G M Cruz-Martinez

J-C Avila
email: jcavilav]@uaemex.mx

A Vilchis Gonzalez

S Abdelaziz
email: abdelaziz@lirmm.fr

P Poignet
email: poignet]@lirmm.fr

Design parameters influence on the static workspace and the stiffness range of a tensegrity mechanism

Keywords: Tensegrity mechanism, static workspace, stiffness range

This paper deals with the impact of the design parameters on the static workspace and the stiffness range of a planar 3-DoF tensegrity mechanism. The static model is established through the energetic approach and the stiffness is derived analytically along the 3-DoF of the mechanism. The design parameters considered here are the spring stiffness and the location of the mechanism attachment points to the base. Results on the impact of these parameters are finally analyzed. This analysis constitutes a first step towards the geometric optimization of tensegrity mechanisms.

Introduction

The term tensegrity was created by Richard B. Fuller as a union of 'tensional' and 'integrity' [START_REF]Synergetics, explorations in the geometry of thinking[END_REF]. A tensegrity structure is formed entirely by a combination of rigid and flexible elements. Its configuration stands by itself and maintains its form solely because its structural members (struts) are suspended in a network of tensional elements (cables or springs) [START_REF]Tensegrity Structures Form, Stability and Symmetry[END_REF]. Tensegrity structures are characterized by being light, deployable and of variable stiffness [START_REF] Azadi | Variable stiffness spring using tensegrity prisms[END_REF]. Working with these structures has been of interest for engineers and researchers since tensegrity applications range from mobile robotics [START_REF] Friesen | Ductt: a tensegrity robot for exploring duct systems[END_REF], manipulators [START_REF] Furet | Prototype of a tensegrity manipulator to mimic bird necks[END_REF][START_REF] Lessardand | A bio-inspired tensegrity manipulator with multi-dof, structurally compliant joints[END_REF] and robots in medical applications [START_REF] Boehler | Experiments on a variable stiffness tensegrity mechanism for an mr-compatible needle holder[END_REF].

Developing mathematical models (a kinematic one, for instance) for tensegrity mechanisms is challenging [START_REF] Henrickson | Shape control of tensegrity structures[END_REF][START_REF] Ji | Kinematics, singularity, and workspaces of a planar 4-bar tensegrity mechanism[END_REF][START_REF] Wenger | Kinetostatic analysis and solution classification of a planar tensegrity mechanism[END_REF] and requires to know the extension of flexible elements at all time so as to establish a relationship between the joint and the cartesian variables. If the measurement of these extensions is not available, static modeling is considered. Several methods have been proposed in the literature to determine the equilibrium configurations of tensegrity mechanisms [START_REF] Furet | Kinetostatic analysis and actuation strategy of a planar tensegrity 2-x manipulator[END_REF][START_REF] Manríquez-Padilla | Form-finding analysis of a class 2 tensegrity robot[END_REF]. Static workspace computation, using a continuous approach, has been proposed by [START_REF] Boehler | Definition and computation of tensegrity mechanism workspace[END_REF] for a 2-DoF tensegrity mechanism.

For the tensegrity mechanism reported in this paper, a potential energy approach is considered in order to determine stable equilibrium configurations based on the stiffness analysis. This paper is an attempt to understand the influence of one geometric parameter on static workspace and the stiffness range. The geometric parameter under observation concerns the mechanism attachment points. This analysis constitutes the first step towards the geometric optimization of tensegrity mechanisms.

This paper is organized as follow. The 3-DoF planar tensegrity mechanism is described in section 2. The respective static and stiffness models are presented in subsection 2.1. These models are synthesized using an energetic approach. The computation of the static workspace and stiffness range are presented in subsection 2.2. The impact of the design parameters on the static workspace and the stiffness range is finally discussed in section 3. Skelton [17], this mechanism is a class-1 tensegrity system. The actuators are connected to the bar, of length 2b, using cables and springs. The springs are considered here identical of stiffnesses k. The cables, attached to the bar on p 1 , are enrolled on pulleys fixed on A 1 and A 2 and are connected to springs before being enrolled on pulleys mounted on the actuators 1 and 2. The other two cables, attached to p 2 , are enrolled on pulleys fixed on A 3 and A 4 and are enrolled on pulleys mounted on the actuators 3 and 4.

Mechanism Description

p i = P + R m m p i (1)
with

R m = cos θ -sin θ sin θ cos θ Let's define 1 = a 1 -p 1 , 2 = a 2 -p 1 , 3 = a 3 -p 2 and 4 = a 4 -p 2
as the distances between the bar's attachment points and the different nodes.

The system initial configuration is defined when the position of the bar's center of mass coincides with the origin of the inertial reference frame and θ = 0. Initial tensions in the cables/springs have minima values. Initial lengths are determined according to equation 2.

0g = 0(g+1) = √ a 2 + b 2 g=1
for cables 1 and 2 (na) 2 + b 2 g=3 for cables 3 and 4

(2)

Due to the presence of springs and in order to determine the static configuration of the mechanism, an energetic approach is considered. It means that the first and second derivatives of the potential energy of the system U are used to establish the stable static equilibrium points. Equation 3 defines the total potential energy.

U = 4 ∑ h=1 1 2 ke 2 h ( 3
)
where e h is the elongation of the spring h that can be computed as in equation 4.

e h = ρ h + h -0h for h=1,2,3,4 (4)
with ρ h being the displacement of the cable h. It is computed as ρ h = rα h , where r is the radius of the actuator's pulley and α h is the angular position of the actuator h.

The static equilibrium of the bar is obtained by, simultaneously, solving the equations 5.

∂U ∂ x = 0, ∂U ∂ y = 0, ∂U ∂ θ = 0 (5)
A stable equilibrium configuration must satisfy inequalities in equation 6.

∂ 2 U ∂ x 2 > 0, ∂ 2 U ∂ y 2 > 0, ∂ 2 U ∂ θ 2 > 0 (6)

Characterization of the Static workspace and the Stiffness range

The static workspace of a tensegrity system is defined as the set of all stable equilibrium configurations that its end-effector is able to reach [START_REF] Boehler | Definition and computation of tensegrity mechanism workspace[END_REF], while taking into account the unilateral nature of the cables, i.e. The tensions in all the cables must remain positive.

Each point in the workspace has a minimum and maximum stiffness value. The range of stiffness for each point is computed by subtracting the maximum and the minimum stiffness values. In order to analyze the static workspace as well as the stiffness range of a tensegrity mechanism, as a function of design parameters, the tensions limits are considered identical in all the study.

The static equilibrium of the mechanism can be expressed in a similar way as for cable-driven parallel manipulators [START_REF] Gagliardini | Determination of a dynamic feasible workspace for cable-driven parallel robots[END_REF][START_REF] Gouttefarde | Wrench-feasible workspace of parallel cable-driven mechanisms[END_REF] in accordance with equation 7

Wτ = f (7)
where W represents a 3 × 4 wrench matrix that depends on the mechanism position P and its orientation θ . The tensions in the cables are identified by vector τ = [τ 1 , τ 2 , τ 3 , τ 4 ] T . The vector f represents the wrench applied to the mechanism by means of the cables tensions. The wrench matrix W is computed by Equation 8.

W = u 1 u 2 u 3 u 4 p 1 × u 1 p 1 × u 2 p 2 × u 3 p 2 × u 4 (8)
where u h represents the unit vector. Its direction is defined as the cable direction (cf. Fig 1). The tension in the cables must remain in between a minimum and a maximum values, respectively τ min and τ max . The stiffness range for a given stable equilibrium configuration is computed by varying the tensions in the cables without affecting the position and orientation of the mechanism. These tensions are computed as:

τ = W + f + Hλ (9)
where W W W + is the Moore-Penrose generalized inverse of W [START_REF] Roberts | On the inverse kinematics, statics, and fault tolerance of cable-suspended robots[END_REF]. H is a vector of dimension 4 × 1 whose column span the null space of W. λ is an arbitrary scalar. To keep a stable equilibrium configuration, the wrench f is considered equal to a null vector. The bounds of λ can be obtained by solving the inequality 10.

τ min ≤ Hλ ≤ τ max (10)
The bounds λ min and λ max allowing to compute two vector tensions solutions that enable to keep the equilibrium:

τ min = Hλ min τ max = Hλ max (11)
Using the vectors τ min and τ max , one can compute the minimum and maximum springs elongations. Solving the equation 4, can be calculated ρ min and ρ max both are vectors that contain the set of minimum and maximum displacements for each actuators. Now the minimum and maximum stiffness are computed using the equation 12 at a given pose of the mechanism (P, θ ) considering ρ min and ρ max .

K min x = ∂ 2 U(P, θ , ρ min ) ∂ x 2 , K min y = ∂ 2 U(P, θ , ρ min ) ∂ y 2 , K min θ = ∂ 2 U(P, θ , ρ min ) ∂ θ 2 K max x = ∂ 2 U(P, θ , ρ max ) ∂ x 2 , K max y = ∂ 2 U(P, θ , ρ max ) ∂ y 2 , K max θ = ∂ 2 U(P, θ , ρ max ) ∂ θ 2 (12)
3 Discussion of the results

This section show the estimation of the static workspace and stiffness range. The static workspace of the system describes the pose of the end-effector in the x,y coordinates and the orientation along z axis. The parameters of the mechanism that are used were: a = 0.1m, b = 0.1m, τ h ∈ [4, 10]N and ρ h ∈ 4 k , 10 k m.

The Fig. 2 shows the relationship between the size of the workspace and the spring stiffness values k. The first column shows the static workspace of the mechanism with n = 1 and k = 270 N/m and the second column shows the static workspace when n = 1 and k = 80 N/m. The black dots represent the end-effector in a stable equilibrium configuration that the mechanism can reach, the red line shows the mechanism's boundary of static workspace with k = 270 N/m. In the second column the green line shows the boundary of static workspace with k = 80 N/m and the red line is superimposed to highlight how the workspace is affected in relationship with the modification of the stiffness springs, noting that the value of k is inversely proportional to the static workspace. In order to analysis the influence of the geometrical parameters on the static workspace and stiffness range, here is presented the results when n = 1 (Fig. 1), n = 0.5 (Fig. 3a) and n = 0.1 (Fig. 3b). These variation of n causes that the symmetry in the y-axis be lost because the nodes A 3 , A 4 reducing the distance between them. The Fig. 4 illustrates the static workspace for the mechanism when n = 1, 0.5 and 0.1. The workspace for n = 1 has ranges from x ∈ (-0.2, 0.2)m, y ∈ (-0.2, 0.2)m and θ ∈ (-1.5, 1.5)rad. The shape is modified throughout the changes of n, this changes are described by the projections on the planes xy, yθ , xθ . The black dots represent the center of mass in a stable equilibrium configuration that the mechanism can reach, the red line shows the mechanism's boundary of static workspace with n = 1 and the green line shows the boundary of static workspace for n = 0.5 and n = 0.1 respectively. As the Fig. 4 pictures the workspace in xy is decreased as n decreases and is shifted to the other side where the attachment points joint. However for the workspace xθ who is showed in row 2 increases as n decreases. The largest workspace in the plane yθ is in the configuration with n = 0.5. The analysis of the stiffness range is shown below. The Fig. 5 shows the stiffness range for K x , the Fig. 6 shows the stiffness range for K y and the Fig. 7 shows the stiffness range for K θ . The workspace is depicted as a volume. In order to observe the behavior of stiffness, it has been discretized in layers. The first column of each figure represents the minimum stiffness and the second column shows the stiffness range, each point in the workspace has a color according to its value. The black line represents the boundary of the workspace with n = 1 and it is superimposed on all the graphs to show how the workspace changes. This tensegrity mechanism could be used as a puncture assistance robot [START_REF] Boehler | Experiments on a variable stiffness tensegrity mechanism for an mr-compatible needle holder[END_REF][START_REF] Bricault | Light puncture robot for ct and mri interventions[END_REF] because it allows stiffness modulation. The procedure requires that the effector has to be rigid when a needle is inserted in the body and in other moment it has to be soft allowing to follow the physiological movements such as breath.

