J Rahmoun
email: jamila.rahmoun@uphf.fr

H Naceur

H Morvan

P Drazetic

C Fontaine

P E Mazeran

Experimental characterization and micromechanical modeling of the elastic response of the human humerus under bending impact

Keywords: Human humerus bone, micromechanics, nanoindentation, drop tower impact, Finite Element

This paper investigates the characterization and numerical modeling of the elastic behavior of the human humerus bone using a recently developed micromechanical approach coupled to nanoindentation measurements. At first, standard three-point bending experiments were conducted under low static loading, using several humerus diaphysis in order to identify the apparent elastic modulus of the bone in static regime.

Then, a drop tower impact experiment was used on the same set of humerus diaphysis specimens, in order to assess the elastic modulus in dynamic regime. These measurements will be used as reference bases for comparison purpose. The originality of this work, lies in the coupling between a two-phase micromechanical approach based on Mori-Tanaka homogenization scheme for cylindrical voids and nanoindentation measurements of the elastic modulus of the bone matrix phase. This model has been implemented using a user defined material subroutine VMAT in ABAQUS c Explicit code. The bone mechanical response prediction using the proposed methodology was validated against previous standard experimental data. Finally, it was shown that the numerical predictions are consistent with the physical measurements obtained on human humerus via the good estimation of the ultimate impact load.

Introduction

With the growing deployment of airbag protection systems by cars manufacturers to increase passengers safety, it has been noticed an increased emphasis on the study of the upper extremity injuries in the automotive environment [START_REF] Kaufman | Severe soft tissue injuries of the upper extremity in motor vehicle crashes involving partial ejection: the protective role of side curtain airbags[END_REF]. These research studies include the investigations on injuries of the upper extremities, in particular humeri, from deploying airbags. The Humerus is the second most common long bone diaphyses known. Its bone functional adaptation to strain is achieved by the addition and redistribution of tissue [START_REF] Santos | Bone remodelling of the humerus after a resurfacing and a stemless shoulder arthroplasty[END_REF]. Moreover, the humeral bone is an hierarchical material whose architecture differs at each level of hierarchy and whose mechanical properties can vary considerably, even on the same specimen, due to the bone heterogeneity. Different approaches have been performed to account for the multi-scale nature of bone. Homogenization techniques have been developed to model its elasticity and fracture risk [START_REF] Marques | Chapter 10: Determination of the Anisotropic Mechanical Properties of Bone Tissue Using a Homogenization Technique Combined With Meshless Methods[END_REF].

Interestingly, continuum micromechanical based approaches allow the modeling of the bone anisotropic mechanical properties [12; 27]. The predictive potential of the so-called micromechanical formulation has been shown using physically and statistically independent sets of experiments.

For the determination of the humerus mechanical properties and its integration in numerical models, characterization tests of humerus bone are needed. Moreover, global tests performed on an humerus are also required for the validation of bone models with respect to the experimental data. Concerning the studies investigating the material properties of the humerus bone, we can cite the study of Singh et al. [START_REF] Singh | Experimental assessment of biomechanical properties in human male elbow bone subjected to bending and compression loads[END_REF] who supplied the needed mechanical parameters given by different global tests (three-point bending, fracture toughness, and axial compression). Hoffler et al. [START_REF] Hoffler | Heterogeneity of bone lamellar-level elastic moduli[END_REF] performed nanoindentation tests on lamellae level and found that the elastic modulus and hardness of human bone tissue depend strongly on tissue type, anatomical location and individual. Nevertheless, most of the existing studies concerning global tests on humerus are mainly done in quasi-static conditions [5; 16]. Impact testing provides information about the response of a material to a dynamic load. This knowledge is essential for materials whose properties are time-dependent, e.g. exhibit viscoelasticity or poroelasticity. Most biological materials have such properties and yet their responses at loading rates that may be found during rapid physiological activities, or when subject to traumatic forces such as during falls or accidents, are still not well understood. Only in few studies, the humerus has been loaded at level of velocity close to those to which the humerus bone could be subjected during a car accident. We can cite the work of Lebarbé et al. [START_REF] Lebarbé | Human Shoulder Response to High Velocity Lateral Impact[END_REF] who investigates the human shoulder response to lateral impact at intermediate velocities. The obtained shoulder injury mechanism appeared to be similar to those observed in the automotive field.

The aim of the present paper is to propose a micromechanical based approach for the accurate characterization and modeling of the elastic behavior of the human humerus under bending impact. The present micromechanical model [30; 31; 36] is based on the coupling between the Mori-Tanaka homogenization scheme [START_REF] Mori | Averages stress in matrix and average elastic energy of materials with misfitting inclusions[END_REF] for the estimation of the elastic properties of the humeral cortical bone, and a Finite Element model at the macro-level for the prediction of the global humerus diaphysis elastic response. The proposed procedure consists in two stages: at first, local measurements of the bone material properties were performed thanks to nanoindentation tests using small specimens extracted directly from the same humerus diaphysis.

Once the bone matrix material parameters (Young's modulus, porosity) were determined, a bending impact test was performed using a solid-shell finite element model [8; 26] to validate the global response of the modeled humain humerus diaphysis. to a virological and serological analysis to ensure that they do not exhibit any bone disease on radiographic examination. All specimens were scanned using a medical scanner. These acquisitions were performed to extract the digital geometry data and saved using the stereolithography (STL) standard format then exported to a Computer Aided Design (CAD) workstation. Finally, the specimens were embalmed using a solution composed of methanol (35%), phenol (10%), glycerin (20%) and distilled water (35%) and stored at 4 o C until the beginning of experiments. Several studies [34; 35; 11] have investigated the effects of embalming bones regarding their mechanical properties. It be founded no or little effect after short to intermediate storage periods on the elastic properties of the human bones measured by experimental tests (see [START_REF] Stefan | Effects of three different preservation methods on the mechanical properties of human and bovine cortical bone[END_REF]).

Each humerus was prepared 24 hours before the starting of experiments in order to fix it rigidly inside two aluminum prismatic brackets (see Figure 1b) which were positioned onto a flat support to ensure their parallelism. One of the metallic brackets was maintained, while the other was free to slide in order to adapt it to the desired length of the bone. For each humerus, four positioning screws (Figure 1b) were used to help maintaining fixed the epiphyses and the lateral epicondyle of the humerus to the brackets. The system humerus-brackets was first positioned vertically and a FASTCAST c Polyurethane resin (type F14-F15 from AXSON Company) was poured into the lower bracket. Three hours later (recommended resin drying duration), the humerus-brackets system was flipped and the same operation was done for the other bracket side. The screws are then removed and the system humerus-bracket was separated from the straight support and placed in a cold room.

Two hours before the starting of experiments, five strain gages (Y series 1-LY41-3/350 from HBM) were glued on the humerus diaphysis to provide maximum tensile and compressive strains. Since the impact will be applied at the diaphysis middle, two gauges are placed on the upper face midway between the contact point and the end of the useful length of the bone (gages 1 and 2) and three other on the lower face respectively facing the two first gauges and the point of contact as shown in Figure 1b. Data recorded using a digital oscilloscope and filtered using CFC 1000 low pass filer to remove high frequency component.

After instrumentation, the system humerus-brackets was scanned using a 3D scanner VIVID 910 KONICA MINOLTA VI910 (0.1 mm of resolution) in order to obtain detailed description of boundary conditions as well as the precise locations of the gages in order to perform comparison with the Finite Element model. Three-points bending experiments were carried out using a drop tower impact apparatus of 2.30 m height.

A drop mass fixed to a carriage was allowed to fall freely while guided on vertical rails. The carriage height can be adjusted to adapt the impact velocity (see Figure 1a). A laser sensor M7L was fixed to the drop tower bed in order to record the successive positions of the impactor. The humerus instrumentation together with high speed camera (3000 fps) provides a precise recording of the evolution of the impact load as well as the displacements/strain curves function of time.

Static bending experiments

First, static three-points bending experiments were performed on humeri diaphysis using several loads (carriage mass 1 kg, 3 kg, 5 kg). The measured parameters are the local strains given by the five gages for each prescribed weight. A least squares minimization technique was performed in order to determine the elastic modulus by means of an inverse analysis which consists in fitting computed data to experimental measurements which leads to optimal set of constitutive parameters (longitudinal Young's modulus in our case).

In Table 1 are listed the geometrical parameters and the mean estimates of the apparent longitudinal Young modulus for each humerus. As it can be observed, the average longitudinal elastic modulus is 19089.8

MPa with a standard deviation of 3082.78 MPa. This estimation fits within the average values given by [39; 25; 33]. We can also observe that the humerus 582 exhibits the lowest value of the elastic modulus. This is probably due to the low mass of this humerus.

Dynamic bending experiments

The dynamic impact experiment on the humerus was chosen to hit in the middle of the diaphysis with a projectile of 8.6 kg mass and 20 mm diameter. A drop height of 750 mm was used to generate an initial velocity of 1.63 m/s at the impact instant. The total impact energy of the present experiment was adjusted to be approximately 10J. This value was shown from previous works [START_REF] Duprey | Experimental and simulated flexion tests of humerus[END_REF], to be necessary to reach the human humerus ultimate strength. The impact load was measured using a 4 components load cell sensor (model KISLTER 9327A). A laser sensor was used to measure the displacement. The humerus instrumentation together with two high-speed video cameras provide a precise recording of the evolution of the impact load as well as the displacements/strain curves function of time.

