Vu-Hieu Nguyen

Giuseppe Rosi

Salah Naili

Adrien Michel

Maria-Letizia Raffa

Romain Bosc

Jean-Paul Meningaud

Christine Chappard

Naoki Takano

Guillaume Haiat
email: guillaume.haiat@univ-paris-est.fr

Guillaume Haïat

anisotropic bone properties on the biomechanical behavior of the acetabular cup implant: a multiscale finite element study

Keywords: Acetabular cup, total hip replacement, finite element analysis, bone, Homogenization

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

Introduction

While hip arthroplasty has become a common surgical intervention with more than 450,000 interventions each year in the USA [START_REF] Wengler | Hip and knee replacement in Germany and the USA: analysis of individual inpatient data from German and US hospitals for the years 2005 to 2011[END_REF], failures still occur, leading to dramatic consequences. Aseptic loosening is one of the most common causes of failure [START_REF] Hsu | The number of screws, bone quality, and friction coefficient affect acetabular cup stability[END_REF][START_REF] Fehring | Initial stability of press-fit acetabular components under rotational forces[END_REF] and is related to the implant biomechanical behavior. The long-term fixation of the acetabular cup (AC) implant is obtained through osseointegration phenomena [START_REF] Bloebaum | Postmortem analysis of bone growth into porous-coated acetabular components[END_REF][START_REF] Haiat | Effects of biomechanical properties of the bone-implant interface on dental implant stability: from in silico approaches to the patient's mouth[END_REF], which leads to a bonded bone-implant interface after the bone healing process. Load transfers at the bone-implant interface are complex due to i) their multiaxial nature (caused by body weight bearing), ii) the complex multiscale properties of bone tissue (in particular, bone is an anisotropic material) and iii) the evolving properties of bone tissue due to remodeling phenomena. The determination of the biomechanical behavior of the AC implant is important to assess its stability and to understand osseointegration phenomena [START_REF] Mueller | Periacetabular bone changes after uncemented total hip arthroplasty evaluated by quantitative computed tomography[END_REF][START_REF] Mueller | Modes of periacetabular load transfer to cortical and cancellous bone after cemented versus uncemented total hip arthroplasty: a prospective study using computed tomography-assisted osteodensitometry[END_REF] around the implant [START_REF] Mathieu | Biomechanical determinants of the stability of dental implants: influence of the bone-implant interface properties[END_REF]. Nowadays, the surgeons rely on their proprioception to assess empirically the AC implant stability by applying manually forces and/or torques to the ancillary.

Coupling three-dimensional images obtained with micro-computed tomography (µCT) and numerical simulation has allowed the development of biomechanical analyses taking into account the influence of the bone microstructure on implants behavior [START_REF] Chiba | In vivo structural analysis of subchondral trabecular bone in osteoarthritis of the hip using multi-detector row CT[END_REF][START_REF] Ruffoni | The different contributions of cortical and trabecular bone to implant anchorage in a human vertebra[END_REF]. Peri-implant bone microarchitecture has been shown to play an important role in the distribution of stresses by forming load transfer paths [START_REF] Matsunaga | Biomechanical role of peri-implant cancellous bone architecture[END_REF][START_REF] Ohashi | Biomechanical role of peri-implant trabecular structures during vertical loading[END_REF]. Bone properties also determine the dynamic implant pull-out force [START_REF] Basler | Peri-implant bone microstructure determines dynamic implant cut-out[END_REF]. To analyze the properties of peri-implant bone tissue, biomechanical investigations based on the trabecular bone structure are necessary. However, none of the aforementioned studies have investigated so far the AC implant behavior. The difficulty lies in the size of the AC implant, that requires to take into account a large volume of trabecular bone in the computation, which explain why, to the best of our knowledge, classical micro-finite element analyses taking into account bone microstructure around the implant have not been applied to study the mechanical behavior of the AC implant.

Numerous studies focused on the effect of the AC implant shape [START_REF] Ma | Optimized design for a novel acetabular component with three wings. A study of finite element analysis[END_REF][START_REF] Phillips | The effect of acetabular cup size on the short-term stability of revision hip arthroplasty: a finite element investigation[END_REF][START_REF] Janssen | Computational assessment of pressfit acetabular implant fixation: the effect of implant design, interference fit, bone quality, and frictional properties[END_REF][START_REF] Goebel | The influence of head diameter and wall thickness on deformations of metallic acetabular press-fit cups and UHMWPE liners: a finite element analysis[END_REF], material [START_REF] Ghosh | Bone remodelling around uncemented metallic and ceramic acetabular components[END_REF] and surface treatment [START_REF] Hsu | The number of screws, bone quality, and friction coefficient affect acetabular cup stability[END_REF] on its biomechanical properties. However, the relation between trabecular bone properties and the AC implant macroscopic mechanical behavior remains poorly established [START_REF] Cook | Interface mechanics and bone growth into porous Co-Cr-Mo alloy implants[END_REF]. Moreover, the effect of the anisotropic nature of bone tissue as well as the distribution of the stress and strain fields around an AC implant remains unknown. Several models have been developed to assess the deformation of the AC implant and the stability obtained after the press-fit insertion [START_REF] Hothi | Explicit finite element modelling of the impaction of metal press-fit acetabular components[END_REF][START_REF] Yew | Deformation of press-fitted metallic resurfacing cups. Part 2: Finite element simulation[END_REF]. Other numerical studies have computed the stress field in peri-implant bone tissue while the AC implant was progressively implanted and identified the AC periphery as the zone with the highest stresses due to the press-fit configuration [START_REF] Janssen | Computational assessment of pressfit acetabular implant fixation: the effect of implant design, interference fit, bone quality, and frictional properties[END_REF][START_REF] Hothi | Explicit finite element modelling of the impaction of metal press-fit acetabular components[END_REF]. Our group has developed a method that can provide information on the implant insertion conditions based on the variation of the force applied between the hammer and the ancillary as a function of time [START_REF] Mathieu | Variation of the impact duration during the in vitro insertion of acetabular cup implants[END_REF][START_REF] Michel | Monitoring the press-fit insertion of an acetabular cup by impact measurements: influence of bone abrasion[END_REF][START_REF] Michel | Ex vivo estimation of cementless acetabular cup stability using an impact hammer[END_REF][START_REF] Michel | In vitro evaluation of the acetabular cup primary stability by impact analysis[END_REF]. However, trabecular bone was modeled as an isotropic medium in all the aforementioned studies and the effect of the peri-implant bone properties on the implant mechanical behavior at the macroscopic level has not yet been studied.

Investigating the AC implant mechanical behavior is an important problem because it may help to better understand implant failures as well as osseointegration phenomena.

The aim of this work is to study the influence of the peri-implant anisotropic bone mechanical properties on the mechanical behavior of the AC implant. In particular, we aim at studying the distribution of the strain and stress fields around an AC implant when anisotropic material properties are considered and at investigating the relation between bone properties and the AC implant macroscopic behavior. The proposed approach consists in coupling numerical simulation tools with high resolution imaging techniques and multiscale analyses in order to understand the determinants of the biomechanical behavior of the AC implant under physiological conditions. Stress and strain distributions in the homogenized peri-implant bone are computed for different loading conditions of the AC implant.

Material and methods

The general strategy employed herein is summarized in Fig. 1 and is described in more details below. The first step consists in the measurement of the microarchitecture of thirteen bone samples, which was used as input data in a homogenization procedure, leading to the determination of homogenized properties at the scale of the centimeter. These anisotropic material properties were then used in a finite element model to determine the macroscopic stiffness of the bone-implant system. All loads were applied through a bar protruding from the implant, which models the ancillary, because it corresponds to a simple situation of clinical interest (in particular when surgeons assess manually the AC implant stability). From the viewpoint of the computational cost and memory requirements, it remains difficult to consider the bone microstructure directly in the finite element computations due to the size of the AC implant, which justifies the use of homogenized bone properties. Such approach is therefore useful to consider the effect of the microstructure of trabecular bone in the numerical analyses.

Determination of the homogenized bone properties

Bone samples imaging

Thirteen trabecular bone samples were obtained from bovine femurs similarly as what was done in [START_REF] Guipieri | Ultrasound Speed of Sound Measurements in Trabecular Bone Using the Echographic Response of a Metallic Pin[END_REF]. The samples were then cut in the proximal region in order to obtain cubic specimens (with a size of approximately 10*10*10 mm) using an electric saw. A X-ray µCT device (Skyscan1176® scanner, Skyscan, Kontich, Belgium) was used to obtain the 3-D image of each bone sample with a resolution of 18 µm. The CT images were then binarized to separate the image into bone tissue and bone marrow. The value of BV/TV (bone volume fraction) was then determined for each sample.

Homogenization method

The binarized 3D images were used as input data in the homogenization procedure described in more details in [START_REF] Hollister | Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue[END_REF] and in the appendix. Numerical models were automatically generated using 18 m sized voxel elements to determine the homogenized stiffness coefficients at the scale of the sample. For the mesh generation and analysis, the Voxelcon software (Quint Corp., Fuchu, Tokyo, Japan) was used, in which a two-scale homogenization method based on the asymptotic expansion theory was implemented [START_REF] Guedes | Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element method[END_REF][START_REF] Lions | Some methods in the mathematical analysis of systems and their control[END_REF].

The interest of this homogenization method lies in that it can take into account the influence of any complex micro-architecture on the macroscopic properties of the bone-implant system. Using this approach, trabecular bone regions can be replaced by regions with homogenized material properties, which can in turn be discretized by coarse finite elements. The size of each microstructure model (or representative volume element; RVE) ranged from approximately 5.5 mm to 9.8 mm, which was large enough to represent the complex and random heterogeneity. The number of voxel finite elements of each RVE ranged from approximately 9 to 23 millions. 3-D periodic boundary conditions were applied to the numerical model to obtain the homogenized properties by solving a self-equilibrium problem based on the two-scale homogenization method. Theoretically, a scale ratio between macro-and micro-scales is assumed first and assigned to the principal of virtual work. Next, the averaging principle is used by taking the limit of zero ratio in order to split the problem into macro-and microscopic equations and to define the homogenized (averaged) properties [START_REF] Guedes | Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element method[END_REF][START_REF] Lions | Some methods in the mathematical analysis of systems and their control[END_REF]. Table 1 shows the material properties used for bone tissue in each RVE.

