Mélanie Lubrano

Yaëlle Bellahsen-Harrar

Sylvain Berlemont

Thomas Walter

Cécile Badoual
email: cecile.badoual@aphp.fr

Diagnosis with Confidence: Deep Learning for Reliable Classification of Squamous Lesions of the Upper Aerodigestive Tract

Diagnosis of head and neck squamous dysplasia and carcinomas is critical for patient care, cure and follow-up. It can be challenging, especially for intraepithelial lesions. Even though the last WHO classification simplified the grading of dysplasia with only two grades (except for oral or oropharyngeal lesions), the inter and intra-observer variability remains substantial, especially for non-specialized pathologists. In this study we investigated the potential of deep learning to assist the pathologist with automatic and reliable classification of head and neck squamous lesions following the 2022 WHO classification system for the hypopharynx, larynx, trachea and parapharyngeal space. We created, for the first time, a large scale database of histological samples intended for developing an automatic diagnostic tool. We developed and trained a weakly supervised model performing classification from whole slides images. A dual blind review was carried out to define a gold standard test set on which our model was able to classify lesions with high accuracy on every class (average AUC: 0.878 (95% CI: [0.834-0.918])). Finally, we defined a confidence score for the model predictions, which can be used to identify ambiguous or difficult cases. When the algorithm is applied as a screening tool, such cases can then be submitted to pathologists in priority. Our results demonstrate that the model, associated with confidence measurements, can help in the difficult task of classifying head and neck squamous lesions.

Introduction

Head and neck squamous cell carcinomas (HNSCC), ranked 6th cancer worldwide, constitute a major public health issue because of their high mortality rate and the morbidity of their treatment regimens [START_REF] Bray | Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries[END_REF][START_REF] Johnson | Head and neck squamous cell carcinoma[END_REF][START_REF] Liao | Health-related quality of life and utility in head and neck cancer survivors[END_REF]. These poor figures can be explained by a late diagnosis, usually at an advanced stage of the disease. However, it is estimated that early diagnosis of potentially malignant head and neck lesions could prevent almost 90% of cancers [START_REF] Mahmood | Use of artificial intelligence in diagnosis of head and neck precancerous and cancerous lesions: A systematic review[END_REF]. The early detection of HNSCC could be allowed by a precise follow-up of precancerous lesions, or squamous dysplasias, depending on their potential to become invasive. The classification of head and neck dysplasias has been a highly controversial issue for many years. Indeed, since the first classification proposed by Kleinsasser in 1963 (5), many different classifications have been proposed by expert pathologists without achieving a strong consensus [START_REF] Gale | Laryngeal dysplasia: persisting dilemmas, disagreements and unsolved problems-a short review[END_REF][START_REF] Hellquist | Developing Classifications of Laryngeal Dysplasia: The Historical Basis[END_REF]. Each of them had different terminologies and methods of grading, but their reproducibility was always low to moderate [START_REF] Gale | Laryngeal dysplasia: persisting dilemmas, disagreements and unsolved problems-a short review[END_REF][START_REF] Mehlum | Laryngeal precursor lesions: Interrater and intrarater reliability of histopathological assessment[END_REF][START_REF] Sarioglu | Inter-observer Agreement in Laryngeal Pre-neoplastic Lesions[END_REF][START_REF] Fleskens | Interobserver variability of laryngeal mucosal premalignant lesions: a histopathological evaluation[END_REF][START_REF] Hu | Diagnostic variability of laryngeal premalignant lesions: histological evaluation and carcinoma transformation[END_REF][START_REF] Krishnan | Inter-and intra-observer variability in three grading systems for oral epithelial dysplasia[END_REF] (Table 1). Nevertheless, higher grades were associated with a higher risk of transformation into carcinoma, confirming their significance [START_REF] Van Hulst | Grade of dysplasia and malignant transformation in adults with premalignant laryngeal lesions[END_REF]. In order to improve inter-rater and intra-rater reliability, the World Health Organization (WHO) recommended to grade laryngeal squamous dysplasias with only two categories : low-grade and high-grade. The high-grade category encompasses moderate, severe dysplasia and carcinoma in situ. This system showed a large difference in terms of severity. In fact, Gale et al. observed in their work that high grade dysplasia were ten times more at risk to evolve to invasive carcinoma than low grade lesions [START_REF] Gale | Evaluation of a new grading system for laryngeal squamous intraepithelial lesions-a proposed unified classification[END_REF]. The last classification taken up by the (WHO) in 2022 [START_REF] El-Naggar | WHO Classification of Head and Neck Tumours[END_REF][START_REF] Zidar | Update from the 5th Edition of the World Health Organization Classification of Head and Neck Tumors: Hypopharynx, Larynx, Trachea and Parapharyngeal Space[END_REF] confirms the simplification of the grading proposed in 2017, even if the difference between high-grade dysplasia and in situ carcinoma is questioned.

For the oral cavity, the WHO grading system kept the distinction of moderate and severe lesions. Interestingly, this is the only grading system keeping three separate grades, even if oral squamous lesions share the same pathophysiology and are induced by the same carcinogens than in the larynx, hypopharynx, trachea and parapharyngeal space. Notably, moderate and severe lesions are reunited in a "high-grade dysplasia" category for squamous dysplasia grading in the uterine cervix [START_REF] Who | Female Genital Tumours WHO Classification of Tumours[END_REF], the anus [START_REF] Roberts | Anal intraepithelial neoplasia: A review of diagnosis and management[END_REF] and the esophagus [START_REF] Who | Digestive System Tumours WHO Classification of Tumours[END_REF]. Two-grades systems are also used for glandular dysplasias such as in colorectal adenomatous polyps or Barrett's esophagus [START_REF] Who | Digestive System Tumours WHO Classification of Tumours[END_REF]. In light of these considerations, the evaluation of oral dysplastic lesions could benefit from a two-grades classification system. Nevertheless, reproducibility between pathologists remains moderate for all grading methods [START_REF] Sathasivam | The clinical utility of contemporary oral epithelial dysplasia grading systems[END_REF]. This difficulty to classify is due to the multiple elements to take into account both at cytological and architectural levels, on an epithelium that can have noticeable variations of thickness depending on the anatomical location, and inflammatory and dystrophic alterations that can sometimes be difficult to distinguish from true dysplasia [START_REF] Zidar | Update from the 5th Edition of the World Health Organization Classification of Head and Neck Tumors: Hypopharynx, Larynx, Trachea and Parapharyngeal Space[END_REF]. Finally, the arbitrary classification categories imposed on a continuous spectrum of lesions that have no absolute and clearly definable boundaries induces more subjectivity.

Given these considerations, the field is in need of new tools to help pathologists make robust and consistent classifications of squamous head and neck lesions, for better clinical management.

In order to help pathologists to perform precise and robust diagnoses, many artificial intelligence (AI) algorithms have been developed these last years [START_REF] Bera | Artificial intelligence in digital pathology-new tools for diagnosis and precision oncology[END_REF]. Deep learning models can learn meaningful patterns without explicit definition by an expert. Weak supervision has proven to be a very powerful strategy for many classification tasks in computational pathology, from cancer detection [START_REF] Bejnordi | Diagnostic assessment of deep learning algorithms for detection of lymph node metastases in women with breast cancer[END_REF][START_REF] Steiner | Impact of deep learning assistance on the histopathologic review of lymph nodes for metastatic breast cancer[END_REF][START_REF] Raciti | Novel artificial intelligence system increases the detection of prostate cancer in whole slide images of core needle biopsies[END_REF] to classifying carcinoma subtypes [START_REF] Coudray | Classification and mutation prediction from non-small cell lung cancer histopathology images using deep learning[END_REF][START_REF] Courtiol | Classification and Disease Localization in Histopathology Using Only Global Labels: A Weakly-Supervised Approach[END_REF], grading [START_REF] Bulten | Automated deep-learning system for Gleason grading of prostate cancer using biopsies: a diagnostic study[END_REF], prognosis, prediction of molecular signatures [START_REF] Schmauch | A deep learning model to predict RNA-Seq expression of tumours from whole slide images[END_REF][START_REF] Coudray | Deep learning links histology, molecular signatures and prognosis in cancer[END_REF] and primary origins [START_REF] Lu | AI-based pathology predicts origins for cancers of unknown primary[END_REF]. Yet, only a few papers about grading dysplasias have been published so far and studies applied to head and neck pathology are even more scarce. This can be explained by the lack of a public database including dysplastic lesion annotations and the difficulty to reach grading consensus, as shown by the low reproducibility even between expert pathologists. Interestingly, most studies used classical supervised machine learning methods rather than deep learning [START_REF] Mahmood | Use of artificial intelligence in diagnosis of head and neck precancerous and cancerous lesions: A systematic review[END_REF][START_REF] Mahmood | Artificial Intelligence-based methods in head and neck cancer diagnosis: An overview[END_REF] and focused on the oral cavity, with no study about laryngeal lesions [START_REF] Mahmood | Artificial Intelligence-based methods in head and neck cancer diagnosis: An overview[END_REF]. Classification of head and neck squamous lesions could similarly benefit from computer-assisted analysis by helping pathologists standardize and reduce bias of their grading. To be integrated in pathologists workflows, AI models should provide an assessment of the models confidence for each prediction. Even though measuring AI model uncertainty has been studied frequently in the past years [START_REF] Gal | Dropout as a bayesian approximation: Representing model uncertainty in deep learning[END_REF][START_REF] Lakshminarayanan | Simple and scalable predictive uncertainty estimation using deep ensembles[END_REF][START_REF] Osband | Deep exploration via bootstrapped DQN[END_REF], it was rarely applied to computational pathology. Most works focused on segmentation [START_REF] Nair | Exploring uncertainty measures in deep networks for multiple sclerosis lesion detection and segmentation[END_REF][START_REF] Camarasa | Quantitative comparison of monte-carlo dropout uncertainty measures for multi-class segmentation[END_REF][START_REF] Scandalea | Deep active learning for axon-myelin segmentation on histology data[END_REF][START_REF] Kohl | A probabilistic u-net for segmentation of ambiguous images[END_REF] but less on diagnosis tasks [START_REF] Thagaard | Can you trust predictive uncertainty under real dataset shifts in digital pathology?[END_REF][START_REF] Senousy | MCUa: Multi-level context and uncertainty aware dynamic deep ensemble for breast cancer histology image classification[END_REF]. In a recent work, Poceviciute et al. [START_REF] Pocevičiūtė | Generalisation effects of predictive uncertainty estimation in deep learning for digital pathology[END_REF] stressed out the need for an AI reliability measure for diagnosis and compared methods to assess it. Lu et al. [START_REF] Lu | AI-based pathology predicts origins for cancers of unknown primary[END_REF] evaluated their prediction model by computing the top-k differential diagnostic accuracy to determine the primary origin of carcinomas. By integrating the prediction probabilities directly in their workflow, their model helped reduce the potential primaries to investigate. Finally Dolezal et al. [START_REF] Dolezal | Uncertainty-Informed Deep Learning Models Enable High-Confidence Predictions for Digital Histopathology[END_REF] proposed a thresholding paradigm not susceptible to domain shift for reliable use of uncertainty measure in clinical practice. As the grading of laryngeal dysplasia is often controversial, even for experts, tempering a model's predictions with a measure of its confidence could help pathologists to integrate them into their grading choice.

