A P S Baghel

Sai Ram

L Daniel

S V Kulkarni

G Krebs

J B B Blumenfeld

L Santandrea

B Sai Ram

An alternative approach to model mechanical stress effects on magnetic hysteresis in electrical steels using complex permeability

Keywords: Electrical steel, complex permeability, magneto-elastic behavior, iron loss, finite element method

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Introduction

Magnetic properties of ferromagnetic materials, used in magnetic circuits of electrical machines, are strongly affected by mechanical stress which affects particularly permeability and losses of core materials [START_REF] Bozorth | Ferromagnetism[END_REF]- [START_REF] Cullity | Introduction to magnetic materials[END_REF]. In high-speed applications, due to design constraints (compact design and reduced weight), the core materials generally have more exposure to mechanical stresses [START_REF] Bernard | Effect of stress on magnetic hysteresis losses in a switched reluctance motor: Application to stator and rotor shrink fitting[END_REF]- [START_REF] Belahcen | Magnetoelastic coupling in rotating electrical machines[END_REF]. Other main causes of induced mechanical stress in the iron sheets are manufacturing processes (e.g. cutting or stamping), assembly processes (e.g. shrink-fitting), temperature gradients, and centrifugal forces [START_REF] Moses | Effects of stresses on magnetic properties of silicon-iron laminations[END_REF]- [START_REF] Baudouin | Effects of laser and mechanical cutting modes on the magnetic properties of low and medium si content nonoriented electrical steels[END_REF]. Core losses are more affected by compressive stress than tensile stress [START_REF] Baghel | Effects of mechanical stress on core losses along orthogonal directions in electrical steels[END_REF]. As an illustration, the effect of mechanical stress on the magnetic properties of a non-oriented (NO) material is shown in Fig. 1.

Figure 1: Variation of (a) Hysteresis loops at 1.5 T, 50 Hz for different stresses levels [START_REF] Baghel | Effects of mechanical stress on core losses along orthogonal directions in electrical steels[END_REF] (b) Permeability at different stress levels at 1.5 T, 50 Hz

The magneto-elastic behaviour of ferromagnetic materials plays a significant role in the performance of electrical machines [START_REF] Miyagi | Estimation of iron loss in motor core with shrink fitting using fem analysis[END_REF], [START_REF] Fujisaki | Motor core iron loss analysis evaluating shrink fitting and stamping by finite-element method[END_REF], [START_REF] Ossart | Effect of punching on electrical steels: Experimental and numerical coupled analysis[END_REF], because of change in magnetic properties of electrical steel [START_REF] Pulnikov | Measuring setup for the investigation of the influence of mechanical stresses on magnetic properties of electrical steel[END_REF]. The accuracy of loss computation is significantly affected if the analysis is performed without considering stress effects [START_REF] Miyagi | Estimation of iron loss in motor core with shrink fitting using fem analysis[END_REF].

Computational time and accuracy are two important aspects that need to be considered during the design and analysis of electrical machines [START_REF] Liu | An improved method of optimization for electrical machines[END_REF]. A significant amount of research has been done on the estimation of iron losses in electrical machines subjected to mechanical stress [START_REF] Bernard | Effect of stress on magnetic hysteresis losses in a switched reluctance motor: Application to stator and rotor shrink fitting[END_REF], [START_REF] Belahcen | Magnetoelastic coupling in rotating electrical machines[END_REF], [START_REF] Zeze | Vector magnetic characteristic analysis of a pm motor considering residual stress distribution with complex-approximated material modeling[END_REF], [START_REF] Xiao | Decoupled magnetoelastic finite element method including magnetostriction effects in electrical machinery applications[END_REF], [START_REF] Rasilo | Multiaxial magneto-mechanical modelling of electrical machines with hysteresis[END_REF], [START_REF] Yamazaki | Effects of multi-axial mechanical stress on loss characteristics of electrical steel sheets and interior permanent magnet machines[END_REF] but major issues remain, viz. lack of predictive hysteretic constitutive magneto-mechanical model and complex numerical implementation.

Numerous hysteresis models for ferromagnetic materials are available in the literature [START_REF] Jiles | Theory of ferromagnetic hysteresis[END_REF], [START_REF] Mayergoyz | The classical preisach model of hysteresis and reversibility[END_REF], [START_REF] Henrotte | An energy-based vector hysteresis model for ferromagnetic materials[END_REF]. Among them Preisach formalism and Jiles-Atherton (JA) model are widely used. Most of the existing magneto-mechanical coupled models are built as extensions of these classical magnetic hysteresis models. Preisach models have been modified for consideration of stresseffects through their distribution functions [START_REF] Bergqvist | A stress-dependent magnetic preisach hysteresis model[END_REF], [START_REF] Sipeky | Preisach-type stress-dependent magnetic vector hysteresis model[END_REF], [START_REF] Bottauscio | Modeling and experimental analysis of magnetostrictive devices: From the material characterization to their dynamic behavior[END_REF], [START_REF] Suzuki | Comparison of jiles-atherton and preisach models extended to stress dependence in magnetoelastic behaviors of a ferromagnetic material[END_REF]. On the other hand, the JA model has been extended in order to consider magneto-elastic effects using the concept of effective field [START_REF] Suzuki | Comparison of jiles-atherton and preisach models extended to stress dependence in magnetoelastic behaviors of a ferromagnetic material[END_REF], [START_REF] Sablik | Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis[END_REF], [START_REF] Sablik | Model for the effect of tensile and compressive stress on ferromagnetic hysteresis[END_REF], [START_REF] Naus | Theoretical developments in magnetomechanics[END_REF]. Another model based on a multi-scale approach, derived through the energy equilibrium for the description of anhysteretic magnetization, has been proposed [START_REF] Daniel | A multiscale model for magneto-elastic behaviour including hysteresis effects[END_REF]. The model is successful in describing the magneto-elastic coupled behaviour of ferromagnetic materials [START_REF] Hubert | Multiscale modeling of the magneto-mechanical behavior of grain-oriented silicon steels[END_REF]. Implementation of complete hysteresis models in Finite Element Method (FEM) simulations is known as intrinsic approach [START_REF] Bernard | Effect of stress on magnetic hysteresis losses in a switched reluctance motor: Application to stator and rotor shrink fitting[END_REF], [START_REF] Dlala | Comparison of models for estimating magnetic core losses in electrical machines using the finite-element method[END_REF], [START_REF] Sadowski | An inverse jilesatherton model to take into account hysteresis in time-stepping finiteelement calculations[END_REF]. Since the approach considers comprehensive hysteretic descriptions, it is a realistic description and very accurate to calculate losses directly in the FEM formulation. However, numerical implementation of these models leads to high computational burden and it poses serious convergence issues [START_REF] Bernard | Effect of stress on magnetic hysteresis losses in a switched reluctance motor: Application to stator and rotor shrink fitting[END_REF], [START_REF] Sadowski | An inverse jilesatherton model to take into account hysteresis in time-stepping finiteelement calculations[END_REF]. Another approach is to decouple the single-valued non-linear curve (anhysteretic curve) for use in field analysis (FEM) and to compute the loss at the post-processing stage using an appropriate loss formula [START_REF] Ionel | Computation of core losses in electrical machines using improved models for laminated steel[END_REF], [START_REF] Gracia | Numerical calculation of iron losses in electrical machines with a modified post-processing formula[END_REF], [START_REF] Belahcen | A posteriori iron loss computation with a vector hysteresis model[END_REF]. This approach is known as a posteriori approach. A significant number of papers are reported in the literature, which have used this approach in order to consider stress effects [START_REF] Ali | Prediction of mechanical stress effects on the iron loss in electrical machines[END_REF], [START_REF] Saeed | Iron loss models under static stress for non-oriented and grain oriented steel[END_REF], [START_REF] Karthaus | Effect of mechanical stress on different iron loss components up to high frequencies and magnetic flux densities[END_REF], [START_REF] Singh | Effect of mechanical stress on excess loss of electrical steel sheets[END_REF]. This approach shows reduced computational time and simpler convergence properties compared to the intrinsic approach (implementation of complete magneto-elastic hysteresis model). However, the approach does not consider hysteresis effects in the FEM formulation itself, which may affect its accuracy.