The output of the homogenization procedure provides a stiffness tensor C o , which was defined according to the local axes of the original sample. However, since the axes of the samples did not necessarily coincide to the principal directions of anisotropy, a rotation procedure was applied to the stiffness tensor in order to determine its principal directions. The required rotation was defined by maximizing the coefficient C 0 3333 and minimizing the coefficient C 0 1111. The aim of this rotation procedure was to obtain the stiffness tensor for which the principal direction associated with C 0 3333 is aligned with the z-axis, similarly as in physiological conditions. Here, the z-axis of the model is aligned with the stiffest principal direction of the homogenized elasticity tensor because the main trabecular orientation, which corresponds to the stiffest principal direction of the homogenized elasticity tensor, follows the main direction of the stresses applied in vivo, due to remodeling phenomena [START_REF] Hart | Bone modeling and remodeling: Theories and computation[END_REF]. The main orientation of the mechanical stresses can be assumed to be oriented along the axis of the AC implant, which can be explained by simple gait analyses. The rotated homogenized stiffness tensor was computed as described in details in [START_REF] Ting | Anisotropic Elasticity. Theory and Applications[END_REF], leading to the determination of the stiffness tensor C H , which is used as input data in the macroscopic finite element model (FEM) described below. This rotation procedure results in a main trabecular orientation parallel to the z axis, which corresponds to a situation of interest due to load bearing constraints.

Geometry and material properties

A 3D FEM was employed to simulate the mechanical behavior of an AC implant inserted in trabecular bone tissue similarly as what was done in [START_REF] Tsukino | Multiscale stress analysis of trabecular bone around acetabular cup implant by finite element mesh superposition method[END_REF], which corresponds to a validation of the computational method. Figure 2 shows the geometrical configuration which consists of three subdomains: trabecular bone Ωt, the AC implant (merged with a bar representing the ancillary) Ωac and cortical bone Ωc.

The origin of the z-axis is taken in the top region of the system.

The implant and bone sizes were chosen similarly as in previous studies [START_REF] Michel | In vitro evaluation of the acetabular cup primary stability by impact analysis[END_REF][START_REF] Michel | Finite element model of the impaction of a press-fitted acetabular cup[END_REF][START_REF] Lin | Deformation of press-fitted metallic resurfacing cups. Part 1: Experimental simulation[END_REF]. Based on typical AC implants used in the clinic, the cup was designed as a cobalt-chromium alloy with an inside diameter of 50 mm and a wall thickness of 4 mm (see Fig. 2). Trabecular (Ωt , 21 mm thickness) and cortical (Ωc, 2 mm thickness) bone regions were defined as hemispheric cups around the AC implant. All subdomains are assumed to be homogeneous and to have a linear elastic behavior. While cortical bone and the cobalt chromium cup were assumed to be isotropic (see Table 1), trabecular bone was assumed to be anisotropic. For each sample, the mechanical properties obtained after the application of the homogenization procedure described in subsection 2.1 were used for trabecular bone.

Numerical simulation method

The macroscopic problem was solved using the Ansys software (ANSYS Inc., Canonsburg, PA, USA). Twenty-noded elements were used to mesh the simulation domain, resulting in around 130,000 elements. A 20 nodes element with quadratic approximation was employed because it is suitable to represent the curved boundaries by a piecewise-quadratic approximation. A mesh sensitivity study to determine the mesh size which provide converged finite element solutions (data not shown). Small displacement assumptions were used in order to simulate the mechanical behavior of the system. The problem is solved following the classical equation of elasticity at equilibrium considered for each subdomain and by neglecting body forces, which correspond to ∇.σ= 0 in Ωt, Ωac and Ωc, where ∇. is the divergence operator and σ is the stress tensor.

The boundary of each sub-domain is divided into different parts corresponding to the nature of the boundary condition: with imposed traction on 𝛤 𝛼 𝜎 , imposed displacement on 𝛤 𝛼 𝑢 or with interface conditions on 𝛤 𝛼 𝑖 (𝛤 𝛼 = 𝛤 𝛼 𝜎 U 𝛤 𝛼 𝑢 U 𝛤 𝛼 𝑖 ) as shown in Fig. 2.

Bone tissue is fixed on the outer circle located at the top surface of cortical bone (see Fig. 2). Therefore the boundary condition imposed on this line 𝛤 𝑐 𝑢 is given by:

𝒖 = 0 on 𝛤 𝑐 𝑢 . ( 1
)
where 𝒖 is the displacement field vector.

Continuity conditions of traction and of displacement were assumed on 𝛤 𝛼 𝑖 , which corresponds to the interfaces between Ωac and Ωt, and between Ωt and Ωc. These conditions represent fully bonded interfaces, which will be discussed in Section 4.

All boundary conditions in 𝛤 𝛼 𝜎 except in 𝛤 𝑎𝑐 𝜎 (see Fig. 2) were considered as free boundary conditions given by:

𝝈𝒏 = 0 ( 2
)
where 𝒏 is the normal unit vector of the three subdomains Ωt, Ωac and Ωc.

The movement of the system is governed by the stresses applied to 𝛤 𝑎𝑐 𝜎 , which corresponds to the circular part of upper part of Ωac. Four different loading conditions were successively considered based on physiological conditions described in [START_REF] Janssen | Computational assessment of pressfit acetabular implant fixation: the effect of implant design, interference fit, bone quality, and frictional properties[END_REF][START_REF] Ghosh | Experimental validation of finite element models of intact and implanted composite hemipelvises using digital image correlation[END_REF]. First, an axial loading in the z-direction consisted in applying a load of Fz =1000 N to the top of the bar. Then, a torsional loading (Tz) of 20 N.m was applied to the top of the bar. Eventually, two horizontal loadings consisted in applying horizontal forces (Fx and Fy) of 1000 N to the top of the bar along the x-and y-directions. The forces Fx and Fy were homogeneously applied to the top of the bar.

Data analysis

The mechanical behavior of the AC implant was described by macroscopic stiffness quantities, which are defined according to the type of loading conditions. Moreover, the effect of the anisotropic properties was assessed qualitatively by plotting the von Mises stresses and the strain field for the various loading conditions described below. The stress field was determined at Gauss points.

When considering the vertical loading condition (application of Fz), the implant stiffness Sz was defined based on the vertical displacement dz of the point located on the axis of symmetry of the AC implant and at the interface between bone tissue and the implant by:

𝑆 𝑍 = 𝐹 𝑧 𝑑 𝑧 . ( 3
)
For the torsional loading (application of Tz), the implant stiffness Sθ was defined based on the rotation angle θz of the AC implant by:

𝑆 𝜃 = 𝑇 𝑧 𝜃 𝑧 . ( 4
)
For the horizontal loading along the x-axis (respectively y-axis), the implant stiffness Sx (respectively Sy) was defined based on the displacement dx in the x-direction (respectively dy in the y-direction) of the points located on the axis of symmetry of the AC implant and at the interface between bone tissue and the implant by:

𝑆 𝑥 = 𝐹 𝑥 𝑑 𝑥 (respectively 𝑆 𝑦 = 𝐹 𝑦 𝑑 𝑦
).

(

) 5
The relationship between each quantity defined above (corresponding to the macroscopic stiffness of the AC implant) and BV/TV was studied using a linear regression analysis.

Moreover, for each sample and each loading condition, all components of the stress and strain tensors were determined and the von Mises stress field was then determined. The maximum value of the von Mises stress was then determined for each sample and each loading condition.

Results

Figure 3 shows the relationship between the different macroscopic stiffness properties (Sz, Sθ, Sx and Sy, obtained for the four loading conditions) and BV/TV. All macroscopic stiffness properties are shown to increase significantly as a function of BV/TV (R 2 >0.85, p<6.5 e-6), because the rigidity of trabecular bone tissue increases as a function of BV/TV (see section 4 for further details).

Figure 4 shows the relationship between the maximum value of the von Mises stress (noted <σMacro>) obtained in the entire trabecular region (Ωt) for the four loading conditions and BV/TV. Again, for all loading scenarios, the maximum value of the von Mises stress is shown to increase significantly as a function of BV/TV (R 2 >0.61, p<1.6 e-3),which will be explained in section 4.

Figure 5 shows the cartography of the von Mises stresses for a sample with a BV/TV value equal to 18% (which was chosen because it corresponds to typical values found in the acetabulum) in the plane Πyz 9 in the AC implant and in the peri-implant bone tissue under vertical, torsional and horizontal loading along the x-axis. Figure 5 shows that all stress fields are not symmetric compared to the z-axis, which can be explained by the anisotropic properties of bone tissue. show that even if the applied loading and geometry of the structure are symmetric with respect to the z-axis, the resulting stress fields are not symmetric due to the anisotropy of trabecular bone tissue. Similarly, Fig. 6 c) shows that the stress field is not symmetric compared to the x-axis, which can also be explained by the anisotropic properties of bone tissue.

Figure 7 shows the cartography of different components of the strain tensor 𝜺 in the vertical loading configuration. Figure 7a) (respectively 7b) and 7c)) shows the results corresponding to εzz (respectively εyz and εxz) obtained in the plane Πyz. Figure 7d) shows the results corresponding to εxz obtained in the plane Πxz. Again, Fig. 7 a) shows that the strain field is not symmetric compared to the z-axis, which can also be explained by the anisotropic properties of bone tissue.

Figure 8 shows the cartography of different components of the strain sensor in the torsional loading configuration. Figure 8a) (respectively 8b)) shows the results corresponding to εzz (respectively εxz) obtained in the plane Πyz. Moreover, Figure 8c) (respectively 8d)) shows the results corresponding to εzz (respectively εyz) obtained in the plane Πxz.

Figure 9 shows the cartography of different components of the strain sensor in the horizontal loading configuration along the x-axis. Figure 9a) (respectively 9b), 9c) and 9d)) shows the results corresponding to εxx (respectively εxz, εyz, and εxy) obtained in the plane Πyz. Figure 9 b) shows that the strain field is not symmetric compared to the z-axis, which can be explained by the anisotropic properties of bone tissue.

Discussion

The approach carried out in the present study may be compared with other works published in the literature. Micro-finite element analyses (see for example [START_REF] Van Rietbergen | Micro-FE analyses of bone: state of the art[END_REF]), which consist in converting trabecular bone µCT images into finite element models has now become a routine procedure in bone biomechanics.