The aim of this work was to develop a fully automated, weakly supervised model for the diagnosis of dysplasias and squamous cell carcinomas of the head and neck associated with a method to assess the models confidence for each prediction. The classification followed the WHO grading system for the hypopharynx, larynx, trachea and parapharyngeal space. We compared the models reproducibility to pathologists and evaluated its performances on a gold standard test set. We propose a measure of confidence of the model's predictions providing pathologists with a score indicating to which extent they can trust the prediction. We showed that this score was consistent with pathologists' hesitations when grading dysplasia, and we believe that it can greatly enhance acceptance of such an automatic grading system.

Material and Method

Selection of patients

Patients were selected retrospectively from 2000 to 2013 from the Hôpital Européen Georges Pompidou (HEGP, Paris, France) clinical database (DxCare® software). Patients were at least 18 years old and diagnosed with head and neck squamous cell dysplasia or carcinoma, either of the larynx, pharynx, nasopharynx, hypopharynx, lateral edge of the tongue or oral cavity. Oropharyngeal cases were excluded from the study, since in this anatomical region most SCC are related to the Human Papillomavirus, have specific aspects [START_REF] Westra | The morphologic profile of HPV-related head and neck squamous carcinoma: implications for diagnosis, prognosis, and clinical management[END_REF], and the existence of dysplastic lesions is still debated with no diagnostic guidelines from the WHO. Carcinomas sampled after chemotherapy or radiotherapy were excluded since the treatment modifies the aspect of the lesion and the data do not fit the use case of the model.

Selection of samples and slides

The samples were identified in the HEGP Pathology Department database (Diamic® software). Both biopsies and surgical samples were included, but not all the surgical samples of carcinomas per patient that were available in the hospital's archives. This selection was made in order to keep a balance between classes in the dataset. When several slides of the same sample were available, one investigator (YBH) selected the slide where the lesion was most visible. Every pathology report was read to assess which types of lesions were present. Samples were excluded if the pathologist mentioned in the report that it was impossible for him to distinguish between high-grade dysplasia and invasive carcinoma because of tangent inclusion. Verrucous carcinomas were also excluded. The slides were stained at the time of the sampling with Hematoxylin Eosin and Saffron (HES) staining.

Digitized dataset constitution

The slides were digitized with a pathology slide scanner (Hamamatsu NanoZoomer® s360) at 20X magnification (pixel resolution of 0.45 µm). All the sections present on the slide were scanned. The quality of the digitization was checked for all the WSIs. Scans were excluded if the digitization failed after two attempts. During digitization, each slide was given an identification number for anonymization purposes. After digitization, the WSIs were uploaded to the EyeDo© platform. Each slide was given a global label corresponding to the most severe lesion in the sample, following the WHO classification, according to the clinical report. These initial labels were thus provided by several pathologists between 2000 and 2013. Slides with no surface epithelium and slides with strong artifacts were excluded but slides with artifacts that did not impair a clear diagnosis were kept in the dataset.

Review of "mild to moderate" dysplasias

Because the samples were selected from 2000 to 2013, many dysplasias were diagnosed at this time with a "mild to moderate" grade. However, this grading does not follow the WHO classification anymore, since mild dysplasia is synonymous with low grade and moderate dysplasia with high grade. The 127 "mild to moderate" samples were reviewed jointly by the pathologist investigators (YBH, CB) in order to assign a grade compatible with the latest WHO grading system.

Blind review for assessment of a gold standard test set

Diagnosis of squamous dysplasias by pathologists lacks reproducibility [START_REF] Mehlum | Laryngeal precursor lesions: Interrater and intrarater reliability of histopathological assessment[END_REF]. In order to assess the model's performance in the best conditions, pathologist investigators made a dual blind review on a selected portion of the dataset. This portion was considered as a gold standard test set. Only biopsies were selected for this test set, as they correspond to the use case of the model (for surgical samples, the diagnosis is usually already known at the time of the surgical resection). The data scientist investigators, not taking part in the grading, were in charge of selecting the slides. The samples were selected based on their labels, such that classes were balanced. To make sure the test samples were independent, slides were selected in the following way: all the patients with only one slide present in the initial dataset were attributed to the test set; then the patients associated with multiple slides (no more than two) were attributed to the test set only if the slides were acquired multiple years apart. Slides from different samples of the same patient but from the same year were discarded. Thus, all slides in the gold standard test set are considered independent from the rest of the cohort. The reference standard for the internal test dataset was determined in two rounds. Two raters, both with expertise in head and neck pathology, but at different career stages (reviewer 1-CB: international expert, reviewer 2-YBH: early-career pathologist) independently reviewed the slides of the test set. The review was carried out on the digitized slides, through the online viewer on the EyeDo© platform. The raters were blind to any clinical information, the initial diagnosis, and the rating of the other assessor. They were aware that the test set had been chosen to be balanced (according to the initial labels). To avoid bias resulting from this information, the raters could not change their diagnosis after a slide had been reviewed and assessed. The two raters finally met during a consensus meeting to discuss the slides on which they disagreed. If the disagreement persisted, the slides were excluded. Label noise in the dataset was measured by comparing final consensus labels with initial diagnosis from patient records.

Data management

To assess the diagnostic capacity of the model, 128 slides were selected from the entire dataset and reviewed to constitute the gold standard test set as described above. The remaining slides (2121 WSIs from 498 patients) were split into 5 randomly sampled training and validation sets following the 80%-20% standard to train the deep learning model and fix hyperparameters according to best practices. To ensure class balance between training and validation sets, the splits were performed in a stratified manner by patients and grades using the Multilabel Stratified K-Fold algorithm from Sedichis (44) (worst grade was kept for each patient). In the training splits, low grades slides were upsampled (1.5 times) to reduce the effect of class imbalance. There was no patient overlap between training, validation and gold standard test sets.

Deep Learning Model

Implementation details are provided in the Supplementary Materials.

Tissue Selection

In order to train the WSI classification model, slides were divided into smaller images of 224x224 pixels at a resolution of 1 µm/pixel. When tiling the entire sample and removing only the white background, WSIs contained up to 8800 tiles (with an average of 1300 tiles per slide), giving a total of 3.9 millions of tiles across the dataset. To reduce the processing time, we removed any tiles not containing epithelial cells (from surface epithelium or tumor). To do so, we first trained a UNet [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] to perform binary segmentation between epithelium and carcinoma tissue (the "foreground") versus any other type of tissue or background (the "background"). The UNet was trained at 10X resolution (1 µm/pixel) on 5439 annotated tiles of 512x512 pixels from 121 slides. The classification threshold was modified to 0.4 in order to minimize false negatives and thus make sure all the tissue of interest was selected. Non-overlapping tiles were then extracted from the selected tissue, resulting in 2.2 millions of tiles.

