Antoine Chalon

Julien Favre

Boris Piotrowski

V Landmann

David Grandmougin

Juan Pablo Maureira

Pascal Laheurte

Nguyen Tran

J-P Maureira

Contribution of computational model for assessment of heart tissue local stress caused by suture in LVAD implantation

Introduction

Cardiovascular diseases remain the leading cause of mortality, and heart failure (HF) therefore represents a major health and economic burden as well as a challenge in therapeutic management [START_REF] Go | Heart disease and stroke statistics-2014 update[END_REF][START_REF] Bui | Epidemiology and risk profile of heart failure[END_REF][START_REF] Braunwald | Heart failure[END_REF]. For a large proportion of patients, a heart transplant is not available and pharmacological treatments are not efficient enough. In these cases, implantation of ventricular assist devices (VADs) is considered either as a lifeprolonging therapy, a bridge to transplant or, in some cases, as a definitive implantation [START_REF] Heidenreich | Forecasting the impact of heart failure in the United States[END_REF][START_REF] Seyfarth | A randomized clinical trial to evaluate the safety and efficacy of a percutaneous left ventricular assist device versus intra-aortic balloon pumping for treatment of cardiogenic shock caused by myocardial infarction[END_REF].

Over the past few years, LVAD has certainly shown clear properties in improving quality of life [START_REF] Rogers | Continuous flow left ventricular assist device improves functional capacity and quality of life of advanced heart failure patients[END_REF][START_REF] Stewart | Mechanical circulatory support for advanced heart failure[END_REF], however, attachment of the device to the heart remains a debated and critical issue [START_REF] Bernhardt | Isolated permanent right ventricular assist device implantation with the heartware continuous-flow ventricular assist device: first results from the European registry for patients with mechanical circulatory support[END_REF][START_REF] Charitos | A modified suturing technique for the implantation of the apical cannula of the HeartMate II left ventricular assist device[END_REF]. In order to minimize the risk of myocardial tearing and bleeding the device is fixed and secured to the ventricle with U-suture using polytetrafluoroethylene (PTFE) pledgets to spread and reduce the mechanical stress. Despite numerous improvements, debate about the risk and optimization of LVAD attachment is still ongoing [START_REF] Bernhardt | Isolated permanent right ventricular assist device implantation with the heartware continuous-flow ventricular assist device: first results from the European registry for patients with mechanical circulatory support[END_REF][START_REF] Hanke | In vitro evaluation of inflow cannula fixation techniques in left ventricular assist device surgery: thoughts and progress[END_REF]. The LVAD surgical implantation remains a complex procedure that requires good knowledge of the technique and great dexterity. Among all the aspects of this procedure, the suture of the device to the myocardium is crucial because it might impact both T acute and long-term success of the LVAD therapy. That is why the study of the myocardium in response to stress and, in this particular case, to suture materials still presents great interest as a solution to analyze and optimize LVAD suture.

The modeling of the left heart and related mechanical behaviors of heart muscle in response to multi-axial traction, compression and shear stress remains a challenging topic due to the complexity and specific mechanical characteristics of the myocardium (Humphrey et al., 1990a). Biaxial and shearing explorations have been widely used to investigate such parameters, but accurate data are somewhat impaired by the method of performing the tissue gripping and the nature of heart samples. In papillary muscle, a highly specific heart structure, some authors have however found good correlation between uniaxial tensile strength response and hyperelastic models (Humphrey et al., 1990b;[START_REF] Hassan | The nonlinear elastic and viscoelastic passive properties of left ventricular papillary muscle of a Guinea pig heart[END_REF]. Recently, numerical models for heart simulations [START_REF] Nash | Computational mechanics of the heart[END_REF][START_REF] Baillargeon | The Living Heart Project: A robust and integrative simulator for human heart function[END_REF][START_REF] Smith | euHeart: personalized and integrated cardiac care using patient-specific cardiovascular modelling[END_REF][START_REF] Horowitz | Comprehensive model for the simulation of left ventricle mechanics[END_REF][START_REF] Sermesant | An electromechanical model of the heart for image analysis and simulation[END_REF] have been developed to describe myocardial tissue with multiple levels of complexity [START_REF] Pinto | Mechanical properties of the heart muscle in the passive state[END_REF]. Most of the models provide an exhaustive description with a large number of parameters. However, these models, which are frequently performed on a specific area of heart tissue, are rather complex to use and hard to implement in terms of calculation time [START_REF] Stevens | Sarcomere length changes in a 3D mathematical model of the pig ventricles[END_REF][START_REF] Sommer | Biomechanical properties of the human ventricular myocardium[END_REF][START_REF] Huyghe | The constitutive behaviour of passive heart muscle tissue: a quasi-linear viscoelastic formulation[END_REF][START_REF] Lin | A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus[END_REF]. Nonetheless, the use of numerical simulation and more precisely of finite element analysis (FEA) seems of great interest. We hypothesize that numerical data on the stress fields near myocardial sutures may be used to determine minimal spacing between sutures to prevent excessive stress concentrations.

To our knowledge, no previous study has reported data relative to a numerical model adapted to myocardial suture.

On the other hand, the literature about suture materials has provided only generic data with global stress studies [START_REF] Naleway | Mechanical properties of suture materials in general and cutaneous surgery[END_REF][START_REF] Paez | Resistance and elasticity of the suture threads employed in cardiac bioprostheses[END_REF]. Again, no study on the impact of suture material on the myocardium has been found.

In this paper, we first intended to establish an isotropic constitutive law with a small number of reliable parameters from uniaxial tensile tests. Following a similar methodology to that which was used to study tendon suturing [START_REF] Rawson | Sutured tendon repair; a multi-scale finite element model[END_REF], we hypothesized that numerical simulation using finite element analyses (F.E.A.) of sutures may provide new data to evaluate the anchoring of a device into the myocardium. Moreover, recent communications from the U.S. Food and Drug Administration (FDA) have confirmed a firm intent to include simulation in the development cycle of biomedical devices [START_REF] Morrison | The role of computational modeling and simulation in the total product life cycle of peripheral vascular devices[END_REF][START_REF] Malinauskas | FDA benchmark medical device flow models for CFD validation[END_REF]. This kind of analysis is cost-effective and allows a drastic reduction in the number of animals required.

The study herein describes a numerical model for left myocardial suture evaluation based on:

• Characterization of mechanical properties of the left passive myo- cardium by uniaxial tensile strength testing.

• Evaluation of mechanical resistance of a U-suture in left myo- cardium samples.

• Setup and validation of a finite element model (FE) for left myocardial suture study.

With the help of the model hereby presented, we aim to provide a numerical tool for the assessment of stress concentrations caused by suture into the left ventricle. The investigation of the stress fields should allow us to define a numerical threshold for suture spacing.

Materials and methods

Study design

This study proposed to investigate local stresses around the sutures following a myocardial suture as described for a LVAD implantation. Following a similar methodology to that reported by [START_REF] Rawson | Sutured tendon repair; a multi-scale finite element model[END_REF], both experimental and numerical investigations were simultaneously conducted to show the limitations of a single experimental evaluation and highlight the contribution of a numerical model to improve the reliability of these investigations. To setup the Finite Element Model (FEM), myocardium uniaxial characterizations were performed. A synthetic diagram of this strategy is presented in Fig. 1.

