Marie Plissonneau

Alexandra Madeira

David Talaga

Sébastien Bonhommeau

Laurent Servant

Renauda L Vallée

Christine Labrugère

Irenea A Goldthorpe

Lauriane Pautrot-D'alencon

Thierry Le Mercier

Thierry Lemercier

Prof Mona Treguer-Delapierre

Efficient passivation of Ag nanowires with 11-mercaptoundecanoic acid probed using in

Introduction

The interest in silver nanowires has surged in recent years as they are becoming to be promising nanostructures in a growing number of applications. In particular, they have received intense attention for their use as flexible, transparent electrodes to replace conductive metal oxides, most commonly indium tin oxide (ITO), in optoelectronic devices such as liquid crystal displays, touch screens, light emitting diodes and solar cells. [1--5 Although there are many synthetic routes to produce silver nanowires (AgNWs), control of their yield and chemical stability over time, both necessary for widespread commercial applications, remain a major challenge. [6--10 The most common way to prepare long silver nanostructures is the solution-phase approach. [1,6--7 Several synthetic approaches have been reported in polyol medium or via hydrothermal routes. [6--7] However, the synthesis often yields the formation of a high proportion of by-products (30% or greater). Secondly, the silver nanowires obtained from these approaches are often stabilized with the polymer polyvinylpyrrolidone (PVP), which serves as a surface adsorbing agent to control the growth morphology. PVP-coated AgNWs are sensitive to daylight and humidity leading to a gradual corrosion of the metal nanostructures and resulting in insufficient device lifetimes. [8] Various materials have been studied to passivate silver nanowires. 11--17 Typically nanowires on a substrate can be encapsulated within a film of organic or inorganic material such as metal oxide (Al2O3, ZnO, TiO2), graphene or polymers. 11--14 However, these matrices affect the intrinsic properties of the nanowire film. Passivating the nanowire surface only, rather than blanketing the nanowires in a film, is a promising alternative strategy as it should not, for example, lower the transparency of a nanowire film or interfere with its mechanical flexibility. [15--17] This can be achieved through passivating AgNWs with short molecules.

Triphenylphosphine has shown to be effective, inexpensive and simple passivation solution, 17 as we will shown here, MUA, a less toxic molecule, is similarly effective. Furthermore, short molecules permit electrical current to traverse nanowire junctions and go from nanowire surfaces to any active material above, thus maintaining electrode conductivity. 15--17 Due to their promise, further studies on nanowire short-molecule passivation are in progress. However, it is still unclear whether these molecules fully passivate the silver surface and replace polymer polyvinylpyrrolidone (PVP) molecules which generally cover the surface of as-synthesized AgNWs in solution, and how long the passivation process can last.

In this paper, large quantities of AgNWs are first synthesized with high yield. To increase the chemical stability of AgNWs, their surfaces are the modified with 11mercaptoundecanoic acid (MUA). UV-visible absorption spectroscopy, X-ray Photoelectron Spectroscopy (XPS) as well as a novel surface-enhanced Raman spectroscopy method (SERS) in total internal reflection (TIR) are used to prove the effective anchoring of the MUA onto the nanowires, and precise the dynamics of the passivation process.

Results and Discussion

AgNWs were prepared by a polyol synthesis process, using PVP as a capping agent and 1,2-propanediol rather than the typical ethylene glycol medium. Details of the synthesis have recently been patented. 18 The wires obtained in this medium have a pentagonal crosssection. They are produced in a single run, at the gram scale (Figure 1). Their preparation in 4 the presence of an increasing amount of nitric acid allows one to gradually tune their overall dimensions. Their high symmetry and yield result from the specific properties (especially its the viscosity and thermal conductivity) of the 1,2-propanediol solvent. 18 While these nanowires are produced at the gram scale with high yield, their PVPcoating does not prevent the corrosion of silver, [8,19--20] and a general strategy has thus been developed to chemically modify the surface of AgNWs and improve their resistance to corrosion. The AgNWs can be thiolated with short organic molecules [15,17] such as MUA that spontaneously adsorb onto the surface and form an efficient protection against oxidation. The details of how MUA molecules anchor to the metallic nanostructure's surface [21] and whether they fully replace the PVP layer is unclear. In our case, to modify the silver surface, the AgNW suspension was simply incubated in a fresh aqueous solution of thiolated MUA molecules overnight. Before surface modification, a thin amorphous layer of PVP polymer (few nm thick) could be seen on the silver surface (Figure 1). After surface modification, the amorphous polymer layer is substituted by a monolayer of MUA molecules, difficult to image even by atomic resolution microscopy (Figure S1 in Supporting Information (SI)). The initial PVP-stabilized silver sol typically has a main absorption band around 374nm and a shoulder at 350nm that corresponds to absorption along the short axis of the nanowires whereas the MUA-coated ones possess the same band slightly red-shifted by a few nm (Figure S2 in SI). Such a red shift is commonly observed upon modifying the surface of metal nanostructures with organosulfur compounds. 22 The MUA-protected AgNWs remain stable in solution, even after several months at ambient temperature, in the presence of air. They are even stable in a strong oxidative medium such as H2O2 solution that can easily destroy PVP-coated nanowires (Figure S2 in SI). These observations suggest a full MUA coating of the wires. In order to get more insight of the interaction of the MUA onto the nanostructure, we characterize the metal surface by XPS and an original SERS method. Figure S3 displays the results of the XPS analyses. The results confirm the formation of the Ag-S bonds after the ligand exchange and the absence of any sulfur oxide. For a better understanding of the mechanism of the PVP-MUA substitution process, surface-enhanced Raman scattering (SERS) of the AgNWs was exploited due to its high sensitivity for molecular sensing. As SERS strongly depends on the size, shape and dielectric environment of noble metal nanostructures, 23 single PVP-coated AgNWs with different diameters were preliminarily characterized using AFM and dark-field Rayleigh scattering microscopic (DFRSM) imaging (Figure 2), this latter technique revealing localized surface plasmon resonances (LSPRs) of AgNWs. 24,25 AgNWs appeared to lay with one facet on the glass substrate (Figure 2E). As the height of their pentagonal cross-section increases, their DFRSM band maximum shifts to higher wavelength (Figure 2A). This size effect on Rayleigh scattering spectra is well reproduced theoretically by means of FDTD simulations considering an incident excitation along the X-axis and a light polarization along the Z-axis, a situation close to the experimental one (Figure 2B and Figure S4 in SI). Pentagonal nanowires are known to support five modes resulting from a coupling of corner modes. 26 One of these modes exhibits a scattering maximum at 525nm where the electric field is confined at the 4 corners best excited by a sloshing of the electrons in the Z-direction of the structure. An electric field enhancement of 4 with respect to the incoming excitation is then obtained, for example, in the case of a 45nmhigh PVP-coated AgNW (Figure S4 in SI). Considering a 561nm irradiation wavelength, slightly off-resonance with the aforementioned mode, a similar electric field enhancement of 4 is observed (Figure 2E). As the electromagnetic SERS enhancement factor (EF) derives, in a first approximation, from the fourth power of this electric field enhancement at the laser wavelength ωL, it reaches 2.610 2 . This value is at least 2 orders of magnitude lower than the one commonly reported for SERS-active nanostructures. 24,25,27 Note that FDTD simulations considering light propagating along the Z-axis with a polarization along the X-axis leads also to scattering spectra very similar to the experimental ones (FigureS5 in SI).

