enlarged vestibular aqueduct syndrome[END_REF][START_REF] Sugimoto | The relationship between endolymphatic hydrops in the vestibule and low-frequency air-bone gaps[END_REF][START_REF] Zhou | Characteristics of vestibular evoked myogenic potentials in children with enlarged vestibular aqueduct[END_REF]. Symptoms vary from one patient to another, with unilateral or bilateral HL, and severity at birth ranging from cophosis to normal hearing. HL is however prelingual and progressive in the majority of cases (50-60% and 70-90% respectively) [START_REF] Miyagawa | Mutation spectrum and genotype-phenotype correlation of hearing loss patients caused by SLC26A4 mutations in the Japanese: a large cohort study[END_REF][START_REF] Van Nierop | Patients with Pendred syndrome: is cochlear implantation beneficial?[END_REF][START_REF] Okamoto | Subgroups of enlarged vestibular aqueduct in relation to SLC26A4 mutations and hearing loss[END_REF][START_REF] Suzuki | Clinical characteristics and genotype-phenotype correlation of hearing loss patients with SLC26A4 mutations[END_REF].

Concerning imagery, both vestibular disorders show signs of increased endolymphatic volume, although the aspect and mechanism are quite different. In MD, CT-scan is normal, MRI can show endolymphatic hydrops concerning both cochlear and vestibular sectors (see Fig. 1), however saccular hydrops seems to be one of the most reproducible markers [START_REF] Attyé | MRI of endolymphatic hydrops in patients with Meniere's disease: A case-controlled study with a simplified classification based on saccular morphology[END_REF][START_REF] Attyé | In vivo imaging of saccular hydrops in humans reflects sensorineural hearing loss rather than Meniere's disease symptoms[END_REF][START_REF] Lopez-Escamez | Systematic review of magnetic resonance imaging for diagnosis of Meniere disease[END_REF][START_REF] Simon | Saccular measurements in routine MRI can predict hydrops in Meniere's disease[END_REF][START_REF] Venkatasamy | Imaging of the saccule for the diagnosis of endolymphatic hydrops in Meniere disease, using a three-dimensional T2-weighted steady state free precession sequence: accurate, fast, and without contrast material intravenous injection[END_REF]. In PS/DFNB4, bilateral enlarged vestibular aqueduct (EVA), containing endolymph, is a constant feature in patients with biallelic mutations and may sometimes be associated with cochlear incomplete partition type II (Mondini dysplasia), as shown in Fig. 2. Both malformations can also be diagnosed on a CT-scan or MRI and are often indicators of PS/DFNB4 that usually precede genetic confirmation.

Vestibular function in MD is remarkable as there is, in most cases, a dissociation between caloric tests and vHIT [START_REF] Van Esch | Video-head impulse test results in patients with Menière's disease related to duration and stage of disease[END_REF][START_REF] Hannigan | Dissociation of caloric and head impulse tests: a marker of Meniere's disease[END_REF][START_REF] Rubin | Comparison of Video Head Impulse Test and Caloric Reflex Test in advanced unilateral definite Menière's disease[END_REF]. This is probably due to the fact that while endolymphatic hydrops distorts the volume of the lateral semi-circular canal, thus inducing caloric hyporeflexia, the semi-circular canals still respond normally to high speed physiological stimulation. In the later stages of MD, the proportion of normal canal function (vHIT) and otolith function (cVEMP and oVEMP) decrease [START_REF] Chen | Evaluation of the otolith function using c/oVEMPs in patients with Ménière's disease[END_REF][START_REF] Van Esch | Video-head impulse test results in patients with Menière's disease related to duration and stage of disease[END_REF][START_REF] Okumura | Assessment of endolymphatic hydrops and otolith function in patients with Meniere's disease[END_REF]. Literature on the vestibular function in PS/DFNB4 is to date very poor due to its rarity, one study reporting canal paresis in 49% using caloric test [START_REF] Jung | Vestibular function is associated with residual low-frequency hearing loss in patients with bi-allelic mutations in the SLC26A4 gene[END_REF]. Studies on EVA series (including PS/DFNB4 patients but not specific to SLC26A4 mutations) report abnormally low cVEMP (at 250 and 500 Hz) thresholds and high amplitudes probably due to a third-window effect [START_REF] Yang | Vestibular pathology in children with enlarged vestibular aqueduct[END_REF][START_REF] Zalewski | Vestibular Dysfunction in Patients with Enlarged Vestibular Aqueduct[END_REF][START_REF] Zhou | Characteristics of vestibular evoked myogenic potentials in children with enlarged vestibular aqueduct[END_REF].

