Professor Pascal Swider
email: pascal.swider@imft.fr

F Delanoë

F Jalbert

S Boetto

P Assemat

E Estivalèzes

F Lauwers

Mechanical properties of fused sagittal sutures in scaphocephaly

Keywords: 2546, Figure count: 5, Table count: 0 scaphocephaly, craniosynostosis, biomechanics, mechanobiology, paediatrics, morphogenesis scaphocephaly, craniosynostosis, biomechanics, mechanobiology, paediatrics, morphogenesis

Background: Craniosynostosis in newborns is caused by the premature closure of the cranial sutures leading to cranial vault deformity. It results in aesthetic imbalance and developmental disabilities and surgery is frequent during the first months of growth. Our study focused on scaphocephaly defined as the premature closure of the sagittal suture. We hypothesised that the effective mechanical properties of sutures were altered as compared to those of the parietal adjacent tissue considered as control.

Methods: The population consisted of seven males and four females (mean age 4.9 months).

Sixteen suture samples and thirty-four parietal tissue samples were harvested during corrective surgery and investigated by using three-point bending tests to obtain the structurestiffness of specimens. An energy model was used to derive the effective Young's modulus. A histological study complemented the experimental protocol.

Findings: Fused sutures were thicker than adjacent bone and the natural curvature of sutures did not influence the static mechanical response. The stiffness of stenotic sutures was significantly higher than that of the parietal bone. The effective Young's modulus of stenotic sutures was significantly lower than that of the parietal adjacent tissue. The parietal tissue showed a parallel bone architecture whereas the central stenotic tissue was disorganised with more vascularisation.

Interpretation: The stenotic suture differed in structural and mechanical terms from the adjacent bone during calvarial growth in the first year of life. Our study emphasised the alteration of effective tissue properties in craniosynostosis.

-Introduction

Cranial growth is affected by fluid pressure and forces exerted by internal organs, such as the brain, ocular globes and cephalic muscles. The cranial vault initially consists of single layers of membranous bones and relative sutures. The monolayer tissue is progressively replaced by a layered tissue, consisting in two layers of cortical bones developed from periosteal apposition and located on both sides of a spongy bone structure, the diploë [START_REF] Couly | Développement céphalique[END_REF]. The anisotropy of material properties depends on tissue fibre orientation [START_REF] Mcpherson | The elastic modulus of fetal cranial bone: A first step towards an understanding of the biomechanics of fetal head molding[END_REF]. The pattern of bone fibres in paediatric calvarial emanates radially from the ossification centres on each cranial plate.

Cranial growth in utero and during early childhood is correlated to brain growth and is enabled by the permeability of cranial sutures. Craniosynostosis is defined by an abnormal craniofacial deformity due to the premature fusion of one or several calvarial sutures. The incidence of this pathology has been estimated to be approximately 1 in 2500 births [START_REF] Slater | Cranial sutures: a brief review[END_REF].

The active underlying brain growth dictates the passive growth of the skull along the suture line [START_REF] Couly | Développement céphalique[END_REF]. In 1890, Virchow [START_REF] Persing | Virchow and the pathogenesis of craniosynostosis : a translation of his original work[END_REF]) was the first to explain that premature fusion of these sutures induced abnormal growth patterns of the skull. He concluded that tissue growth perpendicular to the suture was restricted while compensatory growth occurred on the rest of the calvaria. This concept is still broadly endorsed today. The impaired sutures determine a specific pathological skull pattern [START_REF] Persing | Virchow and the pathogenesis of craniosynostosis : a translation of his original work[END_REF].

Subsequent investigations lead to a classification of deformations (Sear 1937, Montaut and[START_REF] Montaut | Les dysmorphies craniofaciales. 27 th annual congress of the french neuro-surgery society[END_REF].

Our study focuses on scaphocephaly, defined as the premature fusion of the sagittal suture.

Sagittal synostosis is the most prevalent form with 50% of craniosynostosis, followed by metopic, coronal and lambdoid synostosis. Synostosis and uneven cranial growth, as J o u r n a l P r e -p r o o f illustrated in Figure 1a, results in an aesthetic imbalance which may induce developmental disability [START_REF] Van Der Vlugt | Cognitive and Behavioral Functioning in 82 Patients with Trigonocephaly[END_REF]. Correction of the shape and size of the skull is attained via surgery and most procedures are performed through bicoronal incisions preceding large cranial reshaping. Recently, a novel approach based upon a minimally invasive endoscopic procedure has been developed [START_REF] Jimenez | Early management of craniosynostosis using endoscopic-assisted strip craniectomies and cranial orthotic molding therapy[END_REF]Barone 2000, Jimenez et al. 2002). A single resection of the sagittal suture and adjacent bone is performed at the top of the cranium. After surgery, head molding is performed with custom-made helmets, and the cranial vault recovers its harmonious curvature thanks to the osteogenic potential of the dura.

The mechanism of premature synostosis of suture in non syndromic craniosynostosis is multifactorial and unknown (Morris-Kay and Wilkie 2005). Gene receptors and fibroblast growth factors are involved in syndromic faciocraniosynostosis [START_REF] Clarke | Identical mutations in three different fibroblast growth factor receptor genes in autosomal dominant craniosynostosis syndromes[END_REF] whereas non-syndromic context is not well documented [START_REF] Tartaglia | Fibroblast growth factor receptor J o u r n a l P r e -p r o o f mutational screening in newborns affected by metopic synostosis[END_REF]. Factors contributing to in-utero constraints include heavy weight (greater than 4 kg) and large size at birth as well as increased maternal age older than 35 years old [START_REF] Sanchez-Lara | Fetal constraint as a potential risk factor for craniosynostosis[END_REF][START_REF] Oppenheimer | Force-induced craniosynostosis via paracrine signaling in the murine sagittal suture[END_REF]).

It appears that mechanical aspects might play a significant role in the aetiology of craniosynostosis. Suture mechanobiology refers to the mechanical stimuli which influence suture growth. Brain growth and intracranial pressure play a key role. Some animal models have highlighted the role of cyclic forces on facial sutures [START_REF] Delashaw | Cranial deformation in craniosynostosis. A new explanation[END_REF], Kopher et al. 2003) as well as gene activation and transcription factors, showing increased protein synthesis of collagen [START_REF] Mao | Biomechanics of craniofacial sutures: orthopedic implications[END_REF].

Although bone tissue mechanical properties have been investigated in numerous studies, there are not many studies conducted on the cranium [START_REF] Jaslow | Mechanical properties of cranial sutures[END_REF][START_REF] Motherway | The mechanical properties of cranial bone, the effect of loading rate and cranial sampling position[END_REF][START_REF] Maloul | Characterization of the bending strength of craniofacial sutures[END_REF]. Literature is lacking contributions relating to bone material properties of the foetus, the newborn and the infant. The results present a plethora of discrepancies because J o u r n a l P r e -p r o o f of morphological variability, difficulties in harvesting paediatric biological tissue and varying experimental methodologies. Calvarial materials for foetal head molding during vaginal delivery have been examined. Three-point bending tests been mostly used in quasi-static or dynamic studies to investigate the response to impact [START_REF] Coats | Material Properties of Human Infant Skull and Suture at High Rates[END_REF].

Cranial sutures increase in complexity as they grow and interdigitate, hence the evolving mechanical properties show significant variability [START_REF] Herring | Mechanical influences on suture development and patency[END_REF]. Appraisal of the childbirth process, [START_REF] Mcpherson | The elastic modulus of fetal cranial bone: A first step towards an understanding of the biomechanics of fetal head molding[END_REF] showed that suture elastic moduli were lower than those of adjacent osseous shells in one-year-old babies. [START_REF] Margulies | Infant skull and suture properties: measurements and implications for mechanisms of pediatric brain injury[END_REF] reported paediatric cranial elastic modulus twelve times lower than that of the adult cortical calvarial bone. [START_REF] Coats | Material Properties of Human Infant Skull and Suture at High Rates[END_REF], found a correlation between strain-ratedependency and age, which underlined the viscoelastic behaviour of cranial tissue.

Normal calvarial and cranial bone displayed relevant variations in their mechanical properties, depending upon patient age and tissue location on the cranial vault [START_REF] Coats | Material Properties of Human Infant Skull and Suture at High Rates[END_REF]. The elasticity moduli of sutures were lower than those of bone for children aged one week and it was observed that tissue immaturity was associated with low stiffness at this age.

