Arif Badrou

Arnaud Duval

Jérôme Szewczyk

Raphaël Blanc

Nicolas Tardif

Nahiène Hamila

Anthony Gravouil

Aline Bel-Brunon

Development of decision support tools by model order reduction for active endovascular navigation

Keywords: Model Order Reduction, Numerical chart, Endovascular, Catheters, Guidewire, Aorta

Endovascular therapies consist in treating vascular pathologies mini-invasively by inserting long tools towards the area to treat. However, some trajectories are so-called complex (e.g. Supra-Aortic Trunks (SATs)). In order to facilitate the access to complex targets by catheterization, an active guidewire made of Shape Memory Alloy has been developed. Our study focuses on the navigation of this device and associated catheters towards neurovascular targets through the left carotid artery. In a previous study, a finite element model was developed to simulate the navigation of the active guidewire and catheters from the aortic arch to the hooking of the left carotid artery of patient-specific aortas. However, numerical simulations are time-consuming and cannot be used directly in the clinic routine to provide navigation assistance. We present in this study the development of numerical charts aiming to provide a real-time computation, based on high-fidelity FE simulations, of: 1. the behaviour of the active guidewire; 2. the navigation of the active guidewire and associated catheters within a given anatomy for specific guidewire and navigation parameters. These charts are developed using the High Order Proper Generalized Decomposition (HOPGD) method and demonstrate their ability to provide an accurate real-time response from a limited number of preliminary high-fidelity computations.

Introduction

Endovascular therapies have grown significantly in the recent years. It is estimated that in 2026, 80% of cardiovascular problems will be treated by endovascular therapies (Veith 2016). The first step to treat endovascular pathologies is to reach the pathologies area. However, clinicians may be confronted to so-called complex pathways (e.g. renal arteries or Supra-Aortic Trunks (SATs)). It is estimated that 20% endovascular therapies present these complexities which may jeopardize the intervention [START_REF] Madhwal | Predictors of Difficult Carotid Stenting as Determined by Aortic Arch Angiography[END_REF]. In order to facilitate the access to complex targets through catheterization, the French company BaseCamp Vascular (BCV) developed an active guidewire made of Shape Memory Alloy, which distal tip can bend under an electric impulse. This guidewire can include several active modules; for instance for 2 modules placed in opposite directions, the guidewire tip can take an S-shape.

Our work focuses on the access to neurovascular pathologies through the left carotid artery using the active guidewire and associated catheters. Access to cerebral targets is facilitated using the active guidewire but two challenges remain for a given anatomy: (i) to optimize the design of the active guidewire by assessing the number of required actuators and their respective curvature and (ii) to propose navigation sequences maximizing the chances of reaching the target.

A Finite Element (FE) model was developed to simulate the navigation of the active guidewire and catheters from the aortic arch to the left carotid artery in patient-specific aortas (Badrou, Tardif, Chaudet, et al. 2022). The numerical model offers the possibility to test particular guidewire configurations and navigation sequences. However, numerical simulations are time-consuming and cannot be used directly in clinical routine to provide navigation assistance. An alternative is to develop numerical charts to explore in a continuous way a wide range of parameters for a limited computational cost.

Numerical charts are built using Model Order Reduction (MOR) techniques. Two families of MOR are commonly used. The methods known as POD (Proper Orthogonal Decomposition) require calculations in an offline phase (learning phase), further allowing reduction and online resolution in the reduced base (in real-time). In biomechanics and in particular for vascular problems, POD was used for example to process hemodynamic data [START_REF] Kefayati | Transitional flow analysis in the carotid artery bifurcation by proper orthogonal decomposition and particle image velocimetry[END_REF][START_REF] Janiga | Quantitative assessment of 4D hemodynamics in cerebral aneurysms using proper orthogonal decomposition[END_REF][START_REF] Darwish | Proper Orthogonal Decomposition Analysis of the Flow Downstream of a Dysfunctional Bileaflet Mechanical Aortic Valve[END_REF] or to reduce the computational time of complex models (Rama et al. 2016). The methods known as PGD (Proper Generalized Decomposition) based on the separation of variables, do not require upstream calculations. In particular, PGD is used for inverse problem solving: in [START_REF] Barone | Efficient estimation of cardiac conductivities: A proper generalized decomposition approach[END_REF], PGD was used to speed up the process of identifying conductivities of heart tissue. Other works have used PGD for computational surgery, [START_REF] Quesada | Computational vademecums for real-time simulation of surgical cutting in haptic environments[END_REF]; [START_REF] Quesada | Haptic simulation of tissue tearing during surgery[END_REF]; [START_REF] Niroomandi | Real-time simulation of biological soft tissues: a PGD approach[END_REF] for example. One of the limitations of POD is that it is not adapted to non-linear problems (large strains in particular) and that the enrichment of the reduced bases can quickly become expensive for high dimensional problems and/or with relatively large parameter intervals. By considering uniform grids, the number of snapshots is exponential. For example, for a uniform grid of snapshots in a space of 8 parameters with 10 values to be considered in each direction, 10 8 finite element calculations would be required. We then speak of curse of dimensionality. PGD allows to overcome this problem since no snapshot is required. However, it remains an intrusive method and is therefore not adapted to the use of commercial softwares. The method used in the present study is HOPGD (High Order Proper Generalized Decomposition) [START_REF] Modesto | Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation[END_REF]. It is an a posteriori definition of PGD and has been used to produce 10-dimensional (10D) numerical charts in the context of real-time numerical simulation of welding processes (Lu et al. 2018b). We aim to build numerical charts based on our reference FE navigation model, to efficiently answer specific questions regarding device design and navigation sequences.

We first recall the main features of the high-fidelity numerical models used in this study, namely the guidewire model and the active endovascular navigation model. Then, HOPGD is briefly presented and the methods for the development of numerical charts are detailed. Proofs of concept of such charts ,developed to answer specific questions associated to endovascular active navigation, are presented. The results are finally discussed in a last part.

Methods

High fidelity models

In this section, we present the high-fidelity models used to develop the numerical charts: first the active guidewire model and second the navigation model. The active guidewire is composed of a long shaft made of steel. At its extremity, a blade is attached and Nitinol wires are positioned on both sides of the blade and connected to electric wires. A handle allows to send an electric impulse to the Nitinol wires and by shape memory effect, the wires shrink causing the blade to bend [START_REF] Lagoudas | Introduction to shape memory alloys[END_REF][START_REF] Couture | Design and Experimental Validation of an Active Catheter for Endovascular Navigation[END_REF]. When two Nitinol wires are placed on each face of the blade, the distal tip of the active guidewire draws a S-shape to facilitate the endovascular navigation (see Fig. 1).

Numerical model

The model is built using Ls-Dyna (LSTC / ANSYS, USA). The active guidewire is simplified, as not all elements from Fig. 1 are included, and represented as a long shaft with the blade. The Nitinol wires are placed on both sides of the blade and connected by rigid links (see Fig. 2). The guidewire is meshed with Hughes-Liu beam elements. The constitutive law to model the mechanical behavior of the guidewire is hypoelastic and relates, in Eulerian form, the objective Jaumann derivative of the Cauchy stress tensor 𝜎 to the strain rate tensor D by the elasticity tensor C such that:

𝜎 ∇ = C : D (1)
Tensor C can be decomposed into a spherical part C 𝑠𝑝ℎ and a deviatoric part C 𝑑𝑒𝑣 such that:

C = 3𝐾C 𝑠𝑝ℎ + 2𝐺C 𝑑𝑒𝑣 (2)
with 𝐾 the bulk modulus and 𝐺 the shear modulus.

The mechanical properties of the various portions of the guidewire were characterized in [START_REF] Badrou | Characterization of Surgical Tools for Specific Endovascular Navigation[END_REF] and the Young's moduli of the main components are recalled in Fig. 2 with a fixed Poisson's ratio of 0.3 The guidewire activation is simplified and produced by a displacement command as explained in Badrou, Tardif, Chaudet, et al. (2022).

Simulation of the guidewire activation

Simulation of the guidewire is useful for guidewire developers to understand the guidewire performance, related to the Nitinol wires characteristics. The shaft is embedded and a temperature control is applied to both moduli for activation. The computational time for such a simulation is about 5 minutes. The output data are the displacements in 3D of the guidewire distal parts nodes (73 mm blade of the active guide) at the end of the simulation.

Endovascular navigation

Test bench

The endovascular activation simulated in this work has been validated with respect to data acquired on a test bench including a phantom aorta (Fig. 1). The simulation features aim to reproduce this configuration and the phenomena observed on this bench. The set-up is composed of a patient-specific aortic arch which can be changed and a fixed cylinder representing the descending aorta. The active guidewire is inserted and co-manipulated along with catheters.

Endovascular navigation model

The numerical model simulates the endovascular navigation of the active guidewire and associated catheters in the aorta test bench. The catheters and the aorta are meshed with Belytschko-Tsay shell elements. The mechanical properties of the tools are either hypoelastic (using Eq.1) or hypoviscoelastic depending on the different areas. patient specific aorta considered as rigid. The dimensions as well as the material properties can be found in [START_REF] Badrou | Characterization of Surgical Tools for Specific Endovascular Navigation[END_REF]. More details about the full navigation model are given in Badrou, Tardif, Chaudet, et al. (2022). The navigation model, involving guidewire activation but also tools translations and rotations within the aorta, was also validated as described in Badrou, Tardif, Chaudet, et al. (2022) by confronting experimental navigation in patient-specific aortas to simulated ones.

The model is able to reproduce the main movements and phenomena occurring in active navigation: translations of the guidewire and the catheter, rotations of the guidewire and particular effects such as the snapping (Fig. 3). Navigation sequences will be detailed later. ⃝ while a rotation gesture is applied at the end of the active guidewire. As a consequence, the snapping effect appears( 5⃝) allowing to point the distal part of the guidewire in the desired direction and to stabilize the device. The guidewire is pulled from 6 ⃝ to 7 ⃝ to straighten the catheters with a deactivation of the proximal module to further tension it. Finally, the catheter slides over the guidewire until it reaches the left carotid artery in 8 ⃝.