Harvest and shaping of ventricular wall samples

Pig hearts were surgically harvested at the School of Surgery using the facilities of operating rooms (OR) under the supervision of staff certified in experimental animal surgery (authorization number 54-96, Dr. Nguyen Tran). All procedures followed the NIH guidelines of the Guide for the Care and Use of Laboratory Animals and were in accordance with French legislation (Ministerial Authorization n°C54-547-5). Cardiac explantation was performed on animals previously anesthetized and used for training purpose in order to follow the Reduction rule provided by the 3 R's guidelines [START_REF] Bratcher | Creative implementation of 3Rs principles within industry programs: beyond regulations and guidelines[END_REF]. Precautions were taken to preserve myocardial integrity as well as mechanical properties.

A total of 14 pigs (aged 3-5 months, weighing 45 ± 5 kg) were premedicated with midazolam (1 mg/kg, im) and ketamine (10-20 mg/ kg, im). Anesthesia was induced with propofol (100 mg, iv) and maintained (30 mg/h, iv) during the whole procedure. Analgesia was obtained by administration of sufentanyl after catheterization of the right internal jugular vein.

Following surgical guidelines (Humphrey et al., 1990b), a median sternotomy was performed, and the pericardium was opened. Then, the ascending aorta was cross-clamped, and the heart was arrested with a 50-100 ml intracardiac injection of a solution with high potassium concentration. Hearts were harvested and rinsed immediately with cold Krebs-Henseleit buffer (4 °C) to remove blood and clots before complete immersion in this solution. Harvesting procedures were systematically performed less than 4 h before mechanical assessment.

Left myocardial tissue (20 × 30 mm 2 ) was excised with transmural incisions through the anterior aspects of the left and right ventricles as seen in Fig. 2. In order to closely simulate the surgical features of a LVAD implantation and minimize the influence of wall thickness discrepancies, a senior cardiac surgeon validated the location of ventricular sampling sites. For each heart, one sample of left ventricle was obtained. For suture testing (n = 6), raw samples were prepared with suture material.

For tissue characterization (n = 8), the heart section of interest was trimmed and shaped to obtain a parallelepiped of 10 × 30 × 5 mm 3 in line with previously published studies [START_REF] Forsell | Numerical simulation of the failure of ventricular tissue due to deep penetration: The impact of constitutive properties[END_REF]. Specific shape was designed to get proper tissular gripping and ensure that rupture would occur in the center of the sample and not beside the clamps.

Testing apparatus and methodology

A tensile strength testing device (10 kN, ERIKSEN, Germany) was used with a constraint gauge for the strength measurement and a Linear Variable Differential Transformer (LVDT) to assess the displacement (Gefram, Italia). Fig. 3 illustrates a schematic view of both configurations selected for this study. Trials were performed at a speed of 10 mm/minute, which corresponded to a strain rate ε ̇of 0.006 s -1 to preserve relevance with the size of the samples as reported in similar publications [START_REF] Forsell | Numerical simulation of the failure of ventricular tissue due to deep penetration: The impact of constitutive properties[END_REF].

Both parameters were recorded in real-time with a National Instruments acquisition card and LabVIEW software (National Instruments, Switzerland) with a custom LabVIEW application (VI) designed for this experiment with 50 acquisitions per second.

Both tensile and suture strength testing were performed on this device with differences in the clamping method, using (Fig. 3a) two metal plates fixed to each other for tensile testing and (Fig. 3b) fastened with suture material. Methyl cyanoacrylate glue was used between clamps and samples to prevent slipping.

The main goal of these trials was to collect uniaxial stress-strain data for calibration of the model and setup of FE simulation. Published studies on a large panel of soft biological tissues have investigated on uniaxial experiments [START_REF] Baillargeon | The Living Heart Project: A robust and integrative simulator for human heart function[END_REF][START_REF] Bratcher | Creative implementation of 3Rs principles within industry programs: beyond regulations and guidelines[END_REF][START_REF] Forsell | Numerical simulation of the failure of ventricular tissue due to deep penetration: The impact of constitutive properties[END_REF]. Heterogeneous results were reported, consecutive to variable methodologies. Therefore, we decided to carry out dedicated experiments to ensure consistency within this study.

Mean value of the thickness of each sample was used for this study, since ventricular thickness was not uniform with the transventricular samples.

In order to collect comparable data from all samples, a specific protocol for the surgical sutures was designed. The distance between entry points of the U-suture through the piece of medical grade PTFE pledget (15 × 25 × 0.5 mm 3 ) and the free border of the sample was set to 10 mm. Stitches were performed using a 3-0 non-absorbable polypropylene suture. Depth of the sutures within the left ventricular myocardium resulted from the achievable distance run by the needle (about 10 mm deep).

Once prepared with the standardized pledgeted U-suture, the sample was positioned and secured with five ligature knots. A symmetrical positioning was adopted to avoid artefacts and excessive stress that might result from embedding the sample in a fixed jaw.

Finite Element Model (FEM) setup

Finite Element Modeling (FEM) and simulation were performed using Abaqus 6.14-5 (SIMULIA, Dassault Systèmes, USA) Explicit Package. For time optimization purpose, only a quarter of the experimental trial was simulated, then two symmetry planes were used along the Z and Y-axis. Model size was set to 15 × 25 × 15 mm 3 for the myocardium and to 12.5 × 15 × 0.5 mm 3 for the pledget (Fig. 4a andb). Suture diameter was set to 0.245 mm, corresponding to the 3-0 polypropylene suture [START_REF] Naleway | Mechanical properties of suture materials in general and cutaneous surgery[END_REF], typical suture material used in the operating room. An overall displacement of 25 mm was imposed at the top of the suture (Fig. 4b).

Myocardium density was set to 1.053 g/ml following the methodology used in several publications on either rats [START_REF] Vinnakota | Myocardial density and composition: a basis for calculating intracellular metabolite concentrations[END_REF] or human [START_REF] Katz | Estimation of human myocardial mass with MR imaging[END_REF]. Following data from the literature (ASM International, 2009), the pledget was setup as an elastic material with a density of 2 g/cm 3 and a Young Modulus of 550 MPa. Suture wire material data were extracted from the literature [START_REF] Naleway | Mechanical properties of suture materials in general and cutaneous surgery[END_REF], density was set to 0.403 g/cm 3 and Young Modulus to 745.6 MPa.

A hyperelastic isotropic material was used to describe myocardium behavior and its parameters were computed from myocardium tensile test. General contact formulation between wire and heart tissue was setup with a 0.005 friction coefficient based on the work of [START_REF] Rawson | Sutured tendon repair; a multi-scale finite element model[END_REF]. Myocardium and PTFE pledget were tied to simplify model contact.

PTFE Pledget and Polypropylene suture were meshed using respectively 229 and 264 C3D8R hexahedral elements. Left ventricle myocardium was ideally meshed with hexahedral elements. The part was split in three domains, the external bulk myocardium (5460 C3D8R elements), the internal contact sheath (1480 C3D8R elements) and an intermediate domain. The latter pecific volume was meshed using tetrahedral elements (11,019 C3D4) was to be used to link hexahedral domains (Fig. 4c). The internal sheath was created to optimize contact handling inside the simulation. Mesh convergence analysis was performed to ensure the accuracy of the simulation results. An increase of mesh densities of about 100% (number of elements), the maximum relative error on predicted force was found to be lower than 2%.

Calculation, fit and statistical analysis

Displacement and strength were collected from uniaxial tensile strength tests then converted to engineering and then true stress/strain curves when applicable. Numerical stress results were analyzed using equivalent Von Mises stress formulation.

Parameter fitting was performed using Abaqus Evaluate Toolbox. This specific tool was able to optimize parameters for several hyperelastic material laws and to choose the most stable and accurate behavior. The rupture strength (rupture point) was defined as the maximum recorded strength. Therefore, all data beyond the rupture point were excluded (or withdrawn).

