Graduate Student Member, IEEE Ante Lojić Kapetanov

Member, IEEE, Dragan Poljak , Senior Member, IEEE Giulia Sacco
email: giulia.sacco@univ-rennes1.fr

Senior Member, IEEE Maxim Zhadobov
email: maxim.zhadobov@univ-rennes1.fr

Ante Lojić Kapetanović

Dragan Poljak

Area-Averaged Transmitted and Absorbed Power Density on a Realistic Ear Model

Keywords: Absorbed power density (S ab ), electromagnetic (EM) dosimetry, millimeter waves (MMW), realistic ear model

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

Performance improvements compared to preceding generations are reflected through reduced latency and error rate, and increased data transfer rate due to key features such as carrier aggregation, massive multiple-input and multiple-output (MIMO) technology and beamforming [START_REF] Andrews | What will 5G be?[END_REF]. To increase channel capacity when a large amount of data-intensive devices operate, frequency spectrum has also been expanded towards millimeter waves (MMW) frequency bands [START_REF] Rappaport | Millimeter wave mobile communications for 5G cellular: It will work![END_REF].

To fill the gaps of knowledge and to ensure safe use of emerging technologies at these frequencies, the International Commission on Non-Ionizing Radiation Protection (ICNIRP) exposure guidelines [START_REF]Guidelines for limiting exposure to electromagnetic fields (100 kHz to 300 GHz)[END_REF] and the IEEE C95.1 standard [START_REF]IEEE Standard for Safety Levels with Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 hz to 300 GHz[END_REF] have undergone major revisions in 2020 and 2019, respectively. Above 6 GHz, basic restrictions [START_REF]Guidelines for limiting exposure to electromagnetic fields (100 kHz to 300 GHz)[END_REF] (or dosimetric reference levels [START_REF]IEEE Standard for Safety Levels with Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 hz to 300 GHz[END_REF]) are set in terms of the absorbed [START_REF]Guidelines for limiting exposure to electromagnetic fields (100 kHz to 300 GHz)[END_REF] (or epithelial [START_REF]IEEE Standard for Safety Levels with Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 hz to 300 GHz[END_REF]) power density (S ab ) which represents the power per unit area deposited over irradiated surface of the tissue.

The penetration depth of electromagnetic (EM) energy depends on the dispersive dielectric properties of the exposed tissue [START_REF] Hirata | Assessment of human exposure to electromagnetic fields: Review and future directions[END_REF]. With an increase in frequency, the penetration depth decreases and, at MMW, about 90 % of the power transmitted to the human body is dissipated in the uppermost layer of the skin [START_REF] Pisa | Age-dependence of electromagnetic power and heat deposition in near-surface tissues in emerging 5G bands[END_REF]. Analytical [START_REF] Foster | Thermal response of human skin to microwave energy: A critical review[END_REF] and numerical [START_REF] Hashimoto | On the averaging area for incident power density for human exposure limits at frequencies over 6 GHz[END_REF], [START_REF] Funahashi | Averaging area of incident power density for human exposure from patch antenna arrays[END_REF] studies suggest that S ab is to be averaged over a square-shaped surface of 4 cm 2 to correspond to the face of an averaging 10-g cube of tissue (with mass density set to 1000 kg/m 3 ), and thus account for the consistency and continuity with volume-averaged metrics used below 6 GHz. Additionally, between 30 and 300 GHz, S ab should be averaged over 1 cm 2 to account for narrow beam patterns and its value should not exceed twice the value for the 4 cm 2 averaging area [START_REF]Guidelines for limiting exposure to electromagnetic fields (100 kHz to 300 GHz)[END_REF], [START_REF]IEEE Standard for Safety Levels with Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 hz to 300 GHz[END_REF].

Thus far, most of dosimetry studies at MMW used planar tissue-equivalent single- [START_REF] Nakae | Skin temperature elevation for incident power densities from dipole arrays at 28 Ghz[END_REF], [START_REF] Poljak | Assessment of absorbed power density (S ab ) at the surface of flat lossy medium in GHz frequency range: A case of hertz dipole[END_REF], [START_REF] Ziane | Antenna/body coupling in the near-field at 60 GHz: Impact on the absorbed power density[END_REF] or multi-layer [START_REF] Wu | Safe for generations to come: Considerations of safety for millimeter waves in wireless communications[END_REF], [START_REF] Foster | Thermal analysis of averaging times in radio-frequency exposure limits above 1 GHz[END_REF], [START_REF] Ziskin | Tissue models for RF exposure evaluation at frequencies above 6 GHz[END_REF], [START_REF] He | RF compliance study of temperature elevation in human head model around 28 GHz for 5G user equipment application: Simulation analysis[END_REF], [START_REF] Carrasco | Exposure assessment of portable wireless devices above 6 GHz[END_REF], [START_REF] Diao | Effect of incidence angle on the spatial-average of incident power density definition to correlate skin temperature rise for millimeter wave exposures[END_REF] models. One challenge of MMW dosimetry is the assessment of S ab on non-planar body parts with the curvature radius comparable to the wavelength of the EM field absorbed in the tissue. This issue has been addressed in sub-6 GHz range considering human hands [START_REF] Li | Mechanisms of RF electromagnetic field absorption in human hands and fingers[END_REF] as well as in the 6-60 GHz range for a realistic forearm model [START_REF] Diao | Assessment of absorbed power density and temperature rise for nonplanar body model under electromagnetic exposure above 6 GHz[END_REF]. Effects of body part curvatures with radii of the order of several mm at MMW were investigated in [START_REF] Sacco | Exposure levels induced in curved body parts at mmWaves[END_REF], but due to the reduced model dimensions, no spatial-averaging was considered. In [START_REF] Lojić Kapetanović | Assessment of incident power density on spherical head model up to 100 GHz[END_REF] it is shown that the spatial averaging of the incident power density in 3.5-100 GHz range yields to up to 30 % greater values compared to the state of the art (SotA) planar surface. In a recent study [START_REF] Taguchi | Computation of absorbed power densities in high-resolution head models by considering skin thickness in quasi-millimeter and millimeter wave bands[END_REF], S ab is assessed in high-resolution head models by varying structural parameters (such as the skin thickness and smoothness of the surface) at sub-and MMW. It is found that S ab was below the threshold prescribed by exposure limits in all cases except at 6 GHz where the dipole antenna was placed at the separation distance of 45 mm from the pinna. Authors hypothesized that this discrepancy occurs because of the power absorption being concentrated around the pinna owing to its complex morphology.

The aim of this study is to investigate the effect of geometrically complex surface morphology at 26 and 60 GHz. Given the superficial interaction between MMW and the exposed tissue, S ab is impacted by local geometrical features of the exposed surface. Here, we use the adult human ear as the target model for two reasons: i) the front (exposed) surface of the pinna is composed of intricate convex and concave tissue structures which make the computation of the spatially-averaged dosimetric values particularly challenging, and ii) it is often the most exposed body part in the context of the practical exposure scenario, e.g., during a phone call. However, neither ICNIRP nor IEEE clarified a procedure to spatially average S ab on such irregular, curved surfaces. To avoid oversimplification of the spatial domain by any means, e.g., canonization of curved regions, simplification of irregular morphological features, etc., and to ensure the accurate assessment of S ab on the most irradiated surface of the tissue, we propose a numerical technique adopted from computer graphics and geometric processing research and further adapted to the needs of the EM dosimetry.

II. MATERIALS AND METHODS

A. Electromagnetic Exposure Simulations

We consider a realistic 3-D ear geometry, shown in Fig. 1. Dimensions of the model have been chosen to match those of an adult ear; length and width are respectively set to 54.97 and 35.41 mm [START_REF] Sforza | Age-and sex-related changes in the normal human ear[END_REF]. The complex permittivity of the model is that of human dry skin: 17.71 -j16.87 at 26 GHz and 7.98-j10.90 at 60 GHz [START_REF] Gabriel | Compilation of the dielectric properties of body tissues at RF and microwave frequencies[END_REF]. The model is discretized by using a tetrahedral mesh to avoid numerical errors due to stair-casing approximations of the non-planar geometrical features, e.g, curvature or edges [START_REF] Poljak | On the use of conformal models and methods in dosimetry for nonuniform field exposure[END_REF], with the maximal size of a mesh cell set to λ/8, where λ is the wavelength of the EM wave inside the skin, resulting in about 15 million mesh cells in total. Two planewave polarizations have been considered in the EM analysis (see Fig. 1). For both polarization modes, the plane-wave is impinging the ear model with the wave vector oriented along the reverse x-direction; in polarization 1, the magnetic vector field (H) is oriented along the y-axis, while in polarization 2, the electric vector field (E) is oriented along the reverse y-axis. The EM field distribution is computed on the model by using the finite element method (FEM). The perfectly matched layers are imposed in all directions to emulate the free space condition.

