P Kumar

J Fontaine

C Gonzales

F Pigache

P Lavieille

F Topin

M Miscevic
email: marc.miscevic@univ-tlse3.fr

HEAT TRANSFER INTENSIFICATION AND FLOW RATE CONTROL IN DYNAMIC MICRO-HEAT EXCHANGER

Technological advancements to improve flow and heat transfer characteristics in many processes are of great interest. Many high performance systems demand simultaneously the compactness, efficiency and control of heat transfer. In this view, a new concept of micro heat exchanger was proposed for the cooling of electronics devices for which the quality of heat exchange between wall and fluid as well as pumping effect are very critical. In the present work, the ability of a liquid heat exchanger involving a dynamic deformation of one of its walls to cool a microprocessor is investigated. For that purpose, 3-D numerical simulations were performed using commercial software based on the finite volume element in transient regime. Effect of geometrical and actuation parameters has been explored and the ability of such heat exchanger to simultaneously pump the fluid and enhance the heat transfer has been demonstrated. Based on these numerical results, a physical prototype has been designed and realized. First experimental results on the pumping capacity of this prototype have been compared with numerical results. The good agreement obtained allows validating the numerical procedure and thus to be confident in the numerical parametric study presented.

INTRODUCTION

The temperature control and associated heat flux management is crucial in many applications: microelectronics, embedded or fixed power electronics systems, power station, air conditioners, heat pumps, as well as in the field of industrial thermal processes metallurgy, chemistry, food, etc. The will to increase the performance and efficiency of these systems greatly amplifies this need, as in many situations it becomes the limiting factor in the optimization of the system performance. Moreover, lifetime and reliability of many systems are very strongly related to the quality of the thermal management.

It is nowadays common to meet chemical or thermal systems whose channels have sub-millimeter hydraulic diameters. This trend towards miniaturization is mainly due to the increasing demands of new and effective mixing or heat transfer technologies for various industrial fields, associated to the increasing need to control highly exothermic or explosive chemical reactions [START_REF] Kandlikar | Heat transfer, pressure Drop and flow patterns during flow boiling in parallel channel compact heat exchangers of small hydraulic diameters[END_REF][START_REF] Kandlikar | Fundamental issues related to flow boiling in minichannels and microchannels[END_REF]. Heat transfer and pressure drop in sinusoidal corrugated channels have been studied by Nishimura et al. [START_REF] Nishimura | Flow characteristics in a channel with symmetric wavy wall for steady flow[END_REF]. These authors showed that transition between laminar and turbulent flows is obtained at lower Reynolds number (Re = 300) compared to straight channel due to unsteady vortex motion. Similarly to the case of flat channel, the friction factor is inversely proportional to Reynolds number in the laminar flow range, while it is independent of Reynolds number in the turbulent range. Extending this study, Nishimura et al. [START_REF] Nishimura | Flow observations and mass transfer characteristics in symmetrical wavy-walled channels at moderate Reynolds numbers for steady flow[END_REF] studied flow patterns characteristics in symmetrical twodimensional sinusoidal and arc-shaped corrugated channels at moderate Reynolds numbers (20 ≤ 𝑅𝑒 ≤ 300). They concluded that the transitional Reynolds number depends on the corrugation shape. For instance, transition from laminar to turbulent flow occurred at lower Reynolds number for the arcshaped wall as compared with the sinusoidal wall. Niceno and Nobile [START_REF] Niceno | Numerical analysis of fluid flow and heat transfer in periodic wavy channels[END_REF] have conducted an extended numerical study on these corrugated channels. The results indicate that these two corrugation shapes are ineffective in terms of heat transfer rate (slightly higher for sinusoidal channel compare to arc-shaped channel) as compared to flat channel in steady low Reynolds flow. The unsteady regimes appear at different Reynolds numbers for the two corrugation shapes: unsteady regime was observed at Re = 60-80 for arc-shaped channel and at Re = 175-200 for sinusoidal channel. On the other hand, heat transfer rate increases significantly for both corrugation shapes, up to a factor of three, as a result of self-sustained oscillations. Moreover, this transfer rate was found to be higher for arcshaped channel while the friction factor was smaller for sinusoidal channel.

NOMENCLATURE

Naphon [START_REF] Naphon | Effect of wavy plate geometry configurations on the temperature and flow distributions[END_REF] conducted a numerical study on various corrugation geometries arranged in in-phase and out-phase layouts (e.g. flat plate, arc-shaped, trapezoidal and V-shaped) to enhance the thermal performance. He obtained that for a given air flow rate, V-shaped corrugated channel has the most significant effect on the enhancement of the heat transfer.

So, corrugated channels lead to enhance the heat transfer by disturbing the boundary layer. Most of the studies revealed an increase in overall thermal performance from 3 to 5 times depending on the working fluid. However, static corrugated channels have shown to increase significantly the pressure drop. In such corrugated (and grooved) mini-channels, high heat transfer usually leads to high Reynolds number (mostly turbulent) flow.

On the other hand, Léal et al. [START_REF] Léal | Simultaneous integration, control and enhancement of both fluid flow and heat transfer in small scale heat exchangers: A numerical study[END_REF] proposed a very simplistic model of dynamic corrugated mini-channel to be operated at low Reynolds number. This has been achieved by deforming dynamically one of the channel walls. Very high heat transfer has been obtained compared to static corrugated channel. It appeared to be the first study to introduce dynamic wall in such mini-channels heat exchanger.

Very recently, Kumar et al., [START_REF] Kumar | Heat transfer enhancement by dynamic corrugated heat exchanger wall: Numerical study[END_REF] extended this works and proposed a realistic 3-D geometry of dynamic corrugated heat exchanger. In their work, the average height of the channel is fixed while the minimum gap (distance between the lowest point of the deformed wall and the fixed wall) varies as a function of the relative amplitude. Numerical studies have been conducted by imposing high pressure and low pressure at the outlet and inlet sections of the channel, respectively, for an imposed frequency of 50Hz. It was observed heat transfer coefficient increases with increase in amplitude and the requirement of external pump could be completely eliminated due to self-pumping capacity of the device.

A first attempt to realize a physical prototype based on this principle has been made by Miscevic et al. [START_REF] Miscevic | Pumping and Heat Transfer Enhancement by Wall's Morphing[END_REF]. The heat exchanger developed had close (but different) dimensions than the ones considered in the numerical study of Léal et al. [START_REF] Léal | Simultaneous integration, control and enhancement of both fluid flow and heat transfer in small scale heat exchangers: A numerical study[END_REF]. In this prototype, one of the walls constituting the channel was subjected to dynamic deformations in the form of a traveling wave. Electric heaters on the other wall were heating the channel. Actuation was achieved by means of 10 piezoelectric actuators with homemade mechanical amplification systems.

Experimentally, the pumping function and the heat transfer intensification were shown. Nevertheless, the performances were less than expected mainly because the membrane was not rigid enough and induced unwanted deformations.

In partnership with a number of industrial partners, a liquid heat exchanger involving a dynamic deformation of one of its walls was realized [START_REF] Amokrane | Pipe forming part of a heat exchanger and heat exchanger comprising such a pipe[END_REF]. The aim of this paper is to determine the ability of this latter liquid heat exchanger to cool a microelectronic device. Both physical and virtual prototypes have been designed and realized, and parametric numerical simulations have been performed. The designed micro-heat exchanger uses three actuators to deform dynamically one of its walls. A systematic numerical study was conducted on a simplified geometry to understand the impact of operating parameters in enhancing thermo-hydraulic characteristics. Then, the first experimental results obtained with the physical prototype are used to validate the numerical procedure that has been applied to the same geometric system (using CAD of prototype and actuators command).

NUMERICAL PROTOTYPE

In the studied configuration, the lower wall was fixed and subjected to a constant heat flux along the imprint of heating zone while the dynamically deformed upper wall (also called "membrane" in the following) and side walls i.e. inlet and outlet sections were kept adiabatic. Three piezoelectric actuators were employed to dynamically deform the upper wall of a rectangular cross section micro-channel in order to simultaneously enhance heat transfer and pump the fluid. The length of the actuated zone (𝐿 = 𝑥 ! -𝑥 ! ) is 45.7 mm while width (𝑊) is 50 mm. The channel gap (𝑔) is fixed and is 10µm while the average height of the channel (δ) is linked to the wave amplitude employed for wall deformation and the channel gap.

The lengths of input and outlet zones have been chosen long enough to establish the hydrodynamic. Furthermore, the no-slip condition was imposed on the walls.

The influences of relative amplitude (𝐴 ! ), frequency (𝑓 ! ) and wavelength (𝜆) on thermo-hydraulic performances are x y z studied for an imposed value of the pressure difference between outlet and inlet of the exchanger equal to zero. Only three actuators were employed in the present study. The channel cross-section shape is presented in Figure 1 where the actuator positions can be described using 𝑥 ! and 𝑥 ! , 𝑥 ! and 𝑥 ! and 𝑥 ! and 𝑥 ! . The positions 𝑥 ! and 𝑥 ! are fixed to external inlet and outlet zones as dampers. These small zones make the fluid to enter and leave in laminar condition. The microchannel geometry is composed of four main parts: inlet zone, heated surface where the heat power is imposed, outlet zone and membrane. Sidewall damping has been imposed on the lateral side of the actuated zone: along main flow axis, the membrane displacement is linearly interpolated between actuators and fixed zone.

3-D numerical simulations were carried out using the commercial software StarCCM+. This software allows modeling fluid flow and heat transfer in dynamically deformed structures. The flow was considered transient, threedimensional and laminar. The working fluid was liquid water (properties taken from IAPWS-97 at 27°C) whose all thermophysical properties were supposed constant for systematic studies. The imposed heat power (𝑊 ! ) on the imprint (heated zone) was 65W (note that only half of the device is modeled due to symmetry).

The results presented focus on the "active zone" namely between 𝑆 ! and 𝑆 ! sections (see Figure 1). All representative global thermo-hydraulic quantities were calculated in this zone.