Correlation between left ventricular thickness and rupture strength was calculated with GraphPad Prism (GraphPad Software, San Diego, California US). Numerical data from simulation were obtained using Abaqus Toolboxes and Python custom scripts.

Results

Hyperelastic numerical behavior

Experimental curves obtained by tensile tests are illustrated on Fig. 5a. The overall behavior of the left ventricle material was hyperelastic and led to progressive rupture for stress above 100 kPa. The dataset showed some variability due to the stochastic nature of biological specimens. However, global behavior was found to be very similar, and a mean trend can be deduced. Each curve was fitted by a second order polynomial equation = ⋅ + ⋅ σ a ε b ε 2 . Among the available hyperelastic material laws, the reduced polynomial formulation (Table 1.) is found to provide numerical stability of the model at all strains. As illustrated on Fig. 5b, this specific hyperelastic law shows a perfect match with the previously computed mean curve. Parameters of the constitutive law are summarized in Table 1.

The onset of sample damage starts for a von Mises stress above 150 kPa as shown on Fig. 5.a. With a safety factor of 1.5, a statistical rupture threshold for the material was defined at 100 kPa (Fig. 5.a) as a limit beyond which rupture may statistically happen.

Mechanical study of a left ventricle U-suture

Suture strength testing was performed on six harvested pig hearts. An example of load-displacement curve from these tests was plotted in Fig. 6a. The overall trend presents a hyperelastic profile. Unlike standard tensile strength tests, it has not been possible to use stress versus strain curves due to the clamping method leading to a highly heterogeneous stress field. On the left of the marker, force increases uniformly with displacement. Beyond the marker, previous hyperelastic behavior was altered by the occurrence of tissue damage.

This led to the rupture of the myocardium sample at the maximumrecorded force. Thickness and rupture strength results for all samples are summarized in Table 2.

The results from left ventricle sample suture testing have shown a mean rupture strength is 15.43 ± 3.658 N.

Correlation test between thickness and rupture strength has shown a positive relationship between these variables with a R 2 of 0.7131, illustrated in Fig. 6b.

Numerical simulation of a U-suture on the left ventricle

In order to validate our numerical simulation, comparison was made between the experimental response from suture tensile tests and the numerical response. Increasing displacement along the Y-axis was applied in the FE model at the top of the suture, reproducing the equivalent mechanical experiment. Imposed displacement was of 25 mm over the entire simulation time. Numerical simulation started to show instability induced by large strain at 50% of the simulation and was stopped at 75%. Therefore, we chose to use a value of t (percentage of achieved simulation) of 0.5 (with d = 12.64 mm; RF = 10.67 N) as our simulation end. Table 1 Reduced polynomial parameters extracted from experimental tensile tests.

Equation = ∑ - + ∑ - = = U C (I 3) (J 1) i 1 N i0 1 i i 1 N 1 D i el 2i
( Fig. 7a. shows a good match between the model and the experiment, therefore validating the reliability of our model. The maximal error remains under 0.5 N and the prediction remains correct until a displacement as large as 12 mm. For larger displacement, discrepancy occurs, and the simulation is not to be considered beyond this limit.

Assessment of the reliability was confirmed by looking at the peak stress (von Mises) inside model parts as shown in Table 3. Using failure stress data of 48 and 493 MPa for the pledget and suture respectively [START_REF] Naleway | Mechanical properties of suture materials in general and cutaneous surgery[END_REF]ASM International, 2009), we assessed that stresses remain in the elastic domain for the elastic parts.

Simulation results showed expected stress concentration at the suture entry and exit point of the myocardium as illustrated in Figs. 7.b and 8.b. Despite a low friction coefficient (0.005 from [START_REF] Rawson | Sutured tendon repair; a multi-scale finite element model[END_REF]), we observed a movement of the surface near the suture at the top of the model.

Fig. 8 shows the stress field and the stress triaxiality for the maximal displacement achieved with this model. Stress sharply decreased as a function of the distance from the suture point in each direction. For a distance further than 1 mm, the equivalent von Mises stress stabilized around 50 kPa, which was below the previously defined threshold (100kPa). The tissue close to the hole exhibited stress larger than the threshold and was visible at the center (Fig. 8b).

The stress triaxiality factor map on Fig. 8c illustrates the type of mechanical loading. At the wire location, shear stress was predominant. The elements located farther from the entry point, the predominant stress turned to compression. For larger distances, the loading became gradually complex with a combination of shear and tensile strength.

Discussion

This study allowed us to extract two major findings that are (1) the ability to run a numerical model of the left ventricle tissue and (2) a computer-calculated threshold of 2 mm for the space between two adjacent sutures into the myocardium.

Model validation and limitations

Numerous numerical and finite element models of the heart or the myocardium are described in the literature; however, the overwhelming majority are either highly specific to a region [START_REF] Hassan | The nonlinear elastic and viscoelastic passive properties of left ventricular papillary muscle of a Guinea pig heart[END_REF], or complex to reproduce due to the use of a custom material law, for instance [START_REF] Huyghe | The constitutive behaviour of passive heart muscle tissue: a quasi-linear viscoelastic formulation[END_REF]. Material constitutive law with a higher level of complexity could enhance the reliability of simulation data but undoubtedly at a higher computational and experimental cost. The methodology and parameters described in this paper are meant to overcome such complexities by providing everything needed to run our model. The use of a widespread FEA package (ABAQUS, SIMULIA) and a built-in constitutive law are a way to provide a straightforward approach to left myocardium finite element analysis.

With the help of this Finite Element model, we investigated the stress concentrations occurring in the case of a LVAD suture on the left myocardium. The method used to fit experimental data of tensile strength to a stable hyperelastic law proved its efficiency. Indeed, as observed in the work of [START_REF] Forsell | Numerical simulation of the failure of ventricular tissue due to deep penetration: The impact of constitutive properties[END_REF] on ventricle penetration, parameter identification from tensile trials is a commonly used technique. In our model, a reduced polynomial law of second order provided a sufficient degree of complexity to simulate the myocardium behavior for a suture displacement up to 12 mm. Indeed, good correlation was found while comparing experimental suture data on left myocardium to the generated numerical model with an error of less than 0.5 N in this domain of interest. The previous study on tendon suture reported by [START_REF] Rawson | Sutured tendon repair; a multi-scale finite element model[END_REF] allowed them to highlight the good correlation that may be achieved between experiments and simulation as well as the predictive power of such numerical tools. In a similar way, the generation of simulated stress maps allowed us to confirm the reliability of our model and to extensively investigate the influence of the suture on the tissue. This is to our knowledge the first numerical simulation of left myocardial suture. This work reinforces the impact of finite element analysis when used to study surgical techniques.

When juxtaposing experimental and numerical results, we observed that mechanical suture trials were not able to provide as many parameters as the simulation does. Despite a robust methodology, the biological nature of the samples showed some variability (Fig. 5.b) that may restrict a reliable analysis. The use of a constitutive law identified on a mean response of the tissue allows us to overcome this variability. One of the major strengths of the model is its ability to reproduce identical boundary conditions without the influence of the experimental setup. 493 MPa [START_REF] Naleway | Mechanical properties of suture materials in general and cutaneous surgery[END_REF] This numerical model should be considered with respect to its limitations and the assumptions that were adopted. Myocardium behavior is known to be highly anisotropic. An interesting way to improve numerical simulation would be to take in account fiber orientations as described in previous studies [START_REF] Lombaert | Human atlas of the cardiac fiber Architecture: study on a healthy population[END_REF][START_REF] Rohmer | Reconstruction and visualization of fiber and laminar structure in the normal human heart from ex vivo diffusion tensor magnetic resonance imaging (DTMRI) data[END_REF]. The visco-elastic or visco-hyperelastic behavior is also a planned improvement for this kind of FE simulation, as it would enable a timerelated approach of the tissue response. However, it is important to keep in mind that the balance between model complexity and computational cost is a critical parameter for simulation studies. The suture knot was not modelled, yet this is often the failure location of suture repairs [START_REF] Naleway | Mechanical properties of suture materials in general and cutaneous surgery[END_REF]; however, our study focused on the stress in the myocardium tissue and not the suture itself, which would not be affected by this simplification.