1.1.2.3 High fidelity simulations for the construction of decision support numerical charts Two numerical charts are built for the endovascular navigation in two typical aortas: the BH aorta, which is referred to as a standard aorta, and the FM aorta, which includes a bovine arch (the left carotid artery and the brachio-cephalic trunk share the same origin). The key steps of active navigation into these aortas are illustrated Fig. 4.

The distal modulus is systematically activated at the beginning of navigation to follow the shape of the arch and prevent the guidewire from entering the left subclavian artery. Therefore, the time of activation of the distal modulus is not a parameter. The output data recorded are the displacements of the guidewire distal part (73 mm blade) over time. The data are saved every 0.01s of the simulation over a total simulation time of 10.6 s and 11.5 s for the BH and FM aorta, respectively. Using two 2.30 GHz Xeon cores, the duration of a simulation is about 3 h.

Development of numerical charts using reduced order modeling

Now that the high-fidelity FE models have been presented, the High Order Proper Generalized Decomposition (HOPGD) method used to build the numerical charts is presented. A focus is proposed on the choice of the parameters of interest in this work, as it is a critical step.

Then, two types of numerical charts are developed as proofs of concept: an active guidewire design tool focusing on design parameters and navigation assistance tools mixing design and navigation parameters. For each type of numerical chart, the parameter space and the snapshot selection method are presented. An error is finally calculated to evaluate the chart accuracy.

Methods

HOPGD

We consider a function 𝑢 dependent on parameters 𝑝 𝑖=1,𝑑 which can be time, space or control parameters of the problem. These parameters are assimilated to extra-coordinates of the solution and discretized in the parameter space. For each set of parameters, HOPGD seeks an approximate form 𝑢 𝑛 of 𝑢 such that:

𝑢 (𝑝 1 , ..., 𝑝 𝑑 ) ≈ 𝑢 𝑛 (𝑝 1 , ..., 𝑝 𝑑 ) = 𝑛 ∑ 𝑗=1 𝑑 𝑖=1 𝐹 𝑗 𝑖 (𝑝 𝑖 ) (3)
𝑛 is the order of approximation and the functions 𝐹 𝑗 𝑖=1,𝑑 are related to the j-th mode. These functions are determined by solving the minimization problem which consists in finding

𝑢 𝑛 ∈ 𝑉 𝑛 ⊂ L 2 (Ω) minimizing the cost function 𝐽 such that: 𝐽 (𝑢 𝑛 ) = min 𝑢 𝑛 ∈𝑉 𝑛 1 2 || 𝑢 𝑛 -𝑢 || 2 L 2 (Ω) (4)
This minimization problem can be solved by an alternating fixed point algorithm. For a new set of parameters, the new functions 𝐹 𝑖 are linearly interpolated from the existing functions. In this study, the version of the HOPGD algorithm does not use snapshot selection by sparse grids method as introduced in Lu et al. ( 2018). Thus, parameters discretization is conducted using uniform grids. Fig. 5 illustrates the general procedure of the HOPGD method.

Figure 5: General procedure of the HOPGD method: starting from a high-fidelity numerical model, n parameters are considered among the geometry, material and boundary conditions. Then, the parameter space defined by the n axes is discretized using a snpashot selection method. For an uniform grid, 𝑚 snapshots are selected along the axes forming a total of 𝑚 𝑛 snapshots. These snapshots are used to build the reduced model. Considering a new set of parameter within the parameter space, the HOPGD model is capable of providing a real-time response.

Error evaluation

In order to evaluate the numerical charts performance, so-called evaluation points are selected in the center of the subdomains of the snapshot grid in the parameter space.

For each of these evaluation points, an additional finite element calculation is performed and the displacements of guidewire distal part nodes are stored in a reference 𝑈 𝑟𝑒 𝑓 matrix, containing the so-called high fidelity results. The reduced model is used to interpolate the results on this point and the obtained displacements are in turn stored in a 𝑈 matrix. For the considered point, an error 𝛿 is computed such that:

𝛿 = || 𝑈 -𝑈 𝑟𝑒 𝑓 || || 𝑈 𝑟𝑒 𝑓 || (5)
With || • || the 𝐿 2 norm.

Application

Endovascular navigation involves many parameters. They can be classified into three categories:

(i) those related to the design of the active guidewire (e.g., lengths of the active moduli or distance between them), (ii) the parameters related to navigation such as activation times or pushing / pulling times of the surgical tools and (iii) those dealing with geometric parameters (patient-specific aortas). In our study, we decided to work with fixed geometry, i.e. the parameters only relate to the design of the active guidewire and those related to the clinician gestures during navigation. In the following, two types of numerical charts are presented. First, an active guidewire design aid tool with five control parameters that are related to the device design is presented. This tool allows to compute the performance of the activated guidewire for a given set of parameters. Then, considering the design and navigation parameters, decision support numerical charts are also proposed with seven control parameters.

Active guidewire design tool

This first tool aims to provide a design aid tool. From a given guidewire configuration, the tool computes in real time the deformation of the guidewire after activation of the moduli. The high-fidelity model used to generate the snapshots was presented in Section 1.1.1.3. The output of each snapshot corresponds to the distal guidewire position for a given design.

Choice of parameters

Five design parameters are selected for the development of the design support tool (Fig. 6): the lengths 𝐿 𝑝 , 𝐿 𝑑 and 𝑒 that are the lengths of the active moduli and the distance between them, respectively; parameters 𝜖 𝐿 for the two Nitinol wires, which is the recoverable strain for the Nitinol wires in the shape memory effect loop representing the wire performances (change in current intensity or Nitinol grade for instance). Fig. 6 also describes the parameter ranges.

Snapshots selection

As previously mentioned, the version of HOPGD we use in this work does not include the sparse grids method and therefore does not allow for optimal selection of snapshots in the parameter space. Thus, it is chosen for this numerical chart to build a uniform grid with a discretization of three values per parameter (extremal values and middle of each interval), yielding a grid of 3 5 = 243 finite element calculations to feed the HOPGD method and create the reduced model. A MatLab (MathWorks, USA) routine is used to automatically create the snapshots with the design parameters as input data. Once the snapshots are computed, the HOPGD algorithm builds the reduced model with a default number of modes fixed at 20. The reduced model is then evaluated at the center of subdomains formed by the space parameter and using the error defined Section 1.2.1.2.

Navigation assistance tools

Introduction

In this part, more sophisticated numerical charts are proposed taking into account both design and navigation parameters. These decision support tools compute the active navigation in a given anatomy for various sets of parameters. They are proofs of concept of decision support tools which could be used in the preoperative phase. Their main advantage is the real time response.

The high-fidelity model used to generate the snapshots was presented in Section 1.1.2.3.

Choice of parameters

Among the design parameters, we focused on the distal active modulus, which plays a dominant role in active navigation. Thus, parameters 𝐿 𝑑 and 𝜖 𝐿 𝑑 are included (Fig. 6). Only the performance of the NiTi wire given by 𝜖 𝐿 𝑝 is selected to drive the design of the proximal modulus (𝐿 𝑝 fixed at 27 mm and 𝑒 at 13 mm).

The other four parameters drive navigation. From a preliminary sensitivity study, the choice is made to focus on the guidewire pushing and pulling time (𝐷 𝑝𝑢𝑠ℎ and 𝐷 𝑝𝑢𝑙𝑙 ) and the time and duration of the activation of the proximal modulus (noted 𝑇 𝑎𝑐𝑡𝑃 and 𝐷 𝑎𝑐𝑡𝑃 respectively). These parameters are illustrated Fig. 4. A MatLab routine was developed in this study to automatically generate the endovascular navigation models from selected parameters.

Refinement and model accuracy

The accuracy of the navigation assistance tool is evaluated from an error defined, as explained in Section 1.2.1.2, as the difference between the high-fidelity model result and the reduced model result at the center of the hypercube defined by the parameter grid. However, we also propose here to dynamically improve the accuracy by adding a control loop (refinement) during the learning phase. The general procedure is visible in Fig. 7.

For the construction of these numerical charts, the generation of a uniform grid similar to the one used for the design aid chart (3 values per parameter) would have required 3 7 = 2187 snapshots. A method is therefore proposed to limit the generation of many snapshots while allowing the creation of charts with a satisfactory accuracy. Fig. 8. shows an overview of the process considering a 2D parameter space.

This additional procedure allows to determine the axes to be refined (requiring the addition of snapshots at the axis centers) when the error at the center of the hypercube is greater than a threshold value (here 5%). Let us note 𝑃 𝑖 the i-th parameter for 𝑖 = 1, ..., 7, 𝑃 𝑖 𝑚𝑎𝑥 the maximum value at parameter 𝑃 𝑖 (upper limit of the interval in Tab.1) and 𝑃 𝑖 𝑚𝑖𝑑𝑑𝑙𝑒 the middle of the interval of admissible values for the parameter 𝑃 𝑖 . Seven evaluation points, related to the seven parameters, are considered in order to determine which parameters most affect the error sensitivity. The first evaluation point corresponds to {𝑃 1 𝑚𝑖𝑑𝑑𝑙𝑒 , 𝑃 2 𝑚𝑎𝑥 , 𝑃 3 𝑚𝑎𝑥 , 𝑃 4 𝑚𝑎𝑥 , 𝑃 5 𝑚𝑎𝑥 , 𝑃 6 𝑚𝑎𝑥 , 𝑃 7 𝑚𝑎𝑥 }, evaluating the contribution of the first parameter. In the same way the second evaluation point corresponds to

{𝑃 1 𝑚𝑎𝑥 , 𝑃 2 𝑚𝑖𝑑𝑑𝑙𝑒 , 𝑃 3 𝑚𝑎𝑥 , 𝑃 4 𝑚𝑎𝑥 , 𝑃 5 𝑚𝑎𝑥 , 𝑃 6
𝑚𝑎𝑥 , 𝑃 7 𝑚𝑎𝑥 } and so on. The error as a function of time is then calculated for each of these evaluation points. The parameter axes associated with evaluation points whose maximum error exceeds 5% are refined by adding the midpoint on the parameter specific axis, for discretization of the snapshot grid. The procedure on a 2D case is illustrated In this part, we limit ourselves to a level 1 refinement (adding only one snapshot per direction)

on three axes at most, which represents a final grid of 3 3 × 2 3 = 432 snapshots. Figure 8: General procedure for the creation and refinement of decision support charts on typical aortas (learning phase in Fig. 7). The first step is to perform the simulations on the parameter sets at the vertices of the grid. The error during navigation is then evaluated at the center of the hypercube. When this error exceeds a threshold fixed at 5%, the discretization in the parameter space is densified on the axes of the influential parameters (addition of snapshots at the center of these axes). Indeed, evaluation points (in green) are added at the middle of the parameter ranges to estimate sensitivity and errors are computed for both parameters. In the example, the error related to 𝑃 2 exceeds 5%. Consequently, the grid is refined to reduce the error at the hypercube center.

