Stéphane Mitrovic
email: stephane.mitrovic@aphp.fr

Hélène Gouze

Laure Gossec

Thierry Schaeverbeke

Bruno Fautrel

Mucopolysaccharidoses seen in adults in Rheumatology

Keywords: mucopolysaccharidoses, lysosomal storage diseases, joint contractures, spondyloepiphyseal dysplasia, rare diseases, enzyme replacement therapy

Mucopolysaccharidoses are a group of rare lysosomal storage diseases including a great number of polymorph syndromes, each being related to a particular mutation responsible for a deficiency of glycosaminoglycan degrading enzymes, leading to an accumulation of glycosaminoglycans in tissues. Many of them are diagnosed in children or teenagers and have a severe prognosis because of organ failure, and are consequently usually not seen by the adult rheumatologist. However, some of them have a more progressive presentation, with musculoskeletal symptoms at the forefront and a lifespan that nearly reaches that of the general population. These milder forms are more likely to be diagnosed in adults, in patients who have suffered for years and sometimes even decades with unrecognized mucopolysaccharidosis. Indeed, they can sometimes mimic inflammatory rheumatic disorders, and therefore be misdiagnosed for a long time. Recognition and diagnosis of these attenuated forms can be a real challenge as they lead to moderate and/or nonspecific symptoms such as joint pain or stiffness. Hence, rheumatologists should know about them. Early diagnostic is essential since specific treatment, like enzyme replacement therapy, is now available for some subtypes and might, if given early, slow down the development of tissue damage, which is unfortunately irreversible. This article provides the opportunity to review the main clinical and radiographic features, the diagnostic strategy and the update of management, which should be multidisciplinary and led by an experienced physician in a reference centre. The contribution of the rheumatologist is important to ensure symptom control and prevent complications.

A c c e p t e d M a n u s c r i p t

Introduction

Mucopolysaccharidoses (MPS) are a group of rare lysosomal storage diseases including a great number of polymorph syndromes [START_REF] Lehman | Diagnosis of the mucopolysaccharidoses[END_REF]. Most of them are diagnosed in children or teenagers and have a severe prognosis because of organ failure, and are consequently usually not seen by the adult rheumatologist [START_REF] Lehman | Diagnosis of the mucopolysaccharidoses[END_REF][START_REF] Cimaz | Mucopolysaccharidoses[END_REF]. However, some of them have a mild and more slowly progressive presentation, with osteoarticular symptoms at the forefront and with a lifespan that nearly reaches that of the general population [START_REF] Prat | Morquio syndrome: diagnosis in an adult[END_REF]. These milder forms are more likely to be diagnosed in adults, in patients who have suffered for years and sometimes even decades with unrecognized MPS [START_REF] Bruni | The diagnostic journey of patients with mucopolysaccharidosis I: A real-world survey of patient and physician experiences[END_REF][START_REF] Vijay | Clinical presentation and follow-up of patients with the attenuated phenotype of mucopolysaccharidosis type I[END_REF]. Indeed, they can sometimes mimic inflammatory rheumatic disorders, and therefore be misdiagnosed for a long time. Hence, rheumatologists should know about their existence and be able to make the diagnosis as soon as possible, since specific treatment like enzyme replacement therapy or stem cell transplantation are now available and might, if given early, stop or slow the development of tissue damage, which is unfortunately irreversible [START_REF] Coppa | Why should rheumatologists be aware of the mucopolysaccharidoses?[END_REF].

Physiopathology and classification

MPS are mostly autosomal recessive, and represent a heterogeneous group of lysosomal storage diseases including a huge number of polymorph syndromes, each being related to a particular mutation (Table 1). These mutations are responsible for a deficiency of glycosaminoglycan (GAG) degrading enzymes, leading to an accumulation of GAGs in tissues generating impairment. The multiplicity of the enzymes involved in GAGs catabolism, and of the possible mutations and deficiency, account for the numerous subtypes of MPS, but also for the great clinical heterogeneity and various phenotypes inside each subtype, from severe infantile multivisceral diseases to milder musculoskeletal symptoms-prevailing forms of later diagnostic. GAGs are linear sulfated chains which can associate with a protein in order to form proteoglycans that are involved in almost all tissues of the organism. Lysosomal enzymes normally insure the degradation of GAGs. Hence, the deficiency of an enzyme implied in GAG catabolism will lead to GAG storage that will disturb cellular, tissue and organ homeostasis, through alteration of complex multifarious pathways. GAGs are no longer considered just as inert substrates accumulating in tissues, but are biologically active molecules involved in many critical cellular and tissue pathways, including signal transduction, sequestration of extracellular humoral factors and modulation of the cross talk between cells [START_REF] Clarke | Pathogenesis of skeletal and connective tissue involvement in the mucopolysaccharidoses: glycosaminoglycan storage is merely the instigator[END_REF][START_REF] Opoka-Winiarska | Osteoimmunology in mucopolysaccharidoses type I, II, VI and VII. Immunological regulation of the osteoarticular system in the course of metabolic inflammation[END_REF]. Although all the mechanisms are not fully A c c e p t e d M a n u s c r i p t 4 understood, it seems that GAGs accumulation provokes secondary events through a series of metabolic, inflammatory and immunological responses, in bone and cartilage [START_REF] Opoka-Winiarska | Osteoimmunology in mucopolysaccharidoses type I, II, VI and VII. Immunological regulation of the osteoarticular system in the course of metabolic inflammation[END_REF] but also connective tissues [START_REF] Clarke | Pathogenesis of skeletal and connective tissue involvement in the mucopolysaccharidoses: glycosaminoglycan storage is merely the instigator[END_REF], via mechanisms such as Toll-Like Receptor 4 (TLR4) activation ( 9), or increased nitric oxide and inflammatory cytokine release [START_REF] Simonaro | Articular chondrocytes from animals with a dermatan sulfate storage disease undergo a high rate of apoptosis and release nitric oxide and inflammatory cytokines: a possible mechanism underlying degenerative joint disease in the mucopolysaccharidoses[END_REF]. Of capital importance, once initiated secondary consequences of GAG storage can be irreversible, which underscores the critical importance of intervention with enzyme replacement therapy early in the course of the disease, in order to improve long-term outcome [START_REF] Clarke | Pathogenesis of skeletal and connective tissue involvement in the mucopolysaccharidoses: glycosaminoglycan storage is merely the instigator[END_REF]. The joint symptomatology in each of the MPS results from both primary effects of the disease on articular cartilage and the surrounding connective tissue structures, as well as primary bone disease [START_REF] Clarke | Pathogenesis of skeletal and connective tissue involvement in the mucopolysaccharidoses: glycosaminoglycan storage is merely the instigator[END_REF][START_REF] De Franceschi | A molecular and histological characterization of cartilage from patients with Morquio syndrome[END_REF][START_REF] Bouzidi | Mucopolysaccharidosis IVA (Morquio A syndrome): clinical, biological and therapeutic aspects[END_REF]) (Table 2). GAG storage and its consequences also affect almost all the connective tissues, accounting for the potential multisystemic clinical manifestations.

Epidemiology

Owing to the rarity and clinical heterogeneity of the disease, it is very difficult to know precisely MPS epidemiology (Table 1). The overall combined incidence of mucopolysaccharidoses is comprised, according to the countries, between 1 for 16 000 and  1/29 000 live births [START_REF] Meikle | Prevalence of lysosomal storage disorders[END_REF][START_REF] Da Rocha Siqueira | Screening for Attenuated Forms of Mucopolysaccharidoses in Patients with Osteoarticular Problems of Unknown Etiology[END_REF][START_REF] Nelson | Incidence of the mucopolysaccharidoses in Northern Ireland[END_REF][START_REF] Nelson | Incidence of the mucopolysaccharidoses in Western Australia[END_REF].