Multiple Instance Learning architecture

Our model was derived from the Attention-based Multiple Instance Learning (MIL) architecture proposed by Ilse et al [START_REF] Ilse | Attention-based deep multiple instance learning[END_REF]. It consisted of a feature extractor, a scoring module and a classification module. Due to their size, WSIs have to be cut into smaller tiles. Features are extracted from each tile through a frozen convolutional neural network (DenseNet121, (47)), resulting in feature vectors of dimension 1024. A global label (the grade of the worst lesion on the slide) is associated with the bag of tiles. Thanks to an attention mechanism, the network learns which tiles within the bag are most important for the grading of the lesion and attributes a score. The classification module aggregates the attention scores and the extracted tile representations to obtain a slide representation (weighted sum of the tile representations, where the weights are the attention scores) from which the slide-level label is predicted.

Cost-sensitive training

Due to the ordinal nature of our classes, we used a cost-aware classification loss introduced in [START_REF] Chung | Cost-Aware Pre-Training for Multiclass Cost-Sensitive Deep Learning[END_REF]. The network was trained to predict a class-specific risk rather than a posterior probability. The predicted class corresponds to the class minimizing this risk. The risk was defined according to the cost matrix, inspired by the TissueNet Challenge organized by the French Society of Pathology in 2020 [START_REF] Delaune | Le premier data challenge organisé par la Société Française de Pathologie: une compétition internationale en 2020, un outil de recherche en intelligence artificielle pour l'avenir?[END_REF] and penalized large errors (e.g. benign vs high grade dysplasia) more than small errors (e.g. low grade vs high grade). The cost matrix can be found in the Supplementary Material (Table A).

Self-Supervised pre training

We initialized the feature extractor with pretrained weights obtained with self-supervised training. SimCLR [START_REF] Chen | A Simple Framework for Contrastive Learning of Visual Representations[END_REF], a simple architecture relying on data augmentation, was trained on all the tiles in the dataset (3.5 Millions tiles of 336x336 pixels) for 300 hours (143 epochs) on 8 GPUs. During the training, each tile was randomly cropped and resized to 224x224 pixels, flipped and rotated. The H&E staining was modified with RGB to Haematoxylin-Eosin-DAB (HED) color space conversion and colors were randomly altered (contrast, hue, brightness, saturation).

Test and Evaluation

The deep learning model was trained on the five cross-validation training splits. Early stopping, monitoring the validation loss, was used to stop the training (with a patience of 60 epochs). The five models were assembled to make predictions on the gold standard test set. Overall predictions were obtained by averaging the posterior probabilities of the five models. Class-wise classification metrics were computed in a one-versus-all manner, the average of the class-wise scores was performed to compute overall performances. Performances comparing models predictions and consensus labels were measured. Metrics were reported with 95% confidence intervals (CI) using a bootstrapping method (10 000 iterations).

Confidence score

In order to assess the certainty of the model's predictions, a confidence score was computed for every prediction of the model on the gold standard test set. The confidence score was derived from the risk estimation output by the last layer of the network. The softmax of the inverted risk (-risk vector) was computed, turning cost estimation into probabilities. The confidence score was defined as the difference between the two highest risk probabilities: if the probabilities were close, the network was hesitating between two classes, if they were far, the network was considered more confident. As the confidence score is derived from the cost sensitive risk estimation, it takes into account the ordinal characteristic of the classes; smaller confidence values hence reflect pathologists hesitations. This confidence score was designed for potential application of the model in the context of screening. To exclude predictions with poor confidence, a threshold was set to filter out uncertain predictions. The threshold was optimized on the validation set to reach an overall AUC > 0.9. The performance of the model after filtering uncertain predictions was assessed on the gold standard test set.

Analysis of misclassified slides

Attention scores learned by the MIL model reveal tiles that strongly influence the decision and are thus supposed to be of diagnostic relevance. Heatmaps of attention scores were overlaid on WSIs on the EyeDo© Platform in order to inspect important regions. Qualitative analysis of tiles with high predictive value was performed.

Results

Training dataset

The data used for training and validation of the model consisted of 2144 slides. The low-grade dysplasia class was significantly underrepresented (10.7% of the total, 229 slides). Other classes were present in balanced proportions. Patient characteristics and a summary of the cohort are presented in Table 2.

Slides reviews "Mild to moderate" dysplasia

Almost a third of the "mild to moderate" dysplasias were reclassified during the review as not dysplastic. A summary of the review is shown in the Supplementary Materials.

Gold standard test set

After the first round of grading, the two graders independently agreed on 79 slides. The remaining 52 slides were discussed at the consensus meeting. Three slides were excluded: one slide for which it was impossible to distinguish high-grade dysplasia from invasive carcinoma; one slide for which it was impossible to choose between low-grade dysplasia and artifacts; and one slide for which there was a suspicion of carcinoma in the chorion but with no connection to the surface epithelium, which was normal. Consensus was achieved for the 49 other slides, resulting in 128 slides from 110 patients to be used as the gold standard test set. The labels of the gold standard test set before and after review are shown in Supplementary Materials (Table B).

Classification performance of the deep learning model

When considering the consensus labels as an absolute ground truth, the AI model achieved an average AUC on the 4 classes of 0.878 (95% CI: [0.834-0.918]). The AI model reached an AUC > 0.8 for all 4 classes. ROC AUC can be found in Figure 1. Average AUC dropped significantly when using the initial labels as the ground truth rather than the consensus labels to evaluate the AI model's predictions. (AUC=0.832 [0.787-0.875]). This shows that the review reduced the noise in the labeling, leading to better classification performances. Classification performances are summarized in Table 3 and confusion matrices are shown in Figure 2. The misclassified slides are listed in Table C in Supplementary Materials. The majority of the misclassifications came from the "low grade" dysplasia class, with seven slides misclassified as benign. The initial label of all of these slides was "benign", suggesting that there is some ambiguity in these cases. As many slides in the gold standard test set were classified as low grade dysplasias and had a "benign" initial label, these misclassifications could be explained by a significant difference of grading between the validation set and the test set. Four slides of carcinoma were missed by the AI model and predicted as low-grade or high-grade dysplasia, but with a low confidence score beneath the threshold which would have filtered them out. Three of these slides had significant artifacts and the other showed carcinoma under a non-dysplastic epithelium, which could be more difficult for the model to identify because of the rarity of this presentation.

Analysis of misclassified slides

In the test set, three high grade dysplasias were misclassified as carcinomas, two of them with a high confidence score. For two of these slides, the tiles with the highest attention score showed similar aspects, with marked atypia restricted to the basal layers and a corrugated aspect of the lamina propria. This aspect was identified with a high attention score on a slide labeled low grade dysplasia and confidently classified as high grade dysplasia by the model (Figure 3). These lesions were sampled in the larynx. In the validation sets, analysis of five slides misclassified from high grade to carcinoma or from low grade to high grade revealed the same aspects on high attention tiles.

Assessment of inter-rater agreement

To assess the noise present in our ground truth labels we measured the agreement between the reviewers (reviewers 1 and 2), the initial labels and the AI model (Table 4). The main metric used to measure agreement was the linear Cohen's kappa. Agreement between the AI model and the initial labels was slightly lower (linear Cohen's kappa = 0.641 [0.546-0.726]) than the agreement between reviewer 1 or 2 versus the initial labels (linear Cohen's kappa = 0.689 [0.606-0.764] and 0.723 [0.634-0.803] respectively), however it remained substantial [START_REF] Landis | The measurement of observer agreement for categorical data[END_REF]. Agreement between reviewer 1 and reviewer 2 led to a linear Cohen's kappa of 0.676 [0.592-0.753]. These figures were of the same order of magnitude as in the literature [START_REF] Mehlum | Laryngeal precursor lesions: Interrater and intrarater reliability of histopathological assessment[END_REF].

Confidence score assessment

For the correct predictions, the confidence score was on average 0.73 +/-0.303 compared to 0.418 +/-0.303 for incorrect predictions. The confidence threshold, optimized to reach an overall AUC > 0.9 on the 5 validations sets, was set to 0.5. On the gold standard test set, at this threshold, 52 slides (40.6%) were considered as uncertain, most of them being low grade dysplasias. On the remaining slides, the Invasive Carcinoma AUC was 0.987 [0.962-1.000]. No carcinoma slides were missed by the model (Negative Predictive Value of 1.000 [1.000-1.000]). The overall AUC improved by 4.5% (0.931 [0.892-0.965]) when removing slides with low confidence. Conversely, overall AUC computed on the uncertain slides was equal to 0.764 [0.672-0.848] (-12.2% compared to the overall AUC on the full gold standard test set). In Figure 1 (C andD) we see that the confusion matrix on the confident slides is almost diagonal. The confidence score being the difference between the 2 highest probabilities, we observed that the model was always hesitating between two adjacent classes. Additionally, in the Supplementary Figure D we show that when removing slides from the gold standard test set according to their confidence score, the metrics on the remaining slides were consistently increasing, while removing randomly picked slides led to erratic evolution of the performances. In Figure 4, we compared the confidence score distributions for slides dependent on whether the two reviewers agreed or not. The figure suggests that the confidence level of the model reflects the probability of disagreement between reviewers. We note that even for a confidence score of 0, we would expect disagreement in only 50% of the cases. This explains why the distributions are overlapping.

