Peyman Khajavi

Jérome Chevalier

Peter Vang Hendriksen

Joe W Tavacoli

Laurent Gremillard

Henrik Lund Frandsen

Jérôme Chevalier

Peter Vang Hendriksen

Double Torsion testing of thin porous zirconia supports for energy applications: Toughness and slow crack growth assessment

Keywords: Slow crack growth, Porosity, Double torsion, Solid oxide cells, Energy applications

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Ceramics are brittle materials: they fail before plasticity, at low strains and they are sensitive to the presence of defects. Such brittleness needs careful attention when a porous ceramic component with low thickness is desired, as it is the case with thin ceramic membranes and in solid oxide fuel and electrolysis cells (SOCs) [START_REF] Klemensø | Development of a novel ceramic support layer for planar solid oxide cells[END_REF][START_REF] Li | Toughening macroporous alumina membrane supports with YSZ powders[END_REF][START_REF] Atkinson | Mechanical behaviour of ceramic oxygen ion-conducting membranes[END_REF]. Zirconia is one of the most interesting materials in this context due to its excellent combination of fracture toughness and strength [START_REF] Chevalier | The tetragonal-monoclinic transformation in zirconia: Lessons learned and future trends[END_REF]. In addition to its use in dense structures, zirconia and zirconia-toughened materials are thus promising alternatives for use in thin porous components, where a material with high crack resistance is required.

Crack resistance is often described in terms of fracture toughness, KIC, which represents the critical stress intensity factor at which fast fracture occurs. Nevertheless, the mechanical reliability of zirconia like many other oxide ceramics is affected by the Slow (also referred to as Subcritical) Crack Growth (SCG), which represents slow-crack propagation at stress intensity factors below the critical value for fast fracture (KIC). This influences the long-term reliability and lifetime of the ceramic, since it may cause delayed failure. Fortunately, there is a threshold stress intensity factor, KI0, below which the crack propagation rate tends to zero [START_REF] Chevalier | Nanostructured ceramic oxides with a slow crack growth resistance close to covalent materials[END_REF][START_REF] Olagnon | Global description of crack propagation in ceramics[END_REF]. Hence, judicious material selection for a given application requires evaluation of KI0 alongside KIC. For SOCs the stresses are to a high degree determined by thermal gradients, which are sustained over thousands of hours, making KI0 highly relevant [START_REF] Molla | Modeling the Mechanical Integrity of Generic Solid Oxide Cell Stack Designs Exposed to Long-term Operation[END_REF].

SCG is especially promoted in water-containing environments, due to the interaction of water molecules with cracks surfaces. This process has been studied in different environments containing water molecules, such as humid air, water and body fluid. The studies have focused mostly on dense systems [START_REF] De Aza | Crack growth resistance of alumina, zirconia, and zirconia toughened alumina ceramics for joint prostheses[END_REF][START_REF] Zhang | Slow crack growth and hydrothermal aging stability of an alumina-toughened zirconia composite made from La2O3doped 2Y-TZP[END_REF][START_REF] Benzaid | Fracture toughness, strength and slow crack growth in a ceria stabilized zirconia-alumina nanocomposite for medical applications[END_REF][START_REF] Chevalier | Subcritical Crack Propagation in 3Y-TZP Ceramics: Static and Cyclic Fatigue[END_REF][START_REF] Gremillard | Improving the Durability of a Biomedical-Grade Zirconia Ceramic by the Addition of Silica[END_REF]. The measured threshold intensity factor has been reported to be considerably lower than the fracture toughness. For example, De Aza and co-workers [START_REF] De Aza | Crack growth resistance of alumina, zirconia, and zirconia toughened alumina ceramics for joint prostheses[END_REF] measured the fracture threshold of dense 3Y-TZP as approximately 44 % lower than its fracture toughness. In other words, crack propagation can occur at stress intensity factors of 56 % of the toughness in such ceramics, which shows the importance of having the full picture of the crack rate, V, versus applied stress intensity factor, KI (V-KI curves), including KI0. The susceptibility to SCG is also of great importance in porous zirconia ceramics. Boccaccini and co-workers [START_REF] Boccaccini | Influence of porosity on mechanical properties of tetragonal stabilized zirconia[END_REF] studied the mechanical properties of porous 3YSZ ceramics and observed the threshold intensity factor of 49 and 54 % porous samples to be approximately 45 and 52 % lower than their fracture toughness, respectively. Radovic and co-workers [START_REF] Radovic | Fracture Toughness and Slow Crack Growth Behavior of Ni-YSZ and YSZ as a Function of Porosity and Temperature[END_REF] investigated the SCG behavior of porous Ni-8YSZ samples. The authors reported a decrease of the threshold intensity factor with porosity and temperature.

For most oxide ceramics in their dense form, including zirconia and zirconia-toughened ceramics, the V-KI curves observed in air typically consist of three distinct stages and the threshold value (KI0) [START_REF] Chevalier | Nanostructured ceramic oxides with a slow crack growth resistance close to covalent materials[END_REF][START_REF] Freiman | Effect of chemical enviroments on slow crack growth in glasses and ceramics[END_REF], as schematically shown with the curve a in Figure 1.

The first stage (stage I) corresponds to a regime where the rate of crack propagation is limited by the reaction rate between corrosive molecules (e.g. water) and atomic bonds at the crack tip. In the second stage (stage II), the crack growth is controlled by the transport rate of the corrosive molecules and in the third stage (stage III) higher ranges of crack velocities are witnessed, where the crack propagation is relatively independent of the corrosive environment [START_REF] Freiman | Effect of chemical enviroments on slow crack growth in glasses and ceramics[END_REF][START_REF] Lawn | Chemical processes in crack propagation: kinetic fracture[END_REF].

In each stage, the relation between the crack velocity, V, and stress intensity factor, KI, can be represented by a power law:

𝑉 = 𝐴 𝐾 𝐼 𝑛 (1)
where A and n are slow crack growth parameters.

The values of A, n and KI0 depend not only on the material but also on the type and concentration of corrosive agents and the temperature. The variation of these factors can lead to changes in the V-KI curves. For instance, for zirconia and zirconia-toughened ceramics it has been shown that increasing the concentration of water molecules and the temperature shift the first and second stages to higher crack velocities [START_REF] Chevalier | Subcritical Crack Propagation in 3Y-TZP Ceramics: Static and Cyclic Fatigue[END_REF], as schematically illustrated in Figure 1. For crack propagation in water (curve d), only one stage is observed as the crack rate is no longer limited by the diffusion rate of water molecules from the crack mouth to the crack tip. Double torsion is a simple yet powerful method to measure fracture toughness and study the slow crack growth behavior of brittle ceramics. Using the double torsion method, the V-KI diagrams can readily be obtained through load relaxation experiments. Analytical analysis of double torsion specimens indicates that the stress intensity factor is independent of crack length [START_REF] Evans | A method for evaluating the time-dependent failure characteristics of brittle materials -and its application to polycristalline alumina[END_REF][START_REF] Williams | A Simple Method for Studying Slow Crack Growth[END_REF]. However, it has been shown that for an accurate determination of stress intensity factor, crack length needs to be considered [START_REF] Ferber | Subcritical Crack Growth in Dense Alumina Exposed to Physiological Media[END_REF][START_REF] Chevalier | Double-torsion testing a 3Y-TZP ceramic[END_REF][START_REF] Ebrahimi | Slow crack-growth behavior of alumina ceramics[END_REF][START_REF] Shyam | The double-torsion testing technique for determination of fracture toughness and slow crack growth behavior of materials: A review[END_REF]. Different corrections are thus suggested to obtain a more accurate evaluation of the stress intensity factor, KI. Chevalier and co-workers [START_REF] Chevalier | Double-torsion testing a 3Y-TZP ceramic[END_REF] showed experimentally that the stress intensity factor is dependent on the crack length with the following equation:

𝐾 𝐼 = 𝐾 𝐼(𝑎𝑛𝑎𝑙𝑦𝑡𝑖𝑐𝑎𝑙) ( 𝑎 𝑎 0 ) 𝛾 (2)
where KI(analytical) is derived from an analytical solution (introduced in the experimental section), and a0 and a are the notch and crack length, respectively. The γ value for a 2 mm thick 3Y-TZP sample was found experimentally to be 0.18 [START_REF] Chevalier | Double-torsion testing a 3Y-TZP ceramic[END_REF]. Using a three dimensional finite element analysis (FEA), Ciccotti and co-workers [START_REF] Ciccotti | Realistic Finite-Element Model for the Double-Torsion Loading Configuration[END_REF][START_REF] Ciccotti | The double torsion loading configuration for fracture propagation: An improved methodology for the load-relaxation at constant displacement[END_REF] concluded that crack length and geometrical parameters should also be considered in the calculation of stress intensity factor. This was mainly attributed to the non-linear compliance to crack length relationship. A similar conclusion is also drawn by Becker and co-workers [START_REF] Becker | An Evaluation of the Double Torsion Technique[END_REF]. Application of these corrections has also been considered in later studies. Becker and co-workers [START_REF] Becker | An Evaluation of the Double Torsion Technique[END_REF] showed that the Chevalier's correction overestimates the stress intensity factor, while it is underestimated when employing the Ciccotti's correction. Madjoubi and co-workers [START_REF] Madjoubi | Experimental evaluation of the double torsion analysis on soda-lime glass[END_REF] reported that applicability of the analytical model, the corrected model by Chevalier and Ciccotti are all restricted to specific geometries and a general correction cannot be applied. The aforementioned studies highlight the importance of the samples geometry to the dependency of stress intensity factor on the crack length and indicate that the evolution of KI versus crack length should be assessed for any new sample geometry.