The prevalence of all MPS reported in Scandinavian countries varies from 4 to 7 per 1 000 000 inhabitants in 2007 [START_REF] Malm | Mucopolysaccharidoses in the Scandinavian countries: incidence and prevalence[END_REF]. MPS I is the most frequent type with an incidence between 0.69 and 1.66 for 100 000 newborns [START_REF] Muenzer | Overview of the mucopolysaccharidoses[END_REF]. MPS IV A point prevalence varies from 1 per 323 000 in Denmark to 1 per 640 000 inhabitants in Australia, but all these results are compromised by poor study reporting and internal validity. Of note, the parents are consanguineous in up to 20% of cases of MPS IV A [START_REF] Leadley | A systematic review of the prevalence of Morquio A syndrome: challenges for study reporting in rare diseases[END_REF]. However, MPS are certainly underdiagnosed due to health-care professionals' lack of awareness, to poor access to screening and diagnostic methods, and to their extensive clinical heterogeneity [START_REF] Da Rocha Siqueira | Screening for Attenuated Forms of Mucopolysaccharidoses in Patients with Osteoarticular Problems of Unknown Etiology[END_REF]. A recent survey of 60 adult and paediatric rheumatologists in North America and Europe found that  80% were unable to recognize symptoms of MPS I and did not know the appropriate diagnostic tests [START_REF] Cimaz | Joint contractures in the absence of inflammation may indicate mucopolysaccharidosis[END_REF]. Attenuated more progressive forms may also occur, which can make diagnosis even more difficult. A recent study reported that a systematic screening for MPS in a sample of rheumatology and orthopaedic patients with joint complaints of unknown aetiology would identify 1 case out of 55 patients [START_REF] Da Rocha Siqueira | Screening for Attenuated Forms of Mucopolysaccharidoses in Patients with Osteoarticular Problems of Unknown Etiology[END_REF].

A c c e p t e d M a n u s c r i p t 5

Clinical characteristics

Great clinical heterogeneity

A key message is that there is no specific symptom of MPS, which present a great clinical heterogeneity. Each patient is unique, and the age of symptom onset, the order of symptom apparition, the severity and evolution will vary, offering a continuum of clinical expressions: from severe forms leading to premature death in childhood (mainly because of visceral complications) to mild attenuated forms with quasi normal lifespan [START_REF] Montaño | International Morquio A Registry: clinical manifestation and natural course of Morquio A disease[END_REF]. Recognition and diagnosis of these attenuated forms can be a real challenge because they lead to subtle and/or nonspecific symptoms, and the diagnosis is thus often made much later in life during adulthood [START_REF] Da Rocha Siqueira | Screening for Attenuated Forms of Mucopolysaccharidoses in Patients with Osteoarticular Problems of Unknown Etiology[END_REF]. Hence, this implies the need for adult rheumatologists to be prepared to recognize and diagnose MPS.

Musculoskeletal manifestations

Despite the great heterogeneity of clinical features and severity, musculoskeletal involvement is a common feature in all types [START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF]. Symptoms are various (Table 3) since bone, cartilage, ligaments and all the soft tissues may be impaired by GAG infiltration [START_REF] Bouzidi | Mucopolysaccharidosis IVA (Morquio A syndrome): clinical, biological and therapeutic aspects[END_REF][START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF][START_REF] Silveri | Hurler syndrome with special reference to histologic abnormalities of the growth plate[END_REF][START_REF] White | Orthopaedic aspects of mucopolysaccharidoses[END_REF]. The date of apparition of symptoms may vary, but an onset at early age is suggestive. The most common rheumatologic features are development of joint pain and joint contractures without concomitant inflammation [START_REF] Lehman | Diagnosis of the mucopolysaccharidoses[END_REF]. Osteochondrodysplasia, due to abnormal enchondral ossification, is the most characteristic bony manifestation.

Joint stiffness and contractures can be found in all type of MPS, except for MPS IV and MPS IX [START_REF] Aldenhoven | Musculoskeletal manifestations of lysosomal storage disorders[END_REF], and affect all joint type. Physical examination often shows articular limitation in extension, whereas flexion is more likely to be preserved. In the hand, joint stiffness preferentially affects the phalangeal joints, although all joints can be affected. When the interphalangeal joints of the hands are affected, a characteristic claw hand deformity may develop, often resulting in impaired hand function [START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF]. If the stiffness and contractures may mimic rheumatic conditions (such as rheumatoid arthritis (RA), juvenile idiopathic arthritis (JIA) or psoriatic arthritis) [START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF], there are however several important differences [START_REF] Aldenhoven | Musculoskeletal manifestations of lysosomal storage disorders[END_REF]: the pain rhythm is not typically inflammatory (i.e. stiffness worse in the morning and relieved by activity), local signs of inflammation (such as warmth, swelling and tenderness) are lacking, and so are systemic signs of inflammation such as fever and/or elevated acute phase reactants. Finally, there is no response to steroids, but nonsteroidal anti-inflammatory drugs may sometimes relieve some symptoms. Some joints may have a swollen appearance due to underlying bony enlargement, and/or to a clinical entity reported by several authors, named chondrodysplasic rheumatism, where patients with epyphyseal dysplasia A c c e p t e d M a n u s c r i p t 6 present acute "osteoarthritic-like" exacerbations with swollen joints and synovitis, but with mechanic synovial fluid and without any elevation of acute phase reactants [START_REF] Kahn | Chondrodysplasic rheumatism[END_REF][START_REF] Bouvet | Apparently inflammatory early degenerative polyarthropathy[END_REF] (Figure 1). The phalangeal contractures observed in MPS may also mimic the contractures seen in camptodactyly or diabetic cheiroarthropathy. Skin tightening and thickening might accompany the contracture, and resemble the skin changes of scleroderma [START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF]. When stiffness and contractures involve the ankles and Achilles tendons, patients may present with toe-walking [START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF].

In contrast with most types of MPS, where joint stiffness is characteristic, most patients with Morquio syndrome (MPS IV) have joint hypermobility caused by metaphyseal deformity, bone hypoplasia and degradation of connective tissue around the joint [START_REF] Montaño | International Morquio A Registry: clinical manifestation and natural course of Morquio A disease[END_REF]. Most patients have significant joint hypermobility of the distal joints contrasting with proximal stiffness, the result being a waddling gait [START_REF] Montaño | International Morquio A Registry: clinical manifestation and natural course of Morquio A disease[END_REF]. The distal hypermobility often results in a very weak grip and progressive difficulty with activities of daily living, including dressing and personal care [START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF].