Results

Active guidewire design tool

displays the corresponding guidewire displacements.

Navigation assistance tools 2.2.1 Standard aorta

From the snapshots at the grid vertices (2 7 = 128 snapshots), the reduced model is created in 77 seconds. Using the method detailed in 1.2.2.2 to select the axes to be refined, values at the middle of the parameters axes of 𝐿 𝑑 , 𝐷 𝑝𝑢𝑙𝑙 and 𝑇 𝑎𝑐𝑡𝑃 are added, with a total number of snapshots at 3 3 × 2 4 = 432. The new model is built in 263 seconds and the error at the center of the hypercube is reduced. The performance, precision and parameters of the decision support tool developed are summarized in Fig. 10.

Aorta with bovine arch

The procedure is similar for this chart applied to a bovine arch anatomy. The first model is built in 44 s but the error at the hypercube center required a refinement on the parameters axes of 𝐷 𝑝𝑢𝑙𝑙 and 𝑇 𝑎𝑐𝑡𝑃 leading to a model created in 164 s based on 3 2 × 2 5 = 288 snapshots. The errors of the model before and after refinement are displayed Fig. 10 as well as the main characteristics of this numerical chart. For the first numerical chart (standard aorta) a peak occurs at 𝑡 = 2 s with the distal module activation. At 𝑡 = 5 s, snapping occurs and we can see that grid refinement highly improves the error with a better prediction of the position of the guidewire after snapping.

For the second numerical chart, the error curves along time are fairly similar with a peak during snapping. At 𝑡 = 8.5 s, grid refinement allows to better describe the position of the guidewire once pulled and the distal part abruptly hooked the aorta. The accuracy is considered satisfactory considering the relatively low number of snapshots for such a problem.

Conclusions on decision support charts

Overall, the charts show very satisfactory results. The snapping is correctly replayed and the contact well represented. For each new set of parameters, the tools provide an instantaneous response (10 -3 s) compared to nearly 3 h for a high-fidelity FE calculation. The response time of the numerical chart is well below the specifications.

Concerning the error curves in blue for the two charts (Fig. 10), peaks at key stages of the navigation are observed. The first peak occurs when the distal modulus is activated. While snapping, the error increases sharply. For the first chart, this error gradually decreases and then increases again when the guidewire is pulled. The second chart error curve shows successive peaks during snapping, mainly due to guidewire high frequency vibrations. A second peak is visible when the proximal modulus is deactivated.

Discussion

Main results

The HOPGD method was used to build numerical charts and proved to be efficient for problems with many parameters as it was the case in this study.

A first chart has been developed to help the guidewire design optimization. Only guidewire design parameters were studied. Considering the simulation time of the snapshots used to create the reduced model and the preliminary tests, it was chosen to work on a uniform grid with three capture and control the fast movements of the tools. However it should be emphasized that this chart provides the navigation over time and not only the final configuration. After refinement, the error remains below 4% which can be considered as very satisfactory, especially because this maximum error occurs at snapping. We expceted this phenomenon to be much less reductible.

In general, it was interesting to test the performance of the HOPGD method in our problem associating nonlinearities, contact and fast phenomena.

Recent

Study limits

Many tests (charts with less parameters, simulations to study the sensitivity to some parameters) have been conducted beforehand and two main difficulties have been highlighted: the choice of parameters and their range of values. The active guidewire was developed during this work. As a consequence, there was not the necessary hindsight to choose, in an optimal way, the parameters to be incorporated in the chart. We then relied on the experience gained from the numerous simulations performed.

Concerning the values ranges, charts with two or three parameters allowed to show that too large ranges would require many simulations. In order to develop proofs of concept and taking into account the available resources, a maximum of 432 snapshots per chart was set. With seven control parameters, the selected value intervals were therefore quite small and did not allow to explore large variations of the guidewire navigation. The main limitation came from the use of uniform grids. It would be interesting to improve the generation of snapshots with a sparse grid method.

The errors for both decision support charts were evaluated at the center of the hypercube.

An error within 5% was considered satisfactory. This criterion was determined by judging the displacements of the guidewire relative to the aorta: for the tested charts, a higher error corresponded to poor management of the contact between the guidewire and the aorta. Moreover, the peaks occured during the fast phenomena: activation and deactivation of the modules or even snapping. A solution to smoothen the curves could be to save more data as a function of time (reduction of the time step used to save the guidewire displacements) so as to better capture these phenomena. However, it would require a large amount of storage. A method, adapted specifically for this study, allowed us to select the axes to refine the grid when this error exceeded 5%. For intervals with larger extrema, further refinements in the sub-domains may be considered.

The HOPGD method relies on static parameters (scalar values), and recent developments have been focusing on a dynamic ROM builder to better fit transient analysis and reduce the number of learning points [START_REF] Calka | Machine-Learning based model order reduction of a biomechanical model of the human tongue[END_REF]). However, the main difficulty associated with our model is its sensitivity to parameters; even a slight change in them can significantly impact the displacements of the guidewire. Thus, a dynamic ROM might also require a significant number of points or further development to address these issues.

Conclusion

This study presents numerical charts for design and decision support tools dedicated to the use of the active guidewire. These solutions serve as a proof of concept and show very promising

Fig. 2 Figure 1 :Figure 2 :

 212 Fig.2illustrates the assembly of the different tools (guidewire and catheters) navigating in a

Figure 3 :

 3 Figure 3: From 1 ⃝ to 3 ⃝ the guidewire is initially pushed near the left carotid artery entrance. The two modules are activated in 4⃝ while a rotation gesture is applied at the end of the active guidewire. As a consequence, the snapping effect appears(5⃝) allowing to point the distal part of the guidewire in the desired direction and to stabilize the device. The guidewire is pulled from 6 ⃝ to 7 ⃝ to straighten the catheters with a deactivation of the proximal module to further tension it. Finally, the catheter slides over the guidewire until it reaches the left carotid artery in 8 ⃝.

Figure 4 :

 4 Figure4: (a) Proposed navigation key steps for BH aorta hooking (standard aorta). The guidewire is pushed (during 𝐷 𝑝𝑢𝑠ℎ ) and the distal modulus is activated to prevent the device from inserting into the subclavian artery. After the guidewire is pushed, the proximal modulus is activated (at 𝑇 𝑎𝑐𝑡𝑃 and during 𝐷 𝑎𝑐𝑡𝑃 ) and the snapping is initiated. The guidewire is then pulled (during 𝐷 𝑝𝑢𝑙𝑙 ). (b) The steps for navigation in the FM aorta (aorta with bovine arch) slightly differ: the guidewire navigates until it reaches the TSAs, the distal modulus is activated and snapping is triggered. The proximal modulus is then deactivated while pulling the guidewire to attempt to hook the carotid artery. Below each figure, navigation parameters driving the navigation are indicated on an axis representing time.

Figure 6 :

 6 Figure 6: Double stage guidewire activation model and design parameters ranges.

Figure 7 :

 7 Figure7: General procedure used for the development of decision support charts. From the snapshots computed in the parameter space in the learning phase, the reduced model is created and its accuracy is controlled. New snapshots are generated until the reduced model is considered as accurate enough. The real-time numerical chart is then used to give a real-time response given a set of parameters.

Fig

  Fig.8.

From

  the 243 finite element snapshots, the reduced model is created by the HOPGD method in 17 seconds. The accuracy of the reduced model is evaluated at the different centers of the subdomains of the parameter space, i.e. on 32 evaluation points. The model is able to provide a solution in 10 -5 s against 5 minutes for a FE calculation. The percentage errors at the different centers are given Tab.2. It is shown that the error is equal to or below 1%, which is satisfactory for accurately predicting the performance of a guidewire design.The reduced model considerably decreases the computation time and allows to create the numerical chart visible on Fig.9. The graphical interface is developed with Qt Creator (Qt Group, Finland). The set of chosen parameters with the cursor interrogates the model and the interface

Figure 9 :

 9 Figure 9: Numerical chart to help design the active guidewire. The five parameters can be modified and the tool allows to give a real time response of guidewire deformations with an accuracy of about 1%. A part of the rod is represented (left part of the rod) but has not been considered for the model construction. The figures represent different deformations of the guidewire according to the set of parameters defined by the user on the right panel.

  results. Fixed anatomy numerical charts were proposed in this study. A more powerful tool could incorporate geometric parameters and allow, for a new patient, to provide real-time decision support. 5 Backmatter information 5.0.0.1 Acknowledgements The French National Research Agency (ANR) partially supported this work through the DEEP project: Devices for augmEnted Endovascular navigation in complex Pathways (grant n°ANR-18-CE19-0027-01). 5.0.0.2 Authors' contributions A.B. carried out most of the study, performed numerical simulations, and drafted the manuscript. A.D. helped with implementation of the methods. J.S. and R.B. provided the clinical data. N.T. helped for the methodology and the experiments. N.H. provided support for the numerical simulations. A.G. provided support for the model reduction method and revised the article. A.B.B revised the article, contributed to the methodology and the analysis of the results. All authors read and approved the final manuscript. 5.0.0.3 Competing interests The authors declare that there are no conflicts of interest. 5.0.0.4 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a full copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

Table 1 :

 1 Choice of the intervals for the seven parameters of the decision support charts. The intervals are given for the standard aorta case and with bovine arch.