The comparison between all humerus responses shows that only one humerus which did not break under the impacting load at the imposed initial velocity of 1.67 m/s. Regarding the humerus ultimate impact load, its average value was 1299.6 N with a standard deviation of 274.24 N. This value is consistent with the results presented by Duprey et al. [START_REF] Duprey | Experimental and simulated flexion tests of humerus[END_REF] who found a mean maximum force value of 1273 N with a standard deviation of 448 N obtained using dynamic bending tests on humerus with an average velocity of 1.77 m/s. One can also cite the work of Mukherjee et al. [START_REF] Mukherjee | Dynamic properties of the shoulder complex bones[END_REF] who performed dynamic bending tests on the shoulder bones using three different impact velocities. The mean ultimate impact load of humerus bones corresponding to the lower impact velocity considered was about 1275 N with a standard deviation of 671.75 N. This ultimate impact load increased naturally with the increasing of the impact velocity. Quantifying regional heterogeneities in bone characteristics such as the density might improve our understanding of the injuries mechanism of the extremity fractures. Few studies investigate the regional variation of the density of cadaver long bone. We can cite the densitometric measurements of Boos et al. [START_REF] Boosa | The intraindividual agreement of the bone density of the human proximal tibia[END_REF] in 14 cadaver tibias who found that the mean bone densities varied between 123.79 mmg/mm 3 and 267.99 mmg/mm 3 . For the humerus bone, Boos et al. [START_REF] Boosa | The intraindividual agreement of the bone density of the human proximal tibia[END_REF] showed that the mean bone mineral density of the metaphysis region was 0.91 ± 0.224 g/cm 3 , and the one of the epiphysis was 0.559 ± 0.139 g/cm 3 .

In this study, densitometric measurements were performed after each dynamic test at the useful length of the impacted humerus in order to determine the porosity f of the diaphyseal cortical bone of the humerus.

After removing brackets and strain gages, the humeri were cleaned from the bone marrow, cut into 8 zones (z 1 to z 8 ) and weighted using a precision weighing balance from OHAUS company (Figure 3). Then, the true density d t were calculated from specimens weights in air and inside water by means of the Archimedes principle. In Table 3 are listed true densities of each zones of the humerus bones. It can be observed that the mean true densities d t varied between 1.69 g/cm 3 and 1.89 g/cm 3 showing the existence of interindividual differences.

Moreover, regarding the same humerus, there is also intraindividual variances with respect to the eight zones. Finally, the porosity of cortical bone was obtained using the relation f = 1d r where d r is the relative density defined as the ratio of the apparent density d a by the true density d t of the bone. The average porosity value of the diaphyseal cortical bone of the humerus was found to be equal approximately to 0.09.

Micromechanical characterization of the elastic properties

The heterogeneous and hierarchical nature of the diaphyseal cortical bone of the humerus makes it unlikely for a single measurement to fully characterize its structural integrity or accurately predict fracture risk.

Hence, this study aims to understand the contributions of architecture and material properties on the elastic behavior by means of nanoindentation experiments. The well-known principle of nanoindentation lies in bringing a very small tip to the surface of the bone to make an imprint. Elastic modulus and hardness of the material are extracted from experimental readings of indenter load and depth of penetration.

Three small specimens were dissected from the humerus diaphysis and were milled down to a prismatic shape of 8 × 5 × 2mm. The sampling area is located in the humerus distal part and is considered quite far from the rupture zone and has no apparent damage (Figure 4). Two of samples are intended for measures in the longitudinal direction of the humerus. The third one was intended for measures in the radial direction.

These specimens were mechanically polished by an automatic grinding machine having off-centered rotating movements in order to achieve smooth and flat surface with substantially smaller roughness compared to indentation depths.

At first an abrasive polishing is applied with hydration using ultra-pure water and discs of different grain sizes 800, 1200, 2400 and 4000. Every polishing stage was done is 120 s with a rotary speed of 100 rpm.

A final polishing with a felt disk coupled to a suspension of alumina particles of size 0.02 µm was then performed. This last polishing stage was applied with a fixed rotary speed of 100 rpm during 360 s. At the end an ultrasound rinsing bath was applied using ultra-pure water during 5 mn. After this preparatory step, nanoindentation tests were performed with a nanoindenter G200 from AGILENT using a Berkovich tip and the method proposed by Mazeran et al. [START_REF] Mazeran | Determination of mechanical properties by nanoindentation in the case of viscoelastic materials[END_REF]. This method is based on four stages protocol (loading, first 300s hold plateau, partial unloading and second 300s hold plateau) in order to exhibit the time-dependent reversible and irreversible behavior. For each specimen, 40 indents were carried out in order to reduce the error associated with the measurement of the standard deviation. As nanonidentation experiments are conducted with pyramidal indenters, a quadratic dependence between load and displacement can be found. The relation between load F and indentation depth h is given by:

F = 2 π E r h 2 (1)
E r is the reduced modulus which relied to the bone elastic properties (E and ν fixed to 0.3) and the indenter elastic properties (E i = 1141 GPa and ν i = 0.07 for diamond material) by the relation:

1 E r = 1 -ν 2 E + 1 -ν 2 i E i (2)
The load versus indentation depth curve were fitted in the figure 5 using the quadratic rheological model performed by Mazeran et al. [22; 23] for the determination of bone mechanical properties. The average of the micromechanical elastic modulus denoted by E m for infinite strain rate derived from nanoindentation tests on the specimens of the humerus diaphyseal cortical bone has been found to be equal to 19.2 ± 3.1 GPa which fits within the average values available in the literature (see [START_REF] Zysset | Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur[END_REF]).

It has to be noticed that the micromechanical Poisson ratio denoted by ν m was not studied in the present investigation, its value was fixed to 0.3 as commonly proposed for long bones in the literature (see [3; 29]).

Theoretical formulation of the micromechanics based model of the diaphyseal humerus bone

In this section, the micromechanical modeling of the elastic behavior of the diaphyseal cortical bone of the humain humerus will be presented.

The diaphyseal cortical bone of the human humerus, in the present investigation, was considered as a porous media with a matrix phase weakened by micro-pores and exhibits transversely isotropic symmetry. The representative elementary volume REV of the bone is composed of an isotropic linear elastic solid matrix with stiffness C m and of a set of cylindrical shaped pores having an elasticity tensor C p and volume fraction f . The pores were taken to be identical in shape and orientation which characterized by a normal unit vector denoted by n (see Figure 6). Taking advantage of the solution of the Eshelby equivalent inclusion problem [9; 18], the Mori-Tanaka homogenization scheme [START_REF] Mori | Averages stress in matrix and average elastic energy of materials with misfitting inclusions[END_REF] provides the following expression of the homogenized elastic stiffness tensor for the porous media (see [27; 30; 31] for more detail):

C hom = C m + f (C p -C m ) -1 + P -1 : (1 -f )I + f I + P : (C p -C m ) -1 -1 (3)
where I, I i jkl = 1 2 (δ ik δ jl + δ il δ k j ) is the fourth-order symmetric identity tensor and δ i j is the Kronecker delta symbol. P is the Hill tensor [START_REF] Hill | A self-consistent mechanics of composite materials[END_REF] which depends on the shape and orientation of the pores (considered here as cylindrical voids of elastic stiffness tensor C p = 0) and on the elastic stiffness of the solid matrix C m .

We model the void as an infinite cylinder aligned along the e 3 = n (rectangular cartesian coordinate) axis, and of elliptical cross-section of aspect ratio α = b a geometrically prescribed by:

x 2 1 a 2 + x 2 2 b 2 ≤ 1, -∞ < x 3 < +∞ (4)
The determination of the Hill tensor P, which is based on the work of [START_REF] Hill | A self-consistent mechanics of composite materials[END_REF] (see also [18; 37]), consists in evaluating the integral:

P i jpq = α 2π |ξ|=1 ξ i K m (ξ) -1 jp ξ q (i j)(pq) ξ 2 1 + α 2 ξ 2 2 ds(ξ) (5)
for which the integration is on the unit circle centered at the origin of space (ξ 1 , ξ 2 ), defined by | ξ |= 1.

K m ip (ξ) = C m i jpq ξ j ξ q is called the acoustic tensor. The notation (i j)(pq) indicates the symmetrization with respect to the couples (i, j) and (p, q). The analytical evaluation of the tensor P is not an easy task. For transversely isotropic materials, it is interesting for standard notations and the associated tensorial representations to introduce the Walpole's base [START_REF] Walpole | On the overall elastic moduli of composite materials[END_REF] which is constituted of a set of direction-related fourth-order tensors E i , i = 1, .., 6. By using this algebra and for cylindrical pores oriented with respect to the e 3 = n axis, Walpole's components of the Hill tensor P are given by [18; 38]:

P = 2κ p , n, 2µ p , 2µ n , l, l (6)
where κ p , l, n, µ p and µ n the plane-strain bulk modulus, cross modulus, axial modulus under uni-axial strain, axial-shear modulus, and transverse-shear modulus, respectively. These components may be integrated analytically and are given in Appendix Appendix A.

