Béatrice Pano

Zhao * Yishen

Philippe Chevrel

Fabien Claveau

Franck Mars

Shared Control Based on an Ecological Feedforward and a Driver Model Based Feedback

Keywords: Identification for control, Shared control, cooperation and degree of automation, Robust control, Vehicle dynamic systems

Haptic shared control is a consistent way to design an assistance for the lateral control of a vehicle. The most important problem raised by haptic shared control is to minimize useless conflicts between the driver and the assistance. To deal with, this paper proceeds in two stages. The first is concerned with feedforward synthesis in a new way, by identifying mainly the geometric part of driving from real driver data. The torque to apply to the steering wheel and more generally the reference trajectory is thus obtained from a second order model fed by the road curvature. Then, the feedback is designed based on a driver-vehicle-road model, using a mixed 𝐻 2 /𝐻 ∞ control synthesis involving both lane following performance and sharing capabilities indicators. Finally, the shared control strategy is simulated on Matlab/Simulink using a vehicle-road model. The results obtained show good features both in terms of lane following and sharing performances. This control strategy seems then to be an interesting candidate for haptic shared control.

INTRODUCTION

Haptic shared control in the context of lateral control of a vehicle is a solution which allows to involve both the controller and the driver in the steering task. It is investigated in the literature as it improves the lane following performance [START_REF] Benloucif | Online adaptation of the Level of Haptic Authority in a lane keeping system considering the driver's state[END_REF][START_REF] Griffiths | Shared control between human and machine: haptic display of automation during manual control of vehicle heading. 12th International Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems[END_REF][START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF]. Moreover, it can increase the security on the road which is a big challenge in today's world; for example, by preventing the driver to come out of the road when doing a second task [START_REF] Blaschke | Driver distraction based lane-keeping assistance[END_REF].

By using a haptic interface for shared control, the communication between the assistance and the driver is improved. The driver can know the command applied by the assistance through the steering wheel. But this communication have to be intuitive for the driver in order to minimize conflicts between the assistance and the driver [START_REF] Abbink | A Topology of Shared Control Systems-Finding Common Ground in Diversity[END_REF][START_REF] Mugge | Haptic Guidance Needs to Be Intuitive Not Just Informative to Improve Human Motor Accuracy[END_REF]. Then, using a driver model to synthetize the assistance make its actions more understandable for the driver and decreases the control effort applied by the driver [START_REF] Abbink | The importance of including knowledge of neuromuscular behaviour in haptic shared control[END_REF].

Efficient solutions for haptic shared control were proposed earlier using a cybernetic driver model [START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF][START_REF] Sentouh | A sensorimotor driver model for steering control[END_REF] to predict its short term intention and so favouring cooperation over contradiction. The driver model was identified successfully from real drivers [START_REF] Saleh | Human-like cybernetic driver model for lane keeping[END_REF] on the LS2N driving simulator and from real car experiments [START_REF] Hermannstädter | Driver Distraction Assessment Using Driver Modeling[END_REF]. Here, the authors propose to adopt another strategy, making a clear separation between feedforward and feedback actions, to facilitate possible interaction with the tactical level of autonomous cars. Moreover, the feedforward proposed doesn't require infinite dimension FIR model implementation [START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF].

Explicit separation between feedforward and feedback was sometimes considered for lateral control of autonomous vehicles [START_REF] Attia | Reference generation and control strategy for automated vehicle guidance[END_REF][START_REF] Kapania | Design of a feedbackfeedforward steering controller for accurate path tracking and stability at the limits of handling[END_REF][START_REF] Kuwata | Motion Planning in Complex Environments Using Closed-loop Prediction[END_REF], but in a different context, not considering torque command and haptic interactions. The aim in this paper is to take the driver into account in both parts. The feedforward relies on a model identifying mainly the geometric part of driving in order to supply a reference trajectory. The feedback is based on a 𝐻 2 /𝐻 ∞ output feedback taking benefits of a driver-vehicle-road dynamic model, by optimizing some criteria linked with the lane following and sharing performances and with robustness. This paper is organised as follows: section 2 shows the global architecture model used for the haptic shared control strategy. Section 3 presents the way of using identification theory for the feedforward part synthesis of the e-copilot, aiming for an ecological lateral control. Section 4 presents the 𝐻 2 /𝐻 ∞ control synthesis proposed for the feedback part, from the driver-vehicle-road model together including the feedforward action. Section 5 presents the simulation conditions used to assess the control strategy and the results obtained. Finally, the conclusion take place in section 6.

SHARED CONTROL STRATEGY

Architecture

Fig. 1. Scheme of the control strategy

The shared control strategy proposed here is split in two parts (see Fig. 1.). First, a feedforward (green dotted rectangle), which consists in a global identified model of a driver model in interaction with the vehicle-road model (see section 3). This model allows to obtain a reference trajectory constituted by the torque command reference and the state reference for the feedback part. Secondly, a 𝐻 2 /𝐻 ∞ feedback part (red dotted rectangle) is designed to make the vehicle following the reference trajectory in spite of disturbances, while guarantying good sharing properties (for acceptability purposes). The design methodology associated to this part is detailed in section 4.

The two parts, feedforward and feedback are designed sequentially. The level of sharing is controlled at two different places materialised by the two parameters 𝛼 𝑎𝑛𝑡 and 𝛼 𝑐𝑜𝑚𝑝 .

Systems modelling

The useful model for design and simulation, and the associated signals that will be manipulated all along this paper can be defined as follows; a vehicle-road model described in [START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF] which represents the dynamics of the vehicle and the position of the vehicle on the road can be written as:

𝑥̇𝑣 𝑟 = 𝐴 𝑣𝑟 𝑥 𝑣𝑟 + 𝐵 1𝑣𝑟 (Γ 𝑎 + Γ 𝑑 ) + 𝐵 2𝑣𝑟 𝜌 𝑟𝑒𝑓 + 𝐵 3𝑣𝑟 𝐹 𝑤 (1)
With 𝑥 𝑣𝑟 = [ 𝛽 𝑟 𝜓 𝐿 𝑦 𝐿 𝛿 𝑑 𝛿 𝑑 ̇]𝑇 the vehicle-road state where 𝛽 is the slip angle, 𝑟 is the yaw rate, 𝜓 𝐿 is the heading error angle, 𝑦 𝐿 is the lateral error between the vehicle and the road centre at the look-ahead distance 𝑙 𝑠 and 𝛿 𝑑 is the steering wheel angle. Γ 𝑎 and Γ 𝑑 are respectively the assistance and the driver torque applied on the steering wheel, 𝜌 𝑟𝑒𝑓 is the road curvature and 𝐹 𝑤 is the side wind resultant applied on the gravity centre of the vehicle. Matrices 𝐴 𝑣𝑟 , 𝐵 1𝑣𝑟 , 𝐵 2𝑣𝑟 and 𝐵 3𝑣𝑟 can be found in (Saleh, 2012b;[START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF].

The driver model explicitly represented in Fig. 1. (blue box) is a cybernetic driver model (3 rd order model) designed and identified according to the approach proposed in [START_REF] Mars | Modelling human control of steering for the design of advanced driver assistance systems[END_REF][START_REF] Saleh | Human-like cybernetic driver model for lane keeping[END_REF]. The procedure will not be recalled here, but the main point is that coherently with a real driver, the model's input is made of the near and far visual points 𝜃 𝑛𝑒𝑎𝑟 , 𝜃 𝑓𝑎𝑟 , the self-aligning torque Γ 𝑠 , and the steering wheel angle 𝛿 𝑑 and the model's output is the torque applied by the driver to the steering wheel Γ 𝑑 . 𝑥̇𝑑 = 𝐴 𝑑 𝑥 𝑑 + 𝐵 𝑑 [𝜃 𝑓𝑎𝑟 𝜃 𝑛𝑒𝑎𝑟 𝛿 𝑑 Γ 𝑠 ] 𝑇

(2)

Γ 𝑑 = 𝐶 𝑑 𝑥 𝑑
Then, the dynamic model is identified from experimental data either from a driving simulator in [START_REF] Ameyoe | Identification of a Linear Parameter Varying Driver Model for the Detection of Distraction[END_REF][START_REF] Saleh | Human-like cybernetic driver model for lane keeping[END_REF] or a real car in [START_REF] Hermannstädter | Driver Distraction Assessment Using Driver Modeling[END_REF].

In this study, this model is supposed to be known and will be used for the feedback part of the haptic shared control. Notice that the yellow case T1 in Fig. 1. represents the calculation done from the vehicle-road state 𝑥 𝑣𝑟 to obtain the driver model inputs 𝑌 𝑑 = [𝜃 𝑓𝑎𝑟 𝜃 𝑛𝑒𝑎𝑟 𝛿 𝑑 Γ 𝑠 ] 𝑇 .

The next two sections give details on the design methodology for the feedforward and feedback parts, both taking into consideration the driver behaviour, but through two different driver model identifications.

FEEDFORWARD DESIGN: GEOMETRIC DRIVING IDENTIFICATION

Trajectory generator

The reference trajectory involved in the feedforward part in Fig. 1. can be detailed as in Fig. 2.

Fig. 2. Trajectory generator

The reference trajectory is composed of the torque Γ 𝑟𝑒𝑓 and the vehicle-road state 𝑥 𝑟𝑒𝑓 , these signals are assumed to be close to those which were found if the driver would have driven the vehicle alone. This can improve considerably the results in terms of sharing performance by decreasing conflicts between the driver and the assistance. That is why the level of sharing of the feedforward part is applied on the reference command torque as : Γ𝑎 𝑟𝑒𝑓 = 𝛼 𝑎𝑛𝑡 Γ 𝑟𝑒𝑓 .