To illustrate the application of the computation of the figures 5, 6 and 7, two desired stiffness ranges are selected according to a specific application: K x ≥ 30 N/m and K y ≥ 75 N/m. The Fig. 8 illustrates the workspace that satisfies the desired stiffness range, the first row shows K x with n = 1, 0.5 and 0.1 and the second row shows the workspace for K y desired with n = 1, 0.5 and 0.1. The workspace for the range K x is greater with n = 0.5 since it allows reach higher orientation values. The same behavior happens in the workspace for the range K y but the increase is more notorious in the mobility orientation with n = 0.5. Concluding that the biggest workspace that satisfies the design conditions for the application is with the geometrical parameter n = 0.5.

Conclusion

This paper shows the influence of the design parameters on the static workspace as well as in the stiffness range of a 3-DoF planar tensegrity mechanism. An extension of the approach analysis can be applied for tensegrity mechanism with more degrees of freedom. The analysis will help to design a geometric optimization approach that allows to define the location of the attachment points and to select the adequate springs in order to satisfy a required static workspace with a desired stiffness range.

Fig 1 shows a 1 -

 1 Fig 1 shows a 1-bar planar tensegrity mechanism driven by 4 actuators. According to the classification proposed bySkelton [17], this mechanism is a class-1 tensegrity system. The actuators are connected to the bar, of length 2b, using cables and springs. The springs are considered here identical of stiffnesses k. The cables, attached to the bar on p 1 , are enrolled on pulleys fixed on A 1 and A 2 and are connected to springs before being enrolled on pulleys mounted on the actuators 1 and 2. The other two cables, attached to p 2 , are enrolled on pulleys fixed on A 3 and A 4 and are enrolled on pulleys mounted on the actuators 3 and 4.

Fig. 1

 1 Fig. 1 Planar tensegrity mechanism

Fig. 2

 2 Fig. 2 Relationship between static workspace and variation of k

Fig. 3 A

 3 Fig. 3 A) Tensegrity mechanism with n=0.5, B) Tensegrity mechanism with n=0.1

Fig. 4

 4 Fig. 4 Static workspace when n = 1, 0.5 and 0.1

Fig. 5

 5 Fig. 5 The stiffness ranges K x n = 1, 0.5 and 0.1

Fig. 6 1 Fig. 7

 617 Fig.6The stiffness ranges K y with n = 1, 0.5 and 0.1

Fig. 8

 8 Fig. 8 Workspace using K x =30 N/m and K y = 75 N/m


Dan Oron
email: dan.oron@weizmann.ac.il

Eirini Papagiakomou

Vincent De-Sars

Valentina Emiliani

Arbitrary Two-Dimensional Multiphoton Excitation Patterns with Temporally Focused Digital Holograms

Keywords: Temporal focusing, Digital holography, Multiphoton microscopy

Multiphoton excitation has recently found application in the fields of bioimaging, uncaging and lithography. In order to fully exploit the advantages of nonlinear excitation, in particular the axial resolution due to nonlinearity, most systems to date operate with point or multipoint excitation, while scanning either the laser beam or the sample to generate the illumination pattern. Here we combine the recently introduced technique of scanningless multiphoton excitation by temporal focusing with recent advances in digital holography to generate arbitrarily shaped, depth resolved, two-dimensional excitation patterns completely without scanning. This is of particular importance in applications requiring uniform excitation of large areas over short time scales, such as neuronal activation by multiphoton uncaging of neurotransmitters. We present an experimental and theoretical analysis of the effect of spatial patterning on the depth resolution achieved in temporal focusing microscopy. It is shown that the depth resolution for holographic excitation is somewhat worse than that achieved for uniform illumination. This is also accompanied by the appearance of a speckle pattern at the temporal focal plane. The origin of the two effects, as well as means to overcome them, are discussed.

INTRODUCTION

Generation of complex three-dimensional optical excitation patterns is a requirement in many practical applications, including optical imaging, uncaging and lithography. Using currently available ultrafast light sources it is simple to localize optical excitation to a point via multiphoton excitation. By scanning this point of excitation (or the excited sample) it is possible to generate arbitrary three-dimensional excitation patterns. Indeed, this is the mode of operation of most multiphoton microscopes 1 and femtosecond lithography systems 2 to date. Such sequential point-by point scanning of the excitation is, nevertheless, a slow process, despite many attempts to improve scanning systems, for example by the use of acousto-optic deflectors. [START_REF] Lv | Construction of multiphoton laser scanning microscope based on dual-axis acousto-optic deflector[END_REF] For some applications such as uncaging of biologically active molecules, the scanning process may be too slow relative to the time scale of the probed process. This, combined with the fact that current-day laser sources typically provide orders of magnitude more power than needed for single-point excitation, is the main driving force behind the development of multiple-point excitation systems. [START_REF] Buist | Real-time two-photon absorption microscopy using multipoint excitation[END_REF][START_REF] Bewersdorf | Multifocal multiphoton microscopy[END_REF][START_REF] Fittinghoff | Widefield multiphoton and temporally decorrelated multifocal multiphoton microscopy[END_REF][START_REF] Nielsen | High efficiency beam splitter for multifocal multiphoton microscopy[END_REF] Generally, this involves splitting the original beam into several beamlets, each directed to a different point in space. Using beamsplitter arrays, for example [START_REF] Fittinghoff | Widefield multiphoton and temporally decorrelated multifocal multiphoton microscopy[END_REF][START_REF] Nielsen | High efficiency beam splitter for multifocal multiphoton microscopy[END_REF] this usually results in simple 1D or 2D arrays of illumination points.

Recently, the technique of temporal focusing was introduced as a wide-field continuous alternative to these multipoint excitation schemes. [START_REF] Oron | Scanningless depth resolved microscopy[END_REF] Temporal focusing relies on the utilization of geometrical dispersion to produce a short pulse at the image plane of the objective lens, while the pulse is temporally stretched before and after the focus. This concept is exemplified in Fig. 1. In time-multiplexed multipoint illumination systems the high peak intensity at the focal plane is due to spatial focusing of a pulse with a constant duration, as portrayed in Fig. 1a. In contrast, in temporal focusing (Fig. 1b) the nearly plane wave excitation pulse is split into its frequency components which are then combined in phase to generate a short pulse only at the focal plane. The standard setup for temporal focusing, shown in Fig. 2, includes a blazed reflection grating imaged by a high magnification telescope, comprised of a regular lens and an objective lens, onto the image plane. It was shown that for a 2D illuminated area the depth resolution afforded by temporal focusing is equivalent to that achieved by line-scanning, while for a 1D illuminated line (perpendicular to the grating lines), essentially combining temporal focusing with spatial focusing along one spatial dimension, depth resolution is equivalent to that of point scanning. [START_REF] Tal | Improved depth resolution in video-rate line-scanning multiphoton microscopy using temporal focusing[END_REF][START_REF] Zhu | Simultaneous spatial and temporal focusing of femtosecond pulses[END_REF] These two cases have a closed-form analytic solution. However, in many practical applications one would like to utilize arbitrary 2D excitation patterns. Since temporal focusing relies on imaging of the grating onto the sample, it is reasonable that spatial patterning of the excitation beam on the grating, as schematically shown in Fig. 2, should result in similarly patterned excitation on the sample, in a similar manner to a mask being imaged onto a sample in optical lithography. The effects of such spatial patterning towards control over the in-plane excitation pattern have not yet been explored. However, it was recently shown that temporal pulse shaping can be used to control the axial response in temporal focusing. 11

EXPERIMENTAL REALIZATION OF TEMPORALLY FOCUSED DIGITAL HOLOGRAMS

In attempting to apply temporal focusing with spatially shaped excitation two possible experimental realizations come into mind. the first utilizes amplitude shaping, whereby a spatial amplitude filter is imaged onto the grating surface. While this results in a flat phase front of the excitation pulse, its main drawback is the inefficient utilization of the excitation pulse energy, most of which is blocked. An alternative realization is by the use of Fourier synthesis, whereby a spatial phase filter is Fourier transformed onto the grating surface. Using an appropriate optimization algorithm for the phase pattern (e.g. Gerchberg-Saxton 12 ), the excitation light is efficiently converted to the required intensity pattern. Here we explore the latter scheme both experimentally and theoretically, determining the effect of holographic illumination on both the excitation pattern and on the axial resolution.

Experimental setup

The experimental realization for the spatiotemporal control of holographic patterning is schematized in Figure 3.

As a light source we used a mode-locked Ti:Sapphire laser (Tsunami, Spectra-Physics; λ=780nm, Δλ=12nm), whose output beam power was controlled by a liquid crystal variable phase-retarder (Meadowlark Optics, LRC-200-IR1) combined with a polarizer cube (Meadowlark Optics, BB-050-IR1). The beam was spatially expanded (10x) to match the input window of a LC-SLM (PPM -Programmable Phase Modulator -X8267-13, Hamamatsu The grating is aligned perpendicular to the optic axis of a high magnification telescope comprised of a lens and a microscope objective. The excitation beam impinges on the grating at an angle α such that the center wavelength is diffracted towards the optic axis. An arbitrary pattern is projected on the grating, either via amplitude or phase-and-amplitude shaping. For the latter, the excitation beam is shaped by a spatial light modulator followed by a Fourier lens.