Carpal tunnel syndrome and other entrapment neuropathy are very frequent in MPS, up to 50% of patients [START_REF] Cimaz | Mucopolysaccharidoses[END_REF]. Median nerve compression occurs as a result of thickening of the flexor retinaculum and the tissues around the tendon sheaths [START_REF] Cimaz | Mucopolysaccharidoses[END_REF]. Trigger digits are another very common feature of MPS. If carpal tunnel syndrome and trigger fingers are frequent in the healthy adult population and may seem ordinary, the physician should however be particularly careful in front of these pathologies occurring in children or young adults. Furthermore, the association of these two pathologies in the same patient is well recognized as a characteristic of patients with an MPS (2). Dysmorphic features are suggestive but not pathognomonic, and include: brevity of the neck and thorax, thoracic deformation with protrusion of the sternum, kyphoscoliosis, spondyloepiphyseal dysplasia, flessum of the hip, genu valgum, flat feet (Figure 1). If growth abnormalities leading to dwarfism or short stature are frequent in severe paediatric forms, the patients with attenuated forms of MPS however may have normal or near-normal linear growth [START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF]. Dysostosis multiplex is the term used to describe the group of skeletal abnormalities and radiographic changes characteristic of MPS [START_REF] Morishita | Musculoskeletal manifestations of mucopolysaccharidoses[END_REF]. Radiographs show characteristic vertebral abnormalities with early anterior hypoplasia of T12, L1 or L2, which is visible as anterior vertebral beaking and is often responsible for thoraco-lumbar kyphosis. The vertebral abnormalities worsen over time, eventually leading to diffuse flattening of the vertebrae and widening of the intervertebral spaces, which will lead to the classical aspect of platyspondylia on the radiographs (Figure 1). Scoliosis and spondylolisthesis, although not specific of MPS, are often associated. Finally, osteopenia is also a common feature, but seems to be more frequent in MPS VI and VII.

General manifestations and evolution

The general clinical manifestations of MPS are polymorph and may include facial dysmorphia, organomegaly and manifestations related to visceral failure, mainly neurologic, cardiologic and ophthalmologic (Table 3) (1,2, 28-30). They are not always present accord to the subtype, especially in milder progressive forms, but should be always sought.

Lifespan is influenced by the severity of the phenotype and especially the presence or absence of visceral injuries: if rapidly progressing paediatric variants experience death during childhood or adolescence, lifespan might be almost normal in attenuated forms. However, overall lifespan has been gradually improving over the past decades, thanks to progresses in earlier recognition of patients with slower disease progression, advances in supportive multidisciplinary care and the development for some type of disease specific treatments [START_REF] Mitchell | Unique medical issues in adult patients with mucopolysaccharidoses[END_REF].

Differential diagnoses

Differential diagnoses are numerous and MPS are often misdiagnosed (Table 4). MPS are part of a larger class of diseases, the lysosomal storage diseases that all share common clinical features [START_REF] James | Lysosomal storage disorders: A review of the musculoskeletal features[END_REF][START_REF] Manger | Rheumatologic aspects of lysosomal storage diseases[END_REF]. However, MPS are much more often misdiagnosed as rheumatic inflammatory disorders by adult rheumatologists: RA (or JIA if early onset), psoriatic arthritis and sometimes spondylarthritis according to the symptoms. Muskuloskeletal and skin manifestations can be confounded with connective tissue disease like scleroderma or poly/dermatomyositis.

Osteochondrodysplasias can be a manifestation of MPS, but not all dysplasias result from LSDs, and many spondyloepiphyseal or spondylometaphyseal dysplasias can be observed independently, or in link with another underlying disease. However, in front of diffuse dysplasia, the physician should raise the possibility of an underlying MPS, and if necessary investigate further. Furthermore, the adult rheumatologist should be particularly attentive to the medical past history of the patient, especially to diseases or symptoms diagnosed in childhood, such as "growing pains" or primary osteochondritis (also called Legg-Perthes-Calvé disease). This latter can induce secondary hip A c c e p t e d M a n u s c r i p t 8 dysplasia in children, is often bilateral (10% of cases) and familial (6% of cases) [START_REF] Mendelsohn | Spondyloepiphyseal dysplasias and bilateral legg-calvé-perthes disease: diagnostic considerations for mucopolysaccharidoses[END_REF], and can be confounded with the hip dysplasia found in MPS.

Diagnosis

Diagnostic algorithm

Diagnoses of these disorders can be complex, and that's why a diagnostic algorithm can be of help (Figure 2). When an MPS is suspected, the patient should be referred to a geneticist or metabolic specialist in a reference centre for laboratory testing (www.orphanet.org). Indeed, besides the great complexity of the assays, there are potential diagnostic pitfalls that should be avoided. An MPS diagnosis is based on laboratory results from urinary GAG analyses (quantitative and qualitative GAG assays), which act as screening guiding tests, that should secondary be confirmed by enzyme activity assays that measure enzyme activity in tissues (blood leukocytes or fibroblasts).

Orientation screening tests: urine GAG analyses

Quantitative assays measure overall elevation of GAG in the urine, as compared with GAG levels expected in age-matched normal subjects [START_REF] Lehman | Diagnosis of the mucopolysaccharidoses[END_REF]. Qualitative assays (such as GAG electrophoresis) detect the type of GAG excreted. In children, adolescents and young adults, most MPS patients have higher GAG excretion in urine, compared with age-matched normal subjects.

However, urinary GAG excretion varies with age, higher values being found during the first years of life, followed by a slow and constant decrease thereafter (1). Hence, not all MPS patients have a clear elevation of total GAG excretion, especially in adults with milder and more progressive forms.

That's why an accurate diagnosis requires a full GAG profile, including both quantitative and qualitative analysis done in tandem [START_REF] Mahalingam | Diagnosis of mucopolysaccharidoses: how to avoid false positives and false negatives[END_REF][START_REF] Gallegos-Arreola | Urinary glycosaminoglycan excretion in healthy subjects and in patients with mucopolysaccharidoses[END_REF]. In fact, patients with different types of MPS differ not only in the total amount of GAG excreted in urine, but also in the relative proportion of various type of GAG, leading to a particular abnormal pattern for each MPS subtype [START_REF] Piraud | Diagnosis of mucopolysaccharidoses in a clinically selected population by urinary glycosaminoglycan analysis: a study of 2,000 urine samples[END_REF]: the presence of specific GAGs can suggest the MPS subtype and may direct the appropriate enzyme analyses (Table 1). For example, high amounts of heparan sulfate or keratan sulfate essentially characterize MPS III and IV, respectively. Besides the age or the severity of the disease phenotype (1), other factors, such as heparin (that interferes with the assays) or inappropriate sample storage, can influence GAG excretion and provide false negatives. Thus, an MPS diagnosis should neither be confirmed nor ruled out on the basis of a single urine GAG test (although it is usually the first step in the diagnostic pathway), but confirmed by enzyme activity testing.

Biologic confirmation test: enzyme activity measurement in plasmatic leukocytes

The diagnosis of MPS should be confirmed by enzyme activity testing. Enzyme activity is typically measured in plasmatic leukocytes [START_REF] Lehman | Diagnosis of the mucopolysaccharidoses[END_REF]. Some laboratories might also still measure enzyme activity in cultured fibroblasts, although skin biopsy is more invasive than blood sampling. A new technique of measuring enzyme activity from dried blood spot (DBS) has been proposed for many types of MPS [START_REF] Lehman | Diagnosis of the mucopolysaccharidoses[END_REF][START_REF] Cozma | Diagnosis of Morquio Syndrome in Dried Blood Spots Based on a New MRM-MS Assay[END_REF]. DBS-based assays offer considerable practical advantages with respect to sample collection, storage and transport, and multiple enzyme activity tests can be performed on a single DBS. However, although sensitivity and specificity seem correct if appropriate controls are performed, false negatives can occur, it is still recommended that a positive result from a DBS be confirmed by a tissue-based assay (1). Hence, measurement of enzyme activity in plasmatic leukocytes remains the gold standard.

Predicting disease severity and evolution

Once the enzyme deficiency is confirmed, predicting disease severity remains difficult.