GOVERNING EQUATIONS

The incompressible laminar and transient conjugate flow and heat transfer problems were solved. The classical combination of continuity, momentum and energy equations are as follow, considering constant physical properties of the fluid:

𝛻 • 𝑢 = 0, (1)
𝜌 𝜕𝑢 𝜕𝑡 + 𝜌 𝑢 • 𝛻 𝑢 = 𝜌𝑔 -𝛻 • 𝑃 + 𝜇𝛥𝑢 (2)
𝜌𝐶 ! 𝜕𝑇 𝜕𝑡 + 𝑢 • 𝛻𝑇 + 𝜌𝑢 • 𝜕𝑢 𝜕𝑡 + 𝜌 2 𝛻 𝑢 ! • 𝑢 = 𝑘 ! 𝛥𝑇 + 𝜕𝑃 𝜕𝑡 (3)
where, 𝑢 is the velocity vector, 𝑃 is the pressure, 𝑇 is the temperature, 𝑔 is the gravity acceleration, 𝜌 is the density, 𝜇 is the dynamic viscosity, 𝐶 ! is the specific thermal capacity and 𝑘 ! is the thermal conductivity of fluid, respectively.

The numerical resolution used a segregated approach with implicit second order temporal discretization and ad hoc relaxations factors in order to obtain adequate convergence behavior. The displacement of the top membrane is created by:

(1)-fixing the vertical position of the membrane in inlet and outlet zones at chosen height δ (average height of channel),

(2)-adding the movement of the three actuators (Eq. 4), (3)-in between two actuators or one actuator and border, the displacement is simply interpolated. The displacement of actuator is given by the following equation for i=1,2,3 corresponding to actuator along main flow axis:

𝐴𝑐𝑡 ! 𝑥, 𝑡 = 𝐴 ! . 𝑐𝑜𝑠 2𝜋𝑓 ! 𝑡 + 𝛷 ! (4)
where 𝛷 ! =0°, 𝛷 ! , 𝛷 ! are phase of actuators 𝐴𝑐𝑡 ! , 𝐴𝑐𝑡 ! and 𝐴𝑐𝑡 ! , respectively.

3-D NUMERICAL SIMULATIONS

In the studied configuration, the vertical plane passing through the central axis of the channel is a plane of symmetry, so only half of the channel was simulated (i.e. W/2=25mm). The imposed power on the modeled half-imprint was thus 32.5W to carry out numerical simulations (see Figures 1 and2). This allows us to reduce the number of mesh cells to optimize computation time by dividing the simulated configuration by two compared to its actual size. Note that the fluid flow was considered in x -direction while the width and height of the channel were considered in yand z-directions respectively. Meshing strategy was similar to the one used by Kumar et al. [START_REF] Kumar | Heat transfer enhancement by dynamic corrugated heat exchanger wall: Numerical study[END_REF]. It was rather tricky to create a convenient mesh in such highly anisotropic geometrical configuration subjected to large amplitude deformations (up to 98 % of channel height) while keeping a computational time low enough to carry out parametric study without sacrificing precision or convergence of the dynamic transfer.

The deformed channel mesh is presented in Figure 2 in case of an actuator size of 11mm and a phase-shift between two consecutive actuators of 120° (𝛷=0°, -120°, -240°).

DATA REDUCTION

In case of dynamic corrugated channel, surface averaged and volume averaged thermo-hydraulic quantities for all operating configurations were calculated as follow.

The Reynolds number and hydraulic diameter are defined by:

𝑅𝑒 = 𝜌 𝑢 𝐷 ! 𝜇 , 𝐷 ! = 1 𝜆 4𝑆 𝑝 𝑑𝜆 ! ! ( 7
)
Where 𝑆 is the flow fluid passage area along the heated zone and p is the perimeter of the passage section, respectively. Note that these quantities are averaged over a time period.

The local heat transfer coefficient is obtained by the spatial and temporal averaged fluid temperature and wall temperature over the width and on a period (𝜏 = 1/𝑓 ! ):

𝑇 ! 𝑥 = 1 𝜏𝑊 𝑇 ! 𝑥, 𝑦, 𝑡 𝑑𝑦 !!! !!! 𝑑𝑡 !!! ! ( 8
)
𝑇 !" 𝑥 = 1 𝜏𝛿𝑊 𝑇 !" (𝑥, 𝑦, 𝑧, 𝑡)𝑑𝑦 !!! !!! 𝑑𝑧 !!! !,! !!! 𝑑𝑡 !!! ! (9)
The local heat transfer coefficient and Nusselt number are then defined as:

ℎ 𝑥 = 𝑞 𝑥 𝑇 ! 𝑥 -𝑇 !" 𝑥 , 𝑁𝑢 𝑥 = ℎ 𝑥 𝐷 ! 𝑘 ! (10)
In the following, the global heat transfer coefficient and Nusselt number across the channel are then defined as:

ℎ = 𝛤 𝑆 𝑇 ! -𝑇 !" , 𝑁𝑢 = ℎ 𝐷 ! 𝑘 ! (11)
Where * denotes volume and surface averages for both fluid and wall between sections 𝑆 ! and 𝑆 ! .

MESH CONVERGENCE

The calculations to test mesh convergence were performed for amplitude (𝐴 ! ) =85µm and frequency (𝑓 ! ) =20Hz.

Mesh size

We initialized both corrugated shape and fluid flow. Then, calculations were carried out until a periodic stationary regime is reached. This latter point is checked comparing the temporal evolutions of global heat transfer and flow characteristics: calculations were performed until the heat transfer coefficient values between two consecutive time periods differs by less than 1 %. Consequently, an additional time period is added to extract all instantaneous and time-averaged values of all physical quantities. From the Table 1, it can be seen that reducing the mesh size from 3 to 2 mm does not impact strongly on the global properties. The % differences between the properties are respectively: 0.14% for 𝑚, 0.0024% for ! , 0.006% for 𝑇 !" , 0.47% for ℎ , 0.0095% for 𝑇 !! and 0.0095% for 𝑇 !" . On increasing the mesh size, the properties vary significantly while reducing it further do not lead to any additional improvement. Based on these observations and the % difference in the properties, we chose the BMS (Base Mesh Size) =2mm to perform the systematic studies.

Time step requirement

To perform the numerical simulations in terms of time effectiveness as well as the precision, it is very important to obtain an optimized time step (TS). We test the following number of time steps per period: 20, 50, 75 and 100. Based on these time steps, global characteristics have been presented in Table 2. It can be observed that heat transfer coefficient values decreases with increase in TS. On the other hand, Δ𝑇 ! = 𝑇 ! -𝑇 !" increases with increase in TS. In order to obtain an optimized TS value, we have calculated the percentage variation of ℎ and Δ𝑇 ! for different time steps based on the lowest value as a reference value for both these quantities. When TS=50, we observed variation of ℎ equal to 2.84% while variation in 𝛥𝑇 ! (%) is 6.14%. The global results of different characteristics do not vary strongly when increasing TS. Moreover, higher value of TS increases the computational time while the properties vary within a difference of 3%. Hence, TS=50 has been chosen to study the impact of different amplitudes and frequencies. The procedure has already been compared to another numerical study in Schmidmayer et al. [START_REF] Schmidmayer | Thermo-hydraulic characterization of a self-pumping corrugated wall heat exchanger[END_REF]; influence of fluid properties has also been studied in this paper. The results obtained let us confident in the numerical approach. Due to the movement of the channel wall, cold fluid is moved near the heated wall successively at every location; this boundary layer disruption increases sharply heat transfer along with mixing that takes place within the core flow. On temperature field, successive hot and cold "plumes" could be seen (fig. 4).

𝑚 ( 𝑔 𝑠 ) 𝑇 ! (K) 𝑇 !" (K) ℎ (W/m 2 K) 𝑇 !" (K) 𝑇 !" (K

LOCAL RESULTS

Near the inlet, the cold fluid fills the pocket during expansion, then, it is driven towards the heated surface, and eventually transferred below the next actuated zone. The constricted zone acts as a barrier separating inlet and outlet parts. This leads the fluid to fill the expansion zone while being mixed efficiently; it is then transferred in the next pocket over time. These "bursts" repeat cyclically along with mixing thus increasing heat transfer. Qualitatively, thermal and hydraulic fields dynamics remain similar for all tested conditions although some differences in terms of phase-shift or amplitude are observed on temporal variations of temperature, pressure and velocities. Thus, changes in the thermo-hydraulic performances with operating parameters are expected to guide optimal design of the physical prototype.

GLOBAL RESULTS

The global thermo-hydraulic characteristics of the proposed configuration of dynamically morphed heat exchanger are presented in the following figures and tables.

Frequency and Amplitude impact on flow rate

Mass flow rate is proportional to both frequency and amplitude. High frequency leads to fast movement of the corrugated wall, which in turn enhances the mass flow. The latter is therefore directly proportional to the frequency (Figure 5.a). Increasing amplitude (at constant gap) leads to increase the channel volume thus to have more fluid in the channel. This behavior also enhances mass flow rate in the system, which is also directly proportional to the amplitude (Figure 5.b). Note that increasing amplitude at constant gap adds mainly volume to the channel near the membrane and increases average height.

Frequency and amplitude impact on heat transfer

Heat transfer coefficient also depends on both frequency and amplitude imposed. Increasing frequency increases the mixing effect and the fluid velocity. Thus it results in high heat transfer coefficients varying roughly proportionally to the frequency (see Figure 6a).

On the other hand, increasing amplitude -while keeping the gap (minimum height below actuators) constant-leads to increase the average height of the channel and thus reduces the heat transfer coefficient. This one is thus found to decrease linearly with the amplitude (see Figure 6b). Nevertheless, the heat transfer coefficient remains very high (>10 000 W/m 2 K) for all tested cases.

Influence of gap on thermo hydraulic performance

Influence of gap size has been tested on mass flow rate and heat transfer for amplitude 100µ𝑚 and frequency 10 𝐻𝑧. The initial gap was fixed at 10µm. The gap size varied from 10µm up to 35µm. In figure 7, it can be easily observed that the mass flow rate decreases with increasing gap and, as expected, the heat transfer coefficient decreases with increasing channel height. This is due to two main effects: the average fluid thickness increases, and the fluid velocities decrease. Mainly, the most constricted zones become less and less efficient as the gap increases. As these zones (which cross all the channel length) are the locations where the most efficient heat transfer takes place, it is not surprising to observe a net decrease in heat transfer coefficient. Two main conclusions could be drawn from these results: although the heat transfer coefficient decreases when increasing channel height for sub-millimeter cases, it remains high enough to produce a very small thermal resistance compared to the others involved in a chip cooling assembly (e.g. contact resistances etc.). As the flow increases with the channel height, the need to remove relatively high power with limited inletoutlet temperature difference will be a more important design parameter. Moreover, required pumping power, mechanical efforts and constraints will be more easily met for the channel with « large » dimensions i.e. going more towards 1 millimeter than 100 µm. Using these trends along with mechanical power consumption and pressure variations constraints have allowed us to design a physical prototype of self-pumping high performance actuated heat exchanger.