Large deformations (observed above 12 mm of displacement in the present model) could not be studied in our simulations. Nevertheless, this limitation emerges from numerical instabilities of the finite element solver. This issue could be overcome by implementing damage behavior inside the model and/or ventricular failure simulation [START_REF] Forsell | Numerical simulation of the failure of ventricular tissue due to deep penetration: The impact of constitutive properties[END_REF].

Contribution of the model for myocardial suture assessment

Beyond the performance of our model, the major impact of this study is the emergence of a numerical threshold for suture spacing (Fig. 6a). We were able to study stresses inside model elements in multiple directions from the suture entry point. We confirmed the occurrence of high stress next to the suture entrance in each of 4 directions (+X, -X, +Y, -Y). Moreover, we witnessed a rapid decrease in this stress as we looked further from the suture entrance. Almost no residual stress was observed further than one millimeter away from the entry point, as shown on Fig. 8a, even at the highest achievable displacement.

This limit was found to be equal to four times the suture diameter (0.24 mm in that case). This is the first step of a diameter-distance relationship for designing more secure and efficient heart sutures. These results encouraged us to define a minimum space of 2 mm between consecutive sutures to avoid stress overlap. However, precautions must be taken with this suggested threshold. This result may not be relevant for another suture thread, technique or on right ventricle myocardium.

Despite the existence of clinical studies on LVAD implantation [START_REF] Seyfarth | A randomized clinical trial to evaluate the safety and efficacy of a percutaneous left ventricular assist device versus intra-aortic balloon pumping for treatment of cardiogenic shock caused by myocardial infarction[END_REF][START_REF] Bernhardt | Isolated permanent right ventricular assist device implantation with the heartware continuous-flow ventricular assist device: first results from the European registry for patients with mechanical circulatory support[END_REF], no guidelines for the myocardial suture based on a numerical model could be found. The work presented by presented by Charitos and Sievers (2010) on a modified technique for LVAD implantation is a good example of what is usually found in the literature. As they present their methodology, they do not elaborate on the minimum spacing of 2.5 mm between two pledgeted U-suture that they recommend. Nevertheless, our numerical threshold is in good agreement with the LVAD implantation technique presented in their study.

In the work of [START_REF] Hanke | In vitro evaluation of inflow cannula fixation techniques in left ventricular assist device surgery: thoughts and progress[END_REF], the evaluation of four suture techniques is proposed for LVAD implantation. Whilst highlighting the crucial role of the suture technique, their methodology was only based on a visual examination and measurements of sutures on silicon dummies. Despite a relevant comparison of these techniques, no quantitative data are provided on stress concentrations whereas the evaluation of different suture techniques for LVAD implantation was the main topic.

We anticipate that surgical guidelines may benefit from numerical simulations to assess the best practices for suture placement. This approach falls within the current framework delimited by the FDA for medical device certification [START_REF] Morrison | The role of computational modeling and simulation in the total product life cycle of peripheral vascular devices[END_REF][START_REF] Malinauskas | FDA benchmark medical device flow models for CFD validation[END_REF] but also fully respects the 3 R's guidelines on animal studies [START_REF] Bratcher | Creative implementation of 3Rs principles within industry programs: beyond regulations and guidelines[END_REF].

Further work will also aim to extend the model's applications. Thus, several sutures could be evaluated and compared, therefore providing a better understanding of stresses occurring in LVAD implantation.

Conclusions

The proposed model gives access to an enhanced understanding of stresses and strains occurring during U-suture solicitation on the left myocardium. Uniaxial tensile trials were used to identify the mechanical behavior of left ventricle samples. The key-findings of the paper are (i) the identification of an hyperelastic reduced polynomial constitutive law for left myocardial tissue, (ii) the establishment of a finite element model accurately reproducing the global behavior described through mechanical suture assessment and (iii) the definition of a minimal suture spacing of 2 mm between adjacent U-sutures on the left myocardium.

The present work complies well with the current context of animal use reduction (3 R's guidelines) and with the inclusion of simulation work into the process of medical device certification (FDA guidelines). Anticipated applications are about designing more efficient and secure LVAD suture techniques and testing them with a numerical predictive approach.

Acknowledgment

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Fig. 1 .

 1 Fig. 1. Schematic representation of global study strategy.

Fig. 2 .

 2 Fig. 2. Left ventricular sample harvested from fresh porcine heart.

Fig. 3 .

 3 Fig. 3. Schematic view (not to scale) of experimental apparatus for (a) tensile test and (b) suture test. (c) Global view of apparatus before sample setup. (d) Sample view prior to loading.

Fig. 4 .

 4 Fig. 4. Setup of the FE model with (a) dimensions in millimeters, (b) boundary conditions and load and (c) mesh.

Fig. 5 .

 5 Fig. 5. (a) Individual tensile test results (b) mean results and fit provided by Abaqus Evaluate algorithm. The mean behavior is deduced from the average polynomial parameters (red dots). Red bars illustrate the standard deviation over a and b parameters. The mean curve is used to describe the statistical average subject.

Fig. 6 .

 6 Fig. 6. (a) Typical load-displacement curve from suture test. (b) Correlation between ventricle rupture threshold and thickness.

Fig. 7 .

 7 Fig. 7. (a) Comparison of experimental versus numerical behavior under similar load, (b) Global stress map at t = 0.5. Every element in gray is above the 100 kPa threshold.

Fig. 8 .

 8 Fig. 8. (a) Evolution of stress relative to distance from suture at the maximal displacement U= 12.64 mm. The stress profiles are plotted along the horizontal and vertical axis shown with arrows on Fig. 8.b. (b) Close view of the suture hole with pledget masked. Elements presenting a stress over the 100 kPa threshold are plotted in gray. (c) Triaxiality of stress is a new data type available with FEM.

Table 2

 2 Summary of mean thickness and rupture strength from left ventricle samples.

	Specimen (N = 6)		Mean thickness (mm)	Rupture strength (N)
	Left Ventricle	1	12.8	10.82
		2	14.8	16.31
		3	15.1	14.29
		4	13.7	13.47
		5	16.4	15.99
		6	16.5	21.71
	Mean		14.88	15.43
	Standard Deviation		1.463	3.658
	Correlation		R 2 = 0.7131

Table 3

 3 Maximum stress (von Mises) inside elastic model parts compared to literature references.

	Part	Pledget	Suture
	Maximum stress	44 MPa	399 MPa
	Literature failure	48 MPa (ASM International,
	stress	2009)


Marco Cappellini
email: marco.cappellini@univ-amu.fr

Orcid Org

Anna-Katharina Elstermann

Rivens Annick

Mompean

Annick Rivens

Reciprocity 2.0: How reciprocity is mediated through different formats of teletandem learners' logs

Keywords: principle of reciprocity, teletandem, logs, blog

In tandem, two principles are of great importance: learner autonomy and reciprocity between the learners. The goal of the present study is to examine learners' logs used in teletandem (i.e tandem through desktop videoconference) contexts, in order to understand how learners express themselves about the principle of reciprocity. The corpus consists of learners' reflective logs and is composed of three sub-corpora: (1) individual logs written in Word-documents by Brazilian learners of German from a Brazilian-German teletandem; (2) logs of French students on a collective blog from a French-US teletandem; (3) logs of Australian and French students on a collective blog from an Australian-French teletandem. In a qualitative perspective, the study combines content and discourse analysis to build participant-relevant categories of how the principle of reciprocity is implemented and perceived by learners. Moreover, it considers to whom the logs are written, which is meaningful as three different kinds of log formats are used. The aim is to understand and to categorize the representation of the reciprocity principle and of social presence in teletandem sessions. Some extracts correspond to the definitions of the reciprocity principle present in the literature and in addition, new categories have been found that lead us to question these definitions and possibly broaden them.

