Pauline Lallemant-Dudek
email: pauline.lallemant@trs.aphp.fr

Claudio Vergari

Guillaume Dubois

Véronique Forin

Raphaël Vialle

Wafa Skalli

Ultrasound shearwave elastography to characterize muscles of healthy and cerebral palsy children

Ultrasound shearwave elastography to characterize muscles of healthy and cerebral palsy children

Pauline Lallemant-Dudek 1,2* , Claudio Vergari 1 , Guillaume Dubois 1 , Véronique Forin 2 , Raphaël Vialle 3 & Wafa Skalli 1 Shear wave elastography (SWE) is an ultrasound technique to obtain soft tissue mechanical properties. The aim of this study was to establish the reliability of SWE in young children, define reference data on healthy ones and compare the shear modulus of healthy and spastic muscles from cerebral palsy (CP). The reproducibility is evaluated: at rest, on 7 children without any musculoskeletal pathology by 3 different operators, on 2 muscles: biceps brachii long head and medial gastrocnemius. The comparison study was made, on the same 2 muscles, at rest and under passive stretching, with a control group (29 healthy children), a spastic group (spastic muscles of 16 children from CP) and a non-spastic group (non-spastic muscles of 14 children from CP). The intra-operator reliability and inter-operator reliability, in terms of standard deviation, were 0.6 kPa (11.2% coefficient of variation (CV)) and 0.8 kPa (14.9% CV) for the biceps, respectively, and 0.4 kPa (11.5% CV) and 0.5 kPa (13.8% CV) for the gastrocnemius. At rest, no significant difference was found. Under passive stretching, the non-spastic CP biceps were significantly stiffer than the control ones (p = 0.033). Spastic gastrocnemius had a higher shear modulus than in the control muscles (p = 0.0003) or the non-spastic CP muscles (p = 0.017). CP stretched medial gastrocnemius presented an abnormally high shear moduli for 50% of patients.

Cerebral palsy (CP) "describes a group of permanent disorders of the development of movement and posture, causing activity limitation, that are attributed to non-progressive disturbances that occurred in the developing fetal or infant brain" 1 . One of the most frequent consequences is muscular spasticity, which must be evaluated regularly to provide suitable treatments and to measure muscular efficiency. In clinical routine, evaluation is obtained by manually stretching a specific muscle group and grading the resistance encountered, according to the movement speed, with the Modified Ashworth Scale (MAS) [START_REF] Bohannon | Interrater reliability of a modified Ashworth scale of muscle spasticity[END_REF] or the Tardieu Scale 3 . The results are reliable for two muscles groups: elbow flexors 2,3 and ankle plantar flexors [START_REF] Gracies | Reliability of the Tardieu Scale for assessing spasticity in children with cerebral palsy[END_REF] . However, these grading systems do not provide a quantitative measurement of the stiffness of each muscle, which is important when treating with botulinum toxin type A injection [START_REF] Heinen | The updated European Consensus 2009 on the use of Botulinum toxin for children with cerebral palsy[END_REF] .

In vivo techniques were developed to quantify muscle stiffness noninvasively. For instance, magnetic resonance elastography gives access to the shear modulus of the muscle, a mechanical parameter indicating tissue stiffness. Basford et al. [START_REF] Basford | Evaluation of healthy and diseased muscle with magnetic resonance elastography[END_REF] compared right medial gastrocnemius shear modulus between a control group (24.86 kPa) and diseased adults with spastic muscles (41.65 kPa). However, this technique is difficult to implement in terms of time and cost, and especially for young patients who are supposed to stay still for long acquisition times.

Ultrasound elastography has been used to characterize muscle stiffness. For instance, semi-quantitative sonoelastography has been used to obtain a semi-quantitative evaluation of children muscle [START_REF] Vasilescu | Sonoelastography contribution in cerebral palsy spasticity treatment assessment, preliminary report: A systematic review of the literature apropos of seven patients[END_REF][START_REF] Berko | Ultrasound elastography in children: Establishing the normal range of muscle elasticity[END_REF][START_REF] Kwon | Spastic cerebral palsy in children: Dynamic sonoelastographic findings of medial gastrocnemius[END_REF][START_REF] Park | Sonoelastographic evaluation of medial gastrocnemius muscles intrinsic stiffness after rehabilitation therapy with botulinum toxin a injection in spastic cerebral palsy[END_REF] : at rest, spastic muscles appeared twice as stiff as healthy children muscles 8 , while a month after an intramuscular injection of botulinum toxin type A in the gastrocnemius, the stiffness of spastic muscle decreased from 3.4 to 1.5 (without unit) [START_REF] Park | Sonoelastographic evaluation of medial gastrocnemius muscles intrinsic stiffness after rehabilitation therapy with botulinum toxin a injection in spastic cerebral palsy[END_REF] . Acoustic Radiation Force Impulse (ARFI) has been used to evaluate muscular stiffness on children with CP [START_REF] Bilgici | Quantitative assessment of muscular stiffness in children with cerebral palsy using acoustic radiation force impulse (ARFI) ultrasound elastography[END_REF][START_REF] Bilgici | Quantitative assessment of muscle stiffness with acoustic radiation force impulse elastography after botulinum toxin A injection in children with cerebral palsy[END_REF] .