Urinary GAG level cannot be utilized as a reliable indicator of severity, especially in adults [START_REF] Muenzer | Overview of the mucopolysaccharidoses[END_REF]. Genotype-phenotype correlations have been limited by the rarity of the disorders and the large number of mutations, many of which occur only in a single affected family [START_REF] Muenzer | Overview of the mucopolysaccharidoses[END_REF]. Mutation analysis or molecular testing includes looking for the known disease-causing mutations in addition to looking for abnormal sequences in the gene coding for a particular enzyme. Molecular testing can have prognostic value if the mutations that are identified have been characterized [START_REF] Terlato | Can mucopolysaccharidosis type I disease severity be predicted based on a patient's genotype? A comprehensive review of the literature[END_REF][START_REF] Tomatsu | Mutation and polymorphism spectrum of the GALNS gene in mucopolysaccharidosis IVA (Morquio A)[END_REF]. When a patient has been diagnosed with a specific type of MPS and his/her mutation is known, the information can be used for carrier testing and prenatal testing of siblings [START_REF] Lehman | Diagnosis of the mucopolysaccharidoses[END_REF][START_REF] Akella | Amniotic fluid glycosaminoglycans in the prenatal diagnosis of mucopolysaccharidoses -A useful biomarker[END_REF]. It is important to note that except for MPS II (Hunter), the MPS are inherited in autosomal recessive fashion, so carriers have a very small likelihood of having children affected with MPS unless the union is consanguineous (1).

Treatment

A c c e p t e d M a n u s c r i p t 10 MPS should be managed by a multidisciplinary team coordinated by a physician with experience in the treatment of these complex disorders, ideally in a reference centre [START_REF] Valayannopoulos | Therapy for the mucopolysaccharidoses[END_REF]. When available, a disease-specific treatment should be started as early as possible; supportive treatments are always important. The main therapeutic goals are: to improve or slow down (if possible) the systemic evolution of the disease, to improve the quality of life and socio-professional insertion, and to provide clear information about the disease and complications [START_REF]Protocole National de Diagnostic et de Soins (PNDS) sur les mucopolysaccharidoses[END_REF]. Regular follow-up is essential to monitor disease progression and response to treatment [START_REF] Valayannopoulos | Therapy for the mucopolysaccharidoses[END_REF].

Disease-specific treatments

The rationale is to provide the patient with active enzyme to replace the enzyme that is deficient, either exogenously through enzyme replacement therapy (ERT), or endogenously through haematopoietic stem cell transplantation (HSCT) in infants [START_REF] Valayannopoulos | Therapy for the mucopolysaccharidoses[END_REF]. Disease-specific treatments are not curative, but can improve outcome (prevention, stabilization, retardation of disease progression, in addition to improvements in clinical status) and quality of life. Due to the progressive nature of the disease, response to any form of treatment is influenced by the severity of the disease phenotype and the degree of disease progression at treatment initiation [START_REF] Valayannopoulos | Therapy for the mucopolysaccharidoses[END_REF]. Hence, ERT is most effective when started early in life, before the development of irreversible damage [START_REF] Muenzer | Overview of the mucopolysaccharidoses[END_REF][START_REF] Mitchell | Unique medical issues in adult patients with mucopolysaccharidoses[END_REF][START_REF] Beck | The natural history of MPS I: global perspectives from the MPS I Registry[END_REF][START_REF] Gabrielli | 12 year follow up of enzyme-replacement therapy in two siblings with attenuated mucopolysaccharidosis I: the important role of early treatment[END_REF]. Limited data exist on the effects of ERT when started in adulthood and more research is warranted to fill this evidence gap.

Enzyme replacement therapy

ERT is currently available for MPS I, II, IVA and VI, and clinical trials for MPS VII and MPS IIIA are ongoing [START_REF] Gilkes | Mucopolysaccharidosis III (Sanfilippo Syndrome)-disease presentation and experimental therapies[END_REF][START_REF] Sands | Mucopolysaccharidosis type VII: A powerful experimental system and therapeutic challenge[END_REF] (Table 1). ERT has been shown to have favourable effects on urinary GAG levels, endurance, respiratory function, range of joint motion, hepatomegaly, growth (height) and cardiac function [START_REF] Valayannopoulos | Therapy for the mucopolysaccharidoses[END_REF][START_REF] Wraith | Enzyme replacement therapy for mucopolysaccharidosis I: a randomized, double-blinded, placebocontrolled, multinational study of recombinant human alpha-L-iduronidase (laronidase)[END_REF][START_REF] Burton | Safety and physiological effects of two different doses of elosulfase alfa in patients with morquio a syndrome: A randomized, double-blind, pilot study[END_REF][START_REF] Tomatsu | Enzyme replacement therapy for treating mucopolysaccharidosis type IVA (Morquio A syndrome): effect and limitations[END_REF][START_REF] Harmatz | Enzyme replacement therapy for mucopolysaccharidosis VI: a phase 3, randomized, double-blind, placebo-controlled, multinational study of recombinant human N-acetylgalactosamine 4sulfatase (recombinant human arylsulfatase B or rhASB) and follow-on, open-label extension study[END_REF][START_REF] Braunlin | Enzyme replacement therapy for mucopolysaccharidosis VI: long-term cardiac effects of galsulfase (Naglazyme®) therapy[END_REF]. Influence of ERT on the quality of life has not been evaluated in dedicated studies but has been punctually described in the therapeutic trials and seems to have a positive impact on activities of daily living, pain and Health-related quality of life scores [START_REF] Wraith | Enzyme replacement therapy for mucopolysaccharidosis I: a randomized, double-blinded, placebocontrolled, multinational study of recombinant human alpha-L-iduronidase (laronidase)[END_REF][START_REF] Clarke | Long-term efficacy and safety of laronidase in the treatment of mucopolysaccharidosis I[END_REF].

Haematopoietic stem cell transplantation

HSCT is considered the standard of care in infants with severe MPS, associated with neurocognitive impairment, due to the inability of intravenously infused ERT to pass the blood-brain barrier [START_REF] Mitchell | Unique medical issues in adult patients with mucopolysaccharidoses[END_REF][START_REF] Valayannopoulos | Therapy for the mucopolysaccharidoses[END_REF][START_REF] Aldenhoven | Long-term outcome of Hurler syndrome patients after hematopoietic cell transplantation: an international multicenter study[END_REF]. It should be preferably done as early as possible after birth, as the long-term neurocognitive prognosis after HSCT is predominantly determined by the degree of damage to the central nervous system at time of transplant [START_REF] Mitchell | Unique medical issues in adult patients with mucopolysaccharidoses[END_REF].