Introduction

Tandem language learning, under its different forms (face to face tandem, etandem, teletandem), has been based on two main principles i : the principle of autonomy and the principle of reciprocity. These two principles present a strong imbalance in the literature, since the principle of autonomy has received wide attention while the principle of reciprocity has been widely mentioned as a pedagogical principle, but without thorough research allowing to explore its theoretical underpinnings and its empirical manifestations. This article draws on recent attempts to overcome this gap (Koch 2017a(Koch , 2017b) ) to empirically study how reciprocity is implemented in teletandem and how it is mediated in different formats and environments for learners' metacognition.

First we provide a theoretical discussion of the principle of reciprocity based on published literature on the topic. Second, we present our methodology and the data we gathered. In the analysis, we observe and discuss phenomena linked to three areas: the original definition of reciprocity, reciprocity and relationship, the influence of the medium and of the audience on the expression of reciprocity.

Definitions of reciprocity in tandem language learning

Two recent articles from Koch (2017aKoch ( , 2017b) ) aim at providing theoretical foundations to the principle of reciprocity, especially his article on reciprocity in tandem learning (2017a). The second article (2017b) relates reciprocity to contexts of advising and coaching in foreign language learning. In this section, we use his articles as a palimpsest to redraw his arguments in the light of other relevant theoretical references that can subsequently inform our empirical study. We therefore would like to acknowledge the credit for having provided a structured discussion of different arguments that are at stake at the moment.

As a quick search through the literature on tandem confirms, despite the lack of theoretical foundation, the principle of reciprocity appears in every publication and it is largely considered as one of the two main pillars of tandem learning. [START_REF] Brammerts | Principes et objectifs[END_REF] takes a descriptive stance and asserts that tandem learning takes place within a framework where each partner brings his/her competences into the interaction, and that these competences are the other learner's pedagogical objective. The relationship demands each partner to be engaged and to facilitate, to scaffold the other's learning, in order to expect the same help by the interlocutor.

Other researchers, such as [START_REF] Kötter | Negotiation of meaning and codeswitching in online tandems[END_REF], take a more directive and normative stance, stating that this principle 'dictates' that the partners benefit equally from the exchange, which is rendered on a practical level by the fact that the amount of time spent using each language should be equal. All the references to the reciprocity principle in the literature on tandem could be classified according to these two examples: they are rather prescriptive or descriptive. On the practical dimension, the reciprocity principle is then usually associated with the amount of interaction in each language. However, to associate the principle of reciprocity with the division of time in each language is a limitation (Elstermann, 2017, p. 31).

In parallel to tandem learning, in disciplines that deal with conversational interactions and especially in language sciences, reciprocity has taken different, but not unrelated, meanings. In the francophone literature for instance, [START_REF] Bange | Analyse conversationnelle et théorie de l'action[END_REF] develops the concept of reciprocity initially formulated by [START_REF] Schutz | Le chercheur et le quotidien[END_REF] to indicate the perception that each interlocutor has of the other. In other words, in communication each interlocutor projects onto the other a state of general knowledge present before the interaction and a state of understanding of what is happening in the interaction. More recent research has theorized this kind of cognitive phenomenon in terms of alignment [START_REF] Pickering | Toward a mechanistic psychology of dialogue[END_REF]. Within this model, each interlocutor has a model of the ongoing situation and communication is successful when the models of the interlocutors correspond or, in other terms, are aligned. An important difference with these studies, also underlined by Koch, is that contrary to daily communication, in intercultural communication the frames of reference are not the same (Koch, 2017a, p. 125). [START_REF] Bange | Analyse conversationnelle et théorie de l'action[END_REF], who considered intercultural encounters, observed that this lack of shared knowledge leads to different kinds of conversational adjustments that relate, on the cognitive level, to what he called 'bifocalisation', that is the fact that interlocutors are constantly monitoring if they are aligned, if they understand 'the same thing'.

More linked to tandem learning, Koch's article (2017a) discusses the relationship between the principle of autonomy and the principle of reciprocity. Even if autonomy was linked from the beginning to social interaction, initially mainly with a counsellor [START_REF] Holec | Autonomie et apprentissage des langues étrangères[END_REF], recent studies on autonomy have stressed this dimension further [START_REF] Benson | Teaching and Researching Autonomy[END_REF][START_REF] Murray | Social dimensions of autonomy in language learning[END_REF]. Koch notes that the relationship between autonomy and reciprocity may be ambiguous, since on the one hand reciprocity limits autonomy in the sense that the pedagogical objectives of a learner do not necessarily correspond to the partner's expertise. On the other hand, the autonomisation is only made possible through social interaction (Koch, 2017a, p. 119). This reflection runs parallel to Lewis' on the social dimensions of learner autonomy, among which Lewis identifies reciprocity (2014, p. 45). This term is used for the description of autonomous learning communities, in which when a participant contributes to the learning, s/he expects the others to participate in an equal way. These observations lead to a theoretical understanding of the two principles as strictly interrelated in tandem.

After these considerations, Koch (2017a, p. 126-127) concludes with a tentative definition of reciprocity in communication:

Reciprocity is the mode and rhythm of the exchange of information and objects in a given historical sociocultural situation between two or more communicators which bears the obligation to respond to a perceived impulse or gift in a way and time frame that corresponds to an acknowledged convention. It contributes to the building and perception of meaning, social relationship and stratification.

He subsequently identifies five possible dimensions of reciprocity in tandem learning:

(1) Organisational: interactions are divided into two parts and both languages are used. Collaboration between partners is achieved at best through explicit negotiation or usually through implicit adjustments;

(2) Intercultural: intercultural differences are treated as conversational topics and each partner explains to the other one element of his/her culture (for a critical approach to this view of culture in tandem, see also Cappellini & Rivens Mompean, 2015);

(3) Discursive: during tandem interactions the interlocutors adapt to each other in multimodal ways accomplishing social interactional acts such as turn taking [START_REF] Sacks | A Simplest Systematics for the Organization of turn-Taking in Conversation[END_REF] or repair [START_REF] Schegloff | The preference for self-correction in the organization of repair in conversation[END_REF]. This dimension relates mostly to co-or para-verbal dimensions of communication and is largely unconscious;

(4) Semantic: participants negotiate the meaning of words and concepts in order to align their understanding;

(5) Use of the interlocutor's target language: this dimension relates to the conversational adjustments [START_REF] Bange | Analyse conversationnelle et théorie de l'action[END_REF].

Koch concludes his article (2017a) with a call for empirical studies to confirm (and we would add, possibly infirm) this conceptualisation of reciprocity in tandem learning.

Methodology

Research objectives and research questions

The aim of our study is to deepen the understanding of learners' representations of the reciprocity principle in tandem learning and to categorize them. Based on this research objective, we have formulated the following research questions:

(1) How do foreign language learners express aspects of reciprocity, which they experienced in their teletandem sessions, in different forms of reflective environments?

(2) How do the medium and the possible audience influence the reflective writings in the logs?