Shearwave elastography (SWE) [START_REF] Gennisson | Transient elastography in anisotropic medium: Application to the measurement of slow and fast shear wave speeds in muscles[END_REF][START_REF] Bercoff | Supersonic shear imaging: A new technique for soft tissue elasticity mapping[END_REF] allows quantitative estimation of tissue shear modulus with a non-invasive, non-painful and non-irradiating examination. It has been applied to evaluate muscles of CP children [START_REF] Lee | Use of shear wave ultrasound elastography to quantify muscle properties in cerebral palsy[END_REF] and compare them to healthy children [START_REF] Brandenburg | Quantifying passive muscle stiffness in children with and without cerebral palsy using ultrasound shear wave elastography[END_REF] on gastrocnemius. While these studies demonstrate the method's feasibility, its reproducibility remains to be quantified. This aspect is essential for the follow-up of children, as it is necessary to distinguish the uncertainty of the technique from the evolution of the disease. Moreover, assessing reference values for typical children muscles may be useful to assess the severity of the disease.

The aim of this study was to establish the reliability of SWE in young children, define reference data on healthy ones and compare the shear modulus of healthy and spastic muscles from CP at rest and under passive stretching.

Methods

Participants. Before inclusion, children and parents were informed of the purpose of the study and agreed to participating and signed consent, as approved by the ethical committee (CPP 6001 Ile de France VI). Institutional Review Board approval was obtained. All the method was carried out in accordance with relevant guidelines and regulations.

Twenty-nine children younger than 15 years (12.1 ± 3.3 years old, 17 girls and 12 boys, 27 right-handed) were recruited as the healthy control group (Table 1, group 1); nine of them had mild scoliosis (Cobb angle < 20°), while fourteen had local fracture or angioma, and for these subjects the measurements were only performed on the healthy limbs. None of these subjects had any history of musculoskeletal pathology, or previous ankle, knee or elbow surgery.

Sixteen children affected by CP (8.3 ± 2.8 years, 6 girls and 10 boys, 6 right-handed) (Table 2) were also included. This group was constituted of: one monoparesis, four diplegia, eight hemiplegia (five of which at the right side), one child who had three limbs reached by CP and 2 children who had tetraparesia. Patients who had already received more than two intramuscular injections of botulinum toxin type A in the studied muscles were excluded, since this toxin modifies the muscle structure and biomechanical properties [START_REF] Hong | Influence of injection of Chinese botulinum toxin type A on the histomorphology and myosin heavy chain composition of rat gastrocnemius muscles[END_REF][START_REF] Williams | Muscle volume alterations in spastic muscles immediately following botulinum toxin type-A treatment in children with cerebral palsy[END_REF] . Included children had their last botulinum toxin injection at least than 4 months earlier. None of these children have had previous limb surgery. Spasticity of the studied muscles was clinically assessed with the MAS. For the upper limb, the Manual Ability Classification System for cerebral palsy (MACS) [START_REF] Eliasson | The manual ability classification system (MACS) for children with cerebral palsy: Scale development and evidence of validity and reliability[END_REF] (score from 1 to 5) was calculated for each children.

For the lower limb, the Gross Motor Function Classification System for cerebral palsy (GMFCS) [START_REF] Palisano | Development and reliability of a system to classify gross motor function in children with cerebral palsy[END_REF] (score from 1 to 5) was used. Spastic muscles of these children were included in Group 2, while their healthy muscles were included in Group 3 (Table 2).

Measurements. An Aixplorer ultrasound device (Supersonic Imagine, Aix-en-Provence, France), with a 50 mm 8 MHz linear probe was used to measure muscle shear modulus. The probe was applied perpendicularly to the skin and parallel to muscle fibers, and it was placed according to the anatomical landmarks described below. Four series of 8 continuous images were recorded with the device set to "general mode", "low" spatial smoothing and 3-image temporal smoothing. Data was processed in Matlab 2016b (The MathWorks Inc., Natick, MA) as previously described [START_REF] Vergari | Non-invasive biomechanical characterization of intervertebral discs by shear wave ultrasound elastography: A feasibility study[END_REF] . Briefly, an operator defined a rectangular Region of Interest (ROI) of the elastographic image in the first frame of the series. The ROI was placed on the muscle belly, excluding skin, bone, vessels or muscle fascia (Fig. 1), but also excluding the borders of the elastographic chart to avoid border effects. Depth and size of the ROI were adapted to muscle size, in order to maximize the ROI size while avoiding the aforementioned structures. The ROI was then semi-automatically tracked in the following images; the shear modulus was space-averaged in each frame ROI, and a time-average was then calculated from all frames to obtain a single value for the series, then the four series were averaged again to obtain a single value.

Procedure. Measurements were done on the Gastrocnemius Medialis (GCM) proximal third and the Biceps Brachii Long head (BBL) distal third for every child, both on right and left side, at Rest (_R) and under passive Stretching (_S). The subjects were asked to be as relaxed as possible.

For the measurement at rest on the GCM (GCM_R), subject was prone with a knee flexion at 90°, leg against the wall and the ankle free [START_REF] Dubois | Reliable protocol for shear wave elastography of lower limb muscles at rest and during passive stretching[END_REF] . For the BBL (BBL_R), the subject was sitting on a chair, elbow flexion at 90°, hand in supination and the wrist fully extended. A custom elbow splint was used to maintain the position.

In order to stretch the GCM (GCM_S), the subject was prone on a table, the leg extended with the ankle hanging outside the table, while for the BBL (BBL_S), the subject was sitting on a chair and his elbow was dangling fully extended.

