Loubna Martin Jacob
email: martin.jacob@cea.fr

El Gueddari

Jyh-Miin Lin
email: jyhmiinlin@gmail.com

Gabriele Navarro
email: gabriele.navarro@cea.fr

Audrey Jannaud
email: audrey.jannaud3@cea.fr

Guido Mula
email: guido.mula@dsf.unica.it

Pascale Bayle-Guillemaud
email: pascale.bayle-guillemaud@cea.fr

Philippe Ciuciu
email: philippe.ciuciu@cea.fr

Zineb Saghi
email: zineb.saghi@cea.fr

Loubna El Gueddari
email: loubna.elgueddari@gmail.com

Gradient-based and wavelet-based compressed sensing approaches for highly undersampled tomographic datasets

Keywords: Electron tomography, compressed sensing, total variation, wavelets, STEM-EELS/EDX tomography

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

Introduction

Electron tomography (ET) based on high-angle annular dark-field scanning transmission electron microscopy (STEM-HAADF) mode is widely used in materials science for the 3D morphological analysis of objects at the nanoscale [START_REF] Saghi | Electron Tomography in the (S)TEM: From Nanoscale Morphological Analysis to 3D Atomic Imaging[END_REF][START_REF] Hungría | HAADF-STEM Electron Tomography in Catalysis Research[END_REF][START_REF] Leary | Electron Tomography in Materials Science[END_REF]. Recent advances in hardware have allowed the development of analytical ET (AET), which is the extension of ET to spectroscopic signals such as energy dispersive x-ray spectroscopy (EDX) and electron energy loss spectroscopy (EELS) [START_REF] Burdet | A novel 3D absorption correction method for quantitative EDX-STEM tomography[END_REF][START_REF] Leary | Analytical electron tomography[END_REF][START_REF] Collins | Eigenmode Tomography of Surface Charge Oscillations of Plasmonic Nanoparticles by Electron Energy Loss Spectroscopy[END_REF][START_REF] Haberfehlner | Nanoscale voxel spectroscopy by simultaneous EELS and EDS tomography[END_REF][START_REF] Collins | Progress and opportunities in EELS and EDS tomography[END_REF]. AET provides significant insights into nanomaterials' 3D elemental composition, chemical bonding, and optical/electronic properties. However, due to the cross-sections for inelastic electron scattering and X-ray generation, it necessitates longer acquisition times and higher electron doses than STEM-HAADF tomography.

Therefore, to minimize the total acquisition time and beam damage, AET datasets often consist of spectrum image datacubes acquired with a low signal-to-noise ratio and a relatively large tilt increment of 5° to 10°. Under these noisy and undersampled conditions, conventional reconstruction algorithms are not suitable as they yield poor image quality reconstructions with fanning artefacts. Various approaches have been proposed to overcome these intrinsic limitations: in [START_REF] Saghi | Three-dimensional chemical analysis of tungsten probes by energy dispersive x-ray nanotomography[END_REF], the convex hull of an object was estimated by geometric tomography from its binarised STEM-HAADF projections and used to mask the fanning artefacts present in the STEM-EDX reconstructions. Later, Zhong et al. introduced a bimodal HAADF-EDX tomography (HEBT) technique that combined STEM-HAADF and STEM-EDX data into one tomographic reconstruction process [START_REF] Zhong | A bimodal tomographic reconstruction technique combining EDS-STEM and HAADF-STEM[END_REF]. HEBT is suitable for samples where the following assumptions are fulfilled: (1) both STEM-HAADF and STEM-EDX datasets satisfy the projection requirement, and (2) the STEM-HAADF datasets are the weighted sum of the elemental maps for all elements present in the sample. The first implementation of HEBT [START_REF] Zhong | A bimodal tomographic reconstruction technique combining EDS-STEM and HAADF-STEM[END_REF] used the simultaneous iterative reconstruction technique (SIRT) algorithm, yielding STEM-HAADF and STEM-EDX reconstructions that were still affected by fanning artefacts. Recent algorithmic developments using the compressed sensing (CS) framework [START_REF] Candes | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[END_REF][START_REF] Donoho | Compressed sensing[END_REF] have shown promising results for reconstructing volumes from heavily undersampled datasets [START_REF] Leary | Compressed sensing electron tomography[END_REF][START_REF] Goris | Electron tomography based on a total variation minimization reconstruction technique[END_REF][START_REF] Saghi | Three-Dimensional Morphology of Iron Oxide Nanoparticles with Reactive Concave Surfaces. A Compressed Sensing-Electron Tomography (CS-ET) Approach[END_REF] and are becoming increasingly popular for AET applications. These approaches exploit the object's sparsity in a chosen transform domain and employ the l1-norm minimization to recover a sparse solution under an l2-norm data consistency constraint. The choice of the sparsifying transform reflects the prior knowledge we have about the object to reconstruct. The l1-norm of the gradient is commonly called Total Variation (TV) minimization [START_REF] Rudin | Nonlinear total variation based noise removal algorithms[END_REF] and has been employed for the 3D chemical analysis of various nanomaterials using EELS [START_REF] Collins | Eigenmode Tomography of Surface Charge Oscillations of Plasmonic Nanoparticles by Electron Energy Loss Spectroscopy[END_REF][START_REF] Torruella | 3D Visualization of the Iron Oxidation State in FeO/Fe3O4 Core-Shell Nanocubes from Electron Energy Loss Tomography[END_REF], EDX [START_REF] Einsle | Nanomagnetic properties of the meteorite cloudy zone[END_REF] or both modalities [START_REF] Haberfehlner | Nanoscale voxel spectroscopy by simultaneous EELS and EDS tomography[END_REF]. TV promotes sparsity in the gradient domain and is very well suited for objects with piecewise constant regions and sharp edges. Since only the first derivative of the object is considered, staircasing artefacts are observed when the assumption about piecewise constancy does not hold.

Moreover, recent studies have shown that TV's performance is highly dependent on the structural complexity of the object and the noise level [START_REF] Jiang | Sampling limits for electron tomography with sparsity-exploiting reconstructions[END_REF][START_REF] Jorgensen | SparseBeads Data: Benchmarking sparsity-regularized computed tomography[END_REF].

The incorporation of higher-order derivatives has been proposed to overcome these drawbacks. Total Generalized Variation (TGV) [START_REF] Benning | Higher-Order TV Methods-Enhancement via Bregman Iteration[END_REF][START_REF] Knoll | Second Order Total Generalized Variation (TGV) for MRI[END_REF] and polynomial annihilation edge detection methods [START_REF] Archibald | Image Reconstruction from Undersampled Fourier Data Using the Polynomial Annihilation Transform[END_REF], referred to as HOTV (High Order TV), promote piecewise smooth solutions while preserving sharp edges. These approaches have been applied to STEM-HAADF [START_REF] Sanders | Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization[END_REF] and STEM-EDX [START_REF] Huber | Total generalized variation regularization for multi-modal electron tomography[END_REF] datasets with improved performances compared to TV.

Joint HAADF and spectroscopic reconstructions using TV and TGV have also been proposed to improve the reconstructions' quality, but this strategy is restricted to objects with boundaries recovered in both modalities [START_REF] Huber | Total generalized variation regularization for multi-modal electron tomography[END_REF][START_REF] Zhong | EDS tomographic reconstruction regularized by total nuclear variation joined with HAADF-STEM tomography[END_REF].

Wavelet-based CS methods are widely used in MRI [START_REF] Lustig | Sparse MRI: The application of compressed sensing for rapid MR imaging[END_REF][START_REF] Cherkaoui | Analysis vs Synthesis-based Regularization for Combined Compressed Sensing and Parallel MRI Reconstruction at 7 Tesla[END_REF][START_REF] Ye | Compressed sensing MRI: a review from signal processing perspective[END_REF] and have been applied in TEM mainly for denoising [START_REF] Huang | Exploring an optimal wavelet-based filter for cryo-ET imaging[END_REF][START_REF] Sorzano | Improved Bayesian image denoising based on wavelets with applications to electron microscopy[END_REF] and inpainting purposes [START_REF] Li | Compressed Sensing of Scanning Transmission Electron Microscopy (STEM) With Nonrectangular Scans[END_REF][START_REF] Mucke-Herzberg | Practical Implementation of Compressive Sensing for High Resolution STEM[END_REF]. They have recently gained interest in X-ray tomography [START_REF]Sparse reconstruction methods in x-ray CT[END_REF] and ET [START_REF] Leary | Compressed sensing electron tomography[END_REF][START_REF] Guay | Compressed Sensing Electron Tomography for Determining Biological Structure[END_REF][START_REF] Nicoletti | Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles[END_REF], as they apply to a broader range of objects than gradient-based methods. However, only gradient-based methods have thus far been made accessible to the community via open-source packages (e.g. [START_REF] Sanders | Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization[END_REF][START_REF] Huber | Total generalized variation regularization for multi-modal electron tomography[END_REF]).

In this work, we present an open-source toolbox, Pyetomo, where we implemented both gradient-based and wavelet-based methods for 2D slice-by-slice and 3D tomographic reconstructions. The current version of Pyetomo allows the testing of all the wavelet families built in the Pywavelet library, and makes use of cutting edge optimization algorithms initially developed for MRI and astrophysics applications [START_REF] Cherkaoui | Analysis vs Synthesis-based Regularization for Combined Compressed Sensing and Parallel MRI Reconstruction at 7 Tesla[END_REF][START_REF] Farrens | PySAP: Python Sparse Data Analysis Package for multidisciplinary image processing[END_REF].

Using this toolbox, we compare the performance of gradient-based and wavelet-based approaches on a test object and assess the quality of the reconstructions of an undersampled AET dataset. Instead of generating a tilt series from a simulated test object, we use a highly sampled STEM-HAADF dataset of an Er-doped porous Si sample. This material has photoluminescence emission properties that can be tailored by controlling the sample's porosity (3D size, volume and distribution of the pores) and the Erbium distribution within the porous structure. STEM-HAADF tomography has contributed to a better understanding of these structures, as reported in [START_REF] Mula | Doping porous silicon with erbium: pores filling as a method to limit the Er-clustering effects and increasing its light emission[END_REF][START_REF] Printemps | Self-adapting denoising, alignment and reconstruction in electron tomography in materials science[END_REF]. In this work, reference reconstructions from 180 projections are generated and used to evaluate the performances of the different approaches as the number of projections decreases.