Another interesting methodology to describe magnetic properties is a complex permeability based approach [START_REF] Tavakoli | Comparison of a simple and a detailed model of magnetic hysteresis with measurements on electrical steel[END_REF], [START_REF] Baghel | Modeling of magnetic characteristics including hysteresis effects for transformers[END_REF]. In this methodology, nonlinear hysteretic properties of core materials are represented by elliptic (or linear) loops using complex permeability [START_REF] Baghel | Modeling of magnetic characteristics including hysteresis effects for transformers[END_REF]. Applied first without considering the effect of stress, the approach leads to a huge reduction in computational time and shows no convergence issues due to its linear nature. It provides a way to represent magnetic characteristics of the core material as a function of frequency [START_REF] Badgujar | A coupled field-circuit formulation and a duality based approach for analysis of low-frequency response of transformers[END_REF]. Therefore, the approach is frequently used in high-frequency analysis such as sweep frequency response analysis (SFRA) of power transformers [START_REF] Badgujar | A coupled field-circuit formulation and a duality based approach for analysis of low-frequency response of transformers[END_REF], [START_REF] Abeywickrama | High-frequency modeling of power transformers for use in frequency response analysis (fra)[END_REF], [START_REF] Mitchell | Modeling power transformers to support the interpretation of frequency-response analysis[END_REF]. The computation of equivalent complex permeability can be done using two approaches. The first method considers a fundamental harmonic component of B and phase difference between B and H as the hysteresis loss angle, and this approach is called Fundamental Harmonic Method (FHM) [START_REF] Tavakoli | Comparison of a simple and a detailed model of magnetic hysteresis with measurements on electrical steel[END_REF]. The second method considers core losses to compute the imaginary part of the equivalent complex permeability and it also retains the exact values of B max and H max of the hysteresis loop. This method is known as the equivalent core loss (ECL) approach [START_REF] Baghel | Modeling of magnetic characteristics including hysteresis effects for transformers[END_REF].

This paper aims at offering a simple equivalent complex permeability approach to designers and researchers for the estimation of losses in electrical machines subjected to significant mechanical stress levels. The present analysis here is restricted to model the effect of mechanical stresses in elastic range. The approach consists of modification of tanh representation of complex permeability derived from Maxwell's equations. The effects of mechanical stress are modeled using the equivalent complex permeability by representing its real and imaginary part as a function of the stress. The non-linear stress dependence of the complex permeability can be determined using measured loss data at two different stress levels. The paper also discusses computation of equivalent complex permeability using reluctivity with prior knowledge of induction B instead of H, which is often the case in numerical simulations (FEM) and standard measurement systems. The proposed approach is first compared with conventional approaches using FEM simulation of single sheet tester (SST) at zero stress condition, and it is found to give comparable accuracy with significant reduction in computational time. Thereafter, the approach is applied for loss computation over a range of compressive and tensile stress levels (up to 50 MPa). The computed losses are in close agreement with measured ones.

Complex Permeability Representation of Magnetic Characteristics

The magnetic permeability of a material defines its ability to get magnetized. For a ferromagnetic material, the hysteresis losses can be represented in terms of phase difference (θ l ) between B and H. This phenomenon is represented by a delay in the response (B ) to the excitation (H ) and thus, B lags H by angle θ l , [START_REF] Macfadyen | Vector permeability[END_REF]. By considering B and H in the phasor form, the permeability can be defined in complex notations as:

µ l = B H = µe -jθ l = µ -jµ (1)
In addition to the hysteresis loss, in the presence of time-varying magnetic fields, dynamic losses (classical eddy current and excess losses) make the complex permeability frequency-dependent [START_REF] Tavakoli | Comparison of a simple and a detailed model of magnetic hysteresis with measurements on electrical steel[END_REF]. The effective frequencydependent complex permeability is derived from the diffusion equation for a semi-infinite single sheet (as shown in Fig. 2) as:

x Lamination y (0, -b) (0, 0) (0, b) H z (y)
∇ 2 H = jωµ l σH (2)
Here, σ is the electric conductivity of the magnetic material and ω is the angular frequency of the excitation. In the figure, the magnetic field in the z -axes varies along the y-direction. Thus, eq. 2 can be solved as:

∂ 2 H z ∂z 2 = α 2 H z =⇒ H z = A 1 e αy + A 2 e -αy (3)
Here,

α 2 = jωσµ l =⇒ α = √ jωσµ l = (1 + j) jωσµ l /2 = (1 + j)/δ

, and by applying boundary conditions as (H

z (b) = H z (-b) = H max )
for the lamination in Fig. 2, eq. 3 can be reduced to

H z = H max cosh y cosh b (4)
Using eq. 1 and eq. 4, the effective complex permeability (µ ef f ) can be calculated using the average magnetic flux density (B avg ) as given below:

µ ef f = µ -jµ = B avg H max = 1 H max 2b b -b µ l H z (y)dy = µ l tanh αb αb = µ l tanh(1 + j)b/δ (1 + j)b/δ (5)
In the above equation, α, δ are propagation constant and skin depth of electromagnetic field inside a conductor [START_REF] Subbarao | Eddy currents in linear and non-linear media[END_REF], [START_REF] Abeywickrama | Computation of parameters of power transformer windings for use in frequency response analysis[END_REF], respectively. These parameters depend on permeability and conductivity of the material and on the frequency. Equation 5can be used to model the effective complex permeability as a function of frequency. The parameter (µ l ) is derived by using µ ef f values calculated from hysteresis loops at different frequencies, the maximum magnetic field H max being constant [START_REF] Tavakoli | Comparison of a simple and a detailed model of magnetic hysteresis with measurements on electrical steel[END_REF]. However, practical situations might be different since standard measurement systems usually set a maximum value of the magnetic induction B max which is maintained constant for measurements at different frequencies. In this case, the effective complex permeability is calculated in terms of reluctivity using the energy loss. For a sinusoidal flux density (B ), the energy loss (P ) per cycle is:

P = T H(B)dB = T H(B) dB dt dt (6)
The flux density can be written as:

B = B max e jωt (7)
dB dt = jωB max e jωt The magnetic field intensity (H ) can be computed as:

H = real(ν c B) = (ν + ν )B max e jωt = B max (ν cos ωt + ν sin ωt) (8)
Substituting eq. 7 and eq. 8 in eq. 6 and integrating over one time period, yields

ν = P πB 2 max (9)
Using the relations H max = |ν|B max =⇒ |ν| = Hmax Bmax , the real part of reluctivity can be computed as:

ν = |ν| 2 -ν 2 (10)
Using eq. 9 and eq. 10, the complex reluctivity is determined using three frequency-loss data sets (here, loss data at 50, 1000, 2000 Hz are used) in order to compute the frequency-dependent effective complex permeability. Hence, non-linear hysteretic characteristics are basically transformed into linear-elliptical hysteretic loops using the complex permeability approach as shown in Fig. 3.