𝑓 ! (Hz) 𝑚 ( 𝑔 𝑠 ) 𝛥𝑇 ! (K) ℎ (W/m 2 K) 𝑇 !" (K) 𝑇 !" (

EXPERIMENTAL PROTOTYPE

Due to the need of easy control of the frequency, large displacement (>100µm) and traveling wave like, the membrane deformation has to be obtained from forced actuation. A box containing 3 actuators that are fixed on top cover has been realized (fig. 8 left).

Rectangular pads are fixed at the bottom of the actuators and glued to a membrane of suitable mechanical properties. The assembly cover-actuators-pads-membrane is then fixed on the top box (mechanical support, and fluid tightness) and placed above the sole of the heat exchanger. Two grooves are machined in the sole and communicate with the inlet and outlet pipes (fig. 8

right).

The actuator assembly is machined so that at rest, each pad pushes the membrane in contact with the sole. The membrane dynamic deformation is driven by the individual electric supply of each actuator -V -(t) is of the same kind that is described in equation 4 -and for the maximum supply voltage the distance between the sole and the membrane is 200 µm (according to the datasheet of actuators, membrane properties and preliminary tests). Figure 9 shows the configuration of the hydraulic system: adjusting the vertical position of the two constant level tanks imposes the pressure at the inlet and the outlet of the channel. These heights are adjustable and may be changed as required for a given experiment. The mass flow rate is measured thanks to a precision balance, with an uncertainty less than 1% for all experiments. The pump P2 is used to fill the loop prior to each experiment.

RESULTS AND COMPARISON

To date, the experimental setup only allows characterizing the mass flow rate as a function of characteristics of the supply voltage of the actuators (type of signal, amplitude, phase-shift…). Only cold tests (i.e. without thermal solicitations nor measurements) have yet been carried out.

Tested configuration

Specific experiments have been done to determine the flow rate dependence to the phase-shift between actuators (imposed with an uncertainty less than 1°) in case of a sinusoidal variation of voltage of frequency 10 Hz (+/-0.1 Hz). Simultaneously, the virtual prototype geometry has been modified in order to comply with the experimental one (using CAD modelling) and numerical calculations were carried out with the same operating conditions considering peak-to-peak amplitude of 200 µm. The displacement of membrane is taken from the electrical command of the actuators (wave shape, frequency, phase-shift) associated with the exact pad geometry (length, width and spacing).

An additional damping function is used to take into account the relative width of channel and pads and progressively reduce the displacement from pad border to lateral position where the membrane is clamped. In the simulations, the actuator displacement according to time is sinusoidal and phase-shift between actuators 1&2 and 2&3 are equal. The peak-to-peak amplitude is fixed to a constant value of 200 µm. The gap g between the sole of the heat exchanger and the lower position of the membrane is set to 10 µm.

Phase-shift impact on flow rate

Both experimental and numerical results are reported in figure 10 in terms of time averaged flow rate (over a span of multiple times during the actuation period). Both curves exhibit a slightly asymmetric bell shape. As expected, the flow rate is zero for phase shifts of 0 and 180 degrees.

Experimentally, a maximum flow rate of 1.8 g/s is reached for a phase-shift of 60°, while numerically it is 1.70 g/s, obtained with a phase-shift of 55°.

As it can be seen from this figure, and considering the uncertainties on experiments (especially on the real actuator displacement), the agreement between numerical and experimental results is excellent (5% difference). It can thus be concluded that the numerical procedure developed is reliable and could be used for device optimization and parametric exploration. Yet the thermal behavior remains to be validated.

Temporal variations of flow rate

Figure 11 shows the instantaneous inlet and outlet flow rate for 2 phase-shifts between actuators. On the top graph -case athis phase-shift is 120 °, thus the total volume of the channel stays constant. On the bottom graph -case b-the phase shift is 55° and it corresponds to the maximum average flow rate. For both cases, the flow rate varies periodically with time as expected, reverse flow is observed and extreme values of flow rate are largely superior (in norm) to the average one.

For case a, inlet and outlet flow rates are in phase (volume conservation) while in case b there is a time shift induced by the volume variation of the channel. In both cases, the maximum direct flow rate is largely superior to the reverse one.

The ratio between the fluctuation amplitude and the average value depends directly on the actuator phase-shift.

The maximum (respectively minimum) flow rate is about 10 (respectively 3) times the average value for case a, and slightly less than 4 (respectively 2) in case b. Moreover, for case a, the flow rate variations are sinusoidal when it becomes less regular for other cases according to the actuators phaseshift.

For case a, with a phase-shift of 120° the total volume of the channel is constant over time, thus the outlet and inlet mass flow rates are identical at each instant. On the other hand, for case b the 55° phase-shift between actuators leads to temporal volume variations of the channel and thus creates a phase-shift between flow rate at the channel's extremities. This behavior depends on actuator phase-shift and actual dynamic displacement. Parametric influences will be the subject of future research work and used for thermo-hydraulic optimization of dynamic micro-channels.

CONCLUSION

Integration of the pumping function within a heat exchanger can be obtained considering dynamic morphing of at least one of the wall of the proposed heat exchanger. In addition, this dynamic morphing may conduct a significant heat transfer enhancement, making the concept particularly interesting for embedded thermal management systems.

A numerical tool has been developed that allows determining the thermo-hydraulic performances of such a heat exchanger. To meet the application constrains, the dynamic deformation has to be realized with a small number of actuators. So, only 3 actuated zones are considered in the present work. It has then been established that:

§ The mass flow rate is mainly controlled by the frequency and amplitude of the travelling wave, as well as the gap g and the phase-shift between two successive actuated zone; § High heat transfer coefficient values can be obtained, up to 16000 W/m 2 K; The numerical results have been validated comparing the numerical mass flow rates with the ones obtained with a physical prototype. The agreement between the experimental and numerical results is excellent; the numerical procedure appears thus reliable.

Figure 1 .

 1 Figure 1. Cross-section of dynamically corrugated microchannel. The lower wall is subjected to constant heat flux between 𝑥 ! and 𝑥 ! (sections 𝑆 ! and 𝑆 ! ), the gap g is the minimum height of the channel. Upper profiles are drawn for 2 different amplitudes and same gap (see orange and blue colored channels for clear distinction).

Figure 2 .

 2 Figure 2. Mesh view micro-channel at an arbitrary time. Dimension in the z-direction is magnified 50 times. The bottom wall is uniformly heated below the actuated zone (fine mesh), all other walls are kept adiabatic.

Figure 3 .

 3 Figure 3. Instantaneous velocity field: for 𝐴 ! =100µm and 𝑓 ! =10Hz. Color range (Blue : 0 -Red 1 m/s). The vertical scale is magnified 100 times. Channel height is 10 µm below center actuator and total length is 7 cm.

Figure 4 .

 4 Figure 4. Instantaneous temperature field for 𝐴 ! =100µm and 𝑓 ! =10Hz. Vertical scale is magnified 100 times. Cold fluid fill the space below 1 st actuator (here ascending) with small backflow due to the 2d actuator "pressing" the fluid on surface (height is about 50µm). The fluid is mainly driven toward 3 rd actuator and outlet.

Figure 5 .

 5 Figure 5. Influence of (top) Frequency for ! =100µm and, (bottom) Amplitude for 𝑓 ! =10Hz on mass flow rate.

Figure 6 .

 6 Figure 6. Influence of (top) Frequency for 𝐴 ! =100µm and, (bottom) Amplitude for 𝑓 ! =10Hz on heat transfer coefficient.

Figure 7 .

 7 Figure 7. Influence of gap size on (top) mass flow rate and (bottom) heat transfer coefficient for 𝐴 ! =100µm and 𝑓 ! =10Hz.

Figure 8 .

 8 Figure 8. -Left: View of the top box containing the 3 actuators (cover removed). The membrane is glued on the bottom of the actuators. -Right: View of the heat exchanger bottom wall, made of copper. The two grooves constitute the manifolds.

Figure 9 .

 9 Figure 9. Sketch of the setup: the test section is placed between two constant level reservoirs that are open to the atmosphere and whose vertical positions can be adjusted.

Figure 10 .

 10 Figure 10. Comparison between experimental and numerical time averaged mass flow rates as a function of the phase-shift between two successive actuators. The supply voltage of the actuators is sinusoidal with a frequency of 10Hz. The peak-topeak amplitude and the gap are set to 200µm and 10µm, respectively.

Figure 18 -

 18 Figure 18 -Test bench for Canopée pumping performances has been improved during the experimental campaign (replacement of weighting riolis mass-flowmeter, replacement of flexible tubes by rigid fluid circuit …). However teristics of the circuit are identical.

Figure 18 -

 18 Figure 18 -Test bench for Canopée pumping performances e test bench has been improved during the experimental campaign (replacement of weighting achine by Coriolis mass-flowmeter, replacement of flexible tubes by rigid fluid circuit …). However e main characteristics of the circuit are identical.

Figure 18 -

 18 Figure 18 -Test bench for Canopée pumping performances h has been improved during the experimental campaign (replacement of weighting riolis mass-flowmeter, replacement of flexible tubes by rigid fluid circuit …). However cteristics of the circuit are identical.

Figure 11 .

 11 Figure 11. Numerical instantaneous inlet and outlet mass flow rates: Top) 120° phase-shift and (case b -Bottom) 55° phase-shift (Frequency 10Hz, peak-to-peak amplitude 200µm, gap 10µm).

Table 1 .

 1 Presentation of global thermal and flow properties for different mesh sizes (for number of time step per period TS=50).

	BMS	𝑚 (	𝑔 𝑠	)	𝑇 ! (K)	𝑇 !" (K)	ℎ (W/m 2 K)	𝑇 !" (K)	𝑇 !" (K)
	3 mm	1.11	312.51 307.87	13829	301.1	313.8
	2 mm	1.10	312.51 307.85	13765	301.1	313.8

Table 2 .

 2 Presentation of global thermal and flow properties for different

	time steps (for BMS=2mm)
	TS
	(-)

Table 3 .

 3 Presentation of operating parameters (wave amplitude and frequency) on mass flow rate, difference of surface and mean fluid temperatures, heat transfer coefficient, inlet-outlet fluid temperatures,.