6

DFRSM investigations on individual AgNWs suggest a better LSPR excitation for large AgNWs under 561nm irradiation (Figure 2A). However, the SERS EF is still too weak to probe the PVP-MUA substitution at the surface of a single AgNW in ethanol. Therefore, regions including several neighbor AgNWs were excited to take advantage of the presence of hot spots at contact points between AgNWs that are vertically stacked. 28--30 The DFRSM spectrum is then significantly red-shifted (Figure S6 in SI). Such a shift is commonly reported upon decreasing the interparticle gap between nanostructures, and increasing the amount of hot spots. 26 Moreover, the scattering signal at 561nm rises for AgNWs with small pentagonal cross-sections, such as 45nm-high nanostructures that will be exclusively studied hereafter

(Figure S6 in SI).
In order to avoid the fluctuant contribution of free AgNWs in ethanol and reduce that of the ethanol solvent itself, SERS experiments were carried out under 561nm evanescent light excitation (Figures S7,S8, and further details in SI). PVP and MUA signatures can then be distinguished by identifying specific Raman fingerprints of these species (Figure S9 and TableS1 in the SI). Two marker bands are selected, namely the C<C=>O stretching vibration centered at 1766cm <M->1 for PVP and the C-S stretching vibration centered at 630cm <M->1 for MUA. The wavenumber of the C<C=>O mode of PVP can be assigned to the PVP bound to the surface of AgNWs when it ranges between 1750 and 1769cm <M->1 . 31--33 In contrast, free PVP molecules exhibit a C<C=>O stretching vibration centered at 1776cm <M->1 due to the increased force constant of the C<C=>O bond. The wavenumber of the C-S stretching vibration of MUA nicely matches the value expected for the Gauche conformation of the molecule adsorbed on a silver surface. 34,35 Finally, in order to take into account possible intensity variations between SERS spectra, the 885cm <M->1 band of ethanol, assigned to skeletal CCO stretching or CH3 rocking vibrations, [36--37] was chosen as the internal reference.

Even though the bulk Raman signal of ethanol is very weak in regions void of AgNWs under evanescent field excitation, it can be detected easily in little stacks of AgNWs probably due to its SERS enhancement (Figure S9 in SI).

The PVP-MUA substitution mechanism proceeds in two main steps. For t<PVP≈40min, PVP molecules are replaced by their MUA counterparts as reflected by the intensity decay of the IPVP/IEtOH ratio which nullifies for t>PVP, congruent with the disappearance of the 1766cm <M->1 bound-PVP C<C=>O band and the emergence of the 1776cm <M->1 free-PVP C<C=>O band (Figure 3A). This 40min duration is in agreement with the time necessary to replace PVP by cysteamine and methoxy-terminated polyethylene glycol thiol. 31 Parallel to the extinction of the C<C=>O band at 1766cm <M->1 , the C-S marker band at 630cm <M->1 grows (Figure 3B). For PVP<t<MUA≈90min, the intensity of this latter band continues to increase (Figure 3C), which suggests that more C-S bonds are in the nearfield of AgNWs. This derives from the ability of MUA molecules to adsorb on silver by forming COO-Ag or S-Ag bonds. 34 This competition between the two anchor terminal sites of MUA molecules leads to a partial covering of AgNWs through strong Ag-S bonds for t<PVP. For t>PVP, MUA molecules tend to adopt the more stable orientation by breaking COO-Ag bonds to create S-Ag bonds untilMUA is reached. This process is slower than the MUA functionalization of bare silver electrodes which is almost complete within 60min, which suggests the existence of a retardation effect induced by the necessary removal of PVP molecules. 34 Note that it was not possible to follow the intensity change of the COO-Ag Raman band expected at 1394cm <M->1 owing to the unfortunate overlap with the Raman band assigned to ethanol CH2 wagging vibrations (Figure S9 and Table S1 in SI). 34,37 Finally, for t>MUA, all the AgNWs are covered with MUA molecules adsorbed via Ag-S bonds. This two-step mechanism of the PVP-MUA substitution presents a peculiar dependence as a function of the MUA concentration. For 500µM and 100µM MUA solutions, PVP andMUA are not affected, but each step appears globally slower at the lower 100µM concentration. Concerning the PVP desorption after injection of a 500µM MUA solution, the intensity ratio IPVP/IEtOH falls down quickly within 6min and reaches a plateau (IPVP/IEtOH≈0.15) before vanishing at PVP. In contrast, for a 100µM MUA solution, the initial decrease lasts 12min and the plateau occurs at higher intensity ratio (IPVP/IEtOH≈0.60).

Regarding the C-S bond formation, the IMUA/IEtOH ratio increases gradually for a 500µM MUA solution while, after a short initial surge, it stabilizes at IMUA/IEtOH=0.19 after 40min before pursuing its rise for a 100µM MUA solution. This atypical behavior is related to the reduction of the molecular accessibility of hot spot regions with respect to isolated sections of AgNWs, which first react with MUA molecules. For large excess MUA concentration (500µM), most hot spot regions can be simultaneously functionalized. However, at lower MUA concentration (100µM), the PVP-MUA substitution slows down due to the steric hindrance and leads to an intermediate plateau associated with the existence of an incubation time before triggering the PVP-MUA substitution (for t<PVP) and the MUA reorientation (for PVP<t<MUA) mechanisms in hot spot regions.