Investigations carried out on sutures showed that normal sutures were characterised by well-organised and unidirectionally oriented collagen fibres, whereas pathological sutures showed anarchic micro-architectures which, as revealed by a complex ultra-structural arrangement [START_REF] Anderson | Scanning electron microscope and micro-CT evaluation of cranial sutures in health and disease[END_REF]. Furthermore, pathological sutures were considerably thicker with some osseous connections between adjacent osseous shells and synostotic sutures were only partially fused but varied in their extent [START_REF] Regelsberger | Synchrotron-microcomputed tomography studies of normal and pathological cranial sutures: further insight[END_REF]. The combination of micro-architecture topology with tissue mechanical properties results in the local structural stiffness of the suture, which is predominantly governed by mineralised fraction. The newly formed tissue and its space distribution govern the mechanical response J o u r n a l P r e -p r o o f of sutures and cranial growth. These aspects have never been investigated in scaphocephalic newborns and could play a significant role in the pathological process.

In this study, we hypothesised that the effective mechanical properties of sutures in a scaphocephalic infant population were altered as compared to those of parietal adjacent tissue considered as control.

-Material and methods

Specimen collection

The collection of biological specimens was performed in accordance with the protocol approved by the Ethics Committee of Toulouse University Hospital. Children suffering from scaphocephaly were aged between 4 and 7 months at surgery (mean age equal to 4.9 months); the gender ratio was 7 males and 4 females. Eleven sagittal suture specimens were harvested during endoscopic surgery. The explants were harvested en bloc as shown in Figure 1a and Figure 1b. As illustrated in Figure 1c, the thicker central part constituted the pathologic suture and the two symmetrical thinner parts were the parietal plates considered as control. The local reference framework and geometrical parameters l and  describing the natural curvature are detailed in Figure 1c. During surgery, explants were kept in a 4% formalin solution and later stored at -18°C. Two hours were required for thawing prior to conducting the experimental procedures on the explants. First, the remaining periosteum on the external part was removed.

The explants were subdivided into slender beams parallel to the longitudinal axis of the resected tissue, as shown in Figure 1b. Each specimen was cut by using a high-speed rotary tool (Dremel®, Racine, WI) equipped with a diamond wheel. Care was taken to obtain a uniform thickness sample calibrated by using a digital caliper. The slenderness ratio was between 10 and 15.

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A histological study was performed on frontal slices perpendicular to the suture. The specimens were entirely fixed in formaldehyde, embedded in paraffin wax and stained with haematoxylin and eosin.

Analytical mechanical model for test interpretation

Width, thickness, mid-length, shear coefficient and natural curvature of specimen were b, h, l, s and , respectively. The three-points bending test described in Figure 2 shows the pinned-pinned boundary conditions and the force F applied on the convex side and then on the concave side of the specimen. The test output measure was the specimen effective stiffness K obtained by applying a linear fitting of the force deflection response, i.e. F/ V. This was the first step towards comparing pathological sutures to controls on a macroscopic scale.

Although bending was predominant, the contribution of shear and traction/compression due to natural curvature had to be considered to derive the complete expression of the effective Young's modulus E. As explained in detail in the appendix, the strain energy U described by equation (1a) was derived once with respect to F to obtain E knowing F, deflection V and the specimen properties, as expressed by equation (1b). Modulus E is proportional to the specimen stiffness K with  detailed in the appendix.

      /2 2 2 2 2 2(1 ) 12 A z y x r U M T N d s Ebh h                (a) (1)   3 3 2 2 16 F E V b h s l            (b)

Experimental study

The experiments were conducted on a tensile testing machine (Instron 3366®, software Bluehill®, Norwood, MA USA). Measurements were taken at room temperature and specimens were kept moist with saline solution. The span of sample supports ranged from 10

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to 30 mm to adapt to sample length. Three preloading cycles were applied and artefacts, because of time-dependent properties, were suppressed by fixing the displacement rate at 5 mm/min. The specimens were tested in a linear-elastic domain. Force F was applied on the concave surface then on the convex surface of the specimens to assess the influence of preloading and asymmetrical behaviour due to the natural curvature of samples. In both tests, force and defection V were registered with 10 Hz sampling frequency.

In the population of eleven patients, fifty specimens were harvested in explanted cranial sutures. Thirty-four were parietal adjacent tissue and sixteen were harvested from central sutures. Sample size with a confidence interval of 95% and an admissible error of 15%, lead to a statistical power of 45%. Deviations compared to a Gaussian distribution were admissible and the t-test was used with p < 0.05.

-Results

Geometrical properties of tissue specimens:

Measurements of mean (SD) in mm were as follows: l = 30.4 ( 10), b = 6.3 (1.9) and offset  = 1.05 (0.95). The heights of central stenotic sutures and adjacent parietal tissue were h = 2.65 (0.84) and h = 2.05 (0 88), respectively. The thickness difference was significant with p ≤ 0.006.

Tissue mechanical properties

The measurements of mean (SD) of effective stiffness K in N/mm were as follows: stenotic sutures K = 12.9 (1.4) and parietal adjacent tissue K = 3.96 (0.58). The difference was significant with p ≤ 0.005. The force-displacement responses of two samples for pathological (733) with the force applied on the concave side. The moduli obtained on the concave and convex sides displayed no significant differences for both pathological sutures (p = 0.39) and the parietal adjacent tissues (p = 0.4) used as control, as shown in Figures 3b and4b with correlation coefficients of 0.92 and 0.94, respectively. The effective modulus of pathologic sutures was lower than that of adjacent tissue with p < 0.001.

The natural curvature of the sample had no impact on this result since the responses on concave side and on the convex side yielded similar scores with p = 0.007 and 0.0005, respectively. Moreover, it appears that the effective Young's modulus expressed by equation (1b) involves the effective Poisson ratio  since shear is considered. It was confirmed that varying  between 0 and 0.49, with s fixed to 5/6 for rectangular cross-section, induced a relative variation of E lower than 1% For E evaluation,  was selected as equal to 0.3.

Histology

The histological study confirmed that the pathological sutures were thicker than the parietal adjacent structure. Figure 5a shows the parallel bone architecture of parietal adjacent tissue with considerable densification of the inner wall. Conversely, figure 5b shows a disorganised tissue pattern of the central stenotic suture. This structure presented greater vascularisation and haematopoietic tissue as compared to the adjacent parietal bone.

-Discussion and conclusion

J o u r n a l P r e -p r o o f

We put together a homogeneous group of eleven children suffering from scaphocephaly and we initially hypothesised that the effective mechanical properties of sutures were altered as compared to the parietal tissue considered as control. During surgery, the resected sagittal sutures were kept and the mechanical responses of stenotic suture and parietal adjacent tissue were characterised by using a standardised analytical and experimental protocol. To our knowledge, no study in literature is currently investigating the structural properties of fused sutures in craniosynostosis.

Three-point bending tests were implemented with shear artefacts reduced by the slenderness ratio and negligible effects due to pinned-pinned boundary conditions. Tension tests could have given the effective Young's modulus of the tissue, however, given the small size and natural curvature of the explanted specimens, clamping jaws would have interfered in the measurement process. Indeed, the latter would have caused significant initial prestressing to realign specimen and uncontrolled coupling effects in order to determine the effective modules. Compressive tests would be inadequate.

The fraction of mineralised tissue in stenotic sutures and controls was significant and their contribution to stiffness and effective material volume was predominant. Therefore, the effect of process conservation was not impactful, as confirmed by preliminary tests conducted on some fresh samples.

It was confirmed that the natural curvature of suture did not show any significant impact on strain energy, local structural stiffness and finally on the effective Young's modulus of the tissue. The moduli of stenotic sutures were lower than those of the parietal tissue, which was quite similar similar to normal bone. Eight pieces were conserved in formalin and three were conserved in frost. The two conservation methods had negligible effects in line with previous studies showing the limited impact of conservation conditions on the macroscopic mechanical properties of bone tissue [START_REF] Nazarian | Effects of tissue preservation on murine bone mechanical properties[END_REF][START_REF] Berteau | In vitro ultrasonic and mechanic characterization of the modulus of elasticity of children cortical bone[END_REF].