𝐴 (µm)

table below

 below

			:
	arameters name		Unit
	Voltage waveform		trapezoidal/sine/triangle
	Voltage amplitude	Min to Max voltage amplitude	V
	! "#$		V
	! "%&		V
	frequency	Frequency of voltage waveform	Hz
	Φ ()	Phase shift between actuator 1 and 2	degree
	Φ (

* Phase shift between actuator 1 and 3 degree e actuators are supplied by independent voltage sources able to adopt different waveforms as

table below

 below

		Valve (offset of the
		pressure sensor)
		Constant level tank	∆P	Three-way valve
			prototype	Imposed height
		Inlet valve	valve Outlet	difference
				Precision
				balance
		P 1	P 2
		Constant
		level tank
		Valve
				:
	me			Unit
	veform			trapezoidal/sine/triangle
	plitude	Min to Max voltage amplitude	V
				V
				V
	cy	Frequency of voltage waveform	Hz
		Phase shift between actuator 1 and 2	degree
		Phase shift between actuator 1 and 3	degree

are supplied by independent voltage sources able to adopt different waveforms as igure 19.

ACKNOWLEDGEMENT

This work has been realized in the framework of the CANOPEE project and supported by the "Fond Unique Interministériel (FUI) -18th call for projects". We gratefully acknowledge contributions from all project partners.


Franc ¸ois Julien Michel Fontaine
email: fontaine@laplace.univ-tlse.fr

Marc Pigache

Jean-Franc ¸ois Miscevic

Rouchon

Frédéric Topin

Studying impacts of travelling wave shape on pumping for active cooling

Keywords: peristaltic pumping, heat transfer enhancement, active cooling, embedded electronic systems, forced pseudotravelling wave

A planar peristaltic pumping device is studied in the scope of CPU cooling. The wall shape of the channel is imposed by a set of actuators. The purpose is to study the most appropriate driving conditions in order to optimize the coolant flow rate. Among several parameters such as frequency, wave amplitude or position and size of actuators, the phase shift of actuator supply are particularly studied. The theoretical analysis of the flow rate is performed with a simplified computational model. To validate this approach, results are compared to 3D CFD numerical simulations. In some specific operating conditions, it is demonstrated that the simplified approach allows to identifying the appropriate driving conditions.

I. INTRODUCTION

Due to increasing power density, thermal management of embedded electronics systems is nowadays a major challenge. Since 2005, a lot of efforts are conducted to improve the efficiency and avoid thermal losses of CPU with microarchitecture and software solutions [START_REF] Danowitz | Cpu db: recording microprocessor history[END_REF]. An efficient thermal control of the microprocessor temperature also reduces the failure rate [START_REF] Tong | Advanced Materials for Thermal Management of Electronic Packaging[END_REF] and the global power consumption [START_REF] Devogeleer | Modeling the temperature bias of power consumption for nanometer-scale cpus in application processors[END_REF]. In many applications, the cooling solution must be compliant with the requirements of embedded systems such as reliability, MTBF, low consumption, compactness and lightness.

In this context an innovative solution called OnduloTrans [START_REF] Topin | Conduit constitutif d'un echangeur de chaleur et echangeur de chaleur comprenant un tel conduit[END_REF] technology is proposed to cool electronic chips such as a processor (Fig. 1). It consists in a single-phase liquid heat exchanger directly put on the heat source surface. Its function is double: on the one hand it pumps the fluid and on the other hand it enhances the heat transfers between the chip and the coolant by dynamic change of the channel thickness. OnduloTrans principle consists in a flat pumping chamber with dynamic movement of one wall to produce a pseudotravelling wave and therefore a peristaltic pumping. According to the preliminary theoretical results [START_REF] Léal | Simultaneous integration, control and enhancement of both fluid flow and heat transfer in small scale heat exchangers: A numerical study[END_REF], high relative amplitude displacement of such a wave, compared to the chamber thickness, leads to both high heat transfer coefficient and flow rate (Fig. 2). The requirement of a solution size compatible with the processor dimensions implies the use of distributed actuators to produce a forced pseudo-travelling wave. With a set of several actuators, many parameters allow to modifying the travelling wave behaviour and consequently the performances of the device. This paper will focus on the impact of phase shift control between every actuator on the flow rate. An analytical model is presented and compared to 3D CFD numerical simulations, an optimal configuration is determined.

II. THE STUDIED PERISTALTIC PUMPING

A. Origin of this specific wave shape

The thermal power evacuation in the liquid depends on, the fluid properties, the temperature difference between inlet and outlet, and the flow rate (eq.1). With the OnduloTrans solution used for CPU cooling, transfer coefficient above 10000W/K.m 2 could be achieved. With such high transfer coefficient the overall temperature difference between the top of the chip and the liquid is very small. Thus, in eq.1 the ∆T can be approximated to the temperature gradient of the chip. A maximal convenient temperature gradient of 10K is recommended on the die surface. As a consequence, the thermal power dissipated by the device will be mainly limited by the flow rate.

P t = ρc p ∆T Q (1)
The actuation of the wall must be very efficient for satisfying the high flow rate requirement. To dissipate a heat power above 50W , a minimum flow rate of 200mL/min is required [START_REF] Fontaine | Solutions d'actionnement pour méthodes actives de refroidissement des systèmes embarqués[END_REF]. It leads to have a wave amplitude of several hundred micrometers. Considering this displacement amplitude and the size specifications compatible with the processor dimensions, it implies the use of distributed actuators to produce a flow [START_REF] Fontaine | Solutions d'actionnement pour méthodes actives de refroidissement des systèmes embarqués[END_REF]. Finally, the compactness requirement is essential for embedded system and the consequence is a limited number of actuators. The consequence is that an ideal sinus travelling wave cannot be achieved.

B. Hypothesis

With such conditions, the deformation of the wave shape is quasi-static, no resonance or wave propagation are exploited. Moreover, the very low discretization of the wave leads to a pseudo travelling wave working like valves. This type will be qualified as forced pseudo-travelling wave.

In this article it is supposed that the distributed actuators have a rectangular footprint on the elastic wall. All positions and sizes of all these footprints could be choose individually. In the present studied actuators are supposed perfect, which means that footprints keep their planarity and displacements are perfectly controlled. No fluid-structure interaction are taken into account, the wall is rigid enough to avoid inflation.

C. Geometry of the simulated set-up

In the studied case, all footprints are identical, equally spaced along the flow direction (x direction) and symmetrically placed in the transverse flow direction (y direction) (Fig. 3). For the simulated setup 3 actuators are chosen for convenience of presentation of results by limiting the number of phase shifts at two. The size of footprints represent 20% of the Lx length of the pumping chamber and 80% of the Ly length. The relative displacement amplitude is fixed at 95%.

D. Deformation parameters

To control the shape of the wave, time dependant functions define the z-displacement of the three footprints.A same displacement signal is chosen for all three actuators which could be for any waveforms such as sinus, triangle or square. This study will focus on a square waveform because of its high resulting flow rate. Finally the time phase shift signal will be controlled between all three actuators. As recommended in [START_REF] Fontaine | Solutions d'actionnement pour méthodes actives de refroidissement des systèmes embarqués[END_REF] the frequency is fixed at 15Hz.

III. COMPUTATIONAL METHOD FOR FLOW RATE EVALUATION

A. Principle

A theoretical formula to evaluate the flow rate is described in [START_REF] Hoepffner | Pumping or drag reduction?[END_REF] for a peristaltic pumping with a square wave-like deformation. This evaluation has been experimentally validated in [START_REF] Nakahara | A peristaltic micropump using traveling waves on a polymer membrane[END_REF]. The advantage of this method is to take fluid phenomenon To evaluate the flow rate without the use of elements methods and meshing a simple algorithm has been developed. The advantage of this solution is that it can be easily implemented in an optimization algorithm in order to deduce the optimal configuration required for the maximal flow rate.

t(i) t(i+1)
In this computational model, the flow rate is calculated from volume consideration. The pumping chamber is cut in several sections along the flow direction. For each section, the volume difference between two consecutive instants is evaluated to go through the inlet or the outlet. The height of the wall (zdirection) between two sections defines where the volume is moved (Fig. 4). In this study the section length is matching with the footprint size, but finest cutting could be taken if needed for other complex geometries.

Limitations of this model: no fluid properties and behaviour are taken into account. As consequence, no influence of frequency, pressure or viscosity can be studied.

B. Algorithm

Notations:

• The volume in a section k at the instant t(i) is named

V i (k)
• The volume difference between two instants t(i) and t(i + 1) for a section k is named DV i (k).

• The volume leaving in inlet or outlet between two instants t(i) and t(i + 1) are named respectively V in (i) and V out (i)

• At an instants t(i), for an inter-section s, the height of the wall at the center in y-direction is named z i (s)

• Between two instants t(i) and t(i + 1), from a section k to a section m, for the w step of the while loop, parts of volumes which go in direction of the inlet or outlet are named respectively V in i,k (w, m) and V out i,k (w, m)(Fig. 5) In detail, the DV i (k) of a section is evaluated to go in backward and forward sections in function of the height of inter-sections. It corresponds to the initialization of the matrix V in i,k (w, m) and V out i,k (w, m) (eq.2 and eq.3).

t(i) t(i+1)
   DV i (k) = V i (k) -V i+1 (k) V in i,k (1, k + 1) = DV i (k) V out i,k (1, k + 1) = DV i (k) (2)
V in i,k (2, k) = DV i (k) zi+1(k) zi+1(k)+zi+1(k+1) V out i,k (2, k + 2) = DV i (k) zi+1(k+1) zi+1(k)+zi+1(k+1) (3)
Then, for each inter-section j, a conflict occurs if the sum V out i,k (w, m + 1) + V in i,k+1 (w, m) is not null. This sum is therefore redirected in the following step w + 1 towards intersection j -1 and j + 1 in function of their heights. With the notations described above, this principle is interpreted in recursive sequences in (eq.4) and illustrated in Fig. 5.

           V in i,k (w + 1, j) = V in i,k (w, j + 1) + V out i,k (w, j + 2) zi+1(j) zi+1(j)+zi+1(j+2) V out i,k (w + 1, j + 3) = V in i,k (w, j + 1) + V out i,k (w, j + 2) zi+1(j+2) zi+1(j)+zi+1(j+2) (4)
From recursive sequences, the final volume inlet is the sum of first terms of V in i,k (w, m) and the final volume outlet is the sum of the last terms of V out i,k (w, m) (eq.5).

