Nathan Painchaud
email: nathan.painchaud@usherbrooke.ca

Youssef Skandarani

Thierry Judge

Olivier Bernard

Alain Lalande

Pierre-Marc Jodoin

Pierre-Marc Jodoin

P.-M Jodoin

Cardiac Segmentation With Strong Anatomical Guarantees

Keywords: CNN, Variational autoencoder, Cardiac segmentation, MRI, Ultrasound

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

I. INTRODUCTION

M AGNETIC Resonance Imaging (MRI) and ultrasound imagery (US) are the most widely-used cardiac image acquisition devices in clinical routine. While MRI can produce high-contrast, high-resolution and high-SNR images in any orientation, the cardiac function is typically evaluated from a series of kinetic images (cine-MRI) acquired in shortaxis orientation of the left ventricle [START_REF] Michael | Recent advances in cardiovascular magnetic resonance: Techniques and applications[END_REF]. In clinical practice, cardiac parameters are usually estimated from the knowledge of the endocardial and epicardial borders of the left ventricle (defining the left cavity (LV) and the myocardium (MYO)) and the endocardial border of the right ventricle (RV) at the enddiastolic (ED) and end-systolic (ES) phases. MRI is the reference exam for the evaluation of the cardiac function and of the cardiac viability after myocardial infarction. Unfortunately, the MRI device is bulky, expensive and cannot be operated by one person even with the latest innovations.

On the other hand, echocardiography is an highly flexible and low-cost exam to evaluate the cardiac function. Ultrasound devices are small and less expensive that one can carry around the hospital. As such, US provides physicians realtime images in an easy way and is often described as the modern stethoscope. Unfortunately, ultrasound images suffer from a poor SNR, noise artifacts, local signal drop, limited field of view, and a limited acquisition angle. The most widelyused acquisition protocol to evaluate the cardiac function involve a 2D+time long-axis orientation resulting into two and four-chamber view images. As for MRI, the endocardial and epicardial borders are outlined at the ED and ES time instant. The volume and ejection fraction of the LV is then computed with the biplane Simpson's formula [START_REF] Folland | Assessment of left ventricular ejection fraction and volumes by realtime, two-dimensional echocardiography. a comparison of cineangiographic and radionuclide techniques[END_REF].

US and MRI are complementary by nature. US devices can quickly evaluate the heart function, find the source of certain symptoms and detect or exclude pathologies. MRI is an imaging modality to further assess a disease and for longitudinal analysis. Both MRI and US are non-invasive and are non-irradiating imaging techniques.

CNNs have had great success at segmenting these modalities [START_REF] Duan | Automatic 3d bi-ventricular segmentation of cardiac images by a shape-refined multi-task deep learning approach[END_REF]- [START_REF] Zotti | Convolutional neural network with shape prior applied to cardiac mri segmentation[END_REF]. Some neural nets even provide results with overall Dice index and/or Hausdorff distance within the inter and intra-observer variations [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved?[END_REF], [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF]. Unfortunately, these methods still generate spurious anatomically impossible shapes with holes inside the structures, abnormal concavities, and duplicated regions to name a few. Therefore, despite their excellent results on average, these methods are still unfit for a day-today clinical use.

To reduce such errors, some authors integrate shape priors to their model [START_REF] Duan | Automatic 3d bi-ventricular segmentation of cardiac images by a shape-refined multi-task deep learning approach[END_REF], [START_REF] Oktay | Anatomically constrained neural networks (acnns): Application to cardiac image enhancement and segmentation[END_REF], [START_REF] Zotti | Convolutional neural network with shape prior applied to cardiac mri segmentation[END_REF] while others simply post-process the generated shapes with morphological operators or some connected component analysis to remove small isolated regions. Unfortunately, none of these approaches can guarantee 100% of the time the anatomical plausibility of their results.

In this paper, we present the first deep learning formalism which guarantees the anatomical plausibility of cardiac shapes, w.r.t. well-defined criteria, under any circumstances. Our method can be plugged at the output of any segmentation method to reduce to zero its number of anatomically invalid shapes, while preserving its overall accuracy. As will be shown in the results section, the same framework is effective for a variety of segmentation methods both applied on echocardiographic and MR images.

II. PREVIOUS WORK

Although there is more non-deep-learning cardiac segmentation methods than deep learning ones (neural networks are relatively new in the field) we shall focus on the latter due to the very nature of our contribution.

A. MRI segmentation

CNNs: The U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] has become the de facto generic encoder-decoder CNN for biomedical image segmentation and is often used in cardiology. Isensee et al. [START_REF] Isensee | Automatic cardiac disease assessment on cine-mri via time-series segmentation and domain specific features[END_REF], winner of the 2017 MICCAI Automated Cardiac Diagnosis Challenge (ACDC) [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved?[END_REF], used an ensemble of 2D and 3D U-Net, with the addition of an upscaling and aggregation of the last two convolutional blocks of the decoder for the final segmentation. Also, as mentioned by Bernard et al. [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved?[END_REF], several other challengers used a modified version of the UNet. Vigneault et al. proposed a more domain specific approach, Omega-Net [START_REF] Vigneault | ω-net (omega-net): fully automatic, multi-view cardiac mr detection, orientation, and segmentation with deep neural networks[END_REF], which has, at its heart, a localization and transformation network that transforms the input MRI into a canonical orientation which is subsequently segmented by a cascade of U-Nets.

CNNs with shape prior: Although most deep segmentation methods produce accurate segmentation results, they still suffer from anatomical inconsistencies. As a solution, several authors incorporate a shape prior to their model. Oktay et al. uses an approach named anatomically constrained neural network (ACNN) [START_REF] Oktay | Anatomically constrained neural networks (acnns): Application to cardiac image enhancement and segmentation[END_REF]. Their neural network is similar to a 3D U-Net whose segmentation output is constrained to be close to a non-linear compact representation of the underlying anatomy, derived from an autoencoder network. More recently, Zotti et al. proposed a method based on the gridnet architecture that embeds a cardiac shape prior to segment MR images [START_REF] Zotti | Convolutional neural network with shape prior applied to cardiac mri segmentation[END_REF]. Their shape prior encodes the probability of a 3D location point being a member of a certain class and is automatically registered with the last feature maps of their network. Finally, Duan et al. implemented a shape-constrained bi-ventricular segmentation strategy [START_REF] Duan | Automatic 3d bi-ventricular segmentation of cardiac images by a shape-refined multi-task deep learning approach[END_REF]. Their pipeline starts with a multi-task deep learning approach that aims to locate specific landmarks. These landmarks are then used to initialize atlas propagation during a refinement stage of segmentation. Although the use of an atlas improves the quality of the results, their final segmented shapes strongly depend on the accuracy of the located landmarks. From these studies, it appears that only soft constraints are currently imposed in the literature to steer the segmentation outputs toward a reference shape. As will be shown in this paper, shape-prior methods are not immune to producing anatomically incorrect results.

B. Echocardiographic segmentation

CNNs: In 2012, Carneiro et al. exploited deep belief networks and the decoupling of rigid and nonrigid classifiers to improve robustness in terms of image conditions and shape variability [START_REF] Carneiro | The Segmentation of the Left Ventricle of the Heart From Ultrasound Data Using Deep Learning Architectures and Derivative-Based Search Methods[END_REF]. Later, Chen et al. used transfer learning from cross domain to enhance feature representation [START_REF] Chen | Iterative multi-domain regularized deep learning for anatomical structure detection and segmentation from ultrasound images[END_REF]. In parallel, Smistad et al. showed that the U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] could be trained with the output of a state-of-the-art deformable model to segment the LV in 2D ultrasound images [START_REF] Smistad | 2D left ventricle segmentation using deep learning[END_REF]. Additionally, Leclerc et al. showed that a simple U-Net learned from a large annotated dataset can produce accurate results that are much better than the state-of-the-art, on average below the inter-observer variability and close but still above the intraobserver variability with 18% of outliers [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF]. Recently, the same authors proposed to efficiently integrate the U-Net into a multi-task network (the so-called "LUNet") designed to optimize in parallel a localization and a segmentation procedure [START_REF] Leclerc | Lu-net: a multi-task network to improve the robustness of segmentation of left ventriclular structures by deep learning in 2d echocardiography[END_REF]. Their results showed that localization allows the introduction of contextualization properties which improve the overall accuracy of cardiac segmentation while reducing the number of outliers to 11%.

CNNs with shape prior: The ACNN model proposed by Oktay et al. [START_REF] Oktay | Anatomically constrained neural networks (acnns): Application to cardiac image enhancement and segmentation[END_REF] was also applied to the segmentation of the endocardial border in 3D echocardiography. Results showed that the use of an autoencoder network to impose soft shape constraints allowed to obtain highly competitive scores with respect to the state-of-the-art while learning from a limited number of cases (30 annotated volumes). Very recently, Dong et al. developed a deep atlas network to significantly improve 3D LV segmentation based on limited annotation data [START_REF] Dong | Deep atlas network for efficient 3d left ventricle segmentation on echocardiography[END_REF]. The key aspects of this architecture are a light-weight network to perform registration and a multi-level information consistency constraint to enhance the overall model's performance. This method currently has the best scores for 3D LV segmentation in 3D echocardiography. Jafari et al. also proposed to alter the echocardiography fed to segmentation models using a framework that introduces soft shape priors to Cycle-Gan [START_REF] Jafari | Echocardiography Segmentation by Quality Translation Using Anatomically Constrained CycleGAN[END_REF]. By enhancing the quality of the input images through image translation, the authors manage to improve the worst-case performance of standard segmentation networks.