Trajectory generator design methodology

Among classical solutions, one may quote [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF] which manipulates the bicycle model to find relationship between the road curvature assumed to be constant and a consistent reference trajectory; that is to say a constant steering wheel angle, yaw rate and steering angle, a zero lateral error, and what they have called the desired heading error angle.

Note that this solution can be limiting (though very useful and used), both by its restrictive hypothesis (constant curvature), and by the fact that the output considered is the steering wheel angle and not the torque. What is proposed is to make use of experimental data from the driver to identify the geometric part of driving, to obtain Γ 𝑟𝑒𝑓 and 𝛿 𝑑 𝑟𝑒𝑓 , associated to the vehicleroad model, leading to (𝛽 𝑟𝑒𝑓 , 𝑟 𝑟𝑒𝑓 , 𝜓 𝐿 𝑟𝑒𝑓 , 𝑦 𝐿 𝑟𝑒𝑓 , 𝛿 ̇𝑑𝑟𝑒𝑓 ). More precisely, the model to be identified is the one making possible to predict part of driving that can be explained directly from the road curvature. So it doesn't constitute a driver model as the one considered in ( 2), but rather its projection for feedforward control use, hoping the latter is more ecological than classical solution.

The assumption made here is that, when driver is steering the vehicle following a curve, there exists a reference torque and angle to be applied on the steering wheel if the road curvature is known. The driver will actually act back and forth on the steering wheel to change the torque and angle, to stay around the reference values sought on the basis of geometric vision; this despite the uncertainties and disturbances. It is chosen here to consider them as noise, as shown in Fig. 3. Therefore, the output error method (OE) is used here [START_REF] Ljung | System Identification Theory for the User[END_REF], considering the SIMO model of Fig. 3. As depicted, the dynamics are considered as shared by all outputs.

𝐵 1 = 𝑏 1 (1) 𝑠 -1 + ⋯ + 𝑏 𝑛 𝑏 (1) 𝑠 -𝑛 𝑏 … 𝐵 7 = 𝑏 1 (7) 𝑠 -1 + ⋯ + 𝑏 𝑛 𝑏 (7) 𝑠 -𝑛 𝑏 𝐹 = 1 + 𝑓 1 𝑠 -1 + ⋯ + 𝑓 𝑛 𝑓 𝑠 -𝑛 𝑓
For the sake of identification, it could be converted to continuous-time state-space model:

{ 𝑥̇= 𝐴𝑥 + 𝐵𝑢 𝑦 = 𝐶𝑥 + 𝐷𝑢 + 𝑒
where 𝑢 = [𝜌] , 𝑦 = [ Γ 𝑑 𝛽 𝑟 𝜓 𝐿 𝑦 𝐿 𝛿 𝑑 𝛿 𝑑 ̇]𝑇 and 𝑒 = [ 𝑒 1 … 𝑒 7] 𝑇 ; 𝐴, 𝐵, 𝐶 and 𝐷 are matrices in controllable canonical form. It must be noticed that the order of the model to be chosen comes from the experimental data (see next section).

Experiments

First Experiment

The first experiment was carried out on a fixed-base driving simulator (SCANeR-OKTAL). It is equipped with a complete dashboard, a common five-speed gear stick, pedals of gas, brake and clutch, and a TRW direction system with steering wheel. The visual scene is displayed on 3 LCD screens, a central one in front of driver and two others oriented to the centre one with 45°. They cover a field of view of 25° on height and 115° on width. The visual scene transmits the road characteristics as perceived by driver via the windshield. A small family car of type Peugeot 307 is chosen as vehicle model in this experiment.

Two participants (1 female and 1 male) having more than 10 years of driving experience took part in the experiment. They were asked to drive on a virtual road (see Fig. 5) with velocity between 70 and 80 km/h. During experiment, the road curvature corresponding to the road ahead of driver is retrieved by simulator. This replaces the process of getting road curvature on real vehicles, where the border lines of lane are filmed by cameras and proceeded with spline interpolation. In addition, driver torque and steering wheel angles are recorded by the steering system on simulator.

Second Experiment

The second experiment was realized on Matlab / Simulink  by simulating the driver-vehicle-road (DVR) model [START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF] defined in section 2.2.; the detailed driver model (2) had been a priori established via knowledge of human visual and neuromuscular behaviours for vehicle lateral control during turning. The vehicle-road model in the simulation is a bicycle model, which was identified and calibrated by previous trials on the simulator SCANeR in order to ensure coherence of model parameters with the vehicle used in the first experiment. The driver model is able to "drive" the vehicle-road model with a fixed speed 60 km/h on a predefined road (see Fig. 6). As in the first experiment, necessary data for input and outputs is saved after simulation. Fig. 6. Road in second experiment

State-space model identification

In both experiments, the raw data is separated into two parts with one part for identification and another for validation.

The first step to identify the OE model is to define system order. This is accomplished by studying the empirical transferfunction estimate (ETFE) between inputs and outputs. Fig. 7 shows the ETFE based on identification data of female participant in the first experiment, with a Hamming window of 𝛾 = 30. After analysis, a second order system is a reasonable choice.

Fig. 7. Bode diagram of ETFE

The controllable canonical form of matrix 𝐴, 𝐵 and can then be parametrized as

𝐴 = [ 0 1 -𝑓 2 -𝑓 1 ] , 𝐵 = [ 0 1 ], 𝐶 = [ 𝑏 2 (1) 𝑏 2 (2) 𝑏 2 (3) 𝑏 2 (4) 𝑏 2 (5) 𝑏 2 (6) 𝑏 2 (7) b 1 (1) 𝑏 1 (2) 𝑏 1 (3) 𝑏 1 (4) 𝑏 1 (5) 𝑏 1 (6) 𝑏 1 (7) ]
𝑇 They are finally identified thanks to the prediction error minimization (PEM) method [START_REF] Ljung | System Identification Theory for the User[END_REF]) implemented in the system identification toolbox of Matlab (version R2017a).

Results

By lack of place, Table 1 shows only the first transfer functions By comparing the simulated response with validation data, the fit rate could be calculated as:

𝐹𝐼𝑇 = (1 - ‖𝑦 -𝑦 ̂‖ ‖𝑦 -𝑦 ̅‖ ) × 100%
where 𝑦 ̂ is the simulated response, 𝑦 is the validation data and 𝑦 ̅ = 𝑚𝑒𝑎𝑛(𝑦). The comparison of outputs and calculation of fit rate for each participant in first experiment and for the simulation data in second experiment are respectively shown in Fig. 11, 12 and 13 (cf. Appendix). The bode diagrams for each OE model identified are shown in Fig. 14 and15.

In Fig. 11 and 12, the outputs of identified OE model issued from road curvature behave like a reference signal for both driver torque and steering wheel angle. The real data from experiments representing drivers' behaviour changes around these references. This confirms the assumption that the driver will actually try to stay around the reference values sought on the basis of geometric vision with some back and forth behaviour. There is also a large increase in fit percentage between the first and second experiment since the second one uses an a priori identified driver model, which has already eliminated these noises in driver's behaviour and thus results in a more fitting model compared to validation data.

The bode diagram in first experiment (see Fig. 14) shows a similarity of dynamics between the OE model of female participant and the one of male participant. The bode diagram for the OE model in second experiment (see Fig. 15) shows a narrow confidence region around the identified OE model, which means that the identified model is highly credible.

FEEDBACK DESIGN; 𝐻 2 /𝐻 ∞ STATIC OUTPUT FEEDBACK CONTROLLER

The feedback algorithm relies on a output feedback synthesis of a 𝐻 2 /𝐻 ∞ command applied on the difference between the real vehicle-road state, 𝑥 𝑣𝑟 , and the reference vehicle-road state, 𝑥 𝑟𝑒𝑓 . The use of an output feedback allows to select only measurable values for the feedback instead of having to implement an observer to approximate unmeasurable values as the driver state. The torque command can be written as: is the lateral acceleration of the vehicle. 𝑇 𝑐𝑜𝑚𝑝 can be decomposed in column as:

Γ𝑎 𝑓𝑏 =
𝑇 𝑐𝑜𝑚𝑝 = ( 𝑇 Γ𝑎 𝑟𝑒𝑓 𝑇 𝑥 𝑟𝑒𝑓 𝑇 𝜌 𝑟𝑒𝑓 𝑇 𝐹 𝑤 ) with 𝑇 Γ𝑎 𝑟𝑒𝑓 = 𝑄 𝑧 [𝐶 𝑧 -Λ 1 𝐶 𝑑𝑣𝑟 ]Λ 2 𝐵 Γ 𝑎 , 𝑇 𝑥 𝑟𝑒𝑓 = 𝑄 𝑧 Λ 1 , 𝑇 𝜌 𝑟𝑒𝑓 = 𝑄 𝑧 [𝐶 𝑧 -Λ 1 𝐶 𝑑𝑣𝑟 ]Λ 2 𝐵 𝜌 𝑟𝑒𝑓 , 𝑇 𝐹 𝑤 = 𝑄 𝑧 [𝐶 𝑧 -Λ 1 𝐶 𝑑𝑣𝑟 ]Λ 2 𝐵 𝐹 𝑤 , Λ 1 = (𝐶 𝑧 Λ 2 𝐵 Γ 𝑎 + 𝐷 𝑧 )(𝐼 + 𝐾𝐶 𝑑𝑣𝑟 Λ 2 𝐵 Γ 𝑎 ) -1 𝐾, Λ 2 = (𝑝𝐼 -𝐴 𝑑𝑣𝑟 ) -1 ,
The 𝐻 2 criterion is described using the weighting matrix 𝑄 𝑧 defined as:

𝑄 𝑧 = [ 𝑐 1 0 0 0 0 0 0 𝑐 2 0 0 0 0 0 0 𝑐 3 0 0 0 0 0 0 𝑐 4 0 0 0 0 0 0 𝑐 5 𝑐 𝑑𝑎 0 0 0 0 0 1 ] (4)
In this matrix, parameters 𝑐 1 , 𝑐 2 , 𝑐 3 , 𝑐 4 , 𝑐 5 et 𝑐 𝑑𝑎 allow to weight each criterion according to its importance. 𝑐 1 and 𝑐 2 are linked to the lane following performance criteria 𝜓 𝐿 and 𝑦 𝐿 . 𝑐 3 is linked to a comfort criterion, 𝑎. 𝑐 4 , 𝑐 5 and 𝑐 𝑑𝑎 are linked to the sharing performance criteria Γ 𝑎 -𝛼 𝑐𝑜𝑚𝑝 Γ 𝑑 , Γ 𝑑 and Γ 𝑎 . 𝑐 𝑑𝑎 allows to ensure that the two torques Γ 𝑎 and Γ 𝑑 are directed in the same direction.