The different CS approaches are then applied to the 3D STEM-EELS analysis of a Ge-rich GeSbTe (GST) thin film annealed at 450°C. GST compounds have been widely utilized for phase-change memory (PCM) applications. They exhibit interesting properties, including a fast and reversible switch between an amorphous state and a crystalline state, a large resistivity difference between these two states and a high crystallization temperature [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF].

Ge-rich GST materials are of particular interest for applications at high temperatures as they were shown to yield higher thermal stability and better data retention than standard GST compounds such as Ge2Sb2Te5 [START_REF] Navarro | Phase-Change Memory: Performance, Roles and Challenges[END_REF][START_REF] Sousa | Operation fundamentals in 12Mb Phase Change Memory based on innovative Ge-rich GST materials featuring high reliability performance[END_REF]. Recent studies have investigated the phase separation process in these alloys at different annealing temperatures [START_REF] Agati | In-situ transmission electron microscopy studies of the crystallization of N-doped Ge-rich GeSbTe materials[END_REF][START_REF] Agati | Chemical phase segregation during the crystallization of Ge-rich GeSbTe alloys[END_REF]. Although advanced TEM techniques were employed, the interpretation of the results is hampered by the projection effect. Here, we employ STEM-EELS tomography to obtain information about the volume fraction of the two phases and their 3D distribution within the analyzed volume.

Methods

Compressed sensing methods applied to electron tomography

ET aims to reconstruct a 3D object from 2D projections acquired at different tilt angles with a TEM. When the projection requirement is fulfilled, each acquired pixel's intensity is approximately a line integral of a physical property of the object to be reconstructed. The set of projections correspond to the Radon transform of the object. The projection slice theorem states that the Fourier transform of a projection at an angle θ is a slice across the Fourier Transform of the original object at the same angle θ. This enables to formulate the reconstruction problem either in the image domain or in the Fourier domain. Analytical reconstruction approaches, such as filtered back-projection (FBP), aim to recover the object by inverting the Radon transform. These methods yield unsatisfactory reconstructions in the presence of noise and with a limited number of projections.

Iterative methods treat ET as an inverse problem, using the following discrete expression of the forward model:

= (1)
Where is the object to reconstruct, the projection matrix and the experimental projections. The most widely used iterative method is the simultaneous iterative reconstruction technique (SIRT) which solves the following least-squares problem:

‖ -‖ (2)
Reconstructions obtained with iterative methods are also degraded with increasing undersampling as the problem becomes severely ill-posed. A way to stabilize it is to incorporate prior knowledge about the solution :

‖ -‖ + (3)
This so-called variational formulation contains a data consistency term ‖ -‖ and a regularisation term which represents the prior information about . The parameter controls the balance between the two terms.

= ‖ ‖ corresponds to the minimal energy solution to the inverse problem. This regularisation is not sufficient for tomographic reconstruction with an undersampled dataset as it produces images with over-smoothed features.

= ‖ ‖ promotes sparsity of in the transform domain (few non-zero elements in ). In the framework of CS, it was shown that under certain conditions (including sparsity of in and incoherence of and ), the l0 quasi-norm could be replaced by its convex envelope l1 norm, leading to a convex optimization formulation:

‖ -‖ + ‖ ‖ (4)
In the Pyetomo toolbox, we implemented two types of transform domains:

-Gradient-based regularisations:

With = , the regularisation term in Eq. ( 4) is the l1 norm of the gradient of , which is commonly called Total Variation (TV) minimization. TV promotes sparsity in the gradient domain and is very well suited for objects with piecewise constant regions and sharp edges.

Various TV expressions can be found in the literature, including isotropic, anisotropic, upwind [START_REF] Condat | Discrete Total Variation: New Definition and Minimization[END_REF] and directional forms [START_REF] Merveille | nD Variational Restoration of Curvilinear Structures With Prior-Based Directional Regularization[END_REF]. In this paper, we choose the following anisotropic definition:

= | | ! (5)
Where Higher-order derivatives can be incorporated to extend the gradient-based approaches to piecewise-smooth objects. For example, the second-order total generalized variation (TGV) regularisation is defined as:

' = ( | -)| * + + |, ) | * (6)
Where , ) is the symmetric derivative, and + a weighting parameter that balances the effects of the first and the second derivatives [START_REF] Knoll | Second Order Total Generalized Variation (TGV) for MRI[END_REF].

Higher order TV (HOTV) is another approach that makes use of the polynomial annihilation transform [START_REF] Archibald | Image Reconstruction from Undersampled Fourier Data Using the Polynomial Annihilation Transform[END_REF]. In Pyetomo, we implemented HOTV of order k, as described in [START_REF] Sanders | Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization[END_REF]. Note that HOTV of order 1 is equivalent to TV.

-Wavelet-based approaches:

The wavelet transform is based on a multiscale approximation of an object with dilation of a factor 2 . and shifting / of a scaling function 0, and the use of a similarly dilated and translated mother wavelet function 1 to retrieve the details between different approximation levels. The wavelet transform of a 1D signal, with a decomposition level 2, can be written as:

= ∑ 4 ,
with 0 5,6 = 2 95 0=2 95 -/> and 1 .,6 = 2 9. 1=2 9. -/>.

Or, under a compact form:

= ? 5 + ∑ @ .

<9

.:5 [START_REF] Collins | Progress and opportunities in EELS and EDS tomography[END_REF] with ? 5 the approximation coefficients at scale 2, and @ . the detail coefficients between scale j and j+1. This formulation can be extended to higher dimension signals such as images or volumes by separable products of the scaling function and the mother wavelet along the different dimensions. For instance, with a 2D signal and the same scaling and wavelet function, we have the 2D scaling function 0 , ! = 0 0 ! and the 2D wavelet

functions 1 , ! = 0 1 ! , 1 2 , ! = 1 0 ! and 1 3 , ! = 1 1 ! .
In general, the choice of the most effective multiscale transform will depend on the prior knowledge we have about the object's features. However, some properties of the wavelet transform can help make a more appropriate one. For instance, a wavelet with a given number of vanishing moments produces sparse transforms for signals that can locally be approximated by polynomials of degree inferior to this number. The symmetry of the chosen wavelet is also an interesting property that prevents distortion in the reconstructed signals.

Standard orthogonal wavelets are not symmetric. To address this limitation, biorthogonal wavelets have been proposed: in this case, different functions are used for analysis (i.e. two scaling functions 0 and 0′ to generate a multiresolution analysis) and synthesis (two wavelet functions to reconstruct the signal or image). The biorthogonal transform remains invertible even though it is not necessarily orthogonal. Designing biorthogonal wavelets allows more degrees of freedom, particularly the possibility of constructing symmetric wavelet functions.

We refer to the following textbooks for an extensive description of the different wavelets and their properties: [START_REF] Mallat | A Wavelet Tour of Signal Processing[END_REF][START_REF] Starck | Sparse Image and Signal Processing: Wavelets and Related Geometric Multiscale Analysis[END_REF].

In this paper, we use the Haar and the Bior4.4 biorthogonal wavelets with one and four vanishing moments at the analysis (4) and synthesis (4) steps, respectively. Figure 1 shows the Haar (a) and Bior4.4 (b) wavelet functions. Haar wavelet corresponds to Daubechies db1 wavelet. From its shape, the Haar wavelet can be seen as a multiscale gradient, providing an average image and the horizontal, vertical and diagonal gradients at each decomposition level. It is therefore adapted for piecewise constant objects, like TV. For features with a small anisotropy, biorthogonal wavelet transform is more appropriate. For highly anisotropic features, multiscale transforms based on anisotropic basis functions such as ridgelets, curvelets and shearlets, were shown to perform better than isotropic wavelets [START_REF] Starck | Astronomical image representation by the curvelet transform[END_REF].

Pyetomo toolbox

a) b) c) d) e)
f)

The Python toolbox developed in this work is made available in this git repository: www.github.com/CEATomo/Pyetomo. It contains the 2D and 3D implementations of TV, HOTV, and wavelets using the PyWavelets library [START_REF] Lee | PyWavelets: A Python package for wavelet analysis[END_REF]. For the data consistency term, we used the Non-Uniform Fast Fourier Transform (NUFFT) operator and its adjoint, implemented in the PyNUFFT package [START_REF] Lin | Python Non-Uniform Fast Fourier Transform (PyNUFFT): An Accelerated Non-Cartesian MRI Package on a Heterogeneous Platform (CPU/GPU)[END_REF]. Various algorithms have been proposed in the literature to solve the optimization problem in the CS reconstruction (Eq. ( 4)) [START_REF] Foucart | Algorithms for ℓ1-Minimization[END_REF]. In this work, we used the Condat-Vu primal-dual splitting method, included in the ModOpt package [START_REF] Farrens | PySAP: Python Sparse Data Analysis Package for multidisciplinary image processing[END_REF]. A non-negativity constraint was also added to the cost function. Figure 2 Projection operators, sparsity transforms, and optimization algorithms included in the toolbox Pyetomo. In italic are the features that are included but were not tested (FISTA, POGM), and those that can be easily incorporated in the future (TGV, the Radon operator and advanced wavelets from Sparse2D).