III. PROPOSED FRAMEWORK

A schematic representation of our method is given in Fig. 1. The system is used for both short-axis MR images and longaxis echocardiographic images, two fairly different looking cardiac shapes. Overall, the system is made of three blocks, namely: 1) a constrained VAE that learns the latent representation of valid cardiac shapes, 2) an anatomically-constrained rejection sampling procedure to augment the number of latent vectors and 3) a post-processing VAE that warps anatomically invalid shapes toward the closest valid ones. Since the system implements a post-processing for segmentations, the "Segmentation method" block in Fig. 1 is a placeholder for any possible cardiac segmentation method. The anatomical guarantees come from an operation called "Latent space transformation" in Fig. 1, that substitutes the latent vector of an incorrect shape by a close but valid one.

The correctness of a cardiac shape is determined by a set of complementary anatomical criteria. These criteria allow to identify anatomically implausible configurations regardless of the input image. As such, the aim of our system is to output cardiac shapes that always respect these anatomical criteria. Fig. 1: Schematic representation of our method. Although this figure illustrates short axis image segmentation, we use the same framework for two and four-chamber view ultrasound images. The segmentation method is a placeholder for any cardiac segmentation method. The parameters used by the anatomical VAE (p θ , q θ ) are the same ones trained on the constrained VAE.

A. Anatomical Criteria

Because of the orientation used to acquire cine MR and apical ultrasound images, our system uses two sets of anatomical criteria, namely the short-axis and the long-axis criteria (c.f. Fig. 2 and 3 for illustrations). When relevant, thresholds were defined based on the datasets' training set (ACDC for short-axis, CAMUS for long-axis) so that no clinically relevant segmentations were marked as invalid. Both datasets cover healthy and pathological cases, so the thresholds take into account a representative distribution of cardiac configurations, and not only a subset of healthy configurations. Since these criteria are not included in the loss, they do not need to be differentiable. They are evaluated systematically on every sample from the latent space, so they do however need to be computable algorithmically using traditional image processing, for efficiency concerns.

Short-Axis Criteria: Our system uses 16 anatomical shortaxis criteria that each highlight an invalid cardiac configuration. These criteria are the following: their area to that of a circle having the same perimeter (aka circularity metric) exceeds a certain threshold. Long-Axis Criteria: We use 12 anatomical long-axis criteria to highlight invalid configurations. These criteria are:

1) (3 criteria) hole(s) in the LV, MYO and left atrium (LA) 2) (2 criteria) hole(s) between the LV and the MYO or between the LV and the LA 3) (3 criteria) the presence of more than one LV, MYO or LA 4) (2 criteria) the size of the area by which the LV touches the background or the MYO touches the LA exceeds a certain threshold. 5) (1 criterion) the ratio between the minimal and maximal thickness of the MYO is below a given threshold 6) (1 criterion) the ratio between the width of the LV and the average thickness of the MYO exceeds a certain threshold. Both width and thickness are computed as the total width of the structure at the middle-point of the embeded bounding box. The goal is to identify situations for which the MYO is too thin with respect to the size of the LV.

B. Constrained Variational Autoencoder (cVAE)

VAEs [START_REF] Kingma | Auto-encoding variational bayes[END_REF] are unsupervised neural networks trained to learn the latent representation of a set of data. These neural nets are made of an encoder, which projects an input signal x to the latent space, and a decoder, which converts a latent vector z back into the input space. More specifically, the VAE encoder outputs the parameters ( µ and Σ) of a Gaussian distribution p θe ( z|x) where z ∈ R k is a latent vector (k = 32 in our case, and θ e are the parameters of the encoder network). The decoder takes in a latent variable z sampled from p θe ( z|x) and outputs x, the reconstruction of the input vector x. As such, the decoder gets to learn the conditional distribution q θ d (x| z) with θ d as the decoder parameters.

In this work, x and x are 2D cardiac shapes, both ∈ R n×n . Since our overarching objective is to learn the latent representation of valid cardiac shapes, we train our VAE with input values x that are groundtruth cardiac shapes outlined by a medical expert, and thus without any anatomical aberrations. As such, after the VAE has been trained, Gaussian centroids µ i encoded from groundtruth cardiac shapes x will also lead to an anatomically valid reconstructed shape x. In fact, any point z sampled on the manifold of valid cardiac vectors can be decoded to an anatomically valid cardiac shape x. As such, we call these vectors valid latent vectors.

However, as will be shown later, our method needs to linearly interpolate latent vectors. It follows that a latent vector z interpolated between two anatomically valid vectors z i , z j should also be valid (at least most of the time). Furthermore, our method needs that a small translation δ z performed on a valid latent vector z leads to a smooth and anatomically coherent transformation on the resulting decoded image.

These constraints can be fulfilled with a linear manifold that we approach with a constrained VAE (cVAE) [START_REF] Higgins | beta-vae: Learning basic visual concepts with a constrained variational framework[END_REF]. The constraint comes in the form of a single-neuron regression network [START_REF] Bishop | Pattern recognition and machine learning[END_REF] y θc ( z) trained simultaneously with the encoder and the decoder (c.f. Fig. 1). The goal of the linear regression network is to reproduce a domain-specific target t associated to the input image x. Since a single-neuron network with no activation can only learn a linear function, the gradient from the regression loss forces the encoder to learn a more linear (and thus less convoluted) manifold of valid shapes in the latent space.

The resulting loss function of our cVAE is:

IE q θe ( z|x) [-log q θ d (x| z)] + KL(p θe ( z|x) p( z)) + (1)
y θc ( z) -t 2
where the first two terms make up the usual ELBO (Evidence Lower BOund) VAE loss function [START_REF] Kingma | Auto-encoding variational bayes[END_REF], with p( z) as the unitvariance zero-mean Gaussian prior. The last term is the L2 regression loss of the one-neuron net. MRI short-axis linear constraint: Since cine-MR short-axis images x are 2D+time arrays stacked into two 3D volumes, in our study, only the ES and ED phases are considered and then the target predicted by the one-neuron regression network y θc ( z) is the slice index of x normalized between 0 (base) and 1 (apex).

Ultrasound long-axis linear constraint: The ultrasound signal is a 2D+time sequence of images. In this case, the regression network is designed to predict the time instant of the input image x. Here as well, the target value is normalized between 0 and 1, where 0 stands for the end-diastolic time instant and 1, the end-systolic time instant.

C. Anatomically-Constrained Data Augmentation

As mentioned before, once the cVAE is trained, the 2D groundtruth cardiac shapes x can be projected in the 32D latent space, where they form a manifold of valid latent vectors. These latent vectors are "anatomically correct", since the deterministic cVAE decoder can convert them back to anatomically valid cardiac shapes.

The idea behind our method is to warp invalid cardiac shapes toward a close but valid configuration. This is done by projecting any invalid cardiac shape x to the latent space, project its associated invalid latent vector to the closest point on the manifold of valid latent vectors, and then decode the resulting vector. Unfortunately, with 32 dimensions, the latent space has a whopping number of 2 32 quadrants, which is orders of magnitude larger than any annotated cardiac dataset. As such, with too few valid latent vectors, the manifold is too sparse to be effective.

One solution to that problem is to increase the number of valid latent vectors through data augmentation. Since the manifold in the latent space is roughly linear, one can easily sample it with a rejection sampling (RS) method [START_REF] Koller | Probabilistic Graphical Models: Principles and Techniques[END_REF]. The goal is to generate a new set of latent vectors Z such that the distribution P ( z ) of these newly generated samples is close to P ( z), the distribution from which the original valid latent vectors are identically independent and identically distributed (iid) from. Since sampling P ( z) directly is difficult, RS samples a second, and yet easier, probability density function Q( z). A common choice for Q( z) is a Gaussian of mean and variance equal to the distribution of the original valid latent vector derived from the groundtruth segmentation. A key idea with RS is that P ( z) > M Q( z) where M > 1. Given P ( z) and Q( z), the sampling procedure first generates a random sample z j , iid of Q( z), as well as a uniform random value

u ∈ [0, 1]. If u < P ( zj )
M Q( zj ) then z j is kept, otherwise it is rejected. Since in our case P ( z) is unknown a priori, we estimate it with a Parzen window distribution [START_REF] Bishop | Pattern recognition and machine learning[END_REF]. The primary objective with RS is to increase the number of latent vectors. However, since these newly generated points need to lie on the manifold of valid vectors, we want those new vectors to correspond to anatomically valid cardiac shapes. As such, we redefine the RS criterion as follows:

u < 1 (dec( z i )) P ( z j ) M Q( z j ) (2)
where dec( z j ) is the VAE decoder that converts the latent vector z j into a segmentation map and 1 is an indicator function which returns 1 when the input segmentation map respects the defined anatomical criteria and zero otherwise. In Fig. 1, this operation is called anatomically-constrained rejection sampling augmentation. This sampling procedure is repeated up until the desired number of samples is reached. At the end, a total number of 4 million latent vectors have been generated, both for the MRI and the ultrasound datasets.

Each of these vectors have a corresponding valid cardiac shape that respects the aforementioned anatomical criteria (c.f. Section III-A). Samples of cardiac shapes generated with anatomically-constrained rejection sampling augmentation are provided in Fig. 3.

D. Cardiac shape warping

Our system can be seen as a post-processing operator that one can plug after any segmentation method that sometimes generates anatomically erroneous segmentation maps. This is illustrated at the bottom right of Fig. 1, where a VAE is used to convert erroneous segmentation maps into anatomically valid segmentations. This post-processing VAE is in fact the trained cVAE. Thus, any anatomically invalid segmentation map x fed to the VAE encoder gets projected into the latent space where 4 million valid vectors lie. Furthermore, since the VAE decoder is deterministic, any anatomically valid latent vector z is guaranteed to be converted into an anatomically plausible cardiac shape.