Fig. 8. Optimization model

The 𝐻 ∞ criterion is about the system's stability. It ensures that the input gain-phase margin 𝑀𝑚 𝑖 stays above a limit value.

Knowing that this margin can be written according to the sensitivity function 𝑆 𝑖𝑛𝑝𝑢𝑡 as:

𝑀𝑚 𝑖 = 1 max 𝜔 (|𝑆 𝑖𝑛𝑝𝑢𝑡 (𝑗𝜔)|) = 1 ‖𝑆 𝑖𝑛𝑝𝑢𝑡 ‖ ∞
Then the optimization problem can be written as:

Problem P1: H2 / H∞ static output feedback design The H2 / H∞ static output feedback design is defined as;

find 𝐾 such that:

-the driver-vehicle-road system is internally stabilized, -is the solution of 𝑚𝑖𝑛 𝐾 (‖𝑇 𝑧𝑤 ‖ 2 ) under the constraint ‖𝑆 𝑖𝑛𝑝𝑢𝑡 ‖ ∞ < 𝑆 𝑚𝑎𝑥 , with 𝑆 𝑚𝑎𝑥 a constant defined a priori. This optimization is solved using Systune, a tool available in Matlab  which allows to deal with some non-convex problems by using non-smooth optimisation algorithms.

SIMULATION AND RESULTS

Simulation conditions

The shared control strategy was tested by simulating the vehicle-road model (1) driven by the driver model ( 2) and the assistance. This simulation was done in the Matlab / Simulink  environment. The feedforward is tune as shown in the second experiment in section 3.3.2. The vehicle-road model used for the simulation is the same that the one used to synthetized the feedback. The simulation was done by following the road depicted in Fig. 6 and curves curvature along the road goes from 0.002 𝑚 -1 to 0.038 𝑚 -1 . The longitudinal speed of the vehicle is fixed at 𝑉 𝑥 =18 m/s. The wind disturbance input 𝐹 𝑤 is not taken into consideration. Coefficients of the matrix 𝑄 𝑧 (4) are chosen as 𝑐 1 = 200, 𝑐 2 = 20, 𝑐 3 = 3, 𝑐 4 = 10, 𝑐 5 = 1 and 𝑐 𝑑𝑎 = -10. The minimum value for the input modulo margin 𝑀𝑚 𝑖 is 0.5. Both level of sharing 𝛼 𝑎𝑛𝑡 and 𝛼 𝑐𝑜𝑚𝑝 are chosen equal to 50%.

Performance indicators

In order to assess the control strategy developed here in terms of sharing performances, some indicators which were introduced in [START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF] and [START_REF] Saleh | Generalized H2-Preview Control and its Application to Car Lateral Steering[END_REF] :

-Consistency ratio, 𝑇 𝑐𝑜 , defined as the duration during which assistance torque Γ 𝑎 is in the same direction as the driver torque Γ 𝑑 divided by simulation's duration. -Resistance ratio, 𝑇 𝑟𝑒𝑠 , defined as the duration during which assistance torque Γ 𝑎 and driver torque Γ 𝑑 are in opposite direction and assistance torque is inferior or equal to the driver torque divided by simulation's duration -Contradiction ratio, 𝑇 𝑐𝑜𝑛𝑡 , defined as the duration during which assistance torque Γ 𝑎 and driver torque Γ 𝑑 are in opposite direction and assistance torque is higher than the driver torque divided by simulation's duration. -Sharing level that is defined as the effort produced by the assistance divided by the effort produced by the driver

𝑃 𝑚 = 𝐸 𝑎 𝐸 𝑑 = ∫ Γ 𝑎 2 (𝑡)𝑑𝑡 ∞ 0 ∫ Γ 𝑑 2 (𝑡)𝑑𝑡 ∞ 0
-Coherence level that is the cosine value of the angle between the assistance torque and the driver torque

𝑃 𝑐 = cos(Γ 𝑎 ⃗⃗⃗ , Γ 𝑑 ⃗⃗⃗ ) = ∫ Γ 𝑎 (𝑡) × Γ 𝑑 (𝑡)𝑑𝑡 ∞ 0 √∫ Γ 𝑎 2 (𝑡)𝑑𝑡 ∞ 0 × ∫ Γ 𝑑 2 (𝑡)𝑑𝑡 ∞ 0
The lane following performances are assess using the average, the maximal and the standard deviation of the lateral error.

Results

First the design of the feedback part resulted in an input module margin of 0.505 which is higher than the minimal value 0.5.

Results found during the simulation are shown in Fig. 9, Fig. 10 and Table 2. The first figure shows that the assistance is, most of the time, helpful for the driver. It applied a part of the steering torque, allowing the driver to apply less effort on the steering wheel to steer the vehicle.

0,57

However, it has to be said that the track used here presents a very tight bend which can be noticed on Fig. 6, leading at about 30s to unusual torque and lateral error. These results are not representative as the track is not inclined and the speed is too high to be realistic.

Table 2 and Fig. 10 show good lane following performances, with a low lateral error, which average value is 0.22m. Table 2. also shows good results in terms of sharing performance. Indeed, the consistency ratio is close to the one found in [START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF], that used an LQ with preview theory to design a shared lateral control, based on a cybernetic driver modelvehicle-road model. The resistance ratio is equal to 0.41; this value may seem high, but the assistance resists to the driver action mostly in situations during which the torque applied both by the assistance and the driver are very low so it is not noticeable for the driver; to a lesser extent, some resistance occurs during the transition period at the beginning of bends.

Considering now the contradiction ratio, it is even lower than the one found in [START_REF] Saleh | Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty[END_REF] which is remarkable because it corresponds to a frontal conflict between the driver and the assistance. Finally, the coherence level 𝑃 𝑐 is positive which means that the driver and the assistance applied a torque in the same direction most of the time.

CONCLUSION

This paper described a haptic shared control strategy. It proceeded sequentially, considering first the feedforward, and then the feedback based on both the feedforward generator and the cybernetic driver model. This feedforward uses a dynamic model able to predict the torque that should be applied on the steering wheel consistently with the road geometry (curvature). This model is obtained by identification, from experimental data measured on a driving simulator with a real driver. This identification in fact proceeded to a projection of the "geometric part" of human driving, on a second order model with the road curvature as input, and the steering torque and all the vehicle-road states as outputs. Outputs of this model were then used as reference trajectory generator to design the haptic shared control proposed. The feedback relies on a 𝐻 2 /𝐻 ∞ output feedback applied on the difference between the real vehicle-road state and the reference one. Criteria used to design the feedback gains are concerned with lane following performances as well as the quality of sharing between the assistance and the driver, with an evaluation involving a cybernetic driver model. Both feedforward and feedback parts were then designed sequentially leading to nice results on performance aspects with complementary actions between the assistance and the driver.

This study opens interesting perspectives deserving to be studied in depth. Among them, the authors will realize experiments from significant samples of drivers, first on driving simulator. A joint analysis of the results obtained both objectively and subjectively will be made, according to drivers feelings about the shared control tested.

Fig. 3 .

 3 Fig. 3. Driver + Vehicle-Road OE model structure The input is road curvature (𝜌), the outputs are the seven signals shown in Fig. 3. The 𝑒 1 , 𝑒 2 ,…, 𝑒 7 are noise signals representing driver's "back and forth" behaviour. The numerators and denominators of transfer functions are polynomials as follows with 𝑠 the Laplace variable.

Fig. 4 .

 4 Fig. 4. Driving simulator SCANeR©

  𝐾 × 𝑌 𝑑𝑖𝑓𝑓 = 𝑘 𝛽 𝛽 𝑑𝑖𝑓𝑓 + 𝑘 𝑟 𝑟 𝑑𝑖𝑓𝑓 + 𝑘 𝜓 𝐿 𝜓 𝐿 𝑑𝑖𝑓𝑓 + 𝑘 𝑦 𝐿 𝑦 𝐿 𝑑𝑖𝑓𝑓 + 𝑘 𝛿 𝑑 𝛿 𝑑 𝑑𝑖𝑓𝑓 + 𝑘 𝛿 𝑑 ̇𝛿𝑑 ̇𝑑𝑖𝑓𝑓 (3) with 𝑌 𝑑𝑖𝑓𝑓 = 𝑥 𝑣𝑟 -𝑥 𝑟𝑒𝑓 . The gain K is found as the solution of the optimization problem described below. Model used to define the optimization problem is shown in Fig. 8. This model can be described by the following equations: 𝑇 𝑧𝑤 (𝑠) = 𝑇 𝑐𝑜𝑚𝑝 (𝑠)𝑇 𝑡𝑟𝑎𝑗_𝑔𝑒𝑛 (𝑠) 𝑤 = [ρ 𝑟𝑒𝑓 𝐹 𝑤 ] 𝑇 , 𝑤 𝑡𝑟𝑎𝑗 = [Γ𝑎 𝑟𝑒𝑓 𝑥 𝑟𝑒𝑓 𝜌 𝑟𝑒𝑓 𝐹 𝑤 ] 𝑇 , 𝑧 = 𝑄 𝑧 [𝜓 𝐿 𝑦 𝐶𝐺 𝑎 (Γ 𝑎 -𝛼 𝑐𝑜𝑚𝑝 Γ 𝑑 ) Γ 𝑑 Γ 𝑎 ] 𝑇 . 𝑤 𝑡𝑟𝑎𝑗 = 𝑇 𝑡𝑟𝑎𝑗_𝑔𝑒𝑛 𝑤, 𝑧 = 𝑇 𝑐𝑜𝑚𝑝 𝑤 𝑡𝑟𝑎𝑗 , Where 𝑇 𝑐𝑜𝑚𝑝 and 𝑇 𝑡𝑟𝑎𝑗_𝑔𝑒𝑛 are the transfer function corresponding to the rectangle with the same names in Fig. 8, 𝑦 𝐶𝐺 is the lateral error of the vehicle's center of gravity and 𝑎

Fig. 9 :

 9 Fig. 9 : Torque command applied by the driver and the assistance

Fig. 11 .