Thus, for cylindrical voids of elliptical cross-section in an isotropic medium, we obtain the following expression of the longitudinal Young's modulus which it is independent of the aspect ratio α.

E n = 9κ m µ m (1 -f ) 3κ m + µ m (7)
Moreover, if we consider that the aspect ratio is α = 1 (the case of circular cylindrical voids), the transversal Young's modulus reads as:

E p = 18κ m µ m (1 -f )(3κ m + µ m ) 9 f κ m (3κ m + 4µ m ) + 2(3κ m + µ m ) 2 (8)
Making the same assumption of circular cylindrical voids, the components of the homogenized elastic stiffness tensor C hom have been computed by means of the equation (3) and reported in Appendix Appendix B.

Finally, the obtained micromechanical model is implemented in a VMAT within the explicit dynamics code ABAQUS c for the prediction of the mechanical response of the humerus bone under low velocity impact. This model needs three materials parameters: the matrix elastic modulus E m obtained by the nanoindentation tests, the diaphyseal cortical bone porosity f deduced from the densitometric measurements of the humerus bones and the matrix Poisson ratio ν m given by the literature.In order to limit the number of unknown material parameters in this investigation, the aspect ratio is taken α = 1, which corresponds to the assumption of cylindrical voids having a circular cross section.

4. Multi-scale Finite Element model of a human humerus bone under impact

3D mesh generation of the humerus

The selected human humerus to be analyzed was the Humerus 517 which did not fail under the impact of an energy of 10J. Therefore, it is assumed that this humerus exhibited an elastic behavior without damage nor failure and therefore it could be modeled using the present micromechanical elastic model.

The first step of the elaboration of the Finite Element (FE) model was the generation of the 3D CAD geometry of the humerus diaphysis by starting from the digitalized STL standard format. As shown in Figure 5a, the digitalized STL mesh was split into two different parts which represent the inner and outer surfaces of the humerus. Each STL surface was, partitioned along the transverse direction into 10 small parts (Figure 7a) using CATIA c CAD software. Then, small local surfaces were built up using their edges generated previously by CATIA c CAD facilities. Once the total inner and outer surfaces of the humerus diaphysis were reconstituted, a first mapped FE shell mesh model was generated using only quads. Then, a 3D mesh of the humerus volume was extruded using 7920 hexahedrons, thanks to the 3D meshing facilities available in HYPERMESH c software [START_REF]HyperMesh c 10.0 User's Guide[END_REF] (Figure 7b).

Modeling of the drop tower impact on the humerus

The final stage of this investigation was the elaboration of the FE model including boundary conditions, material parameters, contact and loading conditions, in order to simulate the impact bending of the humerus and try to validate the material model. To this purpose, two brackets with concentrated mass elements of 1080 g have been modeled using hexahedral elements with the assumption of a rigid elastic material. The center of mass of each rigid bracket was allowed to move along the X-axis and to rotate around the Y-axis as

shown in Figure 8. The humerus epiphyses were embedded into the brackets using a prismatic shaped solid of 71 × 71 × 55 mm and having the resin material parameters (ρ = 1500 kg/m 3 , E = 400 MPa, ν = 0.3). For the sake of biofidelity, the inner part of the humerus diaphysis was filled by a solid representing the marrow with elastic properties E = 1 MPa, ν = 0.3 and ρ = 1000 Kg/m 3 (see [START_REF] Ho | Comparison of patella bone strain between females with and without patellofemoral pain : a finite element analysis study[END_REF]). The system brackets-humerus was positioned on a plate of 400 × 150 × 10 mm size and of 10, 77 kg mass which has been modeled as an analytical rigid body.

The impactor was considered as a cylindrical shell of 20 mm diameter and 8.6 kg of mass. It has been modeled using S4R shells of ABAQUS c elements and a rigid elastic material (see Figure 8). All contact interfaces were modeled using "General Contact" conditions without friction. The FE simulation was carried out using a total duration of 10 ms to cover the entire impact process. The 3D mesh of the whole FE system includes 7920 C3D8R solid elements and analytical solid. The FE simulation was carried out using the Explicit Dynamics algorithm of ABAQUS c software.

Analysis of the material parameters influence

In order to analyze the influence of materials parameters on the FE simulation of the humerus elastic response under bending impact, different set of parameters are considered. Figure 9 represents the loaddisplacement curves of the modeled humerus 517 under three values of porosity, matrix modulus, longitudinal and transverse elastic moduli. As can bee seen in Figure 9(a), the increased cortical porosity f rendered lower structural stiffness as well as lowered peak force along with an increased ability to absorb energy before failure. On the other hand, we have studied in Fig. 9(b) the variation of the matrix elastic modulus E m around its mean value determined by nanoindentation experiments. We notice that an increase in matrix elastic modulus is correlated with an increase of bone elastic properties namely the bending stiffness. The same phenomenon occurs for the longitudinal elastic modulus E n at fixed transverse one E p (Fig. 9(C). However, there was no detectable effect of the variation of the transverse elastic modulus on the elastic response of the humerus when the longitudinal elastic modulus was fixed (see Fig. 9(d)). For the next

Discussion

This study was performed for the mechanical characterization of the elastic behavior of the human humerus under impact using a newly developed multi-scale model. The originality of the proposed approach consists in the identification of only few material parameters to describe the whole complex anisotropic behavior of the humerus bone.

To investigate the effect of the impact velocity on the elastic response of the humerus under bending impact, three different velocities (1.5, 1.77 and 1.9 m/s) were applied. As we can show in Figures 10(a) and 10(b), the impact velocity affected clearly the elastic properties of the humerus. An increasing of the impact velocity leads naturally to an increasing of bending stiffness and strain. 3, one can notice that the micromechanical model gives an ultimate impact load of 1201 N with a minimum error of 7% [START_REF] Singh | Experimental assessment of biomechanical properties in human male elbow bone subjected to bending and compression loads[END_REF].

The comparison between experimental measurements and the numerical predictions of the impact load shows that the predicted ultimate load is somehow under-estimated, this is probably due to the local bone material identification. Indeed, it has been reported [START_REF] Malandrino | Anisotropic tissue elasticity in human lumbar vertebra, by means of a coupled ultrasound-micromechanics approach[END_REF] that nano-indentation experiments often induce damage into the bone prior to the physical measure, therefore the resulting elastic characteristics are often underestimated even if the embalming solution has a small effect on Young's modulus and other properties measured in static tests. However, some authors [10; 40] found that impact energy absorption seems to be reduced by quite a large amount, and that results of high strain rate tests may be more affected than the results of static tests. Nevertheless the remaining minor deviations could be simply attributed to the natural differences in geometry (size and morphology) between all tested humeral bones, which is common for most of biological materials [START_REF] Aziz | Biomechanical Measurements of Stiffness and Strength for Five Types of Whole Human and Artificial Humeri[END_REF]. 4).

Moreover, the strain response of strain-gauge-acquired values at the mid-diaphysis of human humeri was investigated. At this location, the maximum strain values ranged from 0.25% to 0.97% with an average experimental value of 0.66 ± 0.17. The error of the mean measured maximum strain from the FE-calculated maximum strain was found to be equal to 3%. This minimum error assesses the performance of the Finite Element model in capturing the true humerus bone response for the three-point bending tests. These results seem promising for future applications such as evaluation of injury risk in lateral car crashes [START_REF] Lebarbé | Human Shoulder Response to High Velocity Lateral Impact[END_REF]. As the proposed model can utilize detailed numerical representations of the human humerus with

2 .

 2 Experimental characterization of the mechanical response of the human humerus diaphysis under bending loading 2.1. Three points bending tests of the humerus 2.1.1. Sample preparation and instrumentation Five fresh left humeri were obtained from human cadavers with an average age of 68.6 ± 7.4 years and an average body height of 180 ± 7.8 cm. The humerus bones were supplied by the Department of Anatomy at Lille University School of Medicine in accordance with French regulations. The average length of these specimens was 345 ± 14.1 mm with an average mass of 226 ± 56.8 g. Each specimen has been submitted

  a) Drop tower device b) Humerus preparation and instrumentation

Figure 1 :

 1 Figure 1: Experimental device used for the bending impact on the human humerus

Figure 2

 2 Figure 2 represents the stress-strain curves of the five humeri based on the estimated Young modulus by optimization procedure and the local strain measurement of all three tensile gages Within this load range, the static response of each humerus was always linear.

Figure 2 :

 2 Figure 2: Experimental response of the humerus bones under static bending

Figure 3 :

 3 Figure 3: Specimens localization on the humerus

Figure 4 :

 4 Figure 4: Bone specimens holder for polishing stage and nanoindentation experiments

Figure 5 :

 5 Figure 5: Load as function of the indentation depth

Figure 6 :

 6 Figure 6: Description of the representative elementary volume

Figure 7 :

 7 Figure 7: Humerus Finite Element model

Figure 8 :

 8 Figure 8: Drop tower modeling using Finite Element method

Figure 9 :

 9 Figure 9: Influence of humerus material parameters on the load-displacement curves : (a) porosity, (b) matrix modulus, (c) Longitudinal modulus, (d) transverse modulus

Figure 10 :

 10 Figure 10: Effect of the impact velocity : (a) load versus displacement curve, (b) strain versus time curve

Figure 11 :

 11 Figure 11: Mechanical response of the humerus under impact loading (experiment vs numerical)

Table 1 :

 1 Mechanical properties of human humeral bone obtained from static loading

	Humerus ID	Length	Mass	Elastic modulus
		(mm)	(g)	(MPa)
	535	325	250	18954
	514	361	354	19614
	517	355	305	22445
	485	331	262	14099
	582	351	184	20337

Table 2

 2

summarizes data obtained from the dynamic bending experiments. It can be noticed that the average bending stiffness (defined as the load divided by the deflection) of all specimens was about 465.6 N/mm with a standard deviation of 132.8 N/mm.

