Julien Meyer

Juan N Casimiro

Exploiting the didactic aspect of whistled speech in Gomero Spanish and Mazatec: interactions between phonetic research and education

Introduction

Whistled speech has been introduced at the end of the 90s in primary school in La Gomera, one of the Canary Islands [START_REF] Trujillo | El Silbo Gomero : materiales didácticos[END_REF] and has been included in 2007 in the new official program of secondary school for the Mazatec area of the Oaxaca region in Mexico [START_REF] Casimiro | Programa de lengua y cultura mazateca para la educación secundaria[END_REF]. Both of these initiatives are the result of a lobbying process of the local populations to have this symbolic part of their language revitalized thanks to an introduction in official educative systems. The didactic applications of whistled Mazatec and the Gomero Spanish are different because of specific historical and educational contexts but also of phonetic differences between the strategies of emulation into whistles of tonal Mazatec and non tonal Spanish. After a phonetic description of whistled speech in these two languages, we present how these results have been exploited to pedagogic applications in Canary islands and in Mexico.

A prosodic emulation of the voice influenced by language phonology and frequency perception

The practice of whistled speech consists in emulating selected acoustic cues of the complex frequency spectrum of the spoken voice into a simple modulated pitch. The way these acoustic cues are selected is influenced by the load of information they represent for intelligibility and therefore by their phonologic role in each language. At the same time, whistled speech is adapted to the fact that we perceive two different qualities of heights from the complex distribution of frequencies in the voice. One is the perceptual sensation called timbre in music, resulting from the complex aspects of the vocal frequency spectrum and that strongly characterises the quality of a vowel through the formants. The other is the perceptual sensation called pitch, resulting from the fundamental frequency. In the normal spoken voice, these two perceptual frequency levels can be combined to encode phonetic cues. But as whistled speech reduces the voice spectrum to a single melodic line, the whistlers concentrate their productions primarily on one of these qualities at each instant to select the most relevant parts.

Several languages have been compared in a typology integrating their whistled and spoken forms [START_REF] Meyer | Typology and Acoustic Strategies of Whistled Languages: Phonetic Comparison and Perceptual Cues of Whistled Vowels[END_REF]. This study has shown that two main strategies of whistling a language coexist (figure 1): the one that consists of whistling primarily supra-segmental cues (concerning mostly tonal languages like Mazatec) and the one that consists of whistling primarily segmental cues (concerning mostly non-tonal languages like Gomero Spanish). [START_REF] Meyer | What does the typology of whistled forms of languages teach us about prosody? 7th International Conference of the Association of Linguistic Typology[END_REF][START_REF] Meyer | Typology and Acoustic Strategies of Whistled Languages: Phonetic Comparison and Perceptual Cues of Whistled Vowels[END_REF] has also shown that there is an intermediary category of languages balancing both strategies; it contains either tonal languages with few tones like Surui of Amazonia, or non-tonal languages giving an important role to intonation like Siberian Yupik or Chepang of Nepal. The perception of prosody, which is one of the bases of language acquisition, is therefore reflected in an original way in the phenomenon of whistled speech. All the more that the paramount parameters selected at the frequency level by the whistlers are not systematically limited to the fundamental frequency of the voice. Indeed, in the case of a non-tonal language like Gomero Spanish, the qualities of the vowels even take the principal prosodic role. For example, the highest pitches are attributed to /i/ vowels in order to reflect the acute quality of their timbre, the lowest pitches are attributed to /o/ and /u/, while /e/ and /a/ are in between (this is illustrated on figure 2). Moreover the intervals of distribution of the vowels /i/, /e/, /a/ and /o/ are statistically different (table 1) while /o/ and /u/ highly merge1 , which shows that there are at least four distinct whistled vowels in Spanish Silbo Gomero. This whistled strategy of Spanish with vowels shows that a kind internal prosody of segmental cues is emulated to render the perceptual importance of the most prominent formants that characterise the vowels. This is also the case for consonants. First, the whistled equivalent of a consonant is produced by articulating it in a way which is as close as possible to the spoken articulation. Of course there are additional constraints while whistling because the muscles of the lips and the throat are more tensed. Next, the resulting whistled signal is a combination of frequency and amplitude modulation of the pitch of the surrounding vowels. This way, the acoustic cues of the formant transients of the regular spoken form are adapted to whistles. As illustrated on figure 3, the simple frequency shapes that are obtained for each type of consonants highlight categories of similarities, mostly confined to sounds formed at close articulatory loci. In the case of the four tone Mazatec language, the heavy load of information carried by the tonal system explains why the strategy of whistled speech relies this time on the simple transposition of the fundamental frequency of the voice into a simple pitch. [START_REF] Cowan | Mazateco whistle speech[END_REF] observed that whistled Mazatec reproduces tone levels and tone glides of the spoken form. We confirmed his observations with recent recordings. First, we looked at the distribution of whistled frequencies of the whistled words produced by a same whistler in stable conditions of communication (targeted distance, labio-dental technique of whisling). For the syllable nuclei, we measured that the four tone registers are distributed in four statistically different intervals (figure 4).