All measures were performed by the same operator. Four measurements (i.e., four series of 8 frames) were repeated and averaged for each muscle and each position. This protocol lasted about 15 min.

Reproducibility.

A reproducibility study was performed on seven healthy children from group 1 (5 boys and 2 girls, 8.3 ± 2.2 years old, all right-handed). All measurements were performed at rest on one upper and one lower limb; side (right or left) was randomly selected (all children were right-handed). Measurements were performed by 3 experienced operators, and each measure (i.e., each series of 8 images) was repeated 6 times. The opposite limb was examined by one operator. In other words, inter-operator reproducibility was evaluated on one upper and one lower limb, while intra-operator reliability was measured on four limbs. This protocol lasted about 40 min per subject.

Results

The intra-operator repeatability was 0.6 kPa (11.2% coefficient of variation) for the BBL and 0.4 kPa (11.5%) for the GCM. The inter-operator reproducibility was 0.8 kPa (14.9%) for the BBL and 0.5 kPa (13.8%) for the GCM. ICC was equal or higher than 0.9 for each operator and both muscles, while inter-operator ICC was 0.92 for both muscles. Figure 2 synthesizes the mean shear moduli measured on each muscle and each position for each group. Both GCM and BBL were significantly stiffer when stretched compared to at rest in each group (p < 0.05). BBL did not show any significant difference between groups, neither at rest nor stretched (p > 0.05).

Stretched GCM was slightly stiffer in the dominant side (4.6 ± 1.4 kPa) than in the opposite side (5.1 ± 1.4 kPa, p = 0.02) for the healthy population. Stretched GCM was also significantly stiffer in group 2 (8.8 ± 4.1 kPa) than in group 1 (2.9 ± 0.7 kPa, p = 0.0001) and group 3 (5.0 ± 0.9 kPa, p = 0.05), although the latter comparison was at the limit of significance.

The ratio of stretched GCM shear modulus over modulus at rest was higher in group 2 (3.1 ± 1.8) than in groups 1 (1.8 ± 0.6, p = 0.0001) and 3 (1.9 ± 0.5, p = 0.03). In group 2, 5 patients had abnormally high shear modulus (higher than 95% subjects of group).

No correlations were observed between shear modulus or ratios and MAS, MACS and GMFCS scores (Fig. 3).

Discussion

In this study, SWE reproducibility was assessed in young children, finding an uncertainty of 0.6 kPa for the BBL and 0.4 kPa for the GCM. This threshold is important when assessing possible changes with treatment or evolution disease. This sensibility could provide information about treatment efficacy or loss of efficiency before it can be detected clinically. SWE could be used as a tracking tool in addition with the clinical conclusions to precise evolutions, especially if treatment effect is poor or disability scales difficult to assess. Spastic GCM were stiffer than healthy GCM, either if the latter is from healthy children or the contra-lateral limb of the same CP patient. Stretched GCM presented an abnormally high shear modulus for 50% of CP patients. Interestingly, GCM at rest did not show any difference between groups, nor did BBL either at rest nor stretched. This could be due to measurement reliability; indeed, inter-operator reproducibility was slightly lower in GCM than in BBL. The position adopted by patients for GCM measurements was easy to hold for disabled children. The position for the BBL was less easy to hold; the operator has to take care that the patient keeps the arm in supination. Preliminary tests showed that supination did affect measurements by slightly stretching the biceps muscle. The position used to assess the shear modulus is fundamental. The SWE permit to measure shear modulus on each muscle. The Tardieu Scale 3 is validated on ankle plantar flexors: i.e. lateral gastrocnemius, medial gastrocnemius and soleus. To define the shear modulus muscle by muscle is an opportunity to precise Nevertheless, results were clinically consistent, in the sense that spastic muscles were systematically stiffer than the healthy or non-spastic ones, even if sometimes with no statistical significance. Results confirm that a stretched muscle has a higher shear modulus than a muscle at rest both in healthy muscles, as previously shown in healthy [START_REF] Brandenburg | Quantifying passive muscle stiffness in children with and without cerebral palsy using ultrasound shear wave elastography[END_REF][START_REF] Dubois | Reliable protocol for shear wave elastography of lower limb muscles at rest and during passive stretching[END_REF][START_REF] Hug | Slack length of Gastrocnemius medialis and Achilles tendon occurs at different ankle angles[END_REF][START_REF] Maïsetti | Characterization of passive elastic properties of the human medial gastrocnemius muscle belly using supersonic shear imaging[END_REF] and pathologic muscles [START_REF] Brandenburg | Quantifying passive muscle stiffness in children with and without cerebral palsy using ultrasound shear wave elastography[END_REF] . Nevertheless, the latter study did not find any difference between CP children and healthy ones. The shear modulus measured in this article were smaller to those measured by Brandenburg et al. in lateral gastrocnemius [START_REF] Brandenburg | Quantifying passive muscle stiffness in children with and without cerebral palsy using ultrasound shear wave elastography[END_REF] , which ranged respectively from 7.8 to 28.9 kPa versus 4.6 to 8.8 kPa in the present study. The leg and ankle position adopted in this study to stretch the GCM was similar to the "0° plantarflexion" used by Brandenburg et al. Consistently with their results, this position gave the largest difference between groups and variability in CP group (Fig. 2b). Also, those authors did not find any difference when values of stretched muscle were normalized on the values measured at 20° plantarflexion, which is consistent with the lack of differences found with SWS ratios measured in the present work. Dubois et al. [START_REF] Dubois | Reliable protocol for shear wave elastography of lower limb muscles at rest and during passive stretching[END_REF] reported values for GCM_R (4.7 kPa) and GCM_S (6.2 kPa) similar to those measured in this study, while Lacourpaille et al. [START_REF] Lacourpaille | Supersonic shear imaging provides a reliable measurement of resting muscle shear elastic modulus[END_REF] reported even lower values for GCM_R (3.0 kPa).