-1500 -1000-500 0 500 1000 1500 H (A/m)

Modeling of Stress Effects using Complex Permeability

Magneto-mechanical characteristics of ferromagnetic materials can be modeled using the frequency dependent complex permeability function derived in Section 2. First, the effective complex permeability can be computed using the components of complex reluctivity (eq. 9 and eq. 10) at each stress level. Thus, the real and imaginary parts of the complex permeability are made to change with the stress level. The phasor representation of the effect of stress on B, H and ν is shown in Fig. 4. In the figure, the magnetic flux density is kept constant. In the phasor representation, σ s1 < σ s2 for compressive stress and σ s1 > σ s2 for tensile stress.

Under compressive stress the hysteresis loop generally bends as shown in Fig. 1 and higher H is required (as evident in Fig. 4) to setup a given flux density, and therefore the real part of complex permeability decreases as shown in Fig. 1b. Thus, the phase angle θ ef f between B and H increases as the stress increases from σ s1 to σ s2 as shown in Fig. 4. However, in case of tensile stress, the hysteresis loops straightens about vertical axis and so the required H will be lower to setup a given B and the phase angle (θ ef f ) decreases with increase in stress. In the frequency-dependent complex permeability function eq. 5, the stress effects can be included through µ l to represent these effects on the losses and permeability [START_REF] Baghel | Effects of mechanical stress on core losses along orthogonal directions in electrical steels[END_REF]. The variations of real and imaginary parts of µ l with stress are shown in Fig. 5. Both real and imaginary parts µ

µ lr = µ lr0 e arσs (11a) µ li = µ li0 e a i σs (11b)
Here µ lr0 and µ li0 are the real and imaginary part of µ l at the zero stress condition. σ s is positive for tensile stress and negative for compressive stress. a r and a i are constants describing the behaviour of the real and imaginary parts of the effective complex permeability with stress and their values are different for compressive and tensile stresses. These coefficients can be determined using loss-data sets at two stress levels. Here, the loss data sets at 0 and +/-50 MPa stress levels are chosen to determine these parameters for both type of stress levels (compressive (0 and -50 MPa) and tensile (0 and 50 MPa)). The effective complex permeability as a function of frequency and stress can be written as:

µ ef f (σ s , ω) = µ l (σ s ) tanh αb αb (12)
where, α = jωµ l (σ s )σ and the variation of complex permeability as a function of compressive stress and frequency is shown in Fig. 6. From the figure, one can infer that the variation of frequency dependency of real and imaginary parts of complex permeability is significant for compressive stress (Fig. 6a). In case of tensile stress (Fig. 6b), a notable change is not observed for real and imaginary parts of complex permeability. The elliptic hysteresis

FEM Implementation of the Proposed Magneto-elastic Complex Permeability

Hysteresis loops and corresponding losses are measured for non-oriented electrical steel; grade-M235-35A using a single sheet tester (SST). The measurement setup comprises a pneumatic tension and compression unit as shown in Fig. 8a. Thickness and conductivity of laminations used for measurement are 2b = 0.33 mm and σ = 2.08×10 6 S/m. The performance of the suggested approach is first determined using other approaches (a posteriori and full hysteresis implementation-intrinsic approach) for the zero-stress (unloaded) condition. Then, the magneto-elastic complex permeability is applied to the loss computation in a stressed (loaded) condition by simulating the SST device. The geometry of the setup is shown in Fig. 8b.

Intrinsic approach

In this approach, the JA model is integrated into the FEM formulation. The governing field equation is [START_REF] Kulkarni | Transformer engineering: design, technology, and diagnostics[END_REF]: where, S and N are the cross-sectional area and the number of turns of the winding, respectively. The circuit equation can be written as:

1 µ ( ∂ 2 A ∂x 2 + ∂ 2 A ∂y 2 ) = -J o = - N I S ( 13
)
U = d dt φ + [R ext ]I + d dt [L ext ]I (14)
In the above equations, U is the supply voltage, I is the current drawn, A is the magnetic vector potential, S is the cross-sectional area of the conductor, and φ is the magnetic flux linkages with the winding. R ext and L ext are the resistance and inductance of the winding and, µ is a non-linear function of B, calculated using a hysteresis model. In FEM formulation, the final field and circuit equations can be written as [START_REF] Baghel | Modeling of magnetic characteristics including hysteresis effects for transformers[END_REF]:

[K][A] + [T ] d dt [A] + [D][I] = 0 (15a) [D] d dt [A] + [R ext ][I] + [L ext ] d dt [I] = U (15b)
The non-linear solver uses the local coefficient method (LCM) in the fixedpoint approach [START_REF] Dlala | A fast fixed-point method for solving magnetic field problems in media of hysteresis[END_REF].

In the above equation, [K ] represents the global coefficient matrix, [T ] and [D] correspond to the eddy current term and the source term respectively [START_REF] Kulkarni | Transformer engineering: design, technology, and diagnostics[END_REF]. For material modeling, hysteresis loops are approximated using the JA model in this analysis [START_REF] Baghel | Modeling of magnetic characteristics including hysteresis effects for transformers[END_REF].

In the JA model, the minimum energy state of magnetic materials can be represented using the anhysteretic magnetization [START_REF] Jiles | Theory of ferromagnetic hysteresis[END_REF]. It is defined in terms of three parameters, a, α, and M s as:

M an = M s [coth( H e a ) - a H e ] ( 16
)
H e = H + αM (17)
where, M and H are the total magnetization and the applied magnetic field. The hysteretic behavior is obtained using the energy balance principle with reversible and irreversible magnetization components [START_REF] Jiles | Theory of ferromagnetic hysteresis[END_REF]. It can be represented in its inverse form by the following differential equation [START_REF] Sadowski | An inverse jilesatherton model to take into account hysteresis in time-stepping finiteelement calculations[END_REF]:

dM dB = (1 -c) dM irr dBe + c µo dMan dHe 1 + c(1 -α) dMan dHe + µ o (1 -c)(1 -α) dM irr dBe (18)
where, B and M irr are the flux density and the irreversible magnetization, µ o is the free space magnetic permeability, and δ is the directional parameter with the value +1 for dH/dt >0 and -1 for dH/dt <0. The model is applied on a measured hysteresis loop (1.5 T, 50 Hz) of a non-oriented material (M235-35A) sample. Optimized parameters are given in Table 1. The surface plot of flux density (in the sample) and the computed current waveform are shown in Fig. 9.

A posteriori approach

In this approach, FEM analysis is carried out using the anhysteretic curve and the total losses are calculated at the post-processing stage [START_REF] Belahcen | A posteriori iron loss computation with a vector hysteresis model[END_REF]- [START_REF] Ionel | Computation of core losses in electrical machines using improved models for laminated steel[END_REF]. The loss model is given as [START_REF] Ionel | Computation of core losses in electrical machines using improved models for laminated steel[END_REF]- [START_REF] Gracia | Numerical calculation of iron losses in electrical machines with a modified post-processing formula[END_REF]:

P = k h f B 2 max + k e f 2 B 2 max + k ex f 1.5 B 1.5 max (19)
Here, k h , k e , and k ex are the hysteresis, classical eddy current and excess loss coefficients respectively. B max and f are the peak induction value and frequency respectively. The loss coefficients can be determined using measured loss-frequency data. The FEM analysis is performed with an anhysteretic curve, determined from the JA model as given in intrinsic approach.