Photonics K.K.), which operates in reflection mode. The wave front of the beam at the SLM plane was modified by using a custom-designed software that, given a target intensity distribution at the focal plane of the microscope objective, calculates with an iterative Fourier transform algorithm (IFTA) [START_REF] Gerchberg | A pratical algorithm for the determination of the phase from image and diffraction pictures[END_REF] the corresponding phase-hologram. [START_REF] Lutz | Holographic photolysis of caged neurotransmitters[END_REF] After diffraction by the LC-SLM, typically 50% of the incoming beam goes in the first (+1) order and the rest is distributed among the zero order and higher order components. A phase grating was introduced in phase holograms so as to spatially displace the +1 from the zero order spot. The pulse width after reflection by the SLM was 140fs. The beam reflected from the SLM was Fourier transformed by a 1000 mm focal length achromatic lens (f 0 ) and formed a first image of the target intensity onto a blazed reflectance grating (830 l/mm) placed at the focal plane of L1 and aligned perpendicular to the optical axis of the microscope. An illumination angle of α = 40.5 o was chosen such as the +1 order diffracted beam ( 70% of the incoming beam) at the center frequency of the excitation pulse was directed along the optical axis of the microscope. The grating dispersed the various frequency components of the pattern, which were imaged onto the sample via a telescope comprised of an achromatic lens (f 1 =500 mm focal length) and the microscope objective (Olympus, LUMPLFL60xW/IR2, NA 0.90). This gave rise to a depth-resolved temporally focused excitation pattern at the focal plane of the objective whose lateral spatial distribution was a reduced (≈ 1/170) replica of the pattern generated on the grating. Two-photon holographic patterns were used to excite emission from a 0.9μm thick spin-coated fluorescent layer of Rhodamine in PMMA that was collected by a second objective (Olympus, UPLSAPO60xW, NA 1.20) placed opposite to the excitation one. [START_REF] Lutz | Holographic photolysis of caged neurotransmitters[END_REF] The use of two independent objectives allowed one to straightforwardly image out of focus planes of the excitation volume and therefore to precisely derive the axial propagation of the excitation beam around the objective focal plane (see below). The fluorescence was imaged by a tube collection lens (f tl =150 mm) to a CCD camera (CoolSNAP HQ2, Roper Scientific). To reject the excitation light, an emission filter (Chroma Technology HQ 535/50M) and a dichroic filter (Chroma Technology 640DCSPXR) were placed in front of the CCD camera.

Numerical simulations

Existing calculations on various effects in temporally focused illumination in the geometry shown in Fig. 2 have generally assumed spatially homogeneous, or at least smooth, illumination patterns. In order to calculate excitation patterns with arbitrary phase-and amplitude-modulated excitation we assume a given complex excitation pattern A(x, y) which is frequency independent impinging upon the grating at an angle such that the central frequency of the pulse is diffracted perpendicular to the grating surface for plane-wave illumination. The excitation pulse spectrum is then discretized, and the propagation from the grating to the image plane is solved separately for each spectral component using the angular spectrum of waves approach, [START_REF] Goodman | Introduction to Fourier Optics[END_REF] taking into account the finite aperture of the objective lens. This yields a four-dimensional distribution of complex field amplitudes A image (x, y, z, ω). For each point this is Fourier transformed back into time domain to obtain A image (x, y, z, t), which is then integrated to yield the TPEF intensity according to equation 1. All calculations were scalar, practically assuming a linear polarization of the excitation beam.

I T P EF (x, y, z) = ∞ -∞ dt |A image (x, y, z, t)| 4 (1)
The calculations described in the following were performed using the experimental conditions described above, and using the following parameterizations: For the 2D case the calculation was performed for a 100μm x 100μm area in the XY plane, where the size of each pixel was approximately 0.25μm. Along the propagation direction each pixel was 0.5μm. The pulse spectrum, with a FWHM of 8.5nm, centered at 780nm, was discretized in the calculation to 61 colors spaced in wavelength by about 0.25nm.

The results are, of course, quite general in their applicability to other focusing condition, using the simple scaling of temporal focusing with the excitation numerical aperture. 10, 15

Experimental results

In order to test the possibility of generating depth-resolved arbitrary patterns we consider the simple case of excitation of sharply defined circles of several diameters generated by an IFTA algorithm. [START_REF] Gerchberg | A pratical algorithm for the determination of the phase from image and diffraction pictures[END_REF] The observed excitation patterns in the focal plane, as imaged onto the camera are shown in Fig. 4a. As can be seen, a circular pattern is observed, but it suffers from significant speckle, which is generally not observed in temporal focusing with "smooth" excitation patterns. The appearance of speckle is partly related to the algorithm and to imperfections of the SLM device, but is reinforced by the fact that in the last part of the propagation (from the grating to the objective) a significant portion of the excitation light is diffracted outside the back aperture of the illumination objective. The latter effect is related to rapid phase variations of the illumination beam on the grating, enhancing the formation of dark areas. The relationship between this speckle pattern and the axial resolution will be discussed in the following section.

The axial response of the integrated fluorescence over the entire plane, obtained by moving the relative positions of the excitation objective and the thin fluorescent layer, is shown in Fig. 4b for all three cases. As can be seen, the axial response does not significantly depend on the details of the shape. The observed FWHM of the axial response was 5.5 ± 0.4μm, and the decay at the wings scales as 1/z, as is observed in previous realizations of widefield temporal focusing microscopy, having uniform illumination. [START_REF] Oron | Scanningless depth resolved microscopy[END_REF] The axial resolution is, nevertheless, somewhat worse than in this latter case, where we measured (using the same setup but a uniform illumination on the grating, bypassing both the SLM and the Fourier lens), an axial resolution of 3.2μm. To account for this, let us compare these results with those obtained from full numerical simulations of phase-modulated excitation patterns.

Comparison with simulations

As discussed previously, determination of the axial response for a phase modulated excitation pulse, as in the case of the excitation profile of a digital hologram, is more complex than that of excitation with slowly varying excitation patterns. Indeed, as long as the phase varies smoothly (that is, there is little phase variation over a distance of the magnified diffraction limited spot) the temporal focusing process should be hardly affected. Rapid phase variations lead, however, to broadening of the distribution of scattering angles for each color. This both interferes with the geometrical dispersion which lies at the basis of the temporal focusing process and results in significant scattering of light outside the back aperture of the objective lens, generating a speckle pattern at the image plane. The limit of pure phase modulation has previously been discussed both theoretically 8 and experimentally [START_REF] Tal | Transformation from an ultrashort pulse to a spatiotemporal speckle by a thin scattering surface[END_REF] for the case of head-on excitation through a diffuser (which replaces the grating). It was shown that this results in generation of spatiotemporal speckle at the image plane, stretching, along the propagation direction, to a distance of the order of the spatial extent of the undistorted pulse cτ pulse (For high NA excitation).

Here we analyze numerically the case of a grating illuminated with a rapidly varying phase pattern. For generality, we show here a calculation for a purely random phase (where the intensity at the grating surface was maintained constant but the phase was randomly chosen between 0 and 2π for every region corresponding to a demagnified pixel of 0.25x0.25μm 2 ).

The calculated two-photon image at the focal plane is shown in Fig. 5a. As can be seen, a speckle pattern with rather isolated peaks is generated. The corresponding z response curve is shown in Fig. 5b (solid blue line). It shows a 4.5μm FWHM axial response which is broader than the 3.3μm one obtained for a pure intensity modulation (dashed red line). Clearly the case of a purely random phase modulation is an extreme limit of the holographic illumination patterns presented above. Nevertheless, both the speckle pattern and the decrease in the axial resolution appear in good agreement with the experimental results presented in Fig. 4. Moreover, simulations using the initial conditions of the experiments shown in Fig. 4 (not shown here) yield a similar axial response, highlighting the fact that the holographic beams resemble random phase patterns in many aspects. The main difference between purely random phase and the holographic beams is that the fraction of the excitation light which is coupled into the objective is significantly smaller in the former case.

DISCUSSION

We now consider in more detail the origin of both the appearance of a speckle pattern and of the broadening of the axial response. The speckle pattern has to do with the diffraction efficiency from the grating into the objective back aperture. For a locally "smooth" phase, a case analogous to the standard realization of temporal focusing, most of the light is diffracted to within the objective back aperture. Similarly, where the phase of the excitation beam varies rapidly (on the scale of the demagnified diffraction limited spot on the grating), much of it will be diffracted outside the objective back aperture. Hence, the observed intensity peaks, corresponding to most of the generated two-photon signal, arise from regions on the grating where the phase pattern is rather smooth. Since locally within these regions the depth resolution comparable with "standard" temporal focusing (corresponding to line scanning) the overall axial response is only slightly broader than in the case of a plane wave impinging on the grating. The small broadening, as observed in Fig. 5b, is due to the presence of some background spatiotemporal speckle (arising from regions with rapid phase variations). [START_REF] Tal | Transformation from an ultrashort pulse to a spatiotemporal speckle by a thin scattering surface[END_REF] While for some applications the elimination of speckle from the temporally focused image is unnecessary (for example, in uncaging experiments where the diffusion of the uncaged compounds exceeds the spacing between adjacent speckle peaks), in others it may be important. One possible route to this end is to average over many randomized speckle patterns, for example by introducing a rapidly varying random phase pattern (i.e. a rotating diffuser) after the grating. To generate random patterns the diffuser has to be placed at a distance such that the angular scattering of the diffuser effectively shifts the excitation pattern on the grating by more than a diffraction limited spot, corresponding to L * θ d ≈ M * λ/2/N A (where M is the temporal focusing telescope magnification), corresponding to several centimeters in our case. An experimental demonstration of this type of smoothing can be found in Papagiakomou et al. [START_REF] Papagiakoumou | Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses[END_REF] Overall, the combination of temporal focusing with digital holography offers new paths for generation of controlled depth resolved excitation patterns. Where necessary, the speckle patterns appearing in these experiments can be mitigated by averaging (with possible applications in both multiphoton microscopy and ultrafast lithography). The presented scalar theory based on the angular spectrum of waves approach accounts well for the observations in the experiments. We expect that the combination of digital holography with temporal pulse shaping and with polarization modulation can enable further control over the spatial distribution of multiphoton excitation.

Figure 1 .

 1 Figure1. a) Pulse evolution in standard multiphoton imaging based on spatial focusing. The pulse is focused as it propagates through the sample, but its duration remains unchanged. b) Pulse evolution in temporal focusing based multiphoton microscopy. The pulse becomes shorter as it propagates through the sample, reaching its shortest duration at the temporal focal plane, but its spatial profile remains unchanged.

Figure 2 .

 2 Figure2. Setup used for temporal focusing. The grating is aligned perpendicular to the optic axis of a high magnification telescope comprised of a lens and a microscope objective. The excitation beam impinges on the grating at an angle α such that the center wavelength is diffracted towards the optic axis. An arbitrary pattern is projected on the grating, either via amplitude or phase-and-amplitude shaping. For the latter, the excitation beam is shaped by a spatial light modulator followed by a Fourier lens.

Figure 3 .

 3 Figure 3. Experimental setup for temporal focusing with holographic beam excitation. The phase pattern imprinted by the SLM is Fourier transformed onto the grating. The two-photon fluorescent emission from the temporal focal plane is imaged onto a CCD camera in transmission mode.

Figure 4 .

 4 Figure 4. Images of a thin fluorescent layer placed at the temporal focal plane, illuminated by a temporally focused holograms designed to generate full circles of diameters 10μm, 20μm, 30μm, (left). Z-dependence of the integrated emission for all three cases (solid blue, dashdotted green and dashed red lines, respectively), exhibiting a nearly shapeindependent axial response (right).