V in (i) = w k V in i,k (w, 1) V out (i) = w k V out i,k (w, end) (5)
The sequence (eq.4) is repeated until all volume differences between t(i) and t(i+1) are gone towards inlet or outlet (eq.6). These sums of (eq.5) must converge to the sum of DV i (k). With this simulated setup, less than 100 iterations per time step are needed to converge with an error inferior of 1%.

|V in (i) + V out (i) - k DV i (k)| > err ( 6
)
The algorithm is summarized in the pseudo-code below.

C. Pseudo-code

1: for all time i do 2:

for all section k do 3:

initialization eq.2 et eq.3

4:

end for 5:

w ← 1 6:

while condition eq.6 do

7:

w ← w + 1

8:
for all section k & inter-section j do 9:

recursive sequences eq.4

10:

end for 11:

evaluation of volumes inlet and outlet eq.5

12:

end while 13: end for

IV. CFD NUMERICAL SIMULATION

Numerical resolution uses a segregated approach with implicit second order temporal discretization. The time step is chosen small enough to allow an accurate description of the wall movement: typically 100 time steps per period. A commercial finite volume code (starccm+) is used in this study.

We used a structured anisotropic mesh that is dynamically deformed in order to obtain the desired shape and movement of the top wall for the channel itself (around 150000 cells and about 20 cells along vertical direction). For inlet and outlet regions a polyhedral mesh was preferred (around 50000 cells each).

The following procedure is chosen to manage the mesh deformations: we first mesh a parallelepiped channel whose height is equal to the smallest height in the deformed configuration (5% of the channel height). Then this mesh is dilated to accommodate the displacement of the surface corresponding to the chosen wave. Using this procedure allows to only stretch the initial mesh and obtain a fair control of cell size at all times.

For the tested configuration we consider a transient 3D flow with a simple K-epsilon turbulence model. No-slip conditions are applied on all material surface, inlet and outlet pressure are fixed at atmospheric pressure. The considered fluid is water with constant properties (taken at 20 • C).

The upper channel wall displacement is prescribed using the same square functions than for the analytic case. Only half of the geometry is modelled, the system is supposed symmetric relative to the vertical plane parallel to the main flow axis in the channel. Actuators geometry is identical to the one used in the previous section.

A small (Fig. 6) length of tube is added to the system in order to place inlet and outlet boundaries conditions sufficiently Fig. 6. Meshing of the fluid in 3D CFD simulations, with a scale multiplied by 100 in z-direction far from the region of interest and not induces bias on used results.

V. RESULTS AND COMPARISON

A. General parameters

Since computational model is independent of the frequency, results obtained over one period of time are linear with the frequency.

The width of footprints have been studied with the computational model. But no significant impacts are observed on the flow rate in the framework of this study.

To summarize, results below are obtained with the following simulated setup:

• the geometry represented in Fig. 3 • a frequency of 15Hz

• a square-like signal form identical for all three actuators

• a relative displacement of 95% of the channel height

B. Study of instant volume inlet and outlet

Results in Fig. 7 are obtained with phase shifts (Φ 12 ; Φ 13 ) = (60 • ; 140 • ). Φ 12 and Φ 13 being respectively the phase shift between actuators 1 & 2 and 1 & 3, counting in the x-direction. This case corresponds to the maximum flow rate with our simulated setup.

In Fig. 7 are presented the volumes V in (i) and V out (i) over a period of time. The sum of these volumes over the time represents the final volume which goes towards inlet or outlet. Because the deformation is periodical, these two sums are opposed. It means that the volume which exits at the outlet comes from the inlet. V in (i) and V out (i) are not only negative or positive, which means that back flows occur, especially when the first actuator starts to close the channel (0.5 to 0.7 of the period of time). It is also presented k DV i (k) and the sum of V in (i) and V out (i) to verify the 1% of error.

i V in (i)= -0.1767 mL; Σ i V out (i)= 0.1705 mL V in (i) V out (i) V in (i)+V out (i) Σ k DV i (k)
The same behaviour is observed for both methods. Results from the computation method are naturally smoother than those with CFD simulation. The cause of peaks in Fig. 7b is the too few numbers of time steps.

C. Study of phase shifts

The Fig. 8 shows maps of the resulting flow rate i V out (i) calculated by varying the phase shifts between actuators (Φ 12 and Φ 13 ). The same behaviour is observed with the two methods. The maximum and minimum flow rate are found with same configurations. The maximum error between these 8. Maps of flow rates, in mL/s for all possible phase shifts, 15Hz, square signal form and 95% of relative displacement maps is around 15%. It is found for the maximum flow rate by avoiding the deviant points due to numerical approximation.

Because the geometry is symmetric, both maps have a central symmetry by taking the point (180 • ; 180 • ; 0mL/s).

D. Discussion

These maps of flow rate (Fig. 8) validate the computational approach. Even if the instant volumes can be quite different (Fig. 7), the same behaviour is observed and the resulting flow rate are closed. The important point is that this error does not affect the global behaviour and the best configuration is found.

Additionally the use of this analytical approach is reinforced by its relative fast execution. Around 3h are necessary to evaluate all results (324 cases) show in Fig. 8a with an average personal computer and the MatLab software. And for 3D CFD simulations (378 cases) showed in Fig. 8b, around 30h are needed with the computational power of around 25 processors in parallel.

VI. CONCLUSION

This paper presents a specific pumping principle with the aim of using it in embedded system to cool a CPU. For this purpose a pseudo-travelling wave is produced by a set of actuators. In these conditions, the most constraining parameter is the flow rate. To evaluate this flow rate an computational model is developed. It allows to study the deformation parameters like signal form, amplitude displacement, phase shifts and also the geometry parameters(channel size, position of actuators...). This article is focused on the particular case of three actuators. The phase shift influence is explored as a flow rate control parameter. To validate the results from the computational method, a 3D CFD numerical simulation have been performed. The good accuracy of the model, its ease of use and its high speed computation make it a good solution to be implemented into an optimization algorithm preliminary analysis.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Principle of the OnduloTrans technology

Fig. 3 .

 3 Fig. 3. Studied peristaltic pumping, example with 3 footprints with adimensional lengths

Fig. 4 .

 4 Fig. 4. Principle of the computational model

Fig. 5 .

 5 Fig. 5. Distribution of the volume difference towards inlet and outlet during the while loop

Σ

Fig. 7 .

 7 Fig. 7. Evaluation of instant volumes, in mL for 60 • -140 • and 50 time steps over a period of time

  Fig.8. Maps of flow rates, in mL/s for all possible phase shifts, 15Hz, square signal form and 95% of relative displacement

ACKNOWLEDGEMENT

This work has been realized in the framework of the CANOPEE project and supported by the "Fond Unique Interministériel (FUI) -18th call for projects".


F Nimubona

S Toutain

E Jouneau

C Poullot

A Droitcourt

Dupuy

A Polat

M Dinulescu

S Fraitag

S Nimubona

F Toutain

S Jouneau

E Poullot

C Droitcourt

A Dupuy

Skin manifestations among GATA2-deficient patients

Skin manifestations among GATA2-deficient patients

Accepted Article

. clinical features, dominated by severe infections and haematological disorders such as myelodysplastic syndrome. Up to 70% of GATA2-mutated patients have dermatological features, mainly genital or extra-genital warts, panniculitis or erythema nodosum, and lymphedema. We report 3 patients presenting with common dermatological and haematological features leading to the diagnosis of GATA2 deficiency, but also with skin manifestations that have not been previously described: gingival hypertrophy, macroglossitis and glossitis, and granulomatous lupoid facial lesions. Dermatologists can encounter GATA2-mutated patients and should recognize this disorder.

INTRODUCTION:

Heterozygous mutations of GATA2, a zinc finger transcription factor, were first described in 2011 by Hsu et al. [START_REF] Hsu | Mutations in GATA2 are associated with the autosomal dominant and sporadic monocytopenia and mycobacterial infection (MonoMAC) syndrome[END_REF] in patients with monocytopenia and mycobacterial infections (monoMAC). Further research has confirmed GATA2 mutations in dendritic cell, monocyte, B-and natural killer (NK-) cell deficiency 2 , in familial myelodysplastic syndrome/acute myeloid leukemia (MDS/AML) [START_REF] Scott | GATA2 is a New Predisposition Gene for Familial Myelodysplastic Syndrome (MDS) and Acute Myeloid Leukemia (AML)[END_REF] and in Emberger syndrome (primary lymphedema with myelodysplasia). Spinner et al. [START_REF] Spinner | GATA2 deficiency: a protean disorder of hematopoiesis, lymphatics, and immunity[END_REF] reviewed the medical records of 57 patients with GATA2 mutations and identified a broad spectrum of clinical characteristics with predominantly hematological, infectious, pulmonary, dermatological, neoplastic, vascular and lymphatic features.

We report on three GATA2-mutated patients where cutaneous features preceded the manifestations related to other organ systems.

Accepted Article

.

CASE REPORTS: Case 1:

A twelve-year-old white patient was referred to our department for lymphedema of the right lower leg, evolving since the age of eleven.

He had no medical history until he was 9 when he started to have recurrent aphta and epistaxis. At 11, he developed lymphedema of the right leg.

Physical examination evidenced bilateral lymphedema, plantar warts and gingival hypertrophy which was often hemorrhagic (Figures 1 A andB). The patient was hospitalized for cellulitis of the right leg, treated with antibiotics.

Blood cell counts revealed a normal haemoglobin level alongside macrocytosis, normal platelet count, but low levels of neutrophils, lymphocytes and monocytes. A bone marrow biopsy showed dysmyelopoiesis, without myelodysplastic syndrome, and medium megakaryocyte density without excess blasts. The bone marrow karyotype was normal. The association of congenital lymphedema, multiple warts and leucopenia pointed to Emberger syndrome. Genetic testing confirmed GATA2 mutation (c.1084C>T (p.R362X) on exon 5).

Further tests are underway to investigate any deafness and to study familial GATA2 mutation status.

Case 2

A 28-year-old woman was admitted to the Respiratory department with increasing shortness of breath, dry cough and interstitial lung disease. Surgical pulmonary biopsy showed pulmonary alveolar proteinosis, and broncho-alveolar lavage evidenced lymphocytic alveolitis.

Accepted Article

. She had a history of idiopathic lymphedema affecting both lower legs, diagnosed five years earlier (Figure 1C). Lymphoscintigraphy suggested lymphatic vessel hypoplasia.

Physical examination also revealed multiple warts on the hands, sclerodermiform lesions on the legs and panniculitis on the upper limbs (Figure 1C).