As mentioned before, our aim is to warp an anatomically incorrect cardiac shape toward a close but correct configuration. We do so by translating the latent vector z of an erroneous cardiac shape to a near but anatomically valid latent vector ẑ. This operation can be summarized as:

ẑopt = arg min ẑ || z -ẑ|| 2 , s.t. 1 (dec(ẑ)) = 1.
(3) The result of this optimization is a valid latent vector ẑ that is the closest to z. However, since 1 (dec(ẑ)) = 1 involves nondifferentiable anatomical criteria, the optimization formulation of Eq. ( 3) cannot be solved with a usual Lagrangian solution. An alternative solution is to redefine the problem of finding ẑ as the problem of finding the smallest vector δ z such that ẑ = z +α δ z with α ∈ [0, 1]. In our case, we recover δ z based on the nearest neighbor of z in the augmented latent space, i.e. δ z = ( z N 1 -z) where z N 1 corresponds to the nearest latent vector. This leads to an easier 1D optimization problem:

α opt = arg min α |α|, s.t. 1 z + α δ z = 1 (4)
that we solve with a dichotomic search. Starting with α = 0.5, at each iteration, the anatomical criterion 1 dec( z + α δ z ) dictates which half of the search space should be explored further: lower values of α if 1 (dec(ẑ)) = 1, and higher values of α if 1 (dec(ẑ)) = 0.

Since the dichotomic search reduces the search space exponentially fast, the optimization algorithm is stopped after five iterations. At the end, the selected α is the smallest that validates the anatomical criterion.

E. Robust VAE

Current limitations of the proposed method are the need for millions of latent vectors to be stored in memory and the nearest neighbor search to perform each time a segmentation result is anatomically flawed. In this section, we present an alternative method that does not require the storage of latent vectors, nor the search for nearest neighbors. This method allows for faster processing and reduced memory usage, but without the previous method's anatomical guarantees. The use of either method depends on the application at hand.

Instead of using the post-processing VAE with cardiac shape warping as in Fig. 1, we implemented a robust VAE (rVAE). The goal of this new VAE is to directly convert erroneous segmentation maps x into anatomically plausible configurations x. To do so, we added a step to the VAE training procedure.

Starting with a pretrained cVAE, we fixed the weights of the decoder and of the single-neuron regression network, and fine-tuned the cVAE like a denoising autoencoder, i.e. by feeding it with anatomically implausible maps and training it to reproduce valid segmentations (c.f. bottom of Fig. 4). Since the decoder is fixed, this forces the new encoder of the cVAE (θ e ) to learn to project erroneous segmentation maps close to their corresponding valid latent vectors.

In practice, we generated a synthetic training set of 10,000 pairs of anatomically valid and invalid cardiac shapes, using the generative capabilities of the cVAE. As shown at the top of Fig. 4, we added some noise to the latent vectors obtained from the training data, and decoded the resulting vectors. More precisely, the valid latent vector z of an input image is shifted along the axis defined by the single-neuron regression network parameters to obtain the noisy latent vector z * = z +αθ c . This warped latent vector is decoded to produce a segmentation map x * = dec( z * ). Because of the linear constraint, the distribution is stretched along a plane perpendicular to the the axis defined by the single-neuron regression network, to allow for a linear separation of the domain-specifc target. At equal magnitude, warping the latent vector along the normal of the plane that defines the stretch of the distribution is more likely to produce samples out of distribution than along any other direction in the latent space. Since out-of-distribution samples are more likely to be decoded into implausible segmentation maps, this perturbation of the latent vector is a suitable way to obtain an artificial anatomically invalid cardiac shape paired with the original valid cardiac shape.

The rVAE is trained to recreate x from x * . An additional constraint is used to incite the encoder to project erroneous segmentations close to their corresponding valid latent vectors. This constraint is implemented as an additional KL loss term. This KL loss term minimizes the distance between the latent vector obtained by the rVAE on the noisy data and the original latent vector generated by the cVAE on the clean training data.

For a given x, x * and t the loss function is:

IE q θ e ( z|x * ) [-log q θ d (x| z)] + KL(p θ e ( z|x) p( z)) + (5)
y θ c ( z) -t 2 + KL(p θ e ( z|x * ) p θe ( z|x))

F. Implementation Details

The encoder of our cVAE is made up of 4 convolutional blocks, followed by two fully-connected heads that output the µ and Σ parameters of the posterior distribution. Each convolutional block consists of two 3 × 3 convolutional layers with ELU [START_REF] Clevert | Fast and accurate deep network learning by exponential linear units (elus)[END_REF] activations: the first one with stride 2 (to downsample by half in lieu of pooling), and the second with stride 1 and same padding. The dimensionality of the latent space was fixed at 32, to remain as low as possible while allowing for high reconstruction accuracy.

The decoder follows a similar structure, first using a fullyconnected layer to project to the same volume as the output of the last convolutional block in the encoder. After the FC layer comes a 4-block structure mirroring the encoder. Each block now consists of 2 layers with ELU [START_REF] Clevert | Fast and accurate deep network learning by exponential linear units (elus)[END_REF] activations: the first one is a 2 × 2 transposed convolution with stride 2 (to upsample by 2), and the second one is a 3 × 3 convolution with stride 1 and same padding. A final 3 × 3 convolution layer with stride 1 and same padding outputs the pixel-wise score for each class.

The number of feature maps is set to 48 for the first layer, and doubles at each successive block in the encoder. It follows the reverse logic in the decoder, where it is reduced by half in each block in order to reach 48 just before the final convolution with softmax. The encoder and decoder are trained end-toend with the Adam optimizer [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF], using a learning rate of 6 × 10 -5 for ACDC and 5 × 10 -4 for CAMUS. In both cases, a L2 weight regularization with λ = 0.01 was applied.

The AE mentioned in the ablation study of Table I uses the exact same architecture and hyperparameter values, except for one adaptation. At the end of the encoder, a single fullyconnected head is used to directly obtain the latent vector, instead of the parameters of the posterior distribution.

The segmentations maps were resized to 256 × 256 and registered. In the case of ACDC, the registration process implied centering image on the LV, and aligning the LV and RV on an horizontal line (i.e. aligning according to the centers of the cavities). With CAMUS, registering meant centering the image on the union of the LV and MYO, and vertically aligning the principal axis of the LV. During inference, the registration is based on the results of the segmentation method rather than the groundtruth. Because this is done prior to any of our post-processing, our method is dependent on the original segmentation being at least somewhat accurate w.r.t. the position and orientation of the heart.

IV. EXPERIMENTAL SETUP AND RESULTS

A. Datasets, evaluation criteria, and other methods 1) MRI dataset: The MRI dataset is the 2017 ACDC dataset [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved?[END_REF], which contains short-axis cine-MR images of 150 patients: 100 for training and 50 for testing. Particularly, a series of short axis slices cover the LV from the base to the apex, with one image every 5 or 10 mm, according to the examination. The spatial resolution goes from 1.37 to 1.68 mm 2 /pixel and 28 to 40 images cover the cardiac cycle. The end-diastolic and end-systolic phases were visually selected. As shown in Fig. 6(a), the LV, RV and MYO of every patient has been manually segmented. We report the average Hausdorff distance (HD) and 3D Dice index for the LV, RV and MYO as well as the LV and RV ejection fraction (EF) absolute error. Since our approach can postprocess any segmentation method, we tested it on the test [START_REF] Zotti | Gridnet with automatic shape prior registration for automatic mri cardiac segmentation[END_REF] 82 15 7 0 0 0 Grinias [START_REF] Grinias | Fast fully-automatic cardiac segmentation in mri using mrf model optimization, substructures tracking and b-spline smoothing[END_REF] 89 12 6 0 0 0 Isensee [START_REF] Isensee | Automatic cardiac disease assessment on cine-mri via time-series segmentation and domain specific features[END_REF] 128 21 7 0 0 0 Rohé [START_REF] Rohé | Automatic multi-atlas segmentation of myocardium with svf-net[END_REF] 287 40 21 0 0 0 Wolterink [START_REF] Wolterink | Automatic segmentation and disease classification using cardiac cine mr images[END_REF] 324 42 16 0 0 0 Jain [START_REF] Patravali | 2d-3d fully convolutional neural networks for cardiac mr segmentation[END_REF] 185 28 17 0 0 0 Yang [START_REF] Jang | Automatic segmentation of lv and rv in cardiac mri[END_REF] 572 182 137 0 0 0 ACNN [START_REF] Oktay | Anatomically constrained neural networks (acnns): Application to cardiac image enhancement and segmentation[END_REF] 139 41 21 0 0 0 results reported by ten ACDC challengers. Their methods are summarized by Bernard et al. [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved?[END_REF] except for Zotti-2 [START_REF] Zotti | Convolutional neural network with shape prior applied to cardiac mri segmentation[END_REF] whose results have been uploaded after the challenge. We also report results for the ACNN method of Oktay et al. [START_REF] Oktay | Anatomically constrained neural networks (acnns): Application to cardiac image enhancement and segmentation[END_REF] that uses a latent anatomical prior together with their segmentation CNN. Results from our best ACNN implementation (which involves a U-Net and our VAE) are very close to that of the original paper, despite the fact that the ACDC training set is smaller than in the original paper [START_REF] Oktay | Anatomically constrained neural networks (acnns): Application to cardiac image enhancement and segmentation[END_REF]. HD values are also slightly larger since we use a 3D HD instead of a 2D HD as in the original paper.

2) Echocardiographic dataset: The CAMUS dataset [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF] consists of conventional clinical exams from 500 patients acquired with a GE Vivid E95 ultrasound scanner. The acquisitions were optimized to perform measurements of the left ventricular ejection fraction. For each patient, 2D apical four-chamber and two-chamber view sequences were acquired with the same acquisition protocol and exported from EchoPAC analysis software (GE Vingmed Ultrasound, Horten, Norway). The corresponding videos are expressed in native polar coordinates. The same resampling scheme was applied on each sequence to express the corresponding images into a cartesian coordinate system with a constant grid resolution of λ/2 (i.e. 0.31 mm) in the lateral direction and λ/4 (i.e. 0.15 mm) in the axial direction, where λ corresponds to the wavelength of the ultrasound probe. The dataset is divided in 10 folds of equal size, nine of which are used for training and one for testing. The image quality (poor, good, and medium) and ejection fraction (≤ 45%, ≥ 55% or in between) are uniformly distributed across every fold. A senior cardiologist manually annotated the endocardium and epicardium borders of the left ventricle as well as the atrium of the end-diastolic (ED) and end-systolic (ES) images of every patient.