J o u r n a l P r e -p r o o f

The standard deviation of experimental effective moduli was significant due to the variation in suture thickness. Even if the width and length of the samples were controlled by the experimental protocol, thickness variation was patient-dependent and clinically relevant.

This variation is documented in literature [START_REF] Coats | Material Properties of Human Infant Skull and Suture at High Rates[END_REF] and interpretation can be supported by equation (1b). Indeed, modulus is proportional to stiffness variation and about three times more sensitive to thickness variation. This explains the increase in stiffness associated with tissue alteration. Lastly, it appears that stiffness as local structural property of sutures and effective Young's modulus as tissue intrinsic property are complementary with a view to exploring the biomechanical behaviour of the in vivo suture.

The histological analysis indicated a radial fibres distribution in the parietal tissue samples, significant loss of parallel architecture and increased interstitial tissue inside the pathological suture. The alteration of the effective modulus of stenotic sutures could be associated with the disorganised anisotropic tissue micro-architecture [START_REF] Mcpherson | The elastic modulus of fetal cranial bone: A first step towards an understanding of the biomechanics of fetal head molding[END_REF]Kriewall 1980, Anderson et al. 2006).

In conclusion, we found that the stenotic suture remained different, in structural and mechanical terms, from the adjacent bone during calvarial growth in the first year of life, as aligned with our central hypothesis.

In one sense, the relationships between structure and effective mechanical properties were obtained at the macroscopic level wit respect to the specimens. In further studies, a multiscale modelling approach [START_REF] Shipley | Multiscale Modelling of Fluid and Drug Transport in Vascular Tumours[END_REF][START_REF] Davit | Technical Notes on Volume Averaging in Porous Media I: How to Choose a Spatial Averaging Operator for Periodic and Quasiperiodic Structures[END_REF]) could be considered to explore how these dissimilarities in architecture result in different mechanical properties. To this end, at least two major problems need to be solved, namely the identification of mechanical properties varying at the microscale and the implementation of a reliable numerical method able to perform structural equations upscaling from a complex and heterogeneous microarchitecture.

J o u r n a l P r e -p r o o f

Other local factors such as metabolic factors or vascularisation were not taken into account during data collection as they might impact the in-vivo growth environment. We targeted the resulting mechanical determinants so as to offer a contribution to the aetiology of craniosynostosis.

                                                             78 2 3 A ) sl ( ) -    (A3)
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  Figure4afor control tissue and pathological tissue, respectively. The complex anatomy of

Acknowledgements:

We are deeply grateful to Professor Anne Gomez-Brouchet from IUCT, Toulouse University Hospital, France, for providing the histological data.

APPENDIX

The specimen strain energy is expressed by equation (1a). According to figure 2b, angle  A and curvature radius r are expressed by equation ( A1a) and (A1b) respectively. Tensile force N x , shear force T y and ending moment M z are expressed by equation (A2). After substitution to equation (1a) and integration between  A and /2, U is obtained and then derives once with respect to F. After factorisation, it gives equation (1b) describing the general expression of modulus E as a function of the mechanical response, i.e. F/V, and specimen geometrical properties, i.e. b, h, s, and . Coefficient  is expressed by equation (A3).

  2 arctan 2

Conflict of interest

Authors declare to have no conflict of interest.

J o u r n a l P r e -p r o o f


Aïcha Bah

Merlin Sanicas

Jérôme Nigou

Christophe Guilhot

Catherine Astarie-Dequeker

Isabelle Vergne
email: vergne@ipbs.fr

The lipid virulence factors of Mycobacterium tuberculosis exert multilayered control over autophagy-related pathways in infected human macrophages

Keywords: Autophagy, innate immunity, lipids, virulence, Mycobacterium tuberculosis, macrophages Pattern recognition receptors

Autophagy is an important innate immune defense mechanism that controls Mycobacterium tuberculosis (Mtb) growth inside macrophages. Autophagy machinery targets Mtbcontaining phagosomes via xenophagy after damage to the phagosomal membrane due to the Type VII secretion system Esx-1 or via LC3-associated phagocytosis without phagosomal damage. Conversely, Mtb restricts autophagy-related pathways via the production of various bacterial protein factors. Although bacterial lipids are known to play strategic functions in Mtb pathogenesis, their role in autophagy manipulation remains largely unexplored.

Here, we report that the lipid virulence factors sulfoglycolipids (SL) and phthiocerol dimycocerosates (DIM) control autophagy-related pathways through distinct mechanisms in human macrophages. Using knock-out and knock-in mutants of Mtb and M.bovis BCG (Bacille Calmette Guerin) and purified lipids, we found that (i) Mtb mutant with DIM and SL deficiencies promotes functional autophagy via a MyD88-dependent and phagosomal damage-independent pathway in human macrophages; (ii) SL limit this pathway by acting as TLR2 antagonists; (iii) DIM prevent phagosomal damage-independent autophagy while promoting Esx-1-dependent xenophagy; (iv) and DIM, but not SL, limit the acidification of LC3-positive Mtb compartments.

In total, our study reveals an unexpected and intricate role for Mtb lipid virulence factors in controlling autophagy-related pathways in human macrophages, thus providing further insight into the autophagy manipulation tactics deployed by intracellular bacterial pathogens.

Mtb mutant deficient in DIM and SL promotes autophagy activation

Autophagy mediated by Mtb mutant deficient in DIM and SL is not associated with ubiquitin coating or galectin-3 recruitment

DIM limit phagosomal damageindependent autophagy while promoting Esx-1-dependent autophagy

DIM, but not SL, limit acidification of LC3-positive compartments containing Mtb

Schematic representation of SL and DIM action in autophagy-related pathways in Mtb-infected human macrophages

Figure 7: Mtb resides inside either a damaged or an intact phagosome 1 . The Type VII secretion system Esx-1 promotes phagosomal damage, which leads to xenophagy 2 . However, Esx-1 can also inhibit autophagic flux via an unknown mechanism [START_REF] Romagnoli | ESX-1 dependent impairment of autophagic flux by Mycobacterium tuberculosis in human dendritic cells[END_REF] .

Here, we found that (i) SL limit TLR/MyD88-dependent and phagosomal damage-independent autophagy by acting as a TLR2 antagonist (1). (ii) DIM prevent, to some extent, phagosomal damage-independent autophagy (dotted line) (1) while triggering xenophagy by favoring Esx-1-dependent phagosomal damage (2). (iii) Finally, DIM, but not SL, limit the acidification of LC3positive compartments containing Mtb (3). Ubi: ubiquitin; Gal3: galectin-3. In terms of colors, autophagy modulation by SL and DIM is shown in red (inhibition) and green (activation).

•Figure 1 :

 1 Figure 1: Macrophages were infected for 1 h with the indicated GFP (green fluorescent protein)-expressing Mtb strains; fixed at 2 h, 48 h, 72 h, or 96 h postinfection (p.i.); permeabilized; incubated with antibody against endogenous LC3; and then stained with Alexa-568-labeled secondary antibody. Specimens were analyzed using confocal fluorescence microscopy. (A) Representative confocal images of hMDMs (human monocyte derived macrophages) infected with GFP-expressing Mtb (green channel) at 72 h postinfection, stained for endogenous LC3 (red channel). Scale bar, 5 µm. (B) A quantification of the percentage of Mtb compartments colocalized with LC3 at 2 h and 72 h postinfection in hMDMs. Data are the mean ± s.e.m (standard error of mean); 160-200 fields from four independent experiments; ** p < 0.01; *** p < 0.001 (unpaired t-test). (C) A quantification of the percentage of Mtb compartments colocalized with LC3 at 48 h, 72 h, and 96 h postinfection in THP-1 macrophages. Data are the mean ± s.e.m; 90 fields from three independent experiments; *** p < 0.001 (unpaired t-test). WT: Mtb wild-type; PMM127: Mtb mutant lacking DIM and SL; PMM127/DIM: Mtb mutant lacking SL ; PMM127/SL: Mtb mutant lacking DIM.