Next, we observed that several categories of frequency modulations occur: a) the tonal glides internal to the syllable; there are six of them that had already been observed by Cowan (2-4, 3-4, 4-3, 1-3, 3-2 and2

Applications for school teaching

General aspects

Whistled Spanish of la Gomera has been introduced in school teaching in primary school as a key initiative to reinforce a local process of revitalization of a practice highly devitalized, whereas whistled Mazatec is currently being introduced in secondary school as part of a program of bilingual education Mazatec/Spanish in the Mazatec speaking communities of the Oaxaca state of Mexico. In both cases the phonetic analyzes made by researchers was used as one of the arguments to justify the cultural and linguistic interest of whistled speech for language education. This helped to convince the education authorities to include it in the language lessons. The work of [START_REF] Trujillo | El Silbo Gomero : materiales didácticos[END_REF] and [START_REF] Casimiro | Programa de lengua y cultura mazateca para la educación secundaria[END_REF] also attest that such scientific references were used for developing teaching methods. Whistled speech was considered as a simple natural support for the students to identify various phonetic aspects of their spoken language, especially the tonal system in Mazatec and the perceptual identity of some vowels and consonant in Gomero Spanish. In the following sections, we present and analyse these unprecedented didactic initiatives and we propose to revisit them thanks to our latest findings.

The example of Mazatec

Mazatec was introduced in the 'curso de cultura' in the new 'programa de lengua y cultura mazateca para la educación secundaria tercer grado' [START_REF] Casimiro | Programa de lengua y cultura mazateca para la educación secundaria[END_REF]. As Spanish remains the language of reference for teaching at school in Mexico, this pedagogic program recommends clarifying its main differences with Mazatec. In this perspective, the use of tones is first introduced by showing that Mazatec language uses them to distinguish words. It is also the occasion to present the locally used orthography to signal tones (table 2). Moreover, the pitch differences between tone levels are clarified through a reference to musical notes. To explain more concretely this aspect, whistled speech is then introduced. Phonetically, it has the advantage to help the children to understand tonal levels but also tonal glides (figure 5).

Figure 5: Glides as explained in the 'curso de secundaria' We observe that the glides presented on figure 5 are simplifications coherent with the description made in phonetic research. Yet, they do not distinguish inter and intra syllabic glides (for example, the points 2, 3, 5 illustrate intrasyllabic events, the points 1 and 4 correspond to inter-syllabic events. And the point 6 concerns intra and inter syllabic glides). Moreover, this pedagogic approach focused mainly on relative variations of whistles (no distinction between the 1-3 and 2-4 glides (point 5)).

The example of Gomero Spanish

Nowadays, Silbo Gomero is taught by three teachers at school. One of them, being illiterate, relies only on a traditional form of teaching by imitation. The two others combine the imitation model with a pedagogic discourse that consists in a simplified explanation of the phonetic characteristics of Silbo Gomero (see Trujillo et al 2005 entitled 'Materiales didacticos'). This didactic adaptation has been developed on the basis of the phonetic and phonologic analyzes of [START_REF] Trujillo | El Silbo Gomero: analisis linguistico[END_REF]. It doesn't take into account the linguistic analyzes published by other researchers like [START_REF] Classe | The whistled language of La Gomera[END_REF] or [START_REF] Rialland | Phonological and phonetic aspects of whistled languages[END_REF]. It presents the segmental entities of whistled Spanish as follows: 'It is constituted of four consonantal sounds and two vocalic sounds, their equivalence with vowels and consonants of Castilian are the following' (Trujillo et al 2005, p ) If we confront these interpretations with our observations presented in the previous section and the ones of [START_REF] Rialland | Phonological and phonetic aspects of whistled languages[END_REF] which take into account the amplitude modulations, we conclude that for consonants, the pedagogic simplification fits the phonetic descriptions made by researchers. On the contrary, the simplification concerning vowels contradicts our data showing that at least four whistled vowels are statistically different in whistled Spanish of La Gomera (observations based on the production of the teachers themselves and confirmed thanks to data collected with other native whistlers of la Gomera [START_REF] Meyer | Description typologique et intelligibilité des langues sifflées: approche linguistique et bioacoustique[END_REF]). Trujillo et al support their very simplified interpretation by asserting that 'sólo resulte reconocible el contraste acústico «máximo», es decir, el contraste 'agudo' / 'grave', que no admite -ni puede admitir-matices intermedios' (Trujillo et al 2005 'Materiales didacticos' p.32). Such affirmations are not consistent with the literature documenting the psychoacoustic abilities of discrimination of the human hearing. As a consequence, we developed a psycholinguistic experiment to test the ability of traditional whistler but also of non whistler to identify the four Spanish whistled vowels /i, e, a, o/. The results of these experiments, presented in details in [START_REF] Meyer | Identification of Natural Whistled Vowels by Non-Whistlers[END_REF] and [START_REF] Meyer | Typology and Acoustic Strategies of Whistled Languages: Phonetic Comparison and Perceptual Cues of Whistled Vowels[END_REF] show that a native whistler identified these vowels in 87,5 % of the cases and that even non whistlers were able to categorize these vowels highly above chance although not as accurately (and without any learning).