Table 2 :

 2 Mechanical properties of human humerus bone for impact experiments

	Humerus ID	Velocity	Energy	Bending stiffness	Ultimate impact load
		(m/s)	(J)	(N/mm)	(N)
	535	1.67	11.99	541	1592
	514	1.63	11.42	642	1342
	517	1.67	11.99	473	1239
	485	1.65	11.71	344	1456
	582	1.72	12.72	328	869

Table 3 :

 3 True densities of human humerus bone (g/cm 2 )

	Humerus ID	z 1	z 2	z 3	z 4	z 5	z 6	z 7	z 8 Mean	SD
	535 1.79 1.84 1.87 1.75 1.71 1.90 2.17 1.79	1.85 0.14
	514 1.87 1.92 1.81 1.79 1.86 1.95 1.86 1.51	1.82 0.13
	517 1.66 1.93 1.88 1.75 1.87 2.35 1.90 1.80	1.89 0.20
	485 1.56 1.76 2.36 1.67 1.85 1.81 1.78 1.70	1.81 0.23
	582 1.83 2.13 1.84 1.80 1.98 1.89 1.53 1.84	1.86 0.17

Table 4 :

 4 Comparison of the ultimate impact load and maximum strain of the modeled humerus (Numerical vs. Experiment)

		Load	Time	Maximum strain
		(N)	(ms)	(%)
	FE Model	1201	1.35	0.64
	Experiment (mean)	1299	1.40	0.66
	Error Model	7%		3%

accurate geometric and material properties, a perspective is to realize a geometric personalization of the model. This would allow the assessment of the influence of a model personalization. In addition, this humerus model can be integrated in a whole-body model for applications such as shoulder lateral impacts.

It can be subjected to a given loading condition, producing response characteristics intended to mimic the human body in a real world scenario. The primary advantage of human body models, however, is that they provide insight into the onset of injury and resultant local response characteristics thereafter through the use of stress and strain data measured throughout the entire model. Such information is unobtainable during volunteer or post mortem human subject testing. These models remove the issue of repeatability, allowing for the implementation of parametric studies often used by vehicle designers to improve automotive safety.

Conclusions

In conclusion, the framework of homogenization was proposed for the modeling of elastic behavior for diaphyseal cortical bone. The elastic properties of the human humerus were investigated by coupling the Mori-Tanaka scheme and the micromechanical measurements of the cortical bone properties using nanoindentation experiments.

The proposed model predicts adequately the experimental results via the estimation of the ultimate impact load that the humerus may encounter before fracture. Further improvements will be performed to the present model to be able to simulate the bone fracture by taking into account the nonlinear behavior and including the strain rate effects and effective fracture criteria.

Acknowledgments

The authors gratefully acknowledge the financial support from the French Ministry of Research

Appendix A. Hill tensor for elliptic cylindrical inclusions

The Hill tensor for cylindrical inclusions of elliptical cross-section with the aspect ratio α embedded in an isotropic solid matrix, can be written, by using [START_REF] Clavert | How to determine the bone mineral density of the distal humerus with radiographic tools?[END_REF], in the form:

where κ m and µ m are the bulk and shear moduli of the bone matrix.

Appendix B. Elastic stiffness tensor for circular cylindrical inclusions

The Walpole's components of the homogenized stiffness tensor of the humeral bone are :

where:

The non-zero components of the homogenized elastic stiffness tensor for cylindrical inclusions of circular cross-section (the case of aspect ratio α = 1) and of volume fraction f in an isotropic medium can be calculated analytically, by using ( 3) and (A.1) and are written as:


Fernanda Engel

Sylvie Cotelle
email: sylvie.cotelle@univ-lorraine.fr

Cleder A Somensi

Renan C Testolin

Rogério Corrêa

Héla Toumi

Jean-François Férard
email: jfferard@gmail.com

Claudemir M Radetski
email: radetski@univali.br

Hela Toumi

A 3D ecotoxi-topological profile: Using concentration-time-response surfaces to show peroxidase activity in Zea mays (L.) exposed to aluminium or arsenic in hydroponic conditions

Keywords: Ecotoxi-topology, Phytotoxicity, Maize, Arsenic, Aluminium, Peroxidase

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

Introduction

Biological responses to toxins result from complex and dynamic cascades of events occurring between the initial exposure and the measured endpoints, and these responses may be reversible or irreversible, depending on the concentration-timeexposure [START_REF] Byrne | Numerically modelling time and dose dependent cytotoxicity[END_REF][START_REF] Cho | The reverse control of irreversible biological processes[END_REF]. Nevertheless, most experimental data generated in ecotoxicology studies assess biological responses over a specific exposure time under diverse toxicant concentrations, and the exposure time is represented only in the form of the measured endpoint (e.g., 72-h EC50) [START_REF] Brooks | Historical control data for the interpretation of ecotoxicity data: are we missing a trick?[END_REF][START_REF] Mancini | Method for calculating effects, on aquatic organisms, of time varying concentrations[END_REF]OCDE, 1997;[START_REF] Van Den Brink | Exposure pattern-specific species sensitivity distributions for the ecological risk assessments of insecticides[END_REF]. It is possible that different conclusions on the effect of the same toxicant concentration could be derived for different exposure durations [START_REF] Barata | Comparing Metal Toxicity Among Daphnia magna Clones: An Approach Using Concentration-Time-Response Surfaces[END_REF][START_REF] Byrne | Numerically modelling time and dose dependent cytotoxicity[END_REF][START_REF] Hickey | Microtesting appraisal of ATP and cell recovery end-points after acute exposure of Selenastrum capricornutum to selected chemicals[END_REF][START_REF] Ragas | Trends and challenges in risk assessment of environmental contaminants[END_REF]. In this respect, concentration-time-response surfaces could provide a more complete presentation of the available data, and could reveal crucial information in environmental studies, including risk management, where the aim is to determine precise quantitative ecotoxicity values [START_REF] Barata | Comparing Metal Toxicity Among Daphnia magna Clones: An Approach Using Concentration-Time-Response Surfaces[END_REF][START_REF] Lee | Predicting chronic mortality of chemicals to fishes from acute toxicity test data: multifactor probit analysis[END_REF][START_REF] Paumgartten | Risk assessment for chemical substances: the link between toxicology and public health[END_REF][START_REF] Sun | Estimation of acute toxicity by fitting a dose-time response surface[END_REF].

Enzymatic activity responses can be easily measured over a short temporal scale, and peroxidase enzymatic activity in higher plants is a well-known experimental parameter for assessing the response of an organism exposed to a non-biodegradable toxicant [START_REF] Jouili | Plant peroxidases: Biomarkers of metallic stress[END_REF][START_REF] Stegeman | Enzyme and protein synthesis as indicators of contaminant exposure and effect[END_REF]. Moreover, the study of biochemical parameters associated with more classical parameters (e.g., biomass yield) may help in organism quality assessment although it may be difficult to distinguish between adaptive responses from natural evolution and responses to temporary stress [START_REF] Bijlsma | Environmental stress, adaptation and evolution: an overview[END_REF][START_REF] Calow | Evolution, Ecology and Environmental Stress[END_REF][START_REF] Forbes | The use and misuse of biomarkers in ecotoxicology[END_REF]. Peroxidases are a group of oxidoreductase enzymes utilizing hydrogen peroxide as an electron acceptor molecule. An example of their action in higher plants is the peroxidase transformation of phenolic compounds into phenolic radicals that are then polymerized to give rise to lignin [START_REF] Polle | Apoplastic peroxidases and lignification in needles of Norway spruce (Picea abies L.)[END_REF][START_REF] Tobimatsu | Lignin polymerization: how do plants manage the chemistry so well?[END_REF]. Peroxidase activity is very important for regulating plant growth, asthis enzyme degrades, for example, the phytohormone indoleacetic acid [START_REF] Rama-Rao | Changes in indoleacetic acid oxidase and peroxidase activities during cotton fibre development[END_REF]. However, if this enzyme is used as a biomarker in environmental studies, it is important to remember that this class of enzymes is very susceptible to variations inenvironmental conditions, and is implicated in the oxidation of reactive oxygen species, and thereby help to avoid the damage resulting from oxidative stress [START_REF] Bela | Plant glutathione peroxidases: Emerging role of the antioxidant enzymes in plant development and stress responses[END_REF][START_REF] Gaspar | Peroxidases: a survey of their biochemical and physiological roles in higher plants[END_REF][START_REF] Gill | Reactive oxygen species and antioxidant machinery in abiotic stress tolerance in crop plants[END_REF][START_REF] Sies | Oxidative stress: from basic research to clinical application[END_REF]. Anthropogenic emissions of (semi)metals into the natural environment from a variety of sources (e.g., metallurgy, agriculture, energy production, and waste disposal) can result in these elements being a stress-causing factor in plants and other living organisms, and they may disrupt entire ecosystems [START_REF] Seregin | Physiological aspects of Cadmium and Lead toxic effects on higher plants[END_REF][START_REF] Verkleij | Mechanisms of metal tolerance in higher plants[END_REF]. Arsenic is well-known to be one such plant-growth limiting contaminant, disrupting photosynthetic and respiratory systems and stimulating secondary metabolism (De Gara et al., 1993;[START_REF] Majumder | Evaluation of arsenic induced toxicity based on arsenic accumulation, translocation and its implications on physio-chemical changes and genomic instability in indica rice (Oryza sativa L.) cultivars[END_REF]Panda et al., 2009).