We tested our framework on the output of 7 methods: four conv nets (U-Net [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF], [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF], LUNet, ENet [START_REF] Paszke | Enet: A deep neural network architecture for real-time semantic segmentation[END_REF] and SHG [START_REF] Newell | Stacked hourglass networks for human pose estimation[END_REF]) and three non-deep learning methods (SRF [START_REF] Dollár | Fast edge detection using structured forests[END_REF], BEASMauto [START_REF] Pedrosa | Fast and fully automatic left ventricular segmentation and tracking in echocardiography using shape-based b-spline explicit active surfaces[END_REF], [START_REF] Barbosa | Fast and fully automatic 3-d echocardiographic segmentation using b-spline explicit active surfaces: Feasibility study and validation in a clinical setting[END_REF], and BEASM-semi [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF], [START_REF] Pedrosa | Fast and fully automatic left ventricular segmentation and tracking in echocardiography using shape-based b-spline explicit active surfaces[END_REF]). Note the nondeep-learning methods were state-of-the-art up until 2017.

B. Experimental Results

1) Constrained variational autoencoder: We gauged the linearity property of the latent space generated by our cVAE through the ablation study in Table I. Since our post-processing method relies on latent vector interpolation (c.f. Eq (4)), we computed the percentage of anatomically incorrect results obtained after interpolating a series of two valid latent vectors chosen at random. To do so, we iteratively selected two random groundtruth images from two random patients, projected it to the latent space with the cVAE encoder and linearly interpolated 25 new latent vectors. We then converted these 25 vectors back into the image space with the cVAE decoder and computed their percentage of anatomical errors. This procedure is illustrated in Fig. 5.

We repeated that process 300 times, i.e. combinations between 25 random vectors, (both for Camus and ACDC) for the cVAE with and without registration and with and without the one-neuron regression net. We first tested our full method (i.e. with image registration and a L2 regression constraint), then removed the image registration but kept the regression constraint, then removed the regression and kept the image registration and finally only used the VAE without registration nor regression. As shown in Table I, the combination of image registration and regression constraint reduces the percentage of anatomically implausible results down to 1.25% for ACDC and a negligeable 0.12% for CAMUS, which is more than 4x lower than for any other configuration. As for a simple autoencoder (c.f the AE column), since it provides no constraint on the latent space whatsoever, the percentage of errors is orders of magnitude larger.

2) ACDC Postprocessing results: Results on the ACDC test set are in Table II and Table III. Table II As can be seen from the "VAE" column in Table II, feeding every erroneous segmentation map to our VAE without transforming the latent vector z, significantly reduces the number of anatomical errors, without affecting too much the average III). This comes as no surprise, since the VAE was trained to output similar anatomically correct cardiac shapes (the ACDC test set has a total of 1078 slices). The rVAE further reduces, by a factor of almost 2, the number of anatomical errors, without significantly impacting the overall anatomical metrics. With a processing time 10 times faster than our most accurate method, the rVAE can be seen as a good compromise for real-time applications.

However, like any neural network, a VAE (be it robust or not) comes with no guarantee on the validity of its output. To completely eliminate erroneous segmentations, we tested three variants of our method. At first, we swap erroneous latent vectors with their nearest neighbor (thus forcing α = 1 in Eq. 4) without and with rejection sampling (cf. columns "w/o RS" and "w/ RS"). As mentioned in Section III-C, we increased to 4 million the number of anatomically correct latent vectors with the rejection sampling. Despite the fact that both methods reduce to zero the number of anatomical errors, we can see from Table III that data augmentation systematically produces better results. Also, while the improvements are incremental for top performing methods (e.g. the Dice index of Zotti-2 went from .899 to .909 and its HD from 14.4 to 11.0), they are drastic for methods with a large number of anatomical errors (e.g. Wolterink saw its Dice index go from .752 to .887 and its HD from 32.2 to 13.5). We can thus conclude that our method without a data augmented latent space could hurt the overall accuracy of certain methods.

The last column of Tables II and III shows the results of our complete method, i.e. Eq.( 4) optimized with a dichotomic search on a data augmented latent space. While all results respect the anatomical criteria, the EF error and the Dice index are almost identical to that of the original methods. The HD also never increases more than 1.3 mm. Considering that the average voxel size is near 1.4x1.4x10 mm 3 , the increase corresponds to less than 1 pixel in the image. This shows that our approach does not degrade the overall results of a given approach. Fig. 6 (a) shows erroneous predictions before and after our post-processing. While the correct areas are barely affected by our method, erroneous sections, big or small, get smoothly warped. Our method takes roughly 1 sec to process a 2D image on a mid-end computer equipped with a Titan X GPU. .922 / 5.9 .921 / 5.9 .922 / 5.9 .921 / 5.9 .921 / 6.0 .921 / 6.0 ENet [START_REF] Paszke | Enet: A deep neural network architecture for real-time semantic segmentation[END_REF] .923 / 5.8 .921 / 5.9 .921 / 5.9 .920 / 5.9 .920 / 5.9 .921 / 5.9 SHG [START_REF] Newell | Stacked hourglass networks for human pose estimation[END_REF] .915 / 6. [START_REF] Pedrosa | Fast and fully automatic left ventricular segmentation and tracking in echocardiography using shape-based b-spline explicit active surfaces[END_REF], [START_REF] Barbosa | Fast and fully automatic 3-d echocardiographic segmentation using b-spline explicit active surfaces: Feasibility study and validation in a clinical setting[END_REF] .868 / 10.5 .868 / 10.5 .867 / 10.5 .868 / 10.5 .868 / 10.5 .868 / 10.5 BEASM-semi [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF], [START_REF] Pedrosa | Fast and fully automatic left ventricular segmentation and tracking in echocardiography using shape-based b-spline explicit active surfaces[END_REF] . EF absolute error. However, unlike for ACDC, the robust VAE did not succeed at further reducing errors, especially for the non-deep-learning methods. This may be explained by the fact that the number of anatomical errors are already low with a basic VAE.

Another difference with ACDC is the results for our three nearest neighbors methods. While they reduce to zero the number of anatomical errors, all three methods have almost the same Dice index, HD and anatomical errors. This can be explained by the fact that the long-axis cardiac shapes are roughly similar from one patient to another, regardless of the time instant (c.f. Fig. 5). This is unlike the short-axis view, where the shape varies greatly between the basis of the heart down to the apex. As such, the long-axis valid latent vectors are probably closer together, so a simple nearest neighbor swap is enough to enforce our anatomical criteria on the output while preserving the overall anatomical shape.

However, as can be seen from Table V, like for ACDC, our method does not degrade by a significant manner the anatomical nor the clinical metrics.

4) Inter-observer variability: The inter-observer variability of cardiac MRI and echocardiographic image segmentation was reported by Bernard et al. [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved?[END_REF] and Leclerc et al. [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF]. For MRI segmentation, on average the inter-observer Dice score for the LV, the RV and the MYO at the end-systolic and end-diastolic time instant is 0.90 while the average Hausdorff distance is 9.3 mm [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved?[END_REF] . As can be seen from Table III, the methods with a dice score above 0.90 (column Original) are also above 0.90 after our processing (column Dicho). Also, the only method with a Hausdorff distance below 9.3 mm is that of Isensee [START_REF] Isensee | Automatic cardiac disease assessment on cine-mri via time-series segmentation and domain specific features[END_REF], which is also below 9.3 after our processing.

As for the echocardiographic segmentation, the average inter-observer Dice score reported in [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF] is 0.899 and the average Hausdorff distance is 7.34 mm. Again, as can be seen from the Original column of Table V, the first four methods are within the observer-variability, and still are after our postprocessing (column Dicho).

This reveals that while our method guarantees to produce results that follow pre-defined anatomical guidelines, it does not degrade the overall accuracy of highly effective methods. 5) Post-processsing degenerated results: Our method has its own limits and cannot be regarded as a solution to every harm. While our method guarantees the anatomical validity, w.r.t. the hardcoded criteria, of the output, it by no means guarantees that the produced output is close to the groundtruth. As such, if the erroneous segmentation map x it has to correct has little to no overlap with the groundtruth, our method will not necessarily warp x in the direction of the groundtruth. It will only warp x to the closest correct cardiac shape. Three such examples are provided in Fig. 7 where the result of our method is not closer to the groundtruth than x . In fact, the cardiac shape of Fig. 7(c) is so degenerated that the produced output is perpendicular to the groundtruth (because the inverse registering operation is based on the principal axis of the LV, which in this case is horizontal). Also, despite the fact that the produced shape is anatomically valid, the segmentation is sideways, causing the computation for the LV's width and MYO's thickness (c.f. criterion 6 in sec. III-A) to be inaccurate and to detect an anomaly, hence the 1 and 2 errors reported for the SRF method in Table IV. This particular example also illustrates what can happen when the original segmentation is so bad that even the inference-time registering is inaccurate, as mentioned at the end of sec. III-F. That said, even for inaccurate segmentation methods (e.g. Grinias and Yang in Table III), our method does not worsen their overall scores. Metrics obtained solely on the anatomically incorrect images are provided in the supplementary materials and also show that our method does not reduce the overall metrics.