A limitation of the present study is that the control population was older than the CP children (12.1 versus 8.3 years). Nevertheless, this should not have an impact on the comparison between groups since no significant age effect has been found on shear modulus, consistently with previous studies [START_REF] Dubois | Reliable protocol for shear wave elastography of lower limb muscles at rest and during passive stretching[END_REF] . The values reported in this study on GCM and BBL shear modulus could be used as reference for children with typical development.

No correlation was found in the present cohort between the shear modulus and the disability scales, neither for BBL nor for GCM. This is consistent with the results of Brandenburg et al., who found no association between GCM shear modulus and neither GMFCS level nor MAS grade. Bilgici et al., however, reported a correlation between MAS scales and shear modulus, with ARFI technique [START_REF] Bilgici | Quantitative assessment of muscular stiffness in children with cerebral palsy using acoustic radiation force impulse (ARFI) ultrasound elastography[END_REF] . A correlation between soleus muscle MAS and shear modulus was identified by Vola et al. [START_REF] Vola | Use of ultrasound shear wave to measure muscle stiffness in children with cerebral palsy[END_REF] in an homogenous population of children affected by hemiplegic cerebral palsy. In the present study, the population was more heterogeneous as it included different limb weaknesses; this could explain the different results. Gao et al. found also a correlation between Mas and Tardieu scales in adults with post-stroke spasticity [START_REF] Gao | Quantitative ultrasound imaging to assess the biceps brachii muscle in chronic post-stroke spasticity: Preliminary observation[END_REF] with high spasticity, in particular in cases with muscle retraction. However, a much older population was studied (59 on average, against 8.3 in this study), which is relevant since muscle elasticity changes with age. Larger studies with more subjects might be required to assess the correlation between the shear modulus and the disability scales, and to confirm the interest of measuring stretched spastic muscles to characterize the stage of neuromuscular pathologies and quantify the effects of treatment.

Conclusion

SWE is a reliable technique to quantitatively assess muscle stiffness. This shear modulus measurement is easy to assess even on children, and it can be used in clinical routine. This study reported reference data on healthy children with typical development and new information on the biomechanical properties of spastic muscles. In particular, it appears that SWE could be more suited to assess gastrocnemius, for which large differences were observed between CP and healthy children (or healthy muscles in CP children). Measurement in biceps brachii could be less informative on their pathological status.

Statistical analysis.

  Intra and inter-operator reliability were calculated in terms of standard deviation, as recommended by the ISO 5725 standard. Intraclass Correlation Coefficient (ICC) was also calculated intra-and inter-operators for each muscle. Non-parametric Kruskal-Wallis tests and Dunn's post-hoc analysis were used to compare the 3 groups. Dominant and non-dominant sides were compared for healthy subjects using Mann Whitney tests, while correlation between shear modulus and clinical parameters were analyzed with Spearman's rank test. All calculations were performed in Matlab 2016b (The Mathworks, Natick, USA). Significance was set at p < 0.05.

Figure 1 .

 1 Figure 1. The elastography images of the medial gastrocnemius and below the ultrasonography images.

Figure 2 .

 2 Figure 2. (a) Mean shear modulus and standard deviation per group and position for the biceps brachii long (BBL). (b) Mean shear modulus and standard deviation per group and position for the gastrocnemius (GCM).

Figure 3 .

 3 Figure 3. Relationship of biceps brachii long (BBL) and gastrocnemius (GCM) at rest (R subscript) or stretched (S subscript) with Modified Ashworth Scale (MAS), Manual Ability Classification System for cerebral palsy (MACS) and Gross Motor Function Classification System for Cerebral Palsy (GMFCS). No correlations were observed.

Table 1 .

 1 Characteristics of group 1 (healthy children).

	N°Age (years) Sex	Dominant Side Weight (kg) Height (cm)
	1	14.7	M	Right	57	168
	2	15.9	M	Right	71	194
	3	13.0	M	Right	42	153
	4	10.8	F	Right	47	155
	5	14.5	M	Right	70	165
	6	12.8	M	Right	65	177
	7	8.0	F	Right	24
	8	14.2	F	Right	40	159
	9	13.5	F	Right	45	159
	10	14.8	M	Right	50	164
	11	7.3	F	Right	28	128
	12	14.5	F	Right	42	149
	13	15.5	F	Left	52	162
	14	16.8	F	Right	45	157
	15	11.6	F	Right	40	150
	16	14.7	F	Left	52	172
	17	13.3	F	Right	46	160
	18	15.6	M	Right	65	174
	19	8.5	M	Right	22	120
	20	15.4	M	Right	65	176
	21	12.1	F	Right	42	158
	22	14.3	F	Right	43	160
	23	10.5	F	Right	23.0	135
	24	6.9	M	Right	25.0	126
	25	10.6	M	Right	31.7	144
	26	10.8	F	Right	20.7	120
	27	6.8	M	Right	18.0	116
	28	5.8	M	Right	17.0	112
	29	6.8	M	Right	23.0	120
	Mean	12.1			41.8	151.2
	SD	3.3			16.3	21.4

Table 2 .