Discussion

To the best of our knowledge, we propose the first deep learning model for the grading of head and neck squamous lesions following the WHO classification system. In the literature, studies about grading dysplasia with deep learning are scarce. Most of them focus on cervix Pap Smears [START_REF] Wang | Artificial intelligence-assisted fast screening cervical high grade squamous intraepithelial lesion and squamous cell carcinoma diagnosis and treatment planning[END_REF][START_REF] Bao | Artificial intelligence-assisted cytology for detection of cervical intraepithelial neoplasia or invasive cancer: a multicenter, clinical-based, observational study[END_REF], which does not take into account the epithelial architecture. A model for classification of esophageal lesions was proposed in Tomita et al [START_REF] Tomita | Attention-based deep[END_REF] but didn't differentiate low-grade from high-grade dysplasias. Because no public database with annotated head and neck dysplasias nor "benign" epithelium was available, we collected a large scale dataset of head and neck samples and clinical data from the HEGP, a renown center for head and neck diagnosis and medical care in France.

As dysplasia grading is difficult and reproducibility between pathologists is low to moderate, a blind reviewed test set was generated in order to properly assess the AI model performance. We observed that the agreement between the two reviewers on this test set was in line with previous reports [START_REF] Gale | Laryngeal dysplasia: persisting dilemmas, disagreements and unsolved problems-a short review[END_REF][START_REF] Mehlum | Laryngeal precursor lesions: Interrater and intrarater reliability of histopathological assessment[END_REF][START_REF] Sarioglu | Inter-observer Agreement in Laryngeal Pre-neoplastic Lesions[END_REF][START_REF] Fleskens | Interobserver variability of laryngeal mucosal premalignant lesions: a histopathological evaluation[END_REF][START_REF] Hu | Diagnostic variability of laryngeal premalignant lesions: histological evaluation and carcinoma transformation[END_REF], illustrating once more the difficulty to obtain objective and robust grading of head and neck dysplasia and the need for new tools to help pathologists make reliable diagnoses. We developed and trained a weakly supervised deep learning model that was able to accurately grade head and neck dysplasia, offering a first tool for assisted diagnosis. Even though measuring a diagnostic test reliability is mandatory in pathology (for example, controls for immunomarkings), very few studies in computational pathology developed a confidence score to accompany the model's predictions. In this work, we propose a novel confidence score that is defined as the difference between the posterior probability of the two top classes, ranging between 0 if the two top classes were equally likely for the network, to 1 if the network had maximal confidence in the top class. Our confidence score showed that the model, when uncertain, was always hesitating between adjacent classes, mimicking pathologists doubts. This observation is in line with the fact that epithelial dysplasia belongs to a continuous spectrum of lesions. Our confidence score can be useful to mitigate artificial sharp borders imposed by the WHO grading system and help pathologists decide on the grade with more objectivity. Moreover, we believe that such confidence scores can greatly improve real-world applicability and acceptance: for screening purposes, the application of the tool can be restricted to cases with high confidence, and thus identify the slides for which review by a pathologist would be recommended in priority. Misclassified slides were analyzed regarding their confidence scores. We observed that for slides with low confidence predictions pathologists were more likely to disagree. The analysis of the four false negative carcinoma samples showed that severe technical artifacts (tangent cuts, staining artifacts…) have the potential to negatively impact the classification results. But we also found that they ultimately also lead to low confidence scores and would have been filtered out according to our procedure. Misclassified slides associated with high confidence scores were mostly upgraded by one class (low grade classified as high grade, high grade classified as carcinoma). The analysis of the tile attention scores revealed that the model placed strong attention on severe atypia located in the lower half of the epithelium, with a corrugated lamina propria. The two pathologists reviewed these highlighted tiles together and agreed that these aspects are challenging to interpret and were present only focally in the slides. Since pathologists analyze epithelial surface in its globality, focal severe atypia can be missed. The attention heatmap analysis, associated with the confidence score, could be of great use by pathologists as a tool to focus on the most severe dysplastic aspects, guiding their final grading.

The presented study is monocentric and retrospective. For this reason, it will be necessary to establish an external cohort for further validation. However, we note that the large time range of patient recruitment (13 years) conveys the dataset already a high degree of heterogeneity and thus limits the risk of overfitting.

To conclude, we propose a reliable and powerful deep learning model for the classification of head and neck squamous cell lesions, especially helpful in a context of lack of available experts to screen enough samples or give a second read on difficult interpretations. The confidence score is an original and efficient way to assess the reliability of the model's predictions, making it closer to medical tests standards of use. We believe this method is a significant milestone towards reliable AI assisted diagnosis in digital pathology workflow, especially for subjective tasks such as grading of head and neck squamous lesions. Classification performances are superior when using reviewed labels indicating that the review helped reduce noise in the labels. Confusion matrices show that the model is more confused on the Low Grade (1) and High Grade (2) classes, rather than the Carcinoma class (3) for instance which is justified by the ambiguity carried by this classes, on which even pathologist can struggle. Matrix C corresponds to the confusion matrix on the high confident slides at threshold=0.5, matrix D corresponds to the low confident slides. Matrix C is almost diagonal, and the overall AUC on the confident slides subset is higher by more than 10% than on the unconfident subset. Additionally, we see that most of the Carcinoma slides are considered confident by the model.

Figure 1 -

 1 Figure 1 -AUC ROC for each class on the reviewed gold standard test set -ROC curves were obtained by bootstrapping of the AI model predictions (10 000 bootstrap samples). They were computed for each class in a One vs Rest manner using consensus labels as a ground truth. ROC = receiver operator characteristic. AUC area under the curve. ROC AUC of the Carcinoma class is better than for the other classes, certainly because the diagnosis of this class is often less ambiguous than for the other grades. Thus, the training data contains less noise on this class, as well as the test data. Misclassification on Carcinoma class concerned microinvasive lesions.

Figure 2 -

 2 Figure 2 -Confusion Matrices -AI model's performances are evaluated on the gold standard test set on the reviewed labels (A) and the initial labels (from patient's records) (B). Numbers 0, 1, 2, 3 corresponds respectively to classes Benign, Low Grade, High Grade and Carcinoma. Classification performances are superior when using reviewed labels indicating that the review helped reduce noise in the labels. Confusion matrices show that the model is more confused on the Low Grade (1) and High Grade (2) classes, rather than the Carcinoma class (3) for instance which is justified by the ambiguity carried by this classes, on which even pathologist can struggle. Matrix C corresponds to the confusion matrix on the high confident slides at threshold=0.5, matrix D corresponds to the low confident slides. Matrix C is almost diagonal,

Figure 3 -

 3 Figure 3 -Misclassified slides: attention score analysis -Tiles with high attention scores attributed by the MIL model. Left column: 20X magnification, right column: 10X magnification. A. and B. : slide_1597. High grade dysplasia predicted as invasive carcinoma. The model focused on marked basal atypia with a corrugated lamina propria C. and D.: slide_237. High grade dysplasia predicted as invasive carcinoma. The model focused on marked basal atypia and bulky rete ridges. E. and F.: slide_2712. Low grade dysplasia predicted as high grade. The model focused on marked basal atypia with a corrugated lamina propria. The three lesions are located in the larynx.

Figure 4 -

 4 Figure 4 -Confidence level distributions -Comparison of confidence level and agreement between Reviewer 1 and Reviewer 2. The model is more confident on slides on which reviewers agreed during the dual blind review and is less confident on slides on which they disagreed. This suggests that the confidence score reflects the difficulties inherent to the slides, as pathologists would experiment with it. Significance: Mann-Whitney-Wilcoxon test two-sided with Bonferroni correction, p-value=1.095e-02 U-stat=2.455e+03.

Table 1 -History of dysplasia classificationTable 2 -Cohort descriptionTable 3 -Classification performancesTable 4 -Inter rater agreement

 1234

Acknowledgements

Keen Eye team for thoughtful discussions and technical support. Yan Petit for code implementation assistance.

Our study was approved by the ethics committee of Assistance Publique -Hôpitaux de Paris Centre (CERAPHP. Centre -Institutional Review Board registration #00011928). All the patients were informed by a notification letter of the study and the possibility to refuse the use of their medical data, in line with current legislation. The study was performed in accordance with the Declaration of Helsinki.

Funding ML was supported by a CIFRE PhD fellowship founded by Keen Eye, Paris, France and ANRT (CIFRE 2019/1905). Furthermore, this work was supported by the French government under management of Agence Nationale de la Recherche as part of the "Investissements d'avenir" program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute).

Data Availability Statement

The WSI dataset described in the manuscript were subject to hospital regulations and could not be publicly released.

Conflict of interest

The authors declare no competing interests.

Ethics Approval and Consent to Participate Author Contributions

Concept and design: CB, TW, SB. Ethical approvals processes : YBH, CB, SB. Creation of the clinical and pathology database, slides selection, virtual slides quality control: YBH. Data management and processing, software implementation, experiments realization and statistical analysis: ML. Choices on experiments : ML and YBH. Design of AI methods: ML, TW. Results analysis: ML and YBH. Discussion of results: ML, YBH, TW, CB. Manuscript writing and review: all authors. All authors read and approved the final paper.