Aluminium phytotoxicity appears as a rapid inhibition of root elongation due to damage toroot apex cells,with plants showing a reduced and atrophied root system as a consequence [START_REF] Chandran | Transcriptome profiling identified novel genes associated with aluminum toxicity, resistance and tolerance in Medicago truncatula[END_REF][START_REF] Awasthi | Morpho-physiological analysis of tolerance to aluminum toxicity in rice varieties of North East India[END_REF]. Cellular metabolic disturbance in roots reduces water and mineral uptake, affecting the physiologyof the whole plant, which leads to an imbalance in ROS production entailingan oxidative stress process [START_REF] Darkó | Aluminium toxicity, Al tolerance and oxidative stress in an al-sensitive wheat genotype and in al-tolerant lines developed by in vitro microspore selection[END_REF][START_REF] Sharma | Involvement of oxidative stress and role of antioxidative defense system in growing rice seedlings exposed to toxic concentrations of aluminum[END_REF].

In a general way, metal toxicity effects in plants include inhibition of the mitotic index [START_REF] Gzyl | Cadmium affects microtubule organization and post-translational modifications of tubulin in seedlings of soybean (Glycine max L.)[END_REF], increased tissue permeability (Sen and Mondal, 1987), promotion of metal accumulation, increased energy expenditure to cope with high metal concentrations [START_REF] Israr | Cadmium accumulation and antioxidative responses in the Sesbania drumondii callus[END_REF], reduced photosynthesis or chlorophyll-a synthesis [START_REF] Dube | Excess chromium alters uptake and translocation of certain nutrients in citrullus[END_REF], inhibition of root apex growth by inhibition of DNA synthesis [START_REF] Liu | Effects of Al 3+ on root growth, cell division, and nucleoli in root tip cells of Zea mays L[END_REF], disruption of enzymatic activity [START_REF] Cakmak | Effect of aluminium on lipid peroxidation, superoxide dismutase, catalase, and peroxidase activities in root tips of soybean (Glycine max)[END_REF][START_REF] Jaworska | Heavy metal contents and enzymatic activity in soils exposed to the impact of road traffic[END_REF], and oxidative stress caused by reactive oxygen species [START_REF] Jouili | Plant peroxidases: Biomarkers of metallic stress[END_REF][START_REF] Abdelgawad | Maize roots and shoots show distinct profiles of oxidative stress and antioxidant defense under heavy metal toxicity[END_REF].

Within the ecological context of (semi-)metal phytotoxicity, the goal of this study was to use 3-D response surfaces to show peroxidase activity in the higher plant Zea mays (L.) as a function of time-concentration exposure to arsenic or aluminium ions while under hydroponic conditions. Using such 3D topological responses, a broader vision of the ecotoxicity profile can be obtained, which could be helpful in the field of environmental policy management. For example, sewage sludge can provide a large part of the nutrients required byplants, but aluminium coagulant-flocculant compounds used in wastewater treatment can be phytotoxic [START_REF] Kluczka | Assessment of aluminum bioavailability in alum sludge for agricultural utilization[END_REF]. Thus, it is necessary to understand the phytotoxic relationships between time and concentration responses of pollutants to evaluate the risks related to theapplicationof sewage sludge to land used fornon-human edible culture (e.g., maize used for animal nutrition).

Materials and methods

Contaminants

Sodium arsenite (NaAsO2) and aluminium sulfate Al2(SO4)3 (Anidrol, Diadema, SP, Brazil) were used as the experimental toxins in this study. In this study, the ranges of concentrations used in the media solutions were based on Brazilian legislation (CONAMA resolution 357/2005). Preliminary assays were performed to determine the concentration ranges required to obtain concomitant biomass and biomarker responses.

The specific tested concentrations were 0.0025, 0.005, 0.01, 0.02, and 0.04 mg As 3+ .L -1 , and 0.025, 0.05, 0.1, 0.2, and 0.4 mg Al 3+ .L -1 . The arsenic concentration of 0.04 mg As 3+ .L -1 and the aluminium concentration of 0.4 mg Al 3+ .L -1 were above the Brazilian legislated limits (0.033 mg As 3+ .L -1 and 0.2 mg Al 3+ .L -1 ) for Class 3 freshwater (supplied for human consumption, after conventional or advanced treatment) (CONAMA, 2005). Distilled water was used as a negative control in all exposure experiments.

Plant species

The seeds selected for the tests were obtained from genetically unmodified and pesticide-free plants of Z. mays purchased at the Organic Market in the city of Brumadinho (MG, Brazil). The tests were performed using only one ozone-sterilized seed batch, to eliminate possible problems with variations between different batches.

Phytotoxicity tests in solution media

Toxicant solution phytotoxicity tests were performed on 10-day-old Z. mays plantlets germinated in pots containing 1 kg of commercial autoclaved garden soil.

Assays were performed according to the ISO (1995) guideline, with some slight modifications, i.e., fewer replicates per test series (three instead of four). The following is a summary of the adopted procedures.

Three series of tests were performed at different exposure times of 0, 20, 45, 90, 180, 360, 720, and 2880 minutes. For each series of test plants, three pots (disposable hydrophobic plastic, 120 mL) were used for each test concentration and the controls.

Immediately after preparing the test solutions, 38 Z. mays plantlets were added to each pot. Plants were placed in a culture room with a 25ºC ± 2ºC daytime temperature, 17ºC ± 2ºC night-time temperature, and 16:8 hour light/dark photoperiods with 82 mE m 2 s -1 lighting from fluorescent tubes. Biological parameters were analysed for all exposure times. For each time-analysis, four plants from each pot were harvested and separated into two parts, and the wet weights of the roots and aerial parts were immediately measured on an analytical balance. The total weight of the harvested plant parts (expressed in grams wet weight) was divided by the number of plants harvested from each pot. Half of the biomass was then used to measure the plant dry weight in a stove, while the other half was used to measure enzyme activity and protein.

Measured endpoints 2.4.1. Biomass

Biomass was calculated from the dry mass (as describeb above) in relation to the number of plants (g plant -1 ).

Quantification of total soluble proteins

The protein content in the Z. mays leaf and root samples was determined using bovine serum albumin (BSA) as a standard [START_REF] Bradford | A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding[END_REF]. The protocol was validated according to the linearity of the responses obtained from the samples on a calibration curve obtained using commercial BSA. Thus, a stock solution of the commercial protein (SIGMA, P-8000) was prepared by dissolving 100 mg of the protein in 100 mL of phosphate buffer (50 mM; pH 7.6). A dilution range of 6.25, 12.5, 25.0, 50.0, and 100.0 µg.100 µL -1 was used to prepare the calibration curve used to express the results obtained from the samples. The mean linear regression equation for the three curves was: Y = 0.0038 X + 0.0315 (R 2 = 0.9938). (EC 1.11.1.7) Enzyme activity was measured using a slightly modified version of the published method [START_REF] Byl | Evaluation of peroxidase as a biochemical indicator of toxic chemical exposure in the aquatic plant Hydrilla verticillata, Royle[END_REF]. Briefly, 0.5 g of the fresh aerial and root parts were weighed, homogenized separately using a mortar and pestle, and maintained at 4°C in 4 mL of 50 mM potassium phosphate buffer (pH 7.6). The samples were centrifuged (3000 g, 10 minutes, 4°C) and the supernatants were stored at -20°C awaiting subsequent analysis.

Peroxidase enzyme activity

After defrosting, the supernatant (0.1 mL) was placed in a 1.5-mL glass cuvette, and 0.7 mL of solution A (prepared by adding 810 mg phenol to 25 mg 4-aminoantipyrene in 50 mL of distilled water) was added just before the assay. Then, 0.75 mL of solution B (prepared by adding 0.01% of hydrogen peroxide in 0.01 M Phosphate buffer, pH 7.1) was added to start the reaction, and the absorbance was monitored for 5 minutes at 510 nm. The measured variation in absorbance was reported according to the dry weight of the sample, and was compared with the protein content of each sample. The enzymatic unit of the peroxidase forms 1.0 mg of purpurogallin from pyrogallol in 20 s at pH 6.0 and 20ºC (equivalent to ~18 µM units per minute at 25 °C), and was defined by a calibration curve using horseradish POD (SIGMA, 10670U). The commercial enzyme stock solution (1067 EU mg -1 ) was prepared by dissolving 10 mg of the enzyme in 10 mL of 0.01 M phosphate buffer (pH 7.1). A dilution range was used to prepare the calibration curve utilised to express the results obtained from the samples. The dilutions used to create the calibration curve were: 1/4, 1/6, 1/8, 1/10, 1/12, 1/14, and 1/16. The mean linear regression equation for the three curves was: Y = -49.92 X + 13871 (R 2 = 0.9992). The values obtained from the calibration curve were divided by the protein content of the sample (dry weight basis).