However, such approaches are difficult to be carried out at the scale of the AC implant due to the huge computational power required to account for the trabecular bone microstructure in the entire volume of interest. Approaches based on micromechanics constitute alternative methods to model the multiscale properties of bone tissues [START_REF] Sansalone | Determination of the heterogeneous anisotropic elastic properties of human femoral bone: from nanoscopic to organ scale[END_REF][START_REF] Sansalone | Anatomical distribution of the degree of mineralization of bone tissue in human femoral neck: impact on biomechanical properties[END_REF]. For example, methods involving micromechanics-based conversion of µCT data into anisotropic elasticity tensors were applied to the mandible [START_REF] Hellmich | Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible[END_REF] and to human femoral bone [START_REF] Yosibash | Subject-Specific p-FE Analysis of the Proximal Femur Utilizing Micromechanics-Based Material Properties[END_REF]. However, the microstructure of trabecular bone was taken into account through an average rule of the X-ray attenuation coefficients. A similar approach has been carried out in [START_REF] Spears | Interfacial conditions between a press-fit acetabular cup and bone during daily activities: implications for achieving bone in-growth[END_REF][START_REF] Voigt | Finite element analysis of shear stresses at the implant-bone interface of an acetabular press-fit cup during impingement[END_REF] but bone tissue was modeled as an isotropic material.

While studying the effect of impingement on stresses at the bone-implant interface, Voigt et al. [START_REF] Voigt | Finite element analysis of shear stresses at the implant-bone interface of an acetabular press-fit cup during impingement[END_REF] found similar level of stresses in bone tissue. Differences between the various models in terms of geometrical configurations and bone mechanical properties may explain the slight variations in stress fields and magnitude [START_REF] Voigt | Finite element analysis of shear stresses at the implant-bone interface of an acetabular press-fit cup during impingement[END_REF], which remain however difficult to quantify due to the difference in terms of geometrical configuration. The originality of the approach proposed herein is to employ multiscale mechanical modeling approaches in order to understand the behavior of the AC implant in bone tissue and to determine the effect of the anisotropic biomechanical properties of bone tissue, which is a problem of clinical importance because bone properties depends on load transfer from the AC implant to peri-implant bone.

The choice of applying the loading conditions through the ancillary was made because of several reasons. First, it corresponds to a simple configuration compared to the complex interaction of the AC implant with the liner, which is out of scope of this study since we aim at studying the effect of bone properties on the mechanical behavior of the AC implant. Second, various loading scenarios may be applied to the ancillary during surgery when surgeons assess the AC implant stability manually. Third, we have already studied this configuration in a previous numerical study (in dynamic mode) and we eventually aim at assessing the loading distribution during impaction. The loading conditions were chosen in the range of loads used in experimental [START_REF] Hsu | The number of screws, bone quality, and friction coefficient affect acetabular cup stability[END_REF][START_REF] Curtis | The initial stability of uncemented acetabular components[END_REF][START_REF] Perona | Acetabular micromotion as a measure of initial implant stability in primary hip arthroplasty. An in vitro comparison of different methods of initial acetabular component fixation[END_REF] and numerical studies [START_REF] Spears | Interfacial conditions between a press-fit acetabular cup and bone during daily activities: implications for achieving bone in-growth[END_REF][START_REF] Voigt | Finite element analysis of shear stresses at the implant-bone interface of an acetabular press-fit cup during impingement[END_REF] and because it corresponds to typical stresses that can be applied in vivo. However, hip contact forces may sometimes be higher since they have been measured to be up to three times body weight under normal walking conditions [START_REF] Bergmann | Hip contact forces and gait patterns from routine activities[END_REF]. Since all analyses are linear, the mechanical behavior of an AC implant subject to loading conditions with higher stresses can be derived from the results obtained herein using a simple linear extrapolation. Moreover, the mechanical response of the system to a multiaxial loading can be obtained by a summation of the responses against three fundamental loading conditions presented in this paper.

The results shown in Fig. 3 indicate that the correlation coefficient of the linear regression analysis of the stiffness as a function of BV/TV is comprised between r²=0.85 and 0.97, which indicates that BV/TV of the surrounding trabecular bone tissue may explain from 85% up to 97% of the AC implant stiffness, according to the loading condition considered. This correlation can be explained by the fact that the apparent Young's modulus E of trabecular bone is known to be highly correlated with BV/TV when measured according to the same direction of anisotropy, with determination coefficients typically around 0.85 [START_REF] Haiat | Relationship between ultrasonic parameters and apparent trabecular bone elastic modulus: a numerical approach[END_REF].

However, the correlation between E and BV/TV is lower when all directions of testing are pooled (with a typical determination coefficient around 0.5 or lower [START_REF] Augat | Anisotropy of the elastic modulus of trabecular bone specimens from different anatomical locations[END_REF][START_REF] Van Den Bergh | Speed of sound reflects Young's modulus as assessed by microstructural finite element analysis[END_REF]) because of the influence of the anisotropic properties of trabecular bone tissue. In the present study, complex heterogeneous and multiaxial stress field is generated in bone tissue around the AC implant for each loading configuration described in subsection 2.3. Therefore, the overall stiffness of the bone-implant system is determined by a spatial averaging over the entire trabecular bone volume of the anisotropic local mechanical response of bone tissue. Such spatial averaging is realized over a multiaxial stress field, which explains the significant correlation with BV/TV since the effect of anisotropy has been integrated spatially. However, more samples are needed to compare the correlation coefficient obtained between the stiffness and BV/TV according to the loading conditions.

In order to understand the behavior of the AC implant rigidity, the relation between the maximum value of the von Mises stress obtained in the simulation domain and BV/TV was plotted in Fig. 4. The results are consistent with those obtained in Fig. 3 The interest of determining <σµ> lies in the fact that <σµ> is an important determinant of possible microfractures at the scale of the trabeculae. Figure 10 shows the variation of <σµ> as a function of BV/TV for the four different loading conditions. The results show a significant decrease of the value of <σ µ > as a function of BV/TV for the vertical and torsional loading configurations, which may indicate that bone strength at the trabecular level might increase when BV/TV increases. However, such tendency was not found for the two horizontal loading configurations, which may be explained by the more complex and heterogeneous stress fields obtained in horizontal loading configurations. However, these results should be interpreted with caution due to the strong approximation employed in Eq. ( 6) and to the relatively low number of samples.

For all loading conditions and all samples, the maximum value of the von Mises stress field was always obtained on the bone-implant interface 𝛤 𝛼 𝑐 , which emphasizes the critical importance of this interface for the implant outcome. Note that the fact that the maximum value of the von Mises stress is obtained at the bone-implant interface can also be seen in the results shown in Fig. 5. Figure 5 also shows that the stresses magnitude is the highest around the equatorial rim as well as in the polar area according to the loading scenario, which suggests important bone remodelling in these areas. More specifically, in the vertical loading configuration (Fig. 5a)), important levels of stresses were obtained around the rim periphery and around the cup dome. Figure 7a) shows that the compressive strains are mostly present around the cup dome, while Figs. 7b&d) indicate that shear strains (εxz and εyz) are dominant below the rim periphery. For the torsional loading condition (Fig. 5b)), important levels of stresses were obtained around the rim periphery.

Figures 8b&d) show that the shear strains (εxz and εyz) are mostly present below the rim periphery. For the horizontal loading condition (along the x-axis) (Fig. 5c)), important levels of stresses were obtained around the rim periphery and around the cup dome. Figure 9 shows that the shear strains are significant below the rim periphery (εxy) and around the cup dome (εxz).

The stress field distributions shown in Fig. 5 and the strain field distributions shown in Figs. 7a) and 9b&d) are not axisymmetric compared to the z-axis, which is due to the anisotropic properties of trabecular bone. Similarly, the stress field distributions shown in Fig. 6 are not symmetric compared to the center of the image, which is also related to the anisotropy of trabecular bone.

The strain field distributions shown in Figs. Another effect of bone anisotropy is shown in Figs. 7c), 8a&c) and 9c), where all corresponding strain field distributions are not equal to zero. We verified (data not shown), that for all the aforementioned configurations, the corresponding strain fields are always equal to zero when considering isotropic bone properties. More quantitatively, in the case of vertical loading (Fig. 7), the magnitude of εxz is equal to around 3% (respectively 10%) of that of εyz (respectively εxz). In the case of torsional loading (Fig. 8), the magnitude of εzz is equal to around 10% of that of εyz and εxz. Eventually, in the case of horizontal loading (Fig. 9), the magnitude of εxx is equal to around 4% of that of εxy and εxz.

This study has several limitations. First, bovine bone samples were used, which have different biomechanical properties compared to human peri-implant bone. However, the range of BV/TV values is comprised in [0.11 , 0.44], which is similar to published values for human peri-implant bone [START_REF] Carter | Periacetabular stress distributions after joint replacement with subchondral bone retention[END_REF] and thus bovine bone tissue was chosen to model human pelvis tissue. Moreover, a relatively low number of samples were considered, which is due to availability of the sample. However, the distribution of the BV/TV values cover a relatively wide range of variation.

Second, the procedure using the homogenization method employed in this study leads to uniform material properties around the implant, which constitutes a strong approximation since bone properties are likely to be heterogeneous around the implant. However, to the best of our knowledge, the heterogeneity of bone tissue around an AC implant has not been precisely quantified. Therefore, we chose to consider homogeneous bone properties and more work is needed to quantify bone heterogeneity and to investigate the effect of heterogeneous bone properties on the AC implant behavior. Moreover, we assumed that the main trabecular orientation is aligned with the z-axis, which corresponds to a simple approximation. More work would be required to determine the (possibly non homogeneous) orientation of the trabecular network around the AC implant, which is out of scope of the present study.

Third, the geometrical configuration is quite simple since cancellous and cortical bone geometry were chosen as hemispheric domains to model the hip configuration in a simple and reproducible manner.