Molecular genetics

Although PS/DFNB4 is mainly linked to the biallelic SLC26A4 mutations, digenic mutations have been reported involving FOX11 or KCNJ10 genes [START_REF] Lin | Targeted Next-Generation Sequencing Facilitates Genetic Diagnosis and Provides Novel Pathogenetic Insights into Deafness with Enlarged Vestibular Aqueduct[END_REF]. Molecular genetics in MD, however, are less well understood. The rarer familial form (6 to 9% of MD cases) is a monogenic disorder and most families have an autosomal dominant inheritance with incomplete penetrance and variable expressivity [START_REF] Martín-Sierra | Variable expressivity and genetic heterogeneity involving DPT and SEMA3D genes in autosomal dominant famil-ial Meniere's disease[END_REF][START_REF] Skarp | Whole-exome sequencing suggests multiallelic inheritance for childhood-onset Ménière's disease[END_REF].

Compound heterozygous mutations in OTOG gene have been reported in several unrelated families with MD, suggesting a recessive inheritance pattern [START_REF] Roman-Naranjo | Burden of Rare Variants in the OTOG Gene in Familial Meniere's Disease[END_REF]. The majority of MD patients have a sporadic form, not clearly linked to any specific genetic disorders. Interestingly, sporadic MD does seem to be a polygenic condition and several sensorineural HL genes, including some hypomorphic alleles in SLC26A4, may contribute to the MD phenotype in sporadic cases [START_REF] Azaiez | Genomic Landscape and Mutational Signatures of Deafness-Associated Genes[END_REF][START_REF] Gallego-Martinez | Excess of Rare Missense Variants in Hearing Loss Genes in Sporadic Meniere Disease[END_REF][START_REF] Gallego-Martinez | Enrichment of damaging missense variants in genes related with axonal guidance signalling in sporadic Meniere's disease[END_REF].

Animal models

Lacking any unique genetic background or universally accepted histopathological hypothesis, it has been difficult to develop a specific animal model of MD [START_REF] Gallego-Martinez | Genetic architecture of Meniere's disease[END_REF]. A large number of models have been developed to try and mimic endolymphatic hydrops and fluctuating HL, usually requiring surgical endolymphatic sac destruction (to reduce endolymphatic resorption) or administration of medication to increase endolymphatic production (such as aldosterone) [START_REF] Dunnebier | Twophase endolymphatic hydrops: a new dynamic guinea pig model[END_REF][START_REF] Ferrary | Mechanisms of endolymph secretion[END_REF][START_REF] Horner | Auditory and vestibular function in experimental hydrops[END_REF][START_REF] Kimura | Membranous hydrops in the inner ear of the guinea pig after obliteration of the endolymphatic sac[END_REF]. These models rely on artificial disruption of the endolymphatic homeostasis. PS/DFNB4, on the other hand, has been clearly linked to a biallelic mutation of the SCL26A4 gene, and mouse models specific of this disease have been recently developed to understand underlying mechanisms.

It is first important to specify that in the mouse, development of the inner ear occurs throughout the perinatal period, starting at E9 (embryo day 9) with the otic placode and ending with a final adult structure at P20 (20 days after birth), whereas the human inner ear formation exclusively takes place during the foetal life ranging from 23 days to 8 months, respectively [START_REF] Gorlin | Hereditary hearing loss and its syndromes[END_REF]. More precisely, key steps in mouse inner ear development are as follows: opening of endolymphatic sac lumen at E10.5; opening of cochlear lumen at E14.5; utricule and saccule are formed by E17; neuronal elements continue to develop during a period of differentiation and speciation from E17 to P7; mature endolymph produced at P3; endolymphatic potential matures from P7 to P15; with the onset of auditory function generally at P12; as well as the functional maturation of the vestibulo-ocular reflex which occurs after the opening of the eye at P12 [START_REF] Beraneck | Functional development of the vestibular system: Sensorimotor pathways for stabilization of gaze and posture[END_REF][START_REF] Gorlin | Hereditary hearing loss and its syndromes[END_REF][START_REF] Wangemann | The role of pendrin in the development of the murine inner ear[END_REF][START_REF] Wangemann | Loss of KCNJ10 protein expression abolishes endocochlear potential and causes deafness in Pendred syndrome mouse model[END_REF].