Contexts

Our study investigates data from three tandem settings through desktop videoconference projects, i.e. teletandem [START_REF] Telles | Teletandem -Um contexto virtual, autônomo e colaborativo para aprendizagem de línguas estrangeiras no século XXI[END_REF]: the teletandem between the State University of São Paulo (Brazil) and the Johannes Gutenberg University (Germany) [START_REF] Elstermann | Peergruppen-Beratung im Lernkontext Teletandem[END_REF][START_REF] Elstermann | Lerner-Support im internationalen Kooperationsprojekt[END_REF][START_REF] Elstermann | Learner Support in Telecollaboration: Peer group mediation in teletandem[END_REF], the teletandem between Lille University (France) and Georgetown University (USA) and the teletandem exchange between Lille University and University of Western Australia [START_REF] Garcia Moraes | A typology of metacognition: Examining autonomy in a collective blog compiled in a teletandem environment[END_REF]. In the three telecollaboration projects, learners had a proficiency level ranging between A1 and C1, as defined by Common European Framework (Council of Europe, 2001). In the Brazilian-German project, 14 participants have realised 4 teletandem sessions in average, in the French-American one, there were 32 participants who realised 6 sessions and in the French-Australian one, there were 16 students realising 6 sessions.

Data collection and corpus of analysis

In the three telecollaboration settings, students had to keep a reflective log about their teletandem sessions. Even if the pedagogical objectives of these logs were the same in the three telecollaborations, their formats were different.

In the Brazilian-German exchange, participants were advised, but not obliged, to work with learner logs to document and accompany their own learning process. The learner log model was prepared with questions in a Microsoft Word document and provided to all participants by email. The learner log could be written in their native language -Portuguese. The addressee of the learner logs was, theoretically the learner him/herself and, practically, the teletandem coordinator. The collected corpus gathers about 19 documents with a total of about 10.000 words.

INSERT FIGURE 1 HERE Figure 1. Learner log of the German-Portuguese teletandem project

As for the Lille-Georgetown teletandem, students also had to keep a log. However, this was done within a collective blog, where each student on the French side of the telecollaboration had to post a weekly entry corresponding to his log. Consequently, the addressee of the reflective writing was not only the tutor, but also the entire group of learners on the French side. The aim of the blog was to allow students to share their learning strategies and their impressions, in order to develop their learning strategies and learning resource repertoires [START_REF] Cappellini | Du carnet d'apprentissage individuel aux outils du web 2[END_REF]. The 17 students on the French side were allowed to produce their log in French or in English. A large majority of students decided to write in their native language. This resulted in a total sub-corpus of about 68000 words. The sub-corpus from the Teletandem Lille-UWA presents the same format as the French-American one, but in this case the collective blog was shared on both sides of the telecollaboration. Australian students had to write in French, French students were free to choose the language used. The 16 students participating in the telecollaboration produced a total corpus of about 27000 words. All the data have been collected directly from the students' logs. For the Brazilian logs, they were reproduced the way they were received by the tutor. As for the two blogs, data (including text, pictures and structure of the exchange) were extracted from the blogs and pasted into word documents.

INSERT FIGURE 2 HERE

INSERT HERE FIGURE 3

The following table summarizes the composition of the corpus of analysis:

INSERT TABLE 1 HERE Table 1. Corpus of analysis.

Analysis

In our analysis we have adopted a qualitative approach [START_REF] Ware | Researching classroom integration of online language learning projects: Mixed methods approaches[END_REF], aiming at accessing the students' perspective. In other words, we have analysed our data looking for passages where students talked about their relationship or how they constructed their mutual help for learning. Consequently, we did not start with preexisting categories (such as Koch's) but tried to infer categories of analysis that are participant-relevant [START_REF] Paillé | L'analyse qualitative en sciences humaines et sociales[END_REF]. The inferential process drew mainly on content analysis [START_REF] Bardin | L'analyse de contenu[END_REF] with the sporadic use of discourse analysis, especially to analyse the use of personal pronouns.

On a practical level, each of the authors read the three different sub-corpora and started to produce categories that were later discussed collectively. The collective discussion of categories had two functions: first to have a coherent set of categories covering all the data, i.e. saturating the possibilities of the analysis (Kaufmann, 2008, p. 31); second to move from a thematic analysis (Paillé & Mucchielli, 2008, p. 161) to the construction of "conceptualizing categories" (p. 233). These categories are not only participantrelevant, but they also draw a link with the existing theories and conceptualisations on the topic presented above.

Analysis and discussion

Reciprocity

In this first section of our analysis, we present excerpts of the data which corroborate the original definition of reciprocity found in the literature about tandem learning, that is a mainly organizational form of reciprocity (Koch, 2017a). In the data, we found many examples for the division of time within the sessions and the use of the two languages, but also comments on the way the learners were making decisions jointly about their teletandem partnership and how the partners were able to help each other to meet the needs of the respective learning partner.

Time and language division

Many of the (b)log entries describe how the sessions were divided and with which language the teletandem pair started (for French and Portuguese original quotations the translation into English is given in endnotes):

(1) so we did half our session in French and half of it in English.

This excerpt is representative of how learners affirm the organizational reciprocity, which is probably linked to the introductory meeting learners attended.

Collective decision making

Analysis of the data shows that the learners share many moments in which they jointly take decisions about different aspects of their teletandem partnership:

(2) Procuramos desenvolver mais a fala e a compreensão, visto que ambas são as necessidades das duas. ii (3) Regarding each other's mistakes, we kept on writing them to send explanations afterwards since we found out it worked well.

In the case of the Brazilian learner, he/she talks about a learning need both partners have and are willing to offer help on. Excerpt (3) shows how the learners in the Australian-French partnership agreed on a mutual correction system they thought was working well for them. This collective decision making is a reciprocal action because both learners must be tuned in to the same situation, on which they have to make decisions. The partners have to negotiate their opinions in relation to a specific situation and finally agree on a certain procedure. However, this does not necessarily mean that both have to agree on the same procedure for each language or each activity.

How the partners' needs are met by the native speaker

Another element of reciprocity in relation to learning needs and goal setting is how the learners are able to meet their partner's needs. The following quotations show examples extracted from the data.

(4) they were not taught how to express the future. So she asked me to teach her how to do it, and we spend some time on it.

(5) As for the mistakes, Andie only did a very few that I sent her afterwards. I think this teletandem was useful for her because she really has a great level but doesn't have much opportunity to practice her French. She told me she hadn't noticed any mistake for me.

In both excerpts, the learners try to meet their partner's needs. In excerpt (4) the learner who wrote the log entry agreed on teaching his/her partner the future tense because his/her partner had not learned it yet and wanted to know how this tense works.

Example (5) shows how the partners executed their decisions concerning the correction process and thus tried to meet the need for improvement in the foreign language.

Reciprocity in this aspect of the teletandem learning context is crucial as it affects directly the core of the learning context: a learner detects a learning need and establishes a learning goal he wants to pursue with the help of the native speaker, his/her partner. If the partner does not (even try to) meet those needs, learning is getting harder, frustration may rise and a dropout of the learner is possible. That is why this nuance of reciprocity is frequently described or prescribed in the literature on tandem [START_REF] Brammerts | Principes et objectifs[END_REF]Kötter, 2003 among others).

Comparisons on topics and language skills

The last aspect we found in our analysis, which can be related to definitions in the literature, is the comparison, during teletandem interaction, of different topics, mostly related to the cultures associated with the two countries of the interlocutors.

(6) Fizemos uma comparação com a Alemanha-não imagino isso acontecendo lá-, a questão do desrespeito com a mulher...e além da repercussão do caso na mídia em todo o Brasil. iii This excerpt shows a clear example of Koch's fourth dimension of reciprocity, where students discuss intercultural differences and meanings.