Biopsies of the upper limb lesions concluded to erythema nodosum. The two biopsies showed roughly similar lesions. They were both performed in the subcutis, totally sparing the overlying epidermis and dermis. They showed thick sclerosis with horizontal, thickened and hyalinized collagen bundles associated with fragmented elastic fibers (Orcein). In the periphery some inflammatory cells were observed, grouped in clusters (Figure 1 D andE).

Long-term cultures for mycobacteria were negative in the skin biopsies.

She had an enlarged tongue with several depapillated areas, and she complained of dysgueusia (Figure 1 F).

Blood cell counts showed pancytopenia. Bone marrow biopsy was normo-cellular with threelineage dysplasia. Myelodysplastic syndrome (MDS) without karyotype anomaly was diagnosed. She was thought to have MonoMAC syndrome, and GATA2 mutation (c.1020_1029dup (p.R3444GfsX43) on exon 5) was identified. Over 9 months, MDS remained stable but her respiratory parameters deteriorated. Hematopoietic stem-cell transplantation (HSCT) is being considered.

Case 3

A 20-year-old white woman was referred to the hematology department for pancytopenia lasting 5 years. In childhood she experienced recurrent ear, nose and throat (ENT) infections (otitis, rhinitis) and labial herpes.

Accepted Article

. She presented with fatigue, weight loss, multiple warts on both hands, and lupoid lesions of the cheeks, forehead and temples (Figure 2 A andB). These facial lesions first appeared at age fifteen and none of the different treatments (topics, metronidazole, cyclins and zinc) was effective.

Two skin biopsies were performed at 2 different times, showing a granulomatous infiltrate in the upper and mid dermis in the two lesions, located mainly between hair follicles. This infiltrate was mostly made up of histiocytes, some of them epithelioid, associated with giant multinucleated cells and neutrophils in the deeper part. (Figure 2 C).

Bacterial, mycobacterial and fungal staining tests were negative. Cutaneous cultures were negative for bacteria, mycobacteria and fungi.

Blood cell counts revealed pancytopenia (including low hemoglobin, low platelet, white blood cell, neutrophil, lymphocyte and monocyte counts). Bone marrow examination showed three-lineage dysplasia leading to the diagnosis MDS. Her karyotype was normal. A GATA2 mutation (c.1060A>C (p.T354P) on exon 5) was identified and she was diagnosed with MonoMAC syndrome.

Her parents and sister were tested, but no GATA2 mutation was detected, suggesting that the patient's disorder was caused by de-novo mutation.

Because of the risk of acute myeloid leukemia (AML), she underwent curative phenoidentical allogenic stem-cell transplantation after chemotherapy.

Five months after transplantation she had no further ENT infection and the facial cutaneous lesions rapidly healed. Blood cell counts were within the normal range and the bone marrow showed total remission. Lymphedema of both lower limbs occurred a few month after hematopoietic stem cell transplantation.

Accepted Article

. Table 1 summarizes clinical and blood test results for the 3 patients.

DISCUSSION:

GATA2 is a zinc finger transcription factor that regulates early haematopoietic differentiation, and lymphatic and vascular development. Nearly 100 GATA2 mutations have been described. They appear to cause loss of function of the mutated allele [START_REF] Hsu | Mutations in GATA2 are associated with the autosomal dominant and sporadic monocytopenia and mycobacterial infection (MonoMAC) syndrome[END_REF][START_REF] Spinner | GATA2 deficiency: a protean disorder of hematopoiesis, lymphatics, and immunity[END_REF][START_REF] Pasquet | Mutations GATA2 : une entité clinicobiologique pléomorphe. Recommandations de prise en charge du « club GATA2[END_REF] . Germline mutations arise spontaneously (de novo) but are then transmitted via autosomal dominant inheritance.

GATA2 mutations have been identified in more than 300 patients and 3 large cohorts of GATA2-mutated patients have been reported [START_REF] Spinner | GATA2 deficiency: a protean disorder of hematopoiesis, lymphatics, and immunity[END_REF][START_REF] Pasquet | Mutations GATA2 : une entité clinicobiologique pléomorphe. Recommandations de prise en charge du « club GATA2[END_REF][START_REF] Collin | Haematopoietic and immune defects associated with GATA2 mutation[END_REF] .

Median age at the first clinical manifestations is 20 years (range 5 months to 78 years), although some individuals seem to have no clinical manifestation. Survival has been estimated at 91% 5 years after onset of symptoms and 67% 20 years after onset [START_REF] Spinner | GATA2 deficiency: a protean disorder of hematopoiesis, lymphatics, and immunity[END_REF][START_REF] Pasquet | Mutations GATA2 : une entité clinicobiologique pléomorphe. Recommandations de prise en charge du « club GATA2[END_REF][START_REF] Collin | Haematopoietic and immune defects associated with GATA2 mutation[END_REF] .

GATA2-mutated patients have very heterogeneous presentations (Figure 3) and a wide range of severity, from asymptomatic to life-threatening infections, respiratory failure and leukemia.

Dermatological features appear to be secondary to several conditions. Up to 70% of patients have persistent HPV infections [START_REF] Collin | Haematopoietic and immune defects associated with GATA2 mutation[END_REF] . Severe HPV infections are recalcitrant, possibly generalized, warts and condylomata [START_REF] Spinner | GATA2 deficiency: a protean disorder of hematopoiesis, lymphatics, and immunity[END_REF][START_REF] Pasquet | Mutations GATA2 : une entité clinicobiologique pléomorphe. Recommandations de prise en charge du « club GATA2[END_REF][START_REF] Collin | Haematopoietic and immune defects associated with GATA2 mutation[END_REF] . Absence of cellular immunity caused by the paucity of NK-cells or their dysfunction leads to these severe manifestations. Our 3 patients had numerous warts on the limbs. Patient 2 had no recurrence of warts after HSCT. Patients 1 and 3 had limited manifestations, but were resistant to the treatments instated. Patients infected with oncogenic 7 and non-oncogenic [START_REF] West | Generalized verrucosis in a patient with GATA2 deficiency[END_REF] HPVs have been reported. The majority of these

Accepted Article

. patients develop warts years before GATA2 diagnosis. They may develop HPV-related skin malignancies, including squamous intra-epithelial lesions, bowenoid papulosis and invasive squamous cell carcinoma. Early HPV vaccination is recommended after GATA2 mutation diagnosis.

Other severe infections induced by immunodeficiency in GATA2 syndromes may also entail cutaneous manifestations. Non-tuberculous mycobacterial infections have been described with dermatological manifestations such as ulcers of the lower limbs [START_REF] Chu | MonoMAC versus idiopathic CD4+ lymphocytopenia[END_REF] and nodular skin lesions [START_REF] Spinner | GATA2 deficiency: a protean disorder of hematopoiesis, lymphatics, and immunity[END_REF] . The most frequent complication is cellulitis. Lymphedema, with early care, can be managed with compression stockings, as for patient 1 in our report. For patients 1 and 2 lymphedema was the first symptom of their disease.

Up to one third of GATA2-mutated patients have erythema nodosum or panniculitis, usually on the lower extremities. These conditions can have several causes: NTM infections, bacterial infections or auto-immune phenomena [START_REF] Vinh | Autosomal dominant and sporadic monocytopenia with susceptibility to mycobacteria, fungi, papillomaviruses, and myelodysplasia[END_REF] (lupus-like syndromes, primary biliary cirrhosis-like liver damage and multiple sclerosis-like syndrome). Here, one of the patients (Case 2) presented with sclerodermiform changes located deep in the subcutis, resembling deep morphea. Skin biopsies show panniculitis, erythema nodosum or granulomatous lesions.

Bacteriological samples of nodular lesions may evidence non-tuberculous mycobacteria such as M szulgai, M avium complex, M abcessus.

Finally, dermatological manifestations can be neoplastic. Chronic, recurrent warts and condylomata may evolve into squamous intra-epithelial dysplasia or squamous cell carcinoma. Monitoring of patients by dermatologists is therefore important. Non HPV-related squamous-cell and basal-cell carcinomas have also been described [START_REF] Vinh | Autosomal dominant and sporadic monocytopenia with susceptibility to mycobacteria, fungi, papillomaviruses, and myelodysplasia[END_REF][START_REF] Muszynski | A woman with warts, leg swelling, and deafness[END_REF] . Additionally melanoma and 3 cases of Sweet syndrome are reported in the setting of underlying MDS/AML 4 .

Accepted Article

. Our patients had unusual cutaneous manifestations not described previously. Patient 1 had a history of gingival hypertrophy and recurrent aphta. Patient 3 had a distinctive presentation involving lupoid lesions located exclusively on her face. The skin biopsy revealed granulomatous lesions with mixed acute and chronically inflammatory cells.

Granulomatous skin lesions can occur in patients with immunodeficiency from diverse causes [START_REF] Mitra | Cutaneous granulomas associated with primary immunodeficiency disorders[END_REF] . In our patient, the negative microbiological investigations and the resolution after HSCT are suggestive of this mechanism. Manifestations associated with GATA-2 dysfunction are numerous, they are expressed in a large array of organs, and can be related to several causes (neoplastic, infectious, immunodeficiency). In our patients, it is difficult to ascertain the novelty of the manifestations. If gingival hypertrophy is rather non-specific, the particular presentation of facial non-infectious granulomatous dermatosis (case 3) is worth mentioning, since it has not been reported as a manifestation in other immunodeficiencies. The sclerodermiform changes (case 2) constitute a new finding, although we are unable to provide any clue to the related mechanisms.

In conclusion, we highlight both well-known and new dermatological features in the recently-described GATA2 mutation clinical spectrum. As they can precede other clinical symptoms, dermatologists are crucial in early diagnosis of this multiform disease. Dermatological monitoring is important for patients identified in order to detect or prevent HPV-related or non-HPV-related skin cancers.

Acknowledgement: The authors thank Ms Angela Verdier for editing the manuscript.