FEM analysis using complex permeability approach

A time-harmonic analysis is used involving complex permeability and the loss is computed by the area of the elliptic B -H loop. The final FEM equation can be obtained from eq. 13 and eq. 14 as [START_REF] Badgujar | A coupled field-circuit formulation and a duality based approach for analysis of low-frequency response of transformers[END_REF]:

[K][A] + jω[T ][A] + [D][I] = 0 (20a) jω[D] [A] + [R ext ][I] + jω[L ext ][I] = [U ] (20b)
Here, the elements of the K matrix are complex quantities and eq. 20 is solved in the frequency domain. The surface plot and line plots of magnetic flux density are shown in Fig. 10.

Comparison of the three approaches

The performance of the three approaches discussed previously can be compared in terms of accuracy and computational time, as given in Table 2. The accuracy of the complex permeability is reasonably comparable to the intrinsic approach. Also, a huge reduction in computational time is obtained by using the complex permeability approach.

The approach can now be applied to compute losses under mechanical stress conditions using the magneto-elastic complex permeability given by eq. 12. The loss is computed at 1.5 T for a frequency from 10 Hz up to 2 kHz.

Results and discussion

FEM simulations of the SST device are carried out for each stress level using the stress-dependent complex permeability. Computed and measured losses for different compressive and tensile stress levels are shown in Fig. 11. Maximum error among all stress levels at different frequencies is around 2.5 %. Model parameters for 1.5 T for compressive and tensile stresses are given in Table 3. The same method is also carried out to compute losses for maximum induction levels of 0.5 T and 1.0 T (given in Figs. 12 and13). Since the compressive stress affects the core loss more significantly than the tensile stress, these analyses are performed only for compressive stress levels. Model parameters for these induction levels are given in Table 4.

The magneto-elastic model using complex permeability can be repre- Tensile (σ > 0)

0.0013 6.89 × 10 -5 6.0611×10 -10 4.591×10 -10 sented using a simple function of stress over a wide range of frequencies. The model involves very few parameters, and hence it needs less measured data for parameter identification process which is straightforward. The magnetoelastic effects can be considered in the FEM analysis of electrical machines using the proposed approach. The present approach is isotropic, which particularly ignores stress-induced anisotropy since the magnetic permeability is described as a scalar. However, the anisotropy can be introduced using a tensor form of the effective complex permeability as reported in [START_REF] Abeywickrama | Computation of parameters of power transformer windings for use in frequency response analysis[END_REF]. Moreover, the approach has been applied to simple configurations with uniaxial loading. If the loading is multi-axial, the present approach can be used with equivalent uniaxial stress derived from the equivalence between 2D and 1D magnetostrictive energies [START_REF] Daniel | An equivalent stress for the influence of multiaxial stress on the magnetic behavior[END_REF], [START_REF] Rekik | Equivalent stress model for magnetic hysteresis losses under biaxial loading[END_REF].

Conclusion

This paper is devoted to the modeling of magneto-elastic properties of electrical steels using a complex permeability approach. In this work a frequency-dependent tanh function for complex permeability, derived using Maxwell's equations, has been improved to consider magneto-mechanical effects. Complex permeability has been calculated using reluctivity which is determined using energy loss. The magneto-mechanical effects on permeability and losses are incorporated in the complex permeability. The presented work compares the proposed approach with the conventional intrinsic and a posteriori approaches using the FEM modeling of a single sheet tester under the unloaded condition. The work also discusses the computation of equivalent complex permeability using the reluctivity with a prior knowledge of induction B instead of H, which is of in line with standard measurement systems. The complex permeability approach shows a significant reduction in computational time with reasonable level of accuracy as compared to the existing approaches. The proposed magneto-elastic complex permeability is thereafter used to simulate the SST device under mechanical loading conditions. Computed losses are in close agreement with the measured losses. An advantage of representing core material using complex permeability is that all loss components can be considered in a single function for a wide range of frequencies. The model can be applied successfully over a wide range of frequencies as the skin-effect phenomenon is taken into consideration. Reduction in computation time and simplicity are the main attractive features of the model. The model could also be extended to consider anisotropy, rotational flux, and multiaxial nature of induced mechanical stresses in practical devices [START_REF] Daniel | An equivalent stress for the influence of multiaxial stress on the magnetic behavior[END_REF], which is identified as a future work. Application of the model in FEM simulations of rotating machines has also been identified as a future work.

Figure 2 :

 2 Figure 2: Semi-infinite single sheet in z -direction with x dimensions much greater than the y dimensions

Figure 3 :

 3 Figure 3: Conversion of non-linear hysteresis characteristics to linear-elliptical hysteresis loops at 1.5 T

Figure 4 :

 4 Figure 4: Phasor representation of B, H, and complex reluctivity at two different stress levels (Compressive stress: σ s1 <σ s2 and Tensile stress: σ s1 >σ s2 )

Figure 5 :

 5 Figure 5: Variation of (a) real part of µ l (b) imaginary part of µ l with stress at 1.5 T

Figure 6 :Figure 7 :

 67 Figure 6: Variation of complex permeability at 1.5 T as a function of frequency at different stress levels (a) compressive stress (b) tensile stress

Figure 8 :

 8 Figure 8: (a) SST with a unit to apply mechanical stresses [7] (Source: RENAULT-SAS, Guyancourt, France) (b) Geometric overview of SST

Figure 9 :

 9 Figure 9: Simulation results (a) surface plot of flux density of the sample region shown in Fig. 8b (b) the computed current waveform

Figure 10 :

 10 Figure 10: Simulation results (a) surface plot of flux density of the sample region shown in Fig. 8b (b) flux lines

Figure 11 :

 11 Figure 11: Comparison of measured and calculated loss using time-harmonic FEM for induction level of 1.5 T (a) 50 Hz (b) 2 kHz

Figure 12 :

 12 Figure 12: Comparison of measured and calculated loss using time-harmonic FEM for induction level of 0.5 T (a) 50 Hz (b) 500 Hz (c) 2 kHz

Figure 13 :

 13 Figure 13: Comparison of measured and calculated loss using time-harmonic FEM for induction level of 1.0 T (a) 50 Hz (b) 500 Hz (c) 2 kHz

Table 1 :

 1 Optimized JA parameters M an , is the anhysteretic magnetization. H e is the effective field and it can be written as:

	Parameter Optimized values
	M s	1.22 × 10 6 A/m
	a	85 A/m
	k	70 A/m
	α	2.0 × 10 -4
	c	0.1
	where,

Table 2 :

 2 Comparison of three approaches

	Approaches	Computed	Measured	computational
		values	values	time (s)
		(W/kg)	(W/kg)
	Intrinsic ap-	2.20	2.28	1891
	proach
	Extrinsic ap-	2.17	2.28	450
	proach
	Complex per-	2.40	2.28	2
	meability

Table 3 :

 3 Parameters of complex permeability model for B max = 1.5 T

	Type of stress µ lr0	µ li0	a r (MPa -1 )	a i (MPa -1 )
	Compressive	0.0013	6.89 × 10 -5 6.52 × 10 -9	7.19 × 10 -9
	(σ < 0)

Table 4 :

 4 Parameters of complex permeability model for different induction levels and compressive stresses

	Induction	µ lr0	µ li0	a r (MPa -1 )	a i (MPa -1 )
	level
	0.5 T	0.012	0.0105	4.47 × 10 -8	7.73 × 10 -8
	1.0 T	0.0116	6.5 × 10 -3 4.32×10 -8	7.42×10 -8

Acknowledgements

The authors would like to thank the COCTEL project Piloted by RENAULT-SAS, Guyancourt, France and financed by the ADEME (French Environment and Energy Management Agency).