Figure 5 .

 5 Figure 5. TPEF intensity pattern (a) and calculated depth response (b) for an illumination pattern with random phase. The observed FWHM depth response of 4.5μm (solid blue line) is broader than the 3.3μm FWHM response observed for the case of a constant phase (dashed red line).

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domain: spi phys

text:
P Bourdon
email: pierre.bourdon@onera.fr

J Le Gouët

D Goular

L Lombard

A Durécu

Coherent Combining with Active Phase Control: A Practical Tool for Adaptive and Nonlinear Optics (Invited paper)

Keywords: laser, coherent combining, adaptive optics, nonlinear optics, frequency converter I

Coherent beam combining with active phase control is more than a simple laser power scaling technique. It can also be used to perform more efficient adaptive optics and to extend the capabilities of nonlinear optical devices. In a first part of this paper, an optimized tiled-aperture configuration for coherent adaptive optics is described. In a second part, coherent combining of frequency converters emitting in the mid-infrared is demonstrated and results presented. Finally, the challenges for optical parametric oscillators combining are discussed.

INTRODUCTION

Coherent beam combining with active phase control is a convenient method commonly used to power scale laser sources, far above their limitations due to thermal and nonlinear effects as well as damage threshold. But it's a far more versatile technique than just a way to deliver very high laser power. It can also be used as an adaptive optics tool to compensate for turbulence effects during atmospheric propagation of laser beams. Another usage is the combination of wavelength converters such as optical parametric oscillator or more generally nonlinear optics based frequency converters.

In this paper, adaptive optics (AO) configurations of coherent beam combining are proposed and detailed. The capability of AO configurations to overcome the anisoplanetism limitations of standard adaptive optics is discussed. In a second part of the paper, recent results on coherent combining of mid-infrared wavelength frequency converters are presented. Finally, the challenges presented by the coherent combination of optical parametric oscillators are detailed.

II. LASER COMBINING TECHNIQUES FOR POWER SCALING

To overcome solid-state laser power scaling limitations, either thermal effects, damage threshold, nonlinear effects, laser combining techniques are available to perform efficient addition of laser power emitted by multiple laser amplifiers. A record 105 kW power has been achieved in 2009, combining 7 15-kW slab amplifiers [START_REF] Mcnaught | 100 kW coherently combined slab MOPAs[END_REF] . Multiple multi-kilowatt combining demonstrations have been done.

There are many techniques to combine lasers. Benchmarking of these techniques is generally based on a criterion of efficiency of the combining process, which is the ratio between the available combined power vs. the total power emitted by the N combined lasers. Obviously, the objective of laser combining techniques is to achieve close to 100 % efficiency.

Two very effective techniques for combining laser sources are spectral combining, an incoherent combining approach based on wavelength multiplexing. A 30 kW record has been achieved spectrally combining 96 high power fiber lasers into a single beam with a very high efficiency [START_REF] Honea | Advances in fiber laser spectral beam combining for power scaling[END_REF] .

Coherent combining with active phase control is another efficient technique. Active phase control uses very fast waveguide electro-optic phase modulators with bandwidth going up to 40 GHz for the fastest ones. These components can be all-fibered and lead to very compact and rugged configurations of high power laser sources.

The most practical near-field geometry is the tiled-aperture configuration, where the laser ouput optical apertures are placed side-by-side. The laser beams propagate to the far field where they can interfere, generating a very intense central lobe in the interference pattern if the interference process is constructive. Phase-locking the lasers is needed to achieve such constructive interference in the far field.

III. COHERENT ADAPTIVE OPTICS WITH BEAM COMBINING

The tiled aperture configuration for coherent combining offers a unique design to power scale laser sources without dramatically increasing the power density, mitigating the risk of damaging optical elements placed at the output of the combined laser source.

In such a near-field geometry, as the surface of the tiledaperture grows with the number of combined lasers, the power density can be kept below the critical level of optical damage threshold. For this reason, this near-field geometry is often preferred, especially when dealing with multi-kilowatt power levels.

But just as a deformable mirror offers control of the optical wavefront in adaptive optics, the tiled-aperture configuration coupled with active phase control of each optical aperture gives access to a similar wavefront control.

Different approaches are used to lock in phase the lasers. Vorontsov et al. [START_REF] Weyrauch | Experimental demonstration of coherent beam combining over a 7 km propagation path[END_REF] demonstrated turbulence compensation over 7 km range with such a configuration, using an Stochastic Parallel Gradient Descent algorithm to optimize the phase shift distribution and compensate for wavefront distortion induced by atmospheric turbulence. The phase shift distribution optimization criterion is in this case the intensity back reflected by a target placed in the far-field, 7-km away from the laser.

Onera also demonstrated this capability on a reduced scale, in the laboratory, generating artificial atmospheric turbulence using a hot air blower. But an interesting configuration where frequency-tagging was implemented and backscattered light provided the feedback from the target was proposed 4 (see Fig. 2). The main advantage of this approach is its high phase difference sensitivity, as frequency-tagging provides an error signal evolving linearly with the phase differences between the combined lasers. In these experiments, it was shown experimentally that proper detection configuration of the backscattered signal coming back from a remote surface allowed for target-in-theloop coherent combining in a configuration that is not limited by anisoplanetism, a classical limitation in adaptive optics. Anisoplanetism is induced by a slightly different optical path for the wavefront sensing function and the wavefront control function of the adaptive optics system. Detailed explanation on the way of operation of this frequency tagging approach will be given.

IV. COHERENT COMBINING OF FREQUENCY CONVERTERS

Nonlinear optical processes resulting in frequency conversion, such as second harmonic generation (SHG), difference frequency generation (DFG) and optical parametric amplification rely on a phase-matching condition needed for the process to achieve maximum conversion efficiency. This phase-matching relation allows for indirect phase control of a nonlinear frequency converter and for coherent combining of the converted waves controlling the phase of the fundamental or pump waves with standard high bandwidth, high performance all-fiber electro-optic phase modulators.

Former results obtained combining SHG 5 are presented to demonstrate how frequency converter CBC operates and its capability and limitations. The conditions for simultaneous combining of the fundamental and harmonic waves are explained.

The proper way to perform indirect control in the case of these 3-wave coupling process like DFG is explained [START_REF] Odier | Coherent combining of fiber-laser-pumped 3.4µm frequency converters[END_REF] . Wavelength control has to be obtained using injection seeding and indirect phase control can be achieved using the phase offset relation, just as in the case of the 2-wavelength process of SHG (see Fig. 3). CBC efficiency is discussed as well as the capability for simultaneous pump and idler wave combining. It is shown that for these 3-wavelengths processes, such simultaneous combining is rarely achieved.

Optical parametric oscillators (OPO) combining is discussed next. The presence of a laser cavity in an OPO adds an additional degree of complexity and difficulty to achieve CBC, especially for pulsed OPO.

Final part of this talk is dedicated to discussion of the conditions allowing for OPO CBC and the challenges yet to overcome.

V. CONCLUSION

Thanks to their versatility, some laser combining techniques are much more than just a tool for power scaling lasers.

This paper elaborates on how coherent beam combining with active phase control can be used to perform anisoplanetic adaptive optics and to power scale not only lasers, but also nonlinear optical devices.

Figure 1 .

 1 Figure 1. Schematic of a typical configuration for coherent combining fiber laser sources with active phase control.

Figure 2 .

 2 Figure 2. Coherent adaptive optics configuration using frequencytagging TIL CBC.

Figure 3 .

 3 Figure 3. Example of coherent combining of difference frequency generators configuration.


Victor Naimi

David Peyre-Costa

Alexandra Macgregor

Delphine Capdevielle

Jérôme Attal
email: j-attal@chu-montpellier.fr

Keywords: transcranial magnetic stimulation, treatment-resistant depression, naturalistic, lowfrequency rTMS, high-frequency rTMS

Background: Repetitive transcranial magnetic stimulation (rTMS) is an effective therapy for treatmentresistant depression. High-frequency (HF) rTMS over the left prefrontal dorsolateral cortex is the most frequently used protocol, low-frequency (LF) rTMS over the right DLPFC seems to be as effective.

Objective: In Montpellier university hospital, patients were first treated with LF-rTMS, and switched to HF-rTMS if they did not respond. A 6-months maintenance treatment was available for the responders.

The aim of this study was to assess the efficacy of this protocol. Methods: 119 patients with treatmentresistant depression were treated between 2009 and 2020. Primary outcome was remission rate according to MADRS. Secondary outcomes were response and remission rates according to MADRS and BDI at the end of treatment, at the end of LF-protocol, and at the end of HF-protocol for patients who did not respond to LF. Clinical and demographic characteristics were analysed as potential predictor of response. Results: Response and remission rates were 47.6 and 22.9 % at the end of treatment, 31 and 17 % at the end of LF-protocol, 38.9 and 12.2 % at the end of HF-protocol. None of the baseline variables were found to be associated with a better response. Among patients who benefited from maintenance treatment, around 50% had relapsed at 6 months. Conclusion: These results encourage changing rTMS protocol in case of non-response to a first-line treatment, and highlight the benefits of maintenance treatment.

Aux membres de mon jury

Merci au Professeur Capdevielle, pour avoir accepté de présider ce jury, pour votre participation et votre supervision bienveillante de ce travail.

Merci au Professeur Guillaume, pour avoir accepté de faire partie de mon jury, pour votre soutien et votre bienveillance.

Merci au Dr Attal, pour m'avoir permis de travailler sur cet article et aidé à toutes les étapes de sa rédaction, parfois à des heures tardives et même le week-end, pour ta réactivité et ta disponibilité.

A ma famille

A mes parents, Garance, Alix, à mes grand-mères, pour votre soutien depuis de longues années, pour votre amour et votre présence, même à distance. J'aurais aimé que vous puissiez assister à cette soutenance, si la situation sanitaire l'avait permis.

A mes amis

Merci aux anciens, Adrien, Rémi, Christophe, Alix, Claire, François, Jordane, Jonathan, Manu, Marie, Mario, Matthieu, Pierre-Alexandre, Nathalie, Olivier, Thomas, toujours aussi présents après plus de 10 ans d'amitié, et pour encore longtemps j'espère.

Merci à mes amis d'externat, Malik, Albane, Nicolas, Simon, Nicolas, Louis, Olivier, Adrien, Camille, Adama, Richard, Vicky, Victor, Joël, Hélory, Julien, Edmat, pour ces moments conviviaux passés et à venir. A Mathilde pour ta présence et ton soutien pendant ces années.

Merci à mes amis rencontrés au cours de mon internat, qui m'ont permis d'apprécier cette période. A Victor, Rémy, Meryem, Inès, Marie, Eléonore, Ali, Jacques, à Clémentine pour ta joie de vivre et ta motivation permanente. A mes anciens et actuels colocataires et amis, Julien, Lionel, Aurèle, Valérian, Charles. A David, pour ton aide plus que précieuse pour la réalisation de cet article. A Daniel, pour ces stages passés ensemble, et pour ton aide dans toutes les démarches de thèse, sans toi j'aurais eu beaucoup de mal à soutenir aujourd'hui.