Passivating a AgNW network with MUA significantly improves their stability. As was determined here, by simple submersing AgNWs in a solution of MUA, the molecule fully covers the nanowire surface and this likely acts as a barrier against corrosion (Figure S10 in SI). In addition to being simple, cheap and non-toxic, this passivation layer does not lower the transparency of the AgNW networks nor interfere with its intrinsic conductivity or mechanical flexibility. Therefore, it constitutes a promising, commercially viable passivation approach.

Conclusion

In brief, we have demonstrated that the surface of PVP-coated AgNWs, produced in 1,2-propanediol, can be easily passivated by MUA. The PVP-MUA substitution proceeds in two steps: (i) a first anchoring of the MUA on the metal surface via Ag-OOC and Ag-S bonds, and (ii) the reorganization of the MUA molecules to form only Ag-S bonds. Finally, the promising chemical stability of MUA-coated AgNWs compared to PVP-coated ones opens up exciting possibilities for electro-optical devices that have yet to be explored.

Experimental Section

Materials: Silver nitrate (AgNO3, 99.999%), Ethylene Glycol (J.T. Baker); propylene glycol (Aldrich); Poly(vinylpyrrolidone) MW≈55k (Aldrich); H2O (milliQ water); ethanol 96%; acetone; 11mercaptoundecanoic acid 98% (Aldrich); H2O2 and nitric acid (Thermofisher) were used as received without any further purification.

Synthesis and surface modification of PVP-coated Ag nanowires:

The shape-controlled silver nanocrystals were prepared by a modified polyol method. 18 In a typical process, 6mL of AgNO3 solution (0.1M in 1,2-propanediol) and 8.6mL of PVP solution (concentration in monomer of 0.21M in polyol) was successively added to a volume of 8.6mL of 1,2propanediol in a round bottom flask. After properly mixing the reactant, 70µL of NaCl solution (0.1M polyol) were added dropwise to the solution and after 5minutes under vigorous stirring, the mixture was heated up to 140°C under reflux and mild agitation (1hour). The obtained AgNWs were washed with acetone and water to remove excess polyol and PVP via centrifugation. The AgNWs suspension was subsequently transferred from water to absolute ethanol thanks to five consecutives ten-minute centrifugation cycles at 6000rpm. By using such experimental conditions, AgNWs exhibit a mean diameter of 35+6nm. The aspect ratio of the elongated nanostructures can be tuned by adding nitric acid (0.22M) in the solution as recently patented. 18 A pre-addition of a small amount of HNO3 in the reaction medium increases the diameter of the nanowires from 35nm to 175nm (no HNO3 pre-added (AgNWs diameter: 35nm), 0.05ml HNO3 added (45nm), 0.06ml (62nm), 0.08ml (75nm), 0.1ml (92nm), 0.15ml (135nm), 0.5ml (175nm)).

10

For the surface modification process in solution, a fresh MUA solution of 50mM in absolute ethanol was prepared. The AgNW suspension was diluted in EtOH to reach a Ag concentration of 5mM, and a volume of MUA corresponding to a molar ratio Ag:MUA of 1:4 was added to the nanowire suspension. The mixture was incubated at room temperature overnight under mild agitation, washed twice by a ten-minute centrifugation at 6000rpm and redispersed in the same volume of EtOH as before. The surface passivation could also be performed on AgNWs deposited on a glass substrate by dipping the substrate in a solution of MUA. 50μl of Ag NWs suspension (6mg.ml <M->1 )) was deposited on glass substrates (24×32mm) using a wire-wound metering rod (Meyer rod coating). The substrates were then immersed in an ethanolic solution of MUA (18mM) for 1hour.

Stability of Ag nanowires:

The chemical stability of the Ag nanowires in solution against an oxidizing environment was evaluated by monitoring changes in the optical properties of a colloidal suspension incubated with H2O2 (Figure S2 in SI). 100μl of H2O2 (1M) was introduced in 5ml of a colloidal suspension of AgNWs coated with PVP or MUA. In a separate experiment, the stability of the metallic nanowires in air was evaluated by conductivity measurements. Conductive AgNW networks were rod-coated on glass substrates. All samples were exposed to lab air at ambient conditions (23±2°C and a relative humidity of 70±4%). Four point probe measurements were periodically taken over during a time interval of 4months (Figure S10).

Sample preparation for SERS measurements:

SERS experiments on AgNWs immersed in ethanol were carried out using home-made glass liquid cells following a three-step procedure. A 20µL volume of concentrated ethanolic solution of PVP-coated AgNWs (5mM) was first dried into the cell to allow for the formation of localized AgNW stacks. A 20µL volume of ethanol was then slowly added in order to avoid the complete dispersion of stacks. A few microliters of an ethanolic solution of MUA was finally injected to reach the desired (500µM or 100µM) MUA concentration into the cell and start the PVP-MUA substitution.

Electron microscopy characterization: Transmission electron microscopy (TEM) was performed with a JEOL 2200FS and a JEOL 2100F microscope operating at 200kV. Samples were prepared by depositing one drop of the colloidal dispersion on a carbon-coated copper grid. The scanning electron microscopy images (SEM) were collected on a JEOL 6700-FEG instrument.

Elemental analysis and surface characterization: Inductively Coupled Plasma Optical

Emission Spectrometry (ICP-OES) measurements were performed, using a Varian 720-ES spectrometer, to determine metal nanoparticle concentrations. Samples were prepared in plastic Falcon tubes, where a known volume of colloidal dispersions (>0.5mgL <M->1 ) was attacked by aqua regia. All experiments were repeated 5times.

Optical characterization on colloidal solutions:

The absorption spectra of the colloidal suspensions were recorded in the range of 300--1300nm with a UV-3600 Shimadzu UV-Vis-NIR spectrophotometer by using a 1cm optical-path-length quartz cells.

X-ray Photoelectron Spectroscopy: XPS measurements were performed on a Thermo Fisher Scientific K-Alpha spectrometer with a monochromated Al Kα source (1486.6eV). The x-ray spot size was 200μm and charge compensation was used on insulating samples. The spectrometer was calibrated with monocrystalline gold and silver foils (binding energies of 84.0eV for Au 4f7/2 and 368.25eV for Ag 3d5/2). Surveys were acquired at a 200eV pass energy and the high resolution spectra were acquired with a pass energy of 40eV. ThermoScientific Avantage software was used for fitting and quantification (Scofield table).