Figure 1 :

 1 Figure1: Through the example of Spanish and Mazatec, we present the two main whistled strategies of emulation into whistles. For Spanish (left), the final /to/ is indicated by an elliptic line in both the spoken and whistled form. For Mazatec (right), the spoken Fo and its whistled emulation are also indicated by elliptic lines.

Figure 2 :

 2 Figure 2: Frequency distribution of whistled Spanish vowels(103 vowels produced by the Maestro de Silbo Rodriguez L.)

Figure 3 :

 3 Figure 3: Frequency shapes of consonants in whistled Spanish for an intervocalic configuration /a(Consonant)a/ associated with the loci of articulation. Some consonants like /n/ adopt different close whistled shapes. Moreover, the dashed arrow indicates that the glottal occlusion may occur for [p], [b] [m] and sometimes [v],[f], in addition to [k],[g].

  -3 in tonal notations in use in central america); b) the glides between two vowels of a diphthong carrying distinct tone levels; c) and for rapid whistling pace: the glides between two different syllables carrying distinct tone levels.

Figure 4 :

 4 Figure 4: Whistled frequency distribution of the vowel nuclei for 6 Mazatec sentences produced by the same whistler (notation of tones H=high (nº1); SH= Semi-High (nº2); SL=Semi-Low (nº3); L=Low (nº4))

Table 2 :

 2

		jti (/ti4/)
	No tono	Tono bajo
	"niño"	"pescado"

Presentation of tonal level, as it is made in the program for secondary school. (The notation between brackets refers to the phonetic alphabet in use by most linguists working in the region) ti' (/ti1/) Tono alto ( ' ) "tiempo presente " tí (/ti2/) Tono semi alto (´) "quemarse" ti (/ti3/)

  2 (see table below)

	Vowels		Consonants
	whistled Equivalents in the Spanish	whistled Equivalents in the Spanish
		written alphabet		written alphabet
	I	i, e	CH	t, ch, s
	A	a, o, u	K	p, k
			Y	d, n, ñ, l, y, r, rr
			G	b, f, m, g, j

actually, /o/ and /u/ are already often very near in pronunciation in the spoken dialect of la Gomera. Moreover, /u/ represents only 7 % of the Spanish vowels[START_REF] Classe | The whistled language of La Gomera[END_REF].

'Consta de cuatro sonidos consonánticos y dos vocálicos, cuyas equivalencias con las vocales y consonantes castellanas son las siguientes'


Corentin Lamboley

Tristan Bitard-Feildel

Amélie Chérubin

Anomaly detection in embedding space learned with a contrastive approach

Keywords: data confidence, anomaly detection, self supervised learning, contrastive loss

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

I. INTRODUCTION

When performing a classification task, the maximum achievable accuracy depends on the quality and the quantity of data and on the appropriateness of the chosen learning algorithm [START_REF] Brodley | Identifying mislabeled training data[END_REF]. Large datasets have enabled deep neural networks to achieve remarkable success in various domains, but this success is highly dependent on the quality of the training labels, which can be extremely very to create manually as datasets grow, especially when domain expertise is required.