	Parameters Range of values for the standard aorta / with bovine arch
	𝐿 𝑑 (mm)	[27 ; 32] / [27 ; 32]
	𝜖 𝐿 𝑝	[0.026 ; 0.028] / [0.03 ; 0.033]
	𝜖 𝐿 𝑑	[0.029 ; 0.033] / [0.033 ; 0.0347]
	𝐷 𝑝𝑢𝑠ℎ (s)	[2.0 ; 3.5] / [4.2 ; 5.2]
	𝐷 𝑝𝑢𝑙𝑙 (s)	[0.05 ; 1.5] / [1.7 ; 2.5]
	𝑇 𝑎𝑐𝑡𝑃 (s)	[3.5 ; 4.5] / [4.7 ; 5.3]
	𝐷 𝑎𝑐𝑡𝑃 (s)	[0.1 ; 0.6] / [1.8 ; 2.2]

Table 2 :

 2 Errors at the center of the subdomains of the 5 control parameters for the design aid chart.

	Subdomain number	Set of parameters	Error (in %)
	1	{15.5; 5.5; 20.5; 0.016175; 0.016175}	0.79
	2	{18.5; 5.5; 20.5; 0.016175; 0.016175}	0.85
	3	{15.5; 8.5; 20.5; 0.016175; 0.016175}	0.78
	4	{18.5; 8.5; 20.5; 0.016175; 0.016175}	0.77
	5	{15.5; 5.5; 33.5; 0.016175; 0.016175}	0.72
	6	{18.5; 5.5; 33.5; 0.016175; 0.016175}	0.91
	7	{15.5; 8.5; 33.5; 0.016175; 0.016175}	0.9
	8	{18.5; 8.5; 33.5; 0.016175; 0.016175}	0.88
	9	{15.5; 5.5; 20.5; 0.028525; 0.016175}	1.00
	10	{18.5; 5.5; 20.5; 0.028525; 0.016175}	0.96
	11	{15.5; 8.5; 20.5; 0.028525; 0.016175}	0.82
	12	{18.5; 8.5; 20.5; 0.028525; 0.016175}	0.73
	13	{15.5; 5.5; 33.5; 0.028525; 0.016175}	0.90
	14	{18.5; 5.5; 20.5; 0.028525; 0.016175}	1.01
	15	{15.5; 8.5; 33.5; 0.028525; 0.016175}	0.91
	16	{18.5; 8.5; 33.5; 0.028525; 0.016175}	0.92
	17	{15.5; 5.5; 20.5; 0.016175; 0.028525}	0.85
	18	{18.5; 5.5; 20.5; 0.016175; 0.028525}	0.90
	19	{15.5; 8.5; 20.5; 0.016175; 0.028525}	0.79
	20	{18.5; 8.5; 20.5; 0.016175; 0.028525}	0.79
	21	{15.5; 5.5; 33.5; 0.016175; 0.028525}	0.56
	22	{18.5; 5.5; 33.5; 0.016175; 0.028525}	0.70
	23	{15.5; 8.5; 33.5; 0.016175; 0.028525}	0.67
	24	{18.5; 8.5; 33.5; 0.016175; 0.028525}	0.77
	25	{15.5; 5.5; 20.5; 0.028525; 0.028525}	0.91
	26	{18.5; 5.5; 20.5; 0.028525; 0.028525}	0.98
	27	{15.5; 8.5; 20.5; 0.028525; 0.028525}	0.86
	28	{18.5; 8.5; 20.5; 0.028525; 0.028525}	0.83
	29	{15.5; 5.5; 33.5; 0.028525; 0.028525}	0.68
	30	{18.5; 5.5; 33.5; 0.028525; 0.028525}	0.81
	31	{15.5; 8.5; 33.5; 0.028525; 0.028525}	0.78
	32	{18.5; 8.5; 33.5; 0.028525; 0.028525}	0.81

  research have been focusing on the development of Virtual Reality (VR) simulators to join the growing expansion of endovascular techniques[START_REF] Eves | Augmented Reality in Vascular and Endovascular Surgery: Scoping Review[END_REF]. While these efforts aim at developing training and predictive platforms, the developed physical models remain simple with general cases (not patient specific) and are mainly used to train novice practitioners(Rudarakanchana et al. 2015). The goal of this paper is to provide perspectives on elaborating high-fidelity numerical platforms to enhance VR tools, considering: (i) the inclusion of Finite Element Method (FEM) in VR simulators, capable of accurately simulating passive and active tools, and (ii) addressing the issue of patient-specificity through the use of deep learning techniques,

with Reduced Order Models (ROMs) or statistical shape analysis for instance

[START_REF] Iyer | Statistical shape modeling of multi-organ anatomies with shared boundaries[END_REF]

).

values per axis. Since the ranges were relatively wide, the errors of the reduced model were evaluated at the centers of the subdomains formed by the grid and reached 1%. A refinement was therefore not required for this chart.

Then, the objective was to work on more complex charts combining design and navigation parameters. These tools were thought of as proofs of concept of what could be achieved using model reduction methods in a biomechanical and in particular cardiovascular framework.

Some remarks about the choice of the navigation parameters and their values can be formulated: these parameters are considered to be the most influential for left carotid artery hooking. The extrema of these parameters were determined by a preliminary analysis. With these values the guidewire navigates between the origins of the left subclavian and the brachiocephalic trunk. The values do not overlap and they are associated to specific navigation sequences.

Indeed, the extrema values were chosen such as the main navigation steps are the same over the snapshots: considering the navigation into the BH aorta for instance, the guidewire is first pushed, the proximale module is activated and then the guidewire is pulled. Other sequences can not be obtained with these charts.

In the context of this study, real time is of the order of a second, comparable to the reaction time when using the graphical interface. For integration of numerical chart in a medical robotics environment, we would target a response time of the order of 0.1 s maximum, to be able to


Semyon A Grodsky

Reul Nicolas

Bentamy Abderrahim

Vandemark Douglas

Eastward propagating surface salinity anomalies in the tropical North Atlantic

Upper ocean variations across the tropical Atlantic are strongly seasonal due to corresponding seasonality in surface forcing and continental runoff. This implies that many features in regional upper ocean state or transport anomalies may also be seasonally locked. In the boreal summer and autumn, remote sensing sea surface salinity (SSS) observations show the presence of eastward propagating anomalies concurrent with the seasonal development of fresh Amazon plume and acceleration of the eastward North Equatorial Countercurrent. Interannual variations in these eastward cross-Atlantic SSS signals are investigated in connection with their forcing by wind and circulation patterns. Satellite data show that these SSS anomalies are advected zonally across the entire Atlantic. It is suggested that they originate due to wind-induced changes in the Amazon plume areal extent, which are notorious in the North Brazil Current retroflection. Satellite SSS is instrumental for exploring such signals because in-situ observations do not always capture them due to the limitation in resolved spatial and temporal scales.

Introduction

Meridional migration of the Intertropical Convergence Zone (ITCZ) between its southernmost position in boreal spring and northernmost position in late boreal summer defines the strong seasonality of tropical Atlantic climate [START_REF] Xie | Tropical Atlantic Variability: Patterns, Mechanisms, and Impacts[END_REF]. This implies that major interannual modes of regional sea surface temperature (SST) variability driven by local air-sea interactions [START_REF] Foltz | Seasonal Mixed Layer Heat Budget of the Tropical Atlantic Ocean[END_REF] are also seasonally locked, including the Atlantic Meridional Mode peaking in boreal spring e.g., [START_REF] Nobre | Sea Surface Salinity Estimates from Spaceborne L-Band Radiometers: An Overview of the First Decade of Observation (2010-2019)[END_REF] and the Atlantic Zonal Mode peaking in boreal summer (e.g., [START_REF] Zebiak | Air-Sea Interaction in the Equatorial Atlantic Region[END_REF]. Like the SST, the sea surface salinity (SSS) is also governed by meridional shifts of the ITCZ and its impacts on ocean surface fluxes and continental runoff [START_REF] Killworth | Seasonal Variations in the Horizontal Structure of the Amazon Plume Inferred from Historical Hydrographic Data[END_REF]. But in contrast to SST that can be more rapidly altered by airsea interactions, upper ocean salinity undergoes less change and provides a clearer tracer for oceanic advection [START_REF] Foltz | Seasonal Salt Budget of the Northwestern Tropical Atlantic Ocean along 38°W[END_REF], thus allowing the study of surface transport over larger distances in this tropical basin.

Tropical Atlantic SSS distribution includes a zonal band of relatively low SSS that is formed between 10°S-15°N due to the seasonally shifting ITCZ. It also includes a fresh SSS plume formed by Amazon discharge (peaking in mid-May and decreasing to its seasonal minimum in mid-November) that spreads over an area of 10 6 km 2 by early boreal autumn [START_REF] Dessier | The Sea Surface Salinity in the Tropical Atlantic between 10°S and 30°N-Seasonal and Interannual Variations (1977-1989)[END_REF]. The interannual variability of the plume area is controlled by multiple factors, with Amazon runoff variations accounting for ~50% (Zeng et al., 2008). But other factors, including cross-shore winds that modify offshore plume dispersal [START_REF] Molleri | Space-Time Variability of the Amazon River Plume Based on Satellite Ocean Color[END_REF]; [START_REF] Fournier | Interannual Variation in Offshore Advection of Amazon-Orinoco Plume Waters: Observations, Forcing Mechanisms, and Impacts[END_REF], regional western boundary current variability (Grodsky et al. 2014); [START_REF] Grodsky | A Curious Local Surface Salinity Maximum in the Northwestern Tropical Atlantic[END_REF], as well as Pacific teleconnections [START_REF] Grodsky | Delayed and Quasi-Synchronous Response of Tropical Atlantic Surface Salinity to Rainfall[END_REF] all contribute. The fresh plume water is advected eastward by the North Equatorial Countercurrent, NECC, (e.g., [START_REF] Carton | Estimates of the Zonal Slope and Seasonal Transport of the Atlantic North Equatorial Countercurrent[END_REF], and northwestward along the western boundary towards the Caribbean and Lesser Antilles [START_REF] Hellweger | Tracing Amazon River Water into the Caribbean Sea[END_REF].