Supportive symptom-based treatments

Coordinated by an experienced physician, a comprehensive team of specialists such as rheumatologists, physiotherapists, occupational therapists, orthopaedic surgeons, neurosurgeons, cardiologists, pneumologists and otorhinolaryngologists are necessary to address the many potential comorbidities of these progressive diseases (43) (Table 3). The role of the rheumatologist is essential for information, pain-relief (painkillers prescription, local corticosteroids infiltrations), physical therapy supervision, and discussion of the indications of surgery with orthopaedic colleagues. Of importance, patients with MPS are in general at high risk of anaesthetic and surgical complications because of airway compromise due to GAG accumulation, enlarged tongue, odontoid dysplasia and spinal instability, susceptibility to respiratory infections, restrictive lung disease and cardiac disease [START_REF] Mitchell | Unique medical issues in adult patients with mucopolysaccharidoses[END_REF][START_REF] Walker | Anaesthesia and mucopolysaccharidoses. A review of airway problems in children[END_REF]. Hence, general anaesthesia should be avoided if possible, and when unavoidable, it should be done by an anaesthesiologist with MPS experience [START_REF] Mitchell | Unique medical issues in adult patients with mucopolysaccharidoses[END_REF][START_REF] Valayannopoulos | Therapy for the mucopolysaccharidoses[END_REF][START_REF]Protocole National de Diagnostic et de Soins (PNDS) sur les mucopolysaccharidoses[END_REF]. It is also important to be aware of the considerable psychosocial burden of these chronic, debilitating and progressive conditions. Patients with MPS experience great deterioration of their quality of life [START_REF] Hendriksz | Health-related quality of life in mucopolysaccharidosis: looking beyond biomedical issues[END_REF]. Many of them exhibit psychological symptoms which may currently be overlooked during treatment of physical disease manifestations [START_REF] Ali | Psychological health in adults with morquio syndrome[END_REF]. Hence, a psychological evaluation and support is recommended, especially in patients with milder forms, in whom intelligence is typically preserved and whose psychological health worsens because they understand their disease predicament more fully [START_REF] Kuratsubo | Psychological status of patients with mucopolysaccharidosis type II and their parents[END_REF]. Social workers may be helpful to overcome social insecurity and unemployment [START_REF]Protocole National de Diagnostic et de Soins (PNDS) sur les mucopolysaccharidoses[END_REF][START_REF] Hendriksz | Health-related quality of life in mucopolysaccharidosis: looking beyond biomedical issues[END_REF].

Finally, patient associations may provide invaluable networking opportunities for patients and families to share information and connect with others experiencing the same challenges [START_REF] Valayannopoulos | Therapy for the mucopolysaccharidoses[END_REF][START_REF]Protocole National de Diagnostic et de Soins (PNDS) sur les mucopolysaccharidoses[END_REF].

Conclusion

Even if MPS are rare, they are underestimated and rheumatologists are probably not aware enough of their existence. In addition to the typical severe forms associated with markedly decreased survival, milder musculoskeletal-prevailing forms that may escape diagnosis until adulthood exist. Thus, the rheumatologist may sometimes be the first physician to consider the diagnosis, especially in front of symptoms such as joint pain, stiffness, dysmorphic features associated with dysostosis multiplex on X-rays. Making the diagnosis as soon as possible is essential, because substitutive enzyme therapy is available for some MPS. Given early, it might stop

1: Mucopolysaccharidosis (MPS) classification.

There are 11 known enzymes that give rise to 7 distinct MPS (MPS V and VIII are no longer used). Most of MPS have autosomal recessive transmission, except MPS II, which is X-linked recessive. An enzyme replacement therapy (recombinant deficient enzyme) is now available for four of them, and in development for two more. The multiplicity of the enzymes involved in GAGs catabolism and their deficiency account for the numerous subtypes of MPS, but also for the great clinical heterogeneity and various phenotypes inside each subtype. For instance, different mutations of a same enzyme, α-Liduronidase, will either lead to a very severe phenotype called Hurler syndrome, an intermediary severe phenotype (Hurler-Scheie), and a much less severe phenotype (Scheie) in the MPS I subtype. Milder forms more at risk to be later diagnosed in adults are more likely to be found in the subtypes of MPS type I (Scheie syndrome), IV, VI and VII. Other types concern almost exclusively infantile diseases with a much shorter life span. The forms which are more likely encountered by adult rheumatologists are types IVA (also called Morquio A syndrome), VI (Maroteaux-Lamy) and VII (Sly) which are typically the forms where osteoarticular manifestations prevail, with usually no intellectual deficit, and where visceral injuries are less frequently present. later. In his medical history, symptoms had started in the adolescence, and he had been diagnosed with bilateral "osteochondritis" at the age of 10 and 13, and had consequently received two hip total arthroplasties at the age of 28 and 29. Elevated acute phase reactants were detected during the first years of follow-up, considered related to a pilonidal cyst, and were no longer observed after its removal. Immunological markers (rheumatoid factor, anti-citrullinated protein antibodies, antinuclear antibodies) were absent. Note the metacarpophalangeal hooks, hands and feet epiphyseal dysplasia, kyphoscoliosis and platyspondylia, and the dysmorphic morphological facial features, with a large and short neck. The misdiagnosis with psoriatic arthritis was linked to chondrodysplasic rheumatism, responsible for clinical and ultrasonographic synovitis and destruction of the carpa, the right elbow and the shoulders. However, joint aspiration found an aseptic mechanical fluid with no crystal.

  Hypoplasia of the dens, cervical stenosis and instability are common and severe manifestations (mainly of MPS IV, VI and to a lesser extent I) that may lead to atlanto-axial instability, compression of the cervical spinal cord, and complications during endotracheal intubation. Changes in the lower extremities include dysplastic femoral heads (favored by underdevelopment of the A c c e p t e d M a n u s c r i p t 7 proximal femoral epiphysis), flattened acetabula, hypoplasia of the inferior portions of the iliac bones with flared iliac wings, coxa valga or vara, genu valgum deformities (up to 50% of the patients) (2). Epiphyseal dysplasia can also occur in interphalangeal joints of hands and feet.

A c c e p t e d M a n u s c r i p t 9 A

 9 new technique for evaluation of urinary excretion of GAG based on a multiplex tandem technique using both chromatography and mass spectrometry, is in development and seems promising, but requires further testing and validation[START_REF] Auray-Blais | UPLC-MS/MS detection of disaccharides derived from glycosaminoglycans as biomarkers of mucopolysaccharidoses[END_REF].

Table

A c c e p t e d M a n u s c r i p t

A c c e p t e d M a n u s c r i p t 22 Figure 1 .

 221 Figure 1. Mucopolysaccharidosis (MPS) type IVA (Morquio syndrome) with spondyloepiphyseal dysplasia diagnosed in a 52-year adult. The patient had previously been diagnosed with psoriatic arthritis sine psoriasis at the age of 37, and had received methotrexate and etanercept (with no clinical efficacy) before the final diagnosis of MPS IVA was made 15 years

Figure 2 .

 2 Figure 2. Diagnostic algorithm for attenuated mycopolysaccharidoses (adapted from [1, 20]).+ Newborn infants with MPS, although normal appearing, often have radiological evidence of bone and joint abnormalities. ‡ Overall skin texture in patients with MPS can be thickened and rough. RA, rheumatoid arthritis; JIA, juvenile idiopathic arthritis; ESR, erythrocyte sedimentation rate; CRP, C-reactive protein; ANA, antinuclear antibodies; NSAIDs, nonsteroidal anti-inflammatory drugs; MPS, mucopolysaccharidosis; GAGs, glycosmaminoglycans.

Figure 1 A

 1 Figure 1

Figure 2

 2 Figure 2

Table 2 . Mechanisms of bone and joint disease in the MPS (adapted from (7))

 2

		Articular cartilage		Growth plate
	 GAG deposition			 GAG deposition
	 Enhanced chondrocyte apoptosis		 Altered growth plate morphology
	 Increased nitric oxide production		 Altered trabecular architecture
	 Increased	cytokine	and	chemokine	 Osteoclast dysfunction
	production
	 Macrophage recruitment			 Inhibition of collagenase activity of
					cathepsin K
	 Activation of the TLR4 pathway		 Alteration of STAT pathway
	 Increased MMPs, TNF-			 Decreased IL-6 and IL-6 family chemokines
	GAG, glycosaminoclycan; TLR4, Toll-Like Receptor 4; MMPs, matrix metallopeptidase; TNF-,
	Tumour Necrosis Factor ; STAT, signal transducer and activator of transcription; IL-6,
	interleukine 6

Table 3 : Potential multisystemic symptoms that may be observed in mucopolysaccharidosis (not exhaustive list).