In this work, the applicability of the double torsion technique to study the slow crack growth behavior of thin porous zirconia samples was thus assessed, since this, to the best of authors' knowledge, has not been reported before. The study was performed on three mol% yttria stabilized zirconia (3Y-TZP), as it is one of the most studied tetragonal zirconia ceramics -being material of interest for porous support in asymmetric ceramic membranes and the support layer of solid oxide fuel and electrolysis cells [START_REF] Klemensø | Development of a novel ceramic support layer for planar solid oxide cells[END_REF][START_REF] Boccaccini | Influence of porosity on mechanical properties of tetragonal stabilized zirconia[END_REF][START_REF] Escribano | Shaping of 3YSZ porous substrates for oxygen separation membranes[END_REF]. SCG behavior of porous samples, ranging from 4.5 to 45.5% porosity with thickness of ca. 0.25 mm was then investigated, as zirconia ceramics used for such applications are not dense. Variation of fracture toughness and threshold stress intensity factor with porosity is also reported.

Experimental

Sample preparation

The samples studied in this work were prepared from commercial 3 mol% yttria doped zirconia (3YSZ) powders, (TZ-3Y, TOSOH Corporation) by tape casting [START_REF] Ramousse | Manufacturing of Anode-Supported SOFC's: Processing Parameters and their Influence[END_REF][START_REF] Pihlatie | Dimensional behaviour of Ni-YSZ anode supports for SOFC under RedOx cycling conditions[END_REF]. The manufactured tapes had a thickness of approx. 300 µm after drying, and were cut into different sheets. The green sheets were sintered for 15 h at different temperatures, i.e. 1060, 1200, 1300 and 1340°C.

The sintered samples were laser cut to the size of 20×34 mm 2 . On all specimens, a 500 µm width notch with a length of 8 mm was also laser cut. To obtain a sharp notch tip, the last two millimeters were cut with a V-shape. The sample and notch configuration is shown in Figure 2. Some of the samples were also cut to the dimension of 20×40 mm 2 (and a 10 mm long notch). The results of compliance analysis and toughness measurements on the 34 and 40 mm long samples were completely consistent.

Characterization

The microstructure of the samples was examined using field emission scanning electron microscopy (FE-SEM, Merlin, Carl Zeiss, Germany). The samples were polished and thermally etched at 50°C below their corresponding sintering temperature for 0.5 h, with heating and cooling rate of 8 °C/min, to reveal the microstructure. The sample sintered at 1060°C was thermally etched at 1150°C as the grain boundaries could not be delineated after etching at 1010°C. Grain size distribution and average grain size of the samples were estimated by measuring the size of 150 grains in each sample.

The crack lengths of the samples after relaxation tests were evaluated using electron and optical microscopy. Porosity of the specimens was measured considering their mass and geometric dimensions and the theoretical density of 3YSZ (6.05 g/cm 3 ). X-ray diffraction (XRD, Bruker D8) was used to study the crystalline phase of the sintered samples. The crystalline phase of fractured surfaces after toughness measurement was investigated by Raman spectroscopy (Renishaw InVia spectrometer).

Mechanical testing

The loading configuration of the double torsion test is presented in Figure 2. The V-KI curves were determined by the load relaxation method as first suggested by Williams and Evans [START_REF] Williams | A Simple Method for Studying Slow Crack Growth[END_REF]. In our experiments, samples were loaded with a displacement rate of 0.6 mm/min. When the load (P) reached approximately 0.95 of the critical load for failure (PIC), the crosshead was stopped. Under this constant displacement condition, the load relaxation occurs because of the crack propagation. The load versus time curve was monitored and used for the analysis. The stress intensity factor at the crack tip is first calculated using the analytical equation of the stress intensity factor for the double torsion specimen (without considering its variation with crack length) [START_REF] Evans | A method for evaluating the time-dependent failure characteristics of brittle materials -and its application to polycristalline alumina[END_REF][START_REF] Williams | A Simple Method for Studying Slow Crack Growth[END_REF]:

𝐾 𝐼(𝑎𝑛𝑎𝑙𝑦𝑡𝑖𝑐𝑎𝑙) = 𝑃𝑊 𝑚 𝑡 2 ( 3(1 + 𝜈) 𝑊𝜓(𝑡, 𝑊) ) 1 2 ⁄ ( 3
)
where Wm is the moment arm, and W and t are the width and thickness of the specimen, respectively. ν is the Poisson ratio and 𝜓(𝑡, 𝑊) a thickness correction factor given by [START_REF] Fuller | An Evaluation of Double-Torsion Testing -Analysis[END_REF]:

𝜓(𝑡, 𝑊) = 1 -1.2604( 𝑡 𝑊 ⁄ ) + 2.4( 𝑡 𝑊 ⁄ )exp( -𝑊𝜋 2𝑡 ⁄ ) (4)
Eq. 3 gives the stress intensity factor for a plane stress condition assuming that KI is independent of crack length. The applicability of this equation was next assessed experimentally on the specified samples.

The compliance (C) of the double torsion specimen, defined as the ratio of the specimen deflection (Δ) to the load, was obtained for samples with different porosities from the slope of loaddisplacement curves at different crack lengths.

The initial analysis of double torsion, as proposed by Williams and Evans [START_REF] Williams | A Simple Method for Studying Slow Crack Growth[END_REF] considers that compliance is a linear function of crack length (a)

𝐶 = 𝛥 𝑃 = 𝐵𝑎 + 𝐷 (5)
where B and D are constants depending on the material and geometry. Theoretical analysis of the compliance of double torsion specimens gives the following analytical expression for B:

𝐵 = 6𝑊 𝑚 2 (1 + 𝜈) 𝐸𝑊𝑡 3 𝜓(𝑡, 𝑊) (6)
where E and ν are the Young's modulus and Poisson's ratio, respectively.

To check for linear behavior, compliance versus crack length curves were therefore experimentally obtained for samples with different porosities.

During a load relaxation tests, the crack growth rate, V, can be determined using the compliance analysis. If the compliance follows Eq. 5, the crack velocity at constant displacement (Δ=const.) can be derived to be

𝑉 = ( 𝑑𝑎 𝑑𝑡 ) ∆ = - 𝑃 𝑖,𝑓 𝑃 2 [𝑎 𝑖,𝑓 + 𝐷 𝐵 ⁄ ] ( 𝑑𝑃 𝑑𝑡 ) ∆ (7)
In Eq. 7, Pi,f and ai,f are the load and crack length, respectively in the initial (i) or final (f) stages, and t refers to time. Use of final values is usually preferred, as the initial crack length might not be accurately determined due to the possible crack propagation at the end of the loading stage before the relaxation experiments [START_REF] Madjoubi | Experimental evaluation of the double torsion analysis on soda-lime glass[END_REF]. P and ( 3) and V also vary with time, thus this method enables plotting V-KI curves.

The fracture toughness of the samples was obtained by performing the tests using a fast displacement rate (6 mm/min) in N2 atmosphere (to avoid the possible SCG effect caused by air humidity), both at room temperature and 800°C. In addition, the double torsion tests were carried out in ambient environment with a displacement rate of 0.6 mm/min, and the apparent toughness of the samples under these conditions was determined.