Different geometrical configurations have been used in the literature to model the AC implant biomechanical behavior. Some studies have considered bone as a 2D cylinder made of cancellous bone [START_REF] Hothi | Explicit finite element modelling of the impaction of metal press-fit acetabular components[END_REF][START_REF] Zietz | Influence of acetabular cup design on the primary implant stability : an experimental and numerical analysis[END_REF], while others have integrated a cortical layer to represent the pelvic configuration [START_REF] Yew | Deformation of press-fitted metallic resurfacing cups. Part 2: Finite element simulation[END_REF][START_REF] Spears | The influence of friction and interference on the seating of a hemispherical press-fit cup: a finite element investigation[END_REF]. 3D finite element studies took into account the anatomy of the hip bone [START_REF] Janssen | Computational assessment of pressfit acetabular implant fixation: the effect of implant design, interference fit, bone quality, and frictional properties[END_REF][START_REF] Ghosh | Experimental validation of finite element models of intact and implanted composite hemipelvises using digital image correlation[END_REF][START_REF] Ong | Acetabular cup geometry and bone-implant interference have more influence on initial periprosthetic joint space than joint loading and surgical cup insertion[END_REF][START_REF] Spears | The effect of interfacial parameters on cup-bone relative micromotions. A finite element investigation[END_REF]. We chose not to consider the anatomy of the acetabulum for the sake of simplicity and because the aim was to focus on the effect of trabecular bone properties in a standardized situation, which allows to simply investigate the effect of bone properties only on the AC implant mechanical behavior. Moreover, the ancillary was modeled by a 21 mm long bar in order to reduce the computation time and because it does not affect the results obtained in this study.

Fourth, the interface conditions between the implant and bone tissue were chosen as fully bonded over the entire bone-implant interface since the implant was considered as fully osseointegrated, similarly as what was done in [START_REF] Voigt | Finite element analysis of shear stresses at the implant-bone interface of an acetabular press-fit cup during impingement[END_REF]. However, interfacial parameters may affect the implant behavior [START_REF] Spears | The effect of interfacial parameters on cup-bone relative micromotions. A finite element investigation[END_REF] in particular when considering stronger solicitations and/or healing interfaces, which is out of scope of the present study.

Moreover, in clinical practice, polar gaps may occur [START_REF] Mackenzie | Areas of contact and extent of gaps with implantation of oversized acetabular components in total hip arthroplasty[END_REF] between the AC implant dome and the peri-implant bone and correspond to non-contact conditions in polar areas. Important polar gaps constitutes a critical clinical issue since osseointegration may not occur around this area [START_REF] Mackenzie | Areas of contact and extent of gaps with implantation of oversized acetabular components in total hip arthroplasty[END_REF]. Migration of the AC implant has even been observed for cases with polar gaps larger than 2 mm [START_REF] Nakasone | Incidence and natural course of initial polar gaps in Birmingham Hip Resurfacing cups[END_REF]. However, the influence of polar gap is out of scope of this study.

Fifth, we used an assumption of small displacements, which is justified by the relatively low amplitude of the strain field. As shown in Figs. 7 &8, the magnitudes of the strain field obtained in the studied cases is always lower than 1.5 10-3, which justifies the assumption of small displacements. Using large displacement hypotheses and nonlinear analyses would be relevant to take into account sliding phenomena at the bone-implant interface, but it is out of scope of this paper and will be examined in future studies.

Sixth, in this paper, we focused mainly on the macroscopic behavior of the bone-implant system in relation with external forces. However, the results obtained at the macroscale can also be used using a downscaling analysis that allows to assess local behaviors of bone tissues at the microscale [START_REF] Tsukino | Multiscale stress analysis of trabecular bone around acetabular cup implant by finite element mesh superposition method[END_REF]. Such approach is useful to predict localized effects such as the stress concentration at trabeculae around the acetabular cup, and then to estimate the damage potential at the microscale. However, such analysis is out of scope of this study and further investigations need to be carried out in this direction in the future.

Conclusion

The present study investigates the influence the anisotropic properties of trabecular bone properties on the AC implant biomechanical behavior in a controlled configuration. It also shows that BV/TV is an important parameter determining the AC implant biomechanical behavior. The phenomena occurring around the equatorial rim and in the polar area are important for the AC implant mechanical behavior. The present approach may be used in the future to improve the design of the implant which should take into account the anisotropic biomechanical properties of the trabecular bone.

Appendix: Two-scale asymptotic homogenization method

The aim of this appendix is to describe the multiscale method employed to determine the effective anisotropic material properties of trabecular bone based on the 3D images of trabecular bone retrieved using the X-ray microcomputed tomography device (see subsection 2.1).

The method uses the principle of virtual work for the linear elastic problem described in Fig. 2, which can be written by:

                             ac t c ac ac i i t l k j i H ijkl c l k j i c ijkl ac l k j i ac ijkl d u f d x u x u C d x u x u C d x u x u C , (A.1)
where i u , k u and i f denotes the displacement, the virtual displacement and the traction, respectively.

H ijkl C denotes the homogenized elastic tensor of trabecular bone, which is a symmetric forth order tensor representing the anisotropy. Note that the coordinates given in Fig. 2

             Y n kl m c ijmn c ijkl H ijkl dY y C C Y C  1 , (A.3)
where Y and Y denote a representative volume element (RVE) of the microstructure in trabecular bone region and its volume, respectively. kl m  is the characteristic displacement in the RVE, which forms the perturbed displacement due to microscopic heterogeneity and morphology. It is obtained by solving the following microscopic equations, which is associated with the self-equilibrium of the system:

0                Y j i n kl m c ijmn c ijkl dY y u y C C  (A.4)
The above equations are derived by taking the limit of 0   for averaging, as described in more details in [START_REF] Lions | Some methods in the mathematical analysis of systems and their control[END_REF][START_REF] Guedes | Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element method[END_REF]. This two-scale asymptotic homogenization theory has the advantage over micromechanics methods such as Mori-Tanaka scheme used in [START_REF] Hellmich | Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible[END_REF][START_REF] Yosibash | Subject-Specific p-FE Analysis of the Proximal Femur Utilizing Micromechanics-Based Material Properties[END_REF] that arbitrary complex microarchitecture can be considered without any additional assumption. Moreover, such method is reliable has been validated experimentally by one of the authors by considering porous titanium [START_REF] Takano | Structural strength prediction for porous titanium based on micro-stress concentration by micro-CT image-based multiscale simulation[END_REF], porous alumina [START_REF] Takano | Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling[END_REF], fiber reinforced plastics [START_REF] Takano | Microstructure-based deep-drawing simulation of knitted fabric reinforced thermoplastics by homogenization theory[END_REF] and epoxy perforated plates [START_REF] Matsuda | Macro/micro simultaneous validation for multiscale analysis of semi-periodically perforated plate using full-field strain measurement[END_REF]. The methods has also been validated experimentally in vertebral trabecular bone [START_REF] Yoshiwara | Numerical study on the morphology and mechanical role of healthy and osteoporotic vertebral trabecular bone[END_REF]65]. Note that, in [65], stochastic analysis was performed, and the expected value of the stiffness coefficients coincides with the deterministic prediction used in this paper. However, one drawback of the asymptotic homogenization analysis is the computational cost when compared with the approaches based on micromechanics.

[66] P. Henys, L. Capek, J. Fencl, and E. Prochazka, "Evaluation of acetabular cup initial fixation by using resonance frequency principle," Proc Inst Mech Eng H, vol. 229, pp. 3-8, Jan 2015.  zz in the plane Π xz (10 -4 )  yz in the plane Π xz (10 -4 ) a)

c)

 zz in the plane Π yz (10 -4 )  xz in the plane Π yz (10 -4 ) -0.

Figure 6

 6 Figure 6 shows the cartography of the von Mises stresses for the same sample obtained by cutting the sample in the plane Πxy corresponding z= -26.5 mm (the origin z=0 corresponding to 𝛤 𝑢 𝑐 , i.e. the upper end of cortical bone where the boundary conditions correspond to fixed displacements). For each image, two regions of interest (ROI) can be distinguished. The first ROI corresponds to the outer part of the image and shows the cartography of the von Mises stresses in bone tissue located in the plane Πxy. The second ROI corresponds to the inner part of the image and shows the projection of the von Mises stresses obtained in the bone-implant interface located under Πxy (i.e. for z < -26.5mm) on Πxy. The results are shown under vertical loading (a), torsional loading (b) and horizontal loading along the x-axis (c). Figures 6 a) and 6 b)

  since the maximum von Mises stress is shown to increase when BVTV increases. However, the increase of the von Mises stresses as a function of BV/TV does not indicate an increase of fracture risk because bone strength is also known to increase with BVTV[START_REF] Goulet | The relationship between the structural and orthogonal compressive properties of trabecular bone[END_REF][START_REF] Hodsgkinson | Seperate effects of osteoporosis and density on the strength and stiffness of human cancellous bone[END_REF][START_REF] Hou | Human vertebral body apparent and hard tissue stiffness[END_REF]. Moreover, the maximum of the Von Mises stresses (denoted <σMacro> in what follows) indicated in Fig.4corresponds to macroscopic stresses, which can be related to the mean value of the microscopic (at the scale of the trabeculae) Von Mises stresses <σµ> through the simple following first order relationship: <σMacro>= BV/TV * <σµ>.[START_REF] Mueller | Periacetabular bone changes after uncemented total hip arthroplasty evaluated by quantitative computed tomography[END_REF]

  7b&d) are shown to be slightly different, although similar images are obtained when considering isotropic bone material properties (data not shown). Therefore, the difference in the two images shown in Figs. 7b&d) can also be explained by the bone anisotropy. The same explanation applies when comparing the images shown in Figs. 8b&d).

Figure 1 -

 1 Figure 1 -Simulation procedure employed in the present study. Images obtained from microcomputed tomography scans were processed to determine the elasticity tensor of the trabecular bone sample. This elasticity tensor was then rotated and used in the finite element model. Four loading conditions were studied.

Figure 2 -Figure 3 -Figure 4 -

 234 Figure 2 -Cross-section of the geometrical configuration (lengths are expressed in mm) considered in the 3D finite element model. The black triangles represent the fixation of the outer circle of cortical bone denoted by 𝜞 𝒄 𝒖

Figure 5 -Figure 6 - 5 mm 12 Figure 7 -

 565127 Figure 5 -Crosssectional view in the plane Πyz of the strain field in the implant and in the peri-implant bone for a bone sample (BV/TV=18.0%) under a) vertical loading Fz, b) torsional loading Tz and c) horizontal loading Fx.