Consequently, substitution labeling techniques have been developed such as crowdsourcing [START_REF] Krishna | Embracing error to enable rapid crowdsourcing[END_REF], model-assisted labeling, active-learning [START_REF] Settles | Active learning literature survey[END_REF] and weak supervision [START_REF] Ratner | Snorkel: Rapid training data creation with weak supervision[END_REF]. Nevertheless, these methods inherently generate noisy labels decreasing the performance of deep neural networks, since they have high capacities and tend to overfit to these noisy labels, resulting in poor generalization performance.

To tackle this, methods have been developed to identify mislabeled data [START_REF] Brodley | Identifying mislabeled training data[END_REF][START_REF] Northcutt | Confident learning: Estimating uncertainty in dataset labels[END_REF] or to be robust to label noise [START_REF] Zhang | Mixup: Beyond empirical risk minimization[END_REF][START_REF] Han | Co-teaching : "Robust training of deep neural networks with extremely noisy labels[END_REF][START_REF] Li | DivideMix: Learning with noisy labels as semi-supervised learning[END_REF][START_REF] Liu | Early-learning regularization prevents memorization of noisy labels[END_REF]. In particular, self-supervised contrastive learning [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF] demonstrated great results in the past few years, and turned out to achieve good performance even in the presence of label noise [START_REF] Xue | Investigating why contrastive learning benefits robustness against label noise[END_REF]. Contrastive learning discards all the labels and learns representations by maximizing similarity between differently augmented views of the same data point via a contrastive loss in the latent space. A simple fully connected network can be trained on these representations in a supervised way, given the (potentially noisy) labels, and shows label noise robustness.

In this work, we present methods for outliers and errors detection, as well as learning with noisy labels techniques using representations from contrastive algorithms. Our contributions are two folds.

As a preliminary step, we evaluated the quality of learned representations with a Contrastive Learning approach, and their ability to provide label noise robustness. Second, we evaluated several anomaly detection methods on the learned representations. Anomaly detection algorithms are highly sensitive to the intrinsic data structure, and finding an appropriate method working with learned representations is a challenging task. Such, we investigated the relationship between incorporating noise and performances of anomaly detection algorithms.

II. PRELIMINARIES

A. Contrastive Learning

The goal of contrastive learning methods is to learn an embedding space in which similar sample pairs stay close to each other while dissimilar ones are far apart. A positive pair consists of two different points of view of the same example, obtained using data augmentation (e.g. Random cropping or Color distortion for image data).

Given this new dataset of augmented data, an encoder extracts features and creates an embedding for each example of each pair. The ResNet model is usually the choice for the image encoder, and the final goal of the contrastive approach is to find the correct weights for the encoder to match similar pairs together. The encoder creates representations, and in practice, we add a Projection Head to map the representations ℎ 𝑖 to a lower dimensional vector 𝑧 𝑖 before calculating the contrastive loss. This loss function tends to maximize the similarity between embedding for positive pairs and minimize it for negative pairs. A classical choice is the Noise Contrastive Estimation (NCE) defined as [START_REF] Sohn | Improved deep metric learning with multi-class n-pair loss objective[END_REF]:

𝑙 𝑖,𝑗 = -𝑙𝑜𝑔 exp( 𝑧 𝑖 𝑇 𝑧 𝑗 𝜏 ) ∑ 𝟙 [𝑘≠𝑖] exp( 𝑧 𝑖 𝑇 𝑧 𝑘 𝜏 ) 2𝑁 𝑘=1 (1)
for the positive pair of augmented samples (i, j), where 𝑧 𝑖 is the output of the projection head of the augmented sample 𝑖, 𝟙 [𝑘≠𝑖] is the indicator function and τ the temperature parameter. We compute the final loss across all positives pairs. Fig. 1 provides an example of the full process of this algorithm.

B. Label noise generation

For our experiments, we use the CIFAR10 dataset and follow the same protocol as [START_REF] Northcutt | Confident learning: Estimating uncertainty in dataset labels[END_REF]. For label noise, we work with asymmetric label noise, where noisy labels are obtained by randomly flipping the true labels. This mimics real-world noise.

Let 𝑦 * be the unknown, true, uncorrupted label and 𝑦 ̃ the observed, noisy label. We generate noisy data from clean data by randomly switching some labels of training examples to different classes non-uniformly according to a randomly generated noise transition matrix 𝑄 𝑦 ̃|𝑦 * ≔ 𝑝(𝑦 ̃= 𝑖|𝑦 * = 𝑗), ∀𝑖, 𝑗 ∈ [𝑚] the set of unique class labels. Noise transition matrices have different traces for different noise levels, and have different sparsities. See Appendix A for the noise matrices used in our experiments.