In August -October, about 70% of the Amazon plume water turns eastward in the NECC along the North Brazil Current (NBC) retroflection [START_REF] Killworth | Seasonal Variations in the Horizontal Structure of the Amazon Plume Inferred from Historical Hydrographic Data[END_REF].

The eastward NECC is a possible gateway for zonal salinity anomaly propagation. In contrast to the more commonly observed wave-induced westward anomaly propagation by the Rossby waves [START_REF] Killworth | Seasonal Variations in the Horizontal Structure of the Amazon Plume Inferred from Historical Hydrographic Data[END_REF], eastward propagating anomalies have also been detected in major eastward currents, e.g., on poleward flanks of subtropical gyres [START_REF] Taguchi | Origin of Decadal-Scale, Eastward-Propagating Heat Content Anomalies in the North Pacific*[END_REF]. Here, most of the attention was paid to density compensated subsurface anomalies advected eastward at thermocline depths [START_REF] Sasaki | Observational Evidence for Propagation of Decadal Spiciness Anomalies in the North Pacific[END_REF]. Besides this subsurface regime, mixed layer anomalies may remain surface trapped (thus exposed to the remote sensing) and then advected by local surface currents for a prolonged period of weeks to months, with positive buoyancy supported by the stably stratified thermocline below the mixed layer. Eastward SSS propagation is also evident in the tropical Indian Ocean during negative dipole events [START_REF] Sun | Evolution of Sea Surface Salinity Anomalies in the Southwestern Tropical Indian Ocean During 2010-2011 Influenced by a Negative IOD Event[END_REF]) with an interruption during El Nino-induced westward current reversals [START_REF] Grodsky | Anomalous Surface Currents in the Tropical Indian Ocean[END_REF]. The tropical north Atlantic is an ideal system for observing such surface trapped eastward salinity anomalies produced by highly variable western boundary current dynamics that impact Amazon plume water and its export into the eastward NECC via the NBC retroflection.

Until recently, most information on tropical Atlantic SSS change has come from in situ measurements. In the last decade, traditional in-situ salinity measurements have been augmented by SSS measurements from three microwave satellite L-band (1.4 GHz) instruments (e.g., Reul et al. 2020). Here we exploit the Soil Moisture Active Passive (SMAP, since 2015) [START_REF] Meissner | Remote Sensing Systems SMAP Ocean Surface Salinities [Level 2C, Level 3 Running 8-Day, Level 3 Monthly[END_REF] Oceanographic data (AVISO) multi-satellite merged altimetry (http://marine.copernicus.eu). The Amazon freshwater plume configuration, with SSS≤35 psu, reflects the Amazon runoff entering the ocean at approximately 0°N and its transport northwestward along the western boundary [START_REF] Hellweger | Tracing Amazon River Water into the Caribbean Sea[END_REF]. Importantly, a connected area of relatively fresh 33< SSS <35 psu also extends eastward along the NECC (between 4°N-10°N and 30°W-44°W). This surface water reflects the combined impact of ITCZ rainfall and eastward Amazon plume advection. But in contrast with the August climatological ITCZ rainfall that is stronger east of 40ºW (not shown), this fresh SSS distribution is weighted towards the west (Figure 1) consistent with the expected impact of freshwater advection from the plume (e.g., [START_REF] Foltz | Seasonal Salt Budget of the Northwestern Tropical Atlantic Ocean along 38°W[END_REF]).

Examining SSS variability within the zonal NECC belt across 4°N-10°N (Figure 2a) reveals an eastward propagation in satellite SSS anomalies (SSSA; defined as the deviation from the monthly seasonal SSS cycle), with SSSA signals of ~0.5 psu crossing the entire tropical Atlantic. They develop seasonally along with the NECC, originate in the west by late spring to early summer, and cross the Atlantic by year-end. Figure 2 illustrates their kinematics and potential forcing terms. These eastward salinity signals are not likely forced by local air-sea interactions, as illustrated by Evaporation-minus-Precipitation, EmP, anomalies from the fifth generation of the European Centre for Medium-Range Weather Forecasts atmospheric reanalysis (ERA5, [START_REF] Hersbach | The ERA5 Global Reanalysis[END_REF], which do not seem to display a similar eastward propagation (Figure 2b). Their characteristic propagation speed ~0.2 m s -1 (Figure 2a) corresponds to the NECC zonal geostrophic velocity (Figure 2c). But, NECC acceleration events observed in 2017 and 2018 (Figure 2c) correspond to two opposite sign salinity events with fresh and salty NECC states (Figure 2a), respectively. This, in turn, suggests that SSS anomalies exiting the plume area via the NBC retroflection are further advected eastward by the mean NECC current (𝑢𝑢 �𝑆𝑆′ transport term) while the salinity transport component by anomalous zonal velocity (𝑢𝑢 ′ 𝑆𝑆 ̅ transport term) is not at play, where overbar is the mean and prime is the anomaly.

It is anticipated that the Amazon runoff anomaly may also contribute. But only in 2016 can the saltier NECC state be linked to preceding below-normal Amazon runoff (Figure 2d, runoff data from the Amazon basin water resources observation service, https://hybam.obs- mip.fr/ ). During other years, the sign of SSS anomaly does not correlate with the sign of Amazon runoff anomaly. Amazon runoff anomalies are not coincident with the runoff peak in May but are rather associated with changes in its annual phase and duration (Figure 2d). Regardless of their cross-Atlantic zonal extent (see longitude-time diagrams in Figure 2a), the eastward SSSA signals have a smaller meridional size and are not firmly captured by the existing in-situ observing systems, which do not always sample them due to the limitation in resolved spatial and temporal scales. As an example, Figures 3a and3b show spatial patterns of fresh SSSA observed by the SMAP during two sample months of 2017. In November 2017, the Argo float network (Figure 3d) captures reasonably well the fresh SMAP-observed SSSA pattern located at ~20ºW (Figure 3b). But there is a large discrepancy in September 2017 where the Argo zonal salinity anomaly data (Figure 3c) grossly mispresent regional satellite-observed SSS variations. When captured, the gridded Argo analysis does represent the expected vertical characteristics associated with these eastward SSSA signals, increasing from ~20 m to ~40 m as they propagate from the west into the tropical eastern Atlantic (Figures 3c,3d). In the west and close to the plume, their vertical scale corresponds to the vertical scale of barrier layers in the plume, ~20 m (e.g., [START_REF] Liu | Observed Subseasonal Variability of Oceanic Barrier and Compensated Layers[END_REF]). In the east, it deepens to ~ 40 m that may be interpreted as a result of the vertical diffusion of salinity anomalies as they are advected eastward by the NECC and propagate away from the Amazon plume. From the above considerations, it remains uncertain which mechanisms may be responsible for variability observed in eastward SSSA signals carried in the NECC in this time period each year. As mentioned, the 2016 SSSA increase may be related to a decrease in corresponding Amazon runoff in preceding months (Figure 2). But other years do not show this plausible forcing relationship. This is not surprising because the year-to-year plume variability is also affected by the variability of ocean currents (Grodsky et al. 2014).

Previous research has hypothesized that the strength of cross-shore winds over the tropical northwestern Atlantic can regulate the cross-shore plume extent by modifying its dispersal by mesoscale currents [START_REF] Molleri | Space-Time Variability of the Amazon River Plume Based on Satellite Ocean Color[END_REF]. Such indirect wind-induced changes of plume extent, in turn, modify the salinity of the water that enters the NECC through the NBC retroflection. Examining gridded satellite Advanced Scatterometer (ASCAT) winds [START_REF] Bentamy | Gridded Surface Wind Fields from Metop/ASCAT Measurements[END_REF] during months (May-July) corresponding to the annual development of salinity anomalies in the western NECC for years with fresh (Figures 4a,4b) and salty (Figures 4c,4d) NECC states supports the above hypothesis. In 2017 and 2020, the wind anomalies were offshore (Figure 2a). This favored Amazon plume dispersal off the shelf and allowed for fresher water to be retroflected into the western NECC, which was further advected eastward. Conversely, May-July wind anomalies in 2018 and 2019 were onshore. This appears to lessen the plume area and place it nearer to the coast, ultimately resulting in anomalous salinification of the western NECC. From Figure 4, the potential impact of opposing cross-shore wind anomalies on the plume extent is not clearly visible. In Figure 5, Amazon plume extent composites are compared using satellite SMAP SSS separately for years of salty (2016, 2018, and 2019) and fresh (2017 and 2020) NECC states (see also Figure 2a). Even given the limited statistics available from only 8 5 full years of SMAP data, this comparison illustrates that the plume area contracts somewhat during years of stronger onshore winds, which corresponds to the salty NECC state. The strongest plume contraction is present in the retroflection area and this implies less Amazon freshwater transport into the western NECC during anomalously onshore May-July wind conditions. Variations in this freshwater transport are a key factor of upper ocean salinity variability in the tropical northwestern Atlantic [START_REF] Foltz | Seasonal Salt Budget of the Northwestern Tropical Atlantic Ocean along 38°W[END_REF]).

Figure 1

 1 Figure 1 illustrates the August climatological distribution of tropical Atlantic SMAP SSS and geostrophic zonal currents from the Archiving, Validation and Interpretation of Satellite

Figure 1 .

 1 Figure 1. August climatological zonal geostrophic velocity (U, shaded, positive -eastward) and sea surface salinity (SSS) contoured at 32, 33, 34, and 35 psu. SSS≤33 psu is cross-hatched and 33<SSS<=35 psu is hatched. The latitudinal range (4°N-10°N) of the eastward North Equatorial Countercurrent, NECC, is delineated by solid lines.

Figure 2 .