Experimental data acquisition and processing

STEM-HAADF tomography of Erbium-doped porous silicon

As reported in [START_REF] Mula | Doping porous silicon with erbium: pores filling as a method to limit the Er-clustering effects and increasing its light emission[END_REF], a needle-shaped sample was prepared by focused ion beam (FIB) and mounted onto an on-axis tomography holder (Fischione model 2050). A full 180° tilt range tomographic dataset was acquired in a double-corrected Titan 80-300 kV STEM (Thermo Fisher Scientist) operated at 80kV, with a tilt increment of 1°, a frame size of 1024*1024 pixels and a pixel size of 0.41 nm. Figure 3(a) is the STEM-HAADF projection of the sample at 0° tilt angle. The tilt series alignment was performed following the procedure described in [START_REF] Printemps | Self-adapting denoising, alignment and reconstruction in electron tomography in materials science[END_REF]. SIRT yielded a high-quality reconstruction with fine details about the pores and the Erbium clusters (Figure 3(b-e)). In this paper, we compared the CS reconstructions of a selected slice (indicated in green in Figure 3(a)) using the 2D implementation of TV, HOTV, Haar and Bior4.4 sparse representations. For each of these methods, the 1° reconstruction was used as a reference image.

STEM-EELS tomography of Ge-rich GST material annealed at 450°C

A needle-shaped sample of a Ge-rich GST thin film annealed at 450°C was prepared by FIB and transferred onto an on-axis tomography holder. STEM-EELS acquisition was performed at 200kV in a probe-corrected Titan 80-200 kV STEM (Thermo Fisher Scientist) equipped with a Quantum Gatan imaging filter. 18 STEM-EELS datacubes were acquired over a tilt range of 180°, with a pixel size of 2nm, a frame size of 100x75 pixels, and a dwell time of 0.1 sec/pixel for the energy range of 250-2398 eV. The overlapping of Sb M4,5-edge (528 eV), O K-edge (532 eV) and Te M4,5-edge (572eV), and the presence of Ge in both phases make the use of classical elemental analysis difficult (see Figure S2). We instead used vertex component analysis (VCA) to identify the different chemical components present in the hyperspectral dataset, including the SiN capping, the GST phase, the Ge phase, and the SiO2 substrate. The extraction of the corresponding abundance maps was performed using the SUNSAL solver [START_REF] Nascimiento | Vertex component analysis: a fast algorithm, to unmix hyperspectral data[END_REF]. Figure 4(a) shows the 0° STEM-HAADF image and the region selected for the STEM-EELS experiment (inset in white). Reconstructions with datasets consisting of 90 (2° increment), 45 (4° increment), 36 (5° increment) and 18 (10° increment) projections were then performed and compared to the reconstructions with 180 projections. Figure 6(a) shows a selected region from the reconstructions. The normalized root mean square error (nRMSE) and structural similarity index (SSIM), as implemented in the module metrics from the scikit-image library, were used to assess the images' quality and evaluate the performance of the CS methods as a function of the angular increment (Figure 6(b,c)). Based on these metrics, we see that Bior4. 6 (b,c). These results are coherent with the visual assessment of the reconstructions: we notice that TV and Haar, which can be regarded as a multiscale version of TV, yield similar results and suffer from block artefacts when the dataset is heavily undersampled. This outcome is expected as both regularisations favour piecewise constancy. Bior4.4 eliminates these effects but induces smoothness as the tilt increment increases. HOTV3 reconstructions exhibit noise-like spurious oscillations with a loss of contrast as the tilt increment increases but are visually more resolved than TV and Haar reconstructions, as reflected by the SSIM metric. The 2D porosity was also calculated for each reconstruction after automatic thresholding by Otsu's method. The absolute percentage error on the measurements, compared to the reference images' porosity (reconstructions using 1° increment), is plotted in Figure 7 as a function of tilt increment. We observe that below 3° increment, the absolute percentage error is less than 2% for all methods, with a slight advantage for HOTV3. However, for large tilt increments, Bior4.4 outperforms the other approaches as it shows the smallest deviations.

Results

Effect of undersampling

HOTV3 provides the worst quantitative measures, and we attribute this to the low SNR and contrast in the reconstructions, making the automated segmentation step more challenging.

Visually, we notice, regardless of the approach used for the reconstruction, that the Er clusters are unresolved for increments greater than 2°. These results suggest that the reconstruction algorithm and the experimental conditions have to be carefully adjusted according to the sample complexity and the information sought-after in the reconstructions.

Since the Er clusters' size is close to the resolution limit of classical HAADF-STEM tomography, a large number of projections is necessary to study their distribution within the porous Si structure.

Figure 7 Absolute percentage error between the porosity estimated from the reconstructed images and the reference image (reconstruction from 180 projections).

CS methods applied to STEM-EELS datasets

The GST tilt series was used for the choice of the regularization parameter λ. Figure 8 shows the reconstructions of a selected xy slice using the 2D implementations with 300 iterations and the non-negativity constraint. We see that as λ increases, both TV and Haar yield flat, blocky GST regions and over-regularised edges. HOTV3 and Bior4.4, on the other hand, preserve the surface roughness of the GST grains and recover fine details. HOTV3 reconstruction shows fewer oscillations than in the STEM-HAADF reconstruction of the Erdoped Si sample. We can attribute this to the difference in dimensions of the STEM-HAADF (1024x1024 pixels) and STEM-EELS chemical phase (100x75 pixels) projections. The correlation between the size of the images and the unwanted oscillations is discussed in more details in [START_REF] Sanders | Multiscale higher-order TV operators for L1 regularization[END_REF]. The 3D reconstructions of the Ge and GST volumes were performed using the 3D implementations of the four methods, with 300 iterations, the non-negativity constraint, and a λ value of 0.0003 for TV and HOTV, and 0.0007 for Haar and Bior4.4. Figure 9 shows the 3D rendering of the GST (in red) and Ge (in blue) volumes, and a video showing the slices through the TV and Bior4.4. reconstructions can be found in the supplementary information (SI_movie_2). As expected, the 3D implementations yield better reconstructions for HOTV and Bior4.4. than Haar and TV (see, for example, the region pointed out with the white arrow in the inset of the xz slices). The outer layer observed in all Ge reconstructions is attributed to a redeposition during the FIB sample preparation.

For a quantitative comparison of the reconstructions, we estimated the GST phase's volume fraction after automatic thresholding by Otsu's method. We found 0.491 for TV, 0.494 for Haar, 0.533 for HOTV3 and 0.527 for Bior4. The shape of the GST grains and their inclusion in the Ge volume seem to support the hypothesis of nucleation and growth of the GST phase before the Ge phase's growth, once the demixing has taken place. We also note that both Ge and GST volumes contain pores, which are visible in the STEM-HAADF projection, Figure 4(a). A similar study conducted on thin films annealed at 380°C and 400°C yielded the following conclusions: 1) the size of the pores increases with the annealing temperature; 2) the chemical segregation only happens at the top 60 nm of the thin film at 400°C, while no phase separation is observed at 380°C.

Discussion

In this work, we implemented gradient-based and wavelet-based reconstruction methods in the Pyetomo toolbox and applied them on STEM-HAADF and STEM-EELS datasets. TV and Haar yield very similar results and are mostly adapted for simple piecewise constant structures. TV and Haar are not suitable for more complex geometries and with heavily undersampled datasets. HOTV3 approach outperforms these two methods as it eliminates the block artefacts but suffers from unwanted, noise-like oscillations, which makes the segmentation a challenging task. Our results confirm previous findings that the oscillations are related to the dimension of the reconstructed volume. Bior4.4 yields the best results for STEM-HAADF and STEM-EELS datasets and is in excellent agreement with HOTV3 for the 3D quantification of the STEM-EELS reconstructions. We note that the reconstructions become over-smoothed as the tilt increment increases and that border artefacts can appear around the edges (see the Bior4.4 reconstruction with λ=10, in Figure 5). These limitations have been overcome in MRI and astrophysics by exploring anisotropic multiscale approaches such as ridglets, curvelets and shearlets [START_REF] Starck | The curvelet transform for image denoising[END_REF]. These methods have not yet been explored in the field of electron tomography, but promising results were reported for the edge detection of vesicle membranes in a TEM image by curvelets [START_REF] Gebäck | Edge detection in microscopy images using curvelets[END_REF] and inpainting of a high-resolution STEM-HAADF image of a complex oxide ceramic using shearlet transforms [START_REF] Mucke-Herzberg | Practical Implementation of Compressive Sensing for High Resolution STEM[END_REF].

When the STEM-HAADF and the elemental or chemical phase maps share common features, a joint multi-channel approach can produce reconstructions from all signals simultaneously and with improved quality. While these approaches were reported using TV or TGV regularisations, we believe that wavelet-based regularisations can easily be incorporated into the existing codes, with the potential for further improvements of the reconstructions.

Combining at least two sparsity transforms has also led to promising results (see for example [START_REF] Starck | Very high quality image restoration by combining wavelets and curvelets[END_REF][START_REF] Qu | Sparse View CT Image Reconstruction Based on Total Variation and Wavelet Frame Regularization[END_REF]), and we intend to investigate this strategy for AET applications.

STEM-EELS tomography of the Ge-rich GST sample provided important 3D information about the chemical phase segregation process, which was hitherto exclusively studied in 2D.

The needle-shaped geometry allowed a full tilt range acquisition with no missing wedge artefacts but with a restricted field of view compared to classical FIB lamellae utilized for the 2D characterizations. CS methods do not allow for the correction of artefacts when the missing wedge is larger than 30°, as reported in [START_REF] Jiang | Sampling limits for electron tomography with sparsity-exploiting reconstructions[END_REF][START_REF] Guay | Compressed Sensing Electron Tomography for Determining Biological Structure[END_REF][START_REF] Saghi | Compressed Sensing Electron Tomography of Needle-Shaped Biological Specimens-Potential for Improved Reconstruction Fidelity with Reduced Dose[END_REF]. Strategies for sinogram inpainting have recently shown promising results (see for example [START_REF] Ding | A joint deep learning model to recover information and reduce artifacts in missing-wedge sinograms for electron tomography and beyond[END_REF][START_REF] Tovey | Directional Sinogram Inpainting for Limited Angle Tomography[END_REF]), but further work is required to investigate their effectiveness on complex objects.