Dominique Massiot
email: dominique.massiot@cnrs-orleans.fr

Franck Fayon

Michael Deschamps

Sylvian Cadars

Pierre Florian

Valérie Montouillout

Nadia Pellerin

Julien Hiet

Aydar Rakhmatullin

Catherine Bessada

Detection and use of small J couplings in solid state NMR experiments

Over the years, solid-state nuclear magnetic resonance (NMR) spectroscopy has become an important tool for materials science, with its local point of view that is highly complementary to the structural information provided by diffraction techniques, electron microscopy, and molecular modeling for example. As compared to other interactions that determine the spectral expression of the local structure of the observed nuclei in solid-state NMR experiments, the J coupling, characteristic of the chemical bonds, has received far less attention because of its being generally so small that it is masked in the line-widths. Nevertheless, the scalar or isotropic part of J couplings, which is not averaged by magic angle spinning (MAS), can be evidenced in many systems, and exploited to unequivocally characterize the extended coordination sphere. In a first step we describe the different experiments that permit the observation and the measurement of J couplings, even when dealing with quadrupolar nuclei. We then present new and recently-published results that illustrate the state of the art of NMR methodologies based on or intended for measuring Jcouplings in solids and the novel perspectives that they open towards better understanding of ordered and disordered materials at the sub-nanometric scale, a length scale that is otherwise difficult to access.

Introduction

Because of its ability to selectively observe and characterize the local environments of most constituting atoms of ordered or disordered solids, High Resolution Solid State NMR spectroscopy has become a tool of choice for materials science. The rapid development of new methods now not only provides means for spectrally resolving and quantifying different chemical environment characterized by their chemical shifts but also allows to explore the structure of the surrounding of the observed atoms at different length scales using interactions characteristic of distances (dipolar interaction) [START_REF]Encyclopedia of Magnetic Resonance[END_REF][START_REF] Massiot | [END_REF] or chemical bonds (J indirect coupling) [START_REF]Encyclopedia of Magnetic Resonance[END_REF]. These methods can take different forms ranging from spectral edition to measurement and use the through-space or through-bond interactions in multidimensional experiments. The aim of this contribution is to focus on the measurement and use of indirect J couplings, even when involving quadrupolar nuclei, and to emphasize new developments and perspectives. (e) 29 Si spin-echo MAS NMR spectrum of commercial silica with 99% enrichment in 29 Si. (b) Transmissionelectron microscopy (TEM) image and electron diffraction pattern (inset) and (f) 29 Si{ 1 H} CPMAS NMR spectrum of an hexagonal mesoporous silica composite. [START_REF] Kirmayer | [END_REF] (c) In-plane view of a layered silicate-surfactant mesophase consisting of thin (0.8 nm) molecularly-ordered silicate sheets with five distinct (colored) Si atom sites giving rise to five narrow 29 Si resonances in the corresponding 29 Si{ 1 H} CPMAS NMR spectrum (g), and separated by alkylammonium surfactant species. [5] (d) Schematic representation of the highly ordered silicate framework structure and (h) 29 Si MAS NMR spectrum with extremely narrow resonances of zeolite ZSM-12 (courtesy D.H. Brouwer).

Silica-based materials can be used as a starting point to illustrate the general problems of materials science that can be assessed using solid-state NMR, including by the exploitation of molecular interactions such as J couplings. These materials are of paramount importance in many different fields of materials sciences in the form of inorganic glasses, sol-gel derived materials, bio-compatible or bio-inspired materials, porous or mesoporous materials, zeolites, or organic-inorganic hybrids. The structures of silica-based materials are characterized in particular by various extents of order and disorder at length scales that range from molecular to micrometric dimensions, as illustrated with a few typical examples in Figure 1. Amorphous structures, such as silicate glasses or commercial SiO 2 , which may be used as a silicon source for silicate materials synthesis, have highly disordered molecular structures that are associated with a wide range of local silicon environments giving rise to broad (ca. 10 ppm, full width at half maximum, fwhm) 29 Si NMR lineshapes (Fig. 1e) that barely allow resolution of chemically different Q 3 (i.e., (SiO) 3 Si-OH or (SiO) 3 Si-O -) and fully condensed Q 4 (Si(SiO) 4 ) 29 Si moieties. Similar molecularly-disordered SiO 2 structures are also generally found in the walls of self-assembled mesoporous silica despite potentially high degrees of long-range order in their pore architectures, as illustrated in Figure 1f by the broad lineshapes associated with Q 2 , Q 3 , and Q 4 environments in the 29 Si{ 1 H} cross-polarization (CP) magic-angle spinning (MAS) spectrum of the block-copolymer-silica composite whose representative transmission electron microscopy (TEM) image is shown in Figure 1b [START_REF] Kirmayer | [END_REF]. Increasing extents of molecular order, on the other hand, may be clearly evidenced by narrow 29 Si NMR resonances that allow distinguishing between chemically similar environments on the basis of subtle differences in their bonding geometries. This is for example the case for non-crystalline surfactanttemplated layered silicates with short-range molecular order [5] (Fig. 1c andg) and even more so for high-zeolites such as ZSM-12 [6] (Fig. 1h), where high degrees of long-range three dimensional (3D) molecular order yields extremely narrow (ca. 0.4 ppm) 29 Si MAS NMR lineshapes (Fig. 1h). However, even if the simple 1D 29 Si MAS spectra (direct observation or cross polarization from 1 H) obviously already provide valuable information on the nature and composition of complex materials at the molecular level, the exact attribution of the different resonances in highly ordered compounds or the understanding of the underlying order or disorder requires a more precise description of the coordination sphere of the observed nuclei. Such information, along with the existence of chemical bonds may be obtained by exploiting or measuring the indirect J coupling between (for example) the different silicon sites (homo-nuclear coupling) or between silicon and chemically-bound spin-bearing heteronuclei (hetero-nuclear coupling).

J couplings between I=1/2 nuclear spins

The indirect J-coupling splitting was first observed by Proctor [7] for 121 Sb in a NaSbF 6 solution and identified by Gutowsky and MacCall in 1951 [8] in liquid phosphorus halides ( 31 P/ 19 F), immediately after the first descriptions of the chemical shift effect [9][10][11]. The famous Karplus relation [12], established in 1959, showed that the exact measurement of the 3 J(H,H) scalar coupling constants between vicinal hydrogen atoms could provide detailed information on the conformation of soluble molecules, pointing to the strong influence of dihedral angle on these J-coupling values. The use of this interaction in multidimensional experiments [13] opened the way to many spectral edition or correlation liquid state NMR methods. The recent development of higher speed magic angle spinning (MAS), efficient heteronuclear decoupling, and higher fields leading to improved spectral resolution and sensitivity, have triggered a renewed interest in J-coupling based NMR experiments in rigid solids, for which the small J couplings are often masked by inhomogeneous broadenings [START_REF]Encyclopedia of Magnetic Resonance[END_REF]. These developments offer new ways for separating the through space (dipolar) and throughbond (J coupling) contributions in various applications, measuring previously unknown couplings with high precision, and exploiting them in multidimensional or spectral editing experiments. Because J couplings are characteristic of the existence of a chemical bond between like or unlike nuclei, they allow a more accurate description of the coordination sphere of the observed nuclei extending to molecular motifs up to the nanometer scale [14][15][16][17].

High Resolution Solid State NMR uses fast MAS to mimic the Brownian motion of the liquid state and simplify the broad, orientation dependent, static line-shape of solids into isotropic resolved spectra. The coherent mechanical motion of the rotor around the magic angle allows averaging of all first order perturbations to their traces. Thus, under these conditions, the chemical shift anisotropy tensor (CSA) is averaged to its isotropic part, the indirect J coupling is averaged to its isotropic (scalar) part, and both the dipolar and first order quadrupolar interactions are averaged to zero. Solid-state NMR experiment never (or seldom) succeed in achieving spectral resolution comparable to that of liquid-state experiments because there exist small but significant higher order terms including shifts and broadening (second order quadrupolar effects, second order cross terms between interactions), residual dipolar coupling terms at limited spinning rates, and distribution of the isotropic contributions due to non-ideal ordering or disorder. Nevertheless, a combination of high-frequency spinning, very accurate magic-angle setting (±0.01°) [19] and efficient heteronuclear decoupling allows observation of scalar J couplings in perfectly ordered crystalline phases, as illustrated in Figure 2 with the 13 C CP-MAS spectrum of the (ZnO 3 P C 2 H 4 CO 2 H -0.5 C 6 H 5 NH 2 ) layered phosphonate crystalline compound [18,[START_REF] Massiot | [END_REF]. In this spectrum we observe directly two of the above-mentioned effects. These features are easily masked in routine experiments, due to imperfect shiming, magic angle setting or heteronuclear decoupling, and superimpose to the chemical shift information and possible distribution. Here, the two different α 13 CH 2 directly linked to the two non-equivalent 31 P sites of the inorganic layer are split into doublets by one-bond 31 P- 13 C scalar ( 1 J) coupling of ca. 40Hz (top-right inset) and the 13 C of the benzyl ring linked to the 14 N of the amine reveals a broadening due to a Dipolar/Quadrupolar cross term [19,20] (topleft inset). Even when not visible in a regular 1D MAS spectrum due to inhomogeneous broadenings, the J couplings can be indirectly characterized using a J-resolved experiment, as early described in liquid state experiments [13], and further used in homo-or hetero-nuclear correlation experiments allowing identification of chemically bound sites. This experiment relies on the accumulation of dephasing coming from J-couplings evolution while refocusing all other inhomogeneous interactions and inhomogeneities using a Hahn-Echo. The adaptation of liquid-state NMR experiments to solids in isotropic conditions (i.e., high speed MAS) usually only requires synchronization of the evolution periods with MAS spinning rates, the only limitation remaining the T 2 ' coherence life time of the echo signal [21] which limits the ability to express J-couplings smaller than typically 1/T 2 '. The two-dimensional J-resolved experiment correlates the usual 1D spectrum to the individual J-coupling multiplets allowing a site by site measurement of the coupling constants.