Figure 2 :Figure 3 :

 23 Figure 2: (A-D) THP-1 macrophages were infected for 1 h with the indicated GFP-expressing Mtb strains; fixed at 48 h, 72 h, or 96 h postinfection; permeabilized; incubated with antibodies against endogenous Beclin-1 (A,C) or Atg16L1 (B,D); and then stained with Alexa-568-labeled secondary antibody. Specimens were analyzed using confocal fluorescence microscopy. (A,B) Representative confocal images of macrophages infected with GFP-expressing Mtb (green channel) at 48 h postinfection, stained for Beclin-1 (A) or Atg16L1 (B) (red channel). The boxed areas in the left-hand panels are magnifications of the right-hand panels. Scale bars are 10 μm (left panels) or 2 μm (right panels). (C,D) A quantification of the percentage of Mtb compartments colocalized with Beclin-1 (C) or Atg16L1 (D) at 48 h, 72 h, and 96 h postinfection. Data are the mean ± s.e.m; 90 fields from three independent experiments; *** p < 0.0001 (unpaired t-test). (E) THP-1 macrophages were infected for 1 h with the indicated Mtb strains and lysed 48 h postinfection. Cells were treated with or without 100 nM Bafilomycin A1 (BafA1) during the last 2 h postinfection. Lysates were analyzed using immunoblotting with anti-LC3 or anti-actin antibodies. The densitometric LC3-II/actin ratios are shown underneath the blot. The ratios were normalized to the ratio of noninfected (NI) cells in the absence of BafA1. Data are representative of two independent experiments. WT: Mtb wild-type; PMM127: Mtb mutant lacking DIM and SL

Figure 3 :

 3 Figure3: (B) THP-1 macrophages were treated with different concentrations (μg/mL) of Pam3CSK4 (PAM) for 2 h, and then 100 nM bafilomycin A1 (BafA1) or a DMSO control was added for 2 h more. Lysates were analyzed using immunoblotting with anti-LC3 or anti-Actin antibodies. LC3-II/actin ratios were normalized to the ratio of cells without Pam3CSK4 and BafA1. (C) THP-1 macrophages were pretreated for 30 min with 10 μg/mL of SL synthetic analog and then incubated with 2.5 μg/mL Pam3CSK4 for 2 h. Then, 100 nM bafilomycin A1 (BafA1) was added for 2 h more. LC3-II/actin ratios were normalized to the ratio of cells without Pam3CSK4. Data are representative of two independent experiments. (D) THP-1 macrophages were pretreated for 60 min with 70 μM (100 μg/mL) of purified DIM and then incubated with 2.5 μg/mL Pam3CSK4 for 2 h. Then, 100 nM bafilomycin A1 (BafA1) was added for 2 h more. LC3-II/actin ratios were normalized to the ratio of cells without Pam3CSK4. Data are representative of two independent experiments.

Figure 4 :

 4 Figure 4: THP-1 macrophages were infected for 1 h with the indicated GFP-expressing Mtb strains, fixed 72 h postinfection, permeabilized, incubated with antibodies against endogenous LC3 and ubiquitin (Ubi) or galectin-3 (Gal3), and then stained with Alexa-568-and Alexa-647labeled secondary antibodies. Specimens were analyzed using confocal fluorescence microscopy. (A,C) Representative confocal images of macrophages infected with GFP-expressing Mtb (green channel) and stained for LC3 (red channel) and ubiquitin or galectin-3 (cyan channel). White arrows indicate Mtb compartments positive for LC3 and ubiquitin (A) or galectin-3 (C). Scale bar, 5 μm. (B,D) Quantification of the percentage of Mtb compartments colocalized with LC3 that were positive for ubiquitin (B) or galectin-3 (D). Data are the mean ± s.e.m; 45-55 fields from three independent experiments; * p < 0.05; ** p < 0.01 (unpaired t-test). WT: Mtb wild-type; PMM127: Mtb mutant lacking DIM and SL.

Figure 5 :

 5 Figure 5: (A) Quantification of the percentage of Mtb compartments colocalized with LC3 that were positive for ubiquitin or galectin-3. THP-1 macrophages were infected for 1 h with the indicated GFP-expressing Mtb strains, fixed 72 h postinfection, permeabilized, incubated with antibodies against endogenous LC3 and ubiquitin (Ubi) or galectin-3 (Gal3), and then stained with Alexa-568-and Alexa-647-labeled secondary antibodies. Specimens were analyzed using confocal fluorescence microscopy. Data are the mean ± s.e.m; 45-55 fields from three independent experiments; * p < 0.05; ** p < 0.01 (unpaired t-test). (B,C) Here, hMDMs were infected for 1 h with the indicated GFP-expressing BCG (Bacille Calmette Guerin) strains, fixed 72 h postinfection, permeabilized, incubated with antibodies against endogenous LC3 and ubiquitin (Ubi), and then stained with Alexa-568-and Alexa-647-labeled secondary antibodies. Specimens were analyzed using confocal fluorescence microscopy. (B) Quantification of the percentage of BCG compartments colocalized with LC3 that were positive for ubiquitin. Data are the mean ± s.e.m; 45 fields from three independent experiments. (C) Quantification of the percentage of BCG compartments colocalized with LC3. Data are the mean ± s.e.m; 90 fields from three independent experiments. The inset is a repartition of LC3-positive/ubiquitin-positive and LC3-positive/ubiquitinnegative for BCG::Esx-1 wild-type (WT) or a Δmas mutant (DIM-deficient). * p < 0.05; ** p < 0.01; *** p < 0.001; ns: not significant (unpaired t-test). WT M. bovis BCG Pasteur 1173P2 (DIM positive, Esx-1 negative), M. bovis BCG::ESX-1 (DIM positive, Esx-1 positive), BCGΔmas (DIM negative, Esx-1 negative), and BCGΔmas::ESX-1 (DIM negative, Esx-1 positive). PMM127: Mtb mutant lacking DIM and SL; PMM127/DIM: Mtb mutant lacking SL ; PMM127/SL: Mtb mutant lacking DIM.

Figure 6 :

 6 Figure 6: THP-1 macrophages were infected for 1 h with the indicated GFP-expressing Mtb strains (MOI = 5) and fixed 72 h postinfection. Cells were incubated with LysoTracker Red (LTR) during the last 2 h postinfection. Fixed cells were then permeabilized, incubated with antibodies against endogenous LC3, and stained with Alexa-647-labeled secondary antibody. Specimens were analyzed using confocal fluorescence microscopy. (A) Representative confocal images of macrophages infected with GFP-expressing Mtb (green channel), labeled with LysoTracker Red (LTR, red channel) and stained with LC3 (cyan channel). White arrows indicate acidified LC3-positive Mtb compartments. Scale bar, 5 μm. (B) Quantification of the percentage of Mtb compartments colocalized with LC3 that were positive for LTR. Data are the mean ± s.e.m; 60 fields from three independent experiments; *** p < 0.001; ns: not significant (unpaired t-test). WT: Mtb wild-type; PMM127: Mtb mutant lacking DIM and SL; PMM127/DIM: Mtb mutant lacking SL; PMM127/SL: Mtb mutant lacking DIM.

Acknowledgments: We wish to acknowledge the TRI-Genotoul Imaging facility (Toulouse, France). M.S. was registered in the EMJMD LIVE (Erasmus+ Mundus Joint Master's Degree Leading International Vaccinology Education) cofunded by the EACEA (Education, Audiovisual, and Culture Executive Agency, award 2015-2323) of the European Commission and was financially supported by the IDEXLYON project of the University of Lyon (ANR-16-IDEX-0005).


Pierric Mora

Mathieu Chekroun

Vincent Tournat

Seismic Metashielding by a Line of Resonators Over a Granular Layer

Seismic metamaterials have been the subject of much recent interest, with notable conceptual advances and the demonstration of possible full-scale effectiveness in earthquake protection. Here, through a fine analysis of the dispersion properties and behavior of resonators introduced in a laboratory scale setup, we propose a strategy for the design of an efficient metaseismic barrier. When positioned onto an unconsolidated granular layer, rigid masses of nontrivial shape become elastic resonators by coupling with the relatively soft propagation medium. Additionally, they affect the mechanical boundary conditions and subsurface medium properties through the added weight. We demonstrate that all these ingredients can be rationally combined to improve the shielding effect and control the seismic waves.