 3

	Osteo-articular	Joint stiffness (except in Morquio syndrome*: joint hypermobility of the
		distal joints contrasting with proximal stiffness)
		Joint limitation
		Joint contracture
		Dysmorphic features,	Height variation (from dwarfism to near-normal)
		Osteochondrodysplasia,	Pectus excavatum, hyperlordosis, scoliosis,
		Dysostosis multiplex	kyphosis, odontoid dysplasia
			Hip dysplasia, genu valgum, flat feet
			Dysostogenesis, spondyloepyphyseal dysplasia,
			spondylometaphyseal dysplasia, platyspondylia
		Early osteoarthritis	Stiffness, chondrodysplasic rheumatism**
		Other	Entrapment neuropathy (mainly carpal tunnel
			syndrome), trigger digits, claw hands (phalangeal
			contracture)
	Dysmorphia	Coarse facies (large nostrils, thick lips and ears, macroglossia, thick hair)
		Organomegaly
	Neurological	Psychomotor retardation, behaviour trouble, central impairment, peripheral
		compression, hydrocephalus, compression of the cervical spinal cord
		(hypoplasia of the dens and atlantoaxial instability)
	Cardiological	Valve disease, myocardial infiltration, coronary heart disease
	Respiratory	Tracheal and bronchial collapse, restrictive pulmonary disease***
	Ear, nose and	Macroglossia, tonsils' hypertrophia, perception deafness, otitis media,
	throat/stomatological	recurrent upper tract infections, sleep apnea, dental colorations and gum
		recession
	Ophtalmological	Lens opacity, corneal clouding, retinopathy, blindness
	Digestive	Inguinal and/or umbilical hernias, hepatomegaly
	Dermatological	Thickened and rough skin texture †, pebbly papules ‡
	*Also known as MPS type IV; ** Acute "osteoarthrititic-like" exacerbations in patients with
	epyphyseal dysplasia, with swollen joints and synovitis, but with mechanic synovial fluid and
	without any elevation of acute phase reactants (26, 27); ***Due to spinal deformations (28);
	†Overall skin texture in patients with MPS can be thickened and rough. ‡MPS II (29), and rarely
	MPS I (30) can be associated with a distinctive skin lesion consisting of white "pebbly" papules 2-
	10 mm in diameter, sometimes coalescing in ridges.

Table 4 . Differential diagnoses and common misdiagnoses for MPS based on joint and bone symptoms

 4

	Inflammatory rheumatic disorders
	 Rheumatoid arthritis	 Psoriatic arthritis
	 Juvenile idiopathic arthritis	 Spondylarthritis
	Connective tissue disease
	 Scleroderma
	Poly/Dermatomyositis
	Other lysosomal storage diseases (LSD)
	 Gaucher's disease
	 Fabry's disease
	 Pompe's disease
	 Mucolipidoses
	 Others
	Muscular dystrophy
	Osteochondrodysplasias
	 Epiphyseal dysplasias, including genetic diseases (the vertebral abnormalities are less
	severe)
	 Spondyloepiphyseal dysplasia congenital (including the X-linked form)
	 Spondylometaphyseal dysplasia
	 Dystrophic dysplasias
	 Osteogenesis imperfecta
	 Other dysplasias
	Hypophosphatasia
	Occurring during childhoohd
	 Legg-Perthes-Calvé disease
	 Growing pains
	Polyneuropathy
	Fibromyalgia

or slow down the development of tissue damage, which is unfortunately irreversible. The management of MPS should be multidisciplinary, led by an experienced physician in a reference centre, and the contribution of the rheumatologist is important to ensure symptom control and prevent complications.

Conflicts of interest

None of the authors has any conflicts of interest to declare.

A c c e p t e d M a n u s c r i p t


Vasileios Afentoulis

Vasiliki Tsoukala

Bijan Mohammadi

Experimental and numerical modeling of fluid-seabed international in shallow water

Keywords: Sandy beach morphodynamis, fluid-bed interaction, beach erosion, sediment transport, numerical modelling, shape optimization, hydrodynamics

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

INTRODUCTION

Engineers build various types of maritime structures. Breakwaters and quay walls for ports and harbors, seawalls and jetties for shore protection, are some examples. These structures must perform their functions in the natural environment, being subjected to the hostile effects of winds, waves, tidal currents, earthquakes, etc. To ensure their designated performance, we must carry out comprehensive investigations in order to understand the environmental conditions. The investigations must be as accurate as possible so that we can rationally assess the effects of the environment on our structures [START_REF] Goda | Random Seas and Design of Maritime Structures[END_REF]. Complex multi-physics fields formed by dynamic interactions between fluid flows, seabed profile evolution, and seabed response are natural in a marine environment [START_REF] Nakamura | Development of fluid-sediment-seabed interaction model and its application[END_REF].The ability of wind-generated waves to suspend sediment material is a direct function of wave amplitude and frequency and inversely proportional to water depth [START_REF] Krone | Aggregation of suspended particles in estuaries[END_REF]. However, because of the "One step forwards and one step backwards" nature of the wave motion, the currents may still be very important transporters of wave entrained sediments unless the sediment concentrations vary periodically in step with the wave motion [START_REF] Nielsen | Coastal bottom boundary layers and sediment transport[END_REF]. Motion of the nearshore bed is not a linear function of velocity magnitude or direction, so it is likely that there is a role for the various mechanical properties of the bed [START_REF] Austin | Morphological change and sediment dynamics of the beach step on a macrotidal gravel beach[END_REF]. The response of bed evolution to the coastal processes has also different time spans, ranging from that of an individual event, through to seasonal variation in driving forces.

Modelling and simulation of such fluid-sediment seabed interactions is essential for the construction of the defence structures against beach erosion, which result in the reduction of the incoming wave energy at the shoreward locations. To deal with this type of interaction phenomenon, a numerical model based on shallow water equations, is presented in order to propose a formulation for the wave motion based on fluid and structure coupling using minimization [START_REF] Bouharguane | Minimization principles for the evolution of a soft sea bed interacting with a shallow[END_REF], [START_REF] Mohammadi | Extreme scenarios for the evolution of a soft bed interacting with a fluid using the Value at Risk of the bed characteristics[END_REF]. Minimization principles have been used many times in the past to design defence structures against beach erosion [START_REF] Azerad | Optimal shape design of coastal structures minimizing coastal erosion[END_REF], [START_REF] Isebe | Shape optimization of geotextile tubes for sandy beach protection[END_REF].In these works, the designed structures were independent of time and were built once for all. Hence, this method goes one step further giving the possibility to the structure to change in time. It is worth pointing out that the the fundamental assumption of this proposed method is the fact that bed adapts to the flow by some sort of optimal sand transport in order to minimize some energy expression, optimal transport is seen here as minimal change in the bed shape.The time scales of interest are below a day and recoveries between storms or seasonal and inter-annual variabilities are out of scope.

Measurements from a physical experiment have been used in order to verify the accuracy of the model. This experiment was performed in 2008, in the LHF (Laboratoire d'Hydraulique de France), providing for the first time an extensive quantitative description of the morphodynamics of a rip current system during intermediate beach down-state and up-state transitions [START_REF] Castelle | Laboratory experiment on rip current circulations over a moveable bed: Drifter measurements[END_REF], [START_REF] Michallet | Physical modeling of threedimensional intermediate beach morphodynamics[END_REF], [START_REF] Michallet | Modélisation physique de la morphodynamique d'une plage barrée tridimensionnelle[END_REF]. As it is derived from the experimental results, the changes in prevailing wave conditions increase the rate at which the beach morphology evolves. This interaction has been also investigated, using the proposed numerical model and applying as initial conditions the same wave climates as that of the experimental set-up.