 11 Fig. 11. Validation data vs. OE model, female participant

Table 1 . Identified transfer functions

 1

	𝚪 𝒅 𝝆	and	𝛅 𝒅
		Experi ment	From 𝝆 to 𝚪 𝒅	From 𝝆 to 𝜹 𝒅
		1 st ,	1463.7(𝑠 + 0.64)	302.5(𝑠 + 0.64)
		female	(𝑠 + 0.78)(𝑠 + 4.71)	(𝑠 + 0.78)(𝑠 + 4.71)
		1 st ,	2506.1(𝑠 + 0.44)	479(𝑠 + 0.45)
		male	(𝑠 + 0.49)(𝑠 + 7.9)	(𝑠 + 0.49)(𝑠 + 7.9)
		2 nd	2358.8(𝑠 + 1.07) 𝑠 2 + 1.05𝑠 + 6.62	69.66(𝑠 + 4.45) 𝑠 2 + 1.05𝑠 + 6.62

𝝆

in form of zero-pole-gain converted from the statespace models identified. The conclusions made for the five other transfer functions are very similar to the ones made here for this two transfer functions.

Table 2 . Simulation results Indicators Results

 2

	max(lateral_error)(m)	1,39
	average(lateral_error)(m) 0,22
	Std(lateral_error)(m)	0,31
	𝑇 𝑐𝑜	0,47
	𝑇 𝑟𝑒𝑠	0,41
	𝑇 𝑐𝑜𝑛𝑡	0,11
	𝑃 𝑚	0,22
	𝑃 𝑐

ACKNOWLEDGMENTS

This work was supported by AutoConduct research program funded by the French ANR "Agence Nationale de la Recherche" (grant ANR-16-CE22-0007-05), and RFI Atlanstic 2020, funded by the Region Pays de la Loire.


domain: chim sdv sdv.mp

text:
Dr Marine Blanchet

Dr Diane Borselli

Anne Rodallec

Franck Peiretti

Nicolas Vidal

Dr Jean-Michel M Bolla

Dr Carole Digiorgio

Pr Kelly R W M Morrison

William M Wuest

Jean Michel Brunel

Dr A Rodallec

Dr J M Brunel
email: bruneljm@yahoo.fr

Wuest

Claramines : A new class of broad-spectrum antimicrobial agents with bimodal activity

The emergence of multidrug resistant bacteria/pathogens has highlighted the need for the development of new antibiotics. In this manuscript, we report herein our results dealing with the broad spectrum of antibacterial activity against both sensitive and resistant Gramnegative and Gram-positive bacterial strains of an easily prepared water soluble polyaminosterol compound namely claramine A1. We will also demonstrate its peculiar mechanism of action (different from all the well-known classes of antibiotics) towards Gramnegative and Gram-positive bacteria. Finally, due to its low cytotoxicity, this class of molecules could constitute an effective response to combat the emergence of multidrug resistant bacteria and nosocomial diseases.

Introduction

Over the last 75 years, the development of antibiotics has contributed greatly to the increase in life expectancy. Unfortunately, as a consequence of both their overuse and natural defense mechanisms, multidrug resistance has emerged and has seriously limited the efficacy of antibiotic therapy. [1][2][3] Since 1928, thousands of compounds which target essential pathways have been isolated from natural sources. Nevertheless, few classes have been identified since 1987, and when coupled with the over-prescribing of existing treatments, have led to a drastic increase in resistant bacteria. Antibiotic resistance is an issue of great concern that has attracted the attention of health agencies, media, and global leaders. More specifically, the WHO, European Commission, and CDC have all run public health awareness campaigns to bring greater attention to a specific subset of bacteria, named the ESKAPE pathogens, comprised of Enterococcus faecium, Staphylococcus aureus, Klebsiella pneumoniae, Acinetobacter baumannii, Pseudomonas aeruginosa, and Enterobacter spp., which constitute the main cause of nosocomial infections throughout the world. In this context, there is an urgent medical need for new classes of antimicrobial agents that both target resistant ESKAPE pathogens and be refractory to all bacterial resistance mechanisms. These new antibiotics should present the following features: (i) a mechanism of action ideally avoiding, but more likely prolonging, the rise of antibiotic-resistant strains, (ii) specific targeting of pathogens without affecting the commensal microbiota and (iii) overcoming or limiting natural forms of resistance such as the formation of biofilms and efflux mechanisms. Bacterial membrane structure constitutes an appealing target for the design of new potent antimicrobial agents since it is generally conserved among most species of both Gram-negative and Gram-positive bacteria. This is evident in Nature as bacteria have developed antimicrobial peptides and other small molecules like the polymyxins which target this structural element. [4] Resistance to membrane active compounds requires either an increase in efflux pumps or a major change in membrane structure that in turn influences the permeability barrier, increasing susceptibility to hydrophobic antibiotics.

Polyamino natural products such as squalamine [5,6] , ianthelliformisamines (B and C) [7] , and motuporamines [8] are known to target bacterial cell membranes with modest activity (Figure 1).

Figure 1. Strategy involved for claramine A1 design

Thus, we and others were able to demonstrate the importance of the amphiphilicity of the molecules as well as the crucial nature of the polyamino group linked to a well-chosen lipophilic molecule to encounter interesting antimicrobial activities. [9][10][11][12]

Results and Discussion

Based on our continued interest in squalamine and polyaminosterol derivatives [13][14] we posited that the bile acids sterol core could serve as a platform for the design of potent antimicrobial compounds. Based on all these considerations, we postulated that we could couple these two structural features to design a new class of polyaminosterol compounds. This hypothesis was born out in the first derivative disclosed below which we have named claramine A1. Herein, we present the synthesis of novel antimicrobial derivative claramine A1 demonstrating its broad-spectrum activity as well as its antibiotic-enhancement properties, and elucidation of its unusual mechanism of action against both Gram-positive and Gram-negative bacteria by implementing chemical tools to investigate changes in membrane depolarization and permeabilization.

In order to further investigate the interesting biological activity [5] we were interested in designing a concise and economical synthesis of squalamine derivatives. Toward this end, polyaminosterol parent compound claramine A1 (Figure S1) was prepared in a three-step synthesis (33% overall yield) from deoxycholic acid using an efficient stereoselective titaniummediated reductive amination that controlled the -stereochemistry at the C-3 position (Figure 2).

Figure 2. Claramine A1 synthetic pathway

Claramine A1 was found to be a potent antimicrobial with activity against a wide panel of both Gram-positive and Gram-negative bacteria including Multi-Drug Resistant (MDR) pathogens (Table 1). Evaluation of the activities of claramine A1 and controls (squalamine and colistin) against reference strains was repeated and reproducible, and accurate MICs were obtained. For Gram-negative E. coli ATCC 25922 and P. aeruginosa ATCC 27853, MICs were 2, 2, 16 µg/mL and 8, 8, 4 µg/mL for squalamine, claramine A1, colistin, respectively. For Grampositive S. aureus ATCC 25923, MICs were 2, 2, >16 µg/mL for squalamine, claramine A1 and colistin, respectively. In general, claramine A1 demonstrates antimicrobial activities against a large panel of both Gram-positive and negative bacterial strains with MIC values varying from 2 to 32 µg/mL (Table 1). Claramine A1 exhibited complete killing of the P. aeruginosa reference strain in the same time period (3 hours) than colistin (Figure 3B). However, contrary to colistin which is inactive against Gram-positive bacteria, claramine A1 showed a rapid direct bactericidal effect against the S. aureus reference strain which was favorable when compared to tobramycin, reflected by a nearly 2.5 log drop in the counts of this strain by 0.75 h, with complete killing achieved in 2 hours (Figure 3A).

S. aureus ATCC25923

The first study dealing with the mechanism of action of squalamine against Gram-negative bacteria suggested that squalamine amino groups (positively-charged) strongly interact with the phosphate groups (negatively-charged) in the lipopolysaccharide (LPS) structure disrupting the bacterial membrane integrity. [11] Such a mechanism had been previously described for polymyxin antibiotic colistin, which can be antagonized by increased concentrations of Ca 2+

and Mg 2+ divalent cations, which further inhibits the binding of this polycationic antibiotic to LPS. [15,16] This result indicates that the interaction with the negatively charged phosphate groups in the LPS structure is mandatory for both agents to be active. Although required, the cationic charge is not sufficient to cause either the permeabilization of bacterial membranes or the bacteria killing. [17,18] On the other hand, Dynamic Light Scattering (DLS) was performed to determine whether the compound aggregates demonstrating that samples concentrations (i.e., 500 µM, 50 µM, 16 µM and 2 µM) were too low to meet DLS quality criteria, suggesting the absence of colloidal aggregates at all tested concentrations (Figure S2).