Results and discussion

Characteristics of the samples

The porosity, thickness and average grain size of the samples are summarized in Table 1. The samples are denoted as 3Y-TZP-X, where X represents the average porosity in percentage. The XRD patterns of the samples sintered at different temperatures showed that all the materials are in the tetragonal crystalline form. The grain size distribution of the 3Y-TZP-45.5% is consistent with the particle size of the starting powder (as reported by the supplier to be around 40 nm). This indicates that the sintering process at 1060°C is in the initial stage of sintering, before the grain growth [START_REF] Coble | Sintering crystalline solids. I. intermediate and final state diffusion models[END_REF]. It also assures that the short thermal etching of the 3Y-TZP-45.5% at 1150°C (slightly higher than its sintering temperature) did not cause grain growth. 7) 40 [START_REF] Benzaid | Fracture toughness, strength and slow crack growth in a ceria stabilized zirconia-alumina nanocomposite for medical applications[END_REF] The SEM micrographs of the 3Y-TZP-45.5%, 3Y-TZP-25% and 3Y-TZP-4.5% (Figure 3) show the very small grain size of the sintered materials. A 3Y-TZP ceramic with a fine grain microstructure can be considered as a brittle polycrystalline material that will show R-curve behavior only over very small crack lengths (5-10 µm) [START_REF] Liu | Fatigue of Yttria-Stabilized Zirconia: I, Fatigue Damage, Fracture Origins, and Lifetime Prediction[END_REF][START_REF] Dransmann | Indentation Studies on Y2O3-Stabilized ZrO2: II, Toughness Determination from Stable Growth of Indentation-Induced Cracks[END_REF]. Consequently, the effect of the R-curve behavior on the V-KI curves evaluated in this work can be neglected.

Figure 4a,b illustrates the notch tip and the crack as propagated from the notch after a load relaxation experiment carried out on 3Y-TZP-25%. The notch radius is approximately 50 µm. Figure 4c shows the SEM micrograph of the crack tip.

Compliance analysis

Figure 5 shows the results of the compliance analysis for samples with different porosities. The samples vary not only with respect to porosity, but also (unintendedly) with respect to thickness. To exclude the effect of thickness, enabling a better comparison, the compliance values were multiplied by the cube of thickness (C.t 3 ) in the plot versus the crack length (see Eqs. 5 and 6). As seen, variation of the compliance of all the porous 3Y-TZP samples with crack length in the investigated range (up to 30 mm) can, to a very good approximation, be considered linear. In addition, clearly, the slope of the curves decreases by increasing sample porosity. The experimental B and D values (Eq. 5) calculated from the linear regression of the compliancecrack length data are presented in Table 2. The Young's modulus (E) of the samples at different porosities (derived based on the Eq. 6) are compared with literature values of 3Y-TZP [START_REF] Selçuk | Elastic properties of ceramic oxides used in solid oxide fuel cells (SOFC)[END_REF] and are in a good agreement with the previously reported values. Thus, the linear regression approach provides trustworthy results, although the sample geometry is complex.

Fracture toughness and toughening effect

Table 3 presents the fracture toughness of the 3Y-TZP samples. The apparent toughness of the samples, measured in ambient air with a displacement rate of 0.6 mm/min is also provided in Table 3. It is clear that the stress corrosion caused by the air humidity has a significant effect on the measured toughness, as the toughness values in air are approximately 5-20 % lower than when measured in N2.

The toughness of 3YSZ-4.5% is slightly lower than the value reported for a dense 3Y-TZP (6.1 MPa.m 1/2 ) [START_REF] Chevalier | Subcritical Crack Propagation in 3Y-TZP Ceramics: Static and Cyclic Fatigue[END_REF]. Also, the toughness of the samples with higher porosities is significantly lower. In addition to the effect of porosity, the lower fracture toughness could be a consequence of the very small grain sizes of the studied samples that reduce the tendency of the tetragonal grains to transform to the monoclinic phase hence decrease the effect of phase transformation toughening. In a tetragonal zirconia ceramic, the transformation toughening mechanism is facilitated if the size of grains is close to the critical grain size for the tetragonal to monoclinic phase transformation. If the grains are much smaller than this critical grain size, the tetragonal phase is over-stabilized, i.e. it does not have the potential to transform to the monoclinic phase upon an applied stress. For a dense 3Y-TZP, the critical grain size for the tetragonal to monoclinic phase transformation is approximately 1 micron [START_REF] Lange | Transformation toughening -Part 3 Experimental observations in the ZrO2-Y2O3 system[END_REF] (though higher values have also been reported [START_REF] Trunec | Effect of grain size on mechanical properties of 3Y-TZP ceramics[END_REF]). The effectiveness of transformation toughening in 3Y-TZP ceramics having grain size below approximately 300 nm has been questioned in literature [START_REF] Trunec | Effect of grain size on mechanical properties of 3Y-TZP ceramics[END_REF][START_REF] Eichler | Effect of grain size on mechanical properties of submicrometer 3Y-TZP: Fracture strength and hydrothermal degradation[END_REF]. The average grain size of the samples studied in this work varies from 40-238 nm. It is thus questionable if there is any phase transformation toughening in the tested samples.

Raman spectroscopy analysis of the samples studied in the current work (at different porosities) showed no monoclinic phase on the fractured surfaces. A similar observation is also reported by Theunissen and co-workers [START_REF] Theunissen | Mechanical properties of ultra-fine grained zirconia ceramics[END_REF], where no monoclinic phase could be detected in the fractured surfaces of 2.5YSZ samples with grain sizes of 180 and 300 nm. This might suggest that the transformation toughening mechanism is not effective in the samples studied in this work. However, the measured values of toughness are significantly higher than 8YSZ cubic zirconia samples reported in literature, where no transformation toughening effect is present. For instance, fracture toughness of 8YSZ ceramics having pure cubic phase, 97.6% of the theoretical density and average grain size of 295 nm is reported to be 3.16 MPa.m 1/2 [START_REF] Mazaheri | Two-step sintering of nanocrystalline 8Y2O3 stabilized ZrO2 synthesized by glycine nitrate process[END_REF]. Nevertheless, the 3Y-TZP-8% has 25% higher fracture toughness (3.95 MPa.m 1/2 ), despite its higher porosity. Furthermore, the fracture toughness of 3Y-TZP-8% at 800°C was measured to be 1.62 MPa.m 1/2 (see Table 3); this is approximately 60% lower than the room temperature value (3.95 MPa.m 1/2 ). The high fracture toughness in the porous 3Y-TZP samples is unlikely to be a consequence of ferroelastic domain switching, as this toughening mechanism has not been reported in fine grained TZP ceramics [START_REF] Theunissen | Mechanical properties of ultra-fine grained zirconia ceramics[END_REF][START_REF] Dash | Transparent tetragonal-cubic zirconia composite ceramics densified by spark plasma sintering and hot isostatic pressing[END_REF]. In addition, ferroelastic toughening is temperature invariant [START_REF] Virkar | Ferroelastic Domain Switching as a Toughening Mechanism in Tetragonal Zirconia[END_REF], so its effect should not decrease at 800°C, in contrast to the toughness results obtained in this work.

The increased fracture toughness compared to the cubic 8YSZ sample as well as the observed decrease in toughness with increasing temperature, which is a typical characteristic of the transformation toughening mechanism [START_REF] Hannink | Transformation Toughening in Zirconia-Containing Ceramics[END_REF], therefore suggests that there is some transformation toughening even in the fine grained samples studied here. Note, the tetragonal to monoclinic phase transformation zone in a tetragonal zirconia ceramic under fracturing can be very small. For instance, Zhang and co-workers [START_REF] Zhang | Trade-off between fracture resistance and translucency of zirconia and lithium-disilicate glass ceramics for monolithic restorations[END_REF] have observed this transformation zone in 3Y-TZP average grain size of around 300 nm to be 1 micron. This very small transformation zone can therefore make it difficult to detect any monoclinic phase using Raman spectroscopy in the fractured surfaces of porous, fine grained ceramics studied in this work.

Increasing porosity will usually lower the critical grain size due to the lower levels of strain energy. Furthermore, in a porous material the tetragonal grains can more easily undergo the stress induced transformation resulting from the lower stiffness of the neighboring matrix [START_REF] Lange | Transformation toughening-Part 3 Experimental observations in the ZrO2-Y2O3 system[END_REF]. Thus, the tetragonal to monoclinic phase transformation may take place for smaller grain sizes in a porous material compared to a dense one, as is hypothesized in the present work. Nevertheless, detailed crystalline phase analysis of the fractured surfaces would be required to confirm this hypothesis.