Single nano-object optical spectroscopy:

The instrument allowing for the realization of colocalized TIR SERS and DFRSM measurements has been described in detail elsewhere 24,25 (FigureS7) and in the Supporting Information. Note that measured DFRSM spectra have been corrected to account for the frequency-dependent response of the spectrometer and they have been normalized with respect to the intensity of the incoming light in the investigated 400--800nm spectral range. Furthermore, all the TIR-SERS experiments were carried out above the critical angle αc≈63.8° 12 in ethanol, and more precisely at αi≈66.9° corresponding to a penetration depth δethanol≈200nm. However, as the propagation depth in silver is typically 10 fold lower than in neat ethanol, 35 the genuine δexp value is expected to be lower than 100nm upon excitation of little stacks of AgNWs immersed in ethanol.

Simulation framework:

The optical properties of the various nanostructures deposited on a glass substrate were analysed using a three-dimensional finite-difference time-domain software (FDTD Solutions, from Lumerical Solutions, Inc.) (Ref: Lumerical Solutions, Inc. "Innovative Photonic Design Tools," https://www.lumerical.com/.) The geometry of the structures is a pentagonal silver nanowire considered as infinitely long in the Y-direction and with a distance h (Figure S4) between the base deposited on the glass substrate and the opposite vertex varying from 45 to 62, 75, 92, 135 and 175nm. The nanowires are covered by a thin dielectric layer of PVP (5nm) to mimic the experimental situation. The dielectric properties of the various components are a dispersion-less dielectric permittivity of 2.338 (2.151) for PVP (glass), together with the permittivity of silver from the software database as described by Palik (0--2µm). 38 The simulation space was constructed using perfectly matched layers (PMLs) along the X-and Z-axes. The excitation of the structure was performed by using a broadband 2fs pulse centred at 687THz, with a bandwidth of 625THz, launched along the horizontal X-axis (Figure S3) and polarized along Z. Owing to the implementation of a Total Field Scattered Field formulation, the absorption, scattering and extinction cross-sections of the various nanostructures were obtained in a first step. In a second step, the electric field amplitude profiles were obtained for various resonance modes of interest as well as the amplitude profile corresponding to the used experimental excitation wavelength, fixed at 561nm.

Acknowledgements TEM, HR-TEM and HR-SEM experiments were performed at the Plateforme de Caractérisation des Matériaux and Bordeaux Imaging Center of the University of Bordeauxas well as the Plateforme Castaing of the University of Toulouse. This work was supported by Solvay (project n° 2016-00710).

Supporting Information

Supporting Information is available from the Wiley Online Library.


est destinée au dépôt

  , Aurélie Joubert, K. Gueraoui, S. Durécu, D. Venditti, D. T. Tran, Laurence Le Coq To cite this version: R. Boudhan, Aurélie Joubert, K. Gueraoui, S. Durécu, D. Venditti, et al.. Pulse-Jet Bag Filter Performances for Treatment of Submicronic and Nanosized Particles from Waste Incineration. Waste and Biomass Valorization, 2018, 10.1007/s12649-017-9858-4. hal-01531936


Andrea Mendizabal
email: andrea.mendizabal@inria.fr

Raphael Sznitman
email: raphael.sznitman@unibe.ch

Stephane Cotin
email: stephane.cotin@inria.fr

Force Classification during Robotic Interventions through Simulation-trained Neural Networks

Keywords: Finite element modeling, Bayesian inference, Artificial neural networks, Force estimation in robotics

Purpose Intravitreal injection is among the most frequent treatment strategies for chronic ophthalmic diseases. The last decade has seen a serious increase in the number of intravitreal injections, and with it, adverse effects and drawbacks. To tackle these problems, medical assistive devices for robotized injections have been suggested and are projected to enhance delivery mechanisms for a new generation of pharmacological solutions. In this paper, we present a method aimed at improving the safety characteristics of upcoming robotic systems. Our vision-based method uses a combination of 2D OCT data, numerical simulation and machine learning to classify the range of the force applied by an injection needle on the sclera. Methods We design a Neural Network (NN) to classify force ranges from Optical Coherence Tomography (OCT) images of the sclera directly. To avoid the need for large real data sets, the network is trained on images of simulated deformed sclera. This simulation is based on a finite element method and the model is parameterized using a Bayesian filter applied to observations of the deformation in OCT images.

Results We validate our approach on real OCT data collected on five ex vivo porcine eyes using a robotically-guided needle. The thorough parameterization of the simulations leads to a very good agreement between the virtually generated samples used to train the network and the real OCT acquisitions. Results show that the applied force range on real data can be predicted with 93% accuracy. Conclusions Through a simulation-trained neural network, our approach estimates the force range applied by a robotically guided needle on the sclera based solely on a single OCT slice of the deformed sclera. Being real-time, this solution can be integrated in the control loop of the system, permitting the prompt withdrawal of the needle for safety reasons.

Introduction

Intravitreal injections are among the most common surgical interventions in ophthalmology with more than 4 million injections worldwide in 2014 alone [START_REF] Ullrich | Assistive Device for Efficient Intravitreal Injections[END_REF]. This procedure is principally used in the treatment of diabetic maculopathy and for injecting vascular endothelial growth factor inhibitors in the treatment of age-related macular degeneration. Besides, we observe an increasing demand for such therapy due to the growing prevalence of diabetic patients and aging demographics. Intravitreal injections are mostly performed by doctors and the cost of such therapy has to be reduced. The increasing workload and the reduced reimbursement makes it difficult for hospitals to handle the situation. The time spent by the clinicians performing the injections has to be minimized while preserving the precision and the safety of the patient.

At the same time, robotic assistance in ophthalmology provides the ability to improve manipulation skills, along with shorter and safer surgeries [START_REF] Meenink | Robot-assisted vitreoretinal surgery[END_REF]. To this end, Ullrich et al. [START_REF] Ullrich | Assistive Device for Efficient Intravitreal Injections[END_REF] proposed a robotized intravitreal device capable of assisting injections into the vitreous cavity. However, designing such robotic systems requires to solve multiple challenges in terms of safety, cost and time efficiency and usability. The position accuracy and the orientation of the needle are of particular interest since the injection must be performed in a small region (the pars plana) of the eye. If the region is missed, damage of the eye lens or the retina might occur. In addition to accurate positioning, the ability to estimate or measure the force exerted by the needle on the sclera during the procedure could offer an important additional safety for the patient [START_REF] Jagtap | Applied force during vitreoretinal microsurgery with handheld instruments[END_REF].