 2 Figure 2. Monthly mean 4º-10ºN averages of (a) sea surface salinity anomaly (SSSA), (b) Evaporationminus-Precipitation anomaly (EmPA), (c) total zonal geostrophic velocity (U), and (d) relative anomaly (AmzA = (𝑅𝑅 -𝑅𝑅 s )/𝑅𝑅 s ) of Amazon runoff (R) from its seasonal cycle (𝑅𝑅 s ). Horizontal lines in (d) are drawn 1-st of May each year when Amazon runoff maximizes. Diagonal lines in (a) show 25 cm s -1 propagation speed.

Figure 3 .

 3 Figure 3. Sample SMAP satellite monthly SSS anomaly (shaded) for (a) September 2017 and (b) November 2017 with Argo data coverage hatched by purple dots. (c, d) Corresponding Argo depthlongitude salinity anomaly averaged 4°N-10°N from the Scripps Institute of Oceanography analysis (Roemmich and Gilson 2009).

  Figure 4 also illustrates that changes in the strength of crossshore winds are related to larger-scale changes in northeasterly trade winds, in turn, linked to the meridional-mode-like SST patterns (Fournier et al. 2017), with weaker winds corresponding to warmer tropical North Atlantic SST and vice versa.

Figure 4 .

 4 Figure 4. (shaded) Sea surface temperature anomaly (SSTA), (arrows) scatterometer surface wind anomaly, and (solid lines) SSS=34 psu contours during May-July period of years with (a, b) fresh and (c, d) salty NECC states. SSS contour color is (top row) blue (bottom row) red for better contrast with SSTA shading.

Figure 5 .

 5 Figure 5. May-July climatological SSS (shaded) with SSS=34 psu contour (solid lines) for years of fresh (2017 and 2020, black) and salty (2016, 2018, and 2019, red) state in the NECC.

Acknowledgments. This research was supported by the NASA Physical Oceanography and Ocean Surface Salinity Teams.


Islam Shikder Saiful

Zhang Shanshan

Eggermont Mieke
email: mieke.eggermont@ugent.be

Bruto Maxime

Le Roux Frederique

Defoirdt Tom
email: tom.defoirdt@ugent.beshanshan.zhang@ugent.be

The impact of the multichannel quorum sensing systems of Vibrio tasmaniensis and Vibrio crassostreae on virulence towards blue mussel (Mytilus edulis) larvae

Keywords: Bivalve, Splendidus clade, Larviculture, Immersion challenge, Quorum sensing

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

The impact of the multichannel quorum sensing systems of Vibrio tasmaniensis and Vibrio crassostreae on virulence towards blue mussel (Mytilus edulis) larvae

Shikder Saiful Islam, Shanshan Zhang, Mieke Eggermont, Maxime Bruto,

Frederique Le Roux, Tom Defoirdt

To cite this version:

Shikder Saiful Islam, Shanshan Zhang, Mieke Eggermont, Maxime Bruto, Frederique Le Roux, et al.. The impact of the multichannel quorum sensing systems of Vibrio tasmaniensis and Vibrio crassostreae on virulence towards blue mussel (Mytilus edulis) larvae. Aquaculture, 2022, 547, 737414 (6p.). 10.1016/j.aquaculture.2021.737414. hal-04203708

Introduction

Mussels are the most important aquaculture species in Europe based on live weight. The two main cultivated species are the blue mussel (Mytilus edulis) and the Mediterranean mussel (Mytilus galloprovincialis) (FAO, 2017). Recently, mussel culture in Europe has suffered from mass mortality events with mortality rates up to 100%. In addition to environmental and genetic factors (Benabdelmouna and Ledu, 2016;[START_REF] Polsenaere | Potential environmental drivers of a regional blue mussel mass mortality event (winter of 2014, Breton Sound, France)[END_REF], bacterial pathogens have been linked to mussel mortality [START_REF] Eggermont | Stimulation of heterotrophic bacteria associated with wild-caught blue mussel (Mytilus edulis) adults results in mass mortality[END_REF]Ben Cheikh et al., 2016). Vibrios belonging to the Splendidus clade (including V. crassostreae and V. tasmaniensis) are amongst the major bacterial pathogens of marine bivalves (Beaz-Hidalgo et al., 2010;[START_REF] Travers | Bacterial diseases in marine bivalves[END_REF][START_REF] Le Roux | Oysters and vibrios as a model for disease dynamics in wild animals[END_REF][START_REF] Dubert | New insights into pathogenic vibrios affecting bivalves in hatcheries: present and future prospects[END_REF] and V. splendidus strains have also been implied in mussel mortality events (Ben Cheikh et al., 2016;[START_REF] Oden | Multilocus sequence analysis of Vibrio splendidus related-strains isolated from blue mussel Mytilus sp. during mortality events[END_REF][START_REF] Eggermont | Isolation of Vibrionaceae from wild blue mussel (Mytilus edulis) adults and their impact on blue mussel larviculture[END_REF]. The implication of vibrios in mortality events in mussels is a very recent observation and the pathogenicity mechanisms are currently unknown.

Quorum sensing, bacterial cell-to-cell communication with small signal molecules, is known to control the virulence of many bacteria, including vibrios, and inactivation of these systems often decreases the virulence of these pathogens [START_REF] Milton | Quorum sensing in vibrios: complexity for diversification[END_REF][START_REF] Defoirdt | Virulence mechanisms of bacterial aquaculture pathogens and antivirulence therapy for aquaculture[END_REF]. Vibrios usually contain multichannel quorum sensing systems, in which multiple signal molecules determine the output of the system (Figure 1). Three types of signal molecules can be produced by vibrios (although not all vibrios produce all types): acylated homoserine lactones (AHLs), autoinducer-2 (AI-2), and cholerae autoinducer-1 (CAI-1) [START_REF] Milton | Quorum sensing in vibrios: complexity for diversification[END_REF]. The concentrations of the signal molecules determine the cellular level of the quorum sensing master regulator (a homolog of V. harveyi LuxR), which in turn controls the expression of many genes [START_REF] Van Kessel | Individual and combined roles of the master regulators AphA and LuxR in control of the Vibrio harveyi quorum-sensing system[END_REF]. Virulence-related phenotypes that are controlled by this kind of systems include motility, biofilm formation, and the production of lytic enzymes such as proteases [START_REF] Sultan | Presence of LuxS/AI-2 based quorum-sensing system in Vibrio mimicus: LuxO controls protease activity[END_REF][START_REF] Tian | Involvement of LuxS in the regulation of motility and flagella biogenesis in Vibrio alginolyticus[END_REF][START_REF] Natrah | Regulation of virulence factors by quorum sensing in Vibrio harveyi[END_REF][START_REF] Defoirdt | Virulence mechanisms of bacterial aquaculture pathogens and antivirulence therapy for aquaculture[END_REF]Yang and Defoirdt, 2015). Moreover, multichannel quorum sensing systems have been documented to be required for full virulence of vibrios towards various host organisms [START_REF] Ye | Regulation of Vibrio alginolyticus virulence by the LuxS quorum-sensing system[END_REF]Bjelland et al., 2012;[START_REF] Defoirdt | Monitoring of Vibrio harveyi quorum sensing activity in real time during infection of brine shrimp larvae[END_REF], and inhibitors of these systems (such as cinnamaldehyde, brominated furanones and brominated thiophenones) protect aquatic animals from vibriosis [START_REF] Defoirdt | Quorum sensing-disrupting brominated furanones protect the gnotobiotic brine shrimp Artemia franciscana from pathogenic Vibrio harveyi, Vibrio campbellii, and Vibrio parahaemolyticus[END_REF]Brackman et al., 2008;Yang et al., 2015).

In this study, we aimed at identifying multichannel quorum sensing systems in these pathogens, and at determining the impact of these systems on the virulence of V. tasmaniensis and V. crassostreae towards blue mussel larvae.

Materials and methods

Bacterial strains and growth conditions

V. tasmaniensis and V. crassostreae strains used in this study are described in Table 1. The bacteria were grown in marine LB broth (m-LB; tryptone 10 g/l, yeast extract 5 g/l, Instant Ocean synthetic sea salt 35 g/l) at 18°C with shaking (100 rpm). Cell densities were determined spectrophotometrically at 600 nm.

2.2. Identification of multichannel quorum sensing system genes in V. tasmaniensis and V. crassostreae and confirmation of the activity of the quorum sensing system GenBank was screened for homologs of components of the V. campbellii multichannel quorum sensing system in V. tasmaniensis and V. crassostreae by performing BLAST searches at the website of the National Center for Biotechnology Information (www.ncbi.nlm.nih.gov).

The activity of the quorum sensing system of the vibrios was assessed by introducing the cosmid pBB1 (Bassler et al., 1993) into natural rifampicin resistant mutants through conjugation using the donor strain E. coli SM10 (λpir). The pBB1 cosmid contains a tetracycline resistance gene and the V. campbellii lux operon under control of its native promoter and is activated by homologs of the V. campbellii quorum sensing master regulator LuxR. Hence, vibrios with an active quorum sensing system will produce quorum sensing-dependent bioluminescence. Transconjugants containing the pBB1 cosmid were selected on agar containing rifampicin (100 mg/l) and tetracycline (20 mg/l).

2.3. Construction of V. tasmaniensis and V. crassostreae quorum sensing mutants Deletion of selected genes was performed by allelic exchange using pSW7848T [START_REF] Val | Genome engineering in Vibrio cholerae: a feasible approach to address biological issues[END_REF], a R6K γori-based suicide vector. This vector encodes the ccdB toxin gene under the control of an arabinoseinducible and glucose-repressible promoter, PBAD [START_REF] Le Roux | Construction of a Vibrio splendidus mutant lacking the metalloprotease gene vsm by use of a novel counterselectable suicide vector[END_REF]. Briefly, two 500 bp fragments flanking the gene to delete were amplified and cloned into pSW7848T using the Gibson assembly method according to the manufacturer's instructions (New England Biolabs, NEB). The construct was transferred from an E. coli donor strain to the Vibrio LGP32 or J2-9 by conjugation as described previously [START_REF] Le Roux | Construction of a Vibrio splendidus mutant lacking the metalloprotease gene vsm by use of a novel counterselectable suicide vector[END_REF]. Subsequently, the first and second recombination leading to pSW7848T integration and elimination was selected on chloramphenicol + glucose and arabinose media, respectively. After reisolations, the gene deletion was confirmed by PCR using external primers.