V. CONCLUSION

We proposed a post-processing cVAE that converts invalid cardiac shapes into close but correct shapes. This is done by replacing the latent vector of an invalid shape by a close but valid latent vector. Intensive tests performed on the output of 18 segmentation methods reveal that our method is effective on both short-axis views from MRI as well as on long-axis views from US. Our method relies on a series of anatomical criteria (16 for SA and 12 for LA) that we use both to detect abnormalities and populate a cVAE latent space. One appealing feature of the proposed framework is that anatomical criteria do not need to be differentiable as they are not included in the loss. Furthermore, it has been shown that the warping of the incorrect segmentation shapes did not change significantly the overall geometrical metrics (Dice index and Hausdorff) nor the clinical metrics (the RV and LV ejection fraction). As such, according to the inter and intra-expert variations reported by Bernard et al. [START_REF] Bernard | Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved?[END_REF] and Leclerc et al. [START_REF] Leclerc | Deep convolutional network for 2-d echocardiographic segmentation based on an open large-scale patient database[END_REF], methods such as Isensee, Zotti-2, Khened and Baumgartner for ACDC and LUNet for CAMUS are within the inter-expert variation and, with our method, are now guaranteed to produce results that follow anatomical guidelines defined by the user. From the point of view of a clinical expert, it is preferable to have a plausible segmentation close to the expected one than an efficient system that spuriously provide aberrant segmentations. In that case, users cannot trust the provided physiological parameters that is calculated from these latest data, even if implausible segmentations do not significantly change the parameter values.

1) ( 3

 3 criteria) hole(s) in the LV, the RV or the MYO 2) (2 criteria) hole(s) between the LV and the MYO and between the RV and the MYO 3) (3 criteria) the presence of more than one LV, RV or MYO 4) (1 criterion) the RV is disconnected from the MYO 5) (2 criteria) the LV touches the RV or the background 6) (3 criteria) the LV, RV and MYO has one (or more) acute concavity 7) (2 criteria) both for the LV and the MYO, the ratio of (a) Intra-structure holes (b) Inter-structure holes (c) Connectivity and LV cavity touching background (d) Fragmented structures (e) Concavity

Fig. 2 :

 2 Fig. 2: Examples of anatomically erroneous cardiac shapes for both short and long-axis views.

Fig. 3 :

 3 Fig. 3: Samples generated through anatomically-constrained data augmentation for MRI (short-axis view) and US (long-axis view).

Fig. 4 :

 4 Fig. 4: [Top] Method used to generate invalid cardiac shape from valid ones. [Bottom] The valid/invalid pair of images are then used to train the Robust VAE.

Fig. 5 :

 5 Fig. 5: The left-most and right-most images are groundtruth configurations for both MRI and US while the other configurations were obtained though a linear interpolation.

  contains the total number of slices with at least one anatomical error for 11 different methods, the first ten being official ACDC challengers. Results without our post-processing are under the Original column. As for Table III, we report for the same methods their associated Dice index and Hausdorff distance (HD) [top] as well as their LV and RV ejection fraction absolute error [bottom].

Fig. 6 :Fig. 7 :

 67 Fig.6: Groundtruth and erroneous maps before and after our post-processing method.

TABLE I :

 I Ablation study of our cVAE showing the average % of anatomical errors while navigating through the latent space.

		AE			VAE
	Dataset		-	Registered	Const.	Reg. + const.
	ACDC	64.76	5.84	5.85	8.48	1.25
	CAMUS	41.25	1.48	0.52	3.32	0.12

TABLE II :

 II Number of anatomically invalid segmentation results on the ACDC test set (1076 images) for 11 segmentation methods with and without our post-processing methods (w/o RS: without rejection sampling, w/ RS: with rejection sampling, Dicho: dichotomic search).

		Original		VAE	Nearest Neighbors
	Methods		-	Robust	w/o RS	w/ RS	Dicho
	Zotti-2 [7]	55	16	7	0	0	0
	Khened [23]	55	16	9	0	0	0
	Baumgartner [24] 79	17	8	0	0	0
	Zotti

TABLE III :

 III Accuracy and clinical metrics of SOTA segmentation methods, with and without our post-processing, on the ACDC test set. [Top] Average Dice index and Hausdorff distance (in mm). [Bottom] Average error (in %) on LV and RV ejection fraction (EF).

	clinical metrics (Table

TABLE IV :

 IV Number of anatomically invalid segmentation results in cross-validation on CAMUS (2000 images) for 7 segmentation methods with and without our post-processing methods. The methods in the upper half segment all 3 classes (LV endo , LV epi and LA), whereas the methods in the lower half only segment 2 classes (LV endo and LV epi ).

		Original		VAE	Nearest Neighbors
	Methods		-	Robust w/o RS w/ RS	Dicho
	U-Net [5], [8]	84	16	14	0	0	0
	LUNet [14]	25	11	6	0	0	0
	ENet [31]	69	21	22	0	0	0
	SHG [32]	38	5	5	0	0	0
	SRF [33]	101	46	48	1	2	2
	BEASM-auto [34], [35]	12	2	3	0	0	0
	BEASM-semi [5], [34]	10	4	7	0	0	0

  3) CAMUS Postprocessing results: We perform a similar set of experiments on the CAMUS dataset. Results are reported in Table IV (number of anatomically invalid slices) and Table V (clinical metrics). As for ACDC, the use of a simple VAE significantly reduces the number of anatomical errors, without affecting too much the average Dice index, HD and

TABLE V :

 V Accuracy and clinical metrics of SOTA segmentation methods, with and without our post-processing, in crossvalidation on CAMUS dataset. [Top] Average Dice index and Hausdorff distance (in mm). [Bottom] Average error (in %) on LV ejection fraction (EF).

		Original	VAE			Nearest Neighbors
	Methods		-	Robust	w/o RS	w/ RS	Dicho
	U-Net [5], [8]	.921 / 6.0	.923 / 5.7	.923 / 5.7	.922 / 5.7	.922 / 5.7	.923 / 5.7
	LUNet [14]


Jensheer Botayna Bounor

Shamsudeen Seenath

Sai Gourang Patnaik

David Bourrier

Chau Cam

Hoang Tran

Jérôme Esvan

Laurent Weingarten

Armel Descamps-Mandine

Dominic Rochefort

Daniel Guay

David Pech

Low-cost micro-supercapacitors using porous Ni/MnO2 entangled pillars and Na-based ionic liquids

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

Introduction

The recent development of 3D electrodes based on pseudocapacitive materials [START_REF] Zheng | The road towards planar microbatteries and micro-supercapacitors: from 2D to 3D device geometries[END_REF][START_REF] Sha | Updated insights into 3D architecture electrodes for micropower sources[END_REF][START_REF] Li | Tuning the mechanical and electrical properties of porous electrodes for architecting 3D microsupercapacitors with batterieslevel energy[END_REF][START_REF] Zhang | Advanced three-dimensional microelectrode architecture design for high-performance on-chip micro-supercapacitors[END_REF] has greatly reduced the difference between the characteristics of micro-supercapacitors and micro-batteries for embedded systems and on-chip electronics. Small dimension electrochemical energy storage is especially crucial for the upcoming Internet of Things (IoT) based applications, which involve extensive utilization of miniature sensor nodes for health, environmental or industrial monitoring [START_REF] Kyeremateng | Microsupercapacitors as miniaturized energy-storage components for on-chip electronics[END_REF][START_REF] Pikul | Powering the Internet of Things[END_REF]. Compared to microbatteries, micro-supercapacitors can provide high-power delivery and, more importantly, have a much longer operating lifetime. This comes, however, at the expense of a much lower energy density.

Pseudocapacitive micro-supercapacitors are a category of electrochemical capacitors whose charge storage mechanism relies on rapid and reversible faradaic surface reactions [START_REF] Fleischmann | Pseudocapacitance: from fundamental understanding to high power energy storage materials[END_REF]. When the pseudocapacitive material is deposited as a thin-layer on 3D architectures, high areal energy density is achieved within the limited available space of the electronic circuitry. Using this strategy, we recently reported unprecedented high capacitances per surface area using ruthenium dioxide RuO2 deposited on porous Au or Pt current collectors [START_REF] Patnaik | Porous RuOxNySz electrodes for microsupercapacitors and microbatteries with enhanced areal performance[END_REF][START_REF] Karroubi | Highly porous scaffolds for Ru-based microsupercapacitor electrodes using hydrogen bubble templated electrodeposition[END_REF]. These Ru-based micro-supercapacitors deliver an energy density per unit footprint area very close to that of lithium-based microbatteries, but with superior power and better cycling stability [START_REF] Ferris | 3D RuO2 microsupercapacitors with remarkable areal energy[END_REF].

However, the high and volatile price of platinum and ruthenium, as well as the environmental issues related to the mining and refining of these rare and precious metals, have made these micro-devices relegated to niche applications. Replacing ruthenium with alternative transition metals with higher abundance and lower cost is, therefore, fundamental for commercial scaleup.

Among pseudocapacitive materials, manganese dioxide MnO2 stands out for its high theoretical specific capacitance, wide availability and environmental friendliness [START_REF] Wei | Manganese oxide-based materials as electrochemical supercapacitor electrodes[END_REF][START_REF] Boyd | Effects of interlayer confinement and hydration on capacitive charge storage in birnessite[END_REF]. Although its capacitance is lower than that of RuO2, manganese is the fifth most abundant metal in the Earth's crust making its price derisory compared to the overpriced ruthenium oxide in trace amount. However, MnO2 suffers from low conductivity, inefficient ion diffusion and a low structural stability, which results in low electrochemical utilization and poor cycling life [START_REF] Hsieh | Investigation on capacity fading of aqueous MnO2.nH2O electrochemical capacitor[END_REF].

We show in this study that the electrodeposition of MnO2 nanomaterials onto conductive and high surface area Ni foams overcome these issues. The porous metallic structure facilitates electrolyte penetration and enables efficient electronic and ionic pathways resulting in high electrode capacitance. Moreover, the open structure and the nanoscale deposition of MnO2 in the form of nanoflakes accommodate volume change and mitigate stress upon charge/discharge cycling over long periods of time. Using these inexpensive electrodes along with a costeffective and scalable manufacturing process, we obtain one of the highest cell capacitances for a micro-supercapacitor device.