The first slc26a4 mouse biallelic knock-out model was developed in 1999 but showed a more severe phenotype than in humans, with congenital complete bilateral deafness and vestibular deficit behaviour. Pendrin expression was first detected at E13 in the duct and sac, and then at E15 in the utricule, saccule and cochlea. Enlarged endolymphatic space was demonstrated at E15 with secondary cochlea hair cell and macula destruction from P7 to P45 [START_REF] Everett | Targeted disruption of mouse Pds provides insight about the inner-ear defects encountered in Pendred syndrome[END_REF][START_REF] Everett | Expression pattern of the mouse ortholog of the Pendred's syndrome gene (Pds) suggests a key role for pendrin in the inner ear[END_REF][START_REF] Royaux | Localization and functional studies of pendrin in the mouse inner ear provide insight about the etiology of deafness in pendred syndrome[END_REF]. Further studies reported that pendrin in itself was not essential for hearing but defective pendrin caused HL via secondary mechanisms such as the degeneration, oxidative stress and macrophagic invasion of the stria vascularis [START_REF] Jabba | Macrophage invasion contributes to degeneration of stria vascularis in Pendred syndrome mouse model[END_REF][START_REF] Royaux | Localization and functional studies of pendrin in the mouse inner ear provide insight about the etiology of deafness in pendred syndrome[END_REF][START_REF] Wangemann | Loss of KCNJ10 protein expression abolishes endocochlear potential and causes deafness in Pendred syndrome mouse model[END_REF]. Pendrin was demonstrated to be key in the endolymphatic homeostasis: lack of the Cl -/HCO3 -exchanger pendrin would decrease the endolymphatic pH as soon as E15.5 and thereby increase Ca 2+ and Na + retention (by reducing the current that drives Na + reabsorption through Na + channels in the endolymphatic sac) [START_REF] Kim | Failure of fluid absorption in the endolymphatic sac initiates cochlear enlargement that leads to deafness in mice lacking pendrin expression[END_REF][START_REF] Kim | Epithelial cell stretching and luminal acidification lead to a retarded development of stria vascularis and deafness in mice lacking pendrin[END_REF][START_REF] Li | SLC26A4 targeted to the endolymphatic sac rescues hearing and balance in Slc26a4 mutant mice[END_REF]. Increased Na + endolymphatic concentration would in turn induce reduced endolymphatic potential and retain water creating endolymphatic hydrops. Finally, the mechanical effect of endolymphatic hydrops and increased cellular stress would entail cochlea stria vascularis degeneration around P10 (no data available for the vestibular system) [START_REF] Singh | Free radical stress-mediated loss of Kcnj10 protein expression in stria vascularis contributes to deafness in Pendred syndrome mouse model[END_REF][START_REF] Wangemann | The role of pendrin in the development of the murine inner ear[END_REF]. Other mice models have been developed with similar results, also showing a decreased amount of otoconia and giant or ectopic otoconia probably due to the altered endolymphatic calcium homeostasis [START_REF] Dror | The Slc26a4 loop Mouse Model for Pendred's Syndrome and Nonsyndromic Deafness[END_REF][START_REF] Dror | Calcium oxalate stone formation in the inner ear as a result of an Slc26a4 mutation[END_REF][START_REF] Lu | Establishment of a knock-in mouse model with the SLC26A4 c.919-2A>G mutation and characterization of its pathology[END_REF]. Histological exploration and imagery of these mice models clearly showed endolymphatic hydrops.

Studies of the pendrin action timeframe were conducted on a dox-dependent mouse knock-out model, developed in 2011 [START_REF] Choi | Mouse model of enlarged vestibular aqueducts defines temporal requirement of Slc26a4 expression for hearing acquisition[END_REF]. It was shown that absence of expression slc26a4 expression (no pendrin) before E16.5 or after P2 did not alter auditory brainstem responses (ABR) in these mice. However, absence of slc26a4 expression between E16.5 and E18.5 led to a decreased endolymphatic potential and pH, although with normal ABR. Finally, absence of slc26a4 expression between E18.5 and P2 entailed a more severe state with abnormal ABR [START_REF] Choi | Mouse model of enlarged vestibular aqueducts defines temporal requirement of Slc26a4 expression for hearing acquisition[END_REF]. From these results, a model reproducing the human cochleavestibular phenotype of PS/DFNB4 was developed, with slc26a4 expression deactivated from E17.5 to P2, leading to fluctuating abnormal ABR and a progressive hearing loss at 6 months (vestibular function was not assessed) [START_REF] Ito | Slc26a4-insufficiency causes fluctuating hearing loss and stria vascularis dysfunction[END_REF]. From this model, hypothesis was drawn that the pendrin expression in the endolymphatic sac would be necessary in the mouse to allow acquisition of normal hearing in the perinatal period [START_REF] Ito | Progressive irreversible hearing loss is caused by stria vascularis degeneration in an Slc26a4-insufficient mouse model of large vestibular aqueduct syndrome[END_REF][START_REF] Nishio | Slc26a4 expression prevents fluctuation of hearing in a mouse model of large vestibular aqueduct syndrome[END_REF].