J couplings involving quadrupolar nuclei

Up to this point we considered J-coupled systems only involving I=1/2 nuclear spins which are the most commonly observed in liquid state experiments involving mostly 1 H, 13 C, 15 N, or 31 P nuclei. The presence of a fluctuating quadrupolar interaction (molecular reorientation) introduces a significant relaxation broadening which often precludes observation of resolved spectra for quadrupolar nuclei in the liquid phase but there nevertheless exist a few significant reports of J couplings involving one or even two quadrupolar nuclei in the liquid-state ( ). The case of solid-state NMR, on the other hand, is significantly different in that the quadrupolar interaction, even when strong, does not fluctuate and thus does not induce relaxation effects. As a result, in solids, it is possible to obtain long enough coherence life times [21,54] for the observation of even small scalar couplings of the order of a few Hz which could not be observed in the liquid state. In that sense, solid state NMR surpasses liquid state NMR in terms of resolution and of the size of the couplings that can consequently be assessed. Many examples showing scalar couplings between spin-1/2 and quadrupolar nuclei have indeed been reported, including couplings between 13 C and 35-37 Cl nuclei [56], and between 31 75,14] with applications to the analyses of the details of glass structures and evidence of the presence of µ 3 oxygen bridges in Calcium Aluminate glasses [74] for example. The general case of scalar J-coupling measurements in a solid under fast MAS (fast enough to average out spinning sidebands of central transitions) is depicted in Figure 4 considering a pair of nuclei I-Q consisting of a nucleus I (nuclear spin I=1/2) coupled to a quadrupolar nucleus Q (nuclear spin I=5/2) by a J-coupling interaction. The central transition (as well as the satellite) of the quadrupolar nucleus Q (Fig. 4, top, in blue) is significantly shifted and broadened by the second order quadrupolar interaction, and its coupling to the neighboring nucleus I generates a splitting of the resonance (Fig. 4, top, in green) which usually remains small as compared to the second order quadrupolar effects. However a high-resolution multiple-quantum (MQ) MAS experiment yielded separation of the two components by removing the second-order quadrupolar broadening allowing direct measurement of the J coupling [76]. Under the same conditions, the J coupling of the observed I to Q yields a splitting in 6 (2Q+1) resonances (Fig. 4, bottom, in blue) corresponding to the different spin states of the quadrupolar nucleus. When significant dipolar couplings coexist with a large quadrupolar couplings (Fig. 4, bottom, in green), the complexity of the spectrum increases since the dipolar/quadrupolar cross terms induce shifts and broadenings of the different components of the J-multiplet, as already seen in the case of 13 C/ 14 N for the phosphonate compound of figure 2. An experimental illustration of the complex interplay between quadrupolar and J-coupling interactions is given in Figure 5 with the example of the CsNbF 6 crystalline phase which features Niobium in six fold coordination to crystallographically equivalent Fluorine atoms. 93 Nb has a nuclear spin I=9/2 and its MAS spectrum (Fig. 5a) consists in the superposition of 9 different transitions (central transition plus satellite or outer transitions) affected by second-order broadening (with different scaling factors) and J couplings (7 fold multiplet for the 6 equivalent bound 19 F nuclei). Because the satellite transitions are also affected by first order quadrupolar broadening at finite spinning rates, they break into spinning sideband manifolds that remain separated under our observation conditions (17.6 T spectrometer, 35kHz MAS frequency). The processing of the 93 Nb CsNbF 6 MAS spectrum (Fig. 5a) according to the two-dimensional one pulse (TOP) procedure [55] allows reconstruction of the 2D TOP spectrum separating the different spinning sidebands by order (Fig. 5b) and then the reconstruction of the sum spectrum corresponding to an ideal infinite spinning rate spectrum (Fig. 5c) which can be modeled using the dmfit program [77].

In the particular case of a spin I=9/2, the <±5/2> transitions undergo the smallest second order quadrupolar effects and clearly exhibit the expected seven fold multiplet characteristic of its bounding to six equivalent fluorine atoms. Because tailoring excitation conditions allows to selectively excite the central transition as a fictitious I=1/2 spin using an echo [START_REF]Encyclopedia of Magnetic Resonance[END_REF][START_REF] Massiot | [END_REF] the J multiplet of the 93 Nb central transition can be indirectly revealed in a heteronuclear { 19 F} 93 Nb J-resolved experiment as used to observe 2 J( 27 Al-O-31 P) couplings in Aluminum Phosphates [54,61]. Figure 6 (left) shows the indirectly-acquired (using a { 19 F} 93 Nb J-resolved experiment with a selective refocusing of the 93 Nb central transition) seven-fold J multiplet of the 93 Nb resonance characteristic of the six fold coordination to 19 F nuclei. The 1D MAS NMR 19 F spectrum (Fig. 6, right) similarly exhibits a single contribution for all equivalent fluorine sites but split in a 10-line multiplet corresponding to the ten different 93 Nb spin states (from -9/2 to +9/2). As previously remarked [71] the decuplet is not perfectly symmetric due to spin-state dependent relaxation times and small but nevertheless significant dipolar/quadrupolar cross terms. A { 93 Nb} 19 F J-resolved experiment (Fig. 6, top-right) clearly shows that the 93 Nb π pulse only results in a modulation of the two center lines of the multiplet corresponding to the <±1/2> spin states. These results not only demonstrate that it is possible to excite selectively the central transition of a half-integer quadrupolar nucleus and measure dipolar/quadrupolar and J couplings, but also underline the fact that our current experimental protocols completely discard most of the signal by ignoring the satellite transitions. Nevertheless, new perspective offered by efficient excitation of sideband-modulated satellite transitions using adiabatic pulses [80,81] may change this situation and offer novel possibilities to enhance sensitivity and efficiency of experiments involving quadrupolar nuclei. 93 Nb nucleus and { 93 Nb } 19 F J-resolved experiment showing that only the two center bands corresponding to <±1/2> central transition of 93 Nb is manipulated during the 93 Nb excitation.

Towards more accurate measurements at high MAS spinning rates

As already mentioned the visibility of indirect J-couplings, and thus the ability to measure or use them, relies on the proper averaging of all residual terms by efficient magic angle spinning at a precisely fixed angle. This is illustrated in Figure 7 with the 31 P MAS spectrum of α-CaP 2 O 7 . While the 2 J (P-O-P) coupling remains masked by residual broadenings in a conventional 1D MAS experiment when spinning at 15kHz and can only be measured indirectly using a 2D J-resolved experiment (Fig. 7-top), an increase of the MAS rate up to 30 kHz leads to the observation of a noticeable splitting of the 1D lines and a clearly improved resolution in the indirect experiment. This is due to the improved coherent life time (longer T 2 ') (Fig. 7-bottom) and is to be related to the improved averaging of residual homonuclear dipolar interaction, dipolar/CSA cross terms (n=0 rotational resonance effects) [82]. These effects are known to give rise to unexpected cross peaks at moderate spinning rates and high fields in correlation experiments [37]. The recent commercial availability of very high speed MAS probes capable of spinning rates up to 70kHz is very likely to allow new observations in the coming years, especially in protonated materials, as already demonstrated for organic solids [83], and for hybrid organic-inorganic materials with the measurements of 2 J ( 29 Si-O-29 Si) couplings in mesoporous silica at natural 29 Si abundance (i.e., 4.7%) [84].