B. Absorbed Power Density

The specific absorption rate (SAR) is defined as

SAR(x, y, z) = σ(x, y, z) 2ρ(x, y, z) |E(x, y, z)| 2 (1)
where |E(x, y, z)| is the absolute peak value of the complex phasor electric field at position (x, y, z), σ and ρ are the conductivity and mass density of the tissue, respectively. These last two quantities are considered to be constant. Two definitions of S ab as presented in [START_REF]Guidelines for limiting exposure to electromagnetic fields (100 kHz to 300 GHz)[END_REF], [START_REF]IEEE Standard for Safety Levels with Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 hz to 300 GHz[END_REF] have been adopted for the analysis. Both definitions stem from the Poynting theorem, i.e., the conservation of energy law for EM fields, and are equivalent if the surface surrounding a given volume of the tissue is closed, provided there are no active sources in this volume of interest.

The first definition is given as the area-averaged transmitted power density (TPD)

TPD(y, z) = x 2 x 1 ρ(x, y, z) SAR(x, y, z) dx (2)
on the control surface of area

A S ab, 1 = 1 A A TPD(y, z) dA (3)
where the tissue surface is positioned at x 1 , and x 2 should be sufficiently larger than the EM penetration depth. The second, more rigorous definition is the area-averaged power density flux over the control surface

S ab, 2 = 1 2A A [E(y, z) × H * (y, z)] n dA (4)
where E and H are the peak values of the complex phasor electric and magnetic field on the surface of the model, respectively, denotes the real part of the vector field, and * is the complex conjugate operator. Integral variable vector, denoted by n dA, has a direction normal to the integral area A, where n corresponds to the unit vector field normal to the surface.

C. Conformal Averaging Area

The integral area element is defined as

dA = |n| dydz (5)
where |n| denotes the length of the normal vector. This value is defined as the norm of the cross product between partial derivatives of the exposed surface represented as the vector A common approach in computational dosimetry is to have a surface reconstructed implicitly via cubical cells or structural mesh composed of 2-D simplices [START_REF] Poljak | On the use of conformal models and methods in dosimetry for nonuniform field exposure[END_REF]. The surface integral is then approximated as the sum of contributions computed on each element for which there is a large array of corresponding efficient and accurate quadrature schemes, e.g., for disks [START_REF] Kim | Symmetric quadrature formulas over a unit disk[END_REF], triangles [START_REF] Dunavant | High degree efficient symmetrical Gaussian quadrature rules for the triangle[END_REF] and quadrilaterals [START_REF] Dunavant | Economical symmetrical quadrature rules for complete polynomials over a square domain[END_REF]. We propose an efficient method to approximate surface integrals directly across complex surfaces. In cases where incident fields are either calculated analytically or computed by using mesh-free numerical methods in selected points within 3-D space, it is impractical to reconstruct a given conformal surface implicitly.

The method presented in this work does not require constructed positional connections between points in 3-D space in which the EM field is assessed. Surface reconstruction is performed functionally by enforcing 3-D radial basis function interpolation with thin plate spline kernel [START_REF] Fasshauer | Radial Basis Function Interpolation in MATLAB[END_REF]. At each point on the averaging surface, n is estimated by using the principal component analysis (PCA)-based method (mathematical details available in Appendix A).

Surface integrals of the scalar and vector field in (3) and ( 4), respectively, are approximated by using the 2-D 11th degree Gauss-Legendre quadrature [START_REF] Abramowitz | Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables[END_REF] on parametric surfaces of either 4 cm 2 square area at 26 GHz or both 4 and 1 cm 2 square area at 60 GHz. A parametric surface, placed perpendicularly to the direction of the plane-wave incidence, is the projection of a conformal surface in 3-D space to 2-D space and it represents the integration domain where S ab is computed [see Fig. 2(a) and (b)]. It is important to note that the area of a conformal surface is generally greater than the one defined by the same contour on a planar surface and that the normalization in both (3) and ( 4) is performed by setting A to the value of a conformal area.

D. Maximum Averaged Absorbed Power Density

This subsection overviews the assessment of maximum S ab, 2 and corresponding S ab, 1 as shown in Fig. 3. The conformal surface over which the averaging is performed is a portion of the external surface of the ear defined in 3-D space (red region in Fig. 2) and delimited in the zand y-direction by the square contour of a planar parametric surface parallel to the zy plane with an extension of 4 or 1 cm 2 (in black in Fig. 2). Furthermore, n is estimated and the EM power flow distribution is computed within the boundaries of the current conformal surface. This distribution is mapped onto the parametric surface to perform 2-D quadrature. S ab, 2 is then computed by using the area of the conformal surface. The procedure is carried out iteratively moving the central point of the parametric surface to its first neighboring point in the yand z-direction, respectively, until the front surface is completely analyzed. Finally, the maximal value of S ab, 2 is reported as the worst-case along with associated position of the parametric surface over which S ab, 1 is subsequently computed. If a conformal area is reduced post hoc to match exactly 4 or 1 cm 2 , S ab, 1 and S ab, 2 both remain within 0.5 % of relative difference from original values. This reduction is carried out equally along the yand z-axis to maintain the largest possible S ab, 2 .

III. COMPUTATIONAL RESULTS

The EM field distribution is computed at 26 and 60 GHz. From E and H, the real part of the Poynting vector and TPD are assessed in all points on the surface of the model. To consider the worst case scenario, only the spatial maximum values are reported with corresponding conformal averaging areas in Table I. At 26 GHz, the parametric surface area is fixed at 4 cm 2 resulting in the conformal surface area of 4.83 and 5.85 cm 2 for polarization 1 and 2, respectively. At 60 GHz, the parametric surface area is additionally set to 1 cm 2 . Conformal article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. surface areas are 4.80 and 1.13 cm 2 for polarization 1 and 4.96 and 1.14 cm 2 for polarization 2, corresponding to 4 and 1 cm 2 parametric surface areas, respectively. Conformal surface areas are slightly larger for all considered cases compared to parametric surface areas over which the integration is performed. This is due to the inherent non-planar geometrical features of the pinna, characterized by the intricate positional relationship of concave and convex tissue structures, see Fig. 2.

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Power density distributions on the front surface of the model are shown in Fig. 4, where white squares depict contours of parametric areas resulting in the maximal S ab, 2 . Computed S ab values are inter-compared by means of the relative percentage difference (RPD)

RPD = S ab, 1 -S ab, 2 S ab, planar • 100% (7)
where S ab, planar is the reference value computed on a planar homogeneous model considering normal plane-wave incidence. The most notable RPD of 6.03 % is captured for polarization 1 at 26 GHz. However, it is worth noting that S ab, 1 is 11.89 % larger than S ab, planar for the case of polarization 1 at 26 GHz. This difference is even larger at 60 GHz on 1 cm 2 control surface area where S ab, 1 and S ab, 2 are respectively 20.26 % and 18.81 % greater than S ab, planar for polarization 2. A complete overview of the RPD between S ab, 1 and S ab, 2 with S ab, planar is available in Fig. 5. Even though the RPD between S ab, 1 and S ab, 2 is marginal, it is important to note that in all considered scenarios S ab, 1 is greater than S ab, 2 . This difference most likely stems from the disagreement between S ab definitions -to account for the power deposited within the volume of interest, S ab, 2 should be integrated on all surfaces surrounding this volume and not only on the directly exposed, front surface.

To validate this approach, we compare S ab results with the results obtained from FEM solver within CST Studio Suite. The relative error is computed in a similar fashion as in [START_REF] Pisa | Age-dependence of electromagnetic power and heat deposition in near-surface tissues in emerging 5G bands[END_REF] where, as the reference, the corresponding value of our method is considered. The difference between both S ab definitions is marginal (within 2.5 %) and is reported in the last two columns in Table I. Similar results are obtained solving the EM problem in COMSOL Multiphysics at 26 GHz (data is not shown for the sake of brevity). Relative errors with respect to our method for polarization 1 are -0.24 % and -0.41 % for S ab, 1 and S ab, 2 , respectively. Slightly higher errors of -0.78 % for S ab, 1 and 0.52 % for S ab, 2 are captured for polarization 2.

IV. DISCUSSION

In this study, we presented a novel technique for approximating the surface integral of the vector and scalar field on arbitrary surfaces. The efficiency of the method is demonstrated through an example of computation of S ab considering two different definitions: i) the area-averaged TPD, S ab, 1 , and ii) the EM power flux per unit area, S ab, 2 , over the control surface defined as the most irradiated region on the adult ear model to quantify the superficial local exposure to plane-wave (polarization 1 and 2) at 26 and 60 GHz. This process consists of: i) extraction of the EM field distribution on and inside the model, ii) estimation of n, and the assessment of the TPD and the real part of the time-averaged Poynting vector at the surface of the model, and iii) approximation of the surface integral of the scalar and vector field for S ab, 1 and S ab, 2 , respectively.

The first step in this study is performed by FEM where EM fields are computed over a tetrahedral mesh. It is important to note that proposed averaging technique is numerical method-agnostic as it relies solely on values computed in an unorganized set of sampling points across the exposed conformal surface. This main benefit is due to the surface being functionally reconstructed by using the efficient multivariate interpolation. As such, the dependence on the positional connections between points in which the integrand is defined is eliminated.

In the second step, the TPD is computed by approximating the line integral of SAR depth-wise into the tissue to obtain the TPD distribution over a conformal surface. After n is estimated by using a PCA regression-based method, the EM power flow distribution on a conformal surface is computed as the real part of the time-averaged Poynting vector.