Figure 8 -Figure 9 -Figure 10 -

 8910 Figure 8 -Cross-sectional view of the strain field in the implant and in the peri-implant bone for a bone sample (BV/TV=18.0%) under torsional loading for a) εzz in the plane Πyz, b) εxz in the plane Πyz, c) εzz in the plane Πxz and d) εyz in the plane Πxz.

  are written by i x in Eq. (A.1) to use the Einstein notations. The other notations follow the definition given in subsection 2.3.The analysis of trabecular bone is carried out at the microscale based on µCT images. To do so, and microscales, where L and l are characteristic lengths associated respectively with macro-and microscales. The constitutive equation is defined at the microscale in the trabeculae by;

	coordinates at the microscale defined by i y are introduced. A scale ratio			l L	is defined between macro-
		ij  	c ijkl C 	kl	,	(A.2)
	where ij  and kl  are the tensor components of microscopic stress and strain, respectively. The elastic
	tensor of bone tissue is given in Table 1. Therefore, the homogenized elastic tensor for the trabecular bone
	satisfies	H C 	C	bone	t	where t

 indicates a volumetric average in the trabecular bone region influenced by its morphology. It can be calculated by:

Table 1 . Mechanical properties of materials.

 1

	Material	Young's modulus	Poisson's ratio
		(MPa)

This work has been supported by French National Research Agency (ANR) through the PRTS program (project OsseoWave n°ANR-13-PRTS-0015-02). The authors acknowledge the support of the Ecole Doctorale SIE of the UPE for the funding of AM in Keio University. The authors acknowledge the help of Mr. Kyohei Hatano to run the computations. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 682001, project ERC Consolidator Grant 2015 BoneImplant).


Leonel Cuevas Valeriano

Jean-Baptiste Thomas

Alexandre Benoit

Deep learning for dehazing: Benchmark and analysis

We compare a recent dehazing method based on deep learning, Dehazenet, with traditional state-of-the-art approach, on benchmark data with reference. Dehazenet estimates the depth map from a single color image, which is used to inverse the Koschmieder model of imaging in the presence of haze. In this sense, the solution is still attached to the Koschmieder model. We demonstrate that this method exhibits the same limitation than other inversions of this imaging model.

Introduction

Dehazing aims at improving visibility in images captured in a presence of haze. In general, methods can be classified in two categories. One category aims at the inversion of the Koschmieder model J(x) = I(x)t(x) + A ∞ (1t(x)), which states that the image captured at a position x yields J(x) that is a linear combination of the radiant image I(x) and the contribution of the airlight A ∞ weighted by a transmission factor t(x). A ∞ is defined as the light sent to the camera by an object at infinite distance, i.e. the diffusion of the light by the haze. The transmission factor is t(x) = exp(-β d(x)), where β is the scattering coefficient of the haze and d(x) the distance of the object from the camera. This is performed by estimating t(x) and A ∞ separately or jointly. The other category is based on image enhancement paradigm, and is usually instances of local histogram equalization.

Recently, solutions using deep learning have been introduced. They belong to the first category. For instance Dehazenet [START_REF] Cai | Dehazenet: An end-to-end system for single image haze removal[END_REF] focuses in the estimation of t(x), and AOD [START_REF] Li | Aod-net: All-in-one dehazing network[END_REF] focuses of the joint estimation of t(x) and A ∞ . Two limitations can be observed: 1-the Koschmieder model seems to have a limited validity for heavy amount of haze (See Jessica El Khoury PhD [3]), 2-Networks are trained on simulated material based on the Koschmieder model, which impacts generalization capabilities and thus may limit performance levels on real data. We perform a quantitative analysis of the first point and compare Dehazenet with the state of the art on the CHIC benchmark database [START_REF] Khoury | A color image database for haze model and dehazing methods evaluation[END_REF].

Evaluation

The CHIC database contains color images of the same scene seen through different levels of haze. We applied dehazing stateof-the-art methods, DCP [START_REF] He | Single image haze removal using dark channel prior[END_REF], FAST [START_REF] Tarel | Fast visibility restoration from a single color or gray level image[END_REF], CLAHE [START_REF] Xu | Fog removal from color images using contrast limited adaptive histogram equalization[END_REF] and Dehazenet, on different level of haze. We then compute a selection of metrics for dehazing evaluation [START_REF] Khoury | Color and sharpness assessment of single image dehazing[END_REF], which mostly indicates how well edges are recovered or enhanced (e, r, FADE and VSI). We perform a color analysis of the results based on a color checker, which indicates how well color are recovered (similar to [START_REF] Khoury | HAZE AND CONVERGENCE MODELS: EX-PERIMENTAL COMPARISON[END_REF]). We investigate also how well dehazenet estimates the parameters of the Koschmieder model (t(x)).Note that A ∞ is measured on the dataset and given evenly to all the algorithms.

Conclusion

Deep learning to invert the Koschmieder model is efficient, but still faces limitation of this model. This approach may generate an optimal inversion, but more investigations are required to create a breakthrough in performance.


Mathieu Santonja
email: mathieu.santonja@gmail.com

Laetitia Minguez

Mark O Gessner

Erik Sperfeld
email: eriksperfeld@googlemail.com

Global change ecology

Keywords: Brownification, chemical ecology, global change, zooplankton behavior, humic substances Fig acute prol. acute prol. acute prol. acute prol. Acute stress Prolonged stress

Increasing inputs of colored dissolved organic matter (cDOM), which is mainly composed of humic substances (HS), are a widespread phenomenon of environmental change in aquatic ecosystems. This process of brownification alters the chemical conditions of the environment, but knowledge is lacking of whether elevated cDOM and HS levels interfere with the ability of prey species to evade chemical predator cues and thus affect predator-prey interactions. We assessed the effects of acute and prolonged exposure to HS at increasing concentrations on the ability of freshwater zooplankton to avoid predator threat (imposed by fish kairomones) in laboratory trials with two calanoid copepods (Eudiaptomus gracilis and Heterocope appendiculata). Populations of both species clearly avoided water containing fish kairomones.

However, the avoidance behavior weakened with increasing HS concentration, suggesting that HS affected the ability of copepods to perceive or respond to the predator cue. The behavioral responses of the two copepod populations to increasing HS concentrations differed, with H. appendiculata being more sensitive than E. gracilis in an acute exposure scenario, whereas E. gracilis responded more strongly after prolonged exposure. Both showed similar physiological impairment after prolonged exposure, as revealed by their oxidative balance as a stress indicator, but mortality increased more strongly for H. appendiculata when the HS concentration increased. These results indicate that reduced predator threat evasion in the presence of cDOM could make copepods more susceptible to predation in future, with variation in the strength of responses among populations leading to changes in zooplankton communities and lake food-web structure.

INTRODUCTION

It has become increasingly clear during the past few decades that ecosystems are threatened by global environmental change (Millennium Ecosystem Assessment 2005). Lakes have been recognized as sentinels of this change, because they are sensitive to climate, respond rapidly to shifts in environmental conditions, and integrate information about changes occurring in their catchments [START_REF] Adrian | Lakes as sentinels of climate change[END_REF]. As predator-prey interactions are a primary structuring force in ecosystems [START_REF] Schmitz | Behaviour of predators and prey and links with population-level processes[END_REF], any alteration of these interactions is likely to shift competition among species, population dynamics, community structure, and ecosystem processes [START_REF] Folke | Regime shifts, resilience, and biodiversity in ecosystem management[END_REF][START_REF] Frank | Trophic cascades in a formerly cod-dominated ecosystem[END_REF]. Thus, understanding the effects of environmental conditions on predator-prey interactions is important to predict ecosystem responses to global change.

One prominent facet of global environmental change in lakes is the widely observed increase of colored dissolved organic matter (cDOM) [START_REF] Hongve | Increased colour and organic acid concentrations in Norwegian forest lakes and drinking water -a result of increased precipitation?[END_REF][START_REF] Erlandsson | Thirty-five years of synchrony in the organic matter concentrations of Swedish rivers explained by variation in flow and sulphate[END_REF], which is mainly composed of humic substances (HS) derived from the surrounding terrestrial environment [START_REF] Kullberg | The ecological significance of dissolved organic carbon in acidified waters[END_REF]Williamson et al. 1999;[START_REF] Brothers | A feedback loop links brownification and anoxia in a temperate, shallow lake[END_REF]). This phenomenon is referred to as "browning" or "brownification" [START_REF] Roulet | Environmental chemistry: browning the waters[END_REF][START_REF] Kritzberg | Increasing iron concentrations in surface waters -a factor behind brownification?[END_REF]Solomon et al. 2015). It leads to a yellowish-brownish coloration of lakes, resulting in light regimes and water chemistry that can greatly differ from conditions in clear waters, and effects on species and species interactions [START_REF] Granéli | Photo-oxidative production of dissolved inorganic carbon in lakes of different humic content[END_REF][START_REF] Monteith | Dissolved organic carbon trends resulting from changes in atmospheric deposition chemistry[END_REF][START_REF] Robidoux | Effects of humic stress on the zooplankton from clear and DOC-rich lakes[END_REF]Solomon et al. 2015).

Many freshwater fishes have well-developed visual senses that are used as their primary source of information [START_REF] Guthrie | Role of vision in fish behaviour[END_REF]. Therefore, a significant body of research has addressed the consequences of changes in water optical properties by cDOM or HS on the interactions between piscivorous fish, such as pike (Esox lucius) and pikeperch (Sander lucioperca), and their prey, such as perch (Perca fluviatilis) and roach (Rutilus rutilus) [START_REF] Ranaker | Effects of brown and turbid water on piscivore-prey fish interactions along a visibility gradient[END_REF][START_REF] Ranaker | Piscivore-prey fish interactions: mechanisms behind diurnal patterns in prey selectivity in brown and clear water[END_REF][START_REF] Jonsson | Foraging efficiency and prey selectivity in a visual predator: differential effects of turbid and humic water[END_REF]. Very less attention has been given to interactions between planktivorous fishes and their zooplankton prey, and the focus of those studies has been on foraging efficiency [START_REF] Estlander | Diet shifts and food selection of perch Perca fluviatilis and roach Rutilus rutilus in humic lakes of varying water colour[END_REF][START_REF] Horppila | Gender-dependent effects of water quality and conspecific density on the feeding rate of fish -factors behind sexual growth dimorphism[END_REF][START_REF] Jonsson | Prey-type-dependent foraging of young-of-the-year fish in turbid and humic environments[END_REF]).