A foetal hydrops

PS/DFNB4 in the mouse model seems to be secondary to modification of endolymphatic fluid absorption in the developing inner ear. Although the exact molecular mechanisms may differ in human PS/DFNB4, the process is probably comparable. The timing of these events in the human inner ear is unknown, but by comparing the timetable of mouse and human ear development, we may suppose they could take place during the human foetal and early postnatal life, with the most sensitive moment (corresponding to the mouse perinatal period) taking place in a 3 to 4-month-old foetus, well before birth [START_REF] Gorlin | Hereditary hearing loss and its syndromes[END_REF]. Although gene therapy seems promising [START_REF] Choi | DNAJC14 ameliorates inner ear degeneration in the DFNB4 mouse model[END_REF][START_REF] Kim | Gene therapy for hereditary hearing loss by SLC26A4 mutations in mice reveals distinct functional roles of pendrin in normal hearing[END_REF], this timing causes great difficulties, first in terms of diagnostic opportunities, and then of treatment strategies.

Crossing results from the animal model with children's imagery, we could hypothesise that foetal endolymphatic hydrops, may induce inner ear bulging before cranial ossification occurs, thus rendering the cochleo-vestibular malformations visible on the CTscan at birth. This foetal hydrops may be already advanced at birth, with congenital bilateral cophosis, in which case management would have to rely (as it does today) on auditory rehabilitation such as cochlear implant. In the cases where congenital hydrops is associated with residual to normal hearing, specific treatment, yet to be developed, may become key: on one hand, gene therapy or inner ear medication (research on animal models) and on the other hand, repositioning of established hydrops treatment (currently used in MD) to treat fluctuating episodes.

Conclusion

-MD and PS/DFNB4 are two different inner ear disorders linked to endolymphatic hydrops. -MD is more common and its literature abundant whereas PS/DFNB4 remains poorly described, especially its vestibular characteristics. -The main common feature is fluctuating and progressive HL. -PS/DFNB4 mouse models have helped identify the role of pendrin and how biallelic slc26a4 mutation lead to Na + and water retention in the endolymph. -Parallels may be drawn between mechanisms highlighted in the mouse PS/DFNB4 model and physiopathological hypothesis in MD.

-Mutations in sensorineural HL genes, including SLC26A4, may contribute to MD phenotype. -PS/DFNB4 could be understood as a developmental hydrops and thus, benefit from MD knowledge and therapies

Fig. 1 .

 1 Fig. 1. MRI of hydrops in Menière disease. MRI 3D-FLAIR sequence 4h after intravenous gadolinium injection. Imagery of a patient with right Menière disease. The MRI shows endolymphatic hydrops of vestibular and cochlear sectors in the right ear (and normal left ear). In the inner ear, the perilymph appears in hypersignal and endolymph in hyposignal. A: arrow shows utricular hydrops. B: left-to-right arrow shows cochlear hydrops; right-to-left arrow shows saccular hydrops. Curtesy from Michael Eliezer (Lariboisière Hospital, APHP, Paris, France).

Fig. 2 .

 2 Fig. 2. CT-scan and MRI of hydrops in Pendred syndrome. Imagery of a patient with Pendred syndrome, with bilateral enlarged vestibular aqueduct (EVA), and cochlear incomplete partition type II (Mondini dysplasia). A: MRI T2 sequence, arrow shows the right EVA. B: CT-scan, arrow showing the right EVA with the large bony canal. C: CT-scan showing right Mondini dysplasia in the cochlea (only two turns).

Table 1

 1 Main differences and similarities between MD and PS/DFNB4

	Differences	Similarities
	-Typical age of onset (MD in 40s; PS prelingual)	-Fluctuating and progressive HL
	-Typical long-term HL severity (MD: moderate HL; PS: profound	-Acute HL episodes with vertigo and tinnitus
	to severe)	-Enlarged endolymphatic space on MRI
	-HL frequencies (MD: low-medium frequencies; PS: non-specific)	-Histological evidence of endolymphatic hydrops (cadaveric
	-CT-scan bony modifications (MD: normal; PS: EVA and Mondini)	studies in MD and mouse in PS)

EVA Enlarged vestibular aqueduct; HL Hearing Loss; MD Menière disease; PS Pendred Syndrome.

F. Simon et al. / Interpreting pendred syndrome as a foetal hydrops

Conflict of interest statement

The authors do not have any commercial or other association that might pose a conflict of interest. The authors did not have any financial support to write this paper.