Thus, we attempted to elucidate more precisely the mechanism of action of claramine A1 by investigating its potent permeabilizing, depolarizing, and disrupting behavior of the outer and/or inner membranes of S. aureus ATCC 25923 and E. aerogenes EA289 bacteria, as well as its ability to potentially act as an efflux pump inhibitor (Figure 4A). (Sp, lacking the sterol) were selected as inactive compounds to compare their different behaviors (Figure 4B).

In a first approach, a bioluminescence method was developed to determine the behavior of claramine A1 on the intracellular pool of bacterial ATP. The detection of the external concentration of ATP was then used as a reporter reflecting the permeabilizing effect of claramine A1 along with providing a dose-response curve (Figure 5A). Claramine A1 dramatically disrupted the S. aureus membrane after two minutes as observed by intracellular ATP release kinetics, which was similar to the positive control squalamine. (Figure 5B). Conversely, no significant effect was found by using spermine as a polyamine negative control during the test time. By performing the same experiment against Gram-negative E. aerogenes EA289 a lower ATP efflux was observed for both Claramine A1 and squalamine with only a 20 and 10% ATP efflux release compared to CTAB positive control, respectively, hinting at a different mechanism of action (Figure 5C). These results suggest that LPS damage induced by claramine A1 is clearly greater and faster than that caused by squalamine. Furthermore, this has recently been demonstrated in a study on the interaction of squalamine and colistin with the bacterial lipid bilayer and the consequences of such interactions on the electrical properties of these membranes. [19] Accordingly, the activity of claramine A1 against Gram-negative bacteria may be simulated by the carpet model previously proposed for describing cationic peptide antibiotics, which led to a large disruption of the bacterial membrane due to a detergent-like effect of micelle formation. [20] However, this model is not valid for Gram-positive bacteria since they are devoided of LPS.

To clarify this alternate mechanism, claramine A1 was investigated for its ability to alter the outer membrane integrity of E. aerogenes EA289 via a nitrocefin colorimetric assay wherein a color change from yellow to red occurs when the chromogenic ß-lactam is efficiently hydrolyzed by periplasmic ß-lactamases. As presented in Figure 6, even at low concentration (1.79 µM), claramine A1 increased the rate of nitrocefin hydrolysis compared to the A19treated or untreated control. Otherwise, a similar behavior is observed as seen with the positive controls polymyxin-B (PMB) and squalamine which also provided an increase in the nitrocefin hydrolysis rate. All these data suggest that claramine A1 can permeabilize the outer membrane or disrupt the integrity of Gram-negative bacteria. On the other hand, efflux systems function via an energy-dependent mechanism (active transport) to pump out unwanted substances such as toxins, antibiotics, or dyes through specific efflux pumps. To determine if claramine A1 could act as a disruptor of the transmembrane potential, we used the membrane potential sensitive probe DiSC3( 5) which concentrates at the inner membrane level and self-quenches its fluorescence (Figure 7A).

When a compound impairs the membrane potential, the dye is released in the liquid environment leading to a fluorescence increase. Thus, a strong depolarization of the membrane after 15 minutes of incubation was observed against Gram-positive S. aureus strain both for squalamine and Claramine A1 (Figure 7B) whereas EA289 treatment resulted in a lower but significant depolarization of the membrane (Figure 7C) suggesting a potent disruption of the proton gradient which may affect efflux pumps from the RND family such as AcrAB-TolC. In this case, the active transport of more than 80% of the dye is rapidly observed in non-treated bacteria (Figure 7F, green line). When claramine A1 is added to the bacteria, a significant dosedependent inhibition is observed resulting in more than 90% retention of the dye at a concentration up to 25 µM (Figure 7F, grey line). These results suggest that claramine A1 may act as an inhibitor of the AcrAB-TolC efflux pump. It is noteworthy than squalamine presents a similar behavior but at a higher concentration (of up to 100 µM) demonstrating the better efficiency of claramine A1.

An alternative strategy to safeguard the efficiency of old existing drugs is using antibiotic adjuvants, which can enhance the activity of current drugs and minimize or even directly block, resistance. [21][22][23] This concept of antibiotic adjuvants comes from the successful use of two antibiotic combinations such as gentamicin/ampicillin for the treatment of enterococcal infections. [24,25] Synergistic interactions are achieved through a variety of mechanisms, including enhancement of uptake or suppression of efflux. The result is that efficacy is greater than the sum of the individual agents (synergy) with faster kill times and limiting the emergence of resistant organisms. Thus, we decided to use claramine A1 as a potent adjuvant in combination with various antibiotics based on our recent success using polyamine motuporamine derivatives. [6] We investigated whether this polyaminosterol derivative could restore the potency of the antibiotic doxycycline at doses below its MIC. In our hands the MIC of doxycycline against P. aeruginosa PAO1 and E. aerogenes EA289 was 16 and 40 µg/mL, respectively, so we investigated the use of doxycycline at a lower concentration (2 µg/mL, corresponding to its pharmacokinetic properties in humans [5] ) in the presence of claramine A1.

We speculated that the polyamine agents would disrupt bacterial membrane integrity and enhance antibiotic delivery to the bacteria and thus increase doxycycline potency. Thus, even at this low doxycycline concentration, claramine A1 restored doxycycline activity against E.

aerogenes EA289 and P. aeruginosa PAO1 by using 0.5 and 2 µg/mL, respectively.

Unfortunately, under the same experimental conditions no synergy was observed for MDR K.

pneumoniae Nasey and A. baumannii AYE. Nevertheless, chloramphenicol activity can also be restored at 2 µg/mL against P. aeruginosa PAO1 by using 4 µg/mL of claramine A1 ( Conversely, claramine A1 was unable to induce micronuclei in CHO-K1 cells with or without S9 metabolizing mixture. They indicated that claramine A1 was deprived from direct clastogenic/aneugenic activity and that it was not transformed into clastogenic/aneugenic metabolites by P450 cytochromes (Table S1).

Because of its structural resemblance to steroidal detergents, claramine A1 was assayed for hemolytic activity against human erythrocytes. This activity occurs at higher concentrations than observed for nonselective membrane disruptive amphipathic molecules such as CTAB (Figure S3). Thus, 35% haemolysis was observed for claramine A1 used at a 200 µM concentration. It is also noteworthy that claramine A1 exerts antibiotic activity at concentrations below which erythrocyte disruption occurs.

Recently, the use of insects has become a method of choice for measuring the virulence of microbial pathogens due to the numerous similarities existing between the immune system of insects and mammals. [26,27] Insects are also inexpensive to purchase, house, and led to results in 24-48 h. All these reasons rationalize the fact that insects can be used to evaluate the in vivo activity of antimicrobial drugs. [28,29] Thus, Galleria mellonella larvae were used as an animal model to determine their tolerance to claramine A1 as well as the in vivo activity of claramine A1 against a S. aureus infection. In a first approach, the results indicate no toxicity up to a concentration of 50 µg/mL however larvae inoculate with a dose of 100 µg/mL showed a 90% reduction in viability after 24 h. On the other hand, larvae inoculated with claramine A1 (3.125, 6.25, 12.5, 25 µg/mL) did not show signs of cuticular darkening, an unambiguous sign of acute toxicity (Figure 8A). In order to ascertain the in vivo activity of claramine A1, larvae were infected with S. aureus ATCC25923 (20 µL of a solution containing 10 7 bacterial cells) and subsequently administered with or without claramine A1 (6.25 µg/mL) 4h post infection. Those treated larvae showed 80% survival at 24h whereas only 10% of the untreated ones survived at the same time point (Figure 8B). Nevertheless, caution must be exercised in larvae use as the introduction of foreign material into the insect haemoceol can provoke a non-specific immune response. [30,31]

Conclusion

More broadly, we demonstrated that claramine A1, the first member of a new class of potent antimicrobial agents, possesses an unusual multifaceted mechanism of action against both Gram-positive and Gram-negative bacteria. Claramine A1 exerts its bactericidal effect in a rapid fashion via membrane depolarization against Gram-positive bacteria thereby disrupting its integrity. In contrast, further studies indicate that changes in the transmembrane electrical potential in Gram-negative E. aerogenes EA289 are correlated with the permeabilization of the cell membranes by claramine A1 leading (or concomitantly facilitating) an altered proton homeostasis. Finally, claramine A1 which can disrupt the proton gradient can be considered as a new member of the class of efflux pump inhibitors. These bimodal activities, when coupled with its synergizing abilities, highlights the enormous potential of this class of compounds to fight MDR bacteria. Studies are now underway to improve the activity and cytotoxicity of claramine derivatives to provide a potent human therapeutic.

Experimental Section

All solvents were purified according to reported procedures, and reagents were used as commercially available. Methanol, ethyl acetate, dichloromethane, ammonia and petroleum ether (35-60 °C) were purchased from SDS and used without further purification. Column chromatography was performed on SDS silica gel (70-230 mesh). 1 H NMR and 13 C NMR spectra were recorded in CDCl3 on a Bruker AC 250 spectrometer working at 250 MHz and 63

MHz, respectively (the usual abbreviations are used: s: singlet, d: doublet, t: triplet, q: quadruplet, m: multiplet). Tetramethylsilane was used as internal standard. All chemical shifts are given in ppm.

Synthesis of isopropyl deoxycholate 1

In a 250 mL two necked round flask was introduced in 70 mL of isopropanol and 30 mL of dichloromethane 10 g of deoxycholic acid (0.0255 mol) and 2.2 g of para-toluene sulfonic acid (0.013 mol). The mixture was heated at reflux under vigorous stirring for 8 hours. The solvents were subsequently removed and 100 mL of dichloromethane was added. The organic phase was washed 3 times with 50mL of NHCO3 (10%) solution. The aqueous phases were extracted twice with dichloromethane and the combined organic phases were dried over Na2SO4, filtered, and concentrated in vacuo to afford the expected product as a white solid in 90% yield. NMR

Synthesis of 3-oxo isopropyl deoxycholate 2

In a 250 mL two necked round flask was introduced in 100 mL of toluene and 50 mL of acetone 11 g of isopropyl deoxycholate 1 (0.025 mol). 2 equivalents of aluminum tert-butoxide (12.3 g, 0.050 mol) were subsequently added and stirring was maintained under reflux for 12 hours.