A Lucile

Une très belle rencontre, merci d'avoir été à mes côtés ces dernières semaines, de m'avoir soutenu au cours de mon travail et d'avoir rendu plus facile ces moments.

A mes chefs

Merci à tous les chefs que j'ai rencontrés au cours de ma formation et qui m'ont permis d'apprendre, de progresser, m'ont apporté des visions complémentaires de la psychiatrie, pour leur soutien. Merci en particulier à Thomas Gibon, Fred Coppola, Radu Florea, l'équipe des urgences, l'équipe du SUPA, pour ce que vous m'avez apporté en clinique et en savoir-être.

Aux équipes

Merci aux infirmiers, aides-soignants, et autres membres des équipes que j'ai rencontrés au cours de mon internat.

INTRODUCTION

Depression is a common mental health disorder, with an estimated lifetime prevalence of 15 to 20% [START_REF] Kessler | Lifetime prevalence and ageof-onset distributions of DSM-IV disorders in the National Comorbidity Survey Replication[END_REF].It is a major cause of disability worldwide, and can increase morbidity and mortality.

Antidepressant medications are the first-line treatment for moderate to severe depressions, but it is estimated that a significant number of patients do not respond to these medications [START_REF] Rush | Acute and Longer-Term Outcomes in Depressed Outpatients Requiring One or Several Treatment Steps: A STAR*D Report[END_REF], making them candidates to neuromodulation procedures, electroconvulsive therapy (ECT) and repetitive transcranial magnetic stimulation (rTMS). Being the most studied, rTMS, even if less effective than ECT [START_REF] Eranti | A Randomized, Controlled Trial With 6-Month Follow-Up of Repetitive Transcranial Magnetic Stimulation and Electroconvulsive Therapy for Severe Depression[END_REF][START_REF] Berlim | EFFICACY AND ACCEPTABILITY OF HIGH FREQUENCY REPETITIVE TRANSCRANIAL MAGNETIC STIMULATION (rTMS) VERSUS ELECTROCONVULSIVE THERAPY (ECT) FOR MAJOR DEPRESSION: A SYSTEMATIC REVIEW AND META-ANALYSIS OF RANDOMIZED TRIALS: Review: High Frequency rTMS versus ECT for Major Depression[END_REF], has the advantage of being better tolerated and not requiring general anesthesia.

Unipolar resistant depression is commonly defined as the absence of response to two well conducted antidepressants from two different classes. There is no definition of bipolar pharmacoresistant depression, but a recent British expert group published a consensus, defining bipolar pharmacoresistant depression as the absence of response to two lines of well conducted treatments [START_REF] Hidalgo-Mazzei | Treatment-resistant and multi-therapy-resistant criteria for bipolar depression: consensus definition[END_REF]. Treatmentresistant depression (TRD) has a mortality rate increased by 35% compared to non-resistant depression [START_REF] Reutfors | Mortality in treatmentresistant unipolar depression: A register-based cohort study in Sweden[END_REF]. It is therefore a major public health issue.

Repetitive transcranial magnetic stimulation is a non-invasive neuromodulation process, which creates a magnetic field with a coil, inducing neuronal depolarization. For the treatment of depression, mainly two stimulation methods are used: high frequency (HF) over the left dorsolateral prefrontal cortex (DLPFC) or low-frequency (LF) over the right DLPFC. Several meta-analysis of multiple randomized control trials [START_REF] Berlim | A systematic review and meta-analysis on the efficacy and acceptability of bilateral repetitive transcranial magnetic stimulation (rTMS) for treating major depression[END_REF][START_REF] Zhang | Bilateral repetitive transcranial magnetic stimulation for treatment-resistant depression: a systematic review and meta-analysis of randomized controlled trials[END_REF][START_REF] Berlim | Clinically Meaningful Efficacy and Acceptability of Low-Frequency Repetitive Transcranial Magnetic Stimulation (rTMS) for Treating Primary Major Depression: A Meta-Analysis of Randomized, Double-Blind and Sham-Controlled Trials[END_REF][START_REF] Berlim | High-Frequency Repetitive Transcranial Magnetic Stimulation Accelerates and Enhances the Clinical Response to Antidepressants in Major Depression: A Meta-Analysis of Randomized, Double-Blind, and Sham-Controlled Trials[END_REF][START_REF] Kozel | Meta-Analysis of Left Prefrontal Repetitive Transcranial Magnetic Stimulation (rTMS) to Treat Depression[END_REF][START_REF] Schutter | Quantitative review of the efficacy of slow-frequency magnetic brain stimulation in major depressive disorder[END_REF][START_REF] Lam | Repetitive Transcranial Magnetic Stimulation for Treatment-Resistant Depression: A Systematic Review and Metaanalysis[END_REF][START_REF] Berlim | Response, remission and drop-out rates following high-frequency repetitive transcranial magnetic stimulation (rTMS) for treating major depression: a systematic review and meta-analysis of randomized, double-blind and shamcontrolled trials[END_REF][START_REF] Allan | Transcranial Magnetic Stimulation in the Management of Mood Disorders[END_REF][START_REF] Nguyen | The efficacy of repetitive transcranial magnetic stimulation (rTMS) for bipolar depression: A systematic review and metaanalysis[END_REF][START_REF] Wei | Meta-analysis of the Efficacy and Safety of Repetitive Transcranial Magnetic Stimulation (rTMS) in the Treatment of Depression[END_REF][START_REF] Mutz | Comparative efficacy and acceptability of non-surgical brain stimulation for the acute treatment of major depressive episodes in adults: systematic review and network meta-analysis[END_REF][START_REF] Brunoni | Repetitive Transcranial Magnetic Stimulation for the Acute Treatment of Major Depressive Episodes: A Systematic Review With Network Meta-analysis[END_REF][START_REF] Leggett | Repetitive Transcranial Magnetic Stimulation for Treatment-Resistant Depression in Adult and Youth Populations: A Systematic Literature Review and Meta-Analysis[END_REF][START_REF] Liu | Repetitive transcranial magnetic stimulation as an augmentative strategy for treatment-resistant depression, a meta-analysis of randomized, double-blind and sham-controlled study[END_REF][START_REF] Gaynes | Repetitive transcranial magnetic stimulation for treatment-resistant depression: a systematic review and meta-analysis[END_REF]) have demonstrated the superiority of rTMS over sham-stimulation, in unipolar and bipolar treatment-resistant depression.

However, there are only few naturalistic studies, evaluating efficacy of rTMS in treatment-resistant depression in routine clinical practice. Their results are consistent with randomized controlled trials, with response rates between 30 and 60 % in most of the studies [START_REF] Dunner | A Multisite, Naturalistic, Observational Study of Transcranial Magnetic Stimulation for Patients With Pharmacoresistant Major Depressive Disorder: Durability of Benefit Over a 1-Year Follow-Up Period[END_REF][START_REF] Taylor | A naturalistic, multi-site study of repetitive transcranial magnetic stimulation therapy for depression[END_REF][START_REF] Mcgirr | Effectiveness and acceptability of accelerated repetitive transcranial magnetic stimulation (rTMS) for treatmentresistant major depressive disorder: An open label trial[END_REF][START_REF] Berlim | High frequency repetitive transcranial magnetic stimulation as an augmenting strategy in severe treatment-resistant major depression: A prospective 4-week naturalistic trial[END_REF][START_REF] Fitzgerald | Naturalistic Study of the use of Transcranial Magnetic Stimulation in the Treatment of Depressive Relapse[END_REF][START_REF] Fukuda | Repetitive Transcranial Magnetic Stimulation for depression relapse or recurrence: Naturalistic retreatment series outcomes[END_REF][START_REF] Carpenter | TRANSCRANIAL MAGNETIC STIMULATION (TMS) FOR MAJOR DEPRESSION: A MULTISITE, NATURALISTIC, OBSERVATIONAL STUDY OF ACUTE TREATMENT OUTCOMES IN CLINICAL PRACTICE: Research Article: An Observational Study of TMS[END_REF][START_REF] Ciobanu | rTMS for pharmacoresistant major depression in the clinical setting of a psychiatric hospital: Effectiveness and effects of age[END_REF][START_REF] Frank | Transcranial magnetic stimulation for the treatment of depression: feasibility and results under naturalistic conditions: a retrospective analysis[END_REF][START_REF] Aliño | Efficacy of transcranial magnetic stimulation (TMS) in depression: naturalistic study[END_REF][START_REF] Rachid | Repetitive Transcranial Magnetic Stimulation (5 and 10 Hz) With Modified Parameters in the Treatment of Resistant Unipolar and Bipolar Depression in a Private Practice Setting[END_REF][START_REF] Griffiths | Repetitive transcranial magnetic stimulation (rTMS) for depression: outcomes in a United Kingdom (UK) clinical practice[END_REF][START_REF] Dowling | Repetitive transcranial magnetic stimulation for major depression: A naturalistic observational study in an Australian private hospital[END_REF][START_REF] Godfrey | An open-label feasibility study of repetitive transcranial magnetic stimulation (rTMS) for treatment-resistant depression in the New Zealand healthcare context[END_REF][START_REF] Conelea | Transcranial magnetic stimulation for treatment-resistant depression: Naturalistic treatment outcomes for younger versus older patients[END_REF][START_REF] Philip | 5Hz Repetitive transcranial magnetic stimulation to left prefrontal cortex for major depression[END_REF][START_REF] Galletly | A Comparison of Right Unilateral and Sequential Bilateral Repetitive Transcranial Magnetic Stimulation for Major Depression: A Naturalistic Clinical Australian Study[END_REF][START_REF] Carnell | How effective is repetitive transcranial magnetic stimulation for bipolar depression?[END_REF].

In most of these naturalistic studies, high frequency rTMS over the left dorsolateral prefrontal cortex was used. The present study uses a duration-adaptative treatment design that allows patients to receive up to 60 sessions of rTMS with medical assessment every 15 sessions. This study examines the efficacy of switching to HF rTMS for non-responders to LF rTMS and the efficacy of a maintenance treatment.

In Montpellier, rTMS has been used since 2009 for treatment-resistant depression. Patients are addressed by their referent psychiatrist. This is, to our knowledge, the first study evaluating the efficacy of HF-rTMS for patients who did not respond to LF-rTMS, as well as the first naturalistic study assessing results for LF-rTMS only. Plus, it includes data from maintenance treatment, which is rarely reported in this type of study.

MATERIAL AND METHODS:

This is a naturalistic, observational, retrospective study, conducted in Montpellier University Hospital

Subjects:

Patients were eligible to the rTMS protocol if they were over 18, suffered from a major depressive episode according to DSM IV criteria, and did not respond to at least two antidepressant medications, with optimal dosage and duration. MADRS score at baseline had to be > 21.

Written informed consent was obtained from all participant.