Finally, for all CS methods, and in the absence of ground truth, the choice of the regularisation parameter λ is a difficult task with a significant impact on the reconstructions' quality. While it is common to adjust λ manually based on the visual evaluation of the reconstruction quality, a more in-depth assessment of the acquisition conditions and the nature of the noise can help automate this step [START_REF] Weller | Monte Carlo SURE-based parameter selection for parallel magnetic resonance imaging reconstruction[END_REF].

Conclusion

In this work, we have presented the Pyetomo toolbox and used it to investigate the performance of gradient-based and wavelet-based CS techniques for the reconstruction of heavily undersampled datasets, with a particular interest for AET applications. As an example, STEM-EELS tomography was performed on a Ge-rich GST material to understand better the phase separation process occurring at high annealing temperatures. We showed that polynomial annihilation with order 3 (HOTV3) and the Bior4.4 wavelet provide higher quality reconstructions than the classical TV minimization and the related Haar wavelet, making the segmentation and the quantification steps more reliable. Using an Er-doped Si structure as a test object, we also confirmed, as reported in [START_REF] Jiang | Sampling limits for electron tomography with sparsity-exploiting reconstructions[END_REF], that the minimum number of projections required for a high-quality reconstruction strongly depends on the complexity of the object, regardless of the reconstruction algorithm.

In the future, we plan to (1) include denoising and inpainting routines based on the proposed methods, (2) accelerate the reconstructions with GPU implementations, and (3) explore the advanced transforms implemented in Sparse2D library.

We believe that Pyetomo toolbox will be of great interest not only for AET applications in the field of materials science, but also for the cryo-ET and X-ray tomography communities.

  | | ∶= | # | + | $ |, # and $ being the horizontal and vertical partial derivative operators. For the isotropic form, as initially proposed by Rudin et al. [16], | | is replaced by | | , = &| # | + | $ | .

Figure 1

 1 Figure 1 Haar scaling (a) and wavelet (b) functions; Bior4.4 analysis scaling (c) and wavelet (d) functions; Bior4.4 synthesis scaling (e) and wavelet (f) functions.

  Figure 2 summarises the different features of the toolbox. We point out in italic the options that were not tested in this work but are included in the toolbox or can easily be imported: the proximal gradient methods are included in ModOpt; the Radon-based projection operator can be imported from Astra toolbox [53]; Sparse2D package can be imported from https://github.com/CosmoStat/Sparse2D for more advanced transforms [28].

Figure 3 (

 3 Figure 3 (a) 0° STEM-HAADF projection of the Er-doped Si sample. (b-d) selected xy, xz and yz orthoslices through the reconstructed subvolume. (e) Voxel rendering of the reconstructed subvolume.

Figure 4 (

 4 FigureS3) were aligned and used as input for the CS reconstructions based on TV, HOTV,

Figure 4 (

 4 Figure 4 (a) 0° STEM-HAADF projection of the Ge-rich GST sample and the region (white inset) selected for the STEM-EELS experiment. (b) Spectral components corresponding to the Ge (blue) and GST (red) phases, as extracted by VCA. (c) GST (top) and Ge (bottom) abundance maps at -90°, 0° and +70°. Scale bar: 100 nm.

A

  selected slice through the Er-doped Si needle was reconstructed with the full STEM-HAADF dataset (180 projections), using the 2D implementation of TV, Haar wavelet, HOTV3 (HOTV with order 3) and Bior4.4 sparse representations. The maximum number of iterations was set to 300, and the non-negativity constraint was added to the cost function.Different values of the regularisation parameter λ were tested. As shown in Figure5, a small λ yielded reconstructions influenced mainly by the data fidelity term. By increasing λ, more weight was given to the regularization term, inducing artefacts specific to each sparse representation. Based on the visual quality assessment of the reconstructions, an optimal value of 4 for TV and HOTV3 and 10 for Haar and Bior4.4 was selected.

Figure 5

 5 Figure 5 Reconstructions of a selected slice in the Er-doped Si sample, using the 2D implementation of TV, Haar, HOTV3, and Bior4.4 sparsity transforms. The optimal regularisation parameter λ was 4 for TV and HOTV3, and 10 for Haar and Bior4.4, based on visual assessment (visibility of the small cluster indicated with the white arrow).

  4 yields improved results compared to TV and Haar regularisations, which exhibit the same behaviour and produce strongly degraded images as the angular increment increases. HOTV3 lies between Bior4.4 and TV/Haar, with a relatively high nRMSE at 10° increment. Note that for each sparse representation, the corresponding fully sampled reconstruction was used as a reference image. As shown in FigureS1, selecting the same reference image for all CS Bior4.4 reconstruction) yielded SSIM and nRMSE curves with the same trends as Figure

Figure 6 (

 6 Figure 6 (a) TV, Haar, HOTV_3 and Bior4.4 reconstructions with 1°, 2°, 4°, 5° and 10° increments. (b) RMSE and (c) SSIM scores showing the evolution of the image quality as a function of the angular increment (in degrees).

Figure 8

 8 Figure 8 Reconstructions of a selected xy slice through the GST volume, using the 2D implementation of TV, Haar, HOTV3, and Bior4.4 sparsity transforms, and different values for the regularisation parameter λ.

4 .

 4 These values confirm the capability of TV and Haar on the one hand and HOTV3 and Bior4.4 on the other in achieving similar results. Since HOTV3 and Bio4.4 reconstructions are visually superior to Haar and TV, we can deduce that the true volume fraction is close to 0.53.

Figure 9

 9 Figure 9 Reconstruction of GST and Ge phases using the 3D implementation of TV, Haar, HOTV3 and Bior4.4. From top to bottom rows: volume rendering of the reconstructions; xz orthoslice through the reconstructions; zoomed images from the inset in the xz orthoslices.

Figure 10 2D

 10 Figure 10 2D area fraction of the GST phase as a function of sample depth.

Figure

  Figure S3 Total intensity of the projections corresponding to Ge (blue) and GST (blue) chemical phases, as function of the tilt angle. The sum of the two signals is shown in black.

Acknowledgements:

This work was carried out at the Nanocharacterization Platform (PFNC) of Minatec, supported by the 'Recherche technologique de Base' program of the French Ministry of Research. We thank Tony Printemps for the acquisition of the porous Si dataset. We acknowledge the financial support of the Cross-Disciplinary Program on Numerical Simulation of CEA, the French Alternative Energies and Atomic Energy Commission.

Supplementary information


Etienne Caron
email: etienne.caron59@hotmail.fr

Antoine Gabrion

Matthieu Ehlinger

Nicolas Verdier

Brice Rubens-Duval

Thomas Neri

Pierre Martz

Sophie Putman

Gilles Pasquier

Complications and failures of non-tumoral hinged total knee arthroplasty in primary and aseptic revision surgery: A review of 290 cases

Keywords: Total knee replacement, hinged total knee replacement, failures and complications, nontumoral pathology Auteur

Introduction:

Hinged total knee arthroplasty (TKA) implants are a commonly used option during revision or even primary surgery, but their complications are not as well-known due to the rapid adoption of gliding

implants. The literature is inconsistent on this topic, with studies having a small sample size, varied follow-up duration and very different indications. This led us to carry out a large multicenter study with a minimum follow-up of 5 years to evaluate the complications after hinged TKA in a non-tumoral context based on the indications of primary arthroplasty, aseptic surgical revision or fracture treatment around the knee.

Hypothesis:

Hinged TKA was associated with a high complication rate, no matter the indication.

Material and Methods:

Two hundred ninety patients (290 knees) were included retrospectively between January 2006 and December 2011 at 17 sites, with a minimum follow-up of 5 years. The patients were separated into three groups: primary surgery (111 patients), aseptic revision surgery (127 patients) and surgery following a recent (< 3 months) fracture (52 patients: 13 around the TKA and 39 around the knee treated by hinged TKA). Patients who had an active infection the knee of interest were excluded. All the patients were reviewed based on a standardized computer questionnaire validated by the SOFCOT.

Results:

The mean follow-up was 71 ± 39 months [range, 0 to 188]. Of the 290 patients included in the study, 108 patients (37%) suffered at least one complication and 55 patients (19%) had to undergo revision surgery: 16 in the primary TKA group (16/111, 14% of primary TKA), 28 in the revision surgery group (28/127, 22% of revision TKA) and 11 in the fracture treatment group (11/52, 21% of fracture TKA).

The complications due to the hinged TKA for the entire cohort from most to least common were stiffness (41/290, 14%), chronic postoperative pain (37/290, 13%), infection (32/290, 11%), aseptic loosening (23/290, 8%), general complications (20/290, 7%), extensor mechanism complications (19/290, 6%), periprosthetic fracture (9/290, 3%), mechanical failure (2/290, 0.7%). In the primary TKA group, the main complication leading to re-operation was infection (12/111, 11%), while it was loosening for the revision TKA group (15/127, 12%) and infection (8/52, 15%) for the fracture TKA group.

Discussion:

The 37% complication rate for hinged TKA implants is high, with 19% of them requiring re-operation.

The frequency of complications differed depending on the context in which the hinged implant was used (primary, revision, fracture). The complications requiring revision surgery were major ones that

1) Introduction

In its 2016 report, the ANSM (French National Agency for Medicines and Health Products Safety) [START_REF]Rapport d'activité 2016 de l'agence nationale de sécurité du médicament et des produits de santé[END_REF] documented a 30% increase in the number of total knee arthroplasty (TKA) procedures between 2008 and 2013 in France. This trend was also observed in other countries [START_REF] Barrack | Rise of the rotating hinge in revision total knee arthroplasty[END_REF][START_REF] Kurtz | Projections of primary and revision hip and knee arthroplasty in the United States from 2005 to 2030[END_REF].