I. INTRODUCTION

Seismic metamaterials have emerged in the last decade as strategies to control elastic waves propagating close to the surface of large-scale mechanical systems [START_REF] Brûlé | Emergence of seismic metamaterials: Current state and future perspectives[END_REF]. Similar to metamaterials in various wave systems, the use of local resonators, achieving noticeable effects on traveling waves even with engineered structures of subwavelength dimensions, is particularly appealing for seismic waves or even soil vibrations, which deal with typical wavelengths ranging from meters to kilometers [START_REF] Brûlé | Experiments on Seismic Metamaterials: Molding Surface Waves[END_REF]. In this context, various types of resonator arrangements have been proposed to attenuate or convert waves propagating in elastic layers, either at large scale [START_REF] Brûlé | Experiments on Seismic Metamaterials: Molding Surface Waves[END_REF], including forests [START_REF] Colombi | Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances[END_REF][START_REF] Roux | Toward seismic metamaterials: The METAFORET project[END_REF], for experiments at the lab scale [START_REF] Palermo | Hybridization of Guided Surface Acoustic Modes in Unconsolidated Granular Media by a Resonant Metasurface[END_REF][START_REF] Chen | Harnessing multi-layered soil to design seismic metamaterials with ultralow frequency band gaps[END_REF][START_REF] Zaccherini | Locally Resonant Metasurfaces for Shear Waves in Granular Media[END_REF], or using theoretical and numerical approaches [START_REF] Colombi | A seismic metamaterial: The resonant metawedge[END_REF][START_REF] Miniaci | Large scale mechanical metamaterials as seismic shields[END_REF][START_REF] Achaoui | Seismic waves damping with arrays of inertial resonators[END_REF][START_REF] Achaoui | Clamped seismic metamaterials: Ultra-low frequency stop bands[END_REF][START_REF] Maurel | Conversion of love waves in a forest of trees[END_REF][START_REF] Pham | Hybridized love waves in a guiding layer supporting an array of plates with decorative endings[END_REF].

Of particular relevance for laboratory-scale experiments on seismic metamaterials is the implementation of unconsolidated granular layers, which add complexity in the elastic propagation layer [START_REF] Jacob | Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium[END_REF][START_REF] Bodet | Elasticity profile of an unconsolidated granular medium inferred from guided waves: Toward acoustic monitoring of analogue models[END_REF][START_REF] Bodet | Small-scale physical modeling of seismicwave propagation using unconsolidated granular media[END_REF][START_REF] Bergamo | Physical modelling of a surface-wave survey over a laterally varying granular medium with property contrasts and velocity gradients[END_REF][START_REF] Pasquet | Small-scale seismic monitoring of varying water levels in granular media[END_REF]. Indeed, due to the contact nonlinearity between grains and the hydrostatic pressure increase with depth, an elastic property gradient forms in unconsolidated granular layers [START_REF] Gusev | Acoustic Waves in an Elastic Channel Near the Free Surface of Granular Media[END_REF][START_REF] V. Aleshin | Acoustic modes propagating along the free surface of granular media[END_REF][START_REF] Tournat | Acoustics of unconsolidated "model" granular media: An overview of recent results and several open problems[END_REF]. As a result, the wave-propagation velocities increase with depth.

Such inhomogeneity of the elastic layer, whose characteristics are now reasonably known in the form of an indepth power law for both the longitudinal and shear-wave velocities, leads to the propagation of guided modes called guided surface acoustic modes (GSAMs) or Rayleigh-Hertz modes [START_REF] Jacob | Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium[END_REF][START_REF] Bonneau | Evidence of Rayleigh-Hertz Surface Waves and Shear Stiffness Anomaly in Granular Media[END_REF]. These modes have been extensively studied in laboratory configurations with granular models composed of spherical glass beads of size approximately * pierric.mora@univ-eiffel.fr 100 μm, offering a good fit between theory, simulations, and experiments [START_REF] Palermo | Hybridization of Guided Surface Acoustic Modes in Unconsolidated Granular Media by a Resonant Metasurface[END_REF][START_REF] Jacob | Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium[END_REF][START_REF] Bodet | Elasticity profile of an unconsolidated granular medium inferred from guided waves: Toward acoustic monitoring of analogue models[END_REF][START_REF] Bodet | Small-scale physical modeling of seismicwave propagation using unconsolidated granular media[END_REF][START_REF] Bergamo | Physical modelling of a surface-wave survey over a laterally varying granular medium with property contrasts and velocity gradients[END_REF][START_REF] Pasquet | Small-scale seismic monitoring of varying water levels in granular media[END_REF]. The interest to study seismic metamaterials with granular layers in the laboratory comes from the existence of these GSAM modes. Indeed, in a real geological environment, the inhomogeneities, stratifications, also give rise to the existence of guided modes, to in-depth refraction, in other words, to a complexity that is not present in a homogeneous elastic half-space, supporting only the Rayleigh wave together with bulk modes. Thus, taking into account an elastic inhomogeneity requires the design of advanced seismic metamaterials, capable of operating on several propagation modes, for example, to create a metaseismic barrier.

In this paper, we study experimentally and numerically a metaseismic barrier composed of a line of elastic resonators of simple design, but operating on the two main guided modes polarized in the sagittal plane of an inhomogeneous granular layer. These resonators are rigid masses of nontrivial shape added to the granular surface, which become elastic resonators by coupling with the relatively soft propagation medium. We show, through comparisons between experiments and numerical simulations, and based on elements of theory, that the processes leading to the hybridization of the first two GSAMs are due to the joint effects of the hardening of the medium under the resonators (effect of the added stress on a column of nonlinear granular media) and of two distinct resonances, dependent on the geometry of the mass, which induce a Neumann to Dirichlet transition for the boundary condition on both components of the dynamic surface displacement. Finally, we demonstrate experimentally a significant attenuation effect of the first two modes of propagation, achieved by a single line of resonators and propose possible extensions of this work.

II. INITIAL CONCEPT AND WAVE PROPAGATION WITHOUT THE METABARRIER

A. Initial concept

The idea of the design presented here is that when a massive body is deposited at the surface of the half-space, the granular medium is slightly compressed and turns into a soft elastic solid below the contact area with the mass. The expected behavior is then that of a mass-spring-dashpot system-the role of the spring being played by the granular medium itself and the attenuation being due to the radiation of waves into the half-space. Several resonances can be expected in relation to the different inertial characteristics of the body (mass and angular momenta) and interface stiffnesses (normal, shear, torsion). Among those, two are of particular relevance since they involve free components of the boundary condition and are hence prone to hybridize the propagation of guided waves: a piston mode in which the mass moves vertically, and a shear mode in which the contact area is mostly polarized in the plane of the surface. If properly tuned, the parameters defining the added solid object can lead to a simple resonant system able to affect the boundary conditions seen by all wave components simultaneously. Although approximate analytical expressions of contact resonances are known for homogeneous half-spaces (see Refs. [START_REF] Gladwell | The calculation of mechanical impedances relating to an indenter vibrating on the surface of a semi-infinite elastic body[END_REF][START_REF] Johnson | Contact Mechanics[END_REF] for reviews and Refs. [START_REF] Boechler | Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves[END_REF][START_REF] Hiraiwa | Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves[END_REF] for examples of applications to metasurfaces), our case is significantly more complex due to the strong heterogeneities in the stratum and their interplay with the mass, so that this work of parameter tuning is entirely done numerically. Our experimental setup is presented in Fig. 1 and described in details in Appendix A.

B. Wave propagation in the granular layer without scatterers

At large wavelengths compared to the size of the beads, a granular medium may be described as an elastic medium whose stiffness depends on the applied pressure as a power law (see Refs. [START_REF] Jacob | Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium[END_REF][START_REF] Gusev | Acoustic Waves in an Elastic Channel Near the Free Surface of Granular Media[END_REF][START_REF] V. Aleshin | Acoustic modes propagating along the free surface of granular media[END_REF][START_REF] Bonneau | Evidence of Rayleigh-Hertz Surface Waves and Shear Stiffness Anomaly in Granular Media[END_REF]). Due to the increase of the hydrostatic pressure with depth, a granular halfspace is then described with a strong gradient of bulk-wave velocities:

c P,S (z) = γ P,S (ρgz) α P,S , ( 1 )
in which c P (c S ) is the longitudinal (shear) wave velocity, z the depth coordinate (z = 0 is a stress-free interface), g = 9.81 m/s 2 the standard gravity, and α P,S and γ P,S are characteristic constants of the power law. In this paper we take α P = α S = α = 0.31, γ P = 14.4, and γ S = 6.4 in accordance with previous experimental works (see Refs. [START_REF] Palermo | Hybridization of Guided Surface Acoustic Modes in Unconsolidated Granular Media by a Resonant Metasurface[END_REF][START_REF] Jacob | Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium[END_REF][START_REF] Bodet | Elasticity profile of an unconsolidated granular medium inferred from guided waves: Toward acoustic monitoring of analogue models[END_REF][START_REF] Bodet | Small-scale physical modeling of seismicwave propagation using unconsolidated granular media[END_REF][START_REF] Bergamo | Physical modelling of a surface-wave survey over a laterally varying granular medium with property contrasts and velocity gradients[END_REF][START_REF] Pasquet | Small-scale seismic monitoring of varying water levels in granular media[END_REF]). This slow-to-fast gradient has a guiding effect. In contrast to other heterogeneous half-spaces supporting surface modes, this power-law medium has the peculiar feature not to possess any characteristic length scale. As a consequence, no cutoff frequency exist and an infinite number of channels of surface waves are open at any given frequency. Furthermore, the eigenfrequencies scale with wave number as [START_REF] Gusev | Acoustic Waves in an Elastic Channel Near the Free Surface of Granular Media[END_REF][START_REF] V. Aleshin | Acoustic modes propagating along the free surface of granular media[END_REF]

f n,2 f n,1 = k 2 k 1 1-α , ( 2 )
in which n is the modal order, so that it is enough to obtain them at one wave number and then post-treat the results using Eq. ( 2) to obtain the eigenfrequencies and mode shapes at other wave numbers, or conversely to obtain the eigen-wave-numbers and mode shapes as a function of the frequency. The first two fundamental modes n = 1 and n = 2 are of particular interest in this work, as the energy they carry is most strongly localized at the surface. Higher-order modes propagate faster and with a deeper localization. Figure 2 depicts typical experimental signals, as well as theoretical dispersion relations and mode shapes for the first three modes-obtained with a finite-element software.

III. NUMERICAL MODELING OF THE METABARRIER A. Model of the consolidation caused by a massive object

The basic assumption we make to model this interaction is that the granular medium consolidates only within a cylindrical region below the object whose cross section is constant and equal to the contact area. The magnitude of this consolidation is assumed to follow the constitutive law given in Eq. [START_REF] Brûlé | Emergence of seismic metamaterials: Current state and future perspectives[END_REF]. In this consolidated region, the bulk velocities express as

c cons P,S = γ P,S [ρg(z + z 0 )] α P,S , ( 3 )
with the consolidation depth

z 0 = M ρS , ( 4
)
where M is the mass of the solid and S the contact area with the granular medium. Away from this region, the bulk velocities are kept unchanged and are given by Eq. ( 1). Of course, this is a coarse description of what really happens as one expects the actual response of the substrate to be rather conical. However, we find out via parametric studies that the shape of the consolidation is a parameter of minor influence relatively to others, so that we decide to rely on this simplistic description. In addition, there is no current knowledge about the shape and characteristics of this affected area and how this depends on the preparation procedure.

044002-2

B. Dispersion analysis for a periodic arrangement of scatterers

The numerical results presented below are obtained from a two-dimensional (2D) finite-element (FE) model, after transposition and validation from a three-dimensional (3D) model. The geometrical dimensions of the 3D model directly represent the scatterers used in the experiments, with the assumption that the spacing between neighboring scatterers is (almost) zero. Corresponding rules are used to define the 2D model, which we now describe. A schematic representation is shown in Fig. 3(a). All FE models are built using COMSOL Multiphysics ® , with the Structural Mechanics module.

The 2D model consists in a unit cell of size l UC × h UC = 1.2 × 70 cm 2 filled with an elastic medium of mass density ρ = 1560 kg/m 3 and space-dependent elastic constants deduced from Eq. (3) on a column below the contact with the added solid, and from Eq. ( 1) elsewhere. The mesh is refined near the surface to follow the strong variations of properties-element sides are there required to be no larger than 4% of the shortest wavelength, giving a total of roughly 2 × 10 4 degrees of freedom. Floquet periodic boundary conditions are applied on lateral boundaries, while the (fictitious) bottom end is clamped and the top interface is stress-free. The scatterer is an elastic solid of rectangular shape of size L × D (2D) , with a length L = 5 cm and a height D (2D) that we specify further, and with mechanical constants that are typical of steel (density of 7800 kg/m 3 , Young's modulus of 200 GPa, Poisson's ratio of 0.3). From these latter constants only the density really matters as the frequency range lies far below the first elastic resonances of the object, which indeed behaves as a rigid body. A thin layer made of a light, stiff fictitious material is inserted between the steel cylinder and the granular medium in order to ensure a contact length that does not depend on the geometry of the massive object. The contact length l is defined such that the contact filling ratio of the 2D unit cell matches that of the 3D unit cell: l/l UC = S/l 2 UC , with S = l 2 UC π/4, which gives l ≈ 0.94 cm. The height D (2D) is taken such that the consolidation magnitude z 0 is kept constant: D (2D) = l for the heavy case and D (2D) = l/4 ≈ 0.24 cm for the light case. Finally, when taken into account, the roots are modeled as a single steel central pillar, with a height of 4 cm and a width w root such that w root /l is equal to the ratio of the cross section of all wires to the contact area: we take w root /l = 1/25.

From this 2D model, dispersion analyses are run by sweeping the Floquet wave number k in the longitudinal direction in the range k ∈ (0, π/l UC ) and obtaining the eigenfrequencies at each step. A typical result for a heavy object is represented in Fig. 4. One can clearly see in Fig. 4(a) that the first two modes hybridize and asymptotically tend to flat frequency curves, while higher-order modes are less affected. As highlighted by insets (b1) and (b2), these hybridizations are associated with resonances involving a rigid body motion of the massive solid: mode no. 1 is linked to the vertical motion while mode no. 2 is linked to the longitudinal one. Parametric studies show that these asymptotic values can be tuned independently by changing the mass and angular momentum of the solid.

C. Transmission analysis through a single line of scatterers

The dispersion analysis is complemented with a study on the modal insulation capabilities of a single line of periodically spaced scatterers, as a function of frequency. To this purpose, a finite-element model is built with the following characteristics [see Fig. 3(b)]. An object is placed at the middle of a region of interest, which is large enough to include a dozen wavelengths of propagation on each side and is surrounded with perfectly matched layers (PML). The massive object and its induced consolidation have the same characteristics as in the dispersion analysis. Waves are generated by a time-harmonic line source e iωt δ(xx S )δ(zz S )F with a force vector F = (F x , 0, F z ) T and depth location z S chosen to selectively excite one mode. This solution is not as elegant as inserting the exact modal shape as excitation distribution, but is realistic to implement experimentally and proves to be effective enough for the first three modes. Based on an elementary analysis of the location of the nodes of the 044002-4 (b4) shows that at higher frequencies the medium behaves as a waveguide with clamped surface. (c1)-(c3) analysis of transmission through a single scatterer for (quasi) pure modal incidence, at 700 Hz. lowest-order mode shapes at 700 Hz, we identify that mode no. 1 can be reasonably selectively excited by taking {z S , F} no. 1 (700 Hz) = {1.7 cm, (0, 0, 1) T }, mode no. 2 with {z S , F} no. 2 (700 Hz) = {1.2 cm, (1, 0, 0) T } and mode no. 3 with {z S , F} no. 3 (700 Hz) = {7.1 cm, (0, 0, 1) T }. We use the spatial scaling given in Eq. ( 2) to extrapolate these recipes at other frequencies: z S (f ) = z S (700 Hz) × r with r = (700 Hz/f ) 1/(1-α) the scaling factor. All dimensions relative to the propagation window are also multiplied by r to follow the frequency scaling, so that the number of nodes remains under control over a wide frequency range (about 2 × 10 5 degrees of freedom) and calculations can be run routinely on a personal computer at moderate costs. A 2D model is validated against a 3D model that relies on periodic conditions in the transverse direction (so that only one slice is meshed) and then exploited for parametric studies. As represented in Figs. 4(c1)-4(c3), the outcomes confirm that the hybridization of modes no. 1 and no. 2 observed with the dispersion analysis indeed result in a low transmission, while modes no. 3 and higher transmit most of their energy without scattering significantly. These transmission ratios are measured by averaging the amplitude of the vertical motion at the surface over a window long of several wavelengths and located behind the line of scatterers (see Fig. 3), and by normalizing by the amplitude obtained in the absence of scatterers. Variations of this model are also implemented to analyze separately the roles played by the different constituents: the roots may be included or not, the object may be replaced by a clamping boundary condition acting over a pillar that may be considered consolidated or not. Results are presented in the next section in a comparison with experiments.