Abigail Metcalfe
email: metcalfe@ipgp.fr

Séverine Moune

Jean-Christophe Komorowski

Geoff Kilgour

David E Jessop

Roberto Moretti

Yoann Legendre

Magmatic Processes at La Soufrière de Guadeloupe: Insights From Crystal Studies and Diffusion Timescales for Eruption Onset

Keywords: diffusion timescales, orthopyroxene, magma "mush", unrest, monitoring, eruption style, forecasting, La Soufrière de Guadeloupe

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

A Corrigendum on

Magmatic Processes at La Soufrière de Guadeloupe: Insights From Crystal Studies and Diffusion Timescales for Eruption Onset by Metcalfe, A., Moune, S., Komorowski, J.-C., Kilgour, G., Jessop, D. E., Moretti, R., and Legendre, Y. (2021). Front. Earth Sci. 9:617294. doi:10.3389/feart.2021.617294

In the original article, there was a mistake in Table 2 and in Figures 5, 9 and 10 as published. An error occurred in our calculations of the D 0 value, which was then propagated into the numerical routines used to perform our calculations. Calculations with the corrected D 0 value imply that the timescales of magmatic processes preceding eruptions of La Soufrière de Guadeloupe, shown in Table 2, and discussed in our original manuscript, are lower than previously estimated by a factor of ∼2. The corrected Table 2 andFigures 5 and9 Further errors were made in Figures 11, 12 and 13. The timescales are now corrected in the captions of the figures. The correct timescale values, now presented below, range from 18.8 to 361.0 days confirming that magmatic processes prior to eruption occur on short timescales at La Soufrière de Guadeloupe. Updated and corrected versions of our python scripts are available on GitHub: https://github.com/ djessop/mineral_diffusion_timescales. The corrected figures appear below.

A correction has been made to the Abstract, Paragraph 3: "We model the timescale populations as random processes whose probability distributions provide expected ("mean") timescales and the associated standard errors for each eruption. This provides a new statistical method for comparing magmatic timescales between disparate eruptions. From this, we obtain timescales of magma storage at La Soufrière de Guadeloupe ranging from 18.8 ± 0.37 days to 361 ± 0.40 days, with no clear distinction between eruption style/size and timescales observed. Based on these data, magmatic interaction timescales are a poor predictor of eruption style/size."

A correction has also been made to Section Results, Sub-section Timescale Modelling Results, Paragraphs 1-4:

"Diffusion timescales across the core-rim boundaries for the eruptions studied give a timescale range from <1 to 3,052 days (Table 2). Our method has investigated how the timescale populations are distributed, highlighting clear differences between eruptions, including variations in the maximum values, range of values and expected timescales.

The 5680 Cal. BCE Plinian eruption records short timescales with a range from <1 to 169 days and the expected (mean) timescale calculated as 22.8 ± 0.43 days (Figure 9). The ∼341 Cal. CE Strombolian eruption records a large range of timescales from <1 to 3,052 days. The modelled data yield an expected timescale value of 59.4 ± 0.40 days. This expected value is not comparable to any other eruption studied, though the range of values is comparable.

The 1010 Cal. CE Plinian eruption records the longest timescales from <1 to 2,462 days. These data have an expected timescale value of 361.0 ± 0.40 days, considerably higher than calculated for any other eruption (Figure 9). This eruption is considerably different to the 5680 Cal. BCE Plinian eruption, despite the expectation that these eruptions are comparable. This is a direct consequence of the characteristic crystal populations in the 1010 Cal. CE eruption which shows a large proportion of The crystal number refers to the number of crystals diffusion timescales were calculated on [*Mean timescale not expected timescale, calculated from available data Bourgeoisat ( 2018 Type-2 crystals with diffuse zoning, not present in the 5680 Cal. BCE eruption (Figure 8).

The 1657 Cal. CE Vulcanian eruption records the shortest range of timescales from <1 to of 84 days. The expected timescale was calculated as 18.8 ± 0.37 days, the shortest expected timescale value calculated for the eruptions studied (Figure 9). This expected value is comparable to the 5680 Cal. BCE expected value of 22.8 days, with most crystals for both these eruptions recording timescales in the range of 3 weeks."

A correction has been made to Section Discussion, Subsection How Do We Interpret the Diffusion Timescales, Paragraph 4:

"These processes are reflected in the gamma distribution, which describes all events that share the same properties (i.e., are generated by the same process) and models them as random processes. In this case, the gamma distribution is derived from the individual likelihood of all intrusion events across the eruption's crystal populations. The timescale distribution reflects an intrusion producing a mixing bowl where the crystals come into contact with the intrusion at different times, with the expected timescale being the typical value of the distribution. The expected timescale/typical distribution value shows the average time it took a crystal for a specific eruption to come into contact with the intrusion. Therefore, the gamma distribution allows the probability of a crystal experiencing an event at a given time to be estimated. In the case of La Soufrière de Guadeloupe, crystals have a smaller probability of recording a short delay time/longer timescale (on the order of a year; e.g., 1010 Cal. CE), and a larger probability of recording a longer delay time/shorter timescale (on the order of days; e.g., 1657 Cal. CE). This could relate to several parameters including: the intrusions interaction with the system, the composition of the system (including volatile content) and system geometry (crystals recording a longer delay time/shorter diffusion timescale farthest from the intrusion are more likely to be erupted than those closer to the system base which interact with the intrusion first)."