Consequently, the number of TKA revisions is expected to grow, with Kurtz et al. [START_REF] Kurtz | Projections of primary and revision hip and knee arthroplasty in the United States from 2005 to 2030[END_REF] predicting a 600% increase in the United States by 2030. Pietrzak et al. [START_REF] Pietrzak | Have the frequency of and reasons for revision total knee arthroplasty changed since 2000? Comparison of two cohorts from the same hospital: 255 cases (2013-2016) and 68 cases (1991-1998)[END_REF] showed that the TKA revision surgery rate increased by 6.5 times between 2010 and 2015 for the same team. For these surgical revisions, hinged TKA implants often appear to be the best solution especially when a patient presents with instability or significant bone loss [START_REF] Lustig | Hinged knee prostheses: To be used with due consideration, but indispensable in complex situations[END_REF][START_REF] Pasquier | The role of rotating hinge implants in revision total knee arthroplasty[END_REF][START_REF] Barrack | The use of a modular rotating hinge component in salvage revision total knee arthroplasty[END_REF][START_REF] Berend | Distal Femoral Replacement in Nontumor Cases with Severe Bone Loss and Instability[END_REF][START_REF] Bush | Management of bone loss in revision total knee arthroplasty[END_REF][START_REF] Deehan | The Role of the Rotating Hinge Prosthesis in the Salvage Arthroplasty Setting[END_REF][START_REF] Joshi | Is There a Place for Rotating-Hinge Arthroplasty in Knee Revision Surgery for Aseptic Loosening?[END_REF][START_REF] Pradhan | Salvage revision total knee replacement using the Endo-Model® rotating hinge prosthesis[END_REF][START_REF] Shen | Revision Knee Arthroplasty for Bone Loss: Choosing the Right Degree of Constraint[END_REF][START_REF] Wang | Early catastrophic failure of rotating hinge total knee prosthesis[END_REF][START_REF] Cavaignac | Recurring intraprosthetic dislocation of rotating-hinge total knee prosthesis. Effect of implant design on intrinsic stability[END_REF][START_REF] Pour | Rotating hinged total knee replacement: use with caution[END_REF][START_REF] Hernández-Vaquero | Hinged Total Knee Arthroplasty in the Presence of Ligamentous Deficiency[END_REF][START_REF] Yoon | Rotating hinge knee versus constrained condylar knee in revision total knee arthroplasty: A meta-analysis[END_REF][START_REF] Kouk | Rotating hinge prosthesis for complex revision total knee arthroplasty: A review of the literature[END_REF]. Furthermore, hinged TKA implants have a place in primary surgery with the main indications being major laxity in the collateral ligaments, large deformity, chronic inflammatory arthropathy, neurological conditions and traumatic and post-traumatic lesions [START_REF] Hernández-Vaquero | Hinged Total Knee Arthroplasty in the Presence of Ligamentous Deficiency[END_REF][START_REF] Rodríguez-Merchán | Total knee arthroplasty using hinge joints: Indications and results[END_REF][START_REF] Kouyoumdjian | Hinged total knee arthroplasty for fracture cases: Retrospective study of 52 patients with a mean follow-up of 5 years[END_REF].

But published studies on this topic sometimes have a small sample size [START_REF] Kowalczewski | Primary Rotating-Hinge Total Knee Arthroplasty: Good Outcomes at Mid-Term Follow-Up[END_REF][START_REF] Neumann | Follow-Up of a Modular Rotating Hinge Knee System in Salvage Revision Total Knee Arthroplasty[END_REF][START_REF] Bae | Long-Term Outcome of Total Knee Arthroplasty in Charcot Joint: A 10to 22-Year Follow-Up[END_REF][START_REF] Westrich | Rotating hinge total knee arthroplasty in severly affected knees[END_REF] or short follow-up [START_REF] Westrich | Rotating hinge total knee arthroplasty in severly affected knees[END_REF][START_REF] Lozano | Better Outcomes in Severe and Morbid Obese Patients (BMI > 35 kg/m2) in Primary Endo-Model Rotating-Hinge Total Knee Arthroplasty[END_REF][START_REF] Guenoun | Complications following rotating hinge Endo-Modell (Link) knee arthroplasty[END_REF][START_REF] Chaudhry | Indications, Survivorship, and Clinical Outcomes of a Rotating Hinge Total Knee and Distal Femoral Arthroplasty System[END_REF][START_REF] Rouquette | Early complications and causes of revision after rotating-hinge TKA[END_REF] and some of the larger studies are now dated, since patients were operated more than 30 years ago [START_REF] Deehan | The Role of the Rotating Hinge Prosthesis in the Salvage Arthroplasty Setting[END_REF][START_REF] Pour | Rotating hinged total knee replacement: use with caution[END_REF][START_REF] Bae | Long-Term Outcome of Total Knee Arthroplasty in Charcot Joint: A 10to 22-Year Follow-Up[END_REF][START_REF] Petrou | Medium-term results with a primary cemented rotating-hinge total knee replacement. A 7-to 15-year follow-up[END_REF]. Furthermore, some studies do not differentiate between the tumor indication and non-tumor context [START_REF] Guenoun | Complications following rotating hinge Endo-Modell (Link) knee arthroplasty[END_REF][START_REF] Smith | Comparison of mechanical and nonmechanical failure rates associated with rotating hinged total knee arthroplasty in nontumor patients[END_REF][START_REF] Friesenbichler | Failure rate of a rotating hinge knee design due to yoke fracture of the hinged tibial insert: a retrospective data analysis and review of the literature[END_REF][START_REF] Brown | The survivorship of the link endo-rotational hinge total knee arthroplasty: 5-12-year follow-up of 100 patients[END_REF]. The complication rates reported in the literature vary greatly depending on the features of the study (Table 1).

With this in mind, we conducted a large multicenter study with a minimum 5 years' follow-up to evaluate the complications of hinged TKA implants used in non-tumor cases in the following indications: primary TKA to treat degeneration or fracture and aseptic TKA revision. We hypothesized that hinged TKA was associated with a high complication rate, no matter the indication.

2) Material and methods

Patients

In this retrospective, multicenter study (17 French university hospitals), 290 patients (195 women [67%] and 95 men [33%]) were included who had at least 5 years of follow-up. Patients were operated on between January 2006 and December 2011. The mean patient age at the time when the hinged TKA was implanted was 69 ± 13 years [range, 19 to 96]. The American Society of Anesthesiologist (ASA) score [START_REF] Tiret | Prediction of outcome of anaesthesia in patients over 40 years: a multifactorial risk index[END_REF] and the patients' autonomy level based on the Devane score [START_REF] Devane | Three-dimensional polyethylene wear of apress-fit titanium prosthesis. Factors influencing generation of polyethylene debris[END_REF] are listed in Table 2. Excluded from this study were patients who either had an active infection in the knee in question, had incomplete radiographic records or has no radiological or clinical data at the final follow-up visit.

The patients were separated into three groups: 111 patients (32 men, 79 women) received a hinged TKA during a primary knee replacement, 127 patients (48 men, 79 women) during aseptic revision surgery and 52 patients (15 men, 37 women) as a treatment for a recent (< 3 months) fracture (13 around the TKA and 39 around the knee treated by hinged TKA). The surgical indications are summarized by group in Table 3.

In the context of TKA revision, 72% (91/127) of revised implants were gliding ones, 20% (25/127) were hinged, 6% (8/127) were constrained implants and 2% (3/127) were unicompartmental knee arthroplasty (UKA) implants.

Methods

The patients were evaluated using a retrospective questionnaire approved by the SOFCOT, which was based on prior studies (SOFCOT and SFHG), established beforehand and identical for each participating research site. The questionnaire captured information from the patient's final clinical examination (joint range of motion, laxity in various planes, skin condition). The available radiographs were also analyzed to capture goniometric data and to look for periprosthetic radiolucent lines based on the classification by Ewald [START_REF] Ewald | The Knee Society total knee arthroplasty roentgenographic evaluation and scoring system[END_REF]. The data were collected and tabulated by an independent research assistant through an online platform.

Postoperative stiffness was defined as flexion deficit > 10° and/or flexion < 90°. Residual pain was defined as a level ≥ 4 on a visual analog scale (VAS). The presence of a postoperative TKA infection was confirmed with at least one deep and reliable microbiological tissue sample or had to meet the infection criteria set out by the IDSA [START_REF] Osmon | Diagnosis and Management of Prosthetic Joint Infection: Clinical Practice Guidelines by the Infectious Diseases Society of America[END_REF]. Aseptic loosening was characterized by local radiographic modifications when no infection was present: appearance of a radiolucent line ≥ 1 mm or shifting of the implants. Pathologies of the extensor mechanism consisted of extensor mechanism rupture or patellofemoral instability defined by at least one episode of patellar dislocation. A mechanical complication occurred when the implant broke or disassembled, whether at the hinge or another part of the implant. The occurrence of a periprosthetic fracture was documented.

General complications (vascular, neurological, cardiopulmonary) and mortality after surgery were documented and evaluated based on the classification by Dindo et al. [START_REF] Dindo | Classification of surgical complications: a new proposal with evaluation in a cohort of 6336 patients and results of a survey[END_REF]. Special emphasis was placed on mortality occurring within the first year postoperative.

The radiographic assessment of the knee consisted of AP, lateral, Schuss, 30° sunrise and weightbearing long-leg standing views.

During the surgery to implant the hinged TKA, all patients had their bone stock assessed according to the AORI classification [START_REF] Engh | Ammeen DJ Bone loss with revision total knee arthroplasty: defect classification and alternatives for reconstruction[END_REF]: 47% (60/127) of patients had significant bone loss in their tibia and 45% (57/127) in their femur (AORI ≥ type II). Filling of bone defects was accomplished by adding wedges to the tibia or femur. In two cases, allograft bone was needed. The implants used were cemented and had medullary extension stems. None of the implants used in this study were porouscoated.

Statistical analysis

The statistical analysis was done by the Biostatistics Department of the University of Lille using SAS software (version 9.4, SAS Institute, Cary, NC, USA). The results are presented as counts and percentages for the qualitative variable, and as mean with standard deviation and minimum/maximum values for qualitative variables. Chi 2 and Student's t test were used with parametric variables, while the Wilcoxon and Fisher's exact tests were used with non-parametric variables. The significance threshold was p = 0.05. Fisher's exact test was used when the sample size was less than 5.