Slow crack growth behavior

Figure 6 shows typical load relaxation curves for the studied samples. Having very thin and porous specimens, the measurements entailed working at small loads (in the range of ≈ 0.4-2.5 N) and monitoring very small load drops (≈ 0.1-0.7 N) under the relaxation. The low noise level compared to the systematic variations indicates that the measurements can be considered reliable. Figure 7 shows the V-KI curves obtained from the successive relaxation tests for samples with different porosities. For each porosity, the successive relaxation tests were carried out on the same sample. For the 3Y-TZP-4.5% and 3Y-TZP-8%, a clear shift to lower intensity factors and higher crack velocities is observed. This indicates a clear dependency of the stress intensity factor on the crack length in the test, even with the very thin samples studied (t : W : L ≈ 1 : 75 : 130). The disparity between the two V-KI curves reduces for the samples with higher porosities, i.e. 3Y-TZP-25% and 3Y-TZP-45%.

The geometry of the samples investigated in this work is very different from those studied by Ciccotti and co-workers [START_REF] Ciccotti | Realistic Finite-Element Model for the Double-Torsion Loading Configuration[END_REF][START_REF] Ciccotti | The double torsion loading configuration for fracture propagation: An improved methodology for the load-relaxation at constant displacement[END_REF]. Applying the Ciccotti's correction would thus require extrapolation to very long ranges, which is not recommended by the authors. Here, we followed the strategy proposed by Chevalier et al. [START_REF] Chevalier | Double-torsion testing a 3Y-TZP ceramic[END_REF] and considered variation of KI versus a given by Eq. 2, but with an experimental re-evaluation of the γ component. The corrected V-KI curves are accordingly presented in Figure 7. For each porosity, an exponent providing the best result in reunifying the different curves was determined. The γ exponent for 3Y-TZP-4.5%, 3Y-TZP-8%, 3Y-TZP-25% and 3Y-TZP-45.5% was calculated to be 0.22, 0.21, 0.1 and 0.08, respectively. As seen, the empirical correction primarily obtained for samples with dimensions of t : W : L ≈ 1 : 10 : 20 [START_REF] Chevalier | Double-torsion testing a 3Y-TZP ceramic[END_REF] can be applied for the porous samples studied in this work, after a modification in the value of exponent. That is, by increasing porosity, a lower exponent value is required for the reproducibility of successive V-KI curves.

To explain the change of stress intensity factor in samples with different porosities, the crack length in the tensile and compressive sides of the 3YSZ-4.5% and 3YSZ-25% was accurately measured using SEM. The difference in crack length for the 3YSZ-4.5% was 1.94 mm, while the corresponding value in the 3YSZ-25% was 0.23 mm. This means a lower curvature of crack front (see Figure 2) in the sample at higher porosity. As discussed by Chevalier and co-workers [START_REF] Chevalier | Double-torsion testing a 3Y-TZP ceramic[END_REF] the dependency of stress intensity factor on crack length cannot be due to the change of crack surface area as the crack propagates, neither can it be explained by the corrections considering the effect of curved crack front on crack velocity. However, the buildup of differences in crack length on the tensile and compressive sides, that leave relatively more and more unbroken ligaments on the latter, is a plausible explanation to account for the dependency of the stress intensity factor on crack length. Our work supports this hypothesis; we see a lower dependency of the stress intensity factor with crack length for samples with high porosity, i.e. samples that display smaller differences in crack length, than samples with low porosity. This decreased dependency manifests itself as a lower coefficient in Eq. 2.

V-KI curves for samples with different porosities, calculated using the above-obtained correction coefficients, are shown in Figure 8. The typical three-stages SCG behavior of zirconia ceramics in air is distinguishable in the V-KI curve of the 3Y-TZP-4.5%. The second stage occurs at a crack velocity of approximately 5×10 -4 m/s. 3Y-TZP-8% also shows the three typical stages but with a very narrow second stage. For 3Y-TZP-25% and 3Y-TZP-45.5% samples, only one stage is seen in the crack velocity range of 10 -6 -10 -3 m/s. Crack propagation in the first stage of the V-KI diagram (curve a, Figure 1) is basically controlled by the rate of reaction between the corrosive molecules and chemical bonds of the ceramic at cracks tips. This stage is highly affected by the chemical concentration, temperature and applied stress. Stage II, corresponds to the state where the crack growth is controlled by diffusion of corrosive species to the crack tip. Here, the crack velocity is basically constant. Stage II connects stage I to the stage III, where the crack velocity increases rapidly with the applied stress. The crack propagation rate in the third stage is usually higher than the transport rate of corrosive species to the crack tip. Consequently, the separation of crack surfaces happens without a necessary interaction of reactive species with ceramic bonds. This is similar to the crack propagation without the presence of corrosive species, such that stage III can be approximately corresponded to the fast fracture (KI = KIC) [START_REF] Freiman | Effect of chemical enviroments on slow crack growth in glasses and ceramics[END_REF][START_REF] Lawn | Chemical processes in crack propagation: kinetic fracture[END_REF].

Although the SCG experiments in the present study are only carried out in laboratory air, assuming that the stress-corrosion is caused by water molecules present in air is realistic, as the waterassisted crack propagation in zirconia has well been reported in literature [START_REF] Zhang | Slow crack growth and hydrothermal aging stability of an alumina-toughened zirconia composite made from La2O3doped 2Y-TZP[END_REF][START_REF] Benzaid | Fracture toughness, strength and slow crack growth in a ceria stabilized zirconia-alumina nanocomposite for medical applications[END_REF][START_REF] Chevalier | Subcritical Crack Propagation in 3Y-TZP Ceramics: Static and Cyclic Fatigue[END_REF][START_REF] Gremillard | Improving the Durability of a Biomedical-Grade Zirconia Ceramic by the Addition of Silica[END_REF]. Chevalier and coworkers [START_REF] Chevalier | Subcritical Crack Propagation in 3Y-TZP Ceramics: Static and Cyclic Fatigue[END_REF] reported the slow crack growth behavior of dense 3Y-TZP in ambient air and water. In air, the typical trimodal behavior was observed, and the second stage occurred at the crack velocities of around 10 -4 m/s. In water, however, only one stage was seen, with a slope close to the slope of the first stage obtained in ambient air. The reason can be explained considering that the transfer of water molecules to the crack tip is increased at higher concentration, indicating that the water molecules can interact with the crack tip even at higher crack propagation rates. Accordingly, the second stage shifts to higher crack velocities, as seen in Figure 1. In liquid water, in particular, the water molecules can diffuse and interact with the ceramic bonds even at high crack velocities.

In this work, we evidence a clear role of the porosity on the features of the V-KI curves, which can be explained on the basis of the ability of water molecules to access the crack tip. In the 3Y-TZP-4.5% and 3Y-TZP-8%, the second stage occurred at higher crack velocities than previously reported for dense samples (10 -4 m/s, reported for example in [START_REF] Chevalier | Subcritical Crack Propagation in 3Y-TZP Ceramics: Static and Cyclic Fatigue[END_REF] and [START_REF] Zhang | Trade-off between fracture resistance and translucency of zirconia and lithium-disilicate glass ceramics for monolithic restorations[END_REF]), as water molecules have easier access to the adsorption sites at the crack tip because of residual porosity. In 3Y-TZP-25% and 3Y-TZP45%, only one stage was observed, due to the highly connected porosity of the materials, providing a full percolation (the corrosive species can always reach the crack tip, without any crack rate limitation even in air).

The slow crack growth parameters (n and A) were determined for the first stage of the V-KI curves of 3Y-TZP-4.5% and 3Y-TZP-8% and the entire V-KI curves of 3Y-TZP-25% and 3Y-TZP-45.5%. The results are presented in Table 3.

The fracture thresholds, KI0, for 3Y-TZP samples were estimated by extrapolating the first stage of the corresponding V-KI curves to the crack velocity of 10 -11 m/s. Figure 9 presents the estimated fracture threshold together with toughness of the samples at different porosities. The ratio of fracture threshold to fracture toughness (KI0/KIC) of the samples at different porosities is also presented in Figure 9. As seen, KI0/KIC ratio for all samples is found to be around 0.56 ± 0.06. The crack growth in the samples can therefore occur at stresses as low as 50% of the fracture stress.