A correction has been made to Section Discussion, Subsection Which Mush System Processes are the Timescales Related To?, Paragraph 5:

"The ∼341 Cal. CE and 1010 Cal. BCE eruptions have similar maximum diffusion timescales but different expected timescales (Table 2). This indicates while intrusions may begin at similar times prior to an eruption, the diffusion timescale distribution and resulting expected timescales, suggest the intrusions interact differently with the system. A transition in conduit location to Echelle or the eruption of a monogenetic cone may result in different expected timescales of magmatic processes preceding FIGURE 11 | Schematic sketches of the mush lenses beneath La Soufrière de Guadeloupe and Echelle with representative crystals shown at approximate locations within the mush zone. (A) The La Soufrière de Guadeloupe mush system prior to eruption, this study suggests intrusions begin a between a minimum of 84 and 3,052 days prior to eruption. (B) In the case of 1657 Cal. CE and 5680 Cal. BCE eruptions, the expected value shows that the majority of the system could be affected by an intrusion 19 and 23 days prior to eruption, respectively. The intrusion moves through the system rapidly, in the case of the 5680 Cal. BCE eruption crystals are erupted from deep in the mush system which re-equilibrate during smaller intrusion events which do not destabilise the mush system. The 1657 Cal. CE eruption only samples simple crystals and unzoned crystals. (C) The ∼341 CE eruption expected value shows that the majority of the system could be affected by an intrusion 59 days before eruption. This intrusion has also moved relatively rapidly through the system and variation in intrusion location, results in destabilisation and eruption from the Echelle vent. Both complex and simple crystal populations are erupted. eruptions. In a shallow storage region, crystals interact with melt shortly before eruption and could explain the crystals recording short timescales observed, particularly in Echelle and in other monogenetic systems (Ruprecht et al., 2007;[START_REF] Johnson | Magmatic volatile contents and degassing-induced crystallization at Volcán Jorullo, Mexico: implications for melt evolution and the plumbing systems of monogenetic volcanoes[END_REF][START_REF] Denis | Evidence of dehydration in peridotites from Eifel Volcanic Field and estimates of the rate of magma ascent[END_REF][START_REF] Brenna | Olivine xenocryst diffusion reveals rapid monogenetic basaltic magma ascent following complex storage at Pupuke Maar, Auckland Volcanic Field, New Zealand[END_REF]Figure 11A,C)."

A correction has been made to Section Discussion, Subsection How Do the La Soufrière de Guadeloupe Timescales Fit Into a Global Context, Paragraph 3:

"Some systems show magmatic processes occurring on timescales comparable to La Soufrière de Guadeloupe, such as the 1912 eruption of Novarupta (Alaska), which shows similarly short diffusion timescales. A smaller range of timescales are calculated for this eruption, but the average value, 45 days, is comparable to the expected values calculated for the 1657 Cal. CE, ∼341 Cal. CE and 5680 Cal. CE eruptions [START_REF] Singer | The timing of compositionally-zoned magma reservoirs and mafic 'priming' weeks before the 1912 Novarupta-Katmai rhyolite eruption[END_REF]. Despite the similarities in the timescales, the Novarupta system is much larger and is more evolved than La Soufrière de Guadeloupe, limiting the comparability."

A correction has been made to Section Discussion, Subsection Can We Link Timescales to Unrest at La Soufrière de Guadeloupe?, Paragraph 4: "In the second scenario, long timescales on the order of a year (i.e., 1010 Cal. CE) suggest similar long unrest periods prior to the eruption could be observed. This unrest, recorded over months or years, may show a gradual increase in seismic activity and thermal anomalies, along with geochemical markers of the rising magma batch, peaking in a shallow degassing signature following its emplacement and the thermal (and chemical) exchange with the residing body. Behaviour corresponding to this scenario was observed prior to the May 2008 Bezymianny eruption, characterised by a decrease of CO 2 /H 2 O, S/HCl, CO 2 /S and CO 2 /HCl ratios (Lopez et al., 2013;[START_REF] Davydova | The timescales of magma mixing in the plumbing system of Bezymianny volcano (kamchatka): insights from diffusion chronometry[END_REF]."