THE NUMERICAL MODEL Description of the method and assumptions

This model is an application of control theory to the evolution of sandy bed and the main aim is to propose a formulation for the wave motion based on fluid and structure coupling using minimization principles. For the purpose of this study the sea bed is seen as a structure with low stiffness, and this structure is changing in time. One of the main ingredients in the chain of control is the cost function to be minimized. One expects the bed to act as flexible structure and to adapt to flow conditions in order to minimize some energy-based functional.

For the definition of the approach two dimensional situations with a realistic flow model in shallow domains have been considered. The sea bed ψ : Ω ⊂ R 2 → R + changes with time following the changes in the state given by the flow conditions U, ψ is a univocal function with some regularity. A bed parameterization has been used, based on the the bathymetry given at all the nodes of the fluid mesh. The model for the sea bed evolution is based on minimization of a time dependent functional J(ψ, U(ψ)) where U(ψ) = U(ψ, τ, x, y), τ ∈ [t -T, t], (x, y) ∈ Ω gathers the state evolution in time , solution of a state equation.

In order to describe the flow motion, shallow water equations have been used as state equation with U = t (h, hu) where u = t (u, v) is the depth-averaged velocity with u and v the scalar components in the horizontal directions and h the local water depth:

U t + F(U, ψ) = 0 (1)
where

F(U, ψ) = ∇ • (hu) ∇ • (hu ⊗ u) + gh∇(h + ψ) (2)
Also minimization of J can be seen as a solution of

ψ t = -ρ∇ ψ J(ψ, U(ψ)) ψ(t = 0, x) = ψ 0 (x) = given (3)
where ρ is a positive parameter which depends on the local porosity of the bed and quantify its receptivity to flow perturbations. One remarks then that ρ plays the role of the term 1/(1 -λ p ) in the Exner equation [START_REF] Paola | A generalized exner equation for sediment mass balance[END_REF].

ψ t + 1 1 -λ p ∇ • q = 0, ψ(t = 0, x, y) = given, (4)
where λ p is the porosity of the bed and q is the sediment transport flux. The physical time scales for the fluid and structure (bed motion) are quite different. Indeed, flows have time scales of the order of seconds and the sea bed motion takes place over hours. The cost function involves this state evolution as, for instance , in:

J(ψ, U(ψ)) = t t-T ( j(ψ, U(ψ, τ))dτ (5)
T indicates a time dependency window and also permits to introduce a difference in time scales between sea bed and flow motions. One can , for instance , consider an energy made of water mechanical energy and involving a constraint on sand displacements requiring minimal topobathmetry changes from the bathymetry ψ(t -T ) at the beginning of a time interval of influence [t -T, t]:

J 1 (ψ) = t t-T Ω ( 1 2 ρ w gη 2 + ρ s g(ψ(τ) -ψ(t -T )) 2 )dτdΩ (6)
Where Ω is the physical domain, ρ w and ρ s are respectively the water and sand density and η is the deviation of the wave elevation from a low frequency component evaluated using a time interval T. This is a function of space and time and also depends on the bathymetry :

η(x, y, ψ, t) = h(x, y, ψ, t) - 1 T t t-T h(x, y, ψ, t)dτ (7)
This functional aims at reducing both wave elevations and changes in the bed shape. A fundamental idea motivating the introduction of the second term in functional J 1 is the concept of optimal transport. In other words, one thinks that the bed will adapt to the flow in some optimal way in term of sand transport.

Flow solver

Shallow water equations are discretized by a finite volume formulation [START_REF] Eymard | Solution of Equation in R N (Part 3)[END_REF]. This finite volume implementation preserves steady state solutions on non flat sea beds in the absence of perturbations. Four boundary conditions are applied in slip, inlet, shoreline and outlet boundaries. The use of slip boundary condition is of great importance, since the purpose of this study is to identify the interaction which occurs across the bottom boundaries. The outlet condition is a transmissive boundary condition.

PHYSICAL EXPERIMENT Description of experimental Set-up

The laboratory experiment was undertaken during a 5 week period in a multidirectional wave basin at the SOGREAH (LHF facility, G -INP, France). The basin extended 30 m in both cross -shore and alongshore directions with an offshore wall constituted of 60 independently controlled piston -type wavemakers (Figure 1) [START_REF] Castelle | Laboratory experiment on rip current circulations over a moveable bed: Drifter measurements[END_REF]. A beam sliding on rails supporting the instruments was designed for measuring the waves along crossshore transects and the beach topography (Figure 2). The still water level at the wavemaker was h 0 = 76.5cm for all experiments. Shore-normal irregular waves complying to jonswap spectra were considered. Three categories of wave conditions were applied, defined by their significant wave height and peak period, namely energetic conditions (A: H m0 = 23 cm / T p = 2.3 s), moderate conditions with a large period (B: H m0 = 18 cm / T p = 3.5 s), or a shorter period (C: H m0 = 17 cm / T p = 2.1 s). Each experiment consisted of a series of 7 to 24 twenty minute wave sequences, depending on the amount of morphological changes expected.In addition, the generated JONSWAP irregular waves were designed to have less energy at the center of the wave front by imposing a damped motion on chosen wave paddles. This was done in order to create alongshore nonuniformity in the wave breaking for initiating circulations and, as a result, to induce the initial development of the 3-D patterns. The bathymetry was surveyed between each experiment by means of a laser profiler [START_REF] Michallet | Physical modeling of threedimensional intermediate beach morphodynamics[END_REF].

Experimental results

Alongshore-averaged beach profiles (for 3.12m ≤ y ≤ 18.2m) are shown in Figure 3. An overall accretion of the beach face was first obtained over a 62 h duration of mainly B wave conditions(H m0 = 18 cm / T p = 3.5 s). For larger and shorter waves A conditions(H m0 = 23 cm / T p = 2.3 s) between 66:00 h and 100:40 h, an overall erosion was observed [START_REF] Michallet | Physical modeling of threedimensional intermediate beach morphodynamics[END_REF].

Figure 3: Alongshore-averaged beach profiles at the three main stages of the experiments [START_REF] Michallet | Physical modeling of threedimensional intermediate beach morphodynamics[END_REF].

RESULTS AND DISCUSSION

Model comparisons with experimental data are performed for both waves and beach profiles to ensure that the selected model will yield realistic results. For the simulation of the incoming waves, the water wave elevation at the inlet is represented by the addition of N monochromatic waves :

h(t) = h 0 + 2A i=1,...,N-1 sin( ω i + ω i+1 2 t)cos( ω i -ω i+1 2 t) (8)
A is the water wave amplitude at inlet, H m0 the water height at rest and ω i = 2π/T i are wave pulsations corresponding to the typical values of periods T i .