Materials and Methods

Elaboration of the electrodes

A thin metallic sublayer (100/200 nm of Ti/Ni) was deposited by evaporation on an oxidized silicon substrate followed by DHBT electrodeposition of porous Ni as current collector with thickness ranging from 144 to 257 µm, using a constant current density of 2 A cm -2 in 0.1 M NiCl / 2 M NH4Cl solution. Pulsed electrodeposition of MnO2 was afterwards carried out on Ni DHBT in 0.14 M MnSO4 using a potentiostatic pulse of 1.25 V vs. SCE (saturated calomel electrode) for 2 s followed by a rest period of 3 s at open circuit potential. The ionic liquids and sodium salts used in this study were purchased from TCI Europe. The electrolytes were prepared in an argon-filled glovebox at room temperature. The electrodes were soaked in the electrolyte overnight prior to electrochemical characterizations.

Material characterizations

Scanning electron microscopy (SEM) was performed using a Hitachi S-4800 field-emission microscope. Transmission electron microscopy (TEM) imaging was carried out using a JEOL 2100F microscope equipped with a Schottky field emission gun (FEG) operated at 200 kV and a Gatan RIO16IS CMOS camera. The TEM sample was prepared using an epoxy resin for hardening before mechanical thinning (SiC polishing cloth and concave polishing using a diamond suspension) and final finishing by ion beam. The crystallographic structures were analyzed by grazing incidence X-ray diffraction (GI-XRD) measurements on a Bruker D8 advanced X-ray diffractometer with Cu Ka radiation (1.54184 Å) operating at 40 kV and 40 mA. The surface chemical composition of manganese oxide was estimated via X-ray photoelectron spectroscopy (XPS) using a ThermoScientific K-Alpha system operating with a monochromatic Al Ka X-ray source (1486.6 eV). The spectrometer energy was calibrated using the Au 4f7/2 (83.9 ± 0.1 eV) and Cu 2p3/2 (932.8 ± 0.1 eV) photoelectron lines.

Electrochemical characterizations

The electrochemical synthesis and characterizations were performed with a VMP-3 Biologic potentiostat connected to an external 10 A booster channel. The three-electrode system was made up of the working electrode, a Pt mesh counter electrode, a saturated calomel electrode (SCE) for synthesis and a KCl saturated Ag/AgCl reference electrode for characterizations.

Electrochemical impedance spectroscopy (EIS) measurements were carried out at open circuit potential and frequencies ranging from 100 kHz to 10 mHz.

The accessibility of charges has been investigated by calculating the voltammetric charge, q * , as a function of the sweep rate, v. The outer charge, qo, is obtained from the extrapolation of q * when v → ∞ from the q * = f(1/v ½ ) plot. The total charge, qt, is determined using the extrapolation of the inverse of the voltammetric charge, 1/q * , when v → 0 from the 1/q * =f(v ½ ) plot.

AEF factor calculation of Ni scaffolds

The Area Enlargement Factor (AEF) of the metallic current collector was defined as follows:

!"# = "&'()*+(ℎ'-.(/& !().0' 12*3/(' !*'/ ("!1!) 6'+-')*.(/& !*'/
The EASA of porous Ni DHBT coatings was calculated by integrating the charge associated to the b-NiOOH à b-Ni(OH)2 reduction peak using cyclic voltammetry at 5 mV s -1 in 1 M KOH, considering a cathodic charge value of 2.1 mC cm -2 as a reference [START_REF] Hao | Hydrogen bubble templating of fractal Ni catalysts for water oxidation in alkaline media[END_REF][START_REF] Cossar | Comparison of electrochemical active surface area methods for various nickel nanostructures[END_REF].

Results and Discussion

Porous Ni/MnO2 electrodes

Highly porous Ni current collectors were synthesized by a facile and scalable electrodeposition process on oxidized Si wafers: the dynamic hydrogen bubble template (DHBT) method [START_REF] Plowman | Building with bubbles: the formation of high surface area honeycomb-like films via hydrogen bubble templated electrodeposition[END_REF].

In this process, the electrodeposition of the metallic material from aqueous solutions is performed at high cathodic overpotentials where H + is reduced to H2. The generation of hydrogen gas bubbles acts as a dynamic template for the growth of highly porous metal films interspersed with nanostructured pore walls. This synthesis method is very simple and provide porous structures with good mechanical stability and strong adherence to the substrate.

Moreover, compared to other procedures based on stationary physical templates [START_REF] Eustache | High areal energy 3D-interdigitated micro-supercapacitors in aqueous and ionic liquid electrolytes[END_REF][START_REF] Wen | Multiple nanostructures based on anodized aluminium oxide templates[END_REF], DHBT process does not require any subsequent etching or template removal step, thus reducing postprocessing and associated difficulties or compatibility.

An Area Enlargement Factor (AEF), defined as the ratio between the developed area of the Ni porous structure over its projected area, can be deduced from cyclic voltammograms (CVs) in alkaline media (see Materials and Methods section). Fig. 1a shows the evolution of the CVs and corresponding calculated AEF of different porous Ni foams obtained with increasing DHBT deposition times. As expected, the AEF increases steadily with the deposition duration and hence the film thickness, from 342 cm 2 cm -2 to a colossal AEF value of about 1000 cm 2 cm -2 for 30 min of deposition. The formed metal foams are composed primarily of polycrystalline Ni as confirmed from their X-ray diffraction (XRD) pattern (Fig. 1b). The scanning electron micrographs (SEM) (Fig. 1b inset) show porous surface structure with different pore sizes, with diameters varying between 10 and 50 µm for the largest. Individual pores are constructed with converging nanoscale spicule-like structures, thus providing enormous surface area.

We then electrodeposited the MnO2 as active material using a pulsed current technique on the highly structured nickel current collector (Figure S1). From cross-sectional SEM observations (Figure S2), the electrodes display a pine tree type morphology with uniformly spread active material. High resolution transmission electron microscopy (TEM) imaging (Figure S3) and fast Fourier transform (FFT) analysis (Figure S4) show continuous and uniform deposition of ultra-small nanoflakes with ~77 nm thickness, with interplanar spacings characteristic of ramsdellite phase of the 1D allotropic group of MnO2 [START_REF] Ghodbane | Microstructural effects on charge-storage properties in MnO2-based electrochemical supercapacitors[END_REF]. The elemental mapping images (Fig. 2a) further illustrate the homogeneous distribution and coverage of Mn on the Ni metal support with unfilled open pores/space for electrolyte penetration. The composition of deposited MnO2 was also confirmed through X-ray photoelectron spectroscopy (XPS) studies by tracking the peak splitting difference of Mn-3s states at electrochemically reduced (0 V vs. Ag/AgCl) and oxidized (0.9 V vs. Ag/AgCl) forms (Fig. 2b). The exchange-splitting of the 3s core levels results in a binding energy separation directly related to the valence of manganese and its average oxidation state in the oxide, with a negative linear relationship [START_REF] Toupin | Influence of microstructure on the charge storage properties of chemically synthesized manganese dioxide[END_REF]. The energy splitting of the Mn-3s core level peaks is 4.9 eV for the as-deposited material, and 4.7 eV after oxidation, which is consistent with the occurrence of a MnO2 phase in a Mn(IV) oxidation state [START_REF] Audi | Valence-band x-ray photoelectron spectroscopic studies of manganese and its oxides interpreted by cluster and band structure calculations[END_REF]. This high Mn(IV) content is also in agreement with the quantitative determination computed from the Mn-2p3/2 and O-1s core level spectra (Figure S5). In its fully reduced state (Mn 3+ ), the binding energy difference of the Mn-3s core level peaks should be ~5.4 eV, but in the current case, the peak separation in the reduced state was ~5.1 eV, suggesting incomplete reduction at 0 V. These XPS results are nevertheless in accordance with the established pseudocapacitance reaction based on the change of oxidation state varying between Mn(IV)

and Mn(III) with one-electron transfer in neutral aqueous medium [START_REF] Brousse | Crystalline MnO2 as possible alternatives to amorphous compounds in electrochemical capacitors[END_REF]. indicating small internal electrical resistance and energy loss. The cyclic voltammograms, recorded at different scan rates, show an almost ideal symmetrical rectangular shape (Fig. 2d), revealing easy and efficient access of electrons and cations to the pseudocapacitive 3D electrode to afford fast and highly reversible redox reactions. More importantly, the electrode exhibits a huge areal capacitance of 1.8 F cm -2 when cycled at 0.1 mV s -1 and 2.9 F cm -2 at 10 mHz using EIS (Fig. 2c), which is by far higher than all reported 2D thin-film micro-supercapacitor electrodes [START_REF] Kyeremateng | Microsupercapacitors as miniaturized energy-storage components for on-chip electronics[END_REF][START_REF] Huang | On-chip and freestanding elastic carbon films for microsupercapacitors[END_REF][START_REF] Bu | Recent developments of advanced micro-supercapacitors: design, fabrication and applications[END_REF][START_REF] Jrondi | Major improvement in the cycling ability of pseudocapacitive vanadium nitride films for micro-supercapacitor[END_REF].

Electrochemical characterizations of the porous

The accessibility of the electrolyte to the electroactive material has been further investigated by calculating the voltammetric charge, q * , as a function of the sweep rates, v, from 0.1 to 20 mV s -1 (Fig. 2e) according to a procedure developed by Trasatti and co-workers [START_REF] Ardizzone | Inner" and "outer" active surface of RuO2 electrodes[END_REF]. This advanced electrochemical data analysis has been performed for Na + storage on different samples with increasing number of electrodeposited cycles of MnO2 (Fig. 2f). The difference between the outer capacitance, Co, related to the most accessible Mn 3+/4+ sites at the surface of the MnO2 deposits, and the total capacitance, Ct, gradually increases with deposition cycles indicating that accessibility of active surface area becomes progressively more and more difficult. Indeed, the reaction mechanism involves an adsorption/desorption process of Na + at the surface of MnO2 flakes as well as an insertion/extraction of the alkali ion into the bulk of the material. However, even for the thicker MnO2 coating obtained after 2500 cycles of deposition, the main contribution of the total capacitance Ct comes from the outer capacitance Co, which accounts for 69 % of the total capacitance, depicting the effectiveness of the porous matrix in enabling a large part of the nanostructured MnO2 film to be electrochemically active.