Finally, a correction has been made to Section Conclusions: "By investigating a range of eruption styles, we provide an indepth analysis of the diffusion timescales of magmatic processes occurring at La Soufrière de Guadeloupe and provide new insights in the processes occurring in the mush system. The method constitutes a significant advance for the calculation of orthopyroxene diffusion timescales, eradicating biases induced by fitting the profiles by eye, and optimising data quality by using well-tested and robust numerical schemes and "goodness-of-fit" analyses. The six different crystal population distributions, found across the four various types of eruptions of La Soufrière de Guadeloupe, indicate different eruptions are fed by different mush system lenses, which have distinct histories. We found distinct timescales for similar eruption styles, suggesting the diffusion timescales do not allow us to discriminate between eruptive styles. In detail, we determined expected values of 22.8 ± 0.43 days for the 5680 Cal. BCE Plinian eruption, 59.4 ± 0.40 days for the ∼341 Cal. CE Strombolian eruption, 361.0 ± 0.40 days for the 1010 Cal. CE Plinian eruption and 18.8 ± 0.37 days for the 1657 Cal. CE Vulcanian eruption. The 5680 Cal. BCE and 1657 Cal. CE eruption short timescales correlate to short repose suggesting a magma intrusion hotter than the existing mush moved rapidly through the mush system due to the presence of a magma system with a high proportion of melt. The 1010 Cal. CE eruption long-expected timescale and large range of timescales indicates the system remobilised comparatively slowly with new magma interacting with the system slowly. The majority of timescales calculated in this study are short when compared to global data sets calculated for similar systems. This implies basaltic-andesitic to andesitic volcanoes can rapidly produce large-scale eruptions. Paramount for hazard assessment and crisis response, the lack of a correlation between eruption explosive intensity (VEI) and timescales that also applies to short timescales, indicates that a future eruption of La Soufrière de Guadeloupe could broadly span a range from low to high explosivity. These results underscore the necessity to further: improve the reliability of detecting and interpreting multiparameter monitoring FIGURE 13 | Global database of diffusion timescales (adapted from [START_REF] Costa | Diffusion chronometry and the timescales of magmatic processes[END_REF], for relatively evolved composition eruptions. The majority of studies are done on pyroxene with two examples of olivine studies. This shows the wide range of timescales that can be calculated through diffusion methods, from hours to centuries. Systems incomparable to La Soufrière are marked with an asterisk (*), these systems generally record the longest timescales and are more typically observed in evolved caldera forming systems. The1530 C.E., 1657 Cal. CE and 5680 Cal. BCE (whole rock estimated) eruptions record some of the shortest timescales for systems in a similar compositional range, with timescales most similar to Bezymianny and Novarupta, Alaska, which show similarly short timescales. [START_REF] Davydova | The timescales of magma mixing in the plumbing system of Bezymianny volcano (kamchatka): insights from diffusion chronometry[END_REF][START_REF] Boudon | A new scenario for the last magmatic eruption of La Soufrière of Guadeloupe (Lesser Antilles) in 1530 A.D. Evidence from stratigraphy radiocarbon dating and magmatic evolution of erupted products[END_REF][START_REF] Pichavant | Experimental parametrization of magma mixing: application to the ad 1530 eruption of La Soufrière, Guadeloupe (lesser antilles)[END_REF][START_REF] Singer | The timing of compositionally-zoned magma reservoirs and mafic 'priming' weeks before the 1912 Novarupta-Katmai rhyolite eruption[END_REF][START_REF] Ruth | Crystal and melt inclusion timescales reveal the evolution of magma migration before eruption[END_REF][START_REF] Costa | Petrological insights into the storage conditions, and magmatic processes that yielded the centennial 2010 Merapi explosive eruption[END_REF][START_REF] Weber | A recurrent magmatic pattern on observable timescales prior to plinian eruptions from nevado de Toluca (Mexico)[END_REF][START_REF] Chamberlain | Timescales of mixing and mobilisation in the Bishop Tuff magma body: perspectives from diffusion chronometry[END_REF][START_REF] Costa | Decadal time gaps between mafic intrusion and silicic eruption obtained from chemical zoning patterns in olivine[END_REF][START_REF] Fabbro | Evolution of the crustal magma plumbing system during the build-up to the 22-ka caldera-forming eruption of Santorini (Greece)[END_REF][START_REF] Barker | Rapid priming, accumulation, and recharge of magma driving recent eruptions at a hyperactive caldera volcano[END_REF][START_REF] Flaherty | Multiple timescale constraints for high-flux magma chamber assembly prior to the Late Bronze Age eruption of Santorini (Greece)[END_REF][START_REF] Kilgour | Timescales of magmatic processes at Ruapehu volcano from diffusion chronometry and their comparison to monitoring data[END_REF][START_REF] Gamble | A fifty year perspective of magmatic evolution on Ruapehu Volcano, New Zealand: verification of open system behaviour in an arc volcano[END_REF][START_REF] Saunders | Nanoscale characterisation of crystal zoning[END_REF][START_REF] Fabbro | Evolution of the crustal magma plumbing system during the build-up to the 22-ka caldera-forming eruption of Santorini (Greece)[END_REF][START_REF] Bourgeoisat | Spatio-temporal dynamics of the magmatic reservoir at the origin of the 1530 AD eruption of La Soufriere of Guadeloupe[END_REF][START_REF] Solaro | A system dynamics approach to understanding the deep magma plumbing system beneath Dominica (Lesser Antilles)[END_REF][START_REF] Sundermeyer | Timescales from magma mixing to eruption in alkaline volcanism in the Eifel volcanic fields, western Germany[END_REF].