 2 Characteristics of group 2 and 3 (cerebral palsy children, U = upper limb, I = lower limb, R = right, L = left).

	No	Age (years) Sex	Dominant side Weight (kg) Height (cm) Spastic limbs	MACS (1 to 5) GMFCS (1 to 5)
	1	7.6	M	R			UL _ IR _ IL	3	2
	2	6.9	M	L			UR _ UL _ IR _ IL 2	5
	3	6.0	F	R	22	100	IR _ IL	1	2
	4	5.4	M	L	17.8	111	IR	1	1
	5	5.8	F	L	20		UR _ IR	2	1
	6	5.6	M	L	18	107	UL _ IL	3	1
	7	9.3	M	R	21		IR _ IL	1	2
	8	8.8	F	R	29	133	UL _ IL	2	1
	9	9.4	F	L	35	135	UR _ IR	3	1
	10	7.3	F	R			IR _ IL	1	2
	11	12.4	M	R	24	140	UL _ IL	2	1
	12	12.7	M	_	30		UR _ UL _ IR _ IL 5	5
	13	7.8	M	R	25	128	IR _ IL	1	2
	14	14.8	F	L	50	153	UR_ IR	2	1
	15	5.2	M	L	22	126	UR_ IR	3	1
	16	8.5	M	L	33		UR_ IR	3	2
	Mean	8.3			27.4	125.9
	SD	2.8			8.9	17.0

Author contributions

P.L.-D., G.D. and C.V. collected the clinical information, drafted the main manuscript and performed the statistical analysis. R.V, V.F. and W.S. controlled the methods used and the results. The final manuscript was approved by all coauthors.

Competing interests

The authors declare no competing interests.


Aline Aubry
email: aubry@univ-littoral

Sandric Lesourd
email: lesourd@univ-littoral

Antoine Gardel
email: gardel@univ-littoral

P Dubuisson
email: philippe.dubuisson@loa.univ-lille1.fr

M Jeanson
email: jeanson@univ-littoral

Sediment textural variability

Keywords: beach profile, sand flat, muddy beach, macrotidal

published or not. The documents may come

INTRODUCTION

Sandy tidal flats with heterogeneous sediments, an extremely flat morphology, and subject to variably strong tidal flows as the main hydrodynamic forcing agent are poorly documented in the literature on beaches [START_REF] Malvarez | Sandy Tidal Flat Morphodynamics? Examples from Strangford Lough in Northern Ireland[END_REF]. Sand flats are commonly dominated by wave-induced sediment entrainment and combined wave-current interactions that are expressed as spatial distributions of complex sedimentary assemblages. The most studied in the literature are tidal flats displaying sediment heterogeneity [START_REF] Holland | A review of heterogeneous sediments in coastal environments[END_REF], such as those of the Wadden Sea ( [START_REF] Van Straaten | Tidal action as a cause of clay accumulation[END_REF][START_REF] Reineck | Layered sediments of tidal flats, beaches and shelf bottoms of the North Sea[END_REF][START_REF] Eisma | Intertidal Deposits: River Mouths, Tidal Flats and Coastal Lagoons[END_REF], the Yellow Sea coasts of South Korea [START_REF] Wells | Morphology, sedimentology and tidal channel processes on a high-tide-range mudflat, West-Coast of South-Korea[END_REF][START_REF] Yang | Sedimentation on a wave-dominated, opencoast tidal flat, south-western Korea: summer tidal flat-winter shoreface[END_REF] and the Bay of Fundy [START_REF] Klein | Comparison of sediments from Bay of Fundy and Dutch Wadden Sea tidal flats[END_REF][START_REF] Amos | Fine-grained sediment transport in Chignecto Bay, Bay of Fundy, Canada[END_REF]DASHTGARD et al., 2006). Sometimes associated with such sand flats are beaches with intertidal bar-trough systems, the morphodynamic specificities of which have been highlighted in several recent studies (e.g., [START_REF] Levoy | Morphodynamics of a macrotidal ridge-and-runnel beach[END_REF][START_REF] Masselink | Location and height of intertidal bars on macrotidal ridge and runnel beaches[END_REF][START_REF] Kroon | Morphodynamics of intertidal bar morphology on a macrotidal beach under low-energy wave conditions, North Lincolnshire, England[END_REF][START_REF] Anthony | The influence of Amazonderived mud banks on the morphology of sandy, headlandbound beaches in Cayenne, French Guiana: A short-to longterm perspective[END_REF]ANTHONY et al., , 2005;;[START_REF] Reichmüth | Tidal influence on the intertidal bar morphology of two contrasting macrotidal beaches[END_REF], 2008a, 2008b;[START_REF] Sedrati | Storm-generated morphological change and longshore sand transport in the intertidal zone of a multi-barred macrotidal beach[END_REF]. However, the association between sand flats and such intertidal bar-trough beaches has hardly been considered in the literature, excepting in two studies of the aeolian dynamics of sand flats associated with a large accreting beach in northern France [START_REF] Anthony | Sedimentology and stratigraphy of a transgressive, muddy gravel beach: Waterside Beach, Bay of Fundy, Canada[END_REF][START_REF] Anthony | Sedimentology and stratigraphy of a transgressive, muddy gravel beach: Waterside Beach, Bay of Fundy, Canada[END_REF].