The third step is transformation of the spatial power density distribution -from a conformal onto the parametric surface -and performing 2-D quadrature. As the size of the parametric surface, whose contours are depicted as white squares in Fig. 4, is fixed at 4 or 1 cm 2 depending on the frequency, the corresponding conformal surface is larger because of the non-planar geometry of the ear. Area discrepancies reach up to 1.85 cm 2 (45.25 %) and 0.14 cm 2 (14.00 %). A is chosen to correspond to the actual area of a conformal rather than parametric surface to avoid potential overestimation contrary to the approach in [START_REF] Taguchi | Computation of absorbed power densities in high-resolution head models by considering skin thickness in quasi-millimeter and millimeter wave bands[END_REF]. To confirm the validity of this approach, in the post-processing, the conformal area is reduced to match exactly 4 or 1 cm 2 , and it is found that the overall S ab remains within 0.5 % of relative difference for all studied cases owing to disregarding the points outside the intersection of the original and reduced conformal surfaces.

The analysis demonstrates that in all considered scenarios S ab, 1 is marginally greater than S ab, 2 with the RPD up to about 6 % for polarization 1 at 26 GHz. Discrepancies between values from the two definitions are potentially due to the nonequivalence of definitions themselves -in order for S ab, 2 to be equivalent to S ab, 1 , it must be integrated over an entire closed surface around the volume of interest and not be limited to the directly exposed surface. Substantial RPD is captured between S ab on the ear model and the planar model. For polarization 2 at 60 GHz, S ab, 1 is more than 20 % greater than S ab, planar , while S ab, 2 is about 19 % larger than S ab, planar . Furthermore, the results indicate that the variation of S ab as a function of polarization is present due to the spatial distribution differences in power density on the exposed surface. Larger variations are present for S ab, 1 where polarization 1 leads to 22.26 % and 4.50 % greater values at 26 GHz and 60 GHz (A = 4 cm 2 ), respectively, while 13.50 % lower values at 60 GHz (A = 1 cm 2 ).

Finally, there are three main limiting factors of the proposed method: i) multivariate interpolation of the surface leads to computational complexity of O(N 3 ) time and O(N 2 ) space [START_REF] Wendland | Computational aspects of radial basis function approximation[END_REF] (we bypass this issue for a large number of points, N , by observing k-nearest neighboring points to each interpolation point at a time), ii) the current implementation is not able to consider the uncertainty of the input EM data, and iii) the current implementation can handle only continuous, differentiable (smooth) surfaces.

V. CONCLUSION

This study compares two definitions of S ab as a metric for local exposure at 26 and 60 GHz as recommended in IEEE C95.1-2019 standard and ICNIRP guidelines. The EM dosimetry analysis is performed for the exposure of the anatomicallyaccurate adult ear model by a plane-wave. S ab is computed over conformal surfaces by using a novel averaging technique. Albeit the use of the plane-wave can lead to underestimation of dosimetric quantities, e.g., in the radiative near-field [START_REF] Ziane | Antenna/body coupling in the near-field at 60 GHz: Impact on the absorbed power density[END_REF], [START_REF] Cujia | Experimental exposure evaluation from the very close near-to the far-field using a multiple-multipole source reconstruction algorithm[END_REF], its use is justified in most exposure scenarios [START_REF] Christ | Limitations of incident power density as a proxy for induced electromagnetic fields[END_REF]. The evaluation of S ab under near-field exposure conditions is out of the scope of this paper and represents one of its perspectives. The findings indicate that S ab, 1 provides higher values than S ab, 2 in all scenarios regardless of frequency and polarization of the incident field. As the planar evaluation models could result in underestimated S ab , it is of utmost importance to account for the complexity of conformal anatomical models. The proposed approach demonstrates a promising potential for the retrieval of dosimetric quantities on such models and is validated by using commercial software.

APPENDIX A NORMAL ESTIMATION ON AVERAGING SURFACE

As the proposed averaging method does not require positional connections, the vertices of surface mesh elements are extracted by transforming the model into an unorganized 3-D point cloud, X = {x 1 , x 2 , . . . , x n } ⊂ R 3 . Additionally, for the sake of computational efficacy, n is estimated only at selected points on the conformal surface for averaging. These points are extracted by using the "hidden" point removal operator [START_REF] Katz | Direct visibility of point sets[END_REF] which determines the visible points in a point cloud from a desired viewpoint -in general case, the plane-wave incidence point of view. To avoid a potential oversight of the points in the frontal section located behind extremely emphasized tissue folds, the point of view that determines the "hidden" point removal operator's domain is further adjusted along the yand z-axis. In this way, the domain of the operator is expanded by superimposing multiple points of view.

At each point, x i ∈ X, an oriented tangent plane, tp(x i ), associated with x i and represented with its central point o i and a unit normal vector, ni , is computed so that it minimizes the sum of square distances from o i to local point cloud neighborhood of x i , nbhd(x i ), determined by the k-nearest neighbors algorithm. By using the PCA, an orthogonal basis is derived [START_REF] Hoppe | Surface reconstruction from unorganized points[END_REF], and the symmetric 3 × 3 positive semi-definite covariance matrix of nbhd(x i ) is computed. As the eigenvector with the smallest associated eigenvalue is perpendicular to tp(x i ), it is thus declared as the unit normal vector at x i .

This approach in the normal estimation is chosen based on its superior performance in quality and speed compared to other available optimization-based methods [START_REF] Klasing | Comparison of surface normal estimation methods for range sensing applications[END_REF]. The emergence of deep learning has led to the frequent use of either vanilla convolutional [START_REF] Wang | Designing deep networks for surface normal estimation[END_REF] or structurally more advanced neural networks [START_REF] Charles | PointNet: Deep learning on point sets for 3D classification and segmentation[END_REF], [START_REF] Qi | GeoNet: Geometric neural network for joint depth and surface normal estimation[END_REF], [START_REF] Ben-Shabat | Nesti-Net: Normal estimation for unstructured 3D point clouds using convolutional neural networks[END_REF] tailored specifically to estimate surface normals during classification and segmentation on sets of points. Such methods, although more accurate and robust to noise, require additional computational efforts and often esoteric implementation; thus, have not been considered.

Next step is to consistently orient the tangent planes as the PCA returns arbitrarily oriented eigenvectors. This is treated as graph optimization problem where the graph is connecting neighboring points which should have nearly parallel tangent planes, that is, for two neighboring points, x i and x j , the planes are consistently oriented if ni • nj ≈ 1. If ni • nj < 0, either ni or nj should be flipped. Details are available in [START_REF] Hoppe | Surface reconstruction from unorganized points[END_REF].

Fig. 1 .

 1 Fig. 1. The model of the average middle-age adult ear.

Fig. 2 .

 2 Fig. 2. Conformal surface and its corresponding 2-D parametric projection of 4 cm 2 area: (a) 3-D view, (b) the plane-wave incidence point of view.

Fig. 3 .

 3 Fig. 3. Flowchart of the assessment of the spatial maximum absorbed power density.

Fig. 4 .

 4 Fig. 4. Parametric surfaces for the assessment of S ab . The top and bottom row correspond to polarization 1 and 2, respectively. In (a) and (c), the square averaging area of 4 cm 2 resulting in the maximal S ab, 2 at 26 GHz is shown, while (b) and (d) depict the square averaging area of 4 and 1 cm 2 resulting in two distinct maximal S ab, 2 at 60 GHz.

Fig. 5 .

 5 Fig. 5. Relative differences between the two definitions of S ab computed on the ear and planar homogeneous skin model.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.ACCEPTED MANUSCRIPT / CLEAN COPY

This work was supported in part by European Regional Development Fund under Grant KK.01.1.1.01.0009 (DATACROSS), in part by the French National Research Program for Environmental and Occupational Health of ANSES under Grant 2018/2 RF/07 through the NEAR 5G Project, in part by the Marie Skłodowska-Curie REACH-IT Project through European Union's Horizon 2020 Research and Innovation Program under Grant 899546, and in part by the Marie Skłodowska-Curie IN-SIGHT Project through European Union's Horizon Europe Research and Innovation Program 101063966. (Corresponding author: Ante Lojić Kapetanović.)


domain: sdv chim

text:
Olivier Terrier
email: olivier.terrier@univ-lyon1.fr

Anny Slama-Schwok
email: anny.slama-schwok@inserm.fr

Anti-influenza drug discovery and development: targeting the virus and its host by all possible means

Keywords: antiviral, drug repurposing, replication, entry, immune modulator Coronavirus COX: cyclo-oxygenase HA: hemagglutinin, IAV: Influenza A virus, IFN: Interferon M2: Matrix 2 NA: neuraminidase, NOX: NADPH oxydase NP: nucleoprotein, p09: H1N1 2009-pandemic strain PA: polymerase acidic subunit, PB1: polymerase basic subunit 1, PB2: polymerase basic subunit 2

Influenza infections remain a major and recurrent source of public health concern. Together with vaccines, antiviral drugs play a key role in the prevention and treatment of influenza virus infection and disease. Today, the number of antiviral molecules approved for the treatment of influenza is relatively limited and their use is threatened by the emergence of viral strains with resistance mutations. There is therefore a real need to expand the prophylactic and therapeutic arsenal. This chapter summarizes the state of the art in drug discovery and development for the treatment of influenza virus infections, with a focus on both virus-targeting and host-cell-targeting strategies. Novel antiviral strategies targeting other viral proteins or targeting the host cell, some of which are based on drug repurposing, may be used in combination to strengthen our therapeutic arsenal against this major pathogen.