Lucie Rolland
email: lucierolland24@gmail.com

Jeanne Perrin

Virginie Villes

Valérie Pellegrin

Léon Boubli

Blandine Courbiere

IVF oocyte retrieval: prospective evaluation of the type of anesthesia on live birth rate, pain, and patient satisfaction

Keywords: IVF, Pain relief, Paracervical block, General anesthesia, Live birth rate

Purpose Does the type of anesthesia (paracervical block (PCB) or general anesthesia (GA)) impact live birth rate, pain, and patient satisfaction? Methods A non-randomized prospective cohort study was conducted in women treated for IVF. Two groups of patients were prospectively included: the PCB group (n = 234) and the GA group (n = 247). The type of anesthesia was determined by the patients. The primary endpoint was cumulative live birth rate by OR. Secondary endpoints were self-assessment of the patients' peri-operative abdominal and vaginal pain vs the doctors' evaluations during PCB, post-operative abdominal and vaginal pain level, and patient satisfaction in both groups. Pain levels were assessed with a numerical rating scale (NRS). Results The live birth rate was similar in both groups (19.8% in the GA group vs 20.9% in the PCB group, P = 0.764). During oocyte retrieval in the PCB group, the physicians significantly under-estimated the vaginal pain experienced by the patients (3.04 ± 0.173 for patients vs 2.59 ± 0.113 for surgeons, P = 0.014). Post-operative vaginal and abdominal pain were significantly greater in the PCB group compared to the GA group (2.26 ± 0.159 vs 1.66 ± 0.123, respectively, P = 0.005, and 3.80 ± 0.165 vs 3.00 ± 0.148, respectively, P < 0.001). Patients were more significantly satisfied with GA than with PBC (P < 0.001). Conclusion Because the LBR was similar in both groups and patient satisfaction was high, the choice of anesthesia should be decided by the patients.

Introduction

Transvaginal ultrasound-guided oocyte retrieval (OR) for assisted reproduction was first described in 1985 [START_REF] Wikland | Transvesical and transvaginal approaches for the aspiration of follicles by use of ultrasound[END_REF]. Pain during OR is caused by the aspirating needle puncturing the vaginal skin and ovarian capsule during its manipulation within the ovary during the procedure. OR is a relatively short outpatient procedure. The different types of anesthesia described for OR include general anesthesia (GA), neuraxial anesthesia (epidural or spinal), conscious sedation (CS), and injection of local anesthetic agents (paracervical block (PCB)), or any combination of these [START_REF] Vlahos | Analgesia and anesthesia for assisted reproductive technologies[END_REF]. Many studies, with sometimes contradictory results, assessed the impact of anesthetic agents on in vitro fertilization (IVF) outcome, but two meta-analyses of analgesia during OR reported that propofol, alfentanil, or lidocaine did not affect reproductive outcome [START_REF] Vlahos | Analgesia and anesthesia for assisted reproductive technologies[END_REF][START_REF] Kim | Effects of general and locoregional anesthesia on reproductive outcome for in vitro fertilization: a meta-analysis[END_REF]. In our department, except in cases of anesthetic contraindication or for organizational reasons, the type of anesthesia, GA or PCB, is chosen by the patient. The effectiveness of and satisfaction with PCB compared to GA has not been established in the literature. Due to the absence of recommendations, it is essential to assess pain and patient satisfaction under Breal conditions^to improve anesthesia protocols. PCB is an easily handled anesthesia that is minimally invasive and does not require an anesthesiologist. Koninckx and Renaer [START_REF] Koninckx | Pain sensitivity of and pain radiation from the internal female genital organs[END_REF] reported that the pouch of Douglas or uterosacral ligaments were more sensitive than the uterus, oviducts, or ovaries. Lignocaine, which is used in PCB, anesthetizes both the vaginal mucosa and the peritoneal membrane over the pouch of Douglas as well as the uterosacral ligaments [START_REF] Ng | A prospective, randomized, double-blind and placebo-controlled study to assess the efficacy of paracervical block in the pain relief during egg collection in IVF[END_REF].

The objective of our study was to compare the live birth rate, post-operative pain, and satisfaction associated with the anesthetic technique chosen by the patient, either PCB or GA.

Materials and methods

Population

We performed a prospective study from March 2014 to March 2015 in the Department of Gynecology, Obstetrics and Reproductive Medicine of the University Hospital La Conception (Marseille, France). Each patient gave written informed consent prior to participating in the study. Criteria for inclusion were as follows: (i) patient was admitted to the operating room for oocyte retrieval (IVF or ICSI cycle), and (ii) patient signed informed consent for the survey. Exclusion criteria were as follows: (i) patient undergoing oocyte retrieval for fertility preservation before cancer or genotoxic treatment.

Ovarian stimulation and oocyte retrieval

The gonadotropin dosage was selected individually, taking into account the patient's age, body mass index (BMI), and AMH ((μg/L), Beckman Coulter Kit, Brea, USA) levels and previous response to controlled ovarian stimulation (COS). The ovarian response was monitored via serum estradiol levels and transvaginal ultrasound. Ovulation was triggered using 10,000 IU of HCG (or Ovitrelle®, MerkSerono, Darmstadt, Germany). Transvaginal OR was performed 36 h after triggering under ultrasound guidance with a single lumen aspiration needle (17 GA, Cook, Brisbane, Australia). OR was performed by six different operators with equivalent training, and no flushing was performed in any group.

Anesthetic procedure

The anesthesia technique was decided by the patient during a consultation with the anesthetist before the start of ovarian stimulation. Patients were all counseled individually about the different techniques and possible risks of the procedure. PCB could be imposed in cases of GA contraindication or the unavailability of the anesthetist's medical staff. Patients were allowed to reconsider the choice of anesthesia at any time. On the day of OR, all patients received 25 mg of hydroxyzine at 7 am.

The PCB group also received premedication with 20 mg of nefopam (Medisol, Lyon, France) by the sublingual route 1 h before intervention. PCB with 10 mL of 2% lidocaine (200 mg lidocaine) was administered 5 min before retrieval at 2, 6, and 10 o'clock around the cervix. If necessary, patients received an additional analgesic during surgery.

In the GA group, patients received 1 g of IV paracetamol (B. Braun, Melsungen, Germany), immediately before the procedure. Induction was performed with propofol 2.5 mg/kg and alfentanil 20 μg/kg. Maintenance of anesthesia was assured by propofol boluses (1 mg/kg) and alfentanil (250 to 500 μg) if necessary, depending on the duration of the procedure. Manual ventilation was practiced with 50% O2/50% air or O2 100% and no inhalational anesthetic gas.

Patient characteristics

The clinical and biological characteristics of the patients and each IVF cycle were collected in our medical database (Medifirts, Montigni le Bretonneux, France). We assessed age, BMI, smoking, infertility duration, hormonal dosage (FSH, LH, estradiol, AMH), stimulation cycle (total dose of gonadotropin used, estradiol level day of ovulation triggering), attempt number, causes of infertility, and COS protocol.

IVF outcome

The primary outcome was cumulative live birth rate by OR, which was defined as delivery of a live fetus after 22 completed weeks. We considered cumulative live birth rates including thawing cycles. We evaluated the number of oocytes retrieved, the number of mature oocytes, 2-pronuclear zygotes (fertilized oocytes), and the number of embryos transferred. We also evaluated the clinical pregnancy rate (as defined by an ultrasound-verified pregnancy with fetal heartbeat) and first trimester miscarriage rate.

Assessment of peri-operative pain level in the PBC group

The pain level was assessed with numerical rating scale (NRS) (0 = no pain to 10 = intolerable), which is a commonly used pain assessment scale [START_REF] Rodriguez | Pain measurement in the elderly: a review[END_REF][START_REF] Hawker | Measures of adult pain: visual analog scale for pain (VAS pain), numeric rating scale for pain (NRS pain), McGill pain questionnaire (MPQ), short-form McGill pain questionnaire (SF-MPQ), chronic pain grade scale (CPGS), short form-36 bodily pain scale (SF-36 BPS), and measure of intermittent and constant osteoarthritis pain (ICOAP)[END_REF][START_REF] Bourdel | Systematic review of endometriosis pain assessment: how to choose a scale?[END_REF]. For the PCB group, the patient peri-operative vaginal and abdominal pain level was obtained by a nurse just after OR in the operating room. The physician's estimation of the patient's abdominal and vaginal pain during OR was blindly collected.

Assessment of post-operative pain level and satisfaction

A post-operative survey was given to all patients 4 h after oocyte recovery, and it evaluated vaginal and abdominal pain and patient satisfaction (very satisfied, satisfied, not satisfied, not satisfied at all, or no answer). For patients who had already had both types of anesthesia, we asked what type of anesthesia they would prefer for a future attempt. To investigate the relationship between pain and satisfaction, we compared the post-operative pain of Bsatisfied^patients (those who reported being Bvery satisfied^or Bsatisfied^) with the post-operative pain of Bunsatisfied^patients (those who reported Bnot being satisfied^or Bnot satisfied at all^).

Ethics statement

The French Ethical Committee of Research in Obstetrics and Gynecology (CEROG 2014-GYN-1105) approved this study. Each patient gave written informed consent prior to participating in the study.

Statistical analysis

Analysis of the data was performed with Statistical Package for Social Sciences version 17.0 (SPSS Inc., Chicago, IL, USA). Statistically significant differences between groups were determined using unpaired Student's t tests or chi 2 tests as appropriate. All tests were two-tailed tests, and a P value less than or equal to 0.05 was considered statistically significant. Values were expressed as the mean ± standard deviation unless stated otherwise. We also performed subgroup analysis of peri-and post-operative pain levels among patients undergoing their first attempt (T1) and those who had already had at least one attempt (>T1). The objective was to determine whether an OR history can affect the perception of pain experienced by patients.

Results

A total of 234 patients in the PCB group were compared to 247 patients in the GA group. The clinical and biological characteristics of the patients are shown in Table 1. We did not find significant differences between the two groups in terms of age, infertility duration, smoking, day 3 FSH, AMH level, dose of gonadotropin used, E2 level during ovulation induction, etiologies of infertility, stimulation protocol used, and number of first attempts. The BMI was higher in the PCB group (24.46 ± 5.765 vs 23.36 ± 4.828, P = 0.026).

The live birth rates in the GA group and PCB group were similar, 19.8 vs 20.9%, P = 0.764 (Table 2). In the GA group vs the PCB group, more oocytes (10.29 ± 7.163 vs 9.09 ± 5.335, P = 0.037) and mature oocytes (7.87 ± 5578 Peri-operative vaginal pain estimated by the physicians compared to the patients' evaluations was respectively 2.59 ± 1.639 vs 3.04 ± 2.495, P = 0.014. The physicians' estimation of abdominal pain was not significantly different from that experienced by the patients (Table 3).