Data Availability

The measured data required to replicate these results cannot be shared at this time as the data also forms part of an ongoing work.


Francine Cote

Cathy Vaillancourt

Denis Sarrouilhe
email: denis.sarrouilhe@univ-poitiers.fr

Marc Mesnil
email: marc.mesnil@univ-poitiers.fr

Serotonin and human cancer: a critical view Mini-review article for the special issue devoted to "70 years of serotonin

Besides its classical functions as a neurotransmitter in the central nervous system, local mediator in the gastrointestinal tract and vasoactive agent in the blood, serotonin has more recently emerged as a growth factor for human tumor cell lines of different origins (carcinomas, glioma and carcinoids). Several data are also available on serotonin involvement in cancer cell migration, metastatic dissemination and tumor angiogenesis. The serotonininduced signaling pathways that promote tumor progression are complex and only partly understood in some cancer types. The results of several studies showed that serotonin levels in the tumor played a crucial role in cancer progression. A serotonin production and secretion by neuroendocrine cells have been shown in the progression of several solid tumors and the involvement of a serotoninergic autocrine loop was proposed. Specific receptor subtypes are

2 associated with different fundamental stages of tumor progression and the pattern of receptors expression becomes dysregulated in several human tumors when compared with normal cells or tissues. Serotonin receptors, selective serotonin transporter and serotonin synthesis pathways are potential chemotherapeutic targets for the treatment of several cancers in which therapeutic approaches are limited. Through several asked questions, this critical mini-review discusses the relevance of the involvement of serotonin in human cancer progression.

Keywords: angiogenesis, carcinogenesis, chemotherapy, neuroendocrine cells, serotonin, SSRI.

Abbreviations: 5-HIAA: 5-hydroxyindoleacetic acid; 5-HT: 5-hydroxytryptamine; CNS: central nervous system; CSC: cancer stem cells; EC: enterochromaffin cells; HCC: hepatocellular carcinoma; HDAC: Histone deacetylase; MAO: monoamine oxidase; MMP: matrix metalloproteinase; NE: neuroendocrine; NET: neuroendocrine tumor; PaCa cells: pancreatic cancer cells; PC: prostate cancer; SCLC: small-cell lung carcinoma; SERT: selective serotonin transporter; SSRI: selective serotonin reuptake inhibitors; TPH: Tryptophan hydroxylase.

1-Introduction

Serotonin (5-hydroxytryptamine, 5-HT) is a biogenic monoamine produced from the essential amino-acid tryptophan obtained primarily through diet. Serotonin is mostly located in the periphery of the body and less than 1% of total body serotonin circulates in its free form in the blood [1]. It acts as a neurotransmitter in the central nervous system (CNS), local mediator required for motility in the gastrointestinal tract and vasoactive agent in the blood.

The classification of serotonin receptors recognizes 13 receptor subtypes in human, spreading over 7 receptor families that are widely distributed among many organs [START_REF] Hoyer | International union of pharmacology classification of receptors for 5-Hydroxytryptamine (serotonin)[END_REF]. Serotonin can exert multiple, sometimes opposing actions, and this is determined by the characteristics of the receptor with which it interacts and the intracellular signaling pathway coupled to it.

Within the CNS of vertebrates, a large majority of the cell bodies of serotonergic neurons are located in the nine raphe nuclei of the brain stem, the neurons of the rostral and caudal groups of raphe nuclei giving rise to broad and diffuse projections to the forebrain for the former group and to the hindbrain and spinal cord for the latter one [START_REF] Gaspar | Probing the diversity of serotonin neurons[END_REF]. Serotonin has been linked to a variety of CNS functions and is implicated in many CNS and psychiatric disorders.

Consequently, serotonergic systems are targets for a large array of psychoactive compounds including antidepressants, antipsychotics and hallucinogens [START_REF] Marin | Bockaert. 5-HT Receptor-Associated Protein Networks: New Targets for Drug Discovery in Psychiatric Disorders?[END_REF]. Serotonin is also synthesized and stored in the mucosal enterochromaffin cells (EC) of the gastrointestinal tract and its secretion upon the action of different types of stimuli results in increased absorption by circulating platelets and mast cells that provide a potent reservoir of serotonin. Serotonin released from platelets is critical for normal wound healing in multiple organs [START_REF] Mann | Serotonin paracrine signaling in tissue fibrosis[END_REF]. Besides all its already known functions, serotonin has been shown to be a mitogenic factor for a wide range of non-tumoral and tumoral cells in culture and specific receptor subtypes have been associated with the progression of solid tumors [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF]. Therefore, serotonin might be involved in one or more fundamental stages of their progression, ie growth of the primary tumor, invasion and dissemination up to metastasis.

Through several asked questions, this critical mini-review discusses the relevance of the involvement of serotonin in human cancer progression.

2-What are the arguments for the involvement of serotonin in human cancer progression?

In vitro, serotonin exhibits a growth stimulatory effect on several types of human tumor cell lines ie carcinoma [prostate, bladder, small-cell lung (SCLC), colorectal, bile duct, trophoblast, breast, hepatocellular (HCC)], glioma and carcinoids (Fig. 1). With the exception of glioma and carcinoid tumor, in many studies only a slight stimulatory effect of serotonin on cell growth was observed [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF]. More often the effect of serotonin on cell growth is mediated through 5-HT1 and 5-HT2 receptors and less frequently through 5-HT3, 5-HT4, 5-HT6 and 5-HT7 receptors. Many studies have focused on the action of serotonin on prostate cancer (PC) and suggested that this action is mediated through several receptor subtypes that are present at various tumor stages, 5-HT2B in the initial stages of tumorigenesis, 5-HT1A and 5-HT1B in aggressive PC with high Gleason grades (4 and 5) and 5-HT1A in PC cells metastasized to human lymph nodes and bones [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF][START_REF] Dizeyi | Expression of serotonin receptors and role of serotonin in human prostate cancer tissue and cell lines[END_REF]. Serotonin activates the two interrelated MAP kinase and PI3K/Akt signaling pathways to induce proliferation, migration and differentiation in PC cell lines [START_REF] Dizeyi | Serotonin activates MAP kinase and PI3K/Akt signaling pathways in prostate cancer cell lines[END_REF]. However, the results regarding prostate carcinoma are inconsistent probably due to the involvement at high serotonin concentrations of other serotonin receptor subtypes that have lower affinity for serotonin [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF]. In vitro, serotonin is a potent mitogen for neoplastic placental cells and stimulation of two choriocarcinoma cell lines by a selective agonist of 5-HT2A receptor activates MEK-ERK1/2 and JAK2-STAT3 signaling pathways [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF]. The expression of various 5-HT receptors is involved in HCC progression and serotonin promotes proliferation of serum-deprived HCC cells through a complex cross-talk between signaling pathways including Wnt/β-catenin signaling and activation of mTOR downstream targets [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF][START_REF] Shi | X. 5-Hydroxytryptamine promotes hepatocellular carcinoma proliferation by influencing β-catenin[END_REF]. Sometimes, as it was shown in the SCLC (5-HT1A and 5-HT1D), the mitogenic action of serotonin seemed to involve a complex time course interaction between the signaling pathways of several receptor subtypes [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF]. Immunohistochemical and Western blot analysis demonstrated the presence of 5-HT receptors in cultured cells and sometimes quantitative RT PCR revealed that their mRNA was expressed. Often, as a proof of principle of in vitro experimental results, microarray and immunohistochemistry were used to study 5-HT receptor expression in tumor biopsies and compared to normal tissue. In contrast, several genetic studies support a tumor suppressor role for the human HTR1B gene during lung, renal, oral, osteo carcinogenesis and non-Hodgkin lymphomas [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF]. Among the few studies that have linked serotonin to cancer cell differentiation, in LNCaP PC cells, serotonin was related with a differentiation and acquisition of neuroendocrine (NE) phenotype [START_REF] Dizeyi | Serotonin activates MAP kinase and PI3K/Akt signaling pathways in prostate cancer cell lines[END_REF].