Introduction

Influenza infections remain a major and recurrent source of public health concern. Influenza viruses are the causative agents of annual flu epidemics, marked by up to 1 billion infections and 300,000-650,000 deaths worldwide, with a huge economic burden in terms of hospitalization costs and work/school absenteeism (WHO, 2018; [START_REF] Iuliano | Estimates of global seasonal influenza-associated respiratory mortality: a modelling study[END_REF]). In addition, Influenza A viruses (IAV) have been the cause of several pandemics in recent human history, from the Spanish Flu H1N1 in 1918 to the more recent H1N1 2009 pandemic [START_REF] Krammer | Influenza[END_REF].

Together with vaccines, antiviral drugs play a vital part in the prevention and treatment of influenza virus infection and disease. During a normal influenza season, antiviral drugs are mainly used to treat critically ill patients, such as those hospitalized in intensive care. In a pandemic context, pending the availability of a vaccine, antiviral drugs are essential both to treat patients who have been infected and to prevent infection in those exposed, including healthcare workers. Today, the number of antiviral molecules approved for the treatment of influenza, based on the targeting of viral proteins, is relatively reduced and threatened by the emergence of strains with resistance mutations. There is therefore a real need to expand the prophylactic and reinforce the current therapeutic arsenal. This chapter summarizes the state of the art in drug discovery and development for the treatment of influenza virus infections, with a focus on both virus-targeting and host-cell-targeting strategies (Figure 1). Novel antiviral strategies targeting other viral proteins or targeting the host cell, some of which are based on drug repurposing, may be used in combination to strengthen our therapeutic arsenal against this major pathogen.

2-From existing classic antiviral drugs to new pre-clinical candidates

M2 ion channel blockers (amantadine/rimantadine)

Influenza A M2 is a multifunctional viral homo-tetramer protein [START_REF] Jalily | Put a cork in it: Plugging the M2 viral ion channel to sink influenza[END_REF]. Its transmembrane (TM) domain forms a proton channel. This channel is required for acidification of the viral endosome formed after fusion and endocytosis of the virus within the host cell. This process allows viral ribonucleoproteins (vRNPs) to dissociate from the matrix 1 (M1) protein. The proton conductance mechanism relies on the conserved H37XXXW41 sequence which is responsible for selectively gating H + ions [START_REF] Mould | Mechanism for proton conduction of the M(2) ion channel of influenza A virus[END_REF]132], [START_REF] Hu | Mechanisms of proton conduction and gating in influenza M2 proton channels from solid-state NMR[END_REF]121]. Channel blockers interfere with the proton conductance mechanism by binding to the transmembrane pore [137] (Figure 2). When proton conductance through M2 is blocked by the adamantane drug, this dissociation is prevented and the virus is no longer able to replicate. In recent years, adamantane drug-resistant mutants have become prevalent in circulating viruses. The two most prevalent drug-resistant mutants are S31N, L26F and V27A, all of which are located in the transmembrane region of M2 [138]. Figure 2A shows the strong interaction of amantadine with V27 in the upper part of the pore. Upon drug-resistance V27A mutation, this interaction is lost. Recentlydeveloped spiro-amantadyl amine effectively binds to A27 of the pore (Figure 2B) [136]. Recently, new amantadine derivatives effective against double mutants M2-S31N/L26I and M2-S31N/V27A viral strains have been developed by Musharrafieh et al [START_REF] Musharrafieh | Discovery of M2 channel blockers targeting the drug-resistant double mutants M2-S31N/L26I and M2-S31N/V27A from the influenza A viruses[END_REF]. The antiviral efficacy of such compounds is summarized In Table 1. M2 resistance mutations in H1N1/H3N2 circulating strains prompted the WHO to remove both amantadine and rimantadine from the list of recommended anti-influenza agents for clinical use in 2009 [START_REF] Dong | Adamantane-resistant influenza a viruses in the world (1902-2013): frequency and distribution of M2 gene mutations[END_REF].

Neuraminidase (NA) and hemagglutinin (HA) inhibitors

NA inhibitors

NA inhibitors competitively inhibit and prevent cleavage of the terminal sialic acid residues from glycoproteins and carbohydrates displayed on the surface of mammalian cells and influenza virus particles. Binding of virions to uncleaved sialic acid then impairs virion release and dissemination. Among these NA inhibitors, peramivir, zanamivir, oseltamivir carboxylate are the most frequently prescribed drugs and considered standard-of-care for influenza management (Table 1 and Figure 3).

Resistance to oseltamivir can develop rapidly in both experimental settings and the clinic, and typically originates from substitutions at signature resistance sites in the viral NA protein such as H274Y and I223R (predominant in H1N1 and H5N1 viruses), and E119V, R292K, or N294S (predominant in H3N2 viruses). These three NA inhibitors are currently licensed worldwide for the treatment of influenza A and B infections, oseltamivir being the most widely used. There is still a lot of debate about the effectiveness and real impact of inhibitors on the prevention and treatment of influenza. New oseltamivir derivatives, targeting either multiple sites or different NA cavities (as the "430" or the "150" cavity) have been recently developed. Some of these derivatives are very potent against multiple IAV and IBV strains, including oseltamivir-resistant ones (Table 1).

Hemagglutinin inhibitors

The surface glycoprotein HA enables viral entry into host cells by binding to cell-surface, sialic-acidcontaining glycans and mediating fusion between the viral and host membranes in endosomal compartments. HA is composed of head (HA1) and stem (HA2/HA1) domains. As the regions on HA involved in binding and fusion are highly conserved, they are attractive sites for the design of new antivirals (Table 2). The broad-spectrum antiviral drug arbidol shows efficacy against influenza viruses by targeting the hemagglutinin (HA) stem region [START_REF] Kadam | Structural basis of influenza virus fusion inhibition by the antiviral drug Arbidol[END_REF]. This molecule is currently licensed in Russia and China for the treatment of influenza and other infections [START_REF] Blaising | Arbidol as a broad-spectrum antiviral: an update[END_REF]. A challenging strategy aiming at mimicking antibodies binding sites was successfully developed by Wilson et al, targeting the conserved stem region and more recently at the interface of the trimeric head region [START_REF] Bangaru | A Site of Vulnerability on the Influenza Virus Hemagglutinin Head Domain Trimer Interface[END_REF]141,155] (Figure 4A).

The binding sites of the binding sites for CBS1117 and JNJ4796 were both found in the stem region close to the fusion peptide, highlighting the possibility of further structure-based designed compounds [START_REF] Antanasijevic | Structure of avian influenza hemagglutinin in complex with a small molecule entry inhibitor[END_REF]. De novo design of high-affinity trimeric proteins called "HA mini-binders" that bind influenza A hemagglutinin trimer at a conserved region binding site (Figure 4B) [129]. These molecules were developed as alternative to antibodies. These and other compounds are summarized in Table 2.

Polymerase -nucleoprotein-RNA inhibitors

Polymerase/endonuclease inhibitor (favipiravir, Baloxavir marboxil)

Influenza virus transcribe and replicate their genome in the nucleus of infected cells by the means of a hetero-trimeric polymerase, PA, PB1 and PB2. The polymerase complex function requires the nucleoprotein NP, a protein associated with-and protecting the segmented genomic RNA. Therefore, all four proteins are essential for replication. Whereas replication requires the generation of complementary positive polarity RNA intermediates (cRNA) that are then copied into progeny negative polarity segments (vRNPs), viral message is directly synthesized from vRNPs. Since the influenza virus RdRP lacks enzymatic activity to form 5′ mRNA cap structures, endonuclease activity of the PA subunit is necessary for the generation of viral mRNAs through transfer of 5′-capped RNA primers derived from host mRNAs in a cap-snatching mechanism. The endonuclease active site of PA-N terminal comprises a histidine and a cluster of three strictly conserved acidic residues (Glu80, Asp108, Glu119), which coordinate (together with Ile120) one or two manganese or magnesium ions [START_REF] Dias | The cap-snatching endonuclease of influenza virus polymerase resides in the PA subunit[END_REF] (Figure 5A). PB2 is involved in binding of the capped primers, whereas the PB1 subunit harbors enzymatic activity for phosphodiester bond formation.

Several classes of inhibitors are in the clinics (Figure 6): baloxavir (PA), favipiravir (PB1) and pimodivir (PB2, Figure 5B).

Pre-clinical compounds targeting the polymerase PA-PB1 and PA subunits; escape mutations and resistance.

Pre-clinical candidates, some of them being listed in Tables 3 and4 for which several substitutions (PA I38T/M/F) have been described [START_REF] Omoto | Characterization of influenza virus variants induced by treatment with the endonuclease inhibitor baloxavir marboxil[END_REF]. Similarly, escape mutations from L-742.001[127] and RO-7 [START_REF] Kowalinski | Structural analysis of specific metal chelating inhibitor binding to the endonuclease domain of influenza pH1N1 (2009) polymerase[END_REF] treatments were also characterized although in laboratory resistance-assays, escape mutants were not detected after multiple passages for L-742.001. While very tight affinities have been achieved by designing metal binding inhibitors to block the active site of the endonuclease activity in PA N-terminal (Table 2), the appearance of escape mutants often rapidly decrease their efficacy. Several recent reviews focus on the development of PA and polymerase inhibitors [START_REF] Ju | Designing influenza polymerase acidic endonuclease inhibitors via 'privileged scaffold' re-evolution/refining strategy[END_REF]62,[START_REF] Monod | Learning from structure-based drug design and new antivirals targeting the ribonucleoprotein complex for the treatment of influenza[END_REF]170].