As a matter of fact the knowledge of the force plays a central role in the control loop of surgical robots for patient safety during robotic assisted interventions [START_REF] Weber | Instrument flight to the inner ear[END_REF]. The force can be either measured through force sensors or estimated through vision-based methods. The use of force-based control algorithms allows for an improved human-machine interaction, more realistic sensory feedback and telepresence. Beyond this, force sensing or force estimation can facilitate the deployment of essential safety features [START_REF] Haidegger | Force sensing and force control for surgical robots[END_REF]. A considerable amount of work relying on force sensors has previously been done, focusing on the development of miniaturized devices to ease their integration with actual systems. Force sensors usually need to meet several additional requirements, such as being water resistant, sterilizable and insensitive to changes in temperature [START_REF] Haouchine | Vision-based Force Feedback Estimation for Robot-assisted Surgery using Instrument-constrained Biomechanical 3D Maps[END_REF]. The major limitation of conventional sensors is thus the associated cost since most surgical tools are disposable [START_REF] Haidegger | Force sensing and force control for surgical robots[END_REF]. To overcome this point, alternative solutions have been proposed, such as qualitative estimation of forces based on images [START_REF] Mura | Vision-based haptic feedback for capsule endoscopy navigation: a proof of concept[END_REF][START_REF] Haouchine | Vision-based Force Feedback Estimation for Robot-assisted Surgery using Instrument-constrained Biomechanical 3D Maps[END_REF]. Mura et al. [START_REF] Mura | Vision-based haptic feedback for capsule endoscopy navigation: a proof of concept[END_REF] introduced a vision-based haptic feedback system to assist the movement of an endoscopic device using 3D maps generated with a Shape-from-Shading method where the 3D shape of the surface is recovered from a 2D image of that surface. Haouchine et al. incorporated the use of a biomechanical model of the organ in addition to the 3D maps to estimate force feedback in robot-assisted surgery. This approach is, however, limited to the ability to evaluate tissue properties of the organ quantitatively [START_REF] Aviles | A recurrent neural network approach for 3d vision-based force estimation[END_REF].

Deep learning has already been suggested to improve existent characteristics of robotic assisted surgeries such as instrument segmentation and detection [START_REF] Pakhomov | Deep residual learning for instrument segmentation in robotic surgery[END_REF], as well as force estimation. For instance, in [START_REF] Aviles | A recurrent neural network approach for 3d vision-based force estimation[END_REF], interaction forces in minimally invasive surgeries are estimated with recurrent neural networks using camera acquisitions combined with kinematic variables and deformation mappings. In a follow-up paper, Aviles et al. [START_REF] Aviles | Sensorless force estimation using a neuro-vision-based approach for robotic-assisted surgery[END_REF] used a neuro-vision based approach for estimating applied forces in the same context. In [START_REF] Aggarwal | Covfefe: A Computer Vision Approach For Estimating Force Exertion[END_REF], authors used two neural networks to classify muscle force exertion levels to prevent musculoskeletal disorders based on features extracted from video data and blood volume changes. However, in all these approaches an intermediate step to determine the surface deformation is required.

Our method consists of estimating contact forces directly from an OCT image of the scleral deformation without the need for a specific image feature extraction method beforehand, as in [START_REF] Aviles | Sensorless force estimation using a neuro-vision-based approach for robotic-assisted surgery[END_REF][START_REF] Aviles | A recurrent neural network approach for 3d vision-based force estimation[END_REF]. This work is built on top of our previous paper [START_REF] Mendizabal | September). A Combined Simulation and Machine Learning Approach for Image-Based Force Classification During Robotized Intravitreal Injections[END_REF]. The technique relies on an image classifier for estimating force quantiles during robotized intravitreal injections. An imperative requirement for machine learning algorithms to work is the huge quantity of data to train on. Currently since intravitreal injections are executed manually, there is no available information on the force induced by the needle. Hence, we propose to build a biomechanical model of the sclera to generate a very large number of force-OCT image pairs, which are then used for training any supervised machine learning method. We will show that this approach allows us to avoid the need for large data sets of real OCT images. The simulations are parameterized to match experimental results and compensate for the absence of real data. The parameterization can be carried out with different approaches. In our previous work [START_REF] Mendizabal | September). A Combined Simulation and Machine Learning Approach for Image-Based Force Classification During Robotized Intravitreal Injections[END_REF], we manually matched the simulations with some real acquisitions performing a grid search. Alternatively, simple optimization algorithms can be used to minimize the errors between the output of the simulation and the OCT image over the set of possible parameters. However, in the view of an online estimation of the parameters, we choose to use a Reduced-Order Unscented Kalman filter [START_REF] Moireau | Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems[END_REF] to estimate the stiffness of the scleras which is the main contribution of this paper compared to [START_REF] Mendizabal | September). A Combined Simulation and Machine Learning Approach for Image-Based Force Classification During Robotized Intravitreal Injections[END_REF]. We then train a two-layer image classifier algorithm with the generated images and their corresponding forces. This solution allows a straightforward force estimation process to take place. This twostage process makes it possible to classify force ranges with 93% accuracy while requiring very few experimental data, as demonstrated on several ex vivo porcine eyes undergoing robotically-controlled needle insertions.

Method

In this work, we first construct a numerical model of the interesting portion of the eye to synthesize images of the deformed sclera under needle-induced forces. To be as close as possible to the actual organ behavior, we propose to use Bayesian inference as a means of identifying material parameters. Then, a data generation process takes place in order to train a neural network.

Numerical simulation

Biomechanical model We simulate the deformation of the sclera under needleinduced forces by modeling the eye as an elastic half-sphere subject to Dirichlet boundary conditions (see Fig. 1(a)). Since applied forces and resulting deformations remain small, we choose to describe the stress-strain relationship as linear, using Hooke's law (1):

σ = 2µ + λtr( )I (1)
where is the strain, σ the stress, and λ and µ are the Lamé's constants derived from the Young's modulus E and the Poisson's ratio ν. The Young's modulus is a measure of the stiffness of the material while the Poisson's ratio characterizes the compressibility of the material. The linearity of Hooke's law leads us to a simple relation σ = C where C is the constitutive matrix for an homogeneous and isotropic material. Then, Dirichlet boundary conditions are added to prevent rigid body motion of the sclera, while a constant pressure is applied to the inner domain boundary to simulate the intraocular pressure (IOP), as illustrated in Fig. 1(a).