Given the central role of zooplankton in lake food webs (Thorp and Covich 2010), it is important also to understand to what extent brownification can affect this invertebrate prey, either directly, or indirectly via chemically induced behavior. Previous studies found that HS can have direct physiological effects on zooplankton (e.g. [START_REF] Meems | Direct and interacting toxicological effects on the waterflea (Daphnia magna) by natural organic matter, synthetic humic substances and cypermethrin[END_REF]Steinberg et al. 2006) and could be an important factor determining zooplankton species composition and abundance in northern temperate lakes [START_REF] Shurin | Environmental stability and lake zooplankton diversity contrasting effects of chemical and thermal variability[END_REF][START_REF] Robidoux | Effects of humic stress on the zooplankton from clear and DOC-rich lakes[END_REF]. However, to our knowledge, there have been no previous attempts to evaluate whether increased concentrations of cDOM or HS alter the ability of zooplankton to evade predator threat by planktivorous fishes.

One of the dominant groups of freshwater zooplankton is copepods [START_REF] Balian | The freshwater animal diversity assessment: an overview of the results[END_REF][START_REF] Heuschele | The chemical ecology of copepods[END_REF]. In contrast to fish, most copepod species have limited visual abilities and are instead often restricted to chemosensory and hydro-mechanical information [START_REF] Folt | Allelopathy between zooplankton: a mechanism for interference competition[END_REF][START_REF] Heuschele | The chemical ecology of copepods[END_REF]. Therefore, any alteration of their olfactory system or chemical cues in lake water could reduce the ability of copepods to detect and avoid predators. Thus, HS could disrupt chemical signaling pathways between organisms in aquatic ecosystems with potential consequences on individual fitness, species interactions, and zooplankton community structure [START_REF] Ferrari | Chemical ecology of predatory-prey interactions in aquatic ecosystems: a review and prospectus[END_REF]). In addition, HS could impair the ability of prey to respond to predator cues, which could have the same ecological effect.

The objective of the present study was to evaluate the effect of HS on the ability of copepods to respond to fish scent. We performed olfactory trials with single individuals of two different copepod species in a two-armed choice flume to assess the avoidance response of copepods exposed to water containing both HS at increasing concentrations and olfactory cues released by fish (kairomones). We assessed the ability of the copepods to respond to the fish cues after acute and prolonged exposure to HS and also determined the oxidative balance of the copepods as a physiological stress marker to assess potential negative effects on fitness.

MATERIALS AND METHODS

Plankton collection and maintenance

The study was conducted in August 2015 with two species of calanoid copepods:

Eudiaptomus gracilis (ovigerous females; mean length ± SD, 1.01 ± 0.04 mm) and Heterocope appendiculata (females and males; 1.71 ± 0.05 mm). The animals were collected with a plankton net (250 µm mesh size) on one occasion in Lake Stechlin, a deep clear-water lake in northeastern Germany (53° 8' 35'' N, 13° 1' 41'' E), and kept separately at constant temperature (18 ± 1 °C) in gently aerated 10-L aquaria containing filtered lake water. The photoperiod of 16 h light: 8 h darkness reflected summer conditions in the field. The copepods were fed a Cryptomonas culture (strain SAG 26.80, Culture Collection of Algae at Göttingen University, Germany) every 3 days (density 6.5 ± 1.9 × 10 3 cells mL -1 , ~0.35 mg C L -1 ). The algae were kept in semi-continuous culture in aerated 1-L flasks containing 500 mL of WC medium [START_REF] Guillard | Yellow-green algae with chlorophyllide c[END_REF] modified by using TES buffer (0.5 mM) instead of Tris.

Exposure to low light conditions and frequent dilution ensured that the copepods were supplied with a highly nutritious food.

Humic substances and fish kairomones

HuminFeed ® (http://www.humintech.com; henceforth HF) was used as source of HS. HF is an industrially processed leonardite containing 43% organic carbon, 82% humic substances, 18% low-molecular-weight compounds, and no polysaccharides [START_REF] Meinelt | Reduction in vegetative growth of the water mold Saprolegnia parasitica (Coker) by humic substances of different origin[END_REF]. HF has been previously used as a standard source of humic substances to investigate effects of humic stress on the physiology of aquatic organisms [START_REF] Meinelt | Reduction in vegetative growth of the water mold Saprolegnia parasitica (Coker) by humic substances of different origin[END_REF][START_REF] Euent | Gender-specific lifespan modulation in Daphnia magna by a dissolved humic substances preparation[END_REF]Steinberg et al. 2010). HF of a single batch was mixed into water with and without fish kairomones shortly before use in the olfactory trials. Five concentrations were used, resulting in DOC exposure scenarios for the copepods within an environmentally relevant range from very low to mesohumic (Table 1). For comparison, DOC concentrations across numerous lakes in Quebec ranged from 3.0 to 15.5 mg L -1 [START_REF] Robidoux | Effects of humic stress on the zooplankton from clear and DOC-rich lakes[END_REF] and in Sweden from 3.9 to 19.4 mg L -1 [START_REF] Granéli | Photo-oxidative production of dissolved inorganic carbon in lakes of different humic content[END_REF].

Water containing fish kairomones was freshly prepared before use in the experiments. Four individuals of zooplanktivorous perch (Perca fluviatilis, 71.3 ± 4.3 mm length) were immersed for 4 h in a 40-L (0.1 fish per L) aerated tank kept in the dark to produce the kairomones.

Although average fish densities in Lake Stechlin are considerably lower (0.01-0.02 per m 3 ; [START_REF] Mehner | Discrete thermal windows cause opposite response of sympatric cold-water fish species to annual temperature variability[END_REF], densities of shoaling fish can be locally very high and potentially close to those used in our experiment. Perch were pre-fed with live zooplankton (>250 µm) from Lake Stechlin. Water in the tank was fully oxygenated groundwater that had been passed over a sand filter and an ion exchange resin to reduce its high concentrations of calcium and iron. Before use in the experiments, the water was filtered (Whatman grade no. 4 filter paper, 25 µm average pore size) and transferred to five 8-L tanks.

Experimental design and procedures

A two-armed choice flume designed to conduct pairwise choice experiments was used to determine the olfactory ability of copepods to discriminate between water previously containing fish and untreated control water in both the presence and absence of HS (Fig. 1). Two tanks containing water either with or without fish cues were connected to the choice flume with tubing to create a constant gravity-driven flow of ~5 mL min -1 . Individual copepods were released at the junction of the horizontal arms where flow from the two different water sources meets. The released copepods were free to move 15 cm into either of the two arms (4 cm diameter) connected to the tanks (Fig. 1). The horizontal alignment of the flume prevented the copepods from vertical migrations.

Each trial consisted of a 60-s acclimatization period followed by a test period of 120 s, where the position of the copepod on the right or left side of the flume was recorded at 5-s intervals. The flume was completely emptied after the test period and thoroughly rinsed with tap water. Water sources were switched from one side of the flume to the other after every fourth trial to control for potential side preferences not related to the water source. A total of 20 individual copepods were tested per treatment combination. Two copepods that did not swim in either direction against the water flow during the acclimatization period were removed from the study. We recorded the time (s) the individual copepods spent [START_REF] Meinelt | Reduction in vegetative growth of the water mold Saprolegnia parasitica (Coker) by humic substances of different origin[END_REF] in each of the two arms of the choice flume (i.e. with or without kairomones) and (2) in each of three 5-cm compartments on the left and right side of the flume (Fig. 1). Additionally, we recorded the number of visited compartments during the test period as a measure of locomotor activity. All observations were made under indirect, dim visible light with no light source pointing directly on the flume. There was no evident effect of light source on behavior since the copepods showed no preference for either side of the choice flume.

We tested responses of the copepods under the following conditions:

(i)
Water on either side of the flume contained neither fish kairomones nor HS to assess the horizontal distribution of copepods in the choice flume when both predator cues and HS are absent (control).

(ii) Water contained fish kairomones on one side of the flume and control water without kairomones in the other to assess responses of freshly collected copepods to acute stress by exposure to HS at different concentrations (acute HS stress).

(iii) Water contained fish kairomones on one side of the flume and control water without kairomones on the other to assess responses to HS exposure at different concentrations after maintaining the copepods at the respective test concentration for 5 days (prolonged HS stress).

To assess the effects of prolonged exposure, 50 individuals of each species were kept at the five different HS concentrations (Table 1) for 5 days in 2-L glass beakers containing 1.5 L of lake water that had been passed over a 90-µm mesh. Two glass beakers were used per treatment, one for the olfactory experiment and the other to assess copepod physiological status.

Water with a given HS concentration was prepared in a single batch and distributed among all beakers to avoid any potential differences in HS concentration between species. The copepods were fed at the beginning and after 3 days with the Cryptomonas culture (cell density: 6.5 ± 1.9

× 10 3 mL -1 , ~0.35 mg C L -1 ). Twenty individuals of one beaker were haphazardly chosen for each treatment of the olfactory trials described above.

Physiological stress indicator

The effect of HS on the physiology of the two copepod species was assessed by determining the oxidative balance between antioxidant capacity and oxidative damage at the cellular level as an indicator of oxidative stress. Oxidative stress occurs when the cellular balance between the production of reactive oxygen species and antioxidant defenses shifts towards the former [START_REF] Sies | Oxidative stress: from basic research to clinical application[END_REF] and can adversely affect life-history traits and fitness [START_REF] Monaghan | Oxidative stress as a mediator of life history tradeoffs: mechanisms, measurements and interpretation[END_REF]). After 5 days of exposure to HS (see above), all copepods were collected, allocated to 3-5 subsamples per HS concentration, each comprising 4 H. appendiculata or 9 E. gracilis, which were placed in Eppendorf tubes, flash-frozen in liquid nitrogen, and stored at -80 °C. The frozen samples were later homogenized in 250 µL cold (4°C) potassium phosphate buffer (PPB; 0.1 M, pH 7.2) by bead-beating for 2 min at 20 Hz with stainless steel milling balls (4 mm diameter) in a Mixer Mill MM 400 (Retsch®, Haan, Germany). The homogenate was centrifuged at 10,000 g for 10 min at 4 °C and the supernatant was used for analyses. Intracellular soluble antioxidant capacity was determined using the oxygen radical absorption capacity (ORAC) assay [START_REF] Prior | Assays for hydrophilic and lipophilic antioxidant capacity (oxygen radical absorbance capacity (ORACFL)) of plasma and other biological and food samples[END_REF], modified for copepods by [START_REF] Gorokhova | Trade-offs between predation risk and growth benefits in copepods Eurytemora affinis with contrasting pigmentation[END_REF], and oxidative damage was measured using the thiobarbituric acid reactive substances (TBARS) assay [START_REF] Oakes | Utility of the TBARS assay in detecting oxidative stress in white sucker (Catostomus commersoni) populations exposed to pulp mill effluent[END_REF]. Total protein content was measured according to [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] using bovine serum albumin as standard. The raw data of the ORAC and TBARS assays were first normalized to the quantity of proteins and the ratio between ORAC and TBARS was used as an indicator of the oxidative balance.