For the process of the numerical modelling, the case of the experimental wave basin side of 30 m is considered and the mean water depth is set to h 0 = 0.765, so as to compare the hydrodynamic and morphodynamic characteristics in the same field. The predicted wave record compares reasonably with the measured surface elevation. In Figure 4 the wave time series at a specific point of the basin (x=18.33, y=9.27) is presented, as obtained by the experiment and the numerical model. Simply by visual inspection, enough concordance is observed between the numerical and experimental wave periods, but some small deviations are presented in the wave amplitude. This level of precision continue for all the locations of the wave gauges along the cross-shore profiles, thus the selected numerical model could be considered accurate enough to take to the next level of comparison, looking at evolution of the bed shape. For the calculation of the sediment transport and the evolution of the beach profiles, the wave climates of the experimental set-up have been considered. Thus, the total simulation duration (96.4 h) has been divided into 2 phases, the 62 hours accretive sequence with B wave conditions (H m0 = 18 cm / T p = 3.5 s) and 34.4 hours erosive sequence with A wave conditions (H m0 = 23 cm / T p = 2.3 s). These phases correspond to the so-called down-state and up-state wave transitions (i.e., changes from high to low, and low to high wave energies, respectively) [START_REF] Michallet | Physical modeling of threedimensional intermediate beach morphodynamics[END_REF]. Only the section 6 ≤ x ≤ 26 m has been taken into account, where the sandy beach extends (Figure 1). It is also worth mentioning that the wave front at the inlet of the numerical model is considered uniform, while for the needs of the experiment, the wave forcing at the wave-maker is set to be alongshore nonuniform. However, some alongshore fluctuations are observed, mainly for the first steps of the numerical simulation before the sandbar three-dimensionality starts to decrease. In other words, wavedriven circulations were therefore assumed to be essentially guided and constrained by the 3D sandbar morphology, with negligible effect of the alongshore nonuniform wave generation at the wavemaker [START_REF] Castelle | Laboratory experiment on rip current circulations over a moveable bed: Drifter measurements[END_REF]. The most striking feature of the results illustrated in Figure 5, is that the evolution of the bed shape over the time, follows the same sequence as that of the experiment (Figure 4). Firstly, an overall accretion of the beach face was observed over a 62 hours duration of mainly B wave conditions (H m0 = 18 cm / T p = 3.5 s). During this phase, the obtained results show an onshore migration of the sediment and a significant erosion of the seaward section of the bar (x ≤ 10 m) resulting in an overall onshore migration of the sandbar system. For this wave sequence, comparing the obtained threedimensional bathymetry with that of the experiment (Figure 6), it is shown that the accretion in the case of the numerical model is more intense and extends further seaward. Concerning the second time period 62 ≤ t ≤ 96.4 h with A wave conditions (H m0 = 23 cm / T p = 2.3 s), an overall erosion is presented during the numerical simulation. As it is derived from the Figure 5, the sandbar system has been migrated seaward. The comparison with the experimental data (Figure 7) shows that the erosion is less intense shoreward in the case of the numerical model and the concentration of the sediment in the zone x ≤ 6 is higher than that of the experiment. The present results are direct in agreement with existing studies [START_REF] Russell | Mechanisms for beach erosion during storms[END_REF], [START_REF] Thornton | Bar/trough generation on a natural beach[END_REF], which have revealed that the beach erosion is proportional to the amount of the wave energy in the coastal zone. Furthermore, it is difficult to compare the characteristics of the alongshore morphology, since the flow at the inlet of the numerical analysis is considered alongshore uniform. However, conversely to the study of [START_REF] Michallet | Physical modeling of threedimensional intermediate beach morphodynamics[END_REF], these results seem to be compatible with that of [START_REF] Wright | Morphodynamic variability of surf zones and beaches: A synthesis[END_REF], as a decrease of the beach threedimensionality is presented during the morphological evolution. As concluted from the present work, applying the same wave climate for a long time period resulted in a decrease in the bottom evolution velocity. Hence, the beach tends towards a steady state, by reshaping the bar into an alongshore-uniform pattern. Additionally, for the comparison of the alongshore morphological characteristics, it has to be considered that the lateral boundaries in the physical model act as headlands, increasing the beach three-dimensionality. It has been assumed that the differences in the morphological evolution within and between beaches during storms, are related to embayment geometry and orientation of the shore, while the sediment transport is driven by marked alongshore gradients in breaking wave height and interaction with embayment boundaries [START_REF] Loureiro | Extreme erosion on high-energy embayed beaches: Influence of megarips and storm grouping[END_REF].This phenomenon does not occur during the numerical modelling , since the values at boundary cells are obtained by second order extrapolations normal to the boundary from the values inside the domain.

CONCLUSIONS AND FUTURE RESEARCH

The essential goal of this research is to further our ability to understand wave-sandbed interaction. The proposed numerical model based on shallow water equations was applied to two different categories ( A, B) of shore normal irregular waves propagating over a sand bed field, and a comparison between the experimental data and the numerical results has been well performed. This study appears that the outcomes of the numerical model show enough accuracy for the values of the wave periods and the obtained beach profiles, but some deviations between the results of the model and the experiment have been observed concerning the characteristics of the beach three-dimensionality. Because of these deviations, the procedure of this study is based on the transition from the dissipative (D) to the reflective (R) beach state and back again, ignoring the intermediate sub-states, low tide terrace(LTT), transverse bar and rip (TBR), rhythmic bar and beach (RBB), and longshore bar trough (LBT). These correspond to the most widely accepted sequential beach state classification scheme of [START_REF] Wright | Morphodynamic variability of surf zones and beaches: A synthesis[END_REF]. In order to understand the sediment motion from a design standpoint, the experiments need to be continued, including new investigations in random waves, reflective shorelines, sediment transport, and multi-reflection between reflective structures. Also the numerical model need to be further developed, with potential use in design and in longterm prediction of coastal impact by waves.

  Values at boundary cells are obtained by second order extrapolations normal to the boundary from the values inside the domain. To describe incoming waves we are use an absorbing/generating inlet boundary condition where the values of water depth are prescribed. In open sea we allow for reflected waves to freely exit the domain. Time integration is explicit for the flow. Due to what we said on the difference of time scales between fluid motion and changes in sea bed , several time step will be taken, typically 100 seconds, in the flow solver before a new step by the bed model described by minimization iterations.

Figure 1 :

 1 Figure 1: Schematic diagram of the basin with x and y, the cross-shore and alongshore coordinates, respectively. The mean water depth is h 0 = 0.765m for x ≤ 6m. The sandy beach extends from x = 6m to x = 26m. The sliding beam allows for bathymetric survey in the region shaded in grey. Circles indicate positions of the capacitance gauges[START_REF] Michallet | Physical modeling of threedimensional intermediate beach morphodynamics[END_REF].

Figure 2 :

 2 Figure 2: (a) View of a breaking wave front over the threedimensional bathymetry. Wave paddles are seen in the top left corner and the sliding beam supporting the wave gauges (1 m apart) and velocimeters are seen on top of the picture. (b) View of the emptied basin during a bathymetric survey showing the presence of a crescentic sandbar and sand ripples[START_REF] Michallet | Physical modeling of threedimensional intermediate beach morphodynamics[END_REF].

Figure 4 :

 4 Figure 4: Wave elevation at (x = 18.33, y = 9.27), as obtained by the numerical model (red line) and the experimental data (blue line).

Figure 5 :

 5 Figure 5: Three dimensional shape of the bed (bathymetry) as outcome of the numerical model. Initial (red lines), after 62 hours (blue lines) and after 96.4 hours (green lines).

Figure 6 :

 6 Figure 6: Three dimensional shape of the bed (bathymetry) during the first phase of simulation. Initial (red lines), numerical model (blue lines) and experiment (green lines).

Figure 7 :

 7 Figure 7: Three dimensional shape of the bed (bathymetry) during the second phase of simulation. Initial (red lines), numerical model (blue lines) and experiment (green lines).

1Laboratory of Harbour Works, Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens, Iroon Polytechniou 5, 15780 Athens, Greece.

2 Institut Montpellierain Alexander Grothendieck, Universite de

Montpellier, 34095 Montpellier cedex 5, France

ACKNOWLEDGEMENTS

This work has been financed by the State Scholarships Foundation (IKY), through the program "Research Projects for Excellence IKY/SIEMENS"