The relatively similar KI0/KIC ratio for samples at different porosities can be explained considering the basic Griffith criterion for brittle fracture [START_REF] Griffith | The phenomena of rupture and flow in solids[END_REF]: The critical stress for fracture in a brittle material (σc) is proportional to:

𝜎 𝑐 ∝ √𝐸𝛾 ( 8
)
where E is the Young's modulus of the material, and γ is the surface energy.

In fact, the intrinsic surface energy of a given material is specified considering a fracturing in vacuum, corresponding to the fracture toughness of the material. In a corrosive atmosphere, the surface energy decreases resulting from the interaction of corrosive molecules with the material at the crack tip; the reason why under SCG condition the material can fail at stress intensity factors below its fracture toughness [START_REF] Olagnon | Global description of crack propagation in ceramics[END_REF][START_REF] Lawn | Chemical processes in crack propagation: kinetic fracture[END_REF]. Consequently, the KI0/KIC ratio is correlated to the difference in surface energy under vacuum and in a reactive environment, and hence it be independent of the porosity of the material.

From Figure 9, it is seen that at porosities above ≈ 25%, which is the range of interest for many energy applications of the material, the KI0 drops to very low values, well below 1.5 MPa.m 1/2 . These significantly low ranges of fracture thresholds thus need to be considered when designing thin and porous zirconia based ceramics for energy devices, to fulfill their long term mechanical reliability.

Conclusions

In this work, the slow crack growth behavior of thin (~0.25 mm), porous 3Y-TZP samples, having a porosity in the range from 4.5 to 45.5%, were studied. The fracture toughness, fracture threshold and slow crack growth parameters of the samples were determined, highlighting:  The compliance of the specimens was concluded to be a linear function of crack length.

Previous analyses of the double torsion specimen could be applied here, with some calibration on the KI versus crack length equations. The KI (a) dependency decreased with increasing the porosity of samples. This was explained by the lower extent of unbroken ligaments in samples at higher porosities.  The V-KI curves of the sample with the lowest porosity exhibited the typical trimodal SCG behavior, as shown in previous works for dense 3Y-TZP. As porosity increased, the length of the second stage decreased. In samples with 25% porosity and higher, only one stage was observed, because of the easier access of water molecules to the crack tip.  No monoclinic phase could be detected on the fractured surfaces of the samples.

However, some transformation toughening was hypothesized to take place to account for the results even in the fine grained samples studied.  The KI0/KIC ratio for porous 3Y-TZP samples was determined to be consistent with previous works on dense materials, with a value of 0.56 ± 0.06.  The SCG experiments in the present study were conducted in ambient air and at room temperature. The results can well be applied when e.g. the handling, storage or room temperature use of the components are concerned. However, a full picture of the SCG behavior of the materials is drawn when the phenomenon is also studied under other relevant conditions of use for a given application. For instance, for SOCs applications the SCG studies at 800°C (i.e. the typical operating temperature of the cells) would add complementary information and should also be considered.

Figure 1 :

 1 Figure 1: Typical crack velocity versus stress intensity factor (V-KI) curves observed in (a) air and (d) water. Increasing humidity and temperature of the environment will shift the first and second stages to higher crack velocities as schematically shown by curves (a) to (d).

Figure 2 :

 2 Figure 2: Loading configuration of the double torsion measurement, specimen and notch geometries; the typical curved crack front in double torsion experiments is shown schematically.

  from the load-relaxation experiments. Since P and ( 𝑑𝑃 𝑑𝑡 ) ∆ vary with time (as the crack propagates and the compliance changes), both KI (from eq.

Figure 3 :

 3 Figure 3: SEM micrographs of the polished and thermally etched samples (a) 3Y-TZP-45.5%, (b) 3Y-TZP-25% and (c) 3Y-TZP-4.5%.

Figure 4 :

 4 Figure 4: (a) SEM and (b) optical microscopy images of the notch tip and the propagated crack from the notch and (c) SEM image of the crack tip in the tested 3Y-TZP-25%. The crack path and crack tip in (c) are shown by the black and red arrows, respectively.

Figure 5 :

 5 Figure 5: Compliance analysis of samples with different porosities; a and t refer to the crack length and samples thickness, respectively. The data at a = 8 mm correspond to the compliance analysis for the notch (i.e. before any crack growth).

Figure 6 :

 6 Figure 6: Typical load relaxation curves obtained in this work.

Figure 7 :

 7 Figure 7: V-KI curves for successive relaxation tests in (a) 3Y-TZP-45.5%, (b) 3Y-TZP-25%, (c) 3Y-TZP-8% and (d) 3Y-TZP-4.5%, without (solid symbols) and with (open symbols) correction.

Figure 8 :

 8 Figure 8: V-KI curves for the samples having different porosities.

Figure 9 :

 9 Figure 9: Fracture toughness and threshold of 3Y-TZP samples as a function of porosity, () obtained in the current work and () reported by Chevalier and co-workers[START_REF] Chevalier | Subcritical Crack Propagation in 3Y-TZP Ceramics: Static and Cyclic Fatigue[END_REF].

Table 1 :

 1 Dimensions, porosity, and grain size of specimens. The numbers in parentheses show the standard deviation.

	Sample name	Sintering temperature [°C]	Porosity [%]	Thickness [µm]	Grain size [nm]
	3Y-TZP-4.5%	1340	4.5 (1)	261 (4)	238 (84)
	3Y-TZP-8%	1300	8 (1.5)	262 (2)	-
	3Y-TZP-25%	1200	25 (1)	237 (5)	149 (34)
	3Y-TZP-45.5%	1060	45.5 (1)	310 (

Table 2 :

 2 Results of the compliance analysis for samples with different porosities and dimensions.

	Sample name	Experimental B [N -1 ]	Experimental D [mm/N]	E (GPa), this work	E (GPa), from ref. [34]
	3Y-TZP-4.5%	8.2 × 10 -3	5.2 × 10 -3	189.4	189.9
	3Y-TZP-8%	8.3 × 10 -3	1.93 × 10 -2	183.6	170.9
	3Y-TZP-25%	2 × 10 -2	5.44 × 10 -2	101.2	102.5
	3Y-TZP-45.5%	2.01 × 10 -2	1.89 × 10 -1	44.5	56.1

Table 3 :

 3 Fracture toughness (measured in N2 using a displacement rate of 6 mm/min), apparent toughness (measured in ambient air with a displacement rate of 0.6 mm/min) and slow crack growth parameters of the samples at different porosities. All the measurements except the high temperature fracture toughness reported for 3Y-TZP-8% are done at room temperature. The numbers in parentheses show the standard deviation

	Sample name	Fracture toughness (MPa.m 1/2 )	Apparent toughness (MPa.m 1/2 )	Slow crack growth parameters n A
	3Y-TZP-4.5%	4.27 (0.06)	3.94 (0.10)	42.3 (1.9)	7.8 × 10 -28
	3Y-TZP-8%	3.95 (0.12) [1.62 (0.05) at 800°C]	3.74 (0.02)	33.9 (2)	5.2 × 10 -23
	3Y-TZP-25%	1.93 (0.15)	1.68 (0.06)	46.3 (1.7)	3.8 × 10 -15
	3Y-TZP-45.5%	0.71 (0.00)	0.58 (0.06)	35.6 (2.5)	2 × 10 5

Acknowledgement

The authors would like to thank Innovation Fund, Denmark, for providing funding for this research under the framework of SYNFUEL (sustainable synthetic fuels from biomass gasification and electrolysis) project (File No. 4106-00006B).


Maxime Peralta
email: maxime.peralta@univ-rennes1.fr

Anh Quoc

Antoine Ackaouy

Thibault Martin

Greydon Gilmore

Claire Haegelen

Paul Sauleau

John S H Baxter

Pierre Jannin
email: pierre.jannin@univ-rennes1.fr

Bui

SepaConvNet for Localizing the Subthalamic Nucleus using One Second Micro-Electrode Recordings

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

Introduction

Deep brain stimulation (DBS) is a common neurosurgical procedure in which electrodes are introduced into particular regions of the brain in order to correct for abnormal neural behaviour. The most common disorder treated using DBS is Parkinson's Disease (PD), a quickly evolving neuro-degenerative disease that results in the loss of motor control. Although DBS is not technically a cure for PD, it can greatly enhance the quality of life of the patient by limiting the motor symptoms. There are three common targets for DBS in PD patients, the bilateral Ventral Intermediate nucleus of the thalamus (VIM), medial Globus Pallidus (mGP) and Subthalamic Nucleus (STN) [START_REF] Hamel | Targeting of the subthalamic nucleus for deep brain stimulation: a survey among parkinson disease specialists[END_REF].