Statistical analyses

All statistical analyses and tests of their underlying assumptions (normality of the residuals, homogeneity of variance) were performed in R version 3.2.3 (R Core [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF]). The significance level was set at P < 0.05 unless specified otherwise. To investigate the effect of HS on the ability of copepods to avoid predation threat, we analyzed the time that the copepods spent in the arm of the flume containing water with kairomones (square root-transformed to meet assumptions of normal distribution and homogeneous variances) and the number of visited compartments (as a proxy of locomotor activity) using general linear models with copepod identity and duration of exposure to humic stress as factorial and HS concentration as continuous explanatory variables. The response variable 'time copepods spent in the flume arm containing kairomone water' accounts for the avoidance response of the copepods to fish kairomones and thus includes the kairomone effect.

To assess differences in the horizontal distribution of individuals in the choice flume, we calculated the mean distance of the 20 individuals from the center of the flume where the right and left arm meet and the animals were placed. Mean compartment distances from zero (i.e. -12.5, -7.5, -2.5, 2.5, 7.5, and 12.5 cm, see Fig. 1) were used in the calculation of an individual's mean distance from the center. From the individual mean distances of 20 copepods, a mean value and its 95% confidence intervals (CIs) were calculated to compare the avoidance of copepods to water containing fish kairomones across the different treatment combinations.

Significance was based on non-overlapping 95% CIs.

To assess the effects of prolonged HS stress on the oxidative balance of copepods, we compared the treatments with HS addition to the control treatment without HS. Dunnett's post hoc tests with P-values adjusted according to Holm were conducted to compare responses to HS addition with the controls (0.1 mg DOC L -1 ). Statistical tests to assess oxidative stress were based on the log response ratio of the oxidative balance (i.e. ORAC:TBARS ratio). Taking the logarithm ensured that any increases or decreases of the ratio were given the same weight.

RESULTS

Olfactory trials without kairomones or HS

In the absence of fish kairomones and HS, the average time individuals of both copepod species spent on either side of the choice flume during the 120-s trials was not significantly different from the expected 60 s (Fig. S1; one sample t-test, E. gracilis: t = 1.05, df = 19, P = 0.31, H. appendiculata: t = 0.73, df = 19, P = 0.47). This lack of preference for the left or right side of the flume was also reflected in the horizontal distribution of the copepods in the choice flume in that the mean distance from the centre of the flume was near zero (Fig. 2a,b). The distribution of copepods across the flume was more variable for E. gracilis than for H. appendiculata, as shown by larger CIs, indicating that E. gracilis moved further away from the starting point (i.e. the center of the choice flume) than H. appendiculata. In addition, the larger number of compartments visited by E. gracilis revealed a higher locomotor activity than shown by H. appendiculata (Fig. S2; two sample t-test, t = 2.93, df = 38, P = 0.006).

Effects of population identity, HS concentration, and exposure duration

The two copepods were strongly affected by HS concentration and exposure duration (Fig. 3; Table 2, high variance explained by these main effects). In general, both species spent increasingly more time in compartments containing fish kairomones when the HS concentration increased (Fig. 3; Table 2, HS concentration main effect), and this increase differed between the two tested populations (Fig. 3; Table 2, significant interaction of HS concentration and population identity). Prolonged exposure reduced the ability of both copepods to avoid water containing fish kairomones, but the strength of this effect depended on the population tested (Fig. 3; Table 2, main effect of exposure time, significant interaction of population identity and exposure time).

Olfactory trials under acute stress

The time individuals of both copepod species spent in compartments containing fish kairomones was very short in the absence of HS (Fig. 2c,d). Instead, the copepods stayed almost exclusively in the arm of the flume supplied with water not previously containing fish (Figs. 3a, b, S3), indicating a distinct ability of copepods to perceive predator cues and avoid potential predation threat. This response pattern was maintained, although gradually weakened, with the concentration of added HS increasing up to 7.2 mg C L -1 (Fig. 3a,b). At 19.3 mg C L - 1 , however, predator threat evasion appeared to be partly diminished for E. gracilis (Fig. 3a)

and completely impaired for H. appendiculata (Fig. 3b). This pattern is also reflected in the mean distance of the copepods from the center of the choice flume (Fig. S4), which increased with increasing HS concentration for H. appendiculata (Fig. 4b) and above 3.6 mg C L -1 also for E. gracilis (Fig. 4a). The locomotor activity of E. gracilis decreased with increasing HS concentration (Fig. 5a), whereas no consistent change was observed for H. appendiculata along the HS gradient (Fig. 5b).

Olfactory trials after prolonged stress

The ability of E. gracilis to sense predatory cues was greatly reduced by prolonged HS exposure (5 days), as indicated by individuals spending more time in compartments with fish kairomones already at 1.8 mg C L -1 (Figs. 3c, 4a, S5) compared to acute exposure, where the copepods showed a significant response only at 7.2 mg C L -1 (Figs. 3a,4a). For H.

appendiculata, the mean distance from the flume center continuously increased with increasing HS concentration in the trials testing for both acute and prolonged stress (Fig. 4b). A significant difference in predator cue recognition between the two exposure times was only apparent at 7.2 mg C L -1 (Figs. 3b,d,4b). Predator avoidance by E. gracilis under prolonged exposure was completely suppressed at 3.6 mg C L -1 (Fig. 4a), and that of H. appendiculata only at 19.3 mg C L -1 (Figs. 4a, S5). Copepod locomotor activity was unaffected by exposure duration (Fig. 5;

Table 2); whereas the activity of E. gracilis decreased with increasing HS concentration, there was no consistent change along the HS gradient for H. appendiculata.

Physiological stress

HS also affected the oxidative balance of both copepod species. The pattern observed along the HS gradient is best described as a biphasic response known as hormesis, which is characterized by stimulation at low and inhibition at high concentrations (Fig. 6). Specifically, the oxidative balance was higher than that in the controls at the lowest HS concentration (5 mg L -1 ) but lower at 3.6 and 7.2 mg C L -1 (Fig. 6). The magnitude of the increase and decrease was similar (i.e. about a doubling and halving of the oxidative balance, respectively) and there were no notable species-specific differences along the HS gradient. At the highest HS concentration, the oxidative balance approached the level of the controls (Fig. 6), suggesting that other physiological pathways than those involving antioxidant defenses might counteract stress caused by HS at very high concentrations. Prolonged exposure to HS also had a direct negative effect on copepod survival, as mortality increased with increasing HS concentration after 5 days of exposure (Table 3; linear regressions, E. gracilis: R 2 = 0.51, P = 0.02; H. appendiculata: R 2 = 0.43, P = 0.04).

DISCUSSION

The observed responses of the two copepod populations to the presence of fish kairomones revealed that both E. gracilis and H. appendiculata are clearly capable of detecting olfactory cues and avoiding predator threat. This result is in line with previous experimental studies on other copepod species that observed avoidance behavior by kairomone-induced vertical migration [START_REF] Neill | Induced vertical migration in copepods as a defence against invertebrate predation[END_REF][START_REF] Neill | Population variation in the ontogeny of predator-induced vertical migration of copepods[END_REF][START_REF] Cohen | Photobehaviour as an inducible defense in the marine copepod Calanopia americana[END_REF][START_REF] Jamieson | Coexistence of two similar copepod species, Eudiaptomus gracilis and E. graciloides: the role of differential predator avoidance[END_REF][START_REF] Minto | Experiments on the influence of Chaoborus brasiliensis Theobald, 1901 (Diptera: Chaoboridae) on the diel vertical migration of microcrustaceans from Lake Monte Alegre, Brazil[END_REF][START_REF] Gutierrez | Behavioural responses of two cladocerans and two copepods exposed to fish kairomones[END_REF]. More important, our results also show that HS can impair the ability of copepods to evade predator threat by interfering with the recognition of chemical cues released by fish or by inducing stress that alters copepod behavior. The implication is that by preventing predator evasion, increases in HS concentrations in surface waters can reduce the fitness of prey species. This, together with the finding that females of a freshwater fish (Xiphophorus birchmanni) lose their preference for conspecific male cues upon HS exposure [START_REF] Fisher | Alteration of the chemical environment disrupts communication in a freshwater fish[END_REF], reinforces the conclusion that chemical signal transduction both within and between species, ranging from cue perception to behavioral responses, can be disrupted as a result of surface water brownification.

Physiological stress and altered behavior

Direct physiological effects of HS on freshwater invertebrates have been attributed to the induction of oxidative stress, production of chemical defense proteins, and variations in detoxification enzyme activities (Steinberg et al. 2006;Timofeyev et al. 2006;Steinberg et al. 2010). Our assessment of oxidative balance indicates that HS caused oxidative stress also in the two populations of copepods we investigated. The biphasic pattern observed along our experimental HS gradient suggests a hormetic effect for both copepods, with stimulation at low and a negative response at elevated HS concentrations. This pattern is consistent with previous results showing HS-mediated hormesis of antioxidant enzymes in other crustaceans, Gammarus lacustris and Daphnia galeata [START_REF] Meems | Direct and interacting toxicological effects on the waterflea (Daphnia magna) by natural organic matter, synthetic humic substances and cypermethrin[END_REF]Timofeyev et al. 2006). According to hormesis theory (e.g. [START_REF] Calabrese | Paradigm lost, paradigm found: the re-emergence of hormesis as a fundamental dose response model in the toxicological sciences[END_REF], the stimulation at low HS concentration may be beneficial for organisms by training their defense systems, whereas HS becomes toxic at elevated concentrations. That our copepods showed greater oxidative stress at high HS concentrations is also in line with the greater mortality observed in these conditions after 5 days of exposure, indicating direct toxicity of HS on both copepods. This toxic effect could have influenced the results we obtained after prolonged exposure, at least for E. gracilis, whose avoidance ability was more strongly reduced than after acute exposure. However, potentially reduced fitness was unlikely to affect our results on acute stress, because the acute stress trials were limited to 120 s and used freshly caught copepods that had not previously experienced stress by HS. Thus, our results on acute stress are unlikely to be notably influenced by toxic effects on copepod performance, although copepod behavior could have been affected.