IV. EXPERIMENTAL RESULTS

Experiments are conducted for the two sets of scatterers described above, labeled "light" and "heavy" further on (their mass ratio is of 1 to 4). A typical result for a line of heavy objects is presented in Fig. 5. One can clearly recognize qualitatively the behavior expected from the numerical analysis, namely that fast (high-order) modes are well transmitted while slow (the first two) modes are efficiently stopped. Down-conversion from fast to slow is visible, although because fast modes are essentially localized in a deep channel this interaction is actually largely inefficient from an energetic point of view. Concerning the significant transmission occurring around t = 14 ms, a time-frequency analysis shows that it is a too early event to be a no. 2 → no. 2 transmission, and is indeed mostly a no. 3 → no. 2 down-conversion. More quantitative insight can be gained with a deeper data processing as performed below (see Appendix B for more details).

044002-5

A. Comparison with models

The comparison of the transmission ratios extracted from the experiments with those predicted by the 2D numerical models is presented in Fig. 6. The good agreement proves the relevance of the simplification assumptions made to account for the role of additional consolidation and roots. The achieved effect is a low-pass filter on modes no. 1 and no. 2. The ratio of contact area to wavelength is a key parameter, but significant blocking is obtained at a moderately subwavelength scale: the contact area diameter is 1.2 cm while λ 1 (700 Hz) = 4.7 cm and λ 2 (1000 Hz) = 4.25 cm, so that transmission ratios about 25% (-12 dB) are reached at λ/4 -λ/3. Though broadband, the effect arises from a resonant origin as highlighted by the model without roots. Above resonance, which for the heavy object occurs at 230 Hz (longitudinal) and 260 Hz (vertical), the boundary condition schematically changes from free to clamped, which, together with the additional consolidation, results in a mismatch of mode shapes and in an accordingly high modal impedance barrier whenever the incident wave is localized near the surface. Of course such an idealized massive object without roots would not stand in practice without sinking. The solution retained here to add roots has the consequence to damp the resonance to such a low-quality factor that its peak is no longer noticeable, but preserves the broadband high frequency effect. Nevertheless, recovering a higher quality factor-by improving the device with, for instance, a spring between the mass and the roots-is attractive as transmission of mode no. 1 could be kept at low levels from much deeper subwavelength scales [here λ 1 (260 Hz) ≈ 20 cm, so the scale of the interaction is about D/λ 1 ≈ λ 1 /15 while the numerical model reaches -11 dB transmission]. The extra effect brought by a higher quality factor is less obvious for mode no. 2. We believe that the principal reason is that the configuration involves a too extremely deep subwavelength scale [here λ 2 (230 Hz) ≈ 35 cm, so D/λ 2 ≈ λ 1 /30].

V. CONCLUSIONS

A metabarrier is introduced, featuring a low-pass filter like transmission properties at subwavelength scales for the two fundamental modes guided at the surface of an unconsolidated granular half-space. It relies on a rigid, massive object standing at the surface of the soft, locally compressed substrate, the coupling of both resulting in a mass-spring system on longitudinal and vertical components with low-quality factors. The practical solution adopted to build such scatterers and make them stand on the fragile surface involves roots, which do not hinder the transmitting to insulating transition, but whose adverse effect is to lower the quality factors to such a point that no noticeable deeply subwavelength effect occurs at the resonance frequencies. Based on numerical models showing good agreement with an experimental realization, two essential ingredients are identified to jointly contribute to the broadband insulation effect. The first element is the effective clamping of the surface at high frequencies, which is in turn a consequence of the resonant mass-soil coupling. The second element is the consolidation of the soil below the barrier, which is a consequence of the added pressure at the surface. This extra consolidation induces a change of scale in the depth profiles below the barrier and ensures that the clamping of the surface indeed results in a low motion over the entire energy distribution of incoming, weakly penetrating modes, which then undergo a high impedance mismatch. The role of each resonance is highlighted: mode no. 1 hybridizes principally with a vertical clamping, as already reported, while mode no. 2 requires a longitudinal one to be efficiently affected.

As suggested by a model, an attractive improvement to this study-although at the cost of the extreme simplicity of the scatterers-would be to add springs between the mass and the roots so as to recover strong hybridization around the resonant frequencies and achieve low transmission properties starting from deeper subwavelength scales and with lighter masses. These results contribute to a better understanding of the control of seismic waves by metamaterials placed on the surface of elastic layers. The concept of adding a rigid mass with an appropriate design on the granular elastic system is shown to be suitable for the realization of an efficient seismic barrier, and adds to the previously studied strategies. It is therefore possible to imagine the design of relatively simple seismic metamaterials, capable of operating advanced effects on the propagation of complex subsurface modes, such as trapping, focusing, total shielding, refraction, etc. of diameter 180 μm and has a packing density of ρ = 1560 kg/m 3 . Beads are frequently stirred between experiments to limit accumulation of consolidation with time, and roughly leveled to ensure a reasonably flat surface. For the elastic wave source, a B&K V201 shaker driven by an Agilent 33120A function generator connected to a B&K LDS LPA100 power amplifier, excites a screwed rod embedded into the granular medium with a vertical motion of a few millimeters' amplitude. The chosen excitation signal is a Ricker pulse, centered in frequency at 2 kHz. The source is located at a distance of 1 cm to a wall of the box so as to avoid impulse echos and to produce a radiation pattern which is close to cylindrical for the involved wavelengths (around 4 cm for the shortest one). We measure the vertical particle velocity at the surface with a Polytech laser Doppler velocimetry head. The head is moved with a Newport XPS-RL Motion Controller along an axis within a range of 60 cm starting from a distance to the source of about 12 cm. The vertical velocity is measured at 230 steps ( x ≈ 2.6 mm) along this axis and digitized with a Zurich MFLI card, each 130 ms long signal being averaged 20 times and sampled at a rate of 29.3 kHz.

The metabarrier is made of steel rods (density ρ S ≈ 7800 kg/m 3 , length 5 cm, diameter 1/4 in. for light and 1/2 in. for heavy objects, i.e., masses of, respectively, 11 and 45 g) arranged in a row, which splits the measurement line in two parts of 30 cm each. The rods stand on the sand on a controlled area of 1.2 cm diameter by means of an attached washer, itself connected to thin roots made of a metallic wire to avoid sinking. The rods are lain horizontally on the washers to maximize the inertial momentum. To prevent newly deposited scatterers from strongly disturbing the fragile medium and making previously located ones sink, this preparation relies on first protecting the surface with two sheets of paper, inserting the objects between both, and finally carefully removing the sheets.

APPENDIX B: DATA PROCESSING

The objective of the data processing described here is to extract transmission ratios of pure modal incidence from the recorded signals. Each xt map of signals is split along the abscissa of the interface x S into a map of incident and reflected waves for x < x S , and a map of transmitted waves for x > x S , which are then processed independently. We first clean outliers with a median filter on the xt maps with a patch size 3 × 3. We then proceed to a mode selection in the 2D-Fourier-transformed domain by windowing the ωk plane around the dispersion relation meant to be isolated. Finally, we select the wave train of appropriate arrival by time windowing the phasecompensated signals. This way, maps of no. 1 → no. 1, no. 1 → no. 2, no. 2 → no. 1 and no. 2 → no. 2 transmissions are obtained and combined into maps of no. 1 → (no. 1 + no. 2) and no. 2 → (no. 1 + no. 2) transmissions.

From these latter maps, we measure the incident and transmitted amplitudes by averaging the power spectrum over spatial windows close to either sides of the interface. As this procedure is rather sensitive to the dispersion relation used for Fourier windowing and phase compensation, ω 1 (k) and ω 2 (k) are carefully adjusted for each new set of acquisitions. This is especially true for mode no. 2, which is not easily separated from mode no. 3. In order to account for biases due to this processing, to dissipation, and to geometrical attenuation of the beams, the same procedure is applied to reference maps of signals measured without scatterers, and the obtained transmission ratios are used as normalization factors. Finally, confidence intervals and average values are estimated from repeated measurements.

FIG. 1 .