Besides the adequate choice of structure, the most determinant factor of the surgery's success is the accurate positioning of the stimulating electrodes relative to the structures of interest. This positioning is currently performed in multiple phases. As pre-operative MR imaging is a routine part of clinical care for this procedure, a surgical planning phase is performed involving the identification of the target and the appropriate craniotomy site on the patient's skull, and the corresponding electrode trajectory. The second phase involves mounting a stereotactic frame onto the patient's skull, re-imaging them and using image registration to find the target co-ordinates in the space of the frame, allowing for the electrode to be implanted guided by the stereotactic frame in the operating room. However, preoperative imaging does not guarantee correct positioning of the electrode during the operation for various reasons including the limited resolution of the images and the potential registration error between the patient space and the stereotactic frame space. Additional deformations during surgery due to brain shift resulting from the craniotomy imply that the selected stimulation target coordinates determined in the surgical planning phase may no longer correspond exactly with the selected stimulation target location [START_REF] Park | Systematic stereotactic error reduction using a calibration technique in single-brain-pass and multitrack deep brain stimulations[END_REF]. Lozano et al. [START_REF] Christopher S Lozano | Imaging alone versus microelectrode recording-guided targeting of the stn in patients with parkinson's disease[END_REF] estimated the frequency of sub-optimal electrode implementation to be 20% for DBS performed solely with the preoperative imaging. Thus, an additional "fine-tuning" phase is required to ensure a correct implantation.

This "fine-tuning" stage is performed via "trial-and-error" when a small amount of stimulation is applied to the electrodes and the effects of said stimulation are used to infer whether or not the electrodes are in the correct position. This process is necessary as the ideal target for stimulation is defined functionally rather than purely anatomically, that is, the ideal target is one in which the stimulation has the desired effect. This process however can be made complicated by the use of different anesthesia regimens during the procedure. Local anesthesia maintains the wakefulness of the patient and thus allows the clinical team to test the clinical effects of various electrode positions more easily, incorporating additional behavioral and guided motor activities. However, performing the procedure with the patient awake can be a source of discomfort for the patient and additional patient movement can be a source of risk. Global or general anesthesia implies that the patient is not awake during the surgery, making the surgery more comfortable and controlled. However, this limits the amount of clinically useful information accessible to the surgical team during the procedure. Regardless of the type of anesthesia used, a second source of information that informs the position of the electrode relative to the targeted structure is considered mandatory either to limit the number of "trial-and-error" in the case of local anesthesia or to ensure a higher success rate in the case of global anesthesia.

One possibility is to use interventional MRI (iMRI) to refine the anatomical localization of the electrode during the surgery, but this can be prohibitively expensive and requires a specially designed operating theatre. An alternative approch is MER, which uses the electrical components of the stimulation electrode to record electrophysiological signals along the trajectory selected prior to the surgery. Using a segment of these signals, the clinical team listens to and/or visualizes the raw MER signal to determine if the micro-electrode is within the surgical target nuclei at the time of recording. Performing this assessment at several depths along the implant trajectory provides the surgical team enough evidence to delineate the borders of the surgical target nuclei. Whether to use intraoperative imaging or MER remains under debate. Lee et al. [START_REF] Philip S Lee | Outcomes of interventional-mri versus microelectrode recording-guided subthalamic deep brain stimulation[END_REF] and Liu et al. [START_REF] Liu | Microelectrode recording-guided versus intraoperative magnetic resonance imaging-guided subthalamic nucleus deep brain stimulation surgery for parkinson disease: a 1-year follow-up study[END_REF] compared the usage of iMRI versus MER, showing equivalent clinical outcomes.

We identified two limits of MER that can be leveraged by our approach. Firstly, the MER procedure is time consuming as many depths along the electrode trajectory are to be tested (each depth is an average of 10 seconds in duration). Secondly, this procedure is subjective as whether or not the signal originated from within the desired anatomy is determined by the neuro-physiologist based on their qualitative visual and auditory assessment of the signal. Quantitative criteria used to identify the surgical target are specific neuronal firing patterns and an increase of background noise. However, these criteria are not always obvious and dependant one the interpretation by the clinical team, which requires significant training and expertise in this domain.

Contributions

In

Theory and Previous Work

Automating STN localization with MER is an active field of research. Originally, these strategies were based on developing descriptive features characterizing the MER data and applying a classifier to these features. (A detailed review of such methods has been performed by Wan et al. [START_REF] Rui | A review on microelectrode recording selection of features for machine learning in deep brain stimulation surgery for parkinson's disease[END_REF].) These characteristics fall into two large classes: spike independent features [START_REF] Moran | Real-time refinement of subthalamic nucleus targeting using bayesian decision-making on the root mean square measure[END_REF][START_REF] Zaidel | Delimiting subterritories of the human subthalamic nucleus by means of microelectrode recordings and a hidden markov model[END_REF]9] (e.g. power spectral density) many of which can be computed or approximated with an appropriate filter-bank, and spike dependent features [START_REF] Wong | Functional localization and visualization of the subthalamic nucleus from microelectrode recordings acquired during dbs surgery with unsupervised machine learning[END_REF][START_REF] Cagnan | Automatic subthalamic nucleus detection from microelectrode recordings based on noise level and neuronal activity[END_REF][START_REF] Chaovalitwongse | Pattern recognition approaches for identifying subcortical targets during deep brain stimulation surgery[END_REF][START_REF] Darío | Neurozone: On-line recognition of brain structures in stereotactic surgery-application to parkinson's disease[END_REF][START_REF] Ciecierski | Computer aided subthalamic nucleus (stn) localization during deep brain stimulation (dbs) surgery in parkinson's patients[END_REF][START_REF] Vikram Rajpurohit | Optimizing computational feature sets for subthalamic nucleus localization in dbs surgery with feature selection[END_REF][START_REF] Schiaffino | Stn area detection using k-nn classifiers for mer recordings in parkinson patients during neurostimulator implant surgery[END_REF]] (e.g. standard deviation of interspike intervals). While adding spike dependant features can provide additional information about the signal, it also adds several constraints about signal acquisition [START_REF] Rui | A review on microelectrode recording selection of features for machine learning in deep brain stimulation surgery for parkinson's disease[END_REF].

The large amount of work that has been performed on MER feature engineering for the past decade is indicative that optimal features are likely tedious to develop. However, the fact that trained neurophysiologists can audibly distinguish different MER signals (as it can be in the current clinical workflow) hints that learned features arising from the raw signal itself may provide better outcomes. However, the extent and variety of features investigated demonstrates the hidden complexity of MER signal analysis. To this extent, using a CNN to automatically learn non-linear combinations of convolution filters to address this problem may be considerable easier than using hand-designed ones given the large span of linear and non-linear features that have been prevously been considered.

Spectrogram representation of MER

In current clinical practice, MER signals can be interpreted by a trained neurophysiologist by listening to them, indicating that the patterns of interest within these signals are detectable using the human ear. It is well-known in many fields such as perceptual psychology that the ear performs a frequency decomposition of incoming auditory signals and that this decomposition is the data provided to the central nervous system. Spectrograms have previously been used for this application; Karthick et al. [START_REF] Pa Karthick | Detection of subthalamic nucleus using time-frequency features of microelectrode recordings and random forest classifier[END_REF] successfully classified STN MER signals by designing features in a time-frequency domain. Thus, we chose a spectrogram representation of these signals as an initial stream of input features. This representation allows us to provide a more complex and predictive input data representation without the complex feature engineering and can be applied in real-time facilitating its integration into clinical workflow.

Convolutional Neural Networks

Originally developed by LeCun et al. [START_REF] Lecun | Gradient-based learning applied to document recognition[END_REF], CNNs are a type of deep neural network based on convolution layers. These layers consist of several tunable kernels operating on the input space by a linear convolution operation usually followed by a point-wise non-linear activation. Stacking these convolution layers allows the neural network to learn to construct higher level features from the original input space which are more readily used for classification tasks. Following the convolutions layers, typically one or two fully connected layers are added, which use the high level features to perform the classification. During the training process, these kernels and the weights in the fully connected layers are iteratively updated through a process of optimizing a loss function which acts as a surrogate for optimizing accuracy.