3) RESULTS

Complications

At a mean follow-up of 71 ± 39 months [range, 0 to 188], 108 of the 290 patients (37%) suffered at least one complication on the hinged TKA. Fifty-five patients (19%) required revision surgery. These complications are summarized in Table 4. The complications in the overall population are listed by the most to least prevalent: 2) Chronic postoperative pain was the second most common complication: 13% of patients (37/290) had pain on VAS ≥ 4.

3) Infection was in third place, with 11% of patients (32/290) having suffered a postoperative infection around their hinged TKA implants. These infections mainly occurred in the first 2 years after the implantation, with a mean time to occurrence of 12 months ± 13 [range, 0 to 61] (Table 5). 6) Periprosthetic fractures occurred in 3% of patients (9/290). These mainly occurred in the femur (8 knees) and more rarely in the tibia (1 knee). There were no patellar fractures. 7) Mechanical failures were a rare complication (0.7%, 2/290) with the hinge breaking in one patient and the femoral extension stem breaking in another patient (who also had documented femoral loosening).

Surgical revisions

In all, 23% of patients (68/290) required a surgical revision because of complications. While joint contracture and chronic postoperative pain were two most common complications, they did not lead to many surgical revisions; in fact, only two patients who had a joint contracture underwent an arthrolysis surgery, with no other revisions required later on.

Of the 32 patients who suffered an infection, 31 patients had to undergo surgical revision that involved major procedures: 12 implant changes, 4 above-knee amputations and 2 tibiofemoral arthrodesis (Table 5). Also, 13 patients underwent joint lavage but the implants were not changed.

Only one patient (79-year-old female) did not undergo surgical revision because anesthesia was contraindicated. Seventeen of the 23 patients who had implant loosening underwent revision surgery, with 9 femoral and tibial components, 5 isolated tibial and 3 isolated femoral revisions.

Complications related to the extensor mechanism had a lower surgical revision rate, since only 4/8 patients who suffered an extensor mechanism rupture were re-operated. The revision rate was even lower for patellofemoral instability; 2/11 patients underwent revision surgery, both in the primary surgery group. All the patients who suffered a mechanical implant failure or periprosthetic fracture underwent surgical revision (11 patients).

General complications and mortality

General complications occurred in 20 of the 290 patients (7%). Two patients (0.7%) had a grade I complication as defined by Dindo et al. [START_REF] Dindo | Classification of surgical complications: a new proposal with evaluation in a cohort of 6336 patients and results of a survey[END_REF] (transient common fibular nerve damage). Eleven patients (4%) had a grade II complication: 9 patients (3%) had a deep vein thrombosis and 2 (0.7%) had a pulmonary embolism. Three patients (1%) had a grade IVa complication (two heart attacks and one ischemic stroke). There was one (0.3%) grade V complication: early death due to a stroke. Two strokes (0.7%) and two postoperative heart attacks (0.7%) occurred.

At the follow-up, 40/290 patients (14%) had died. The mean age at time of surgery of the patients who died was 76 years ± 7 [range, 60 to 96]. The mean time between the surgery and death was 57 months ± 35 [range, 0 to 149]. Only 5 deaths occurred during the first year postoperative, including the one patient who suffered a massive stroke and died on the 2nd postoperative day; he was in the revision TKA group (Table 4).

Complications by group

In the subset of patients who underwent primary TKA with a hinged implant (111 patients), the most common complication was infection (12/111 patients; 11%), following by joint contracture (11/111 patients; 10%) and extensor mechanism damage (8/111 patients; 7%).

In the patients who received a hinged implant in the context of TKA revision (127 patients), the most common complication was stiffness (23/127 patients; 18%), followed by chronic pain (21/127 patients; 16%) and loosening (15/127 patients; 12%). Infection was the fourth most common (12/127 patients; 9%).

In the subset of patients who received a hinged TKA implant because of a fracture, the main complications were infection and pain (8/52 patients each; 15%), then postoperative stiffness (7/52 patients; 13%). The complications by group are summarized in Table 4 and Figures 2 and3.

4) DISCUSSION

In this study of 290 hinged TKA implants used for non-tumor and non-infection indications with at least 5 years' follow-up, the complication was high since 108 patients suffered at least one complication after surgery (37%), with 55 of them also requiring surgical revision (19%). This high number of complications can be explained by the counting of complications that did not require surgical revision such as chronic pain and stiffness. In fact, surgical revisions were done when the complications threatened the patients' life or autonomy: infection, symptomatic loosening, fracture, implant failure. Despite their high frequency, pain and stiffness are not well studied complications, where a surgical solution is rarely adopted given the complexity of the surgical treatment or the patient's fragility [START_REF] Lustig | Hinged knee prostheses: To be used with due consideration, but indispensable in complex situations[END_REF][START_REF] Pasquier | The role of rotating hinge implants in revision total knee arthroplasty[END_REF][START_REF] Joshi | Is There a Place for Rotating-Hinge Arthroplasty in Knee Revision Surgery for Aseptic Loosening?[END_REF][START_REF] Hernández-Vaquero | Hinged Total Knee Arthroplasty in the Presence of Ligamentous Deficiency[END_REF][START_REF] Kouyoumdjian | Hinged total knee arthroplasty for fracture cases: Retrospective study of 52 patients with a mean follow-up of 5 years[END_REF][START_REF] Kowalczewski | Primary Rotating-Hinge Total Knee Arthroplasty: Good Outcomes at Mid-Term Follow-Up[END_REF][START_REF] Lozano | Better Outcomes in Severe and Morbid Obese Patients (BMI > 35 kg/m2) in Primary Endo-Model Rotating-Hinge Total Knee Arthroplasty[END_REF][START_REF] Felli | The Endo-Model<Superscript>®</Superscript> rotating hinge for rheumatoid knees[END_REF]. Our study has several strong points, and it was the second largest recent study on hinged TKA done, after the study by Cottino et al. [START_REF] Cottino | Painful knee arthroplasty: current practice[END_REF]. Contrary to that study, our study did not include hinged TKA implantations performed in an infected joint, which means that we could study the development of postoperative infection more reliably. The multicenter nature of our study allowed us to study a large number of patients and to reduce the center effect. The mean followup in our study (71 months) is comparable to other published studies on this topic and allowed us to analyze complications occurring in the short and medium term after hinged TKA implantation (Table 1).

The infection rate in our study (11%; 32 patients) appears to be in the average of the literature [START_REF] Deehan | The Role of the Rotating Hinge Prosthesis in the Salvage Arthroplasty Setting[END_REF][START_REF] Joshi | Is There a Place for Rotating-Hinge Arthroplasty in Knee Revision Surgery for Aseptic Loosening?[END_REF][START_REF] Pour | Rotating hinged total knee replacement: use with caution[END_REF][START_REF] Kouk | Rotating hinge prosthesis for complex revision total knee arthroplasty: A review of the literature[END_REF][START_REF] Bae | Long-Term Outcome of Total Knee Arthroplasty in Charcot Joint: A 10to 22-Year Follow-Up[END_REF][START_REF] Lozano | Better Outcomes in Severe and Morbid Obese Patients (BMI > 35 kg/m2) in Primary Endo-Model Rotating-Hinge Total Knee Arthroplasty[END_REF][START_REF] Guenoun | Complications following rotating hinge Endo-Modell (Link) knee arthroplasty[END_REF][START_REF] Rouquette | Early complications and causes of revision after rotating-hinge TKA[END_REF][START_REF] Smith | Comparison of mechanical and nonmechanical failure rates associated with rotating hinged total knee arthroplasty in nontumor patients[END_REF][START_REF] Friesenbichler | Failure rate of a rotating hinge knee design due to yoke fracture of the hinged tibial insert: a retrospective data analysis and review of the literature[END_REF][START_REF] Brown | The survivorship of the link endo-rotational hinge total knee arthroplasty: 5-12-year follow-up of 100 patients[END_REF][START_REF] Streitbuerger | Knee salvage in revision arthroplasty after massive bone loss of the femur condyles (≥Engh III) with a single-modular-hinged knee revision implant[END_REF][START_REF] Bistolfi | Results With 98 Endo-Modell Rotating Hinge Prostheses for Primary Knee Arthroplasty[END_REF][START_REF] Hossain | Midterm assessment of causes and results of revision total knee arthroplasty[END_REF][START_REF] Farid | Intermediate-Term Results of 142 Single-Design, Rotating-Hinge Implants: Frequent Complications May Not Preclude Salvage of Severely Affected Knees[END_REF][START_REF] Gudnason | Implant survival and outcome after rotating-hinge total knee revision arthroplasty: a minimum 6-year follow-up[END_REF][START_REF] Sanguineti | Total knee arthroplasty with rotating-hinge Endo-Model prosthesis: clinical results in complex primary and revision surgery[END_REF][START_REF] Yang | Primary total knee arthroplasty using rotating-hinge prosthesis in severely affected knees[END_REF][START_REF] Kearns | Rotating Hinge Implants for Complex Primary and Revision Total Knee Arthroplasty[END_REF]. This complication always requires surgical treatment except if a major contraindication exists. This rate was higher than after gliding TKA (partially constrained or not), which was reported to be 2% in 2013 by Argenson et al. [START_REF] Argenson | Survivalanalysis of total kneearthroplasty at a minimum 10 years' follow-up: A multicenter French nation wide study including 846 cases[END_REF]. It is the most serious complication that can endanger the viability of the lower limb. This is one of our most important findings. While prior infections in the operated limb were excluded, the infection rate after hinged TKA remains elevated in our three subsets of patients. The patient's pre-existing local and general medical conditions (Tables 2,3) bring us to seriously consider the background on which hinged TKA implants are used. In fact, patients in our study were on average older, overweight or even obese, had a history of cardiovascular disease and had limited autonomy in 56% of cases (162 patients).