Motility, protease and biofilm formation assays

Swimming motility was assessed as described previously by Yang and Defoirdt (2015). Briefly, 5 µl aliquots of the isolates (OD600 = 1) were inoculated in the centre of LB35 soft agar (0.2 % agar) plates. Plates were incubated upright at 18°C, and motility halos were measured after 24 h.

Caseinase and gelatinase activities were determined according to [START_REF] Natrah | Regulation of virulence factors by quorum sensing in Vibrio harveyi[END_REF]. For each assay, overnight grown cultures were diluted to an OD600 of 0.5, and 5 μl aliquots of the diluted cultures were inoculated to the centre of the test plates. Caseinase and gelatinase activities were assessed on agar plates containing 2% skimmed milk powder and 0.5% gelatin, respectively. Colony and clearing zone diameters were measured after 4 and 7 days incubation at 18°C for caseinase and gelatinase, respectively. In order to visualise the clearing zones in the gelatinase assay, saturated ammonium sulphate (80% solution in distilled water) was poured over the plates.

Biofilm formation was measured by crystal violet staining as described by Brackman et al. (2008).

Briefly, overnight grown cultures were diluted to OD600 of 0.5 and inoculated into the wells of a 96-well polystyrene plate. The plates were incubated for 24h. After incubation, the OD600 of the wells were measured. After this, the wells were rinsed 3 times with tap water, and stained for 20 min with a 0.1% crystal violet solution. The stain was removed, wells were rinsed 3 times with tap water, and air dried. The dye bound to adherent cells was redissolved in 95% ethanol, and absorbance was measured at 570 nm and expressed relative to the OD600.

Challenge tests with blue mussel D-larvae

Challenge tests were performed as described previously [START_REF] Eggermont | Isolation of Vibrionaceae from wild blue mussel (Mytilus edulis) adults and their impact on blue mussel larviculture[END_REF]. Wild-caught mature blue mussels were stimulated to spawn by thermal shocks in sterile sea water at 5°C and 20°C until gametes were released. Spawning males and females were transferred to sterile plastic cups containing 50 ml sterile sea water and allowed to spawn for 15 minutes. Sperm and eggs were collected and gently mixed at a 10:1 ratio in a beaker containing 1 l of sterile sea water. After the appearance of polar bodies, the eggs were gently rinsed with sterile sea water using a sterile 30 μm sieve to remove excess sperm. Fertilized eggs were incubated in 2 l of sterile sea water (max 100 eggs/ml) containing chloramphenicol, nitrofurazone and enrofloxacin (each at 10 mg/l). After two days of incubation, D-larvae were harvested on a sterile 60 μm sieve. The larvae were washed gently with sterile sea water to remove the antibiotics. Rinsed D-larvae were transferred to a beaker containing 1 l of sterile sea water and distributed uniformly using a plunger.

Subsamples were taken to calculate the larval density, and the density was corrected in order to obtain a final concentration of 250 larvae/ml. All manipulations were performed under a laminar flow hood.

One ml aliquots of the larval suspension in synthetic sea water supplemented with 10 mg/l tryptone and 5 mg/l yeast extract were subsequently transferred to 24-well plates. The final larval density was 200 larvae/ml. Vibrios were inoculated into the rearing water at 10 5 cells/ml. In the experiment with cinnamaldehyde, 10 µM of cinnamaldehyde (Sigma) was added to the wells [START_REF] Pande | Quorum sensing-disrupting compounds protect larvae of the giant freshwater prawn Macrobrachium rosenbergii from Vibrio harveyi infection[END_REF]. Larvae to which no bacteria were added and that were otherwise treated in the same way as challenged larvae, were used as controls. Each treatment was performed in 24 replicates. The plates were incubated at 18°C. Each day, four replicates per treatment were stained with lugol (5% (v/v)), and stained larvae were counted under a binocular microscope (Nikon Eclipse E 200, Nikon Instruments Europe). Larvae were considered alive when stained black by lugol, death if only parts of the larvae were stained or if shells were empty.

Statistics

All statistical analyses were performed using the SPSS software, version 24. A significance level of 1% was used in all analyses.

Results and discussion

3.1. Virulence of V. crassostreae J2-9 to blue mussel larvae V. tasmaniensis LGP32 and V. crassostreae J2-9 are well-known pathogens of oysters, that have been used as model strains to explore virulence mechanisms and immune responses in oysters [START_REF] Duperthuy | The major outer membrane protein OmpU of Vibrio splendidus contributes to host antimicrobial peptide resistance and is required for virulence in the oyster Crassostrea gigas[END_REF][START_REF] Duperthuy | Use of OmpU porins for attachment and invasion of Crassostrea gigas immune cells by the oyster pathogen Vibrio splendidus[END_REF]Toffiano-Nioche et al., 2012;[START_REF] Lemire | Populations, not clones, are the unit of Vibrio pathogenesis in naturally infected oysters[END_REF][START_REF] Vanhove | Outer membrane vesicles are vehicles for the delivery of Vibrio tasmaniensis virulence factors to oyster immune cells[END_REF][START_REF] Le Roux | Oysters and vibrios as a model for disease dynamics in wild animals[END_REF][START_REF] Bruto | Vibrio crassostreae, a benign oyster colonizer turned into a pathogen after plasmid acquisition[END_REF]. Presence of genetically related strains has also been documented in mussels [START_REF] Vezzulli | Aquatic ecology of the oyster pathogens Vibrio splendidus and Vibrio aestuarianus[END_REF]. We previously reported that V. tasmaniensis LGP32 is also pathogenic to blue mussel larvae [START_REF] Eggermont | Isolation of Vibrionaceae from wild blue mussel (Mytilus edulis) adults and their impact on blue mussel larviculture[END_REF]. In order to determine pathogenicity of V. crassostreae J2-9 to blue mussel larvae, we used the same immersion challenge test with sterile D-larvae [START_REF] Eggermont | Isolation of Vibrionaceae from wild blue mussel (Mytilus edulis) adults and their impact on blue mussel larviculture[END_REF]. V. crassostreae J2-9 showed to be pathogenic to the larvae, leading to significant mortality from day 2 onwards when compared to the unchallenged control (independent samples t-tests, P < 0.01) (Figure 2).

3.2. Identification of components of a multichannel quorum sensing system in the genomes of V. tasmaniensis and V. crassostreae and confirmation of the activity of the system Similar to many other Vibrio spp., vibrios belonging to the Splendidus clade have recently been suggested to contain multichannel quorum sensing systems (Zhang and Lee, 2021). Based on the genome sequences that are available in GenBank [START_REF] Le Roux | Genome sequence of Vibrio splendidus: an abundant planctonic marine species with a large genotypic diversity[END_REF][START_REF] Wang | Vibrio campbellii hmgA-mediated pyomelanization impairs quorum sensing, virulence, and cellular fitness[END_REF][START_REF] Lemire | Populations, not clones, are the unit of Vibrio pathogenesis in naturally infected oysters[END_REF], we identified homologs of the components of the V. campbellii multichannel quorum sensing system in the genomes of V. tasmaniensis and V. crassostreae (Table 2). This suggests that these two species also contain a multichannel quorum sensing system, with AHL, AI-2 and CAI-1 as signal molecules and a signal transduction cascade with LuxU, LuxO and LuxR, and is consistent with detection of AHLs, AI-2 and CAI-1 in Splendidus clade vibrios (including V. splendidus, V. chagasii and V. pomeroyi) by using signal molecule reporter strains (Yang et al., 2011). Recently, [START_REF] Girard | Characterization of N-acyl homoserine lactones in Vibrio tasmaniensis LGP32 by a biosensor-based UHPLC-HRMS/MS method[END_REF] reported that V. tasmaniensis LGP32 produces various AHLs, which were identified by mass spectrometry.

The activity of the quorum sensing system was investigated by conjugating the cosmid pBB1 into the vibrios. This cosmid contains the V. campbellii lux operon under control of its native promoter and is activated by homologs of the V. campbellii quorum sensing master regulator LuxR. We could confirm activity of the V. tasmaniensis quorum sensing system as V. tasmaniensis LGP32 pBB1 produced the typical V-shaped bioluminescence pattern that is the hallmark of quorum sensing-regulated bioluminescence in vibrios (Figure 3). Unfortunately, it was not possible to introduce cosmid pBB1 into V. crassostreae J2-9 as this strain is naturally resistant to tetracycline, the antibiotic required to select pBB1 carrying bacteria.

3.3.

Impact of quorum sensing on motility, protease activity and biofilm formation of V.

tasmaniensis and V. crassostreae

To explore their role in QS-related phenotypes, the luxM, luxS and luxR genes were successfully deleted in V. tasmaniensis LGP32, and the luxM, luxS and cqsA genes were deleted in V. crassostreae J2-9. We determined the impact of these knock outs on phenotypes that have been previously associated with quorum sensing-regulated virulence of other vibrios, i.e. motility, protease activity and biofilm formation [START_REF] Defoirdt | Virulence mechanisms of bacterial aquaculture pathogens and antivirulence therapy for aquaculture[END_REF]. Both V. tasmaniensis LGP32 and V. crassostreae J2-9 were highly motile (Table 3). There were no significant differences between wild types and mutants, except for the luxM deletion mutant of V. tasmaniensis LGP32 (which was more motile than the wild type) and the cqsA deletion mutant of V. crassostreae J2-9 (which showed lower motility than the wild type). The higher and lower motility of the luxM and cqsA deletion mutant of V. tasmaniensis and V. crassostreae, respectively, might be explained by a (yet unknown) signal transduction pathway that does not involve the known shared signal transduction pathway (using LuxU, LuxO and LuxR). A similar effect has been previously observed for the vhh hemolysin gene in V. harveyi, which was differentially expressed in a luxS deletion mutant, whereas inactivation of other components of the multichannel quorum sensing system had no effect [START_REF] Ruwandeepika | Quorum sensing regulation of virulence gene expression in Vibrio harveyi in vitro and in vivo during infection of gnotobiotic brine shrimp larvae[END_REF]. Another explanation for the higher motility of the luxM mutant of V. tasmaniensis is that both the production of AHLs and motility are energy-consuming processes [START_REF] Mccarter | Polar flagellar motility of the Vibrionaceae[END_REF][START_REF] Keller | Communication in bacteria: an ecological and evolutionary perspective[END_REF] and consequently, inactivation of the AHL synthase LuxM might result in increased cellular energy levels which in turn might lead to higher motility. Further, the strains tested positive for caseinase and gelatinase activities, with no significant differences in these activities between wild types and quorum sensing mutants. Finally, all strains were capable to form biofilms on polystyrene (Table 3). The quorum sensing mutants of V. tasmaniensis showed lower biofilm formation than the wild type. However, the difference was only significant for the luxS deletion mutant. There were no significant differences between wild type and mutants of V. crassostreae.