Exclusion criteria were contraindication to rTMS (intra-cranial foreign object, non-stabilized epilepsy, cochlear implant, pacemaker, pregnancy, non-stabilized medical affection).

119 patients were included, all of them benefited from rTMS in Montpellier University Hospital between 2009 and 2020. Current treatment was not modified.

rTMS procedure:

First-line treatment was one cure of 15 sessions of low-frequency rTMS over the right prefrontal dorsolateral cortex. Then, depending on the clinical response, several options were considered: in case of excellent clinical response, a six-months consolidation treatment of LF rTMS was proposed. In case of minimal response but with a hope of better improvement, a second cure of 15 sessions of right LF rTMS was proposed. In case of absence of response after one LF cure or insufficient response after 2 cures, a change of protocol was made, and one or two cures of 15 sessions of high-frequency rTMS over the left prefrontal dorsolateral cortex was undergone. In that case, if clinical response was satisfying, a sixmonths consolidation treatment was proposed; if not, rTMS was stopped. See figure 1.

All the therapeutical decisions were based on clinical criteria, and not on the scales used for the study.

Treatment parameters:

The medical device (Super Rapid 2 from Magstim company) has a CE label and has the FDA agreement for treatment-resistant depression.

LF rTMS was administered at 1 Hz over the right prefrontal dorsolateral cortex at 120% of motor threshold, patients received 6 trains of 60 seconds stimulation separated by 30-seconds inter train periods, for a session duration of 8 min 30 s and a total of 360 pulses. This protocol has proven its efficacy in a French multicenter trial [START_REF] Brunelin | The Efficacy and Safety of Low Frequency Repetitive Transcranial Magnetic Stimulation for Treatment-resistant Depression: The Results From a Large Multicenter French RCT[END_REF]. HF rTMS was administered at 10 Hz over the left prefrontal dorsolateral cortex at 110% of motor threshold, patients received 40 trains of 5 seconds stimulation separated by 25-seconds intertrain periods, for a session duration of 20 minutes and a total of 2000 pulses. Sessions were daily or twice daily five days per week.

The resting motor threshold was determined using visual methods (visible contraction of the thumb) [START_REF] Pridmore | Motor threshold in transcranial magnetic stimulation: a comparison of a neurophysiological method and a visualization of movement method[END_REF] and was reassessed every 15 sessions. Site of stimulation was determined, during the first years, using the 6 cm method (6 cm forward from motor site in a sagittal plan), then using the Beam-F3 method [START_REF] Beam | An efficient and accurate new method for locating the F3 position for prefrontal TMS applications[END_REF]. During the stimulation, the patient was instructed not to sleep and was allowed to talk with the nurse.

Outcome measures:

For the measurement of efficacy, Beck Depression Inventory (BDI) [START_REF] Beck | An inventory for measuring depression[END_REF] and Montgomery-Adsberg Depression Rating Scale (MADRS) [START_REF] Montgomery | A new depression scale designed to be sensitive to change[END_REF] scales were assessed before treatment, at the end of each 15 sessions, and in case of consolidation protocol, at 1, 3 and 6 months after the end of the initial protocol.

Side effects were assessed by the nurse at each session and the physician every 15 sessions.

Demographic information, diagnosis, treatment, treatment resistance, duration of the episode and of the disease were collected by the physician during the first consultation.

Statistical analysis :

The primary outcome was the remission rate based on the MADRS. duration was analyzed as a qualitative variable (<24 months vs > 24 months), since the efficacy of rTMS in chronic depression seems to be uncertain [START_REF] Van Eijndhoven | A randomized controlled trial of a standard 4-week protocol of repetitive transcranial magnetic stimulation in severe treatment resistant depression[END_REF].

For the descriptive analysis, qualitative variables were described with their numbers and associated percentage. Quantitative variables were described with their means and standard deviation. Baseline BDI score 36.9 ± 10.1

Treatment outcomes

The average number of rTMS sessions across the acute phase was 32.7.

There was a statistically significant improvement of both MADRS and BDI scores from baseline at the end of the rTMS treatment (-12.9; p < 0.0001 and -12.85; p <0.0001 respectively).

Regarding the primary outcome, MADRS remission rate at the end of rTMS-treatment (all protocols combined) was 22.9%. MADRS response rate was 47.6%. Response and remission rates according to the BDI were 46.4% and 33.7%, respectively.

In detail, at the end of low-frequency rTMS protocol, response and remission rates were 31% and 17% according to the MADRS; 29.1 % and 22% according to the BDI.

Among patients with an insufficient response to LF-rTMS and who were then treated with HF-rTMS, response and remission rates were 38.9% and 12.2% according the MADRS, 34.8% and 25.5% according to the BDI.

Predictive factors of response, analysis of moderators of treatment outcome

Among the analysed parameters (gender, age, main diagnosis, episode duration, disease duration, number of current treatments, number of failed pharmacological treatments, baseline MADRS score), none of them was associated with a significantly better response rate, in the univariate and multivariate analyses.

A comparison was made between the population that responded to HF-rTMS and the population that responded to LF-rTMS. Patients that responded to HF-rTMS had a higher mean number of failed pharmacological treatments during the episode (8.6 vs 6.3, p<0.05). There was no other difference in the clinical and demographical characteristics of the two populations.

Safety and tolerability

No serious adverse event occurred during the course of treatment, particularly no seizure. For 6 patients, poor tolerance caused a change in the protocol. Two patients had to stop rTMS because of side-effects during low-frequency protocol, two who were supposed to switch to high-frequency protocol did not because of mediocre tolerance of low-frequency, two had to stop high-frequency protocol (one of them switched back to low-frequency). Main side-effects were headaches and discomfort in the stimulation area. Results of this study show that rTMS is an effective therapy for treatment-resistant depression, and that therapeutical response to high-frequency rTMS can be high even in case of non-response to lowfrequency rTMS. Naturalistic studies are important to assess the efficacy and acceptability of treatment in clinical practice due to non-research patients often having a high rate of psychiatric and somatic comorbidity. In this one, response and remission rates are consistent with those found in both shamcontrolled randomized clinical trials and other naturalistic studies. Depending on the depression scales used, response rate is usually between 30 and 60%. This is higher than the 16.8 % response rate to a third-line pharmacological treatment, as reported in the STAR*D study [START_REF] Rush | Acute and Longer-Term Outcomes in Depressed Outpatients Requiring One or Several Treatment Steps: A STAR*D Report[END_REF].

European recommendations are in favour of rTMS treatment for major depressive disorder after failure of one well-conducted antidepressant medication [START_REF] Van Eijndhoven | A randomized controlled trial of a standard 4-week protocol of repetitive transcranial magnetic stimulation in severe treatment resistant depression[END_REF].

Diminution of BDI and MADRS scores from baseline was highly significant, like in other rTMS studies.

The study population was similar to those found in other naturalistic studies for the mean age and gender ratio [START_REF] Carpenter | TRANSCRANIAL MAGNETIC STIMULATION (TMS) FOR MAJOR DEPRESSION: A MULTISITE, NATURALISTIC, OBSERVATIONAL STUDY OF ACUTE TREATMENT OUTCOMES IN CLINICAL PRACTICE: Research Article: An Observational Study of TMS[END_REF][START_REF] Frank | Transcranial magnetic stimulation for the treatment of depression: feasibility and results under naturalistic conditions: a retrospective analysis[END_REF][START_REF] Aliño | Efficacy of transcranial magnetic stimulation (TMS) in depression: naturalistic study[END_REF][START_REF] Dowling | Repetitive transcranial magnetic stimulation for major depression: A naturalistic observational study in an Australian private hospital[END_REF][START_REF] Conelea | Transcranial magnetic stimulation for treatment-resistant depression: Naturalistic treatment outcomes for younger versus older patients[END_REF][START_REF] Carnell | How effective is repetitive transcranial magnetic stimulation for bipolar depression?[END_REF] but is different in terms of treatment resistance level (8 treatment failures) and episode duration (34 months) that implies a very difficult to treat population. Patients were often addressed by their referent psychiatrists after several years of therapeutical stagnation. In other similar naturalistic studies, the number of failed pharmacological treatments was either not reported or inferior ; 2 to 6,6 [START_REF] Berlim | High frequency repetitive transcranial magnetic stimulation as an augmenting strategy in severe treatment-resistant major depression: A prospective 4-week naturalistic trial[END_REF][START_REF] Carpenter | TRANSCRANIAL MAGNETIC STIMULATION (TMS) FOR MAJOR DEPRESSION: A MULTISITE, NATURALISTIC, OBSERVATIONAL STUDY OF ACUTE TREATMENT OUTCOMES IN CLINICAL PRACTICE: Research Article: An Observational Study of TMS[END_REF][START_REF] Aliño | Efficacy of transcranial magnetic stimulation (TMS) in depression: naturalistic study[END_REF][START_REF] Philip | 5Hz Repetitive transcranial magnetic stimulation to left prefrontal cortex for major depression[END_REF]. The relatively high response rate in this population suggests that rTMS can be an interesting treatment even for patients with a high level of resistance. Besides, there was no statistically significant difference in the response and remission rates according to the number of failed pharmacological treatment or the duration of current episode.

None of the other baseline sociodemographic or clinical characteristics were associated with a statistically better response or remission rate. This is consistent with the existing literature, most of the studies didn't find any reliable predictive response factors. Contradictory results exist concerning age, a higher age is sometimes found associated with a statistically significant lower response [START_REF] Carpenter | TRANSCRANIAL MAGNETIC STIMULATION (TMS) FOR MAJOR DEPRESSION: A MULTISITE, NATURALISTIC, OBSERVATIONAL STUDY OF ACUTE TREATMENT OUTCOMES IN CLINICAL PRACTICE: Research Article: An Observational Study of TMS[END_REF][START_REF] Lefaucheur | French guidelines on the use of repetitive transcranial magnetic stimulation (rTMS): safety and therapeutic indications[END_REF][START_REF] Aguirre | Age predicts lowfrequency transcranial magnetic stimulation efficacy in major depression[END_REF],

sometimes not [START_REF] Ciobanu | rTMS for pharmacoresistant major depression in the clinical setting of a psychiatric hospital: Effectiveness and effects of age[END_REF][START_REF] Frank | Transcranial magnetic stimulation for the treatment of depression: feasibility and results under naturalistic conditions: a retrospective analysis[END_REF][START_REF] Griffiths | Repetitive transcranial magnetic stimulation (rTMS) for depression: outcomes in a United Kingdom (UK) clinical practice[END_REF][START_REF] Dowling | Repetitive transcranial magnetic stimulation for major depression: A naturalistic observational study in an Australian private hospital[END_REF]. There are also contrasting results for baseline depression scores, a lower score [START_REF] Carpenter | TRANSCRANIAL MAGNETIC STIMULATION (TMS) FOR MAJOR DEPRESSION: A MULTISITE, NATURALISTIC, OBSERVATIONAL STUDY OF ACUTE TREATMENT OUTCOMES IN CLINICAL PRACTICE: Research Article: An Observational Study of TMS[END_REF] or on the contrary a higher score [START_REF] Dowling | Repetitive transcranial magnetic stimulation for major depression: A naturalistic observational study in an Australian private hospital[END_REF] can both be found to be a statistically significant predictive response factors.