Preliminary results on Cordierite (Mg 2 Al 4 Si 5 O 18 )

Since the small homo-or hetero-nuclear 2 J couplings across bridging oxygens can be evidenced in alumino-silicate or phosphate materials, they can be further exploited in a variety of experiments that allow characterization of the coordination sphere or structural network with increased details. It then becomes possible to build relayed transfer experiments that allow transferring repeatedly the magnetization from a starting nucleus to its first and second neighbors [15,16] [START_REF] Bystroem | Arkiv foer Kemi[END_REF]. This compound has a well defined structure featuring some chemical Al/Si disorder (Figure 8a). The unit cell is made of 3 equivalent T1 sites, mostly occupied by Al atoms, and 6 equivalent T 2 sites mostly occupied by Si atoms, both with tetrahedral geometry. The T 1 sites are connected to four T 2 sites with a T 1 -O-T 2 angle of 129° while T 2 sites are connected to two T 1 and two T 2 sites with a T 2 -O-T 2 angle of 172° [START_REF] Bystroem | Arkiv foer Kemi[END_REF]. The 1D 29 Si MAS spectrum of our cordierite sample unequivocally pictures a much more complex situation with several overlapping lines that are likely to translate the variety of possible local environment of 29 Si nuclei, and clearly evidences the silicon occupancy of T 1 sites based on chemical shifts values [86][87][88][89][90] (around ~80 ppm, see Figure 8c). From this simple measurement we can already characterize the T 1 /T 2 occupancy ratio. At that stage we can remark that our limited knowledge on 29 Si-O 29 Si 2 J couplings seems to indicate that there exist a relation between the T-O-T angle and the scalar coupling with the strongest coupling observed for T-O-T angles close to 180°, as also reported for 29 Si-O-29 Si 2 J in CaSiO 3 and justified by cluster ab-initio computations (i.e. Gaussian) [22,42]. The J resolved spectrum of Cordierite presented in Figure 8b shows very contrasted J splittings (vertical dimension) for T 1 and T 2 sites showing the strongest 2 J couplings for the sites featuring the largest T-O-T bond angle (Fig. 8d). From this observation it becomes possible to show that the Q 4 (3Al) site (main resonance of the T 2 group) is mostly coupled to a neighboring 29 Si T 2 for which larger bond angle are expected. Obtaining complementary structural information from 27 Al NMR experiments is more complicated, since the simple MAS 1D spectrum does not allow separation of different lines, even at high magnetic field [91,92]. In such a case the spin counting experiment [17] allows characterizing the connectivity of 27 Al atoms with neighboring 29 Si by generating various multiple quantum coherence order through the evolution under the 27 Al-O-29 Si 2 J scalar couplings. Interestingly, in -cordierite, counting the neighboring 29 Si sites around 27 Al nuclei reveals on average three neighboring Si for Al in T 2 sites, whereas only 2 Si are counted for Al in T 1 sites, even though T 1 sites are surrounded by four T 2 sites which are occupied predominantly by Si atoms. This unexpected smaller number of neighboring Si atoms for T1 sites could be explained by a weaker J coupling in T 1 -O-T 2 bonds leading to less efficient excitation of higher coherence orders. A through space dipolarmediated spin counting experiment could infirm or confirm this interesting result. We note that such analyzes may be of considerable interest for solving the long-standing problem of Al distributions and repartitions is molecular sieves. 29 Si MAS NMR and (d) 29 Si J-Resolved spectra of 99% 29 Si-enriched cordierite featuring the 2 J( 29 Si-O-29 Si) multiplets in the indirect dimension, (e) spectral editing of 27 Al NMR spectra in 99% 29 Si-enriched -cordierite, corresponding to the 1D spectrum (in red),and the contributions of Al(OSi) 1 (red), Al(OSi) 2 (purple), Al(OSi) 3 (yellow) and Al(OSi) 4

(blue) motives. Since inorganic and organic-inorganic materials may have various extents of order and disorder at different length scales, as discussed above (Figure 1), it is particularly interesting that scalar couplings can be measured in amorphous materials as well. The as purchased 99% 29 Si-enriched silica material (Cortecnet), which may be used as a silicon source for silicate materials synthesis, is a good example of a disordered system of complicated and unknown structure (see Figure 9a andb). Its 1D spectrum can be acquired either by direct polarization (Figure 9a, in black) of 29 Si (leaving time for long relaxation times) or by a cross polarization experiment that transfers magnetization from the silanol OH protons to the associated Q 3 sites, and to a lesser extent to nearby Q 4 sites. The first experiment is close to quantitative (providing long enough recycle delays, i.e. typically of the order of tens to hundreds of seconds in disordered silica materials) and is dominated by a Q 4 broad line that represents 85% of the total intensity. In contrast the Q 3 contribution can be selectively enhanced and turned to dominate the 1D 29 Si spectrum when carried out using a polarization transfer. The 29 Si J-resolved experiments carried out using these two types of excitation thus allows to probe separately the 29 Si-O-29 Si 2 J couplings for these two types of environments (Figure 9). Despite a large broadening of both Q 3 and Q 4 lines (typically 8.5 ppm, i.e. 500 Hz at 7 T), and as observed in the case of Phosphate glasses [33,35,36,14], it is possible to reveal J coupling spectra showing multiplet structures : a quadruplet for Q 3 linked to three other 29 Si nuclei ( 2 J couplings ~14.5 Hz) and a quintuplet for the Q 4 linked to four 29 Si nuclei ( 2 J couplings ~16.5 Hz). What is also remarkable is that the 2D plot of the J-resolved experiment is clearly structured and features well identified ridges with a clear correlation between 2 J( 29 Si-O- 29 Si) couplings and isotropic 29 Si chemical shifts values across the Q 3 and Q 4 lines and a nonrandom distribution of the individual J couplings values [35,22]. It is of particular interest to interpret such remarkable features of the NMR spectra of disordered silicate and phosphate materials and to understand their implications for the local structure.

Disordered materials

Understanding J couplings

In addition to attesting directly of the existence of chemical bonds (covalent or even hydrogen bonds [28,88]), scalar couplings may provide important local structural information in inorganic and hybrid organic-inorganic materials through the exploitation of their magnitude, which is highly related to the local geometries of the coupled nuclei. By comparison to dipolar couplings for example, deriving structural information from J-coupling magnitudes is not straightforward, since these interactions are affected by many local structural parameters that include (among others) bond lengths, bond angles and dihedral angles [93], but also the electronegativity of surrounding nuclei [94]. The relative extents to which these parameters influence the J-coupling value notably depend on the coupling type ( 1 J, 2 J, or 3 J), and on the surrounding bond orders. Because of this complexity, computational approaches are required to extract reliable structural information from J couplings. Semi-empirical calculation approaches have been proposed [START_REF] Facelli | Encyclopedia of Nuclear Magnetic Resonance[END_REF], but recent studies have demonstrated that methods based on density functional theory (DFT) are generally more robust and applicable to a broader range of systems.

For solid materials, DFT calculations of J couplings can be conducted using cluster approaches, where a small molecular system is extracted from the solid and considered in isolation. Such approaches are particularly useful for studying local structural disorder, since angular dependences of scalar couplings [93,42,22] (and of other NMR parameters [START_REF] Clark | [END_REF]97]) can be easily explored. This was very recently exploited to demonstrate unambiguously that the strong correlation between 29 Si chemical shifts and 2 J( 29 Si-O-29 Si) couplings observed for glassy Wollastonite CaSiO 3 (and very similar to that observed in Figure 9 for amorphous 29 SiO 2 ) can be attributed to distributions of 29 Si-O- 29 Si angles that can further be characterized [22]. However, while reliable trends may be established, reproducing quantitatively experimental coupling constants is generally more challenging.

Recent investigations on model Sigma-2 and ZSM-12 zeolite systems [42] have nevertheless demonstrated that, at least in the particular case of zeolites, 2 J( 29 Si-O-29 Si) couplings, computed with good accuracy from cluster approaches using appropriate locally-dense basis sets and cluster definitions, agree well with that measured experimentally at natural 29 Si abundance. These 2 J( 29 Si-O-29 Si) couplings proved to be highly sensitive to the fine details of the local structures of crystalline silicates, which, in contrast to amorphous silica, may consist of more distorted SiO 4 tetrahedra (for example), such that 2 J( 29 Si-O-29 Si) couplings do not reflect the Si-O-Si angles as directly. In the case of zeolite ZSM-12 (Figure 10), these studies suggest in particular that the description of local framework geometries might be dramatically improved by integrating scalar couplings into structure-refinement protocols. We anticipate that such 'NMR crystallography' methods may become one of the major applications of J couplings in materials in the future. For example, J couplings could readily be integrated, along with other NMR interactions (chemical shift or quadrupolar interaction), in least-square structure-minimization algorithms based on the comparisons between experimental and calculated NMR parameters, as proposed by D.H. Brouwer for siliceous zeolites using 29 Si CSA interactions. [98,99] The combination of diverse interactions with different physics and thus different sensitivities to the local structures may considerably improve the reliability and robustness of NMR-based structure determination methods for diverse classes of materials with atomic ordering for which diffraction techniques alone are generally inconclusive or yield poorly resolved structures (e.g., layered materials). Furthermore, in the future, solid-state NMR studies of periodic systems and the protocols for solving or refining their structures will greatly benefit from the new developments in planewave-based approaches for the calculation of J couplings [100]. Encouraging agreements between experimental and calculated couplings have already been reported for couplings involving different combinations of nuclei [100], including 2 J( 31 P-O-29 Si) couplings in silicophosphates and hydrogen-bond mediated 2h J NN in ribbon structures [88]. Furthermore, DFT calculations of J couplings with periodic boundary conditions can in principle also potentially be used investigate small amplitude disorder in otherwise crystalline solids, following an approach very recently proposed by some of us [101] on the basis of correlated chemical shifts distributions [41], which could readily integrate J-coupling distributions. The strong potential of such distributions of J couplings for the structural interpretation of local disorder, such as the characterization of bond angle distributions for silicate glasses for example [22], is further increased by novel possibilities to examine even highly disordered solids using DFT in periodic boundary conditions, in combination with molecular dynamics and solid-state NMR [102,103].