Aseptic loosening made up 8% of the complications (23 patients), which is consistent with other published studies in which the loosening ranged from 1% to 13% [START_REF] Kouk | Rotating hinge prosthesis for complex revision total knee arthroplasty: A review of the literature[END_REF][START_REF] Chaudhry | Indications, Survivorship, and Clinical Outcomes of a Rotating Hinge Total Knee and Distal Femoral Arthroplasty System[END_REF][START_REF] Rouquette | Early complications and causes of revision after rotating-hinge TKA[END_REF][START_REF] Brown | The survivorship of the link endo-rotational hinge total knee arthroplasty: 5-12-year follow-up of 100 patients[END_REF][START_REF] Streitbuerger | Knee salvage in revision arthroplasty after massive bone loss of the femur condyles (≥Engh III) with a single-modular-hinged knee revision implant[END_REF][START_REF] Bistolfi | Results With 98 Endo-Modell Rotating Hinge Prostheses for Primary Knee Arthroplasty[END_REF][START_REF] Hossain | Midterm assessment of causes and results of revision total knee arthroplasty[END_REF][START_REF] Farid | Intermediate-Term Results of 142 Single-Design, Rotating-Hinge Implants: Frequent Complications May Not Preclude Salvage of Severely Affected Knees[END_REF][START_REF] Kearns | Rotating Hinge Implants for Complex Primary and Revision Total Knee Arthroplasty[END_REF]. We included the loosening cases that were not reoperated on (Ewald's radiographic criteria [START_REF] Ewald | The Knee Society total knee arthroplasty roentgenographic evaluation and scoring system[END_REF]), which may increase the incidence of this complication relative to other studies where surgical revision was the only criterion for labelling loosening as a complication [START_REF] Chaudhry | Indications, Survivorship, and Clinical Outcomes of a Rotating Hinge Total Knee and Distal Femoral Arthroplasty System[END_REF][START_REF] Rouquette | Early complications and causes of revision after rotating-hinge TKA[END_REF][START_REF] Brown | The survivorship of the link endo-rotational hinge total knee arthroplasty: 5-12-year follow-up of 100 patients[END_REF][START_REF] Streitbuerger | Knee salvage in revision arthroplasty after massive bone loss of the femur condyles (≥Engh III) with a single-modular-hinged knee revision implant[END_REF][START_REF] Hossain | Midterm assessment of causes and results of revision total knee arthroplasty[END_REF]. We noticed that aseptic loosening is mainly observed in the subset of patients who were undergoing revision surgery, and mainly occurred at the femur. This trend was also found in the meta-analysis by Chaudhry et al. [START_REF] Chaudhry | Indications, Survivorship, and Clinical Outcomes of a Rotating Hinge Total Knee and Distal Femoral Arthroplasty System[END_REF].

These findings can probably be explained by the presence of localized bone defects.

Mechanical failure of TKA implants is now rare because of improvements in their design and the use of hinged rotatory models [START_REF] Cavaignac | Recurring intraprosthetic dislocation of rotating-hinge total knee prosthesis. Effect of implant design on intrinsic stability[END_REF][START_REF] Friesenbichler | Failure rate of a rotating hinge knee design due to yoke fracture of the hinged tibial insert: a retrospective data analysis and review of the literature[END_REF][START_REF] Bistolfi | Results With 98 Endo-Modell Rotating Hinge Prostheses for Primary Knee Arthroplasty[END_REF][START_REF] Kearns | Rotating Hinge Implants for Complex Primary and Revision Total Knee Arthroplasty[END_REF][START_REF] Barrack | Evolution of the rotating hinge for complex total knee arthroplasty[END_REF][START_REF] Bistolfi | Rotating-hinge Total Knee for Revision Total Knee Arthroplasty[END_REF]. The extensor mechanism continues to be a cause of complications, with patellar instability being more common than extensor mechanism rupture.

These findings are also consistent with the literature [START_REF] Joshi | Is There a Place for Rotating-Hinge Arthroplasty in Knee Revision Surgery for Aseptic Loosening?[END_REF][START_REF] Hernández-Vaquero | Hinged Total Knee Arthroplasty in the Presence of Ligamentous Deficiency[END_REF][START_REF] Neumann | Follow-Up of a Modular Rotating Hinge Knee System in Salvage Revision Total Knee Arthroplasty[END_REF][START_REF] Guenoun | Complications following rotating hinge Endo-Modell (Link) knee arthroplasty[END_REF][START_REF] Petrou | Medium-term results with a primary cemented rotating-hinge total knee replacement. A 7-to 15-year follow-up[END_REF][START_REF] Smith | Comparison of mechanical and nonmechanical failure rates associated with rotating hinged total knee arthroplasty in nontumor patients[END_REF][START_REF] Friesenbichler | Failure rate of a rotating hinge knee design due to yoke fracture of the hinged tibial insert: a retrospective data analysis and review of the literature[END_REF][START_REF] Cottino | Painful knee arthroplasty: current practice[END_REF][START_REF] Farid | Intermediate-Term Results of 142 Single-Design, Rotating-Hinge Implants: Frequent Complications May Not Preclude Salvage of Severely Affected Knees[END_REF][START_REF] Gudnason | Implant survival and outcome after rotating-hinge total knee revision arthroplasty: a minimum 6-year follow-up[END_REF]. Periprosthetic fractures are rarer but mainly occurred in the femur and always required re-operation as described in the literature [START_REF] Deehan | The Role of the Rotating Hinge Prosthesis in the Salvage Arthroplasty Setting[END_REF][START_REF] Pour | Rotating hinged total knee replacement: use with caution[END_REF][START_REF] Hernández-Vaquero | Hinged Total Knee Arthroplasty in the Presence of Ligamentous Deficiency[END_REF][START_REF] Westrich | Rotating hinge total knee arthroplasty in severly affected knees[END_REF][START_REF] Petrou | Medium-term results with a primary cemented rotating-hinge total knee replacement. A 7-to 15-year follow-up[END_REF][START_REF] Smith | Comparison of mechanical and nonmechanical failure rates associated with rotating hinged total knee arthroplasty in nontumor patients[END_REF][START_REF] Cottino | Painful knee arthroplasty: current practice[END_REF][START_REF] Streitbuerger | Knee salvage in revision arthroplasty after massive bone loss of the femur condyles (≥Engh III) with a single-modular-hinged knee revision implant[END_REF][START_REF] Bistolfi | Results With 98 Endo-Modell Rotating Hinge Prostheses for Primary Knee Arthroplasty[END_REF][START_REF] Hossain | Midterm assessment of causes and results of revision total knee arthroplasty[END_REF][START_REF] Farid | Intermediate-Term Results of 142 Single-Design, Rotating-Hinge Implants: Frequent Complications May Not Preclude Salvage of Severely Affected Knees[END_REF][START_REF] Gudnason | Implant survival and outcome after rotating-hinge total knee revision arthroplasty: a minimum 6-year follow-up[END_REF]. General complications were not very common in our study, while their incidence varies greatly in the literature (Table 1) [START_REF] Deehan | The Role of the Rotating Hinge Prosthesis in the Salvage Arthroplasty Setting[END_REF][START_REF] Pour | Rotating hinged total knee replacement: use with caution[END_REF][START_REF] Hernández-Vaquero | Hinged Total Knee Arthroplasty in the Presence of Ligamentous Deficiency[END_REF][START_REF] Guenoun | Complications following rotating hinge Endo-Modell (Link) knee arthroplasty[END_REF][START_REF] Chaudhry | Indications, Survivorship, and Clinical Outcomes of a Rotating Hinge Total Knee and Distal Femoral Arthroplasty System[END_REF][START_REF] Petrou | Medium-term results with a primary cemented rotating-hinge total knee replacement. A 7-to 15-year follow-up[END_REF][START_REF] Smith | Comparison of mechanical and nonmechanical failure rates associated with rotating hinged total knee arthroplasty in nontumor patients[END_REF][START_REF] Cottino | Painful knee arthroplasty: current practice[END_REF][START_REF] Farid | Intermediate-Term Results of 142 Single-Design, Rotating-Hinge Implants: Frequent Complications May Not Preclude Salvage of Severely Affected Knees[END_REF][START_REF] Long | A biomechanical evaluation of hinged total knee replacement prostheses[END_REF]. The high number of complications with hinged TKA implants relative to gliding implants [START_REF] Argenson | Survivalanalysis of total kneearthroplasty at a minimum 10 years' follow-up: A multicenter French nation wide study including 846 cases[END_REF] along with the number of deaths found in our study and in the literature highlights the fact that the patient's general health or local medical conditions are against us when implanting hinged TKAs [START_REF] Pour | Rotating hinged total knee replacement: use with caution[END_REF][START_REF] Hernández-Vaquero | Hinged Total Knee Arthroplasty in the Presence of Ligamentous Deficiency[END_REF][START_REF] Rodríguez-Merchán | Total knee arthroplasty using hinge joints: Indications and results[END_REF][START_REF] Siqueira | Modes of Failure of Total Knee Arthroplasty: Registries and Realities[END_REF][START_REF] Böhm | Is there a future for hinged prostheses in primary total knee arthroplasty? A 20-year survivorship analysis of the Blauth prosthesis[END_REF].