50 mL of a 2N H2SO4 solution was added and the mixture was stirred for an additional 1 hour.

The organic phase was washed 3 times of a 2N H2SO4 solution and 50 mL of water. The combined organic phases were dried over Na2SO4, filtered, and concentrated in vacuo to afford a crude product which was purified by flash chromatography on silica gel (ethylacetate/ petroleum ether (1/1)). The expected 3-oxo isopropyl deoxycholate 2 was successfully obtained as a white solid in 70% yield. NMR

Synthesis of 3-spermino isopropyl deoxycholate (claramine A1)

In a 100 mL two necked round flask was introduced 100 mL of methanol. A mixture of the ketone 2 (3.5 g, 8 10 -3 mol), titanium(IV) isopropoxide (7.15 mL, 2.4 10 -2 mol), and spermine (3.2g, 1.6 10 -2 mol) was stirred under argon at room temperature for 24 hours. After cooling the flask at -20°C, sodium borohydride (0.9 g, 2.4 10 -2 mol) was then added and the resulting mixture was stirred for additional 12 hours. The reaction was then quenched by adding water (4 mL). Stirring was continued at room temperature for 1 hour then the reaction mixture was filtered over a pad of Celite which was subsequently rinsed with NH4OH and methanol. The mixture was concentrated in vacuo to afford the expected crude compound which was purified by flash chromatography on silica gel using CH2Cl2/MeOH/NH4OH (32%) 7:3:1 as eluent. The expected claramine A1 was obtained as a viscous yellow oil in 52% yield. NMR

Synthesis of claramine A1 hydrochloride salt

Claramine A1 is dissolved in a minimum of anhydrous methanol and a anhydrous HCl solution in diethylether (2M, 8 equivalents) was slowly added under vigorous. The formed precipitate was filtrated, washed with anhydrous diethylether and dried under vacuum. The claramine A1 hydrochloride salt is obtained in a quantitative yield as a white solid stable to air and moisture.

Determination of minimal inhibitory concentrations

Antimicrobial activity of the compounds was studied by determination of minimal inhibitory concentrations (MIC) according to the NCCLS guidelines M7-A2 using the microbroth dilution methods. The bacteria strains were grown on trypticase soy agar (Becton Dickinson) at 37 °C for 24h. Inocula were prepared in TCE (tryptone 0.1%, NaCl 8%, wt/vol) by ajusting the turbidity at 623 nm to obtain 1-3 10 5 CFU/mL.

Antimicrobial activities of the compounds were determined by using a broth microdilution method performed in sterile 96-well microplates. All compounds were solubilized in water at a concentration of 10mM and were transferred to each microplate well in order to obtain a twofold serial dilution in 100 µL of broth and 100 µL of inoculum containing 2-6 10 5 CFU of each bacterium were added to each well. Some wells were reserved for positive controls and inoculum viability. After 24 h incubation, MIC was defined for each agent from duplicate observations as the lowest concentration of compound allowing no visible growth.

Time-kill assays

Time-kill assays were conducted with concentrations corresponding to the MIC value of claramine A1, colistin and tobramycin against reference strains of P. aeruginosa ATCC27853 and S. aureus ATCC25923. Claramine A1, colistin or tobramycin was added to a bacterial suspension of approximately 5 × 10 5 CFU/mL of each bacteria. 2 mL of the tested suspension were sampled at 0, 0.5, 1, 2, 3, and 4 h for viable cell counting that was conducted by spiral plating on Trypticase Soy Agar medium (bioMérieux, Craponne, France) followed by incubation at 37°C for 24 h.

Membrane depolarization assays

Bacteria were grown in MH broth for 24 h at 37°C and centrifuged at 10000 rpm at 20°C. The supernatant was discarded, and the bacteria were washed twice with buffered sucrose solution (250 mM) and magnesium sulfate solution (5 mM). The fluorescent dye 3,3′diethylthiacarbocyanine iodide was added to a final concentration of 3 µM, and it could penetrate bacterial membranes during 1 h of incubation at 37°C. Bacteria were then washed to remove the unbound dye before adding compound A1 at different concentrations Compound was then added at different concentrations. Fluorescence measurements were performed using a Jobin Yvon Fluoromax 3 spectrofluorometer with slit widths of 5/5 nm. The relative corrected fluorescence (RCF) was recorded at time intervals of 0, 3, 5, 7, 9, 11, 13, 15, 17, 19, and 21 min. The maximum RCF was that recorded with a pure solution of the fluorescent dye in buffer (3 µM).

Nitrocefin hydrolysis assay

Outer membrane permeabilization was measured using nitrocefin as a chromogenic substrate of periplasmic -lactamase. Ten milliliters of MH broth were inoculated with 0.1 mL of an overnight culture of EA289 bacteria and grown at 37°C until the OD600 nm reached 0.5. The remaining steps were performed at room temperature. Cells were recovered by centrifugation (4000 rpm for 20 min) and washed once in 20 mM potassium phosphate buffer (pH 7.2) containing MgCl2 (1 mM). After a second centrifugation, the pellet was re-suspended and adjusted to a OD600 nm to 0.5. Then, 50 µL of either Polymyxin B (positive control) or the A1 compound were added to 100 µL of the cell suspension to obtain a final concentration varying from 0.98 µM to 500 µM. Fifty microliters of nitrocefin were then added to obtain a final concentration of 50 µg/mL. Nitrocefin hydrolysis was monitored spectrophotometrically by measuring the increase in absorbance at 490 nm. Assays were performed in 96-well plates using a M200 Pro Tecan spectrophotometer.

Glucose-triggered 1,2'-diNA efflux assays

Bacteria were grown until the stationary phase was reached, collected by centrifugation and resuspended at OD600 nm= 0.25 in PPB supplemented with Carbonyl cyanide m-chlorophenyl hydrazone (CCCP, 5 μM), and incubated overnight with 1,2'-Dinaphthylamine (1,2'-diNA, 32 μM) at 37°C. Before addition of the desired compounds at a 100 μM concentration, the cells were washed with potassium phosphate buffer (PPB). Glucose (50 mM) was added after 300 s to initiate bacterial energization. Membrane-incorporated 1,2'-diNA was followed by monitoring the fluorescence (λex= 370 nm ; λem= 420 nm). Cell suspension was added at 100 μL/well and the fluorescence read every 30 s at 37°C. An Infinite M200Pro reader (Tecan) was used. Assays were performed in Greiner Bio-One 96 well plates, ref 675076 (half area, black with solid bottom).

Measurement of ATP efflux

Squalamine solutions were prepared in doubly distilled water at different concentrations. A suspension of growing S. aureus or E. aerogenes (EA289) to be studied in MH broth was prepared and incubated at 37°C. 90 µL of this suspension was added to 10 µL of squalamine solution and vortexed for 1 second. Luciferin-luciferase reagent (Yelen, France; 50 µL) was immediately added to the precedent mix and luminescent signal quantified with an Infinite M200 microplate reader (Tecan) for five seconds. ATP concentration was quantified by internal sample addition. A similar procedure was done for spermine (100 µg/mL) and for A1 (4 times the MIC).

Cytotoxicity assays

The cytotoxic activities of compounds were assessed on 5 cell lines provided from ATCC-LGC Results were expressed as percentages of cell viability about the control (culture medium-only), which corresponded to 100% cell viability. Dose-response curves were calculated by non-linear regression analysis with TableCurve V2 software. The Inhibitory Concentration 50% (IC50) was defined as the concentration of compounds that induced a 50% decrease of viable cells.

In vitro micronucleus assay

The micronucleus assay was performed on a Chinese Hamster Ovary cell line CHO-K1 (ATCC, USA). This cell line was chosen for its rapid cell cycle (doubling time of 24 hours) and its genetic stability. It has been validated and accepted for the MNvit test by the OECD. Cells were maintained in McCoy's 5A medium supplemented with 10% fetal calf serum, 1 mM glutamine and 100-U/mL-10 µg.mL -1 of a mixture of penicillin-streptomycin. They were incubated at 37°C in 5% CO2.The CHO-K1 cells, suspended in Mac Coys'5A medium, were transferred into Labteck wells at a concentration of 100,000 cells/ml, and incubated for 24 hours at 37°C in CO2 (5%). When the test was performed without metabolic activation, the compounds were added into cell cultures at concentrations previously defined. A negative control containing culture medium, and a positive control containing 0.6 µg/ml of mitomycin C were added. When the assay was performed in the presence of metabolic activation, S9 mix metabolizing mixture was added to cell cultures at a concentration of 10%. The S9 fraction was made with a centrifuged supernatant (9000 x g) of a liver homogenate prepared from male Sprague-Dawley rats treated with a single injection of Aroclor 1254 (500 mg kg-1 body weight). The metabolizing mixture (S9 mix) contained 10 % S9, 5 mM G6P, 4 mM NADP, 33 mM KCl and 8 mM MgCl2.Then the compounds were added to the cell cultures at concentrations previously defined. A negative control containing culture medium, and a positive control containing 5 µg/ml of benzo-a-pyrene were added. After 3 hours of incubation at 37 °C in CO2 (5%), the culture medium was removed, the cells were rinsed with phosphate buffered saline (PBS), and The cytostasis index (CI%), i.e. the percentage of cell replication inhibition, was calculated using the following formula: CI% : 100-{100x(CBPItest material-1)/(CBPIsolvent control-1)} After this step, only the doses inducing a decrease of less than 55+5% of CI% as compared to the negative control were considered for counting micronuclei. The rates of micronuclei were evaluated for the presence of independent nuclear core entities in 1000 binucleated cells per well, which corresponds to 2000 cells examined by test substance dose. Micronuclei were identified as small nuclei well differentiated from cell nucleus, stained in the same manner and having a diameter less than one third of that of the cell nucleus. Micronuclei rates obtained for different doses of test substances were compared to the negative control by a χ2 test. The assay was considered positive if:

-A dose-response relationship was obtained between the rate of micronuclei and the doses tested, -At least one of these doses induced a statistically significant increase (P < 0.05) in the number of micronucleated cells as compared to the negative control.