Study area

The study area, a beach east of Calais on the North Sea coast of France (Fig. 1), is exposed to fetch-limited (T=4-6 s), relatively low-energy waves (modal Hs < 0.6 m) punctuated by storm activity (Hs up to 3 m). This environment is affected by semi-diurnal tides with a mean spring tide range of about 6.4 m in Calais, with flooddominated residual flow towards the NE. The combination of storm winds and waves and large tidal ranges also generates strong longshore currents that affect both the shoreface and the beaches of the southern North Sea (ANTHONY and ORFORD, 2002;[START_REF] Sedrati | Storm-generated morphological change and longshore sand transport in the intertidal zone of a multi-barred macrotidal beach[END_REF][START_REF] Oblinger | Wave attenuation and intertidal morphology of a macrotidal barred (ridge-and-runnel) beach behind a breakwater: Dunkerque, northern France[END_REF]. This site is one of the rare actively accreting sectors of coast in the southern North Sea, most probably due to sand supply generated by the onshore migration and coastal welding of a nearshore sand bank, in the twentieth century, leading to the accumulation of a shore-attached sand reservoir of 400,000 m3 in nearly 80 years [START_REF] Garlan | L'apport des levés bathymétriques pour la connaissance de la dynamique sédimentaire[END_REF], and to the formation of the large upper beach sand flat fronting the dunes. The sand flat and contiguous beach exhibit large variability in sediment composition, ranging from pure sand to significant fractions of mud, depending on the morphology, which is a combination of multiple intertidal bars and troughs (IBT), an upper beach platform with lower, middle and upper sand flat segments (respectively LSF, MSF, USF in Figure 1), and a foredune. The IBT and LSF are characterised by unimodal fine to medium sand (mean grain size, Xm=0.19-0.33 mm), the MSF by silt to fine sand (Xm =0.01-0.24 mm) with most of the sediment being bimodal, and the USF by silt and clay (Xm= 0.01 mm).

MATERIELS AND METHODS

A representative 1850 m-long cross-shore transect, covering the full range of surface textures from mud to sand, was set up on the sand flat and three field experiments (in March, September 2007, andin April 2008), involving variable wave and tidal conditions and spanning different seasons, were conducted. The transect was surveyed using a total station with errors within ±3 mm for distance and ±0.0015° for direction. An uncertainty band (5 cm) was determined as a margin of error of measurements of net change in profile morphology. All the surveys were referenced to a benchmark of the French National Geodesic Service (I.G.N. 69).

Simultaneously, subsurface sediment samples (2 cm depth) were collected along this central transect from survey points spaced 10-20 m apart. The grain-size distribution (sand-to-clay fraction) was analysed using a Laser Beckman-Coulter LS 230. Hydrodynamic data were collected during each experiment at three locations (Fig. 1) along the transect (on IBT, LSF and USF). Directional wave and current data were obtained using an InterOcean S4 electromagnetic current meter and two ADVs (Acoustic Doppler Velocimeter). Hourly wind data (speed and direction) were obtained from Meteo-France meteorological stations located a few kilometres inland of the experimental site.

RESULTS

Energy conditions

The experiments were conducted over twenty tides covering spring-to-spring cycles. The data presented concern only the first three days of each experiment, as the hydrodynamic conditions were sufficiently energetic as to influence the cross-shore morphology and the sediment distribution. The experiments were realised under similar tidal range conditions (between 6 and 6.37 m). The incident wave heights and the associated weather conditions during the considered periods of each experiment are displayed in Figure 2. The high-energy conditions in March 2007 were characterised by several strong wind events comprising NE to E winds (speeds of up to 13 m.s-1) that then slightly weakened on veering to W, then NW, regaining strength once again with speeds of more than 11 m.s-1. These wind events reinforced the mean current velocities on the sand flat (with peak current speeds exceeding 1.9 m. s-1) and were responsible for waves with significant heights of about 2.58 m (Fig. 2).

Waves under low-energy conditions rarely exceed 1 m on average, and the mean current velocities never exceed 1 m.s-1. Such conditions are associated with wind speeds that do not exceed 5-6 m.s-1 (Fig. 2).

Wave and current attenuation during typical rough weather

Wave height attenuation (see locations of current meters in Figure 1) between the IBT and the LSF is very important (approximately 90 %), and still remains significant at 23 % between LSF and USF (Fig 3b). During the storm event in march 2007 strong winds exceeding 14 m.s-1, were associated with significant wave heights that exceeded 2.5 m on the beach, but that did not exceed 0.5 m at the same time on the LSF or USF (Fig. 3b). Over the bare sandy surface of the sand flat, the incoming waves were reduced in height due to breaking processes and bottom friction over the flat gradient, and the significant wave height over USF remained less than 0.3 m in spite of the storm event. The mean overall current velocities (U, sum of longshore and cross-shore currents) exhibited similar behaviour (Fig 3d). The largest velocities were, as expected, recorded on the beach, with currents becoming particularly strong (0.8-1 m. s-1) when flows were forced during the storm. Velocities decreased slightly towards the LSF (0.42-0.49 m.s-1), except during slack water just before 01:00 (Fig. 3d), when the currents were reinforced (0.55 m.s-1) by the wind notably under the very shallow water depths. Currents became very weak on the USF (0.4-0.2 m.s-1). During high tide, longshore-dominant currents did not exceed 0.6 m.s-1 on the IBT, and decreased towards the LSF (0.2 m.s-1) and the USF (0.06 m.s-1). At the same time, cross-shore currents (0.4 m.s-1 on the IBT, 0.3 m.s-1 on the LSF and 0.2 m.s-1 on the USF), were dominantly offshore. This large upper beach platform results in quasi-complete attenuation of waves and currents even during storm conditions. This dissipation of energy over the intertidal sand flat encourages sediment deposition.