The value Ct reaches 4.0 F cm -2 (i.e. ~110 F g -1 , as expected for gravimetric capacitance of ramsdellite 19 ) for the sample with the highest active material loading. This is the highest capacitance per unit area ever reported for 3D MnO2 micro-supercapacitor electrodes [START_REF] Eustache | MnO2 thin films on 3D scaffold: microsupercapacitor electrodes competing with "bulk" carbon electrodes[END_REF][START_REF] El-Kady | Engineering three-dimensional hybrid supercapacitors and microsupercapacitors for high-performance integrated energy storage[END_REF][START_REF] Hu | 3D interdigital Au/MnO2/Au stacked hybrid electrodes for on-chip microsupercapacitors[END_REF][START_REF] Wang | Silicon-based 3D all-solidstate microsupercapacitor with superior performance[END_REF][START_REF] Bounor | On chip MnO2-based 3D microsupercapacitors with ultra-high areal energy density[END_REF].

In order to verify whether the DHBT structure can provide a reliable electrical connection to the inherently poorly conductive MnO2, the long-term behavior of the electrode was tested by repeated galvanostatic charge/discharge cycles at high current of 4 mA cm -2 (Fig. 2g). The cycling experiment indicates excellent stability of the composite porous electrodes with more than 80 % retention of the initial capacitance after 10 000 cycles, and SEM images after cycling tests show that morphology of the MnO2 is preserved (Figure S6). This impressive stability of nanocrystalline MnO2 when extra-long measurements are performed can be explained by the conductive and porous structure of the metallic current collector as well as the beneficial effect of nanosizing on transport properties which govern the electrode reversibility [START_REF] Julien | Nanostructured MnO2 as electrode materials for energy storage[END_REF]. Moreover, unlike 2D thick-film electrodes, delamination issue is not a concern for these binder and additive-free structures.

Cell performances

Motivated by the excellent capacitive performance of porous Ni/MnO2 architectures in threeelectrode configuration, their integration and functioning in full-cell microdevices were subsequently examined. The realization of a 3D configuration at the device-level integrating nanostructured electrodes is an important milestone to further improve the surface-to-volume ratio and obtain the desired combination of energy, power, lifetime on small footprint areas [START_REF] Liu | Advances on three-dimensional electrodes for micro-supercapacitors: a mini-review[END_REF]. While the interdigitated planar configuration can shorten the diffusion length between the positive and negative electrode [START_REF] Pech | Influence of the configuration in planar interdigitated electrochemical micro-capacitors[END_REF], a better areal capacitance and energy can be achieved for a micro-supercapacitor in stack configuration [START_REF] Kyeremateng | Microsupercapacitors as miniaturized energy-storage components for on-chip electronics[END_REF]. We provide here an innovative framework to shown in Figure S10) to maximize their density per unit area (see Table S1 for example).

Important to note here is that this general scheme of construction can be easily extended to other class of substrates since the fabrication process is facile and needs thin metallic films, from which porous Ni foams can be grown through aqueous electrodeposition.

Fig. 3c shows the cyclic voltammograms in 1 M Na2SO4 of a 15 mm 2 micro-supercapacitor cell based on 179 µm thick porous Ni/MnO2 electrodes. The Ni/MnO2 micro-device exhibits a remarkable cell capacitance of 846 mF cm -2 at 1 mV s -1 , which is the highest value ever reported for a full-cell micro-supercapacitor [START_REF] Zheng | The road towards planar microbatteries and micro-supercapacitors: from 2D to 3D device geometries[END_REF][START_REF] Eustache | High areal energy 3D-interdigitated micro-supercapacitors in aqueous and ionic liquid electrolytes[END_REF][START_REF] Bounor | On chip MnO2-based 3D microsupercapacitors with ultra-high areal energy density[END_REF][START_REF] Brousse | Facile and scalable preparation of ruthenium oxide-based flexible microsupercapacitors[END_REF][START_REF] Gao | A seamlessly integrated device of micro-supercapacitor and wireless charging with ultrahigh energy density and capacitance[END_REF][START_REF] Zhang | Biomimetic platinum forest enables 3D micro-supercapacitors with enhanced areal performance[END_REF][START_REF] Sajedi-Moghaddam | Inkjet printing of MnO2 nanoflowers on surface-modified A4 paper for flexible all-solid-state microsupercapacitors[END_REF] including those based on 3D Ru oxides [START_REF] Patnaik | Porous RuOxNySz electrodes for microsupercapacitors and microbatteries with enhanced areal performance[END_REF].

Moreover, the CV profiles did not show resistive behavior even at high scan rate of 50 mV s -1 .

MnO2 micro-supercapacitor based on Na-based ionic liquids

The use of aqueous electrolyte restricted the operating voltage range because of water decomposition and partial dissolution of MnO2 into soluble MnOOH species above ca. 1 volt.

The development of advanced solid-state electrolytes suitable for Na + charge storage with extended electrochemical stability window (ESW) is therefore an important challenge as energy stored is directly proportional to the square of the cell voltage. We have demonstrated in previous studies that a high pseudocapacitive effect of RuO2 with extended ESW could be obtained using protic ionic liquids [START_REF] Rochefort | Pseudocapacitive behaviour of RuO2 in a proton exchange ionic liquid[END_REF][START_REF] Seenath | Investigation of protic ionic liquid electrolytes for porous RuO2 microsupercapacitors[END_REF]. Herein, we have synthesized and tested various innovative electrolytes using Na salts diluted in aprotic pyrrolidinium-and imidazolium-based ionic liquids solvents for MnO2. Figure S11 shows the structure of the different ionic liquids explored and Figure S12 their electrochemical behaviour with Ni/MnO2 electrodes. Ionic liquids are considered safe alternatives to conventional aqueous and organic electrolytes due to their non-flammability, low volatility, high ionic conductivity and widened potential windows.

Moreover, ionic liquids can be easily turned into quasi-solid state by the use of ionogels [START_REF] Bideau | Ionogels, ionic liquids based hybrid materials[END_REF][START_REF] Guillemin | Solid-state 3D microsupercapacitors based on ionogel electrolyte: influence of adding lithium and sodium salts to the ionic liquid[END_REF] and address the packaging issues of micro-supercapacitors.

We tested the micro-device using 1 M sodium bis(fluorosulfonyl)imide (NaFSI) salt diluted in aprotic 1-methyl-1-propylpyrrolidinium bis(fluorosulfonyl)imide (Pyr13FSI) ionic liquid (Fig. 3d), where Na + ion can be expected to be the dominant contributor to faradaic pseudocapacitance [START_REF] Lindberg | Charge storage mechanism of a-MnO2 in protic and aprotic ionic liquid electrolytes[END_REF] and greatly enhances charge storage [START_REF] Li | Doped butylmethylpyrrolidinium-dicyanamide ionic liquid as an electrolyte for MnO2 supercapacitors[END_REF][START_REF] Benedetti | In search of an appropriate ionic liquid as electrolyte for microporous manganese oxide film electrochemistry[END_REF]. Ionic liquid based on FSI - anions are known to be chemically stable and to provide relative low viscosity [START_REF] Shkrob | Why bis(fluorosulfonyl)imide is a "magic anion" for electrochemistry[END_REF][START_REF] Kerner | Ionic liquid based lithium battery electrolytes: fundamentals benefits of utilising both TFSI and FSI anions?[END_REF], which often correlates with good ionic conduction. CVs were performed at 2 mV s -1 with increasing cell voltage windows. To our surprise, the micro-supercapacitor was able to cycle up to 2.6 V with no oxidation peaks that would be related to active material degradation. The voltammetric charge/discharge ratio of Figure S13 also reveals an appreciable level of stability over this voltage range. This wide extension of cell voltage could suggest that manganese oxide pseudocapacitance may rely on oxidation states above +IV using stable ionic liquids, with more than one-electron transfer, according to the following reaction:

Mn n+ On/2 + (n-3)Na + + (n-3)e -↔ Na + (n-3)Mn 3+ On/2

where n ³ 4 is the maximum oxidation number of Mn.

Mn has indeed stable oxidation states, ranging from +2 to +7, in different known oxides [START_REF] Song | Anomalous pseudocapacitance behavior of a nanostructured, mixed-valent manganese oxide film for electrical energy storage[END_REF][START_REF] Ghosh | Diversity in the family of manganese oxides at the nanoscale: from fundamentals to applications[END_REF].

A significant portion of the stored energy could also come from the electrochemical doublelayer capacitance (EDLC) of aprotic Pyr13FSI solvent with the highly porous structure.

Moreover, earlier studies on MnO2 supercapacitors using neat ionic liquids without added salts have shown that small anions can intercalate into the structure to support faradaic charge storage [START_REF] Chang | X-ray photoelectron spectroscopy and in situ Xray absorption spectroscopy studies on reversible insertion/desertion of dicyanamide anions into/from manganese oxide in ionic liquid[END_REF]. Although this high voltage comes at the expense of a lower cell capacitance (343 mF cm -2 ), the specific energy reaches in this case an outstanding value of 1159 mJ cm -2 (i.e. 0.3 mWh cm -2 ).