Number of failed treatment during the episode is also sometimes found as a negative predictor of response to rTMS [START_REF] Aguirre | Age predicts lowfrequency transcranial magnetic stimulation efficacy in major depression[END_REF][START_REF] Fregni | Predictors of antidepressant response in clinical trials of transcranial magnetic stimulation[END_REF].

Several meta-analysis and naturalistic studies compared low-frequency rTMS over the right prefrontal dorsolateral cortex and high-frequency rTMS over the left prefrontal dorsolateral cortex [START_REF] Mutz | Comparative efficacy and acceptability of non-surgical brain stimulation for the acute treatment of major depressive episodes in adults: systematic review and network meta-analysis[END_REF][START_REF] Leggett | Repetitive Transcranial Magnetic Stimulation for Treatment-Resistant Depression in Adult and Youth Populations: A Systematic Literature Review and Meta-Analysis[END_REF][START_REF] Ciobanu | rTMS for pharmacoresistant major depression in the clinical setting of a psychiatric hospital: Effectiveness and effects of age[END_REF][START_REF] Trevizol | Predictors of remission after repetitive transcranial magnetic stimulation for the treatment of major depressive disorder: An analysis from the randomised non-inferiority THREE-D trial[END_REF],

none of them found a statistically significant difference between the two protocols. LF-rTMS is usually better tolerated, with a lower risk of seizure in particular, that is why this was the first-line treatment in this protocol. Besides, the duration of a low-frequency rTMS session is shorter than a high-frequency session (8.30 vs 20 minutes) and is less likely to cause a coil overheat.

The response and remission rates in right-low frequency observed in this study are consistent with this, with results within the range of usually observed response/remission rates.

Among patients who did not respond to LF rTMS, around 40 % obtained a clinical response when switching to the high-frequency left protocol. This rate is interesting, because it is similar to response rate of patients who had never been treated with rTMS. We could have expected a lower response rate in that case. There may be two reasons to explain these results. First, the remission rate may depend on the number of sessions as shown by some studies [START_REF] Cao | Response and Remission Rates Following High-Frequency vs. Low-Frequency Repetitive Transcranial Magnetic Stimulation (rTMS) Over Right DLPFC for Treating Major Depressive Disorder (MDD): A Meta-Analysis of Randomized, Double-Blind Trials[END_REF]. Second, the TRD population is heterogeneous in terms of neurobiological underpinnings. A subgroup of TRD may be sensitive to LF rTMS and another subgroup may be sensitive to HF rTMS [START_REF] Beuzon | Predictors of response to repetitive transcranial magnetic stimulation (rTMS) in the treatment of major depressive disorder[END_REF]. It would be useful to capture the predictive factors to response to one or another therapy. Outside of a slightly higher level of treatment-resistance in the HFresponders, our study did not find a difference in these two subgroups but future investigations may find biomarkers either electrophysiological or imaging.

To our knowledge, this is the first naturalistic study to analyse this protocol change. An open-label study found a 26% remission rate with right low-frequency rTMS among 81 patients who did not respond to left high-frequency rTMS [START_REF] Speer | Opposite effects of high and low frequency rTMS on mood in depressed patients: relationship to baseline cerebral activity on PET[END_REF].

Very few studies have been published about maintenance rTMS after acute rTMS treatment, and have inhomogeneous results. An open-label trial found a 71% relapse rate at one year with maintenance rTMS [START_REF] Fitzgerald | An open label trial of clustered maintenance rTMS for patients with refractory depression[END_REF], another one 62% sustained response at 6 months [START_REF] Connolly | Effectiveness of transcranial magnetic stimulation in clinical practice post-FDA approval in the United States: results observed with the first 100 consecutive cases of depression at an academic medical center[END_REF]. Another trial compared the clinical evolution of 59 responders to acute rTMS, among them, over a period of 20 weeks, 37 had maintenance treatment, 22 did not. Relapse rate was significantly higher in the non-maintenance group (37.8% vs 81.8%) [START_REF] Richieri | Maintenance transcranial magnetic stimulation reduces depression relapse: a propensity-adjusted analysis[END_REF]. A randomized control trial evaluated efficacy of 8 months rTMS maintenance over 17 patients who responded to rTMS : depression score was significantly better in the active groupe between the first and fourth month [START_REF] Benadhira | A randomized, shamcontrolled study of maintenance rTMS for treatment-resistant depression (TRD)[END_REF].

In our study, at least 50% of the patients experimented relapse within the 6 months following acute rTMS treatment. One hypothesis is that a fornightly period between two rTMS session is insufficient to maintain the antidepressant effect.

No serious adverse effects, including seizure induction, occurred during the protocol. Adherence rate was high, only a few patients (4) interrupted rTMS because of adverse events (mostly headaches). rTMS is known to be a generally well tolerated treatment, with few side effects ; in a meta-analysis, there was no statistically significant difference in drop-out rates due to adverse event between active and sham rTMS groups [START_REF] Wei | Meta-analysis of the Efficacy and Safety of Repetitive Transcranial Magnetic Stimulation (rTMS) in the Treatment of Depression[END_REF].

The main limitation of this study was the loss of data due to the retrospective analysis, for many patients, especially those treated during the first years of the initiation of the protocol (between 2009 and 2013) when data were not recorded on computer. For example, for the main outcome measures, 8

patients could not be included in the analysis due to the absence of final MADRS score. Another limitation is the absence of comparison with a sham group, knowing that a part of the therapeutical response is likely due to other factors than rTMS. The presence of nurses during sessions is likely

  Anesthésiologie-réanimation et médecine péri-opératoire) PERRIGAULT Pierre-François (Anesthésiologie-réanimation et médecine péri-opératoire) QUANTIN Xavier (Pneumologie) ROUBERTIE Agathe (Pédiatrie) VIEL Eric (Soins palliatifs et traitement de la douleur) Maîtres de conférences des universités -Praticiens hospitaliers MCU-PH Hors classe

  Mean differences in the MADRS and BDI change post-treatment vs baseline were compared with a Student test for matched data.For the analyses of potential predictive factors of response, Chi-square test was used for qualitative variables (main diagnosis, gender, episode duration); Wilcoxon test was used for quantitative variables (age, number of failed pharmacological treatments, baseline depression scores, number of current treatments, disease duration). All the analyses were performed with SAS 9.4 software.

Figure 1 .

 1 Figure 1. rTMS protocol

Figure 2 .

 2 Figure 2. Flowchart

Maîtres de conférences des universités -Médecine générale MCU-MG de 1 ère classe COSTA David MCU-MG de 2 ème classe

	JEZIORSKI Éric MIOT Stéphanie		Pédiatrie Médecine interne ; gériatrie et biologie du vieillissement ; addictologie
	KUSTER Nils		Biochimie et biologie moléculaire
	PINETON DE CHAMBRUN Guillaume	Gastroentérologie ; hépatologie ; addictologie
	MCU-PH de 1 ère classe SOUCHE François-Régis		Chirurgie viscérale et digestive
	MAKINSON Alain		Maladies infectieuses, Maladies tropicales
	BERTRAND Martin		Anatomie
	PANTEL Alix		Bactériologie-virologie ; hygiène hospitalière
	BOUDOUSQ Vincent		Biophysique et médecine nucléaire
	PERS Yves-Marie		Thérapeutique ; addictologie
	BOURGIER Céline		Cancérologie ; Radiothérapie
	BRET Caroline ROUBILLE Camille		Hématologie biologique Médecine interne ; gériatrie et biologie du vieillissement ; addictologie
	COSSEE Mireille SZABLEWSKY Vanessa		Génétique Anatomie et cytologie pathologiques
	GIRARDET-BESSIS Anne		Biochimie et biologie moléculaire
	LAVIGNE Géraldine		Hématologie ; transfusion
	LESAGE François-Xavier		Médecine et Santé au Travail
	MATHIEU Olivier		Pharmacologie fondamentale ; pharmacologie clinique ; addictologie
	MENJOT de CHAMPFLEUR Nicolas	Radiologie et imagerie médicale
	MOUZAT Kévin		Biochimie et biologie moléculaire
	FOLCO-LOGNOS Béatrice
	BADIOU Stéphanie OLIE Emilie OUDE ENGBERINK Agnès		Psychiatrie d'adultes ; addictologie Biochimie et biologie moléculaire
	BOULLE Nathalie PANABIERES Catherine		Biologie cellulaire Biologie cellulaire
	CACHEUX-RATABOUL Valère PHILIBERT Pascal Maîtres de conférences associés -Médecine générale Génétique Biologie et médecine du développement et de la reproduction ; gynécologie médicale
	CARRIERE Christian RAVEL Christophe LOPEZ Antonio		Bactériologie-virologie ; hygiène hospitalière Parasitologie et mycologie
	CHARACHON Sylvie SCHUSTER-BECK Iris MILLION Elodie		Physiologie Bactériologie-virologie ; hygiène hospitalière
	PAVAGEAU Sylvain
	FABBRO-PERAY Pascale STERKERS Yvon REBOUL Marie-Catherine		Epidémiologie, économie de la santé et prévention Parasitologie et mycologie
	GIANSILY-BLAIZOT Muriel THEVENIN-RENE Céline SERAYET Philippe		Hématologie ; transfusion Immunologie
	HILLAIRE-BUYS Dominique TUAILLON Edouard	Bactériologie-virologie ; hygiène hospitalière Pharmacologie fondamentale ; pharmacologie clinique ; addictologie Praticiens hospitaliers universitaires
	PUJOL Joseph MCU-PH de 2 ème classe BARATEAU Lucie		Anatomie Physiologie
	RICHARD Bruno CHIRIAC Anca BASTIDE Sophie		Médecine palliative Immunologie Epidémiologie, économie de la santé et prévention
	RISPAIL Philippe SEGONDY Michel DE JONG Audrey DAIEN Claire DU THANH Aurélie GATINOIS Vincent		Parasitologie et mycologie Anesthésiologie-réanimation et médecine péri-Rhumatologie opératoire Bactériologie-virologie ; hygiène hospitalière Dermato-vénéréologie Histologie, embryologie et cytogénétique
	GOUZI Farès GOULABCHAND Radjiv		Physiologie Médecine interne ; gériatrie et biologie du vieillissement ; addictologie
	HERRERO Astrid LATTUCA Benoit		Chirurgie viscérale et digestive Cardiologie

Efficacy of high frequency rTMS for non-responders to low frequency rTMS, a naturalistic study in treatment-resistant depression in a French academic center.

  Merci en particulier à Lydie, pour m'avoir soutenu au cours d'un de mes premiers stages au CHU, à l'équipe d'Euzière pour votre convivialité.