Different strategies have been undertaken to attempt overcoming induced resistance. Interfering with its proper assembly of the RdRP polymerase to inhibit function is pursued using protein-protein interaction (PPI) inhibitors. The advantage of such an approach is the relatively large interacting surface between the two proteins as compared to the binding site of an active-site ligand. Indeed, inducing simultaneous mutation of at least one residue on both proteins while maintaining their interaction is less likely to develop resistance and suggests that PPI inhibitors could be less prone to drug resistance than inhibitors of enzyme active sites. The recent identification of a single-domain antibody (nanobody) allowing to disrupt dimerization of FluA polymerase is among these lines [START_REF] Fan | Structures of influenza A virus RNA polymerase offer insight into viral genome replication[END_REF]. PPI inhibitors have been developed

based on the structural insight given by PA-PB1 crystal structures in 2012 [START_REF] Massari | Polymerase Acidic Protein-Basic Protein 1 (PA-PB1) Protein-Protein Interaction as a Target for Next-Generation Anti-influenza Therapeutics[END_REF]. The inhibition of the polymerase PA-PB1 subunit interface has become an active field of research with the goal of remaining active against resistant strains to amantadine and to oseltamivir ( [START_REF] Fan | Structures of influenza A virus RNA polymerase offer insight into viral genome replication[END_REF]102,110,144] and deeper insight in the multi-protein assembly required for during replication / transcription.

Broad-spectrum inhibitors

Favipavir is a drug with broad-spectrum antiviral activity in cell culture, inhibiting RNA viruses of the arenavirus, bunyavirus, flavivirus, alphavirus, norovirus, picornavirus, paramyxovirus, and rhabdovirus families, in addition to influenza viruses [160]. This drug is incorporated into newly synthesized RNA by the viral polymerase in place of purines but not pyrimidines, resulting in increased frequencies of Cto-U and G-to-A transition mutations. Although the barrier for resistance is relatively high, this drug seems to present toxicity issues. N 4-hydroxycytidine (NHC) is also a broad-spectrum antiviral candidate, which showed oral efficacy against RSV and both highly-pathogenic avian and seasonal influenza viruses as well as SARS-CoV-2 virus [140].

Pre-clinical compounds targeting the polymerase PB2 subunit

Crystal structure of the PB2 cap-binding domain have been exploited to develop different 7methylguanine derivatives [100]. Pimodivir (VX-787) is an inhibitor targeting the polymerase PB2 subunit at the m 7 GTP-binding site, forming extensive stacking interactions with several aromatic residues His (Figures 5B and6). It inhibits influenza virus replication and reduced viral load in animal infection models of H3N2 and H1N1 viruses, although potency was highest against H1N1 strains [START_REF] Byrn | Preclinical activity of VX-787, a first-inclass, orally bioavailable inhibitor of the influenza virus polymerase PB2 subunit[END_REF][START_REF] Clark | Discovery of a novel, first-in-class, orally bioavailable azaindole inhibitor (VX-787) of influenza PB2[END_REF]. Phase-2 clinical studies indicated that this drug is well-tolerated, reduced viral load, and resulted in slightly faster resolve of clinical signs. Further derivatives of pimodivir have been designed [START_REF] Mcgowan | Design, Synthesis, and Biological Evaluation of Novel Indoles Targeting the Influenza PB2 Cap Binding Region[END_REF].

Targeting the PB1-PB2 interface by PPI inhibitors has been challenging: although PP7 exhibited antiviral activities against influenza virus subtypes A pandemic H1N1, H7N9 and H9N2, resistances have been unexpectedly detected in laboratory assays [162].

Pre-clinical compounds targeting the nucleoprotein or the nucleoprotein-RNA interactions

The nucleoprotein associated with viral RNA and the polymerase complex is essential for transcription and replication [START_REF] Coloma | Structural insights into influenza A virus ribonucleoproteins reveal a processive helical track as transcription mechanism[END_REF]145,146]. The assembly of NP-RNA oligomers into RNP has been determined by cryo-electron microscopy studies [3,[START_REF] Coloma | Structural insights into influenza A virus ribonucleoproteins reveal a processive helical track as transcription mechanism[END_REF][START_REF] Coloma | The structure of a biologically active influenza virus ribonucleoprotein complex[END_REF]146]. In the X-rays structures of the NP [156], the protein adopts a trimeric structure. NP self-association to achieve trimer formation is mediated by a flexible tail-loop that protrudes into a pocket of the adjacent subunit, via the formation of a critical interaction between R416 of one subunit and E339 of the adjacent subunit. The R416A mutant lacking this interaction adopts a monomeric structure [START_REF] Chenavas | Monomeric nucleoprotein of influenza A virus[END_REF]. The native protein can also be purified in a monomeric form at low salt and concentration conditions [START_REF] Chenavas | Influenza virus nucleoprotein: structure, RNA binding, oligomerization and antiviral drug target[END_REF][START_REF] Chenavas | Monomeric nucleoprotein of influenza A virus[END_REF]133]. The ability to modify the oligomeric state of NP is the structural basis of most NP inhibitors presently developed. Nucleozin was the first NP inhibitor developed as a molecule impeding nuclear accumulation. Nucleozin enhanced higher order structures [START_REF] Kao | Identification of influenza A nucleoprotein as an antiviral target[END_REF] , [START_REF] Gerritz | Inhibition of influenza virus replication via small molecules that induce the formation of higher-order nucleoprotein oligomers[END_REF]. Figure 5C shows the interactions of one of the nucleozin ligands found in the X-ray structure (PDB ID 5B7B) stabilizing the interface between two NP subunits [START_REF] Pang | Structural Characterization of H1N1 Nucleoprotein-Nucleozin Binding Sites[END_REF]. Escape mutants to nucleozin have been identified in laboratory assays. The opposite approach to impede nucleoprotein self-association has also been pursued by disrupting the important salt bridge R416-E339 mediating NP oligomerization [123]. Recently, new compounds with high affinity for NP were designed stabilizing monomeric NP [150]. Impeding NP binding to viral RNA has been achieved by naproxen drug repurposing, naproxen being a known inhibitor of cyclo-oxygenase (COX) [START_REF] Lejal | Structure-based discovery of the novel antiviral properties of naproxen against the nucleoprotein of influenza A virus[END_REF]. As NP oligomerization is enhanced by the presence of RNA, naproxen binding to NP reduced NP oligomers and favored monomeric NP. Docking and single mutations studies identified Tyr148, the only aromatic residue within the RNA binding groove and residues of the C-terminal part of NP R355, R361, Phe489 being involved in the interaction of naproxen with NP. Laboratory assays showed no resistance after 8 cell passages infected with Influenza A. Naproxen exhibited antiviral effects in mice models of Influenza A infection [START_REF] Dilly | From Naproxen Repurposing to Naproxen Analogues and Their Antiviral Activity against Influenza A Virus[END_REF][START_REF] Lejal | Structure-based discovery of the novel antiviral properties of naproxen against the nucleoprotein of influenza A virus[END_REF] as well as Influenza B virus [168]. Further structure-based design yielded new naproxen derivatives with improved antiviral effects and selectivity for NP without COX inhibition (Figures 5D and6) [START_REF] Dilly | From Naproxen Repurposing to Naproxen Analogues and Their Antiviral Activity against Influenza A Virus[END_REF]134] (Table 4). Some of these derivatives were found inhibiting NP-PA interactions [START_REF] Dilly | From Naproxen Repurposing to Naproxen Analogues and Their Antiviral Activity against Influenza A Virus[END_REF]143]. Naproxen derivatives also present antiviral properties against oseltamivirresistant strains [START_REF] Dilly | From Naproxen Repurposing to Naproxen Analogues and Their Antiviral Activity against Influenza A Virus[END_REF]. Additional compounds with some similarity of their hydroxyquinoline scaffold to the methoxy naphthalene scaffold of naproxen called NUD were designed and were also found to be resistant in escape mutation laboratory assays [START_REF] Makau | Identification of small molecule inhibitors for influenza a virus using in silico and in vitro approaches[END_REF].

Drugs targeting the non-structural protein-1 (NS1)

NS1 has a plethora of strategies to inhibit the host immune response due to its ability to establish effector domain have been designed with low micromolar antiviral efficacy [START_REF] Kleinpeter | Structural analyses reveal the mechanism of inhibition of influenza virus NS1 by two antiviral compounds[END_REF] (Table 4).