Prolonged exposure to HS, however, could exacerbate the negative effect on avoidance ability by directly increasing mortality or by physiologically weakening the copepods as a result of oxidative stress.

It currently remains unknown which mechanism was responsible for the observed effects.

HS could alter the chemical structure of fish kairomones such that these molecules become undetectable to the chemoreceptors of the copepods. However, since HS bind to hydrophobic chemicals such as steroid pheromones [START_REF] Mesquita | Partition of fish pheromones between water and aggregates of humic acids. Consequences for sexual signaling[END_REF], rather than to hydrophilic ones such as fish kairomones (von Elert and Loose 1996), this scenario is rather unlikely.

Alternatively, HS could block or damage the chemoreceptors, as found in a goldfish where HS reduced the response of the olfactory epithelium and olfactory bulb to sexual pheromones [START_REF] Hubbard | Possible disruption of pheromonal communication by humic acid in the goldfish, Carassius auratus[END_REF]. Both of these mechanisms could cause the observed impairment of information flow. In addition, HS could alter copepod behavior by imposing stress. Thus, future studies need to distinguish between the modification by HS of kairomone chemical structure, impairment of copepod chemosensory ability as a cause of infodisruption, and HS-induced stress that elicits other behavioral effects on copepods.

Population-specific responses to humic stress

A notable outcome of our experiments is that the two tested copepod populations showed differences in their abilities to respond to fish kairomones. Under conditions of acute exposure, the avoidance ability of H. appendiculata was reduced at low HS concentrations compared to that of E. gracilis, suggesting a higher sensitivity to HS of H. appendiculata. After prolonged exposure, the two species showed opposite patterns, but this result needs to be interpreted with caution because of potentially concomitant direct toxic effects of HS after 5 days of exposure.

Furthermore, the threshold-like response of E. gracilis to increasing HS concentrations was dependent on exposure time, whereas H. appendiculata showed a similar and steady reduction in its ability to avoid water containing fish kairomones at both exposure times. This suggests that surviving H. appendiculata is better at evading predator threat after prolonged HS stress than E. gracilis, in spite of a higher mortality at elevated HS concentrations than E. gracilis. It is important to note, however, that our experiment was not designed to assess the response of both species in general, because populations from different lakes could deviate in their sensitivities to both HS and predator kairomones.

The alteration of predator avoidance under HS stress that we observed could increase the susceptibility of copepods to predation in the future as brownification of surface waters continues, because this effect may ultimately reduce the distance between copepods and planktivorous fish. The differences we observed between the two copepod populations further suggest that H. appendiculata populations could be more prone to predation than E. gracilis under conditions of acute humic stress, whereas E. gracilis population could be more affected when exposed to prolonged humic stress. Conversely, the direct negative effect of HS on copepod survival observed here may favor E. gracilis over H. appendiculata populations, because the latter showed a higher mortality after prolonged exposure. Selection is expected to act more strongly on populations less tolerant to humic stress, as a result of both direct physiological effects and changes in predator avoidance, potentially leading to changes in community composition. For instance, since E. gracilis is much smaller than H. appendiculata, it is harder for fish to visually detect this prey species, even though the ovigerous (egg saccarrying) females of E. gracilis we used are more susceptible to fish predation than males or females without egg sacs (Winfield and Townsend 1983;Svensson 1992).

Potential zooplankton community effects of lake brownification

Increasing evidence indicates that chemical cues of predators induce diel vertical migration (DVM) in copepods as a defense strategy against predation [START_REF] Neill | Induced vertical migration in copepods as a defence against invertebrate predation[END_REF][START_REF] Neill | Population variation in the ontogeny of predator-induced vertical migration of copepods[END_REF][START_REF] Cohen | Photobehaviour as an inducible defense in the marine copepod Calanopia americana[END_REF][START_REF] Jamieson | Coexistence of two similar copepod species, Eudiaptomus gracilis and E. graciloides: the role of differential predator avoidance[END_REF][START_REF] Heuschele | The chemical ecology of copepods[END_REF]. This includes E. gracilis, where the migration amplitude depends on season and other factors [START_REF] Ringelberg | Diel vertical migration of Eudiaptomus gracilis during a short summer period[END_REF]). E.

gracilis can use fish kairomones as a warning signal triggering DVM [START_REF] Jamieson | Coexistence of two similar copepod species, Eudiaptomus gracilis and E. graciloides: the role of differential predator avoidance[END_REF]) but, as our data show, may lose this ability under elevated HS levels resulting from surface water brownification. Very little is known about the DVM behavior of H. appendiculata, probably because this species is rarely dominant in lake zooplankton communities (Walseng et al. 2006).

However, H. appendiculata more often than E. gracilis appears to occur in lakes characterized by lower HS concentrations [START_REF] Berzins | Occurrence of limnic micro-crustaceans in relation to pH and humic content in Swedish water bodies[END_REF], suggesting that E. gracilis may cope better with increased lake brownification expected in the future.

The HS-mediated reduction in the ability to evade predator threat could increase the susceptibility of copepods to predation in lakes. Alternatively, however, brownification could protect zooplankton by impairing the visual detection ability of fish, although experimental studies on fish predation in relation to brownification have shown mixed results. Brownification has decreased predation efficiency of some visually hunting planktivorous fishes [START_REF] Estlander | Diet shifts and food selection of perch Perca fluviatilis and roach Rutilus rutilus in humic lakes of varying water colour[END_REF][START_REF] Estlander | Troubled by the humics -effects of water colour and interspecific competition on the feeding efficiency of planktivorous perch[END_REF], but no effects have been observed in other cases [START_REF] Horppila | Gender-dependent effects of water quality and conspecific density on the feeding rate of fish -factors behind sexual growth dimorphism[END_REF][START_REF] Jonsson | Prey-type-dependent foraging of young-of-the-year fish in turbid and humic environments[END_REF]. For instance, perch (Perca fluviatilis) consumed significantly less phantom midge larvae (Chaoborus flavicans) in highly humic than in clear water [START_REF] Estlander | Troubled by the humics -effects of water colour and interspecific competition on the feeding efficiency of planktivorous perch[END_REF], whereas a significant effect of reduced water clarity on roach (Rutilus rutilus) feeding on copepods has not been observed [START_REF] Jonsson | Prey-type-dependent foraging of young-of-the-year fish in turbid and humic environments[END_REF]. Further, the average body size of zooplankton in lakes with fish increases with increasing cDOM concentrations (Symons and Shurin 2016), suggesting that brownification weakens top-down control of large zooplankton species, which is consistent with the hypothesis that fish predation is less intense at high HS levels. Thus, the consequences on the zooplankton community resulting from species-specific differences in both zooplankton and fish responses to HS could be complex and entail cascading effects on lake food webs and ecosystem functioning.

Fig. 1 Fig. 2

 12 Fig. 1 Schematic of the experimental choice flume. Individual copepods were released at the

Fig. 4 Fig. 5 Fig. 6

 456 Fig. 4 Responses of (a) Eudiaptomus gracilis and (b) Heterocope appendiculata to increasing

Fig. 1 Fig. 2

 12 Fig. 1

  Fig. 3

Fig. 6

 6 Fig. 6

Table 1

 1 Summary of water-chemical and physical characteristics along the experimental humic substance gradient prepared using HuminFeed ® (HF). Dissolved organic carbon (DOC) and

	water color increased along the HF gradient
	HF	DOC	Color intensity
				pH
	(mg L -1 )	(mg L -1 )	(absorption at 436 nm)
	0	0.1	<0.01	7.1
	5	1.8	0.03	7.2
	10	3.6	0.06	7.2
	20	7.2	0.13	7.1
	50	19.3	0.32	7.2

Table 2

 2 ANOVA results of general linear models testing for the effects of copepod population (P), duration of exposure to humic stress (= exposure time; E) and humic substance concentration (HS; continuous) on copepod avoidance behavior assessed as the time spent by copepods in the arm of the choice flume containing kairomones (square root transformed data)

	and on the number of visited compartments (untransformed data). Significant effects are
	indicated by asterisks: * for P < 0.05, ** for P < 0.01 and *** for P < 0.001
	Source of variation	Time spent in the choice-flume arm containing kairomones	Number of visited compartments
		df	Sum of squares	Variance (%)	F-value	df	Sum of squares	Variance (%)	F-value
	Copepod population (P) 1	0.37	<0.1	0.1	1	17.4	2.3	11.3 ***
	Exposure time (E)	1	327.4	9.6	68.1 ***	1	0.1	<0.1	0.1
	HS concentration (HS)	1 1115.5	32.7	231.9 ***	1	78.3	10.2	50.6 ***
	P × E	1	64.5	1.9	13.4 ***	1	7.5	1.0	4.9 *
	P × HS	1	22.7	0.7	4.7 *	1	54.0	7.1	35.0 ***
	E × HS	1	1.3	<0.1	0.3	1	1.0	0.1	0.7
	P × E × HS	1	0.11	<0.1	0.0	1	3.7	0.5	2.4
	Residuals	390 1875.8	55.0		390 602.8	78.8

Table 3

 3 Mortality of E. gracilis and H. appendiculata after 5 days of exposure to humic

	633
	634	substance (HS; HuminFeed) at different concentrations
	635
				Glass 1	Glass 2
		Population	HS (mg C L -1 )	No. dead individuals	Mortality (%)	No. dead individuals	Mortality (%)
		E. gracilis	0.1	2	4	1	2
			1.8	1	2	1	2
			3.6	8	16	5
			7.2	7	14	7
			19.3	8	16	7
		H. appendiculata	0.1	3	6	5
			1.8	8	16	11
			3.6	12	24	10
			7.2	15	30	12
			19.3	12	24	14
	636

ACKNOWLEDGMENTS

We thank Thierry Perez for the two-armed choice flume, Michael Sachtleben for technical assistance, Uta Mallok for DOC analyses, and Stella Berger, Thomas Mehner and Jens Nejstgaard for advice and discussion. Special thanks go to Anatole Boiché for his tireless assistance during the experiments and with zooplankton collections. MS received a GDR MediatEC 3658 research Grant (France) and LM and ES were supported by postdoctoral Grants through IGB's Frontiers in Freshwater Science program. The study also benefitted from support received through the EU project MARS (contract no. 603378) funded under the 7th Framework Programme and the project ILES (SAW-2015-IGB-1) funded by the Leibniz Association.