Cross-shore morphological change

The topographic changes recorded on the central profile aredepicted in Figure 4. Much of the beach profile under mean highwater neaps was affected by significant change (>0.2 m) between two survey profiles, with accretion and an onshore migration of IBT. Alternating zones of erosion and deposition occurred across the seaward slope of the bar, and there is some evidence for a landward movement of these zones, which could be analogous to the onshore migrating bed oscillations described by [START_REF] Greenwood | Swash bar morphodynamics in the Danish Wadden Sea: sand bed oscillations and suspended sediment flux during an accretionary phase of the foreshore cycle[END_REF]. The largest relative variations of topography on the beach were associated with IBT (0.39 to 0.45 m) and highlight a regular onshore supply of sand between the beginning of the survey in March 2007 and the end in April 2008. The net topographic differential over the survey period shows that much of the change is above the 5 cm uncertainty band (Fig. 4). The LSF was relatively stable. The topographic variations of the MSF over these experimental periods are moderate (<0.1 m) and globally correspond to a progressive filling of the depression at the landward end of the MSF.

The USF variations are not depicted here, but this zone showed relative morphological stability. Analysis of the sediment textural and spatial patterns over a oneyear period show an increase in the mud fraction in the LSF, and the onshore migration of these fine sediments onto the USF (crossshore spatial fluctuations in the mud content), resulting in significant muddy sedimentation in this latter zone. The analysis of long-term satellite data (results not presented here) shows that the presence of mud on this uppermost part of the beach is rather unusual. This pattern shows, however, that in an accretionary context of a sand-rich, stormwave dominated macrotidal coast with available mud, the morphodynamic conditions may favour the significant trapping of mud.

Analysis of surface sediment change and temporal variation

DISCUSSION AND CONCLUSION

As is common throughout the English Channel [START_REF] Larsonneur | The Holocene shorelines in the superficial sediments of the English Channel and its Western Approaches[END_REF][START_REF] Anthony | Long-term marine bedload segregation, and sandy versus gravelly Holocene shorelines in the eastern English Channel[END_REF]LESOURD et al., 2003a), fine sediments are found in sheltered bays and estuaries where this grain-size fraction can easily be trapped. Two specificities of this study area are that it is one of the rare actively accreting sectors of coast in the southern North Sea, and it exhibits a significant fraction of mud for an open coast. The morphological system is composed of a beach with IBT succeeded by a large upper beach platform that ensures considerable wave and current attenuation (90 % by the IBT and 23 % by the sand flat) during typical rough weather affecting the southern North Sea. Energy attenuation by this system and local sediment availability explain the possibility for muddy sedimentation behind the uppermost swash bar. The system found associated with these flats thus differs from that of other mudrich sandy beaches such as those of South America where active decadal-scale beach rotation is induced by Amazon-derived mud banks migrating alongshore [START_REF] Anthony | Shortterm changes in the plan shape of a sandy beach in response to sheltering by a nearshore mud bank, Cayenne, French Guiana[END_REF][START_REF] Anthony | The influence of Amazonderived mud banks on the morphology of sandy, headlandbound beaches in Cayenne, French Guiana: A short-to longterm perspective[END_REF]. Fine material is generally trapped in the topographic depressions (middle of MSF). The initial topography in March, 2007 influenced the future sediment distribution. During mean high water spring, the sand flat is flooded. At low tide, the very weak slope behind the swash bar and especially the topographic depression prevent water from being drained. As a consequence, fine particles can accumulate. A demarcation zone (fig. 5) highlights the depositional boundary between the outer sand flats and the USF or mixed flats.