	Sommaire
	Abstract……………………………………………………………………………………………………………………………19
	Introduction (français)……………………………………………………………………………………………………..20
	Introduction…………………………………………………………………………………………………………………….22
	Material and methods……………………………………………………………………………………………………..23
	Subjects……………………………………………………………………………………………………………….23
	rTMS procedure…………………………………………………………………………………………………..23
	Treatment parameters…………………………………………………………………………………………24
	Outcome measures………………………………………………………………………………………………24
	Statistical analysis………………………………………………………………………………………………..25
	Results…………………………………………………………………………………………………………………………….26
	Demographic and clinical characteristics
	of study population……………………………………………………………………………………………..26
	Treatment outcomes…………………………………………………………………………………………..27
	Predictive factors of response, analysis of
	moderators of treatment outcomes……………………………………………………………………28
	Safety and tolerability…………………………………………………………………………………………28
	Maintenance………………………………………………………………………………………………………29
	Discussion………………………………………………………………………………………………………………………30
	Conclusion……………………………………………………………………………………………………………………..33
	Conflict of interest………………………………………………………………………………………………33
	Contributors……………………………………………………………………………………………………….33
	Acknowledgements…………………………………………………………………………………………….33
	References…………………………………………………………………………………………………………………….34
	Serment…………………………………………………………………………………………………………………………39
	Résumés et mots-clés…………………………………………………………………………………………………….40

INTRODUCTION

La dépression est une maladie psychiatrique fréquente, on estime sa prévalence vie entière entre 15 et 20%. Elle est une cause majeure d'incapacité dans le monde, et augmente la morbidité et la mortalité.

Les médicaments antidépresseurs sont le traitement de première ligne des dépressions modérées à sévères, cependant une proportion significative des patients ne répond pas à ces traitements. Les techniques de neuromodulation, en particulier l'électroconvulsivothérapie (ECT) et la stimulation magnétique transcrânienne répétée (rTMS) sont des alternatives intéressantes. La rTMS, bien que moins efficace que l'ECT, a l'avantage d'être mieux tolérée et de ne pas nécessiter d'anesthésie générale.

La dépression unipolaire résistante est généralement définie par l'absence de réponse à deux traitements antidépresseurs de deux classes différentes, à posologie et durée efficaces. Il n'y a pas de définition officielle de la dépression bipolaire résistante, cependant un groupe d'experts britanniques a récemment proposé de la définir par l'absence de réponse à deux lignes de traitement bien conduites.

La dépression résistante entraine une augmentation de 35% de la mortalité par rapport à la dépression non résistante, il s'agit donc d'un problème majeur de santé publique.

La rTMS est une

technique de neuromodulation non-invasive, basée sur l'induction d'un champ magnétique par une bobine, entraînant une dépolarisation neuronale. Pour le traitement de la dépression, deux protocoles sont principalement utilisés : rTMS haute-fréquence sur le cortex préfrontal dorsolatéral gauche, et rTMS basse-fréquence sur le CPFDL droit. Plusieurs méta-analyses d'essais cliniques randomisés ont démontré la supériorité de la rTMS versus placebo, dans la dépression résistante unipolaire et bipolaire. Cependant, il y a moins d'études naturalistiques, évaluant l'efficacité de la rTMS en population clinique de routine. Leurs résultats sont similaires à ceux des essais cliniques, avec un taux de réponse compris entre 30 et 60%. La plupart des études naturalistiques évaluent l'efficacité de la rTMS haute-fréquence. Dans cette étude, un protocole adaptatif est utilisé, permettant aux patients de recevoir jusqu'à 60 séances de rTMS avec évaluation médicale toutes les 15 séances. Les patients n'ayant pas répondu à la rTMS basse-fréquence ont ensuite été traités par rTMS haute-fréquence. Elle évalue aussi l'efficacité d'un traitement de consolidation.

  Remission was defined by a MADRS score ≤10. Secondary outcomes were response rate, defined by a >50 % reduction of MADRS score, remission and response rates based on the BDI score (remission if BDI < 15, response if 50% diminution of the BDI score), evolution on MADRS and BDI scores during the consolidation treatment, and predictive factors of response according to several criteria (age, gender, number of current antidepressant treatments, number of failed antidepressant or potentializing treatment in current episode, episode duration, disease duration, main diagnosis, baseline depression scores). Episode

Table 1 . Demographic and clinical characteristics of study population

 1

	Variable	Value
	Age (mean ± SD)	52 ± 13.3
	Age range	19-83
	Gender
	Male	39 (33.3%)
	Female	77 (66.7%)
	Main diagnosis
	Bipolar depression	31 (26.7%)
	Unipolar depression	85 (73.3%)
	Failed pharmacological treatment	8 ± 4.3
	during the current episode
	Duration of current episode	34 ± 33.5
	(months)
	Disease duration (months)	207 ± 146
	Baseline MADRS score	31.6 ± 5.9

Table 2 . Treatment outcomes: categorical variables End of treatment End of LF-protocol End of HF-protocol MADRS

 2

	Response rate	47.6%	31%	38.9%
	Remission rate	22.9%	17%	12.2%
	BDI
	Response rate	46.4%	29.1%	34.8%
	Remission rate	33.7%	22.2%	25.5%

Table 3 . Treatment outcomes : continuous variables

 3

	Variables	Mean difference (SD)	P value
	MADRS before and after treatment	12.90 (10.74)	<0.0001
	BDI before and after treatment	12.85 (12.86)	<0.0001
	DISCUSSION :

Mots clés : stimulation magnétique transcrânienne ; dépression résistante ; naturalistique ; rTMS basse fréquence ; rTMS haute fréquence

Remerciements

Acknowledgement

We thank the nurses of the USC (P. Bonnafé, S. Flores, C. Brassart, F. Icher) who made the rTMS sessions.

A Montpellier, la rTMS dans la prise en charge de la dépression résistante est utilisée depuis 2009. Les patients sont adressés par leur psychiatre traitant.

A notre connaissance, il s'agit de la première étude à évaluer l'efficacité de la rTMS haute-fréquence chez des patients n'ayant pas répondu à la basse-fréquence, ainsi que de la première à publier des résultats portant uniquement sur la basse-fréquence. Par ailleurs, elle comporte des données de traitement de consolidation, ce qui est rarement publié dans ce type d'étude.

responsible for part of the clinical benefit. It is known that placebo is part of response to rTMS, with significative effect on depression scores [START_REF] Fitzgerald | An open label trial of clustered maintenance rTMS for patients with refractory depression[END_REF].

CONCLUSION :

In this naturalistic study, efficacy of rTMS among patients with treatment resistant depression is consistent with the published literature. For the non-responders to LF rTMS, HF rTMS seems to be an interesting treatment. None of the potential predictive factors analysed showed a significative difference in clinical response.

Role of funding source

No funding source

Conflict of interest

Dr Attal reports speaker fees, advisory board and research grants from Otsuka, Lundbeck, Eisai, Janssen and Boehringer-Ingelheim. Dr Naimi, Macgregor and Peyre-Costa have no conflict of interest.

Contributors

Jerôme Attal confirmed the medical indication, assessed the motor threshold and evaluated the patients, designed the study and the data collection, revised the manuscript. Victor Naimi conducted the literature searches, wrote the first draft and made the data collection. David Peyre-Costa undertook the statistical analysis. Alexandra Macgregor and Delphine Capdevielle revised the manuscript. All authors contributed to and have approved the final manuscript.

SERMENT

En présence des Maîtres de cette école, de mes chers condisciples et devant l'effigie d'Hippocrate, je promets et je jure, au nom de l'Etre suprême, d'être fidèle aux lois de l'honneur et de la probité dans l'exercice de la médecine.

Je donnerai mes soins gratuits à l'indigent et n'exigerai jamais un salaire au-dessus de mon travail.

Admis dans l'intérieur des maisons, mes yeux ne verront pas ce qui s'y passe, ma langue taira les secrets qui me seront confiés, et mon état ne servira pas à corrompre les moeurs, ni à favoriser le crime.

Respectueux et reconnaissant envers mes Maîtres, je rendrai à leurs enfants l'instruction que j'ai reçue de leurs pères.

Que les hommes m'accordent leur estime si je suis fidèle à mes promesses. Que je sois couvert d'opprobre et méprisé de mes confrères si j'y manque.

Résumé

La dépression est une maladie mentale fréquente (prévalence vie entière d'environ 15 à 20%) et invalidante, qui entraîne une augmentation de la morbi-mortalité. Les médicaments antidépresseurs constituent le traitement de première ligne de la dépression, cependant 20 à 40 % des patients n'obtiennent pas de réponse clinique satisfaisante, même avec plusieurs lignes de traitement bien conduites. La stimulation magnétique transcrânienne répétée (rTMS) est une technique de neuromodulation non invasive ayant démontré son efficacité dans la dépression résistante unipolaire ou bipolaire au travers de nombreuses méta-analyses d'essais cliniques randomisés vs placebo, ainsi que d'études naturalistiques. Dans la plupart des études, un protocole de rTMS haute fréquence stimulant le cortex préfrontal dorsolatéral gauche est utilisé, d'autres études utilisent un protocole basse fréquence stimulant le cortex préfrontal dorsolatéral droit, les méta-analyses comparant ces deux protocoles ne retrouvant pas de différence significative.

Dans cette étude naturalistique rétrospective réalisée au CHU de Montpellier, les patients présentant une dépression pharmacorésistante étaient inclus dans un protocole de rTMS basse fréquence, puis en cas de réponse insuffisante le protocole était changé pour de la rTMS en haute fréquence. Le taux de réponse et de rémission étaient mesurés, et des facteurs sociodémographiques ou cliniques associées à une meilleure réponse recherchés.

Parmi les 119 patients inclus dans l'étude, 47,6% ont répondu à la rTMS, et 22,9 % étaient en rémission à la fin du traitement, selon l'échelle MADRS. Les taux de réponse et rémission à la fin du protocole de rTMS basse fréquence étaient de 31% et 17% respectivement. Parmi les patients n'ayant pas répondu à la rTMS basse fréquence et pour lesquels un protocole haute fréquence a été effectué, les taux de réponse et de rémission étaient de 38,9% et 12,2%. Parmi les facteurs sociodémographiques et cliniques recherchés (âge, sexe, diagnostic principal, durée de l'épisode, durée de la maladie, nombre de résistances médicamenteuses, nombre de traitements en cours, score MADRS initial), aucun n'était associé à une différence de réponse significative.

Cette étude, à notre connaissance la seule à étudier la rTMS haute fréquence chez des patients n'ayant pas répondu à la basse fréquence, retrouve des taux de réponse et de rémission comparables aux autres études randomisés ou naturalistiques analysant les résultats de la rTMS dans la dépression résistante. Malgré un niveau de résistance élevée (8 traitements en moyenne), la réponse à la rTMS est satisfaisante. Par ailleurs, le taux relativement élevé de répondeurs en haute fréquence en cas d'échec de la basse fréquence est en faveur de la poursuite du traitement par rTMS avec un protocole différent en cas de non-réponse à un premier protocole.