3.4. Impact of the multichannel quorum sensing system of V. tasmaniensis and V. crassostreae on virulence towards blue mussel larvae

We further compared mortality in blue mussel larvae caused by wild types and quorum sensing mutants of V. tasmaniensis and V. crassostreae. For V. tasmaniensis, there were no significant differences in virulence between wild type and quorum sensing mutants (Figure 4A). For V. crassostreae a slightly (but significantly) increased mortality was observed for larvae challenged with the luxS deletion mutant when compared to larvae challenged with the wild type from day 2 onwards (independent samples t-test, P < 0.01) (Figure 4B). Survival of larvae challenged with the luxM and cqsA deletion mutants was similar to that of larvae challenged with the wild type.

In a last experiment, we used a chemical biological approach to block the multichannel quorum sensing systems of V. tasmaniensis and V. crassostreae by adding cinnamaldehyde to the rearing water.

Cinnamaldehyde has been shown before to block the multichannel quorum sensing in vibrios by inhibiting the DNA-binding activity of the quorum sensing master regulator LuxR, and the compound blocked the virulence of V. harveyi towards brine shrimp and giant river prawn larvae (Brackman et al., 2008;[START_REF] Pande | Quorum sensing-disrupting compounds protect larvae of the giant freshwater prawn Macrobrachium rosenbergii from Vibrio harveyi infection[END_REF]. However, no significant differences in survival of mussel larvae challenged with V. tasmaniensis or V. crassostreae were observed after treatment with cinnamaldehyde (Figure 5). Together, our data indicate that inactivation of the quorum sensing system of V. tasmaniensis and V. crassostreae does not attenuate their virulence. A multichannel quorum sensing system has been reported to be required for full virulence in several Vibrio species, such as V. alginolyticus, V. campbellii and V. salmonicida [START_REF] Ye | Regulation of Vibrio alginolyticus virulence by the LuxS quorum-sensing system[END_REF]Bjelland et al., 2012;[START_REF] Defoirdt | Monitoring of Vibrio harveyi quorum sensing activity in real time during infection of brine shrimp larvae[END_REF], whereas it has no effect on the virulence for V.

tasmaniensis and V. crassostreae, which is similar to what has been reported for V. anguillarum [START_REF] Li | The impact of quorum sensing on the virulence of Vibrio anguillarum towards gnotobiotic sea bass (Dicentrarchus labrax) larvae[END_REF].

Conclusions

In this study, we identified the components of a multichannel quorum sensing system in the genomes of the bivalve model pathogens V. tasmaniensis LGP32 and V. crassostreae J2-9. We found that motility is controlled by HAI-1 in V. tasmaniensis and by CAI-1 in V. crassostreae and that biofilm formation is controlled by AI-2 quorum sensing in V. tasmaniensis, whereas the multichannel quorum sensing systems of V. tasmaniensis and V. crassostreae have no effect on protease activity, and on virulence of the pathogens towards blue mussel larvae. Hence, since quorum sensing controlling virulence is not a general feature in vibrios, it is not possible to extrapolate the impact of quorum sensing on virulence of vibrios from one species to another.

Allam, B., Raftos, D., 2015. Immune responses to infectious diseases in bivalves. J. Invertebr. Pathol. 131, 121-136.

Balbi, T., Fabbri, R., Cortese, K., Smerilli, A., Ciacci, C., Grande, C., Vezzulli, L., Pruzzo, C., Canesi, L., 2013 Luminescence/OD600 Time (h)

Figures

  Figures

  Figure 1. Generic scheme of multichannel quorum sensing systems of vibrios. The LuxM, LuxS and CqsA enzymes synthesise acylated homoserine lactone (AHL), autoinducer-2 (AI-2) and cholerae autoinducer-1 (CAI-1), respectively. These signal molecules are detected at the cell surface by the LuxN, LuxPQ and CqsS receptors, respectively. The receptors feed a shared phosphorylation/ dephosphorylation signal transduction cascade involving the LuxU and LuxO proteins. This cascade controls the production of the master regulator LuxR. The level of LuxR is proportional to the concentration of the signal molecules, and LuxR determines the transcription of the quorum sensing target genes. "P" denotes phosphotransfer. Based on Defoirdt et al. (2008).

Figure 3 .

 3 Figure 3. Quorum sensing-dependent bioluminescence of V. tasmaniensis LGP32 pBB1. The data points are averages of three replicates. Error bars are too small to be visible on the graph.

Table 1 .

 1 . Interactions between Mytillus galloprovincialis hemocytes and the bivalve pathogens Vibrio aestuarianus 01/032 and Strains used in this study.

	Vibrio splendidus LGP32. Fish Shellfish Immunol. 35, 1906-1915.
	Bassler, B.L., Wright, M., Showalter, R.E., Silverman, M.R., 1993. Intercellular signalling in Vibrio harveyi: sequence
	and function of genes regulating expression of luminescence. Mol. Microbiol. 9, 773-786.
	Beaz-Hidalgo, R., Balboa, S., Romalde, J.L., Figueras, M.J., 2010. Diversity and pathogenicity of Vibrio species in
	cultured bivalve molluscs. Environ. Microbiol. Rep. 2, 34-43.
	Ben Cheikh, Y., Travers, M.A., Morga, B., Godfrin, Y., Rioult, D., Le Foll, F., 2016. First evidence for a Vibrio strain
	pathogenic to Mytilus edulis altering hemocyte immune capacities. Dev. Comp. Immunol. 57, 107-119.
	Benabdelmouna, A., Ledu, C., 2016. The mass mortality of blue mussel (Mytilus spp.) from the Atlantic coast of France
	is associated with heavy genomic abnormalities as evidenced by flow cytometry. J. Invertebr. Pathol. 138, 30-
	38.
	Binesse, J., Delsert, C., Saulnier, D., Champomier-Vergès, M.C., Zagorec, M., Munier-Lehmann, H., Mazel, D., Le Roux,
	F., 2008. Metalloprotease Vsm is the major determinant of toxicity for extracellular products of Vibrio
	splendidus. Appl. Environ. Microbiol. 74, 7108-7117.
	Bjelland, A.M., Sorum, H., Tegegne, D.A., Winther-Larsen, H.C., Willassen, N.P., Hansen, H., 2012. LitR of Vibrio
	salmonicida is a salinity-sensitive quorum-sensing regulator of phenotypes involved in host interaction and
	virulence. Infect. Immun. 80, 1681-1689.
	Brackman, G., Defoirdt, T., Miyamoto, C.M., Bossier, P., Van Calenbergh, S., Nelis, H., Coenye, T., 2008.
	Cinnamaldehyde and cinnamaldehyde derivatives reduce the virulence in Vibrio spp. by decreasing the DNA-
	binding activity of the quorum sensing response regulator LuxR. BMC Microbiol. 8, 149.

Table 3 .

 3 Motility, caseinase and gelatinase activities and biofilm formation of V. tasmaniensis LGP32 and V. crassostreae J2-9 wild types and quorum sensing mutants (average ± standard deviation of three independent experiments). Diameter of the motility zone (mm) 2 Ratio between the activity zone and the colony diameter 3 OD570 of crystal violet-stained biofilms on polystyrene multiwell plates/OD600 * Significantly different from the wild type (independent samples t-test; P < 0.01)

	Strain	Motility halo 1	Caseinase activity 2	Gelatinase activity 2	Biofilm formation 3
	V. tasmaniensis LGP32
	LGP32 WT	62 ± 4	1.4 ± 0.1	2.6 ± 0.2	0.22 ± 0.03
	LGP32 luxM	78 ± 2*	1.4 ± 0.0	2.7 ± 0.1	0.14 ± 0.03
	LGP32 luxS	72 ± 5	1.6 ± 0.1	2.6 ± 0.2	0.11 ± 0.02*
	LGP32 luxR	63 ± 3	1.4 ± 0.1	2.7 ± 0.2	0.18 ± 0.04
	V. crassostreae J2-9
	J2-9 WT	72 ± 5	1.4 ± 0.0	2.5 ± 0.2	0.17 ± 0.04
	J2-9 luxM	72 ± 4	1.4 ± 0.0	2.6 ± 0.2	0.13 ± 0.02
	J2-9 luxS	75 ± 4	1.4 ± 0.0	2.7 ± 0.2	0.19 ± 0.01
	J2-9 cqsA	56 ± 3*	1.3 ± 0.1	2.6 ± 0.2	0.22 ± 0.02
	1

Acknowledgements

This work was supported by the China Scholarship Council, the Scientific Research Fund of Flanders (FWO -project n° 1500219N) and the Special Research Fund of Ghent University (BOF-UGent). The authors thank Pieter Geijsen (Roem van Yerseke, The Netherlands) for providing us with blue mussel adults. We thank Tom Baelemans for excellent technical assistance.

Table 2. Homologs of components of the V. campbellii ATCC BAA-1116 (Vca) multichannel quorum sensing system identified within the genomes of V. tasmaniensis LGP32 (Vta) and V. crassostreae J2-9 (Vcr), and nucleotide identities between the homologs.

Gene Function

Locus tag 1 Vca (chromosome) LGP32 + cinnamaldehyde J2-9 J2-9 + cinnamaldehyde