Conclusion

From selected examples of new or recently published data we have shown that it now becomes possible to evidence, measure and use small scalar homo-or hetero-nuclear J couplings in solid state inorganic or hybrid materials. This allows direct examination of the chemical bonds around the selectively observed nucleus and opens ways to characterize extended structural motifs at the sub-nanometer scale in ordered or disordered materials, even when broadening of the resonances due to disorder becomes significantly greater than the J couplings themselves. It is especially remarkable that it is possible to measure couplings involving quadrupolar nuclei in rigid solids while they remain unobservable in liquid state experiments because of quadrupolar relaxation. From a selection of examples we emphasized on several important and promising points. The increasing possibilities opened by new hardware availability (very high speed MAS spinning); the development of new methods allowing 'walking' through a three dimensional network (from one nucleus to its successive like or unlike neighbors), or selecting resonances of groups of bound nuclei in spin counting experiments; the chemical relevance of the measured couplings in terms of local structure as jointly viewed with ab-initio computations using cluster or newly developed periodic approaches. This approach should apply to large classes of inorganic or hybrid materials with possible application to structural refinement, sorting between spatial proximity and chemical bonding, or evidencing local ordering in globally disordered structures.

Figure 1 :

 1 Figure 1 : (a) Schematic representation of an amorphous SiO 2 structure, with SiO 4 tetrahedra shown in red, and (e) 29 Si spin-echo MAS NMR spectrum of commercial silica with 99% enrichment in 29 Si. (b) Transmissionelectron microscopy (TEM) image and electron diffraction pattern (inset) and (f) 29 Si{ 1 H} CPMAS NMR spectrum of an hexagonal mesoporous silica composite.[4] (c) In-plane view of a layered silicate-surfactant mesophase consisting of thin (0.8 nm) molecularly-ordered silicate sheets with five distinct (colored) Si atom sites giving rise to five narrow 29 Si resonances in the corresponding 29 Si{ 1 H} CPMAS NMR spectrum (g), and separated by alkylammonium surfactant species.[5] (d) Schematic representation of the highly ordered silicate framework structure and (h) 29 Si MAS NMR spectrum with extremely narrow resonances of zeolite ZSM-12 (courtesy D.H. Brouwer).

Figure 2 :

 2 Figure 2 : 13 C CP-MAS spectrum (300 MHz, 14 kHz) of the crystalline layered phosphonate (ZnO 3 P C 2 H 4 CO 2 H -0.5 C 6 H 5 NH 2 ) [18] acquired with an accurate setting (± 0.01 °) of the MAS angle and optimized proton decoupling, which allows evidencing the 31 P-13 C 1 J splitting on the first carbon of the aliphatic chain and the splitting of the 13 C-14 NH 2 resonance by the dipolar/quadrupolar cross term (R{ 14 N} 13 C).

Figure 3

 3 shows an ultimate example of resolution for J couplings in inorganic materials with the measurement of coupling constants down to a few Hertz in the case of CaSiO 3 Calcium Silicate polymorphs consisting in chains of cross-linked Si-based Q 2 units[22]. J-coupling based methods are now established as valuables approaches for examining the molecular topologies and structures of a variety of organic and inorganic ordered or disordered solids with examples of homo-and hetero-nuclear couplings. These include homonuclear couplings: one-bond 13 C-13 C[23-25,3] and 31 P-31 P[26,27] 1 J couplings, hydrogen-bond-mediated 15 N-15 N 2h J couplings[28]; and two-bond 2 J couplings such as31 P-O-31 P[29-37], 31 P-N-31 P[38] or 29 Si-O-29 Si[39-42,22] 2 J couplings in crystalline or disordered compounds or glasses, and also heteronuclear couplings such as one-bond 19 F-207 Pb[43], 31 P-113 Cd, and 31 P-77 Se[44-46] 1 J couplings, and two-bond 2 J( 29 Si-O-31 P) couplings [47-49], among others.

Figure 3 :

 3 Figure 3 : J-resolved experiment on the crystalline Wollastonite Ca 29 SiO 3 revealing 2 J( 29 Si-O-29 Si) couplings of a few hertz. The full J-resolved spectra can be perfectly modeled by considering 29 Si isotopic enrichment and strong coupling effects due to small chemical shift differences[adapted from ref 22]

  17 O-35 Cl[50],17 O-55 Mn[51],17 O-95 Mo[52],17 O-51 V[53]

Figure 4 :

 4 Figure 4 : Schematic representation of the effect of the J coupling between a quadrupolar nucleus Q (I=5/2) and a dipolar nucleus I (I=1/2). The central transition of the quadrupolar nucleus Q (top, in blue) is broadened to second order by the quadrupolar interraction and split in two by the J coupling to I (in green). The second order quadrupolar broadening can be removed in an MQMAS experiment allowing to only observe the J-coupling multiplet[76]. The signal of the I nucleus is split in a 2Q+1 (e.g., 6 for I=5/2) multiplet. Additional second order broadenings and shifts arise when R (the Dipolar Quadrupolar cross term) becomes significant.

Figure 5 :

 5 Figure 5 : TOP processing of the 93 Nb MAS spectrum of CsNbF 6 , δ Nb = -1580 ppm, C Q = 10.2 MHz, η Q = 0.45 (a) allowing 2D reconstruction of the TOP spectrum (b) and the computation of the infinite spinning rate TOP spectrum. The TOP spectrum can be modeled (c) considering a 1 J coupling of 344 Hz to 6 chemically bound cristallographically equivalent fluorine, which is reflected by the splitting of each observed transition of the 93 Nb resonance in a septuplet.

Figure 6 :

 6 Figure 6 : Central transition selective { 19 F} 93 Nb J-resolved experiment and its model with a 7 fold multiplet -1D MAS spectrum, δ F = 110.1 ppm, 1 J = 344 Hz showing coupling to the 10 spin states of a single93 Nb nucleus and {93 Nb } 19 F J-resolved experiment showing that only the two center bands corresponding to <±1/2> central transition of93 Nb is manipulated during the93 Nb excitation.

Figure 7 .

 7 Figure 7. 31 P J resolved MAS Spectra (7.0 T) of α-Ca 2 P 2 O 7 acquired at exact Magic Angle (~±0.01°) showing the increased resolution of the 2 J( 31 P-O-31 P) coupling with increasing MAS rate, allowing improved removal of residual contributions to transverse dephasing.

Figure 8 :

 8 Figure 8 : (a) -Cordierite XRD structure[START_REF] Bystroem | Arkiv foer Kemi[END_REF], (b) connectivity of T 1 and T 2 sites, (c)29 Si MAS NMR and (d)29 Si J-Resolved spectra of 99%29 Si-enriched cordierite featuring the 2 J( 29 Si-O-29 Si) multiplets in the indirect dimension, (e) spectral editing of27 Al NMR spectra in 99%29 Si-enriched -cordierite, corresponding to the 1D spectrum (in red),and the contributions of Al(OSi) 1 (red), Al(OSi) 2 (purple), Al(OSi) 3 (yellow) and Al(OSi) 4(blue) motives.

Figure 9 :

 9 Figure 9 : J-resolved experiments performed on a 29 Si enriched SiO 2 sample « from the bottle » with (a) direct detection and (b) cross-polarization from 1 H. One-dimensional spectra superimposed to the 2D-lineshapes are projection onto the MAS dimension. The slices taken at along the J-resolved dimension at the peak maxima show a quadruplet for Q 3 and a quintuplet for Q 4 tentatively modeled with J-couplings of J(Q 3 ) ~ 14.0 Hz and J(Q 4 ) ~ 16.5 Hz.

Figure 10 :

 10 Figure 10 : (a) Schematic representation of the structure of ZSM-12. (b) Solid-state 2D refocused-INADEQUATE 29 Si{ 29 Si} NMR spectrum of siliceous zeolite ZSM-12 at natural abundance (black contour plots) and 2D spectral deconvolution (colored map) from which 2 J( 29 Si-O-29 Si) values were extracted. (c) 1D 29 Si NMR slices extracted from the experimental spectrum (in black) and from the 2D deconvolution (in red), along with the measured J couplings[adapted from ref. 42].

  P and27 Al[57][58][59][60][61][62]54,15,16],63,65 Cu[26,27,63-65], 31 P-113,115 In[66,67], 31 P-55 Mo[68], 31 P-101,99 Ru[69], 31 P-17 O[70], and 19 F-

93

Nb

[71]

. These examples show a variety of situations with often strong dipolar/quadrupolar cross terms leading to complex spectra even in rather simple compounds. Finally there exist very few reports of quadrupolar/quadrupolar J-coupling interactions until recently:

11

B-75 As [72], 17 O-17 O[73], or 27 Al -17 O [74,

  31 P}31 P, { 29 Si} 29 Si, { 27 Al} 31 P, { 27 Al} 29 Si [36,43,14,17]. These new possibilities can be applied to the study of crystalline -cordierite magnesium alumino-silicate (Mg 2 Al 4 Si 5 O 18 )

, as if 'walking' across the covalent 3D network structure. It is also possible to describe experiments dedicated to counting the different NMR-active neighboring nuclei (or to editing the spectrum according to this count) with examples on pairs of nuclei such as {

Acknowledgements

We acknowledge financial support from CNRS, Région Centre CNRS, ANR RMNSOLIDE-HR-HC ANR-05-BLAN-0317 and we thank Bruno Bujoli, Florence Babonneau and Christian Bonhomme for numerous and fruitful scientific discussion.