Graphical

The graphic drawings shown in this study were made with Origin software (OriginLab Corporation, Washington, USA).

Statistical analysis

Three test series were performed at three different periods (20-day intervals between the series). For each test series, data on enzyme activity, biomass, and protein content were generated in triplicate (three pots) for each treatment (or control; n = 9).

After checking the data for normality (Shapiro-Wilk's test) and homogeneity of variances (Hartley's test), analysis of variance (ANOVA) was performed, followed by generation of the lowest observable effect concentration (LOEC) and no observable effect concentration (NOEC) values using Williams' test (p ≤ 0.05) [START_REF] Williams | A test for differences between treatment means when several dose levels are compared with a zero dose control[END_REF].

TOXSTAT 3.0 software (University of Wyoming, Laramie, WY, USA) was used for these calculations.

Results and discussion

It is difficult to predict how the toxicity of a specific concentration of a toxin varies as a function of the exposure duration. A possible method to alleviate this problem is to use a 3D topological profile of the measured endpoint response, such as enzyme activity. In this type of data representation, the relationships between time and concentration-exposure can be seen from different perspectives, as the representation system allows for 360° rotation. Thus, in this phytotoxicity study, discussions of peroxidise activity are based on NOEC and LOEC values, which are useful for exploring more generic ecotoxicological situations (e.g., in a hypothesis test). In many environmental issues, the acquisition of accurate data (i.e., point estimation approach) can be problematic, as is the case where toxicity effects must be associated with different concentrations of toxins and different exposure durations. The main value of a hypothesis testing approach occurs in the initial stages of investigations, and it may not result in the most insightful metric for judging toxicity effects (OECD, 2006).

Therefore, we created 3D ecotoxicological profiles showing the LOEC values for peroxidase activity and dry biomass measured in the leaves of maize plantlets exposed to different concentrations of arsenic over different durations (Table S1 -Supplementary information). Fig. 1 (panels A-D) shows different 3D profiles of peroxidase activity as a function of concentration-time-exposure. We found a LOEC2880 min of 0.04 mg.L -1 for dry biomass of Z. mays leaves, whereas for the peroxidase activity endpoint, the LOEC720 min value was 0.005 mg.L -1 . The shortest exposure time over which peroxidase showed increased activity was 90 minutes, with a 0.04 mg L -1 exposure concentration.

Figure 1 Two different regions are of particular interest in Fig. 1. The first region (the white region or NOEC region) is formed by exposures (i.e., points for time-concentration pairings) that were not statistically different from the results of the control points (i.e., zero toxicant concentration and all exposure-times), whereas the second region (the grey region or LOEC region) is formed by exposure pairings with results that were statistically different to those obtained from control pairings.

The two profiles shown at the bottom of Fig. 1 represent diametrically opposed views of the exposure conditions. Thus, it is possible to obtain an ecotoxi-topological view of the time when a given concentration of the toxicant begins to cause significant adverse effects on the exposed maize plantlets. A more detailed analysis of Fig. 1 shows that at the point of the greatest exposure values (i.e., the longest exposure duration time and greatest toxicant concentration), peroxidase activity showed a decrease, just at the point where a significant decrease in leaf biomass began.

Quantitative sensitivity relationships (QSR) between biomarkers and classical endpoints have received little attention, despite their importance. These responses try to numerically link lower and higher levels of biological responses, for example, the LOEC value for enzyme activity variation and "catastrophic" EC50 or LC50 values.

Thus, QSRs could be useful for regulatory purposes in the environmental management domain, because there are a lack of studies that could facilitate establishment of a numerical relationship range for chemical exposure among the responses observed at different levels of biological organization in the same or different species (Corrêa et al., 2006;[START_REF] Silva | Arsenate (As V) in water: quantitative sensitivity relationships among biomarker, ecotoxicity and genotoxicity endpoints[END_REF].

It is important to note that in our experiments, the quantitative relationships among the different assessed endpoints are not subject to medium interference, because distilled water will not generate different LOEC values; this is not the case with data obtained for soil exposure (as an example), where different soil properties will generate different ecotoxicity values [START_REF] Martins | Assessing the Brazilian prevention value for soil Arsenic: Effects on emergence and growth of plant species relevant to tropical agroecosystems[END_REF]. In our experiment, where Z. mays leaves were exposed in solution to different arsenic concentrations and exposure-times, the LOEC dry biomass/enzyme activity ratio was 8.

The same endpoints (i.e., LOEC values for peroxidase activity and dry biomass) measured in the roots of maize plantlets exposed to arsenic are presented in Fig. 2 that shows the 3D profile of peroxidase activity as a function of concentration-timeexposure in four angles (panels A-D) (Table S2 -Supplementary information).

Figure 2 The data presented in Table S2 indicate that the LOEC2880 min for the dry biomass of Z. mays roots exposed to As 3+ was 0.04 mg L -1 . A LOEC720 min of 0.0025 mg.L -1 was found for peroxidase activity in roots, while a LOEC of 0.04 mg.L -1 exposureconcentration was found after an exposure time of 45 minutes. In the case of Z. mays roots, the LOEC dry biomass/enzyme activity ratio was 16.

Again, it is possible to observe two different regions in Fig. 2, with these showing similar profiles to those observed in Fig. 1, including the profile of the point of greatest exposure values (i.e., the longest exposure duration and the greatest concentration),

where peroxidase shows a tendency to decrease its activity, just at the point where a significant decrease in root biomass begins.

These similarities were expected, as both figures represent the same plant species exposed to the same conditions, despite the sensitivities of the two plant parts (i.e., leaves and roots) being different. Previous studies have also shown alterations in the activity of peroxidase enzyme due to the influence of different concentrations of arsenic in different plant species [START_REF] Armendariz | Arsenic toxicity in soybean seedlings and their attenuation mechanisms[END_REF][START_REF] Khan | Modulation of antioxidant defense system for Arsenic detoxification in Indian mustard[END_REF]. A significant synergistic effect on antioxidant enzyme activity was noted in Lemna minor (L.) when these macrophytes were exposed to different time-concentrations of As(III)

and As(V) ions under hydroponic conditions [START_REF] Duman | Biological responses of duckweed (Lemna minor L.) exposed to the inorganic arsenic species As(III) and As(V): effects of concentration and duration of exposure[END_REF].

Fig. 3 shows the results from the same experimental design described previously, but with the leaves of Z. mays exposed to different concentrations of aluminium solutions. Numerical data are presented in Table S3 (Supplementary information). The phytotoxicity data indicate a LOEC2880 min for the dry biomass of Z. mays leaves exposed to an Al 3+ concentration of 0.4 mg.L -1 . A LOEC720 min of 0.025 mg.L -1 was found for peroxidase activity in Z. mays leaves, while a LOEC of 0.4 mg.L -1 was found after an exposure-time of 90 min. In the case of Z. mays leaves, the LOEC dry biomass/enzyme activity ratio was 8.

Fig. 3 shows a similar profile to the previous figures, despite it being for a different toxic element. The same observations made for maize leaves exposed to As 3+ are valid for maize leaves exposed to Al 3+ .

Figure 3 Fig. 4 shows the results measured in roots of Z. mays exposed to aluminium under hydroponic conditions and numerical data are shown in Table S4 (Supplementary information). For biomass, the LOEC value increased significantly at an exposureconcentration of 0.4 mg L -1 after an exposure-time of 2880 min. For peroxidase activity in Z. mays roots, a LOEC720 min was found at a 0.02 mg.L -1 concentration of aluminium, while the shortest duration over which peroxidase showed increased activity in roots was 90 min at a 0.4 mg.L -1 exposure-concentration. For Z. mays roots, the LOEC dry biomass/enzyme activity ratio was 16. In relation to the variation in peroxidase activity response, it is well-known that (semi-)metals generally promote the formation of reactive oxygen species, oxidative stress [START_REF] Abdelgawad | Maize roots and shoots show distinct profiles of oxidative stress and antioxidant defense under heavy metal toxicity[END_REF][START_REF] Ahmed | Toxicity assessment of metal oxide nanopollutants on tomato (Solanum lycopersicon): A study on growth dynamics and plant cell death[END_REF];[START_REF] Tang | Oxidative stress-induced toxicity of CuO nanoparticles and related toxicogenomic responses in Arabidopsis thaliana[END_REF], and consequently oxidative damage [START_REF] Gill | Reactive oxygen species and antioxidant machinery in abiotic stress tolerance in crop plants[END_REF][START_REF] Hassan | Sulfur alleviates growth inhibition and oxidative stress caused by cadmium toxicity in rice[END_REF]Tiryakioglu et al., 2006), before they affect the biomass of plant species. However, oxidative damage could be counterbalanced by the anti-oxidative defence system [START_REF] Foyer | La résistance des plantes à l´oxygène[END_REF][START_REF] Sies | Oxidative stress: from basic research to clinical application[END_REF], and the equilibrium point between these processes can be seen at the limit points of Figs. 1-4 (i.e., near the longest duration and greatest concentration exposures), precisely where biomass begins to decrease significantly. An overview of the data pool measured in this study is shown in Table 1.