The progressive filling of this depression (end of MSF) between March, 2007 andApril, 2008, recorded in Figure 4, confirms the increase in proportion of settled fine particles depicted in Figure 5. The response of sediments to size-sorting processes has been discussed by several authors (e.g. [START_REF] Mclaren | The effects of sediment transport on grain-size distributions[END_REF][START_REF] Gao | Net sediment transport patterns inferred from grain-size trends, based upon definition of "transport vectors[END_REF]LE ROUX 1994;[START_REF] Anthony | Sedimentology and stratigraphy of a transgressive, muddy gravel beach: Waterside Beach, Bay of Fundy, Canada[END_REF]. In many tidal systems, surficial sediment distribution shows distinct sizesorting patterns controlled by local energy gradients. The observed seasonal pattern demonstrates that mud is easily resuspended by currents and wave action in winter (CHANG et al., 2006). As a consequence, the sand fraction becomes predominant on the upper beach and on the sand flat in the course of the winter season. Aeolian transport of sand is also facilitated as sand dries out [START_REF] Anthony | Sedimentology and stratigraphy of a transgressive, muddy gravel beach: Waterside Beach, Bay of Fundy, Canada[END_REF]. In response to the higher energy input by storm waves, sand is redistributed over the sand flat, resulting in the LSF and MSF, characterised by mixed sediment in September 2007, evolving into mud-depleted sand flats in April 2008, and thereby contributing to the bimodal grain-size distribution of the sediments. Mud deposition is controlled by very high tide levels and by the hydrodynamic regime, two parameters evincing a seasonal pattern. This study shows an increase in the mud fraction on the beach in one year. Several factors can explain this phenomenon: the specific morphology and its effect on wave attenuation, the availability of muddy sediment from the shoreface, a decrease in wave energy during summer, 2007, and notably surface drying with the formation of mud crusts with desiccation cracks that can be dispersed by wind. In this case, the in situ percentage of mud decreases on the surface. Fine sediments, as indicated earlier, had never been noticed (satellite observations) on the beach until September, 2007 demonstrating the recent appearance of the phenomenon. Analyses of short cores with interbedded mud and sand (layer <1 cm) and observation of muddy sedimentation on the USF (up to 5 cm thick) confirm, however, these sedimentological patterns. Facies analyses of short cores show a recurrent process of sedimentation and not an isolated event. The proximity of the port of Calais, the numerous shoreface sand ridges and the mud-rich sediments found in troughs between these ridges, increasing suspended particulate matter concentration in the Channel, or a cyclic modification of local or large-scale sediment transport may explain this input of mud. Mud has been observed on the shoreface and on parts of the intertidal beach in areas near the study site [START_REF] Anthony | The influence of Amazonderived mud banks on the morphology of sandy, headlandbound beaches in Cayenne, French Guiana: A short-to longterm perspective[END_REF][START_REF] Oblinger | Wave attenuation and intertidal morphology of a macrotidal barred (ridge-and-runnel) beach behind a breakwater: Dunkerque, northern France[END_REF], as well as off the Belgian coast (FETTWEIS and VAN DEN HEYDE, 2003;[START_REF] Fettweis | Suspended particulate matter dynamics and aggregate sizes in a high turbidity area[END_REF]. In parallel, after this consequent supply of mud to the lower beach under low-energy conditions (September, 2007), an onshore migration of fine sediments occurred in the central part of the MSF in 6 months. During winter, characterized by high-energy events, cross-shore processes due to waves have certainly played an important role in spite of the significant contribution of longshore processes. The sediments also undergo progressive size sorting in the course of landward transport and onshore migration towards the sand flat. In summary, the results of this study show the possibility of muddy sedimentation on an open macrotidal storm-wave setting due to the influence of the beach morphology. Mud deposition is controlled by a seasonal hydrodynamic regime, and begins by an increase in the mud fraction on the beach, followed by onshore transfer and incorporation into the upper beach sand flat.

  Surface sediments along the transect are composed of three grainsize fractions representative of the local sediment stock: fine sand (250-125 μm), very fine sand (125-63 μm), and silt and clay (Figure 5). Medium and coarse sand fractions are not included in this study because they represented a weak but constant proportion (<10 %) of the total sediment during the three experiments. Mud (grain sizes below 63 μm) is further subdivided into silt (63-2 μm) and clay (< 2 μm). With the exception of the USF (exhibiting 15 to 90 % of silt and clay), the sediments of the beach and sand flat are dominated by fine sand which forms more than 70 % of the stock. Muddy areas are relatively sheltered from wave action and fine material is generally found trapped in a topographic depression (landward end of the MSF). On the USF, in March 2007, the mud content in the superficial sediments increased, attaining up to 50%, at a distance of 1100 m landward of the IBT. This implies that mud is supplied to the sand flat when the small topographic depressions are flooded, because the area is protected from waves by the uppermost intertidal bar, a swash bar. Mud was found in two locations in September 2007 and April 2008. The mud fraction attained up to 90% at the landward limits of the MSF in autumn, and in the middle of the USF in spring 2008, thus highlighting an onshore migration (450 m) of these fine sediments onto the USF. The other location of mud concentration was the LSF in September 2007 and only below the MSL mark in April 2008. Mud temporarily deposited on the beach (important supply during calm conditions in September 2007) seems to be easily resuspended during winter storms, and migrates onshore onto the USF.

FIGURESFigure 1 :

 1 FIGURES

Figure 2 :

 2 Figure 2: Three-day incident wave height and wind speed records during the March, September 2007 and April 2008 experiments. The broken vertical bands indicate the time interval corresponding to sediment sampling.

Figure 3 :

 3 Figure 3: Wind conditions (a) from a nearby station, and significant wave height Hs (b), local water depth h (c), and mean overall current U (d) recorded on the beach, sand flat and upper sand flat (see Fig. 1) during storm conditions in March 2007.

Figure 4 :

 4 Figure 4: Changes in profile morphology between the 3 experiments. Note that USF is not shown in full.

Figure 5 :

 5 Figure 5: Changes in proportion of sediment size classes and in spatial distribution of sediment on the surveyed beach transect.

ACKNOWLEDGEMENTS

This work benefited from the financial support of the Research Council of the Université du Littoral Côte d'Opale and of the French national programme INSU Reliefs de la Terre: PLAMAR. Aline AUBRY holds a PhD grant from the French Ministry of Education. The authors would like to thank the urban community of Calais for logistic support and technical assistance during the field experiments. We wish to thank Vincent Sipka for technical assistance, and Edward Anthony for his constructive suggestions.