Host-targeting & drug repurposing approaches for the treatment of influenza

Considerable progress has been made in understanding the interactions between influenza viruses and the host cell in recent years. In this context, and in light of the emerging problem of resistance to available classical antivirals, many studies have focused on targeting host factors to limit virus replication, but also to modulate host immune response. The targeting of host-factors and/or signaling pathways makes sense in the context of virally-induced hypercytokinemia (also known as "cytokine storm"), which is directly correlated with tissue injury and an unfavorable prognosis of severe influenza [START_REF] Liu | The cytokine storm of severe influenza and development of immunomodulatory therapy[END_REF]. Indeed, approaches to control or attenuate this disproportionate immune response are of particular interest and are the subject of numerous pre-clinical and clinical studies. As with all viruses, influenza viruses depend on cellular machinery for their replication and propagation. Many cellular factors essential for the replication of influenza viruses have been uncovered through genome-wide RNA interference approaches [START_REF] Karlas | Genome-wide RNAi screen identifies human host factors crucial for influenza virus replication[END_REF][START_REF] König | Human host factors required for influenza virus replication[END_REF][START_REF] Meliopoulos | Host gene targets for novel influenza therapies elucidated by high-throughput RNA interference screens[END_REF]128] but also more broadly through different integrated cell biology approaches using interactome and transcriptome data, for example [109,148]. In order to list the different host-targeting strategies developed, a distinction can be made between molecules with a mode of action associated with a relatively well-defined stage of the viral cycle, and molecules associated with the modulation of signaling pathways. It is these two main classes that will be described in the following sections.

Drugs targeting host cell component at different stages of influenza replication cycle

The replication cycle of influenza viruses can be divided into several distinct phases, 1) entry 2) nuclear import of viral genome (viral ribonucleoprotein; vRNPs) 2) genome replication and protein synthesis,

3) Nucleo-cytoplasmic export of vRNPs, and 4) plasma membrane transport and budding of neo-virions (Figure 1). A number of molecules targeting host factors in these different steps, at different preclinical/clinical development stages, are known today.

Viral entry is a target of great interest, as it is likely to allow prophylactic approaches, by blocking the infection in its early stages. One of the most advanced strategy consists to target the viral receptor.

DAS181 (Table 5) (Fludase, Ansun BioPharma) is a sialidase fusion protein that cleaves both the 5), e.g. targeting the endosome acidification step by inhibition of V-ATPase (ex: bafilomycin A1, concanamycin), or inhibition of the internalization (ex: Dynasore) or cleavage steps of haemagglutinin (ex: camostat). Most of these strategies were primarily evaluated at the preclinical stage and have not been further evaluated as their efficacy was either limited or accompanied by cytotoxicity. One exception is the protease inhibitor aprotinin, which was approved as anti-influenza drug in Russia [169].

The step of nuclear import of vRNPs is a crucial one, for which there are today very few molecules with antiviral potential described in literature. Interestingly, it has been shown in vitro that ivermectin (Table 5), a well-known anti-parasite drug, was able to inhibit viral replication via inhibition of importins (IMPa/b), and therefore the nuclear import of vRNPs [START_REF] Götz | Influenza A viruses escape from MxA restriction at the expense of efficient nuclear vRNP import[END_REF].

Targeting the replication stage of the virus is one of the earliest host-targeting strategies, with pioneer works on the antiviral efficacy of ribavirin in the 1970s [START_REF] Durr | Efficacy of 1-beta-D-ribofuranosyl-1,2,4-triazole-3-carboxamide against influenza virus infections in mice[END_REF]. However, this nucleoside analogue or its prodrug, less toxic, do not appear to be options being considered for the treatment of influenza virus infections. of influenza viruses, despite interesting preliminary in vitro and in vivo results [125]. (Table 5). Other, more recent strategies propose to target mRNA splicing. Influenza viruses are known to hijack cellular splicing machinery to their benefit, making them extremely dependent on it [START_REF] Dubois | Influenza viruses and mRNA splicing: doing more with less[END_REF][START_REF] Dubois | The Nonstructural NS1 Protein of Influenza Viruses Modulates TP53 Splicing through Host Factor CPSF4[END_REF].

Several studies show that the inhibition of Cdc2-like kinase 1 (CLK1), involved in the alternative splicing of M2 gene of influenza, appears to be an interesting antiviral option, with several molecules available (TG003, Clypearin, Corilagin, Table 5). Of all its molecules, Clypearin has relatively low EC50s and very low toxicity, making it an attractive potential antiviral candidate. [START_REF] Karlas | Genome-wide RNAi screen identifies human host factors crucial for influenza virus replication[END_REF]171].

While strategies to prevent the nuclear import of vRNPs are relatively uncommon, paradoxically there are many more therapeutic approaches to block the nuclear-cytoplasmic transport of vRNPs. Indeed, in contrast to the inhibition of importins, the inhibition of exportin 5).

Apical transport and budding, the last part of the last major step of the replication cycle is also the object of several antiviral strategies, notably by blocking the transport of viral proteins to the plasma membrane (ex: Clonidine; [START_REF] Matsui | Stimulation of alpha2-adrenergic receptors impairs influenza virus infection[END_REF]), or the cholesterol pathway, which would reduce virion egress.

(U18666A; [START_REF] Musiol | Annexin A6-balanced late endosomal cholesterol controls influenza A replication and propagation[END_REF]). One of the most advanced strategies is Nitazoxanide, initially licensed for the treatment of parasitic infections, for which anti-influenza properties were first documented by Rossignol et al. [113]. Interestingly, the proposed mode of action of nitazoxanide toward influenza is clearly distinct to that for which it was designed in its initial indication, acting at the post-translational level by selectively blocking the maturation of the viral glycoprotein HA, with a consecutive impact on its intracellular trafficking and insertion into the host plasma membrane [112]. This drug presents potent antiviral activity against a large panel of circulating strains [139]. The effectiveness of nitazoxanide in treating patients with non-complicated influenza was successful in a Phase IIb/III trial [START_REF] Haffizulla | Effect of nitazoxanide in adults and adolescents with acute uncomplicated influenza: a double-blind, randomised, placebocontrolled, phase 2b/3 trial. The Lancet[END_REF] and is currently being assessed in a Phase III clinical trial (NCT01610245).

Drugs targeting host cell signaling pathways and host-response that are crucial for influenza replication cycle.

Our increased knowledge of signaling pathways that are crucial in the response to infection and/or those hijacked by the virus has allowed many research teams to explore complementary antiviral strategies that can be described here (Table 6). The targeting of the ref/MEK/ERK channel, mentioned above, could of course also have been listed here. At the crossroads of the regulatory pathways of the immune response and the stress response, the NF-kB pathway was one of the first to be studied (Table 6). In the context of cell biology approaches, it was initially shown that the anti-inflammatory drug acetylsalicylic acid (ASA) had interesting antiviral effect against influenza viruses in vitro and in vivo, via inhibition of the NF-kB activating IkkB kinase [START_REF] Mazur | Acetylsalicylic acid (ASA) blocks influenza virus propagation via its NF-kappaB-inhibiting activity[END_REF]153,159]. Several drugs targeting the NF-kB pathway have been evaluated since then, such as pyrrolidine dithiocarbamate or SC7574; with encouraging in vivo results [START_REF] Ehrhardt | The NF-κB inhibitor SC75741 efficiently blocks influenza virus propagation and confers a high barrier for development of viral resistance[END_REF][START_REF] Haasbach | The NF-kappaB inhibitor SC75741 protects mice against highly pathogenic avian influenza A virus[END_REF]149]. BAY81-8781/LASAG (D, L-Lysine acetylsalicylate-glycine) (Table 6), a modified version of ASA demonstrates antiviral activity against several human and avian influenza viruses in vitro. In a mouse infection model, inhalation of LASAG resulted in reduced lung viral titers and protection of mice from lethal infection [START_REF] Droebner | Pharmacodynamics, Pharmacokinetics, and Antiviral Activity of BAY 81-8781, a Novel NF-kappaB Inhibiting Anti-influenza Drug[END_REF]. More recently, a Phase II proof-of-concept study comparing LASAG versus placebo in patients with severe influenza demonstrated that aerosolized LASAG improved the time to symptom alleviation compared to placebo, despite the absence of a statistically significant reduction of viral load in LASAG-treated group [116].

Based on clinical observations, hydroxyl methylglutaryl-coenzyme A (HMG-CoA) reductase inhibitors such as statins (Table 6), approved for their use as cholesterol metabolism regulators, have demonstrated pleiotropic anti-inflammatory and immunomodulatory properties, which could be of benefit to improve survival of patients with severe influenza [START_REF] Fedson | Treating influenza with statins and other immunomodulatory agents[END_REF][START_REF] Mehrbod | Mechanisms of action and efficacy of statins against influenza[END_REF]. However, most in vivo studies reported so far failed to clearly demonstrate such a beneficial effect in the specific context of influenza infection [START_REF] Belser | Simvastatin and oseltamivir combination therapy does not improve the effectiveness of oseltamivir alone following highly pathogenic avian H5N1 influenza virus infection in mice[END_REF][START_REF] Kumaki | Effect of statin treatments on highly pathogenic avian influenza H5N1, seasonal and H1N1pdm09 virus infections in BALB/c mice[END_REF]115].

On the other hand, a few observational studies highlighted an association between statin treatment with a reduction of mortality in patients hospitalized with laboratory-confirmed seasonal influenza [START_REF] Enserink | Infectious disease. Old drugs losing effectiveness against flu; could statins fill gap?[END_REF]142].