Table 1 If we compare sensitivity between the different parts of the plantlets for the same endpoints, the roots of Z. mays can be seen to be more sensitive to hydroponic solution exposure than the leaves, with this being the case for both toxicants. In a similar manner, it was reported that shoots of Indian mustard (Brassica juncea L. Czern.)

seemed to be less efficient than roots at scavenging reactive oxygen species, as indicated by different responses to Cd stress shown by peroxidase and catalase activities [START_REF] Mohamed | Cadmium tolerance in Brassica juncea roots and shoots is affected by antioxidant status and phytochelatin biosynthesis[END_REF]. A similar observation was made on the peroxidase response of roots and primary leaves of bean seedlings as a part of the defence mechanism against copper-and zinc-imposed oxidative stress [START_REF] Cuypers | Peroxidases in roots and primary leaves of Phaseolus vulgaris Copper and Zinc Phytotoxicity: a comparison[END_REF].

The two regions of the 3D ecotoxi-topology plots shown in all figures (i.e., with and without statistical significance or NOEC and LOEC) are dependent on the level of significance used. In this sense, environmental toxicological studies relate statistical significance with biological relevance (or significance) of a toxic effect, but this does not always represent the real ecological consequence (e.g., in the case of reversible toxic effects). Therefore, in the 3D graphical interpretation shown above, we must bear in mind that the statistical NOEC/LOEC values are very dependent on the range of tested concentrations, generated data variability, and level of statistical significance applied in the analysis [START_REF] Newman | Ecotoxicology: a comprehensive treatment[END_REF]. However, from a practical point of view, the management of pollution issues can be greatly enriched when 3D ecotoxi-topology profiles are used as a complementary ecotoxicity approach.

Conclusions

In this study, measured toxicity endpoints (i.e., dry biomass and peroxidase enzyme activity) in Z. mays showed different sensitivities, with biomass showing a response only at the highest exposure-concentration and highest exposure-duration, whereas peroxidase activity responses generally occurred at lower exposure-concentrations and highest exposure-durations for both the toxicants As 3+ and Al 3+ .

However, peroxidase also responded to lower exposure-durations at higher exposureconcentrations. The highest (semi-)metal exposure-concentration and highest exposureduration produced a less intense increase in enzymatic activity, just at the point where a significant decrease in biomass was beginning. For peroxidase activity, a 3D ecotoxitopological view can be obtained to indicate the time at which a given concentration of the toxicant begins to cause significant adverse effects on the exposed organism. These ecotoxi-topological views based on concentration-time-response surfaces can be used to predict ecotoxic concentration levels at different exposure durations, which can be very useful in setting regulatory goals to enhance, protect, and preserve ecosystems.

However, this ecotoxi-topology approach must be considered as an approximate approach for now, because additional studies are necessary to improve and validate the methodology.

CRediT authorship contribution statement

Figure 4 Fig. 4

 44 Figure 4

Fernanda Engel :

 : Investigation, Methodology; Sylvie Cotelle: Formal analysis, Writing -original draft; Cleder A. Somensi: Investigation, Writing -review and editing; Renan C. Testolin: Methodology; Editing; Rogério Corrêa: Resources, Formal analysis; Hela Toumi: Instrumental analysis, Methodology; Jean-François Férard: Writing -review and editing, Supervision; Claudemir M. Radetski: Writing -review and editing, Supervision.

Fig. 1 .

 1 Fig. 1. Different 3D profiles of peroxidase activity as a function of concentration-timeexposures measured in the leaves of maize grown in arsenic (As 3+ ) solution. Coordinate references were: A (Azimuth= 310; Inclination = 15.8; Roll = 0.2); B (Azimuth= 319; Inclination = 81.0; Roll = 0.8); C (Azimuth= 220; Inclination = 15.8; Roll = 0.2); D (Azimuth= 40; Inclination = 15.8; Roll = 0.2).

Fig. 2 .

 2 Fig. 2. Different 3D profiles of peroxidase activity as a function of concentration-timeexposures measured in roots of maize grown in arsenic (As 3+ ) solution. Coordinate references were: A (Azimuth= 310; Inclination = 15.8; Roll = 0.2); B (Azimuth= 319; Inclination = 81.0; Roll = 0.8); C (Azimuth= 220; Inclination = 15.8; Roll = 0.2); D (Azimuth= 40; Inclination = 15.8; Roll = 0.2).

Fig. 3 .

 3 Fig. 3. Different 3D profiles of peroxidase activity measured in the leaves of Zea mays as a function of concentration-time-exposures to aluminium (Al 3+ ) in solution. Coordinate references were: A (Azimuth= 310; Inclination = 15.8; Roll = 0.2); B (Azimuth= 319; Inclination = 81.0; Roll = 0.8); C (Azimuth= 220; Inclination = 15.8; Roll = 0.2); D (Azimuth= 40; Inclination = 15.8; Roll = 0.2).

Acknowledgments

This study was financially supported by Universidade do Vale do Itajaí (Brazil). F. Engel is grateful to the Brazilian Ministry of Education -Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) by scholarship #41005015004P7. CM Radetski gratefully acknowledges a grant from CNPq-Brasil (302124/2019-5).

Declaration of competing interest

The authors have no conflicts of interest to declare in relation to the work described in this study.


Firouzé Bani-Sadr
email: fbanisadr@chu-reims.fr

Maxime Hentzien

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Corticosteroid therapy for patients with COVID-19 pneumonia: a before-after study

Keywords: COVID-19, SARS CoV2, COVID-19 pneumonia, corticosteroid

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Introduction

There is evidence that severe CoVID-19 patients present overwhelming inflammatory reactions with high levels of cytokines and inflammatory biomarkers, leading to lung injury [START_REF] Zhang | The use of anti-inflammatory drugs in the treatment of people with severe coronavirus disease 2019 (COVID-19): The Perspectives of clinical immunologists from China[END_REF][START_REF] Mehta | COVID-19: consider cytokine storm syndromes and immunosuppression[END_REF]. Anti-inflammatory drugs such as corticosteroids may beneficially modulate the host immune response to CoVID-19 pneumonia. With an average of 2-3 days between the occurrence of dyspnea and intensive care unit (ICU) admission, we postulate that corticosteroid treatment initiated as soon as the patient has shortness of breath or needs oxygen therapy, might be effective in preventing acute respiratory distress syndrome and death [START_REF] Huang | Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China[END_REF]. Therefore, since 27 March 2020, we have systematically included corticosteroids in the treatment of patients with CoVID-19 pneumonia. Prednisone or methylprednisolone at a dose of 1 mg/kg equivalent per day (0.5 mg/kg for patients also receiving antiviral therapy with ritonavir as coadministration of corticosteroid and ritonavir lead to an increase corticosteroid plasma concentrations and their half-life) for 3 to 4 weeks, according to the severity of pneumonia, with dose tapering over the last week, was added to our initial therapeutic protocol for hospitalized CoVID-19 patients [START_REF] Busse | Influence of Antiretroviral Drugs on the Pharmacokinetics of Prednisolone in HIV-Infected Individuals[END_REF]. This protocol included antiviral therapy (lopinavir plus ritonavir or darunavir plus ritonavir) and/or hydroxychloroquine, empiric broad-spectrum antibiotic treatment for 14 days and preventive anticoagulation for 14 to 21 days. The long duration of corticosteroid treatment was chosen by analogy with that recommended for severe pneumocystis pneumonia in order to additionally prevent pulmonary fibrosis [START_REF] Bozzette | A Controlled Trial of Early Adjunctive Treatment with Corticosteroids for Pneumocystis carinii Pneumonia in the Acquired Immunodeficiency Syndrome[END_REF]. As lopinavir-ritonavir treatment was not available after mid-March due to a drug shortage in our hospital, most of our patients received another HIV protease inhibitor (darunavir-ritonavir) after this date.

In order to evaluate the impact of addition of corticosteroids to the hospital protocol for treatment of suspected or confirmed CoVID-19 pneumonia, we compared rates of death (primary outcome) or intensive care unit (ICU) admission and/or death before ICU admission (secondary outcome) in a before-and-after study, with the introduction of corticosteroids in our therapeutic protocol as the event defining the start of the "after" period.