Fig. 3e and Figure S14 show the cycling performance of micro-supercapacitor prototypes up to 2000 cycles in various ionic liquid-based media. Using NaFSI/Pyr13FSI, a slight increase of capacitance is observed at the beginning of cycling ascribed to a gradual penetration of the electrolyte within the porosity, followed by a very high stability, pointing out the reliability of the microdevices on long cycles. The overall performances of the cells are finally compared with state-of-the-art reports on micro-supercapacitors in an area-normalized Ragone plot (Fig. 4 and Table S2) [START_REF] Eustache | High areal energy 3D-interdigitated micro-supercapacitors in aqueous and ionic liquid electrolytes[END_REF][START_REF] Huang | On-chip and freestanding elastic carbon films for microsupercapacitors[END_REF][START_REF] Zhang | Biomimetic platinum forest enables 3D micro-supercapacitors with enhanced areal performance[END_REF][START_REF] Pech | Ultrahigh-power micrometre-sized supercapacitors based on onion-like carbon[END_REF][START_REF] Lin | Laser-induced porous graphene films from commercial polymers[END_REF][START_REF] Robert | On chip interdigitated micro-supercapacitors based on sputtered bifunctional vanadium nitride thin films with finely tuned inter-and intracolumnar porosities[END_REF][START_REF] Ferris | 3D interdigitated microsupercapacitors with record areal cell capacitance[END_REF]. Our economical aqueous MnO2 microdevice rivals the best reported RuO2 micro-supercapacitor while the ionic liquid-based one outperforms it.

Conclusion

We have demonstrated the possibility of realizing low-cost micro-supercapacitor MnO2-based electrodes having ultra-long lifetimes and areal capacitances competing with the archetypal pseudocapacitive RuO2. Furthermore, these performances can be easily improved by increasing the depth of the 3D scaffold and tuning the MnOx thickness accordingly. We also lay down general scheme of microfabrication process to construct full encapsulated devices that could be easily extended to other substrates and geometric shapes/forms. The entire technological process is cost-effective, environmentally friendly, with all processing steps performed at room temperature, from the electrodeposition of Ni DHBT and MnO2 active material to wafer-level integration of the micro-devices. To enable extended operational potential window, we have screened various ionic liquid-based media and show prototype cells with optimized electrolyte having superlative performance. Each of the sub-components of the final device is tailored to be economically feasible for scale up, thus opening avenues for successful commercialization. )

Areal power density (mW cm -2 )

3D MnO 2 (EMIM-TFSI) 17 Activated C (NET 4 BF 4 / PC) 51 CDC (in H 2 SO 4 ) 23 Carbon Onions (NET 4 BF 4 /PC) 51 Graphene (in H 2 SO 4 ) 52 VN (in KOH) 53 3D PEDOT (LiCl/PVA) 37 The size, shape, height and density of the pillars on a given surface can be easily adjusted to optimize 3D Gain, defined as the ratio between the exposed surface including all the pillars, S3D, and the exposed surface without pillars, S2D. Table S1 shows some examples of pillar topology on a S2D = 4 mm 2 surface. The comparison between NaFSI and NaTFSI was to evaluate if the transport of ions (and viscosity) has an impact on the charge storage properties. FSI -anions provides higher conductivities from the better mobility of the smaller ion. Regarding the EMIM-FSI and Pyr13-FSI solvents, they were chosen for their relatively low viscosity (25 and 53 cP, respectively). EMIM + cation has better transport properties but is less stable at lower potential values because of the acidity of the proton at the C2 position (the carbon between both N on the cycle). Pyr13 + cation has been applied with more success as battery electrolyte † since the absence of acidic protons and of conjugation on the cycle decreases the reactivity. † X. Wang No significant difference is observed between the different investigated ionic liquids on the performances (power rating and cell voltage) of the MnO2 micro-supercapacitor. The limitations seem therefore to come from interfacial reactions and/or ion transport within the active material, rather than ion transport within the electrolyte itself. Moreover, the potential limits do not appear to be too stringent for EMIM + cation (i.e. the negative limit is not negative enough for EMIM + to react) for a difference to be observed with the Pyr13 + .

  Ni/MnO2 electrode (25 min of Ni DHBT and 1500 pulses of MnO2 electrodeposition) were performed in a three-electrode configuration in a nitrogen-purged 1 M Na2SO4 aqueous electrolyte. Fig. 2c shows the obtained electrochemical impedance spectroscopy (EIS) measurements along with the simulated fit using a classical equivalent circuit model to distinguish pseudocapacitance from double-layer capacitance. The composite electrode is characterized by a low equivalent series resistance (ESR) of 7.0 W cm 2

  realize three-dimensional micro-supercapacitors consisting of entangled pillars of porous Ni/MnO2, as schematically shown in Fig.3a,b. The microfabrication steps are detailed in FigureS7and assembling details in FigureS8. The principle is based on the electrodeposition of Ni pillars inside photoresist molds, followed by DHBT electrodeposition of porous Ni and electrodeposition of MnO2. This new concept of 3D device design combines both the advantages of the interdigitated and the ones of the stack configuration, with reduced interelectrode distance and increased active material loading over limited surface area. This arranged matrix of 3D porous electrodes also facilitates better electrolyte percolation and higher electronic conductivity, thus resulting in superior interfacial kinetics. The entire process of fabrication is easily scalable (FigureS9) thanks to the simplicity of the DHBT template, and can be used with pillars of different geometries (square, hexagonal, parallelogram or spinner as

Fig. 1 .Figure 2 Fig. 2 .

 122 Fig. 1. Characterizations of Ni porous current collectors. a) Evolution of the Area Enlargement Factor (AEF), deduced from CVs performed at 5 mV s -1 in 1 M KOH, with DHBT deposition time. Large AEF up to ca. 1000 cm 2 cm -2 were obtained. b) XRD pattern showing the diffraction

1 O K ! 1 Mn K ! 1 Figure 3

 1113 Figure3

Fig. 3 .Figure 4 CDC

 34 Fig. 3. Cell performances. a) Illustration of a 3D stacked micro-supercapacitor design

Fig. 4 .

 4 Fig. 4. Comparison with state-of-the-art micro-supercapacitors. Ragone plot showing the

Figure S1 .

 S1 Figure S1. Potentiostatic pulsed electrodeposition of MnO2 on porous Ni current collectors. Each cycle consists of a potentiostatic pulse of 1.25 vs. SCE for 2 s followed by a rest period of 3 s at open circuit to stabilize the porous/electrolyte interface.

Figure S2 .Figure S3 .Figure S4 .Figure S5 .

 S2S3S4S5 Figure S2. Cross-sectional SEM image of a Ni DHBT/MnO2 electrode. a) Low magnification. b) High magnification showing uniform deposition of MnO2 active material.

Figure S6 .

 S6 Figure S6. SEM image of a Ni DHBT/MnO2 electrode after long cycling tests. a) Low magnification. b) High magnification showing the preservation of the MnO2 nanoflakes.

Figure S7 .

 S7 Figure S7. Microfabrication of micro-supercapacitors based on 3D entangled pillars: topview and cross-section schematics of the different processing steps. a) Deposition and patterning using conventional photolithography techniques of a thick WBR photoresist on an oxidized silicon wafer coated with a thin Ti/Ni sublayer. b) Electrodeposition of Ni inside photoresist molds to obtain Ni pillars after WBR stripping. c) Design of square electrode area using a 400 µm-thick WBR photoresist. d) Uniform electrodeposition of porous Ni using the DHBT technique on the exposed surface (flat surface and pillars). e) Pulsed electrodeposition of MnO2 on DHBT Ni. f) Protection of electrode area and electrical contact pads by a sacrificial WBR photoresist. g) Wet etching of the exposed Ni flat surface. h) Application of a doublesided self-adhesive tape (Tesa ® chemical resistant filmic tape) on the first electrode to form a cavity. i) Filling of the cavity with electrolyte and final assembly of the two electrodes by controlled adjustment of the interspacing.

Figure S8 .

 S8 Figure S8. Assembling details. The FC150 -FlipChip Bonder equipment was used to assemble the interdigitated device with a precision of ± 1 µm by following the steps below:

Figure S9 .

 S9 Figure S9. Electrochemical cell dedicated for 4-inch substrates for large-scale electrolytic deposition of the porous current collector and active material. a) Front view. b) Side view. c) Immersed in the deposition bath. The custom-made cell was designed in collaboration with Yamamoto-MS.

Figure S11 .

 S11 Figure S11. Structures of the cation and anion groups of ionic liquid candidates explored for MnO2 micro-supercapacitors. a) Na salts. b) Ionic liquids solvents.

Figure S12 .

 S12 Figure S12. Electrochemical supercapacitor behaviour in Na salts-based ionic liquids using very thin film of Ni / MnO2 electrodes (5 min Ni DHBT + 1000 cycles of MnO2). a) Cyclic voltammogram recorded at 50 mV s -1 up to 2.5 V. b) EIS characteristics from 100 kHz to 10 mHz.

Figure S13 .

 S13 Figure S13. Voltammetric charge/discharge ratio Qc/Qd with increasing cell voltage in 1 M NaFSI /Pyr13FSI computed from Fig. 3d. The charge/discharge ratio is constant from 1 to 2.6 V, indicating appreciable level of stability of the micro-supercapacitor within this voltage range ‡, §

Figure S14 .

 S14 Figure S14. Long-term cycling performance of porous Ni/MnO2 micro-supercapacitor cells in various ionic liquid-based electrolytes. 1 M Na2SO4 and 1 M NaFSI / Pyr13FSI were tested using a 179 µm thick Ni / MnO2 electrodes. 1 M NaTFSI / Pyr13FSI and 1 M NaFSI / EMIMFSI were tested using a thin film of Ni / MnO2 electrodes (5 min Ni DHBT + 1000 cycles of MnO2).

Table S2 . Performance table with state-of-the-art micro-supercapacitors.

 S2

		120
	(%)	100
	Capacitance retention	20 40 60 80			1M Na 2 SO 4 1M NaFSI / Pyr 13 FSI
					1M NaTFSI / Pyr 13 FSI
		0			1M NaFSI / EMIMFSI
		0	500	1000	1500	2000
				Number of cycles

Acknowledgements

The authors acknowledge the support from the European Research Council (ERC Consolidator Grant, ERC-2017-CoG, project 771793 3D-CAP and ERC Proof-of-Concept, ERC-2022-PoC, project 101069259 3D-APP). This work was supported by LAAS-CNRS technology platform, a member of Renatech network.

Sunit = 25980