The intraocular pressure plays an important role in the apparent stiffness of the eye and its variability is well studied, as high eye pressure can be an indication for glaucoma. It is worth-mentioning that the common IOP measurement devices are influenced by the stiffness of the eye. The value measured by the tonometer is not absolute but linearly related to the Young's modulus [START_REF] Hamilton | Youngs modulus in normal corneas and the effect on applanation tonometry[END_REF]. The external force due to IOP is given by f p = S × P where S is the surface area of the eye (in m 2 ) and P the intraocular pressure, given in P a. Note that f p is normal to the surface.

To simulate the needle pushing on the sclera, we apply a local force f n in a small region of interest near the virtual needle tip. The external forces of the system are then formed by the IOP, the force induced by the needle and the gravitational force f g applied in the negative y direction,. Finite Element simulation We solve the equation for the constitutive model using a finite element method. The eyeball is considered as nearly spherical and is discretized using a quadrilateral surface mesh of a half sphere of radius 12 mm, discretized using the Catmull-Clark subdivision method. The obtained quadrilateral surface is extruded conforming to the scleral thickness in order to generate almost regular hexahedra (see Fig. 1(b)). Scleral thickness plays an important role in the deformation of the sclera. Under a given force, a thick sclera is less deformed than a thin one, therefore it is important to take this thickness into account. Finally, the deformation is specified by the nodal displacements u and the nodal forces f, according to the following equation:

Ku = f p + f g + f n (2)
The matrix K is the stiffness matrix, and can be computed thanks to the elastic parameters of the material E and ν similarly as in [START_REF] Bronielsen | Realtime volumetric deformable models for surgery simulation using finite elements and condensation[END_REF].

To compute accurately the deformation of the sclera, the finite element mesh needs to be sufficiently fine (to avoid discretization errors). In our simulation, we use a mesh composed of 14, 643 hexahedral elements, resulting in about 5 seconds of computation time to obtain the static solution of the deformation. All our experiments are run on a Dell Precision laptop equipped with an intel Core i7 2.90GHz, a Quadro M1200 Graphics Processing Unit and 16Go of RAM. Since this computation has to be repeated thousands of times to generate the training data set, we take advantage of the linearity of the model and pre-compute the inverse of K to speed up the generation of the training data. This leads to a substantial computational speed-up (x10).

Model parameterization

Our finite element simulations depend on parameters of the constitutive model and the geometry of the eye: Young's modulus, Poisson's ratio, intraocular pressure and scleral thickness. It is therefore essential to understand which parameters can be assumed constant, and which ones vary (and within what range) to properly generate training data.

Data from the literature [START_REF] Olsen | Porcine sclera: thickness and surface area[END_REF] report a thickness for corneal-scleral limbus in porcine eyes ranging from 630 µm to 1030 µm. We perform thickness measurements on porcine eyes and get a variation in thickness of more than 35%. Hence, we choose to consider the thickness as a parameter in the training, and we simulated scleras with five different thicknesses: 400 µm, 500 µm, 600 µm, 700 µm and 800 µm.

The IOP is also known to vary from patient to patient, and can be measured using a tonometer. So if we were to apply our method on a patient, we could use this information to parameterize the simulations used for the training. However, this is different for the porcine eyes used in our study. The IOP decreases gradually with postmortem time [START_REF] Balci | The importance of measuring intraocular pressure using a tonometer in order to estimate the postmortem interval[END_REF] and is halved only three hours after death. The IOP we measured ranged from 1 to 4 mmHg which is very small and does not affect much the deformation of the sclera. Therefore we considered the IOP constant and equal to 2 mmHg (266 P a) for our experiments and simulations.

The Poisson's ratio, ν is a constant value for the sclera according to the literature [START_REF] Asejczyk-Widlicka | The elasticity and rigidity of the outer coats of the eye[END_REF] and can be set to ν = 0.45. This leads to a nearly incompressible behavior during the deformation. With this in mind, we can reasonably assume that our training data set can be generated from numerical simulations in which the thickness, Poisson's ratio and IOP are known and constant.

The value of Young's modulus E, however, is more difficult to estimate as it varies depending on the porcine breed and experimental conditions. Therefore, values from the literature are not directly applicable. On the other hand, measuring it using a "classical" experimental biomechanics approach would be burdensome. For this reason, we propose to use a Bayesian approach to estimate the value of E using observations from our OCT images. Such an approach could also be used to perform data assimilation on actual patients.

The knowledge of the elasticity parameters is key to build a good model of the sclera. The Young's modulus defines the ratio of stress to strain. The goal of this work being the estimation of the force range based on the shape of the sclera, it is therefore very important to correctly estimate E to avoid introducing errors in the force prediction. Since the exact value of E is not a priori known (only its average value based on data from the literature), we describe it as a stochastic parameter associated to a Gaussian probability density function (PDF). Initially E ∼ N (µ 0 , σ 0 ) with µ 0 the mean value of E reported in the literature, and σ 0 its standard deviation. The aim of the assimilation process is to reduce the standard deviation σ in order to find the most likely value for µ. For this, the PDF of the parameter E is then transformed based on observations. Although our stressstrain relation is linear, we choose to model the transformation of the PDF using a reduced-order Unscented Kalman filter (ROUKF) [START_REF] Moireau | Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems[END_REF] which can handle non-linear processes, and is computationally efficient.

Data set generation

Once the model is correctly parameterized, we generate a synthetic data set {(f nk , I k )} N k=1 of N samples where f nk is the needle-induced force for sample k and I k is the corresponding simulated image of the deformation. The forces range from 0.0 N to 0.06 N and are applied at random locations and normally to the scleral surface for each of the different thicknesses. For each sample, a 2D crosssection of the complete 3D mesh is extracted in order to simulate the OCT image I k . The simulated images have to be informative of the scleral thickness and its deformation, hence a binary image suffices for our purpose. Therefore the images are post-processed with a contour detection algorithm (findContours OpenCV function) and binarized (threshold function).

Neural network image classification

We look into modelling a function that can estimate the range of forces applied by a needle when observing a single OCT image and the deformation within it. To do this, we make use of an artificial neural network (NN) to provide a robust and reliable function capable of estimating forces applied to the sclera. In our case, the input to the model is the cross-sectional OCT image that depicts anatomical information of the sclera, from its surface to 1 millimeter below. In order to provide high-frame rate imaging, we opt to use 2D OCT cross-sections as the imaging modality over 3D volumetric OCT scans that are more common but slower to acquire. In our set up, we use the low-cost solution introduced in [START_REF] Apostolopoulos | Efficient OCT volume reconstruction from slitlamp microscopes[END_REF] to image 2D OCT cross-sections.