Patients and Methods

Between March 3 rd and April 14 th 2020, 319 patients with CoVID-19 diagnosis defined as a positive result on an polymerase-chain reaction testing of a nasopharyngeal sample or presence of characteristic findings on chest CT scan were followed in the University Hospital of Reims, France [START_REF] Xu | Computed Tomographic Imaging of 3 Patients With Coronavirus Disease 2019 Pneumonia With Negative Virus Real-time Reverse-Transcription Polymerase Chain Reaction Test[END_REF]. Two periods were considered for the purposes of our study: the first, from March 3 rd to 20 th , corresponded to the "before" period, and the admission of the first cases to our center. During the "before" period, corticosteroid therapy was not recommended. The second period comprised March 26 th through April 14 th 2020, ("after"), with wide use of corticosteroid therapy in this period following our decision to introduce it systematically due to the biological rationale of its use in the inflammatory phase. Patients with initiation of corticosteroid therapy during the transition period (from March 21 st to March 25 th 2020) were not included in the before-after analysis. Patients with fewer than 7 days between symptom onset and April 14 th , 2020 -that was the end point date of follow up -were not included. Individual follow-up was defined as the time from first symptoms to death during hospitalization for the primary outcome and to ICU admission or death before ICU admission for the secondary outcome. ICU admission alone was not considered as an outcome, since we did not exclude patients aged over 80 years and/or with comorbidities, who were less likely to have access to ICU care. Data are expressed as mean ± standard deviation, or number (percentage), as appropriate. Quantitative variables were compared between the two periods using the Student t test and qualitative variables using the Chi square test or Fisher's exact test, as appropriate. For the impact of the period on death and on ICU admission and/or death, we constructed Kaplan Meier curves and compared them using the log rank test. For multivariate analysis, we used Cox proportional hazard models systematically adjusted for age, National Early Warning score and institutionalization status at hospital admission [START_REF] Williams | Royal College of Physicians, National Early Warning Score (NEWS), Standardising the assessment of acute-illness severity in the NHS, London. 8 Clinical-management-of-severe-acute-respiratory-infection-when-novel-coronavirus[END_REF].

Results

At the time of data extraction, a total of 319 patients were included in the cohort, namely 85 patients in the "before" period (until March 20 th , 2020), 62 patients in the transition period (March 21 st -25th), and 172 patients in the "after" period (March 26 th through April 14 th ).

Eleven patients (12.9%) received corticosteroid therapy in the "before period", 20 (32.3%) in the transition period and 119 (69.2%) in the "after" period. The main characteristics of the 257 patients in the "before" and "after" periods are summarized in Table 1. Patients in the "after" period were significantly more frequently nursing home residents, had higher prevalence of dementia, a longer time from symptom onset to hospitalization, less frequently received lopinavir and/or hydroxychloroquine, and more often required oxygen therapy than in the "before" period. Patients in the "after" period also had higher serum creatinine. The mean duration of follow-up was 16.0 ± 7.0 days, and was similar between periods (16.0 ± 8.7 versus 16.1 ± 6.2; p=0.92). Of note, deceased patients hospitalized in medical ward were older than those who were transferred to ICU (mean age 83.9 (±11.3) versus 69.6 (±7.2) years).

The "after period" was not associated with a lower risk of death (hazard ratio (HR) =0.86; 95% confidence interval (CI), 0.47-1.56; p=0.62) by bivariate analyses but was associated by multivariate analysis adjusted for age, National Early Warning score and institutionalization status (HR = 0.47; 95% CI 0.23 -0.97; p=0.04).

The "after period" was associated with a lower risk of ICU admission and/or death before ICU admission by bivariate analyses (HR=0.25; 95% CI = 0.11-0.55) and by multivariate analysis adjusted for age, National Early Warning score and institutionalization status (HR =0.37 95% CI 0.21 -0.64; p=0.0005).

Discussion

In this before-and-after study of 319 hospitalized CoVID-19 patients, after adjustment for age, National Early Warning score and institutionalization status, the "after" period (n=172) -during which corticosteroids were routinely recommended for patients presenting with CoVID-19 pneumonia at our institution-was associated with a lower risk of death (HR =0.47; 95% CI 0.23 -0.97; p=0.04), and a lower risk of ICU admission and/or death before ICU admission (HR =0.37 95% CI 0.21 -0.64; p=0.0005).

To this day, corticosteroids are not recommended by the World Health Organization for the treatment of CoVID-19 pneumonia due to their potential adverse effects, such as secondary infections and prolonged virus shedding [8]. However, with our improving knowledge of the role played by overwhelming inflammation in severe CoVID-19 patients, immunomodulatory drugs such as Interleukin-6 or -1 blockade or anti-tumor necrosis factor therapy are being evaluated and all are in favor of a beneficial effect of immunomodulatory drugs during the inflammatory phase of CoVid-19 infection [START_REF] Zhang | The use of anti-inflammatory drugs in the treatment of people with severe coronavirus disease 2019 (COVID-19): The Perspectives of clinical immunologists from China[END_REF]9]. Corticosteroids are old medicines that are inexpensive and accessible to the whole world. In our study, they were associated with a decrease of over 50% in mortality, and in the rate of death and/or ICU admission, even though patients were more dependent and more often required oxygen in the "after" period at the censoring date (although follow-up duration was similar between the two groups).

We acknowledge that a before-and-after study yields a low level of evidence, the difference may be the result of overall better patient care with improvements in thrombosis prophylaxis and some of these patients remained hospitalized at end of follow-up and were thus censored for outcomes. Furthermore, the favorable outcome observed with corticosteroids may be partly due to the use of concurrent antiviral drugs in our patients.

Another limitation of our study is that CoVID-19 pneumonia diagnosis was more often performed by chest CT scan in patients who received corticosteroids group than in patients who did not. Positive reverse transcriptase polymerase-chain reaction is the gold standard for confirming diagnosis of COVID-19 but its performance presents variable sensitivities, ranging from 37% to 71% [START_REF] Rubin | The Role of Chest Imaging in Patient Management During the COVID-19 Pandemic[END_REF]. Although chest CT scan is highly sensitive for detecting COVID-19 pneumonia, overlapping CT image features with others viral pneumonia and other respiratory diseases make an exclusion diagnosis difficult and could be therefore a source of bias in our study [START_REF] Rubin | The Role of Chest Imaging in Patient Management During the COVID-19 Pandemic[END_REF]. Finally, the unavailability of safety data should be acknowledged as a limitation.

Nevertheless, these preliminary data support the initiation of clinical trials testing corticosteroids during the inflammatory phase of CoVID-19, and may potentially lead to a change in treatment recommendations.

Fig 1 :

 1 Fig 1: Kaplan Meier curves for death before ICU admission between patients "before" and "after" implementation of corticosteroids for CoVID-19 pneumonia in Reims University Hospital

Table I : Main characteristics of patients in the periods before and after introduction of corticosteroids for CoVID-19 pneumonia in Reims University Hospital

 I

	185	†Among those who received oxygen therapy.
			Before (N=85)	After (N=172)	p
			n (%) or mean ± SD	n (%) or mean ± SD
		Received corticosteroids	11	12.9	119	69.2	<0.0001
		Age	70.1	±15.1	71.8	±16.4	0.44
		Male sex	46	54.1	51.7	41.7	0.72
		Charlson comorbidity score	1.8	±2.0	2.05	±1.94	0.42
		Dementia	8	9.4	33	19.2	0.04
		Nursing home resident	8	9.4	47	27.3	0.001
		Time from symptom onset to	5.8	±4.2	7.5	±4.9	0.009
		hospitalization (days)
		Diagnosis by positive PCR	80	94.1	143	83.1	0.01
		Diagnosis by chest CT scan	5	5.9	29	16.9
		Risk factor of severity	71	83.5	156	90.7	0.09
		-Immunocompromised	11	12.9	22	12.8	0.97
		-Cardiovascular disease	41	48.2	94	54.7	0.33
		-Complicated diabetes	7	8.2	23	13.4	0.23
		-Cirrhosis	1	1.2	3	1.7	0.99
		-Chronic respiratory	22	25.9	32	18.6	0.18
		disease
		-Chronic renal disease	4	4.7	16	9.3	0.20
		-Cancer	7	8.2	10	5.8	0.46
		-BMI>40	2	2.4	13	7.7	0.15
		-National Early Warning	6.2	3.8	6.9	3.2	0.12
		Score
		Biological characteristics
		-Lymphocyte count G/L	1.1	±0.56	1.1	±1.0	0.73
		-Lymphopenia<1G/L	43	51.2	91	53.9	0.69
		-Neutrophil count, G/L	5.0	±3.6	5.6	±4.0	0.26
		-C-reactive protein, mg/L	98.0	±90.2	89.9	±77.1	0.46
		-Serum creatinine, mol/L	103.5	±106.2	137.7	±174.3	0.05
		Treatment use with expected	63	75.0	135	79.4	0.43
		antiviral activity
		-Lopinavir	46	54.8	13	7.9	<0.0001
		-Darunavir	27	32.5	133	78.2	<0.0001
		-Hydroxychloroquine	11	13.3	10	6.0	0.049
		Antibiotic therapy	80	95.2	162	95.9	0.99
		Evolution
		-Required oxygen therapy	52	61.9	125	76.7	0.01
		-Maximum oxygen flow in	5.0	±7.6	5.7	±5.2	0.48
		medical ward †
		-Death	17	20.0	31	18.0	0.70
		-ICU admission and/or	29	34.1	40	23.6	0.07
		Death

Kaplan Meier curves for ICU admission and/or death before ICU admission between patients "before" and "after" implementation of corticosteroids for CoVID-19 pneumonia in Reims University Hospital

The "before" period was until March 20 th , 2020 and the "After" period began on March 26 th , 2020. Log -rank: (p=0.006)

DECLARATIONS