A randomized placebo-controlled Phase II clinical trial (NCT02056340) aimed at evaluating the potential effect of atorvastatin to reduce the severity of illness in influenza-infected patients is currently undergoing. The combination of naproxen with clarithromycin and oseltamivir twice daily reduced the both 30-and 90-day mortality and length of hospital stay of patients hospitalized for A(H3N2) influenza [START_REF] Hung | Efficacy of Clarithromycin-Naproxen-Oseltamivir Combination in the Treatment of Patients Hospitalized for Influenza A(H3N2) Infection: An Open-label Randomized, Controlled, Phase IIb/III Trial[END_REF]. Other approaches, at the preclinical validation stages, propose to target the TNF-alpha (Etanercept);) or NOX2 (Apocynin/Ebselen) or lipoxygenase/COX pathway (Celecoxib/Mesalazine) pathways [START_REF] Carey | Pharmacologic inhibition of COX-1 and COX-2 in influenza A viral infection in mice[END_REF][START_REF] Davidson | Treating Influenza Infection, From Now and Into the Future[END_REF][START_REF] Lejal | Turning off NADPH oxidase-2 by impeding p67(phox) activation in infected mouse macrophages reduced viral entry and inflammation[END_REF][START_REF] Oostwoud | Apocynin and ebselen reduce influenza A virus-induced lung inflammation in cigarette smoke-exposed mice[END_REF]124,157,167]. A phase III clinical trial is currently investigating the benefit of celecoxib for the treatment of severe influenza (NCT02108366). These molecules could be of interest to better control the inflammatory response, which is a very important aspect of the pathology.

Modulation of immune and inflammatory responses is a therapeutic avenue that has been much

explored, but which may present risks given the ambivalent aspect of these pathways in relation to viral replication and the evolution of the pathology. Indeed, such treatment should stimulate induction of antiviral genes to control IAV spread, without driving immunopathology. In this context, IFN-lambda (Table 6) appears as a potent anti-influenza therapeutic, without the inflammatory side effects of IFNalpha treatment [START_REF] Davidson | IFNλ is a potent anti-influenza therapeutic without the inflammatory side effects of IFNα treatment[END_REF]. Intranasal administration of IFN-λ2/3 was shown to significantly suppress infection of various influenza strains, including WS/33 (H1N1), PR (H1N1), and H5N1 in the mouse lung, and was accompanied by greater up-regulation of ISGs [67]. More recently, using a transcriptomebased screening approaches, we identified and validated diltiazem, a calcium channel blocker used as an anti-hypertensive drug, as a very promising host-targeted inhibitor of influenza infection.

Interestingly, the study of the mode of action revealed that diltiazem was a strong induced or type III IFN [107]. An ongoing French multicenter randomized clinical trial is investigating the effect of diltiazem-oseltamivir bi-therapy compared with standard oseltamivir monotherapy for the treatment of severe influenza infections in intensive care units (FLUNEXT trial NCT03212716).

Perspectives and concluding remarks

Among all the molecules listed in this chapter, some are already available on the market for other therapeutic indications and fall within the scope of drug repurposing. This is the case for naproxen, diltiazem, LASAG or Nitazoxanide, for example. The basis of drug repurposing relies on bypassing the long, risky and expensive preclinical an early clinical evaluation stage conventionally used for de novo drug development and exploiting available extensive human clinical, pharmacokinetics and safety data as the starting point for the development [106] All these aspects make the repositioning of drugs a very interesting approach, in particular to enable a rapid response to the need for new antiviral strategies in the context of the emergence of a virus with pandemic potential.

Another very interesting perspective is the interest in combining different antiviral approaches with each other, including classical approaches targeting the virus with those targeting the host cell. The concept of combining therapies has already been used successfully, notably in the design of antiretroviral The potential arsenal for fighting influenza virus infections is potentially very extensive, in particular thanks to the combination of new molecules targeting the virus, resulting from docking and structurebased design strategies, with approaches targeting cellular factors and signaling pathways. In this context, the quality and relevance of the preclinical models, as well as the quality of the tools for evaluating combinations of molecules, are important critical elements.

Beyond influenza viruses, many of the antiviral molecules described in this chapter have the potential for broader-spectrum use. Indeed, some virus-targeted strategies can target viral determinants with very strong similarities between different viruses. This is particularly the case with Naproxen for which we have previously demonstrated antiviral activity against both influenza viruses and SARS-CoV-2 [START_REF] Lejal | Structure-based discovery of the novel antiviral properties of naproxen against the nucleoprotein of influenza A virus[END_REF]135]. This property is explained by the fact that the nucleoproteins N of enveloped, positive-sense, single-stranded viruses Coronavirus (CoV) share with negative-sense single-stranded viruses such as

PA-PB1

Compound 12a 0.9-2.

  multiple protein-protein and protein-RNA interactions. NS1 hampers different pathways both in the cytoplasm and in the nucleus of infected cells. NS1 antagonizes interferon-mediated antiviral host response by binding to double-stranded (ds) viral RNA, thus protecting it from cellular factors, by blocking retinoic acid inducible gene-I (RIG-I) and NF-kB activation. One pathway by which NS1 increases virulence is through the activation of phosphoinositide 3-kinase (PI3K) by binding to its p85β subunit [17]. NS1 has two structural domains-RNA-binding domain (RBD) and the effector domain (ED)-connected by a short linker (LR), and a disordered C-terminal tail. New drugs binding to NS1

Neu5Ac α( 2

 2 ,3)and Neu5Ac α(2,6)-Gal linkages of sialic acid on host cells. DAS181 is administered as an inhalable dry powder to deliver sialidase to the pulmonary epithelium for cleavage of sialic acids, which renders the cells inaccessible to infection by virus[80]. DAS181 was demonstrated to have broadspectrum activity, given the conserved nature of influenza and parainfluenza viruses binding to respiratory epithelium. Preclinical in vitro and in vivo studies demonstrated that DAS181 has activity against a number of seasonal influenza strains including those containing the H274Y mutation (conferring resistance to oseltamivir), highly pathogenic avian influenza strains (H5N1), and pandemic 2009 influenza A (H1N1). This compound was assessed in different Phase I and Phase II clinical trials (NCT 00527865, NCT 01651494, NCT01037205) with results indicating a significant reduction of viral load in treated influenza patients[START_REF] Moss | A phase II study of DAS181, a novel host directed antiviral for the treatment of influenza infection[END_REF] but with identification of respiratory adverse events and rapid clearance of the drug being consistent with the induction of antibodies against DAS-181 -this could be a limitation in the duration and dosages of such treatment[163]. Other approaches targeting viral entry have also been described (Table

  1 (XPO1) by Verdinexor (XPO1 antagonist KPT-335) allows to significantly reduce viral production in vitro and in vivo [101]. Another compound, DP2392-E10, inhibits nuclear export of both viral NP and nuclear export protein (NEP). More specifically, in vitro pull-down assays revealed that DP2392-E10 directly binds cellular CRM1, which mediates nuclear export of NP and NEP -highlighting CRM1 as a target of interest [19]. With the same objective, other strategies consist to target the Raf/MEK/ERK signaling pathway, known to be involved in the export of vRNPs [120]. Several MEK inhibitor molecules have been studied for their ability to inhibit the replication of influenza viruses, such as CI-1040 or U0126 [24, 108]. Interestingly, Schräder and colleagues have demonstrated that Trametinib (GSK-1120212), a licensed MEK inhibitor used for the treatment of malignant melanoma, efficiently blocks influenza viral replication of different subtypes in vitro and in vivo [119] (Table

  treatments [13]. Combination therapy can have several objectives, such as reducing the risk of the emergence of resistance by simultaneously targeting several viral proteins and/or key host factors, but also increasing the effectiveness of the treatments by obtaining additive or synergistic effects. While there is relatively little convincing evidence to support the use of conventional virus-targeting antivirals in combination [41, 103], there are interestingly a growing number of examples of combinations of combination host-targeted approaches with oseltamivir. For example, we have shown that the combination of diltiazem and oseltamivir provides a much greater reduction in viral titers in a reconstructed human epithelium model compared to single treatments [107]. More recently Schloer and colleagues have shown that a combination treatment of an antifungal molecule, itraconazole, with oseltamivir, achieves much greater antiviral activity compared to monotherapy, making it possible to consider reducing the concentrations of drugs used, and thus possibly reducing the problems of adverse effects and emergence of resistance mutations [117]. These results open up interesting prospects for the development of future therapeutic strategies, particularly for the treatment of severe forms of influenza.

Influenza A virus the

  ability to bind to-and protect genomic viral RNA without sequence specificity and to form self-associated oligomers. Despite their differences, viruses induce and divert many common cellular pathways. As a result, host-targeted approaches can identify molecules with a broad spectrum of antiviral activity. An example is diltiazem, for which we have shown antiviral activity against influenza viruses [107], but which has been shown to be effective against other respiratory viruses, such as SARS-CoV-2 [104, 105], due to its mode of action involving the type III interferon response. Efforts to identify anti-influenza molecules therefore open up very interesting prospects for the broader development of antivirals. In many ways, antiviral research on influenza viruses is pioneering in this area and provides a starting point for the study of other emerging viruses.