Frontiers in Earth Science | www.frontiersin.org August 2021 | Volume 9 | Article 723763 6 data as eruption precursors, expand eruption forecast modelling, develop probabilistic expert judgement for crisis response, as well as enhance risk reduction and societal resilience."

  appear below. The corrected Figure 10 also appears below, and the trend of the figure is not altered.

  ); Boudon et al. (2008); Pichavant et al. (2018)].

FIGURE 5 |FIGURE 9 |

 59 FIGURE 5 | SEM greyscale intensity as a function of traverse location extracted from the SEM image for a sample from the 1010 Cal. CE eruption (blue dots), the data selected for fitting by the model (red dots), and the model solution (black line). Also shown are the fitted parameters (timescale, diffusion coefficient, D, and effective temperature), the theoretical profile midpoint (μ-gray line), and the "goodness-of-fit" (R). The gray shaded area represents the mean ±1 SD of the selected data.

  FIGURE 11 | Schematic sketches of the mush lenses beneath La Soufrière de Guadeloupe and Echelle with representative crystals shown at approximate locations within the mush zone. (A) The La Soufrière de Guadeloupe mush system prior to eruption, this study suggests intrusions begin a between a minimum of 84 and 3,052 days prior to eruption. (B) In the case of 1657 Cal. CE and 5680 Cal. BCE eruptions, the expected value shows that the majority of the system could be affected by an intrusion 19 and 23 days prior to eruption, respectively. The intrusion moves through the system rapidly, in the case of the 5680 Cal. BCE eruption crystals are erupted from deep in the mush system which re-equilibrate during smaller intrusion events which do not destabilise the mush system. The 1657 Cal. CE eruption only samples simple crystals and unzoned crystals. (C) The ∼341 CE eruption expected value shows that the majority of the system could be affected by an intrusion 59 days before eruption. This intrusion has also moved relatively rapidly through the system and variation in intrusion location, results in destabilisation and eruption from the Echelle vent. Both complex and simple crystal populations are erupted. (D) Processes resulting in the 1010 Cal. CE eruption occurred slower than the other eruptions with the expected value showing the majority of the system could be affected by an intrusion 361 days prior to eruption. The very long delay time suggests that magma may have stalled in the mid-upper mush system, crystals with the diffuse zoning have spent the longest time in contact with the intrusion. (E) System destabilisation results in eruption of populations of simply zoned and unzoned crystals, perhaps from the upper lenses.

FIGURE 12 |

 12 FIGURE 12 | Maximum, minimum and average timescale values for the different crystal populations recorded in each eruption. For single points, only one crystal was identified. The largest range of values are observed in the simple crystals Type-1 and Type-2; however, this may be a reflection of population size. Type-1 is found in all eruptions and records the shortest timescales. Type-2, is mainly found in the 10101 Cal. CE eruption and records the longest timescales and a large range of timescales. Type-3 has the fewest number of crystals and shows the smallest range of values. While the 1657 Cal. CE, ∼341 Cal. CE and 5680 Cal. BCE eruptions show similar averages, the 1010 Cal. CE eruption shows a higher average and minimal overlaps with the other eruptions.

TABLE 2 |

 2 Summary table for the eruptions showing the key features for each eruption and sample location.

	Eruption	Vent	Sample GPS position	Eruption	Expected	Median	Min.	Max.	Timescale	Crystals	Temp	Av.	VEI
			UTM N (m)	UTM O (m)	Unit sampled from	style	timescale (days)	timescale (days)	timescale (days)	timescale (days)	std. error (days)	analysed	°C (±30 °C)	Bulk SiO2 (wt %)
	1657 CE	Soufrière	641,466	1,773,774	Fallout Unit	Vulcanian	18.8	12.00	0.1	84.3	0.37	41	975	58.1	2-3
	1530 CE	Soufrière	643,318	1,774,407	Fallout Unit	Sub-Plinian	20.5*	-	10	90	-	24	900	57.5	3
	1010 CE	Soufrière	638,266 638,228	1,769,743 1,769,738	Fallout Unit	Plinian	361.0	192.2	0.4	2,462.3	0.40	34	1,025	59.7	4
	341 CE	Echelle	663,019	178,011	Scoria	Strombolian	59.4	30.9	0.4	3,051.7	0.40	33	1,010	51.2	2
					Clasts
	5680 BCE	Soufrière	637,417	1,770,276	Fallout Unit	Plinian	22.8	11.2	0.9	167.9	0.43	31	1,010	-	4

Frontiers in Earth Science | www.frontiersin.org August 2021 | Volume 9 | Article 723763

The authors apologize for these errors and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.

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