The complication rate varies within the different subsets of patients in our study according to the surgical indication (Fig. 2,3 and Table 4). The surgical revision and fracture subsets had a higher complication rate, which can be explained by the patients' worse overall health, unfavorable conditions around the knee and complexity of the surgical procedure [START_REF] Barrack | The use of a modular rotating hinge component in salvage revision total knee arthroplasty[END_REF][START_REF] Berend | Distal Femoral Replacement in Nontumor Cases with Severe Bone Loss and Instability[END_REF][START_REF] Bush | Management of bone loss in revision total knee arthroplasty[END_REF][START_REF] Deehan | The Role of the Rotating Hinge Prosthesis in the Salvage Arthroplasty Setting[END_REF][START_REF] Joshi | Is There a Place for Rotating-Hinge Arthroplasty in Knee Revision Surgery for Aseptic Loosening?[END_REF][START_REF] Pradhan | Salvage revision total knee replacement using the Endo-Model® rotating hinge prosthesis[END_REF][START_REF] Shen | Revision Knee Arthroplasty for Bone Loss: Choosing the Right Degree of Constraint[END_REF][START_REF] Kouyoumdjian | Hinged total knee arthroplasty for fracture cases: Retrospective study of 52 patients with a mean follow-up of 5 years[END_REF][START_REF] Streitbuerger | Knee salvage in revision arthroplasty after massive bone loss of the femur condyles (≥Engh III) with a single-modular-hinged knee revision implant[END_REF][START_REF] Gudnason | Implant survival and outcome after rotating-hinge total knee revision arthroplasty: a minimum 6-year follow-up[END_REF][START_REF] Long | A biomechanical evaluation of hinged total knee replacement prostheses[END_REF][START_REF] Parratte | Primary total knee arthroplasty in the management of epiphyseal fracture around the knee[END_REF]. In the primary TKA subset, the high rate of infection and mortality is a reminder of the specific predispositions for these patients: either local ones such multiple ligament lesions, considerable knee laxity, large deformity or multiple prior surgeries or in patients who have systemic diseases such as inflammatory arthropathy that involve long-term immunosuppressant therapy [START_REF] Kowalczewski | Primary Rotating-Hinge Total Knee Arthroplasty: Good Outcomes at Mid-Term Follow-Up[END_REF][START_REF] Bae | Long-Term Outcome of Total Knee Arthroplasty in Charcot Joint: A 10to 22-Year Follow-Up[END_REF][START_REF] Lozano | Better Outcomes in Severe and Morbid Obese Patients (BMI > 35 kg/m2) in Primary Endo-Model Rotating-Hinge Total Knee Arthroplasty[END_REF][START_REF] Felli | The Endo-Model<Superscript>®</Superscript> rotating hinge for rheumatoid knees[END_REF][START_REF] Cottino | Painful knee arthroplasty: current practice[END_REF][START_REF] Böhm | Is there a future for hinged prostheses in primary total knee arthroplasty? A 20-year survivorship analysis of the Blauth prosthesis[END_REF][START_REF] Abdulkarim | Rotating-hinge knee prosthesis as a viable option in primary surgery: Literature view & meta-analysis[END_REF].

Nevertheless, our study has several limitations: 1) Excluding patients who had an active infection or history of bone/joint infection in their knee helped to limit the bias due to an infection. But this criterion is also a study limitation since implanting a hinged TKA in an infected knee joint was not studied. This was a conscious choice in order to study the occurrence of an infection more reliably after performing TKA with hinged implants. 2) The retrospective nature of this study is a limitation; while it allowed us to accumulate data from a large set of patients, the data collection was not exhaustive despite using a standardized questionnaire to limit this bias. 3) Even with the large sample size, the subgroup analysis was difficult in some instances because of the rarity of some events; thus one should be cautious about drawing conclusions on some of these analyses.

5) CONCLUSION

Hinged TKA implants are associated with a high complication rate that differs by the surgical indication. The most frequent complications (pain and stiffness) rarely required surgical treatment due to the complexity of the revision procedures and its risks. Infection and periprosthetic fractures require surgical treatment in nearly every case, despite their risk. Problems related to the extensor mechanism and implant loosening were treated surgically or conservatively depending on the patient's discomfort, local conditions and general health. Hinged TKA implants have a place in our prosthetic arsenal but they should be used in a carefully and calculated manner given the frequency of complications.

1 )

 1 Stiffness was the most frequent complication: 14% of patients (41/290). The mean range of motion in patients diagnosed with joint contracture was 76° ± 26° [range, 0 to 120] in flexion, 9° ± 10° [range, 0 to 40] flexion deficit and 0° ± 2° [range, 0 to 10] recurvatum. The patients who had a joint contracture were younger (63.8 years ± 15.6 [range, 25 to 94]) than the rest of the population (71.5 ± 11.1 [range, 19 to 89]) (p < 0.001).

4 )

 4 Aseptic loosening of an implant component made up 8% of the complications (23/290) and occurred after an average of 45 months ± 32 [range, 3 to 120]. Loosening affected the femoral implant in 17 knees and the tibial implant in 13 knees. Loosening of the patellar implant occurred in only 1 knee. Both implants (tibia and femur) had loosened in 8 patients. The patients who had implant loosening were younger at the time of implantation (mean age at surgery of 64.1 ± 11 [range, 41 to 82]) relative to those who did not experience implant loosening (70.2 ± 31.1 [range, 19 to 96]) (p = 0.007). 5) Complications related to the extensor mechanism made up 7% (19/290) of hinged TKA complications. Eleven patients (4%) had patellar instability while 8 patients (3%) suffered an extensor mechanism rupture.

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Flow chart Figure 2: Summary of the various complications (number of cases) in the general population Figure 3: Diagram of the main complications (in percentage) by group, excluding rare complications (mechanical failures and deficit of the common fibular nerve)

Table 1 :

 1 Complications after hinged TKA in the literature. *: primary surgery, ** revision surgery *** patellofemoral (see table excel) CFN: Common fibular nerve damage; DVT: Deep vein thrombosis, PE: Pulmonary embolism. The article by Smith et al. [31] compares two sets of patients.

Table 2 :

 2 Characteristics of the population and subgroups (Mean ± SD and min/max)

	TKA: Total knee arthroplasty, BMI: Body mass index

Table 3 :

 3 Surgical indication for hinged TKA by group

	Primary TKA		Revision TKA	Trauma (fracture)
	Number of patients	111	Number of patients	127	Number of patients	52
	Large deformity 61 (55%)	Aseptic loosening 75 (59%)	Post-traumatic sequelae 25 (48%)
	Arthropathy	29 (26%)	Ligament laxity	50 (39%)	Fracture in older adult 17 (33%)
	Ligament laxity	11 (10%)	Other	2 (2%)	Nonunion	8 (15%)
	Primary OA	10 (9%)			Laxity	2 (4%)
	OA: osteoarthritis

Table 4 :

 4 Summary of complications by group (N = number of cases (% by group))

		Total	Primary TKA	Revision TKA	Trauma group	p value
			group	group
	Number of patients	290	111	127	52	-
	Complications	108 (37.2 %)	32 (28.8 %)	56 (44.1 %)	20 (38.5 %)	0.05
	Type of complication
	Stiffness	41 (14.1 %)	11 (9.9 %)	23 (18.1 %)	7 (13.5 %)	0.19
	Pain	37 (12.8 %)	8 (7.2 %)	21 (16.5 %)	8 (15.4 %)	0.08
	Infection	32 (11.0 %)	12 (10.8 %)	12 (9.4 %)	8 (15.4 %)	0.51
	Loosening	23 (7.9 %)	6 (5.4 %)	15 (11.8 %)	2 (3.8 %)	0.39
	Extensor mechanism	19 (6.6 %)	9 (8.1 %)	6 (4.7 %)	4 (7.7 %)	0.52
	(instability and rupture)
	Periprosthetic fracture	9 (3.1%)	1 (0.9 %)	7 (5.5 %)	1 (1.9 %)	0.11
	Common fibular nerve	2 (0.7 %)	2 (1.8 %)	0 (0%)	0 (0%)	0.32
	deficit
	Mechanical failure	2 (0.7 %)	0 (0%)	1 (0.8 %)	1 (1.9 %)	0.47
	Surgical revision	55 (19.0 %)	16 (14.4 %)	28 (22.0 %)	11 (21.2 %)	0.29
	Death	40 (13.8%)	19 (17.1%)	12 (9.4%)	9 (17.3%)	0.17
	Died within 1 year	4	1	2	1	0.67
	Died beyond 1 year	36	18	10	8	0.12
	Mean time surgery/death	57 ± 35	59 ± 28	69 ± 53	38 ± 27	0.17
	(months)	[0 to 149]	[6 to 109]	[0 to 149]	[3 to 66]

Table 5 :

 5 Infections with their treatment and mean time between surgery and occurrence of infection (N = number of cases) (Mean ± SD and min/max)

		Total	Group	Group	Group	p value
			Primary TKA	Revision TKA	Trauma (fracture)
	Number of	290	111	127	52	-
	patients
	Infections	32 (11%)	12 (10.8%)	12 (9.4%)	8 (15.4%)	0.51
	Revision for	31	11 (9.9%)	12 (9.4%)	8 (15.4%)	0.47
	infection
			Treatment of infection
	Lavage	13	7	4	2	0.35
	TKA implant	12	4	4	4	0.72
	change
	Fusion	2	0	1	1	0.71
	Amputation	4	0	3	1	0.16
		Mean time surgery/infection (months)
	Mean time	12 ± 13 [0 to 61] 8 ± 8 [1 to 26] 18 ± 16 [0 to 61]	7 ± 9 [0 to 27]	0.25

TKA: Total knee arthroplasty

Acknowledgements

We are grateful to the research sites and the symposium participants not included on the author list (Amiens, Béclère, Fort-de-France, Grenoble, Lille, Lyon, Nancy, Nantes, Nîmes, Poitiers, Saint Etienne, Strasbourg, Toulouse, Tours), to the Biostatistics Department in Lille and the persons who worked on this project. This study was based on a symposium held during the 2017 SOFCOT conference on "Results of hinged total knee arthroplasty".

Funding: Funding was provided by the SOFCOT to carry out the online data collection and statistical analysis by an independent investigator.

Conflict of interest disclosure: None of the authors have conflicts to declare related to this study.

Outside this study: Etienne Caron was the recipient of a scholarship from Arthrex. Antoine Gabrion is a consultant for X-Nov. Matthieu Ehlinger is a consultant for Depuy-Synthès, Lépine, New-Clip and Amplitude. Pierre Martz is a consultant for Serf. Sophie Putman is a consultant for Corin. Gilles Pasquier is a consultant for Zimmer-Biomet. The other authors have no conflict of interest outside this study.