 1 FIG. 1. Experimental setup showing one line of heavy scatterers [(a),(b)]. A light (c) and a heavy (d) scatterer.

FIG. 2 .FIG. 3 .

 23 FIG. 2. Vertical velocity at the surface of the granular medium generated by a Ricker impulse, in the absence of scatterers. (a) Space-time signals, (b) experimental and the first three theoretical dispersion curves, (c1), (c2), and (c3) corresponding theoretical mode shapes at 700 Hz: (solid) longitudinal v x and (dashed) vertical v z /i components. λ 1 (700 Hz) = 4.7 cm, λ 2 (700 Hz) = 7.1 cm, and λ 3 (700 Hz) = 8.7 cm.

FIG. 4 .

 4 FIG. 4. Numerical study on a 2D model of a heavy scatterer: (b1)-(b4) first four mode shapes for a periodic arrangement of scatterers displayed at a quarter-wavelength scale (d/λ = 4) and (a) dispersion curves (solid) compared to the reference medium (dashed), showing a high hybridization of modes no. 1 and no. 2 with longitudinal and vertical rigid-body-like resonances of the massive object.(b4) shows that at higher frequencies the medium behaves as a waveguide with clamped surface. (c1)-(c3) analysis of transmission through a single scatterer for (quasi) pure modal incidence, at 700 Hz.

1 FIG. 5 .

 15 FIG.5. Vertical velocity of a field interacting with one line of "heavy" scatterers located at 420 mm from the source: (a) space-time signals, (b),(c) experimental dispersion curves obtained from the first (120 to 420 mm) and second (420 to 720 mm) halves of the data, together with theoretical curves (dashed) of the first three modes.

FIG. 6 .

 6 FIG.6. Transmission ratio of vertical motion at the surface through one line of light (blue) and heavy (orange) scatterers, for incident modes (a) no. 1 and (b) no. 2: (symbols) experimental values against numerical models (dotted) with or (dashed) without account of roots.

ACKNOWLEDGMENTS

We acknowledge H. Méziere, J. Marudai and E. Egon for manufacturing the mechanical parts and E. Brasseur for his assistance in setting up the experiment.

APPENDIX A: EXPERIMENTAL SET-UP

The experimental setup shown in Fig. 1 derives from the ones of Refs. [START_REF] Jacob | Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium[END_REF][START_REF] Bodet | Elasticity profile of an unconsolidated granular medium inferred from guided waves: Toward acoustic monitoring of analogue models[END_REF][START_REF] Bodet | Small-scale physical modeling of seismicwave propagation using unconsolidated granular media[END_REF][START_REF] Bergamo | Physical modelling of a surface-wave survey over a laterally varying granular medium with property contrasts and velocity gradients[END_REF][START_REF] Pasquet | Small-scale seismic monitoring of varying water levels in granular media[END_REF][START_REF] V. Aleshin | Acoustic modes propagating along the free surface of granular media[END_REF]. The dimensions of the sand box are 100 × 55 × 30 cm, with a filling height of 25 cm. The granular medium is composed of calibrated silica beads 044002-7


dir. J.-Y Empereur

Mélanie Henry

« Empereur

Fragments palestiniens : pouvoir, territoire et société

EMPEREUR J.-Y.(dir.), Alexandrie dans la Première Guerre mondiale, Alexandrie, Centre d'études alexandrines, 2018

Mélanie Henry 1 Ce beau-livre décrit la ville d'Alexandrie, requalifiée en base arrière durant la Première guerre mondiale, en 433 pages abondamment illustrées de sources iconographiques. Les Britanniques occupant l'Égypte depuis 1882, le pays était sorti du giron de l'Empire ottoman et participait de fait à l'effort de guerre aux côtés des alliés. Alexandrie, principal port méditerranéen du pays, devint un lieu de transit, notamment en lien avec la bataille des Dardanelles qui opposa les forces alliées à l'armée ottomane. La ville accueillit ainsi troupes et équipements militaires sur ses plages et ses ports (partie 1 et 2), puis nombre de blessés et de malades dans ses structures hospitalières (partie 3) et enfin les nombreux défunts de cette guerre qui reposent dans ses cimetières (partie 4). La ville étant alors dans sa période dite « cosmopolite », l'ouvrage explore en outre l'impact de la guerre sur ses différentes communautés (partie 2), en glissant sur les Égyptiens et en insistant sur les Français. Paru à l'occasion du centenaire de la fin de la Première guerre mondiale, l'ouvrage est dédié à ceux qui moururent « pour des empires voués à disparaître ». L'Alexandrie cosmopolite se prête bien à cette approche à distance des commémorations militaires et nationales : les rivalités inter-impérialistes sont venues y surprendre la vie locale des différentes communautés. À côté de cela, l'insensibilité à la question coloniale se manifeste dans la structure de l'ouvrage et au sein des différents textes par l'indifférence au point de vue égyptien. Effacés de la plupart des contributions, les Égyptiens font l'objet d'une sous-partie, « Les Égyptiens et la Première Guerre mondiale », située au terme de la partie 2, dont l'intitulé tranche avec celui des sousparties précédentes consacrées quant à elles aux différentes communautés « à Alexandrie ». Pourtant en 1919, le pays connaît une révolution en lien direct avec le rejet de l'occupation britannique et l'effort de guerre qui lui a été imposé. L'Égypte constitue ainsi un cas édifiant pour étudier la participation des dynamiques coloniales à l'histoire de la Première Guerre mondiale, ce qui implique la mise en oeuvre de méthodologies de recherche adéquates.

Systématiquement suivies de sources reproduites ou retranscrites, les contributions des quatorze auteurs sont de factures diverses. Le travail sur le matériel commémoratif est très présent, notamment au travers d'une partie consacrée aux cimetières qui ont durablement modifié le paysage urbain alexandrin. On trouve aussi des descriptions informées des listes de noms apposées sur les monuments aux morts ou encore un « Répertoire biographique des Alexandrins morts au cours de la Première Guerre mondiale », élaboré à partir des noms des individus relevés dans le carré militaire français du cimetière de Chatby et sur la stèle qui figure au Consulat de France. Une série d'articles et de cartes inédites étayent un abondant travail de localisation dans la ville des visiteurs exceptionnels de la guerre : des troupes aux navires de guerre en passant par les camps de prisonniers et de réfugiés. L'ouvrage s'efforce non moins de restituer les histoires d'individus pris dans le tourbillon de la guerre. Avec l'article sur les « Camps d'Alexandrie : alliés, réfugiés et prisonniers/internés » (Cécile Shaalan), des parcours singuliers sont ainsi mis en valeur au détour de descriptions denses sur les camps. On peut aussi citer l'article « Un Égyptien de Paris », tiré d'un travail universitaire et adapté à la visée grand public de cet ouvrage, qui relate la vision changeante de l'Orient chez un soldat parti de Corrèze pour se battre aux Dardanelles, à partir des témoignages croisés de l'homme et d'une quinzaine d'autres combattants (Francine Saint-Ramond). Parmi les articles les plus problématisés du volume, celui d'Anne-Marie Moulin met en perspective l'objet de l'ouvrage du point de vue de la médecine militaire. Ces textes abondants coexistent avec des contributions plus concises comme « Le Zion Mule Corps » (Jean-François Faü) ou « L'aviation » (Jean-Yves Empereur).

Destiné à un grand public, l'ouvrage contribue à la littérature mémorielle et historique sur la présence française parmi d'autres communautés étrangères (principalement européennes) à Alexandrie, durant l'épisode exceptionnel de 1914-1918.

2C

  'est suite à une exposition sur « la vie des Alexandrins pendant le conflit », conçue par Nicole Garnier (Conservateur général du patrimoine chargé du musée Condé à Chantilly) et André Pelle (photographe), élaborée par le Centre d'études alexandrines en collaboration avec l'Université francophone Senghor et exposée à l'Institut français d'Alexandrie, que cet ouvrage a vu le jour. Ce travail est aussi alimenté par des travaux de longue haleine de collectes documentaires qu'effectue le Centre d'études alexandrines sur d'histoire de l'Alexandrie « cosmopolite », que ce soit en matière de presse francophone, de cartographie, d'iconographie (l'article de Marie-Delphine Martellière a par exemple extrait de ce corpus les cartes postales d'« Un Vierzonnais du Corps expéditionnaire d'Orient à Alexandrie ») mais aussi d'archives.

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