ResNeXt

ResNeXt [START_REF] Xie | Aggregated residual transformations for deep neural networks[END_REF] is an extension of ResNet [START_REF] Gross | Training and investigating residual nets[END_REF], which are both well known architectures in the computer vision community. Aside from its good performance, the structure of ResNeXt is highly scalable. Indeed, one of the motivations of the original study [START_REF] Xie | Aggregated residual transformations for deep neural networks[END_REF] was to be able to control the shape of the structure of the network with only three parameters, where former well performing CNN models needed almost each layer to be tuned manually. Therefore, it is common to reuse pretrained models and finetune them, but there is no major publicly available CNN model pretrained on MER spectrograms. The ability of ResNeXt to be scalable motivated us to use it as a CNN baseline, to compare the performances of our proposed model.

Material and Methods

Data acquisition

The MER signals in this study were recorded from 57 PD patients having undergone DBS surgery at London Health Sciences Centre at Western University hospital. The Bens gun was used to advance 3-5 microelectrodes as a unit. Signals were recorded from 10.0 mm above the pre-operatively determined target zero point to 4.0/5.0 mm below the zero-point, the end-point being detectable activity from the Substantia Nigra. The drive was advanced in 1.0 mm increments and 0.5 mm increments within the target nucleus. At each depth, a 10-second recording was obtained once a clean recording was observed (i.e. free from drive noise). 10,000) and digitally filtered (bandpass: 500-5000 Hz, notch: 60Hz) using the Leadpoint recording station (Leadpoint 5, Medtronic). The ground truths were determined by the electrophysiologist and neurosurgeon at the time of the recording in the operating room. The database was approved by the local ethics board at Western University (REB 1090485).

Database construction

By observing the signals individually, we noticed that the signals were highly temporally redundant. Usually, the neurophysiologist can be certain of the location of the electrode by listening to several seconds of signal. We hypothesised that a deep learning algorithm can exhibit good performance with far less signal (i.e only one second) which could improve clinical workflow by reducing procedure time. Reducing the duration of the signal has three positive effects for the training. Firstly, a reduced input dimensionality makes the deep neural network less prone to overfitting, thus allowing better generalisation performance with a limited number of training samples. Secondly, a smaller input limits the memory amount required to store the input, the gradient, the inference tensors, etc. This smaller memory consumption allows to train the neural network with a larger batch size, and thus train the network more quickly. Lastly, not using the whole 10 second signal allows us to take several shorter windows of each signal, thus increasing the database size.

We took advantage of the third property to balance our databases. Indeed, in our database, there are approximately three times more signals labeled as outside of the STN ('0') than signals labeled as inside of the STN ('1'). To overcome this class imbalance, for each signal labeled as '0' one 1 second window was extracted, were three different 1 second windows were used for each signal labeled as '1', thus balancing the dataset.

To split the data into training, validation/test sets, we used a stratified 5-fold cross-validation (CV). This data splitting technique consists in splitting the data in 5 different folds, with approximately the same number of signals in each fold, with the constraint that all signals coming from a single patient are assigned to the same fold. This constraint is mandatory to ensure that the estimation of network performance is representative of new patients as no patient appeared in both the testing and training sets for either class.

Once the stratified fold splitting is done, 4 folds were used as training data, and the last one as testing/validation data. This process was repeated 5 times in total in order to have every fold used as testing/validation once.

We obtained a database with 9055 one second signals labelled as '0' (outside the STN) and 8255 labelled as '1' (inside the STN), each signal having a length of 24000 samples.

Signal preprocessing

The first step of signal preprocessing was to threshold the signal, in order to limit the effects of non-informative acquisition artifacts. That being done, the temporal input signal is converted into a spectrogram representation. To compute the spectrogram, a Short Term Fourier Transform (STFT) was used, which applies a sliding window to the signal and computes the Fourier transformation for each window. From this Fourier transform, only the magnitudes of the vector were retained. Using STFT leads to a fundamental tradeoff: if the sliding window is wide, the spectrogram will have a higher accuracy in the frequency dimension, but will lose resolution in the time dimension. The STFT was performed with a Hann window of 512 samples width and a hop length of 10 samples, giving us input spectograms with 257 frequency bands and 2400 time points. An example MER spectrogram is shown in Fig. 1.

Proposed Convolutional Neural Network

In the literature, convolution kernels are often 2D as most CNNs are used to address computer vision problems, in which the input space is composed of two spatial dimensions. Spectrogram classification with 2D CNNs has already been successfully performed on music [START_REF] Kim | Human detection and activity classification based on micro-doppler signatures using deep convolutional neural networks[END_REF][START_REF] Hershey | Cnn architectures for large-scale audio classification[END_REF] and doppler radar [START_REF] Yandre | An evaluation of convolutional neural networks for music classification using spectrograms[END_REF] which present at least some informative frequency shift-invariant properties. However, for MER signals, the two axes of our spectrograms are fundamentally different and there is no practical reason that a pattern detected in the low frequency bands would be equivalent to one in the high frequency bands. Thus we claim that in our use-case, 1D kernels are theoretically more adequate and our input signals are not treated as 2D images, but as 1D vector-valued signal with each element being the intensity in a frequency band.

Furthermore, in MER analysis, the amount of data available is limited. Thus, we replaced traditional convolutions with separable ones in our proposed CNN structure. Separable convolutions have fewer trainable weights and are therefore faster to train for a similar theoretical computational power, allowing to achieve similar results with a lighter network [START_REF] Mamalet | Simplifying convnets for fast learning[END_REF]. For small datasets with high dimensionality, a lighter model can limit the impact of overfitting, thus leading to better classification results and training stability. Separable convolution works in two steps. First, a timewise convolution is performed, using K kernels per feature. Second, a pointwise convolution is used in order to mix channels Step 1: timewise convolution

Step 2: pointwise convolution to produce N new features. Given an appropriate choice of K and sufficiently large kernels, this can largely reduce the number of parameters in the total convolution operator. Figure 2 shows these two stages of a separable convolution operation with K = 1 and N = 1 and would output a 1D-vector. In our paper, the hyperparameters K and N have been optimized through a Bayesian process, described in Section 3.6.

Our proposed CNN structure, called SepaConvNet (Separable Convolution-based neural Network) is presented in Figure 3. It consists of D successive computational blocks followed by a global average pooling layer (along the time-axis) and a fully-connected neuron with sigmoid activation, in order to perform the binary classification. Each computational block is composed of a spatial dropout with a drop rate of 0.

Accuracy and loss metrics

As classes remain slightly unbalanced, we used balanced accuracy (Eq. 1) to measure the classification performance and to compare methods. Each classifier was trained with class weighting, giving a weight to training sample inversely proportional to the representation of the belonging class in the training set, thus assigning the same total weight to both classes regardless of the number of samples in each. BACC = 1 2

T P P + T N N (1)

Hyperparameters Optimization (HPO)

An HPO has been done using Bayesian optimization, with Gaussian processes as a surrogate model, and expected improvement as a criteria, with a 5-fold cross validation. The number of points tested was the square of the number of hyper-parameters to optimize plus one.

Software environment

All neural networks have been developed in Python with Keras (version 2.2.4), with Tensorflow (version 1.12) as a backend. STFT has been performed with Librosa (version 0.7.0).

Experiment

Our network was compared against two baselines: ResNeXt 2D, which is the standard version of ResNeXt, and ResNeXt 1D, with every 2D operation replaced by its 1D equivalent. Each CNN has been trained and tested with the same 5-fold CV partitions. We used a learning rate of 0.001 for both ResNeXt versions, 0.005 for SepaConvNet, with Adam optimizer and a batch size of 32.

For SepaConvNet, we performed HPO on the parameters D, K and N as presented in Section 3. 1: Mean classification performances for the three methods investigated. 'Inside the STN' is considered the positive class.

Results of the 5-fold CV are reported in Figure 4 and Table 1. Classification results between SepaConvNet and both ResNeXt versions were statistically significant with a paired sample t-test (p < 0.05).

Discussion

The results presented in Section 4 confirm our hypothesis that for this particular problem, the spectrograms should be treated as 1D vector signals. Despite the increased capability for parameter re-use, the ResNeXt 2D version did not significantly outperform its 1D counterpart, suggesting that MER signals do not have any significant non-trivial frequency invariant features (i.e. those in which the shift invariance in the frequency domain would provide a benefit in detecting).

Secondarily, SepaConvNet significantly outperformed both baselines. After HPO, our proposed CNN used fewer trainable parameters than both 2D and 1D ResNeXt (resp. 16.752, 373.953 and 240.449). This decrease in parameters however is not a sign that the ResNeXt networks were overfit as HPO did cover configurations with lower parameterization. However, it does indicate that generic but lighter weight models (largely using separable convolutions) can detect important features in neurological MER signals.