Several data are available on serotonin involvement in cancer cell migration and metastatic processes. Serotonin promoted the invasiveness of certain PC cells and 5-HT1A receptor was shown to be involved in PC cell migration [START_REF] Dizeyi | Serotonin activates MAP kinase and PI3K/Akt signaling pathways in prostate cancer cell lines[END_REF]. Serotonin also potently stimulated migration and invasion of various human glioma cell lines [START_REF] Merzak | Expression of serotonin receptors in human fetal astrocytes and glioma cell lines: a possible role in glioma cell proliferation and migration[END_REF]. In triple-negative breast cancer cells, a highly aggressive subtype of breast cancer, serotonin promoted proliferation and a strong invasion via 5-HT7 receptors and increased the protein expression of TPH1 suggesting that the monoamine promotes cancer progression through an autocrine loop.

Interestingly, downstream signaling molecules responsible for transmitting signals from 5-HT7 receptor differed during invasion and proliferation: 1) Gαs-linked generation of cAMP, Gβγ-activated kinase signaling (Src/ERK and PI3K/Akt) and matrix metalloproteinase-9 (MMP-9) during invasion and 2) Gβγ-activated PI3K/Akt signaling during proliferation [START_REF] Gautam | Tryptophan hydroxylase 1 and 5-HT7 receptor preferentially expressed in triple negative breast cancer promote cancer progression through autocrine serotonin signaling[END_REF].

5-HT1D receptor is overexpressed in colorectal cancer biopsies and modulates human colorectal tumor cells invasion/migration in vitro by regulating Axin1/β-catenin/ LEF1/TCF4/MMP-7 signaling pathway [START_REF] Sui | 5-hydroxytryptamine receptor (5-HT 1D R) promotes colorectal cancer metastasis by regulating Axin1/β-catenin/MMP-7 signaling pathway[END_REF]. Moreover, 5-HT1B and 5-HT1D receptors are also overexpressed in pancreatic cancer cells (PaCa cells) where they play an important role in the regulation of the proliferation and invasion of these tumor cells [START_REF] Gurbuz | Down-Regulation of 5-HT1B and 5-HT1D Receptors Inhibits Proliferation, Clonogenicity and Invasion of Human Pancreatic Cancer Cells[END_REF]. The data of the studies are consistent with the following tumor PaCa cells 5-HT1B and 5-HT1D receptors signaling pathways associated with tumor progression: 1) the two receptors mediate β1integrin activity to recruit a Src-FAK complex promoting proliferation and migration; 2) the two receptors overexpression promotes the activation of urokinase plasminogen activator receptor (uPAR) and of MMP-2, facilitating invasion; 3) they stimulate the expression of the zinc finger transcriptional regulator of epithelial-mesenchymal transition (Snail and ZEB1) which, in turn, repress the expression of epithelial markers (claudin-1 and E-cadherin) supporting the proliferation and invasiveness [START_REF] Gurbuz | Down-Regulation of 5-HT1B and 5-HT1D Receptors Inhibits Proliferation, Clonogenicity and Invasion of Human Pancreatic Cancer Cells[END_REF]. An autocrine proliferation role of serotonin was suggested in human carcinoid cells mediated through 5-HT1A, 1B receptors inhibition of cAMP production in pancreatic tumor and 5-HT2 receptor induced phosphorylation of ERK1/2 and activation of JNK pathway in bronchopulmonary NET and small intestinal NET [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF]. In contrast, 5-HT2B receptor expression decreased during dissemination of ovarian tumor cells supporting a tumor suppressor role for serotonin during the invasive step of carcinogenesis [START_REF] Henriksen | Expresion of serotonin receptors 5-HT1A, 5-HT1B, 5-HT2B and 5-HT4 in ovary and in ovarian tumours[END_REF]. A correlation was shown between 5-HT1A receptor expression, invasiveness of PC3 and DU145 cells and metastatic PC to human lymph nodes and bones [START_REF] Dizeyi | Expression of serotonin receptors and role of serotonin in human prostate cancer tissue and cell lines[END_REF][START_REF] Dizeyi | Serotonin activates MAP kinase and PI3K/Akt signaling pathways in prostate cancer cell lines[END_REF]. Moreover, in 159 bone metastases from a spectrum of primary carcinomas and sarcomas, expression of serotonin in combination with tumor necrosis factor receptor 1 is correlated with poor survival [START_REF] Chiechi | Elevated TNFR1 and Serotonin in bone metastasis is correlated with poor survival following bone metastasis diagnosis for both carcinoma and sarcoma primary tumors[END_REF].

Angiogenesis processes contribute for primary tumor progression and also for metastasis in colonized tissues. It was recently reported that serotonin at concentrations lower than those seen in human serum activates in human endothelial cells the angiogenic Src/PI3K/AKT/mTOR/p70S6K phosphorylation signaling [START_REF] Zamani | Serotonin activates angiogenic phosphorylation signaling in human endothelial cells[END_REF]. Using in vitro models, serotonin stimulates the proliferation of endothelial cells via activation of 5-HT1, 5-HT2 and 5-HT3 receptors and proliferation of aortic smooth muscle cells via 5-HT2 receptors suggesting that the monoamine is also involved in tumor behavior by affecting angiogenesis [START_REF] Peters | Dopamine and serotonin regulate tumor behavior by affecting angiogenesis[END_REF]. Moreover, serotonin exerts complex actions on blood vessels, dependent on its interaction with a multiplicity of receptors and several serotonin receptors have been localized on the blood vessels feeding human tumors. Thus, 5-HT1D and 5-HT2B receptors were shown to be highly expressed in vascular endothelial cells in both benign and malignant prostate tissues [START_REF] Dizeyi | Expression of serotonin receptors and role of serotonin in human prostate cancer tissue and cell lines[END_REF][START_REF] Dizeyi | Expression of serotonin receptors 2B and 4 in human prostate cancer tissue and effects of their antagonists on prostate cancer cell line[END_REF]. Immunohistochemical analysis of patients with breast ductal carcinoma, revealed the expression of 5-HT1A and 5-HT2B receptors in blood vessel-related cells of malignant and non-malignant specimens [START_REF] Kopparapu | Expression and localization of serotonin receptors in human breast cancer[END_REF].