Inoculation of Galleria mellonella larvae

Ten larvae of G. mellonella were stored in the dark at 15°C. Larvae of the same age and weighing around 0.2 g were inoculated with 20 µL of water containing 5 10 7 S. aureus cells through the last pro-leg using a Myjector U100 insulin syringe (Terumo Europe, Leuven, Belgium).

In vivo toxicity assay

Larvae were injected with 20 µL of claramine A1 solution (31.25, 62.5, 125, 250, 500 or 1000 µM) or water. Larvae were incubated at 30°C for 24 h prior to quantifying survival.

Effect of claramine A1 on survival of larvae infected with S. aureus

Larvae were injected with 20 µL of claramine A1 solution (62.5 µM) 4 h post-inoculation with S. aureus. The control consisted of larvae inoculated with S. aureus treated or not with water (20µL). Larvae were incubated at 30°C and survival was assessed at 24 h.

Figure 3 .

 3 Figure 3. Time kill studies for claramine A1 against (A) P. aeruginosa ATCC27853 and (B)

Figure 4 .

 4 Figure 4. General points investigated for claramine A1 mechanism of action study against both Gram-positive and Gram-negative bacteria Squalamine, polymyxin B, and cetyltrimethylammonium bromide (CTAB) were chosen for

Figure 5 .

 5 Figure 5. Dose dependent ATP release for claramine A1 (A) treated S. aureus ATCC 25923 (B) and E. aerogenes EA289 (C) strains

Figure 6 .

 6 Figure 6. Study of outer membrane permeabilization of E. aerogenes EA289 by evaluation of nitrocefin hydrolysis rate (A-C) and claramine A1 dose dependent effect on nitrocefin hydrolysis rate (D).

Figure 7 .

 7 Figure 7. A-D) Membrane perturbation study of E. aerogenes EA289 and S. aureus ATCC 25923 by DiSC3(5) fluorescence evaluation. E-F) Study of effect on efflux performance of E. aerogenes EA289 by evaluation of glucose-triggered 1,2'-diNA efflux Therefore, claramine A1 was tested for its ability to inhibit efflux pumps that are proteinaceous

Figure 8 .

 8 Figure 8. A) Larval survival 24h after administration with water or claramine A1 (3.125, 6.25, 12.5, 25, 50, 100, 1000 µg/mL). B) Survival of larvae infected with S. aureus ATCC25923 following administration with claramine A1 solution (6.25 µg/mL) 4h after infection.

  then returned to culture in McCoy's 5A medium containing 3 µg/ml of cytochalasin B. After a 21-hour incubation period at 37°C, cells were rinsed with phosphate buffered saline (PBS), fixed with methanol and stained with 10% Giemsa for 20 minutes. The analysis of results was performed under a microscope at x1000 magnification. The antiproliferative activity of test substances was estimated by counting the number of binucleated cells relative to the number of mononucleated cells on a total of 500 cells for each dose (250 cells counted per well). The proliferation index (Cytokinesis Blocked Proliferative Index CBPI) was calculated using the following formula:

Table 1 .

 1 Antimicrobial activities of squalamine, colistin and claramine A1 MIC (µg/mL)

		Strains	Squalamine triflate	Colistin sulfate	Claramine A1
		S. aureus (340)	2	>16
	bacteria	S. aureus ATCC25923 S. intermedius 1051997	2 2	>16 >16
	Gram-positive	B. cereus 7132392 E. faecalis 1051997 Nocardia spp	8 4 2	>16 >16 ND
		S. australis sp	ND	ND
		E. coli AG100	8	4
		E. coli ATCC 25922	2	16
		E. coli 0157H7	2	16
		E. aerogenes EA289 (MDR)	16	16	32
		E. cloacae ATCC 23355	4	4
	bacteria Gram-negative	K. pneumoniae NTLC13443 K. pneumoniae ST258 K. pneumoniae NASEY P. aeruginosa PA01 P. aeruginosa PA14	8 8 16 16 16	4 8 8 2 4	16 32
		P. aeruginosa ATCC 27853	8	4
		P. aeruginosa PA3337	8	4
		A. baumannii ATCC 17978	2	0.5
		A. baumannii AYE	8	4	32

Table 2

 2 Concentration of claramine A1 used (µg/mL). cValues equivalent to the MIC of claramine A1 against these bacterial strains (cf Table1)

	).

a antibiotic used: DOX: doxycycline, CHL: chloramphenicol. b

Table 2 .

 2 Concentration of claramine A1 used to restore antibiotics activity against various bacterial strainsThe cytotoxic activity of claramine A1 was also investigated. Cell viability was assessed by evaluating two different physiological mechanisms: the activity of mitochondrial dehydrogenases which cleave the tetrazolium salt WST-1 to formazan, and the ability of lysosomal membranes to concentrate Neutral Red. Results showed that claramine A1 exerted a weak cytotoxic activity with an IC50 around 70 µM. No differences could be observed in IC50 regarding the cell line or the vital dye, suggesting that the cytotoxic activities did not result from a specific mechanism but from a global impact on several intracellular targets (Table3).

	IC50 (µM) as assessed by WST1 vital dye	IC50 (µM) as assessed by neutral red vital dye
	CHO		HEPG2	MDCK	3T3	Hacat	CHO	HEPG2	MDCK	3T3	Hacat
	70.1+2.6	81.3+2.6	74.3+11.2	77.4+ 3.8	86.4+3.5	75.3+2.4	79.8+3.4	79.4+6.5	82.6 + 0.7 83.1+5.3.2
	IC50	Inhibitory Concentration 50% (µM)

Table 3 .

 3 Cytotoxic activities of claramine A1

  .15, 68.95, 59.06, 50.74, 50.70, 49.30, 48.97, 48.42, 48.27, 47.77, 45.83, 44.08, 40.78, 37.58, 37.14, 36.82, 35.97, 35.92, 34.94, 34.59, 33.56, 32.72, 32.45, 30.52, 29.98, 28.84, 28.65, 28.40, 28.29, 27.64, 25.04, 24.10, 22.27, 17.71, 13.37. MS (ESI

	1 H (250 MHz,
	CD3OD) : δ (ppm) = 4.96 (m, 1H), 3.94 (m, 1H), 2.88-2.46 (m, 13H), 2.39-2.18 (m, 2H), 2.04-
	1.12 (m, 40H), 1.01-0.95 (m, 7H), 0.71 (s, 3H). NMR 13 C (63 MHz, CD3OD) : δ (ppm) =
	175.66, 74

+ ): m/z 619.5519

([M+H] + )

Acknowledgements M.B. acknowledges Virbac company for a PhD grant. Keywords: Antibiotics -Steroids-Polyamine derivative -Antibacterial agents -Bile acid

Table of contents

The synthesis of water soluble polyaminosterol compound namely claramine A1 and its broad spectrum of antibacterial activity against both sensitive and resistant bacterial strains were reported. The peculiar mechanisms of action towards Gram-negative and Grampositive bacteria was fully investigated suggesting that this class of molecules could constitute one of the most appropriate response against the questionable emergence of multidrug resistant bacteria


Pin Lisa

Ansart Florence

Le Maoult

Advances in the field of new smart thermal barrier coatings

Keywords: thermal barrier coatings, sol-gel, filling-up, topography

This paper deals with the development of a new synthesis technique for functional materials such as Yttria Stabilized Zirconia (YSZ) in the field of thermal barrier coatings. Currently, Thermal Barrier Coatings (TBCs) are manufactured by dry route technologies (EB-PVD or plasma spray) but such methods are directional and often require costly investments and complex operations. For these applications, the sol-gel route, a non directional method, is developed, to process, by suitable chemical modifications, nanocrystalline materials with a controlled morphology. The main advantage of this method is to decrease the crystallization temperature, much lower than the conventional processes, allowing the synthesis of reactive substituted zirconia powders with nanometric particles size. In this study, several suitable architectures for thermal barrier coatings have been achieved in order to show that this process is appropriate for repairing damaged TBC compared to conventional processes. The next step is to investigate spallation mechanisms and overall TBC durability by cyclic oxidation. Preliminary results are promising and research will be develop further to optimize both processing and cyclic oxidation behavior.