Future work

For future work, we would like to test SepaConvNet on other MER databases to determine if these networks can transfer well to different institutions with different MER hardware.

We would like to investigate on the impact of input signal length on the performance of the system. We would also like our system to allow arbitrary signal lengths to be used, in order to enhance the system ability to work in real time.

Finally, we would further define the classification block of SepaConvNet. Currently, we are using time average pooling followed by a fully-connected neuron. We hypothesize that replacing it with a recurrent layer could enhance the classification performances, as the network could learn the optimal time-pooling strategy.

Conclusions

We proposed a custom CNN architecture, referred as SepaConvNet, based on 1D separable convolution to analyze STFT spectrograms of MER signals. We experimentally showed that, for MER spectrogram analysis, the SepaConvNet structure outperformed one state-of-the-art structure for image analysis. Our results suggest that deep learnt spectrogrambased features allow the achievement of comparable, or more optimal classification results, than commonly used time domain features. Our system can accurately detect the STN with one second of MER signal. An automatic analysis of MER signal with our system could thus greatly enhance the DBS procedure by significantly reducing its duration.

Figure 1 :

 1 Figure 1: Raw spectrogram of 0.2 seconds of MER signal inside the STN after normalization.

Figure 2 :

 2 Figure 2: Example of a separable convolution. On the first step, 5 kernels (one for each feature band) of size 3 are convolving along the time axis. The resulting matrix is passed as input of the second step, which performs a convolution along the time axis with N kernel of size 1, mixing all the features together at each timestep. The dimensions of the output matrix are the number of timesteps times N.

Figure 3 :

 3 Figure 3: SepaConvNet structure. Figure (a) presents the composition of a computational block. Figure (b) presents the global network, the classification block being an average time-pooling layer followed by a fully-connected neuron with sigmoid activation.

  42ND ANNUAL INTERNATIONAL CONFERENCES OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY IN CONJUNCTION WITH THE 43RD, ANNUAL CONFERENCE OF THE CANADIAN MEDICAL AND BIOLOGICAL ENGINEERING SOCIETY -MAY 18, 2020

  ANNUAL INTERNATIONAL CONFERENCES OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY IN CONJUNCTION WITH THE 43RD, ANNUAL CONFERENCE OF THE CANADIAN MEDICAL AND BIOLOGICAL ENGINEERING SOCIETY -MAY 18, 2020

	this paper, we propose a deep learning framework named SepaConvNet (Separable Convolution-based neural
	Network) for the detection of MER signals arising from the STN, differentiating them from nearby structures, using 1
	second MER recordings. This state-of-the-art method shows high accuracy using class balanced accuracy metrics and
	outperforms ResNeXt, a state-of-the-art Convolutional Neural Network (CNN) architecture. This framework can work
	in real-time augmenting

the clinical teams capability in terms of DBS electrode implantation for Parkinson's Disease (PD).

42ND

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The signals were sampled (24kHz, 8 bit), amplified (gain:

  1, followed by a 1D separable convolution with kernel size of 15 with ReLU activation, a concatenation layer and a 1D max pooling layer of size 2 and stride 2 on the time axis. All computational blocks are identical in parameterization, except the last one, which doesn't have a max pooling layer. 42ND ANNUAL INTERNATIONAL CONFERENCES OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY IN CONJUNCTION WITH THE 43RD, ANNUAL CONFERENCE OF THE CANADIAN MEDICAL AND BIOLOGICAL ENGINEERING SOCIETY -MAY 18, 2020

	input	Input (2400x257)
	Spatial Dropout	Computational Block 1200x32
		Computational Block
	Separable convolution 1D	600x32
		Computational Block
	ReLU	300x32
		Computational Block
	Max Pooling 1D	300x32
		Classification Block
	output	Output
	(a) Computational block	(b) Complete network

  [START_REF] Philip S Lee | Outcomes of interventional-mri versus microelectrode recording-guided subthalamic deep brain stimulation[END_REF]. For both versions of ResNeXt, we optimized the number of filters in each convolution layer and the depth of the network, and fixed the cardinality to 16. It is to note that the time resolution of input spectrograms had to be decreased for ResNeXt 2D due to an excessive memory consumption. 42ND ANNUAL INTERNATIONAL CONFERENCES OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY IN CONJUNCTION WITH THE 43RD, ANNUAL CONFERENCE OF THE CANADIAN MEDICAL AND BIOLOGICAL ENGINEERING SOCIETY -MAY 18, 2020 Figure 4: Quantitative results showing the distribution of 5-fold CV balanced accuracies for the three methods investigated.

	Network	BACC Sens.	Spec.	f1
	SepaConvNet 80.9% 75.6% 86.1% 79.2%
	ResNeXt 2D	77.3% 70.1% 84.5% 74.9%
	ResNeXt 1D	76.8% 66.0% 87.6% 73.4%
	Table

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Acknowledgments

Maxime Peralta's PhD is funded by the Fondation pour la Recherche Médicale (FRM). John Baxter is supported by a Post-Doctoral Fellowship from the Natural Sciences and Research Council of Canada (NSERC) and by the Institut des Neurosciences Cliniques de Rennes (INCR).


Dr Dominique Savary
email: dsavary74@gmail.com

François Morin

Marc Fadel

Pierre Metton

J F Richard

Alexis Descatha

Considering the challenge of the

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Manuscript:

The world is facing a pandemic involving the Covid-19. One potential consequence of such crisis is the possibility of contamination of a bystander or a rescuer during resuscitation. Indeed, early cardiopulmonary resuscitation (CPR) is a key factor in out-of-hospital cardiac arrest (OHCA).

The risk of COVID-19 transmission outbreak may impact negatively the willingness of laypersons to provide bystander cardiopulmonary resuscitation (CPR), just like for other viruses such as HIV, SARS, MERCOV or EBOLA (1).

The rate of resuscitation by layperson in the Northern French Alps Emergency Network is close to 40% each year and this rate could drop dramatically with the epidemic (2).

ILO/WHO have provided guidelines for first responders in case of public health emergency (https://www.ilo.org/wcmsp5/groups/public/---ed_protect/---protrav/---safework/documents/publication/wcms_633233.pdf ), however there is a lack of guidelines for resuscitation performed by laypersons.

As much as possible, we may recommend first responders not to perform rescue breaths or mouth-to-mouth ventilation, limiting themselves to chest compressions only, particularly on an unknown victim, even if the cause of the OHCA is primary respiratory arrest.

Concerning rescuers, because of the heightened awareness of the possibility that victim may have COVID-19, to recognize cardiac arrest they should not listen or feel breathing by placing their ear and cheek close to the patient's mouth.

Taking into account the possibility that the victim may carry COVID-19, rescuers should not listen or feel breathing by placing their ear and cheek close to the patient's mouth in order to recognize cardiac arrest.

Moreover, in the current guideline, lay rescuers are recommended to use mouth-to-mouth ventilation (MMV), while healthcare professionals provide bag-valve-mask ventilation (BMV) in a 30:2 ratio for adult patients in the absence of an advanced airway, with and without supplementary oxygen (3).

The MMV realization shouldn't be recommended in the current context.

Other devices like the mouth-to-face-shield ventilation or mouth-to-pocket-mask may seem more reasonable because they prevent contact with the victim, but we lack perspective on the efficacy and safety.

Certain medical interventions currently used by out of hospital team in our network, such as BVM and intubation (in 70% of cases in our network), may generate aerosol that can allow airborne transmission to those closely involved in the procedure. Careful execution of infection control measures is necessary with personal protective equipment (PPE) (fluid-resistant gown, gloves, eye protection, full face shield) and it is probably desirable to favor disposable BVM. Hand hygiene must be performed after the reanimation. Alcohol hand gel is recommended if soap and water is not available.

In conclusion, we believe that clear guidelines for the protection of bystanders and rescuers are crucial in the context of this pandemic, and that their impact should be evaluated using existing OHCA registers.

  Considering the challenge of the Covid-19 pandemic, is there a need to adapt the guidelines for basic life support resuscitation? Dominique Savary, François Morin, Marc Fadel, Pierre Metton, J.F Richard, Alexis Descatha To cite this version: Dominique Savary, François Morin, Marc Fadel, Pierre Metton, J.F Richard, et al.. Considering the challenge of the Covid-19 pandemic, is there a need to adapt the guidelines for basic life support resuscitation?. Resuscitation, 2020, 85 (1), pp.103075. 10.1016/j.resuscitation.2020.03.010. hal-