3-Are serotonin levels sufficient to act on tumor progression in human?

Platelets and platelet activation have been linked to tumor progression and angiogenesis [START_REF] Bambace | The platelet contribution to cancer progression[END_REF]. Moreover, thrombocytosis at the time of diagnosis was associated with a shorter survival in many types of solid tumors [START_REF] Buergy | Tumor-platelet interaction in solid tumors[END_REF]. In the thrombotic environment of tumors, platelet aggregation frequently occurs and leads to significant release of serotonin, which may constitute one of the mechanisms of tumor progression and angiogenesis. Such plateletderived serotonin level present in tumor microenvironment would be much higher than the blood serotonin level of normal healthy subjects which is about 0.7 µM (below the age of 16 years) and 0.4 µM (above the age of 16 years) [START_REF] Leboyer | Whole blood serotonin and plasma betaendorphin in autistic probands and their first-degree relatives[END_REF].

Moreover, serotonin production and secretion by neuroendocrine (NE) cells have been shown in the progression of several types of solid tumors (prostate carcinoma, urinary bladder carcinoma, SCLC, carcinoid tumors). Nicotine stimulates the release of serotonin by NE cells in SCLC suggesting an involvement of a serotoninergic autocrine loop in the control of proliferation. The 30-50 10 -9 M serotonin concentration found in the medium after nicotinic stimulation was compatible with this mechanism [START_REF] Cattaneo | Nicotine stimulates a serotoninergic autocrine loop in human small-cell lung carcinoma[END_REF]. Increased serotonin secretion is also found in carcinoid tumors which are slow-growing NE tumors (NET) of the diffuse NE system. The involvement of an autocrine proliferation role of serotonin is also suggested in human carcinoid cells and serotonin levels in blood (15-20 times higher than in control subjects) and tumor tissue are compatible with such a mechanism [START_REF] Drozdov | Auto-regulatory effects of serotonin on proliferation and signalling pathways in lung and small intestine neuroendocrine tumor cell lines[END_REF]. In cases of liver metastases, serotonin reaches the systemic circulation bypassing hepatic inactivation, and engenders the relatively uncommon carcinoid syndrome. In human cholangiocarcinoma cell lines, a dysregulation of the cellular machinery responsible for the metabolism of serotonin was observed and resulted in an increased production and secretion of the monoamine at levels compatible with stimulation of tumor cells. These results were further confirmed in vivo and on human biopsies [START_REF] Alpini | Serotonin metabolism is dysregulated in cholangiocarcinoma, which has implications for tumor growth[END_REF]. During breast carcinoma progression, TPH1 expression augments which corresponds to an increase in serotonin biosynthetic capacity [START_REF] Pai | Altered serotonin physiology in human breast cancers favors paradoxical growth and cell survival[END_REF]. All these results show that serotonin levels in the tumor play a crucial role in cancer progression.

Serotonin produced by NE cells may also act on the growth, differentiation of neighboring cells through paracrine mechanisms and may facilitate tumor recurrence and metastases, correlated with poor prognosis and shortened patient survival.

Serotonin and its metabolites have been already used as tumor markers of carcinoid tumors and carcinoid syndrome and serotonin was further proposed as a potential diagnostic and prognostic marker for other tumor types [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF].

4-Is tumor progression accompanied by changes of serotonin receptor expression?

The studies on serotonin involvement in tumor progression suggest that its receptors might react in a tissue-specific manner. They may also suggest that the biological response to serotonin could be determined by the combined effect of several receptors but also that serotonin receptor expression could change during this phenomenon. An immunohistochemical analysis of patients with breast cancer was performed in a tissue microarray and showed that the tightly regulated pattern of serotonin receptors becomes dysregulated in a complex way in human breast cancer cells, with ectopic expression of some isoforms and suppression of others, but without correlation with tumor grade [START_REF] Kopparapu | Expression and localization of serotonin receptors in human breast cancer[END_REF][START_REF] Pai | Altered serotonin physiology in human breast cancers favors paradoxical growth and cell survival[END_REF]. The 5-HT1B, 1F, 2B, 3C and 7 types were shown to be down-regulated and all the others up-regulated in human cholangiocarcinoma cell lines compared with the H69 human cholangiocyte cell line [START_REF] Alpini | Serotonin metabolism is dysregulated in cholangiocarcinoma, which has implications for tumor growth[END_REF]. Moreover, 5-HT1B and 2B receptors were significantly overexpressed in tumor tissue compared with the nontumoral adjacent liver [START_REF] Soll | Expression of serotonin receptors in human hepatocellular cancer[END_REF]. In ovarian cancer, 5-HT1A, 1B, 2B and 4 receptors were strongly expressed in benign and non-invasive cancer cells of patients and decreased in invasive malignant cells. Moreover, decreased expression of 5-HT2B strongly correlated to the dissemination of the disease [START_REF] Henriksen | Expresion of serotonin receptors 5-HT1A, 5-HT1B, 5-HT2B and 5-HT4 in ovary and in ovarian tumours[END_REF]. Two contradictory studies showed the differential expression of 5-HT receptors in HCC tissues and their corresponding non-tumor tissues, 2-HT2B being the only to be overexpressed in HCC in the two studies [START_REF] Shi | X. 5-Hydroxytryptamine promotes hepatocellular carcinoma proliferation by influencing β-catenin[END_REF][START_REF] Soll | Expression of serotonin receptors in human hepatocellular cancer[END_REF]. The action of serotonin on prostate carcinoma is mediated through several receptor subtypes that are present at various tumor stages. 5-HT2B receptor expression was associated with the initial stages of prostate tumor. A strong expression of 5-HT1A and 5-HT1B receptors was shown in PC with high grades. And 5-HT1A receptors were also demonstrated in PC cells metastasized to human lymph nodes and bones. 5-HT4 receptor expression was found predominantly in high-grade tumors suggesting that this receptor subtype may facilitate cell growth in an androgen-depleted environment [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF][START_REF] Dizeyi | Expression of serotonin receptors 2B and 4 in human prostate cancer tissue and effects of their antagonists on prostate cancer cell line[END_REF]. Thus, a systematic analysis of the modulation of serotonin receptor expression during progression of various cancers could be very instructive in order to develop an effective directed pharmaco-therapy.

5-Can serotonin system-directed pharmaco-therapy affect cancer progression?

Serotonin system might represent an interesting chemotherapeutic target for the prevention and treatment of several cancers in which therapeutic approaches are limited (hormone refractory prostate carcinoma, HCC, glioma and carcinoid syndrome) and in SCLC characterized by early metastases which cannot be surgically resected. Serotonin receptors, selective serotonin transporter (SERT) and serotonin synthesis pathways are potential molecular targets in cancer directed pharmaco-therapy. The pharmacology of serotonin and serotonin receptors is highly developed and numerous safe and effective serotonin-targeting drugs are available, some of them being currently used in the treatment of CNS disorders. In several in vitro studies, the notion of serotonin receptor-directed pharmaco-therapy has emerged (hormone refractory prostate carcinoma, carcinoma of the urinary bladder, breast cancer, SCLC, colorectal carcinoma and carcinoid). The results of these studies show that 5-HT receptor antagonists inhibit cancer cell growth through various effects (cell cycle arrest, cytotoxicity and tumor cells apoptosis). However, the use of serotonin receptor antagonists as anticancer agents in human is actually limited due to the side effects of these compounds [START_REF] Sarrouilhe | Serotonin and cancer: what is the link?[END_REF].