Even if comparisons are usually about cultural topics, we have also found a comparison which relates to language skills, as in the following excerpt.

(7) Tu as l'air d'avoir un bon niveau en anglais, a-t-elle (sic.) aussi le même niveau que toi en français? iv In this excerpt, students are comparing proficiency level in the respective foreign languages. This phenomenon, which is largely present in (e/tele)tandem settings, has been linked to assessment and autonomy [START_REF] Cappellini | Interactions plurielles d'étudiants en autoformation guidée et autonomisation[END_REF][START_REF] Garcia Moraes | A typology of metacognition: Examining autonomy in a collective blog compiled in a teletandem environment[END_REF]. This topic of comparison is not present in the literature on reciprocity but, in our opinion, it is one that practitioners should be aware of in order to prevent possible inhibitions due to large differences in the proficiency levels in the respective foreign languages.

Reciprocity and relationship

Beyond these original dimensions of reciprocity, our analysis highlights other dimensions that stand between reciprocity as it is usually referred to in the literature and what might be called intuitively the 'relationship' between participants.

Affective and emotional dimensions

Analysis of the logs showed that learners express their feelings about the contact they have with their partners. Unsurprisingly, this is largely present in UNESP-JGU individual logs and in the Lille3-Georgetown blog, but not in the Lille3-UWA blog, where the partners are also part of the audience. The following excerpts provide examples of this phenomenon:

(8) Mesmo com as dificuldades para falar, nos entendemos bem. v (9) On a plutôt bien accroché, c'est une fille sympa. L'entretien est passé très vite et je lui ai un peu expliqué en quoi consistera la prochaine session. vi

In the examples ( 8) and ( 9), the Brazilian and the French learners state that, despite the language barrier, partners got along well on the one hand and that contact was established in a satisfying manner on the other hand. These excerpts can be seen as an explicit and, for excerpt (9), a shared reflection about the emotional state of the exchange. We think that this dimension is relevant to the principle of reciprocity in two ways. First, this friendly climate is conducive of involvement and motivation and could therefore foster the will to spend time discussing with each other and to reach successful communication even when linguistic competence falls short. Second, it represents another point of contact between the two main principles of tandem. In fact, authors such as O'Leary (2014) add an emotional dimension to definitions of autonomy. More precisely, O'Leary conceptualises an 'emotional intelligence' which would consist, among others, in the ability to make explicit the emotional dimension of learning, of encouraging one another and of empathizing.

Mutual interests

Learners' written reflections show that during teletandem interactions, they spend some part discussing their common interests and hobbies, as in the following examples, taken from the Lille3-UWA blog:

(10) Now, let's get to the core. We spent this whole first Skype conversation dealing with the 1st activity, aiming at learning more about each other. We discovered we had quite a lot of common points. Beyoncé, the sun, languages and travelling are some of the things we both like.

(11) Cette séance m'a ouvert les yeux à de nombreux traits et désirs où goûts que nous avons en commun (la lecture, le jardinage, la nature, les animaux..

.). vii

In these examples, as in others from the two other teletandem projects, it is clear that part of the discussion, especially in the initial stages of the exchange when learners are getting to know each other, is spent not discussing differences possibly related to the intercultural dimension of the exchange, but rather searching for common or mutual interests. Therefore, this phenomenon does not fit clearly in the classical definitions of reciprocity, nor in Koch's five elements of reciprocity in tandem. This search for common interests is well documented in the literature on telecollaboration, both in formal [START_REF] Dooly | Competences of the telecollaboratively efficient person[END_REF] and informal [START_REF] Lamy | Social media-based language learning: Inshights from research and practice[END_REF] settings. For Lamy and Mangenot, common interests are a fundamental element to support engagement in online communities and make them live, allowing informal learning for participants (p. 211). In a similar vein, Murphy (2014, p. 128) observes that the lack of shared interests leads to the disintegration of online language learning communities. [START_REF] Dooly | Crossing the intercultural borders into 3rd space culture(s)[END_REF][START_REF] Dooly | Competences of the telecollaboratively efficient person[END_REF] develops the idea that the internet may be conceived of as a 'third space', a space that does not depend on specific cultural norms, but whose norms are developed within the interaction. The discovery of mutual interests is part of the construction of this third / shared space and has been observed by [START_REF] Yang | Learner Interpretation of shared space in multilateral English blogging[END_REF] in telecollaboration through blogs. Among others, she observes that the discovery of preexisting common interests (shared space through commonality) was highly conducive of engagement and interaction, even if this did not necessarily lead to discussion of differences.

Drawing on these observations, we think we may interpret our data as a very important moment in the construction of interlocutors' relationship since the exploration of shared and mutual interests allows on the one hand to overcome the lack of common frames in intercultural encounters (see above) and on the other hand to build a sort of platform permitting to further engage in the exploration of cultural differences (second dimension of reciprocity according to Koch). In other words, mutual interests help building a safe environment to compensate for the possible absence of common ground and the resulting uncertainty. This however does not imply that it is the only way, but that it is a possible way to scaffold reciprocity.

At the end of this section, we can summarize that relationship is directly linked to the principle of reciprocity since it is a foundation for it. In the case of the affective dimension, it seems to be conducive of subsequent engagement and sufficient motivation to overcome the limitations in the interlocutors' communicative competences. In the case of mutual interest, the reciprocity is expressed through the building of a safe common ground on which it is possible to deal with the uncertainty of different frames of reference.

The influence of the medium and of the audience

In this final section, we would like to consider the format of logs, which may influence the expression of the learners. The group format does not affect the expression of reciprocity itself but has an influence on the global expression of relationship experience, which is why we mention it here.

Forms of address and group identity

We will first consider the different forms of address observed, depending on the medium used. In the following examples, we can observe the expression of a sense of belonging to a group: Analysis shows that the forms of address change depending on whether they are addressed to the partner, to the group of partners, within the own (blog) group or joining both language groups, leading to the use of "they" in the Lille-Georgetown blog, instead of "we" in the Lille-UWA blog. In a web 2.0 dynamic, this could be linked to how one reconstructs one's identity within the group [START_REF] Baldauf | The effects of social media on the dynamics of identity[END_REF], compared to identity only shared with the tutor through the logbook. In fact, we argue that the format not only influences the forms of address but also influences the content in some ways, as the focus may move from personal reflection about one's learning to general reflections about the general climate (above), with obvious links to facework [START_REF] Goffman | Interaction ritual[END_REF]. In other words, considering that learners reconstruct their identity within the group, they may want to show the more pleasant dimensions of their tandem experience. This may also be linked to a desire for emulation, based upon the comparisons with other pairs. In other words, learners contributing to the same blog seem to co-construct a tandem relationship that goes beyond the pair and that leads to the development of a (tele)tandem group the students feel they belong to.

Community of practice in collective blogs

This kind of group which is co-constructed by teletandem learners in collective blogs shares features of a particular kind of community that has been widely studied in applied linguistics: community of practice [START_REF] Lave | Situatd learning: Legitimate peripheral participation[END_REF]. We consider two main features: sharing learning strategies and objectives and the comparing teletandem sessions.

In the blog format, without any difference between the Lille-UWA and the Lille-GT blogs, learners share their strategies and learning objectives, as in the two next following excerpts taken from a comment on the Lille-GT blog:

(15) Bonjour (author of the post) !