Figure legends Figure 1 .Figure 2 :Figure 3 :Figure 4 :

 legends1234 Figure legendsFigure 1. Influenza viral particle and viral cycle; current state of anti-influenza drug discovery and development. (A) Influenza A virus (IAV) particle. The IAV genome is composed of eight ribonucleoprotein complexes (vRNPs). Each one consists of single-stranded negative-sense viral RNA (vRNA) encapsidated by viral nucleoprotein (NP) and a viral polymerase complex (PA, PB1, and PB2) positioned at the extremity of the vRNA segment. Three viral proteins are embedded within the viral membrane, hemagglutinin (HA), neuraminidase (NA), and ion channel protein (M2). Matrix protein 1 (M1) underlies the viral envelope and holds the vRNPs inside the virion. (B) The viral particle binds to sialic acid receptors and enters the cell via receptor-mediated endocytosis. Acidification of the endocytic vesicles leads to virus uncoating mediated by the M2 ion channel. vRNPs are then released into the cytoplasm and transported into the nucleus. There, the viral RNA-dependent RNA polymerase complex snatches the host mRNA caps to initiate the negative vRNA transcription. Transcribed vRNAs then need to undergo an mRNA maturation phase, including the pre-mRNA splicing, before export to the cytoplasm to be translated. vRNAs are also replicated in the nucleus to generate new vRNPs in association with neosynthesized viral proteins. Progeny vRNPs are transported toward the cytoplasmic membrane with viral components to be packaged into new infectious particles which are formed by cellular envelope budding. Classic virus-targeting strategies are highlighted in red, and virus-hosttargeted strategies in blue. Figure created by BioRender.com

Figure 5 :

 5 Figure 5: Structure of some of the pre-clinical candidates targeting the polymerase A: Active-site PA N-terminal inhibitor compound 22[START_REF] Credille | SAR Exploration of Tight-Binding Inhibitors of Influenza Virus PA Endonuclease[END_REF]; B: PB2 inhibitor Pimodivir[START_REF] Clark | Discovery of a novel, first-in-class, orally bioavailable azaindole inhibitor (VX-787) of influenza PB2[END_REF] (the numbering are associated with this structure corresponding to the full-length PB2, C: nucleozin-NP oligomeric complex PDB ID 5B7B, monomers A and B are in cyan and yellow, respectively; D: Naproxen F1-NP monomeric complex from docking studies[START_REF] Dilly | From Naproxen Repurposing to Naproxen Analogues and Their Antiviral Activity against Influenza A Virus[END_REF].

Figure 6 :

 6 Figure 6: Structures of the approved polymerase inhibitors and some pre-clinical candidates

  Figure 1

Table 3

 3

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  151. Wright ZVF, Wu NC, Kadam RU et al. (2017) Structure-based optimization and synthesis of antiviral drug Arbidol analogues with significantly improved affinity to influenza hemagglutinin. Bioorg Med Chem Lett 27:3744-3748 152. Wu G, Yu G, Yu Y et al. (2020) Chemoreactive-Inspired Discovery of Influenza A Virus Dual Inhibitor to Block Hemagglutinin-Mediated Adsorption and Membrane

	Fusion. J Med Chem 63:6924-6940
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Table 1 . Summary of the activity and structures of the main antiviral compounds bound to their target, the proton channel M2 of Influenza A or the neuraminidase NA of Influenza A and B.

 1

	Tables
	Target	Compound	IC 50	PDB ID	Stage (year approval)	references
		Amantadine	100 µM (H1N1 WT) > 500µM (S31N) 15.7 µM (WT channel a, ) [155]	6BKK	Approved (1976)	[137], [10]
	M2	Rimantadine	0.1 µM (H1N1 WT) > 200µM (S31N)	2RLF	Approved (1994)	[118]
		Spiro-adamantyl amine	18.7 µM (WT channel a ) 0.2 µM (V27A a )	6BMZ 6OUG 6NV1	Pre-clinical	[136, 137]
		Oseltamivir (Tamiflu)	0.8 nM (N5 NA)	2HT7	Approved (1999)	[114]
		Peramivir	3.4 nM	2HTU	Approved (2014)	[114]
		Zanamivir	0.6 nM (N5 NA)	3CKZ	Approved (1999)	[21]
			1.36 ± 0.36 µM (H1N1 PR8)
	NA	Chebulinic acid Chebulagic Acid	(Oseltamivir resistant and H1N1 pdm09 viruses)		Pre-clinical	[75]
			CC 50 > 100µM
		Oseltamivir derivatives	0.66 µM (H5N1)	Docking 150/430 cavity	Pre-clinical	[1, 58, 166]
		Triazol oseltamivir derivatives C1-modified oseltamivir derivatives	0.05-0.15 µM (H5N1, H5N2 virus) and H5N6) 0.1 µM (H5N1, H5N6) 0.7 µM (Oseltamivir resistant	Docking 430 cavity	Pre-clinical	[60]

a: Patch clamp assays

[136]

Table 2 : Recent antiviral candidates targeting HA, their activity and structures of their complexes with HA

 2

	Target	Compound / binding site	IC 50 / CC 50	PDB ID	Stage	references
		Arbidol / Stem region	4-12 µM		Pre-clinical and	[63, 147,
				5T6S, 5T6N	clinical	151]
			CC 50 = 59µM		NCT03787459
		F0045(S) / Stem region	0.5-2 µM (H1 HA)	6WCR	Pre-clinical	[155]
		JNJ4795 / Stem region	0.01-0.07 µM (H1 HA)	6CF7	Pre-clinical	[141]
	HA	IY7640 / Stem region	0.5-7 µM (H1 HA) CC 50 > 800µM	Docking studies	Pre-clinical	[66]
		CBS1117 / Stem region	3µM For H5 HA	6VMZ	Pre-clinical	[2, 45, 55]
		MB2746 / Stem region	0.3µM (H1 HA) CC 50 >100µM	Docking studies	Pre-clinical	[5]
		De novo design of "Mini-binder" proteins	0.15-0.19 nM (H3 and H1 HA)	6KUY		[129]
		Peninddone		HA1 and HA2	Pre-clinical	[152]

Table 3 : Inhibitors of PA, PA-PB1 interactions and PB1

 3

	Target	Compound	IC 50 / CC 50	PDB ID	Stage	References
		Baloxavir marboxil	0.3-1 µM (H1N1/H3N2)	6FS6 6FS9	Approved (2019) NCT0294901 NCT02954354	[96]
		L-742,001	3 µM (WT H1N1) 24µM (WT H1N1 pdm09) 236µM (H1N1 pdm09	5CGV 5D9J	Clinical trial NCT01526785	[127]
			PA F105S)
	PA	RO7	16 nM (WT H1N1) 3 nM (H1N1 pdm09)	5VPX	Pre-Clinical	[59, 70]
		Ana-0	0.8µM	Docking	Pre-clinical	[161]
		Compound 22	110 pM	6E6W	Pre-clinical	[25]
		N-acylhydrazone derivatives	11 µM	5EGA	Pre-clinical	[11]
		"312"	37 µM (H1N1, H2N2 and H3N2)	PA -C-terminal	Pre-Clinical	[78]

Table 6 . Drugs targeting host-cell signaling pathway and host-responses that are crucial for influenza replication cycle.

 6

	Host signalling pathway/response	Drug name	Mode of action	Research phase	References
		Acetylsalicylic acid		Approved	Mazur et al. 2007[83]
		pyrrolidine dithiocarbamate		preclinical	Wiesener et al. 2011[149]
	NF-kB pathway	SC75741	Immune dysregulation Inhibition of caspase/vRNP export inhibition	preclinical	Ehrhardt et al. 2013[39] Haasbach et al. 2013[49]
					Droebner et al.
		LASAG		Phase II	2017[35] Scheuch et al.
					2018[116]
	C-Jun-N-terminal-kinase	SP600125	C-Jun N-Terminal kinase inhibitor -Immune dysregulation	preclinical	Nacken et al. 2012[93]
	p38 MAPK	NJK14047	Immune dysregulation	preclinical	Choi et al. 2016[18]
					Fedson et al.
					2013[43]
	HMG-CoA	Statins	Immunomodulation	Phase II	Mehrbod et al. 2014[85]
					Fedson et al.
					2018[43]
			Anti-inflammatory drug -
	TNF-alpha	Etanercept	Prevents TNF-mediated lung	preclinical	Shi et al. 2013[124]
			injury and edema
		Apocynin	ROS scavenger, inhibits Nox2 activity	preclinical	Ye et al. 2015[157]
	Nox2		ROS scavenger and		Oostwoud et al.
		Ebselen	glutathione peroxidase	preclinical	2016
			mimetic, inhibits Nox2
		Celecoxib	Immune dysregulation	Phase III	Davidson et al.
					2018[28]
	Lipoxygenase &				Carey et al.
	COX pathways	Mesalazine	Immune dysregulation	preclinical	2010[12] Zheng et al.
					2008[167]
					Davidson et al.
	Type III IFN response	Type III IFN Diltiazem	Induction of type III IFN response	preclinical Phase II	2016[29] Kim et al. 2017[67] Pizzorno et al. 2019[106, 107]

Clonidine alpha2-adrenergic receptors inhibitor -Inhibits transport of HA transport to plasma membrane Matsui et al. 2018[82]