Octreotide LAR, which was known as an inhibitor of serotonin release and able to lengthen progression of well-differentiated metastatic NET has no effect on survival in patients with metastatic midgut NET (PROMID trial) [START_REF] Rinke | Placebo-Controlled, Double-Blind, Prospective, Randomized Study on the Effect of Octreotide LAR in the Control of Tumor Growth in Patients with Metastatic Neuroendocrine Midgut Tumors (PROMID): Results of Long-Term Survival[END_REF]. In patients with carcinoid syndrome and diarrhea not adequately controlled by octreotide, a TPH inhibitor, telotristat ethyl is currently developed in clinical trials to treat patients by reducing the serotonin production within the metastatic NE cells (TELECAST phase 3 trial) [START_REF] Pavel | Telotristat ethyl in carcinoid syndrome: safety and efficacy in the TELECAST phase 3 trial[END_REF].

The incidence of depression is greatly enhanced in patients with cancer and there is a debate about whether antidepressant medications must be avoided or are safe in patients with cancer [START_REF] Busby | Selective serotonin reuptake inhibitor useand breast cancer survival: a population based cohort study[END_REF][START_REF] Isenberg-Grzeda | Antidepressants appear safe in patients with carcinoid tumor: Results of a restrospective review[END_REF]. Indeed, SSRI, the most commonly prescribed drugs for treating depression, elevates the serotonin levels in the synaptic cleft by blocking serotonin re-uptake. As a side effect, higher levels of serotonin that result from SSRI antidepressant medication treatment could contribute to the growth of tumors. Interestingly, genetic variations in the SLC6A4 gene, which codes for the SERT, seem to contribute to poor survival in colorectal cancer patients [START_REF] Savas | Serotonin transporter gene (SLC6A4) variations are associated with poor survival in colorectal cancer patients[END_REF]. In contrast, fluoxetine, and a range of SSRIs, are known to have antiproliferative and cytotoxic effects at high concentrations in several cancer cells. Thus, the secondary mechanisms of action associated with these drugs began to be studied to repurposing them as first-line anticancer drugs or to combine them with standard chemotherapies [START_REF] Radin | A current perspective on the oncopreventive and oncolytic properties of selective serotonin reuptake inhibitors[END_REF].

Cancer Stem Cells (CSC) have recently been identified in several solid tumors, including prostate, breast, colon, ovary, pancreas and glioma. CSC are clonal tumor-forming chemotherapy and radiotherapy-resistant, indefinite self-renewing cells which are suggested to cause tumor relapse and metastasis. Using an in vitro approach, unanticipated results showed that a SSRI (sertraline), a 5-HT1B agonist (CGS-12066) and a 5-HT2C agonist (tegaserod) killed all glioma neural stem cell lines tested [START_REF] Pollard | Glioma stem cell lines expanded in adherent culture have tumor-specific phenotypes and are suitable for chemical and genetic screens[END_REF]. Therefore, future studies are needed to show if the development of specific therapies targeting the serotonin system in CSC could be used for treatment of resistant solid tumors.

6-Conclusion

What is the relevance to consider whether serotonin is involved in human cancer progression? Most of the results were obtained in vitro and proofs of principles are still needed in vivo for many tumors. With the exception of glioma and carcinoid cells, in which a strong stimulatory effect of serotonin on cell growth was observed in vitro, in many other studies, serotonin has a slight effect. The effects of serotonin on glioma CSC and on glioma cell proliferation, migration and invasion request further studies [START_REF] Merzak | Expression of serotonin receptors in human fetal astrocytes and glioma cell lines: a possible role in glioma cell proliferation and migration[END_REF][START_REF] Pollard | Glioma stem cell lines expanded in adherent culture have tumor-specific phenotypes and are suitable for chemical and genetic screens[END_REF]. The data available on the involvement of serotonin in the progression of carcinoid tumors and in the development of the carcinoid syndrome are more prevalent and an inhibitor of TPH is currently developed in trials to treat patients by reducing the serotonin production within the metastatic NE cells [START_REF] Pavel | Telotristat ethyl in carcinoid syndrome: safety and efficacy in the TELECAST phase 3 trial[END_REF].

The results of many studies showed that serotonin levels in the tumor play a crucial role in cancer progression and a serotoninergic autocrine loop is proposed in several cancers.

Serotonin produced by NE cells may also facilitate tumor recurrence and metastases and is correlated with poor prognosis and shortened patient survival. The crucial unsolved point in many studies is whether the serotonin concentration in the primary tumor or in the metastases is compatible with its involvement in cancer progression and angiogenesis.

Studies suggest that specific serotonin receptors are involved in different fundamental stages of carcinogenesis but also that serotonin receptor expression could change during this phenomenon (Fig. 1). Thus, a systematic analysis of the modulation of serotonin receptor expression during cancer progression would be instructive to develop an effective directed pharmaco-therapy. The use of serotonin receptor antagonists as anticancer agents in human is currently limited due to their side effects. Thus, the selective killing of a tumor cell population, without affecting normal tissues is a challenge for serotonin receptor-directed pharmaco-therapy. 5-HT1A receptor being involved in the growth of carcinoid and many human tumor types (prostate, bladder, SCLC, colorectal, cholangiocarcinoma), it would be of prime interest to develop novel molecules to target it specifically [START_REF] Corvino | The Role of 5-HT1A Receptor in the Cancer as a New Opportunity in Medicinal Chemistry[END_REF]. Likewise, in pancreatic cancer, which is one of the most lethal human cancers, targeting the 5-HT1B/1D receptors with new selective antagonists is a therapeutic option to be explored for the future [START_REF] Gurbuz | Down-Regulation of 5-HT1B and 5-HT1D Receptors Inhibits Proliferation, Clonogenicity and Invasion of Human Pancreatic Cancer Cells[END_REF]. 5-HTT gene, which codes for SERT, is epigenetically downregulated by histone deacetylases (HDAC) in several types of human cancer, suggesting that HDAC inhibitors, which are expected to decrease the serotonin levels in the micro-environment of the tumor cells, may be used for therapeutic purposes [START_REF] Phi Van | Histone deacetylase HDAC1 downregulates transcription of the serotonin transporter (5-HTT) gene in tumor cells[END_REF]. Moreover, the development of specific therapies targeted at serotonin system in CSC and the use of SSRIs as cytotoxic drugs could be a new hope for treating resistant tumors.

More in vivo studies are needed to explore the role of the serotoninergic system in cancer and to elucidate whether serotonin is a major factor or an epiphenomenon in tumor progression and its relevance as a chemo-therapeutic target.

Figure 1 :

 1 Figure 1: Expression of serotonin receptors in human cell lines and cancer biopsies according to tumor progression. * Expression in endothelial cells of the tumor vasculature.

Conflict of interest

None declared

Author contributions

DS wrote and edited the manuscript, conceived and designed the major ideas developed in the manuscript. MM prepared the figure and made substantial, direct and intellectual contribution to the work. All authors read and approved the final manuscript.

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