[…] Je vois que tu t'entends bien avec (partner of the author of the post), j'ai lu tes différents articles, il a l'air d'être sympa avec toi et personnellement, je trouve ça cool qu'il te donne des expressions de la vie courante, des abréviations et tout ça peut toujours te servir ! Je crois que je vais demander à (partner of the author of the comment) aussi de faire ça :) Vous avez l'air de bien échanger et c'est important pour découvrir la culture de l'autre. J'espère que tout continuera de bien se passer pour toi ! x Beyond observing the affective and emotional dimensions that we have already highlighted, excerpt (15) presents a comparison which leads not only to make the learning practice explicit, but also to the enrichment of such practice as the experience lived by the author of the post feeds the experience of author of the comment. This was one of the reasons why the logs had been originally transferred on a collective blog [START_REF] Cappellini | Du carnet d'apprentissage individuel aux outils du web 2[END_REF]. In the dynamics of web 2.0, that can be seen as a way to emphasize the development of autonomy [START_REF] Garcia Moraes | A typology of metacognition: Examining autonomy in a collective blog compiled in a teletandem environment[END_REF].

The second phenomenon that leads us to argue that collective blogs are conducive of the formation of a community of practice is the comparison of teletandem sessions. This is observed in the post below from the Lille-UWA blog:

(16) Vous avez été efficaces pour arriver à la question de la famille typique. Avec (partner of the author of the comment), nous n'avons même pas eu le temps de finir les questions pour mieux se connaître tellement on avait de choses à dire. xi (17) J'espère que vos prochaines conversations seront tout aussi intéressantes! :D xii In a way which is somewhat similar to the comparison of proficiency levels or to the comparison of the emotional climate, excerpts ( 16) and ( 17) show that learners compare the course of their teletandem sessions. In our opinion, this is a way for them to situate their own practice in an area that, especially at the beginning of the exchange, is largely unknown. Reciprocity helps them find landmarks in their learning process, landmarks that may have a reassuring effect as it helps them fix new goals. As such, this phenomenon is to be linked with the search for mutual interests, as it provides information on how to accomplish the teletandem sessions, or at least how they may be accomplished.

These two observations fit in the description that Rivens Mompean (2013, p. 150) makes of community of practices for language centres, which can be adapted to (tele)tandem blogs: a collaborative space to pool knowledge and provide support via the community of practice that ultimately shares the same doubts and goes through the same phases of discovery. xiii To summarize the different elements observed in this section, data indicate that the format of the blog has an impact on the possible construction of a group presenting characteristics of a community of inquiry, mainly through sharing learning strategies and objectives and through comparison of teletandem sessions. This group or community is characterized not only by these cognitive phenomena, but also by the construction of a certain group identity and pleasant climate that we have linked to a web 2.0 dynamic. These dimensions go beyond the strict reciprocity principle since they expand on the teletandem pair and construct a wider community which, in turn, impacts the pairs' reciprocity. In fact, the exchange at the level of the group has proven to possibly change the learning strategies and/or to favor expression of support asked to the partner, which is the fifth dimension Koch identified for reciprocity.

Conclusions

At the end of our empirical analysis, we will now consider how it relates to previous theoretical discussions of the principle of reciprocity. Before doing this though, we would like to highlight that our analysis does not consider actual interactions during teletandem sessions, but reflective writings after those interactions.

In this sense, our study informs us about the dimensions of reciprocity as reported by students in their written reflections on teletandem sessions. This could explain some differences between theoretical discussion and our empirical analysis.

Our analysis has confirmed empirically the presence of the organizational dimension of reciprocity, which we presented in the section 'Time and language division'. We have also related some log extracts to the semantic dimension ('comparison of topics') and to the use of the interlocutor's target language ('collective decision making', 'helping within the limits…'). We have not found traces that could be linked to the intercultural and to the discursive dimensions as defined by Koch.

Moreover, this study has allowed us to explore the way reciprocity at the micro level can be linked to the meso level of the relationship between groups, which we previously modelized as the bilaterality dimension (Rivens Mompean & Cappellini, 2015). First, we have seen how reciprocity is more broadly linked to the social relationship, either concerning the affective and emotional dimensions contributing to a friendly climate, or searching for mutual interests in co-constructing an online third space [START_REF] Dooly | Crossing the intercultural borders into 3rd space culture(s)[END_REF].

Second, we have highlighted how a specific format of students' logs, the collective blog, is conducive for the construction of a group identity that present features of a community of inquiry [START_REF] Lave | Situatd learning: Legitimate peripheral participation[END_REF] linked to Koch's (2017a) fifth dimension of reciprocity.

As for the practical implications of our analysis, we think that it informs us about what is perceived by students and considered relevant for mentioning in their written reflections. In this sense, the results of this analysis, if they are found in other teletandem contexts, may become the basis to different forms of counselling and advice in order for teletandem learners to become aware of other dimensions of reciprocity and to be able to develop metacognition on them.

At the end of our article, we would like to propose a wider definition of the principle of reciprocity that is built on Koch's initial definition (2017a, p. 126):

Reciprocity is the mode and rhythm of the exchange of information and objects in a given historical sociocultural situation between two or more communicators which bears the obligation to respond to a perceived impulse or gift in a way and time frame that corresponds to an acknowledged convention. It contributes to the building and perception of meaning, social relationship and stratification.

Communicative reciprocity can be attained by the search of mutual interests.

Reciprocity is influenced by the affective and emotional dimensions of the relationship between the two partners and possibly more broadly of the group. If a group is formed, reciprocity on the pedagogical level is influenced by the interactions within the group sharing learning strategies and objectives.

separately. Calvet [START_REF] Creizet | Interactional practices of third language learners: principles and documentation[END_REF] also add a 'minor principle ' (ibid., p. 209) called the 'principle of authenticity', which is related to meaningful interaction.

ii We try to develop our speaking and listening skills, as they correspond to the needs expressed by both of us.

iii We made a comparison with Germany -I do not imagine it happening there -, the issue of disrespect with a woman... and beyond the repercussion of the case in the media throughout Brazil.

iv It looks like you have a good proficiency level in English, does she have the same proficiency level as you in French?

v Even with our difficulties to talk, we get on well. x Hello (author of the post)! [...] I see that you get on well with (partner of the author of the post), I read your different articles, he seems to be nice to you and personally, I find it cool that he gives you expressions of everyday life, abbreviations and all that can always be useful to you! I think I'll ask (partner of the author of the comment) also to do that :) You seem to be good at exchanging and it's important to discover each other's culture. I hope everything will continue to go well for you! xi You have been efficient to discuss the question of the traditional family. With (name of the partner of the author of the comment) we haven't even had the time to finish the questions to know each other, since we had too many things to say.

xii I hope that your next conversations will be as interesting! :D xiii Our translation from the original : 'un espace collaboratif pour mutualiser les acquis et apporter un soutien via la communauté de pratiques qui partage finalement les mêmes doutes et passe par les mêmes phases de découverte'.

Figure 2 .

 2 Figure 2. Learner log (blog) of the Lille -Georgetown teletandem project.

Figure 3 .

 3 Figure 3. Learner blog from the Lille-Australian teletandem project.

  Bonjour mes chers Télétandemeurs! (13) Bonjour chers Blogsters :) viii UNESP-JGU (14) Minha pergunta: Mesmo nas interações de português falamos muito em alemão... eu fico um pouco frustrada... o que eu devo mudar? ix

vi

  We got along pretty well, she is a nice girl. The interview/exchange went by very quickly and I told her a little what next session will consist of. vii This session has opened my eyes to many features and wishes or tastes we have in common (reading, gardening, nature, animals...). viii Hello dear Teletandemers! Hello dear Blogsters :) ix My question: even in the Portuguese part of the interactions we still speak a lot of German… I feel a bit frustrated… what should I change?