Introduction

Thermal Barrier Coatings are used as insulators on hot section components to reduce operating temperatures in aircraft engines and industrial gas turbines. The TBC system consists of two layers: the ceramic top coat, typically Yttria Stabilized Zirconia (YSZ) manufactured generally by EB-PVD or PS with low conductivity, and the bond coat generally MCrAlY, M=Ni and/or Cr or Co or Pd or Pt modified aluminides. Recently, studies have focused on an alternative technique to deposit YSZ thermal barrier coatings on nickel based superalloys substrates : the sol-gel process [1]. Getting thermal barriers by sol-gel route is a controlled process, which allows to obtain a homogeneous YSZ surface. This coating presents an isotropic porosity, which confers to the barrier an interesting compromise between thermal and mechanical properties. Due to this process choice, sol-gel thermal barriers have a different oxidation damage mode than conventional thermal barriers. Indeed, EB-PVD thermal barriers suddenly and totally fracture, conversely to sol-gel thermal barriers, for which spallation is initiated by the growing of microcracks network [START_REF] Sniezewski | ICMTF-International Conference on Metallurgical Coatings and Thin Films[END_REF]. These micro-cracks arise from stress relaxation during the step of YSZ sintering at high temperature (about 1100°C). Consequently a better control of micro-cracks network growing should allow manufacture sol-gel thermal barrier more resistant to cyclic oxidation. The originality of this paper is to develop a "filling-up" process aiming at strengthening microcracked barriers. The filling-up process consists in performing the dip-coating step twice, i.e. to immerse damaged thermal barriers in a sol loaded with powders or not, then to withdraw it at constant speed and to heat it at high temperature (950°C-1050°C). Xia and al [START_REF] Xia | [END_REF] have underlined the interest to fill these micro-cracks by the repetition of dip-coating step. This paper presents, on one hand, a feasibility study on micro-cracks closing by sol-gel route and on the other hand, the influence on surface topographies of the powder content in the sol for filling-up and the number of dip-coating.

Experimental.

Substrate preparation. Two nickel based superalloy substrates have been studied : Hastelloy X and AM1. Only AM1 is grit-blasted, which allows to get surface roughness Ra close to 1µm. The aim is to show the feasibility of filling-up, which is the reason why those preliminary studies have been performed on samples without Pt.

Sol-gel Process. Thermal barrier coating, with 9.7% mol of yttrium stabilized zirconia, is prepared by sol-gel route [4]. Precursors used are zirconium (IV) propoxide (Zr(OPr) 4 ) (Aldrich), yttrium (III) nitrate hexahydrate (Acros Organics) and the solvent is 1-propanol. Acetylacetone (AcAc) as complexing agent, is used to reduce hydrolysis rate of zirconium alcoxyde [5]. Volume rates AcAc/Zr(OPr) 4 and H 2 O/Zr(OPr) 4 are respectively : 0.8 and 9.5. YSZ powders synthesized by sol-gel route are prepared after gel drying by the solvent evaporation in supercritic conditions of the propanol (solvent) [6]. Then powders are heat treated at 700°C. To elaborate YSZ coatings by the dip-coating technique, slurry is composed of starting sol (9.7%mol YO 1.5 ), loaded at 40% with commercial TOSOH YSZ powder or with powder directly coming from supercritic drying. After immersion of the substrates into the sol, they are withdrawn at controlled speed (250mm/min), before a final heat treatment at 950°C during 2h to carry out ceramics layers. To proceed to a controlled damage of thermal barriers, samples are heated at 1150°C during 1 hour. The parameter "powder content" into the slurry has been studied to optimize the filling-up. Analyzed samples are referred in the 1. Experimental data of each sample Surface topography, cyclic oxidation behaviour and microstructural analyses have then been carried out for all samples.

Characterization. The surface topographies of the samples were quantified using white light confocal microscopy (ALTISURF 520) with a dynamic range of 15nm-350µm. In addition, this technique allows to roughly evaluate the deposited thickness (∆z en µm) during repairing steps. YSZ coatings were first embedded in epoxy resin (EpoFix, STRUERS) and metallographically prepared down to 3µm using a diamond spray. Surface and cross-sectional microstructural analyses were also carried out using optical microscopy. The cyclic oxidation tests were performed using an automated cyclic oxidation furnace. Each cycle consisted of a 15 min heat-up to 1100 °C, a 60 min dwell at 1100 °C, and a 15 min forced-air cooling to ambient temperature. All the tests are performed in laboratory air.

Results and discussion

Study of feasibility of damaged thermal barrier repair. Feasibility study is first performed on Hastelloy X substrates. Thermal barrier coating damage is generated by sample exposure during 1 hour at 1150°C, as seen on Figurea. After the filling-up with load sol at 40%wt with commercial powder, sample is heated at 950°C during 2 hours. Figure 1b allows to compare different possibilities of repair between 1 and 2 coatings. Indeed one coating with load sol allows to fill in the cracks network. A second coating allows to recover more homogeneously the cracks network and to get smoother surface, close to a non-damaged coating surface. From this simple metallographic analysis, it can be concluded that thermal barrier coating repair is possible using multiple successive dip coating. In the next section, a more specific investigation on surface topography, barrier microstructure and cyclic oxidation behaviour of repaired barrier is presented.

Filling-up step. Different parameters, such as the number of coatings, the powders content to get the best filling-up conditions have been investigated. The samples are referred in table 1. One of the first parameters required to quantify the efficiency of filling-up is the thickness of coated matter, referred to as ∆z, directly linked to the filling-up process. First, in figure 2a, is presented the surface topography of samples before the annealing damage and in figure 2b, the sample after the annealing damage, i.e. after a heat treatment at 1150°C. In these two cases, ∆z values are similar (about 60-70µm), but micro-cracks network is larger and cracks are bigger for the damaged sample, because at high temperature micro-cracks network continues to progress. The Figure 2c shows the surface topography of sample D, i.e. sample after filling-up with 1 dip-coating with sol loaded at 40%wt of powder. We can remark that ∆z is smaller, but there is an additional matter on surface. Then studies of surface topographies correlated to filling-up samples with 2 dip-coating have been performed. The surface topography of sample covered by not loaded sol is similar to surface topography of sample before filling-up, i.e. directly after heat treated at 1150°C. On graph (see figure 3) corresponding to topographic measurements, ∆z has been evaluated for different powder load conditions in the sol, then both samples (B et C) are compared with a filling-up sample with not loaded sol (A). We can see in figure 3a, the differences between sample A and sample B. We observe that the value of z parameter, representing surface top is quite the same in both cases, while the value of z representing the bottom of the cracks is larger for sample B. This shows that there is a best filling-up with the sol loaded at 20%wt, because it allows to reduce cracks depth. This powder content is the best compromise to optimize the filling-up conditions. Then, we can see in figure 3b the different surface topographies between sample A and sample C. First, the value of z, representing the bottom of the cracks is the same in the two cases, while the value of z corresponding to the upper surface is larger for sample C. This shows that a powder content of loaded sol of 40% of powder is too high. The sol cannot penetrate properly into the micro-cracks. Consequently, the matter only recovers the top of the surface. To confirm this point, figure 4 shows 3D surface topographies of samples filling-up with different powder contents in the sols. It allows to illustrate previous observations. Main disadvantage of filling-up with sol loaded at 40%wt of powder is the additional matter brought from first dip-coating. Finally, for filling-up, powder loading at 20wt% allows to reach the best compromise corresponding to a satisfactory filling-up without recovering the surface. So, if necessary, the number of dip-coating can be increased to get a sample with a minimum ∆z value. Cyclic oxidation tests. As indicated above, samples tested in cyclic oxidation have been prepared on NiAl substrates without Pt addition. Consequently alumina rapidly grows during oxidation test, because there is not Pt to limit Al diffusion [START_REF] Sudhangshu | High Temperature Coatings[END_REF]. This fast oxide growing leads to an early damage of the thermal barriers. In this case, the number of cycles cannot exceed fifteen in general.

Our first objective has been to discriminate the suitable powder load content for the filling-up. First, cyclic oxidation tests have been performed on a sample with no filling-up, which is used as a reference for oxidation behavior. Figure 5 shows a damaged sol-gel thermal barrier. In opposition to damaged EB-PVD thermal barrier in which cyclic oxidation induces a non-progressive delamination of the major part of the coat, damaged sol-gel thermal barrier progressively proceeds through spallation. We can notice that the samples are more damaged on edges due to edge effects. For the filling-up of sample C containing a loaded sol at 40% of powder, damage mechanism is not the same. Indeed in figure 6, the topographies exhibit local buckling which can be due to two main reasons : first, the deposit is probably too loaded and we can see an important recovering of the upper surface of the sample. So, this impregnation is not suitable because the active matter is mainly located on the surface. The second reason is, of course, that 1150°C is probably a too high temperature to prevent from delamination, however, note that this choice has been done to accelerate the cracks network formation. According to Evans [START_REF] Evans | [END_REF], observation of buckling suggests a poor adhesion between coating and substrate : cracks propagate at the interface and lead to delamination as a consequence of high stresses in the coating. Stresses resulting from the mismatch between thermal expansion coefficients of multilayers and alumina oxide. In our case, additional stresses may be due to the additional matter on the surface top during the filling-up.

Conclusion

The research presented in the paper shows the feasibility of repairing damaged sol-gel thermal barrier coatings using dip-coating in loaded sols. Industrially, it is of utmost concern to develop repair processes as locally damaged thermal barrier coatings are usually rejected. This stands for a technical and economic viable way to increase lifetime and durability of thermal barrier coatings.

Prospects are now to evaluate the interest of this filling-up process on more realistic conditions from an industrial point of view : NiPtAl substrates and less severe thermal conditions. Studies on this topic are now in progress.

Figure 1 .

 1 Microscopy of sample a) before filling-up b) after filling-up

a b c Figure 2 .

 2 Surface topographies of sample a) before damage, b) after damage at 1150°C, c) after filling-up with 1dip-coating with sol loaded at 40%wt

a b Figure 3 .Figure 4 .

 34 Figure 4. 3D surface topographies of sample after filling-up a) sample A b) sample B c) sample C

a c Figure 5 .Figure 6 .

 56 Figure 6. Cyclic oxidation test at 1100°C for filling-up sample with loaded sol of 40% of powder a) after 1 cycle, b) after 4 cycles, c) after 13 cycles

table 1 :

 1

	Sample name	Number of coatings	Load content	Heating temperature
	A	2	0%	1h_600°C + 2h_950°C
	B	2	20%	1h_600°C + 2h_950°C
	C	2	40%	1h_600°C + 2h_950°C
	D	1	40%	1h_600°C + 2h_950°C
		Table