While we are interested in estimating the force applied by the needle, we choose to categorize the applied forces into three interval ranges. This reduces the need to be sensitive to exact force values, which not only is unnecessary in this instance, but also allows us to set up our inference task as a classification problem, whereby forces are grouped into ranges of clinical relevance. To do this, our NN consists of two fully connected hidden layers and a classifier as output layer (see Fig. 2). The input layer has 5600 neurons (corresponding to the size of the input images 140 × 40) while the hidden layers have 600 neurons. These optimal values are found through a grid search. We use ReLu activations throughout the network and a softmax activation at the output layer. The network was implemented using Tensorflow and the Keras Python library.

Given the above simulation model presented in Sec. 2.1, we can train our NN with virtually an infinite amount of synthetically generated data. With the objective of stopping an incumbent needle from damaging the sclera, we use our simulation model to generate OCT images with forces between 0.0 N and 0.06 N applied on the Finite Element mesh of the sclera. This range was then divided into three ranges, or classes, consisting of:

-Class 0: force values smaller than 0.005 N -Class 1: force values from 0.005 N to 0.03 N -Class 2: force values bigger than 0.03 N whereby class 0 corresponds to virtually no danger to the sclera, class 1 indicates a considerable force and class 2 is a dangerous force that should trigger a needle removal signal. The complexity of our problem makes it challenging to establish a clear cut between 'no danger to the sclera' and 'a needle removal is advised'. For this reason we introduced an intermediate class which can be seen as a gray area between the two bounding classes. If the force is classified in this gray area, it becomes the clinician's responsibility to stop or continue the insertion.

We train our NN from scratch using a gradient descent and the cross-entropy loss. A 0.8 dropout factor between layers was used to help with generalization.

Results

In this section, we first describe how data acquisition on ex vivo porcine eyes was performed. Then, we present the virtually generated data set, and associated training, with an emphasis on the parameterization of the biomechanical model. Finally, we validate the neural network on unseen real data to demonstrate the high level of accuracy of our approach at classifying contact forces.

Experimental set up

To validate the predictive accuracy of the NN on real data, we acquired a collection of {(f nk , I k )} M k=1 of M samples from ex vivo porcine eyes. Five porcine eyes were obtained from the local abattoir and transported to the experiment room while kept at low temperature. Experiments began within 3 hours of death, and we ensured they were completed less than 10 hours postmortem. During the tests, the eyes were moisturized with water and fixed with super glue on a 3D-printed holder to ensure fixed boundary conditions on the lower half of the eyeball. We choose super glue as it preserves the tightness of the eyeball. We then measured the IOP with a tonometer and obtained, for all the eyes, an IOP close to 2 mmHg (about 266 P a). The intraoperative pressure is lower than usual since it decreases dramatically after death [START_REF] Balci | The importance of measuring intraocular pressure using a tonometer in order to estimate the postmortem interval[END_REF]. However, we did not inject any fluid during the experiments to compensate for this low IOP.

A surgical robotic arm that was designed for high-precision drilling during robotic cochlear implantation [START_REF] Weber | Instrument flight to the inner ear[END_REF] was used to measure the force applied by a needle. The robotic arm is fitted with a six-axis force/torque sensor (Mini40, ATI) at its wrist underneath a quick release for the end effector. After mounting a 22G Fine-Ject needle (0.7 x 30 mm) at the tip of the end effector, the robotic arm guided the needle forward along its axis. The needle was positioned as close as possible to the B-scan without intersecting it to bypass the generation of shadows in the OCT image. The margin between the needle and the B-scan was considered in the simulation. The robot was programmed to move towards the center of the eye along a path normal to the sclera. Contact and insertion forces, in the direction of motion, were continuously recorded during the insertion process. We also recorded the associated OCT images by storing B-scans over time. The custom-designed OCT device uses a 840 nm ± 40 nm wavelength light source, with an A-scan rate of 50 kHz for a resulting 2D image of resolution 512 × 512 pixels with 12 bits per pixel, corresponding to an area of 15 × 4 mm 2 . In these images, the black bands surrounding the OCT focus are removed leading to images of size 140 × 40 pixels.

In Fig. 3, a fragment of the collected data including 5 complete acquisitions is shown. To each trial corresponds one OCT image captured at a punctual time and a continuous flow of force values. The forces are filtered so that the noise is reduced. As the images were collected at a lower frequency than the forces, the corresponding forces were averaged over an interval of two seconds around the imaging time. The vertical lines correspond to the imaging times. The relaxation properties of soft tissue explain the slight decrease of the force a few seconds after the force is applied. The computed average force is used as ground truth for the following supervised learning. For each eye, one position near the cornealscleral limbus was selected and the needle moves forward 0.5 or 1 mm in the same Table 1 Distribution of samples in the three force ranges and scleral thickness for each eye.

direction. Note that the pierced samples are excluded from the data set. Overall, 45 valid trials were performed on different eyes. The spread of each acquisition among the force classes is depicted in Table 1.

Stochastic identification of the Young's modulus

According to the collected porcine data, the Young's modulus E of the biomechanical model is estimated using the ROUKF. The PDE of E is transformed based on observations taken on the OCT images acquired during the experiment on an eye (see Fig. 4(a)). We consider the corresponding ground truth force (measured with the robot's force sensor) to run the simulations. According to [START_REF] Asejczyk-Widlicka | The elasticity and rigidity of the outer coats of the eye[END_REF], we set µ 0 and σ 0 to 0.49 M P a and 0.34 M P a respectively. We estimated the Young's modulus for each eye independently based on all OCT images where observation points can be extracted. We extract 10 observations on each OCT image for a given eye (see Fig. 4(a)). The finite element mesh is registered to the OCT image using rigid registration. To each observation in the OCT (yellow dots) corresponds a predicted observation attached to the model (red dots). During the assimilation, the known force is applied and the observations obtained are used by the filter correction phase to compute the Kalman gain. We employ the simplex version of the ROUKF, and since we only want to estimate one parameter, two evaluations of the model are performed in each prediction phase of the assimilation process (i.e. there are two sigma points). The evolution of µ and σ with the iterations of the ROUKF for eye 1 are shown in Fig. 5. After convergence, we see that the final value of µ is 0.27 M P a, as reported in first column of Table 2. When applied to other porcine eyes, estimated values of E vary only slightly, as seen in Table 2. Therefore we consider the Young's modulus E to be constant across all our experiments, with an average value of 0.25 M P a. Using this values leads to very good visual agreement between the OCT images and the simulations for the three force ranges for all the eyes (see Figs. 6 and7) thus validating the assumption of linearity from section 2.1. Once the OCT images have been processed to look like the simulated ones, we can use them as input to the NN and perform force predictions. For each OCT acquisition, the force measured by the robot is converted into a class label (0, 1 or 2) and is taken as the ground truth (target class). A class with label 0 corresponds to a minimal force for which there is no risk of damaging the sclera. A class with label 1 corresponds to forces ranging from 0.005N to 0.03N and indicates that the sclera is being considerably deformed. A force class with label 2 means that the sclera is potentially being damaged and that a withdrawal of the needle is advised.