The post-operative pain level and satisfaction of various procedures as scored by the patients are summarized in Table 4. Distribution of post-operative abdominal and vaginal pain in GA and PCB group are summarized in Fig. 1. Postoperative pain was significantly higher in the PCB group than in the GA group, with NRS 2.26 ± 2.413 vs 1.66 ± 2.114, P = 0.005, for vaginal pain and 3.80 ± 2.499 vs 3.00 ± 2.324, P < 0.001, for abdominal pain. In the GA group, 98.4% of patients were very satisfied or satisfied vs 80.8% in the PCB group, and patients were more significantly satisfied in the GA group (P < 0.001). Patients who reported being not satisfied or not satisfied at all were almost always in the PCB group (P < 0.001). For patients with a history of OR with two anesthetic techniques (n = 102), 62.75% (n = 64) reported preferring GA and 37.25% preferred PCB. We reported that patients who were Bnot satisfied^had significantly more pain than patients who were Bsatisfied,^with 4.47 ± 2.712 vs 1.74 ± 2.102 for post-operative vaginal pain (P < 0.001) and 6.25 ± 2.369 vs 3.15 ± 2.299 (P < 0.001) for post-operative abdominal pain, respectively.

A subgroup analysis was performed to assess whether OR history can affect the perception of pain experienced by patients, and it is summarized in Table 5. Post-operative abdominal and vaginal pain were similar in the T1 and >T1 groups. In the PCB group, peri-operative vaginal pain was higher in the T1 group than in the >T1 group (3.41 ± 2.433 vs 2.67 ± 2.502, P = 0.029). The peri-operative abdominal pain level was similar in both groups. On 234 patients in PCB group, 10.3% (n = 24) needed supplementary analgesia (five had alfentanil, seven had CS (alfentanil and propofol), four had sublingual acupan, five had inhalation of nitrous oxide, for three patients, the additional anesthesia was undefined). Two hundred thirteen patients received PCB by choice, 9 for medical reason, and 12 for the unavailability of the anesthetist's medical staff. Post-operative abdominal and vaginal pain were not statistically different between groups (Table 6).

Discussion

In this study, anesthesia protocol used had no impact on IVF LBR. Our results are similar to those reported in the literature, but these studies have a low statistical power. Bümen et al. [START_REF] Bümen | A comparison of intravenous general anesthesia and paracervical block for in vitro fertilization: effects on oocytes using the transvaginal technique[END_REF] reported in 2011 the same LBR in a prospective study comparing remifentanil/propofol-based GA (n = 32) vs PCB (100 mg of 2% prilocaine and intramuscular (IM) meperidine) (n = 38). Christiaens et al. [START_REF] Christiaens | Comparison of assisted reproductive technology performance after oocyte retrieval under general anaesthesia (propofol) versus paracervical local anaesthetic block: a casecontrolled study[END_REF] reported no impact on a casecontrol study comparing alfentanil/propofol-based GA (n = 101) with PCB (400 mg mepivacaine hydrochloride with alfentanil) (n = 101). In our study, the number of oocytes retrieved and the number of mature oocytes was significantly higher with GA, without a clinical difference in LBR. Hammadeh et al. [START_REF] Hammadeh | Effects of general anaesthesia vs. sedation on fertilization, cleavage and pregnancy rates in an IVF program[END_REF] reported in 1999 that general anesthesia improved the success rate of oocyte retrieval. They explained their results as improved comfort for both the patient and gynecologist during OR. In addition, general anesthesia enables the gynecologist to harvest even smaller follicles, increasing the retrieval of small and immature oocytes.

In the present study, we observed significantly higher postoperative vaginal and abdominal pain with PCB than GA. To our knowledge, there are no clinical trials comparing postoperative pain associated with these two types of anesthesia. We consider that the significant difference in the postoperative pain level for both types of anesthesia is clinically acceptable. Indeed, post-operative vaginal pain was <3 in both groups, and the difference in post-operative abdominal pain scores, 3 for GA and 3.8 for PCB, was not clinically significant. One of the main limitations of this study is the lack of randomization. The aim of our study was not to assess the superiority of one method over the other. Our goal was to assess pain and patient satisfaction Bin real life,^when the type of anesthesia is decided by the patient. Only BMI differed slightly in the patient characteristics between the two groups. The BMI was higher in the PCB group than in the GA group. Other authors observed in a randomized study comparing PCB with vaginal gel that BMI is positively correlated with total pain [START_REF] Tummon | Lidocaine vaginal gel versus lidocaine paracervical block for analgesia during oocyte retrieval[END_REF][START_REF] Egan | Anesthetic impact of body mass index in patients undergoing assisted reproductive technologies[END_REF], which could partly explain the difference in pain scores between our two groups. We consider two other weaknesses of our study. First, because we did not randomize, anesthesia protocols and the management of post-operative pain were not standardized. We did not quantify the amount of analgesic used to relieve patient post-operative pain. Second, patient's anxiety before OR was not assessed in our study. Indeed, higher levels of anxiety during oocyte retrieval seem positively associated with pain intensity and anxiety [START_REF] Ng | Anxiolytic premedication reduces preoperative anxiety and pain during oocyte retrieval. A randomized doubleblinded placebo-controlled trial[END_REF][START_REF] Cerne | Pre-ovarian block versus paracervical block for oocyte retrieval[END_REF][START_REF] Frederiksen | Predictors of pain during oocyte retrieval[END_REF].

We report a high degree of satisfaction in both groups, but patients who reported being not satisfied or not at all satisfied were almost always in the PCB group. In a prospective randomized study between PCB and PCB+CS, 80% of patients with PCB alone were very satisfied or satisfied [START_REF] Ng | Paracervical block with and without conscious sedation: a comparison of the pain levels during egg collection and the postoperative side effects[END_REF]. In the literature, there is satisfaction with GA of between 88 and 100% [START_REF] Ben-Shlomo | Midazolam/ketamine sedative combination compared with fentanyl/propofol/isoflurane anaesthesia for oocyte retrieval[END_REF][START_REF] Casati | Anaesthesia for ultrasound guided oocyte retrieval: midazolam/remifentanil versus propofol/fentanyl regimens[END_REF][START_REF] Guasch | Comparison of 4 anesthetic techniques for in vitro fertilization[END_REF]. The lowest degree of satisfaction in our PCB group may be related to the higher peri-and post-operative pain for these patients. Notably, despite the high peri-operative pain in the PCB group, only 10.3% of patient needed additional analgesia during the retrieval (89.7% of retrievals were performed with PCB only). For [START_REF] Ng | Paracervical block with and without conscious sedation: a comparison of the pain levels during egg collection and the postoperative side effects[END_REF], oocyte retrieval was successfully performed without any additional sedation in 89.3% of patients in the PCB group. This paradox may indicate that infertile patients undergoing oocyte retrieval are highly motivated and may be reluctant to demonstrate pain for fear of distracting the surgeon and interfering with the success of the procedure [START_REF] Trout | Conscious sedation for in vitro fertilization[END_REF]. This is supported by the observation that despite the high satisfaction rate in both groups, most patients who already had two types of anesthesia would choose GA for a future IVF attempt.

Some studies reported that pain scores during OR may be influenced by previous experience. Gohar et al. [START_REF] Gohar | The use of sedation only during oocyte retrieval for in vitro fertilization: patients' pain self-assessments versus doctors' evaluations[END_REF] reported that the second cycle was less painful than the first cycle. In our study, post-operative pain was not related to the number of attempts.

In conclusion, the type of anesthesia chosen by our patients had no impact on LBR. GA seems to be the least painful and most satisfactory technique for our patients. Nevertheless, PCB seems a reasonable alternative, and the choice of anesthesia (excluding medical contraindication) may be given to patients but patients should be advised that PCB IVF may be more painful. In our center, many parameters, such as peri-and postoperative pain management and psychological factors, must be evaluated and improved to make this procedure more endurable.

Compliance with ethical standards The French Ethical Committee of Research in Obstetrics and Gynecology (CEROG 2014-GYN-1105) approved this study. Each patient gave written informed consent prior to participating in the study.

Funding None declared.

Conflicts of interest

The authors declare that they have no competing interests.

Fig. 1

 1 Fig. 1 Distribution of postoperative abdominal and vaginal pain in general anesthesia group (GA) and paracervical block (PCB) group. NRS numerical rating scale

Table 1

 1 Clinical and biological characteristics of patients undergoing vaginal oocyte retrieval in general anesthesia group (GA) and paracervical block group (PCB)

	GA (n = 247) PCB (n = 234)

a t test b Chi 2

Table 2

 2 IVF results of patients undergoing vaginal oocyte retrieval in general anesthesia group (GA) and in paracervical block group (PCB)

	GA (n = 247)	PCB (n = 234)

Table 3

 3 Peri-operative evaluation of vaginal and abdominal pain felt by the patient and considered by the physician in paracervical block group (numerical rating scale)

		Patient	Physician
	Peri-operative pain level (mean ± SD) a
	Vaginal pain	3.04 ± 2.494	2.59 ± 1.639*
	Abdominal pain	4.36 ± 2.628	4.00 ± 2.35
	*Statistically significant (P < 0.05)
	a t test

b Chi 2

Table 5

 5 Subgroup analysis of OR pain level among patients undergoing their first IVF attempt (T1) and those who already had at least one IVF attempt (>T1)

		T1	>T1
	PCB peri-operative pain level (mean ± SD) a
	Vaginal pain	3.41 ± 2.433	2.67 ± 2.502*
	Abdominal pain	4.25 ± 2.74	4.39 ± 2.547
	PCB post-operative pain level (mean ± SD) a
	Vaginal pain	2.50 ± 2.534	2.04 ± 2.290
	Abdominal pain	3.88 ± 2.701	3.74 ± 2.317
	GA post-operative pain level (mean ± SD) a
	Vaginal pain	1.6 ± 2.060	1.71 ± 2.161
	Abdominal pain	2.88 ± 2.350	3.09 ± 2.308

*Statistically significant (P < 0.05) a t test

Table 6

 6

	Paracervical block
	group: Comparison of pain level between patients who had a PCB		Post-operative vaginal pain level (mean ± SD) a	Post-operative abdominal pain level (mean ± SD) a
	by choice or by obligation
	(general anesthesia (GA)	Choice	2.12 ± 2.305	3.70 ± 2.401
	contraindication, unavailability of	n = 213
	the anesthetists' medical staff)	GA contraindication	3.00 ± 3.055	4.78 ± 2.700
	(numerical rating scale)	n = 9
		Unavailability of the	3.46 ± 2.700	4.07 ± 3.050
		medical staff
		n = 12
		*Statistically significant (P < 0.05)

a t test