The performance of the classification is reported in the confusion matrix in Table 3. Each row of the table gives the instances in a target class, and each column gives the instances in a predicted class. For each category, we highlighted the correct decisions in red and show that the overall accuracy of the classifier is very high (93%). For all the experimental data set, the lowest score of the NN was obtained for the force class 0 with 71% accuracy. For target class 2, the precision reached 100%. In Fig. 10 are shown the raw force values (measured with the robot's force sensor) and the force range thresholds. The plot shows that the forces measured are uniformly spread throughout the force ranges. Note that the three misclassified samples are close to the upper bound of the force range and they are overestimated. We believe that misclassification of contact forces in the lowest ranges has a limited impact since the risk of damaging the sclera with such forces is almost null. On the other hand, it is essential that the forces of range 2 are predicted correctly, which appears to be the case on our (limited) data set.

Conclusion and Discussion

This paper introduces a method for improving the safety features of robotized intravitreal injections. We show that our vision-based method, which combines numerical simulation and neural networks, can accurately predict the level of force applied by a needle, using only 2D OCT images of the scleral deformation. By being real-time, this classification can lead to an immediate withdrawal of the needle once it reaches a certain alarm threshold. To cope with the issue of performing a large number of experiments to populate our training data sets, the NN is trained on synthetic images generated from simulations of sclera deformations.

To automatically parameterize the simulations from the experimental data, we use a Kalman filter which performs data assimilation using the sequence of OCT images.

In order to use our method in clinical practice (e.g. in vivo eyes) further simulation efforts should be performed. For instance, anatomically reasonable boundary conditions should be considered such as muscle fixation and eye movement should equally be included. It also seems essential to include the intraocular pressure as an additional input in the data set. Indeed, IOP is known to play a role in the deformation of the sclera and cornea of patients. To perform the prediction, a measure of the IOP would simply need to be performed on the patient using a tonometer. The reason we have not done it yet comes from the inaccuracy of the IOP measurement which is influenced by the stiffness of the eye. This coupling makes it more challenging to parameterize our simulations. Another improvement of the method would be to use adaptive force thresholds depending on the scleral thickness and stiffness as for thinner or softer scleras, the puncture force is lower. The simulated images could also be improved to match actual surgical scenarios better. In particular, adding the shadows generated by the needle in the OCT image would be an essential feature. We also propose to address the sensitivity of the NN predictions to image framing and scaling by randomly cropping each simulated image, and augmenting the data set with these additional images. Note that in this paper, the optical interference phenomenon happening in OCT is not simulated. Instead, the synthetic and real images are binarized. This skeletonization is a way of filtering the complicated aspects of the the OCT images that are a priori noninformative for our purpose. Training a network directly from the OCT images without the skeletonization would lead to a significantly more complex problem requiring the simulation of light propagation and the use of Convolutional Neural Networks.

Finally, the objective of this paper was to estimate a force range, but it would also be pertinent to estimate the location and the angle of the force as a slight error in the latter might damage the retina or the eye lens. In this context we could augment the data set by including various needle insertion angles and locations.

Fig. 1

 1 Fig. 1 (a) Simplified model of the sclera. (b) Deformed hexahedral mesh. Note that the colors of the hexahedra are just for visibility.

Fig. 2

 2 Fig. 2 Artificial neural network used for image classification. The input is an image of size 140 × 40 pixels resulting in an array of size 5600.

Fig. 3

 3 Fig. 3 Continuous acquisition of the robot force sensor and corresponding punctual OCT images for one eye. The vertical lines give the imaging times. eye ID 1 2 3 4 5 Total scleral thickness in µm 800 500 650 560 800 number of samples in class 0 0 1 2 2 2 7 number of samples in class 1 11 2 0 1 1 15 number of samples in class 2 14 2 3 2 2 23 Total 25 5 5 5 5 45

Fig. 4

 4 Fig. 4 (a) Observation points in the real OCT image. (b) Predicted observations (in red) and real observations (in yellow) for the first estimation of E and (c) for the final estimation of E.

Fig. 5

 5 Fig.5Variation of µ and σ for the Young's modulus estimation using the ROUKF for 24 OCT images. The value of the parameter converges to 0.27 M P a.

Fig. 6

 6 Fig.6Real OCT images of the eye used for the data assimilation and matching simulated images with E = 0.25 M P a for the three force ranges.

Fig. 7

 7 Fig. 7 Real OCT images of the sclera and their matching simulated images with E = 0.25 M P a for the three different force ranges.

3. 3 Fig. 8

 38 Fig. 8 (a) Loss and Accuracy curves for training and validation sets. (b) Fragment of the training data set generated by our numerical simulation.

Fig. 10

 10 Fig.10Filtered force values corresponding to the 45 OCT acquisitions. The three misclassified samples are overestimated. Note that we only kept the samples under 0.06N which is the point of rupture of the thinnest scleras. To correctly account for the elements above that point of rupture, the puncturing process should be included in our model which would complicate the simulation without bringing any gain.

Table 2

 2 Mean and standard deviation of the estimated Young's modulus in 4 different porcine eyes after performing a data assimilation with a ROUKF. The fifth eye is not included since the observations required in the assimilation process are not consistent across the OCT acquisitions for this eye.

Table 3

 3 Confusion matrix

	Target	Prediction	Class 0	Class 1	Class 2	Precision
	Class 0		5	2	0	0.71
	Class 1		0	14	1	0.93
	Class 2		0	0	23	1.00
	Recall		1.00	0.88	0.96

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Acknowledgements The authors would like to thank Jan Hermann and Tatiana Fountoukidou for the help in the experimental data gathering, and Igor Peterlik for his advice and code on Bayesian filtering.

Conflict of Interest:

The authors declare that they have no conflict of interest. This article does not contain any studies with animals performed by any of the authors.

Informed consent: This articles does not contain patient data.