Definition (sparsity).

A statistic defined by the fraction of zeros in the off-diagonals of 𝑄 𝑦 ̃|𝑦 * . A high sparsity quantifies non-uniformity of label noise, common to real-world datasets. Zero sparsity means that every noise rate in 𝑄 𝑦 ̃|𝑦 * is non-zero, while a sparsity equal to one means that there is no noise because all off-diagonals of 𝑄 𝑦 ̃|𝑦 * are zeros.

C. Outliers detection

Outliers are items in a dataset that are rare and deviate from the general data distribution. It is as if they were generated by a different mechanism. The detection of outliers is an active area of research in the field of data mining, and has various practical applications such as credit card fraud detection, telecom or medical analysis. In particular, classification algorithms mislabeled instances can be considered outliers and be removed from the training set to improve the performance of the classifier.

There are a great number of different outlier detection algorithms, and we propose to use the following ones in our future experiments:  Auto-Encoder: A fully connected neural network that uses the reconstruction error as the outlier score [START_REF] Vincent | Extracting and composing robust features with denoising autoencoders[END_REF].

 Isolation Forest: An ensemble-based method that isolates anomalies using tree classifiers [START_REF] Liu | Isolation forest[END_REF].

 Average/Median KNN: A simple proximity-based method using the average or median of the k nearest neighbors as the outlier score [START_REF] Angiulli | Fast outlier detection in high dimensional space[END_REF].

 LOF: "Local Outlier Factor" An algorithm also using the k nearest neighbors to estimate density. The samples with low densities are considered outliers. [START_REF] Breunig | LOF: Identifying density-based local outliers[END_REF].

 CBLOF: The cluster-based version of LOF that can use any clustering algorithm [START_REF] He | Discovering cluster-based local outliers[END_REF].

 KDE: "Kernel Density Estimation" A well-known method using kernels with a particular bandwidth to estimate the probability density function [START_REF] Latecki | Outlier detection with kernel density functions[END_REF].

 PCA: "Principal Component Analysis" A method for outliers' detection using a Principal Component Classifier [START_REF] Shyu | A novel anomaly detection scheme based on principal component classifier[END_REF].

 COPOD: "Copula-based Outlier Detection" that constructs an empirical copula to predict tail probabilities to determine the level of "extremeness" of a sample [START_REF] Li | COPOD: Copula-based outlier detection[END_REF].

 ECOD: "Empirical Cumulative Outlier Detection" using the empirical cumulative distribution per dimension of the data to predict tail probabilities across dimensions [START_REF] Li | ECOD: Unsupervised outlier detection using empirical cumulative distribution functions[END_REF].

III. EXPERIMENTS

A. Exploring label noise robustness and representation's quality

In this experiment, we first demonstrate how Contrastive Learning improves label noise robustness, even when using sub-optimal hyperparameters to generate representations in the latent space. Moreover, we evaluate the algorithm's ability to separate samples into relevant clusters, and the side effects of generating representations in an unsupervised way.

B. Finding labelling errors using anomaly detection

If Contrastive Learning provides a certain robustness against label noise, then it also allows for the discovery of labeling errors in the latent space of representations.

First, a sample's representation created by the encoder tend to be close to similar samples representations and far from others, independently of the associated noisy label. Therefore, in the latent space, samples are globally regrouped into clusters corresponding to their true label. This has the consequence for a mislabeled example to be far away from the cluster associated with its true label. To some extent, a labeling error can be seen as an outlier in the distribution of representations of its associated class. Given that, it is possible to use outliers' detection methods on the latent space to detect labeling errors. Section IV.C benchmarks the best outliers' detection methods described earlier for this purpose.

The first problematic in dealing with outlier detection algorithms is the way of measuring their performance. In most cases, these algorithms generate an anomaly or outlier score that does not correspond to a probability of being an outlier. Hence, considering samples with a score higher than 0.5 as outliers may not work well.

Yet, without knowing the threshold to use for a particular method that separates well errors from clean samples, it is still possible to speculate how good this method can be at the task of separating the distribution of errors and clean samples. To do so, we will use AUC ROC scores.

The process to test out an outlier detection method is the following:

 The dataset is the representations of the 50000 CIFAR10 images generated with the encoder, with the labels flipped according to a noise matrix.

 Class by class, we use the algorithm to assign an outlier score to every sample belonging to this particular class, and the scores are normalized. A sample belongs to a class if its noisy labels correspond to this class. In theory, we consider that outliers are errors and should not belong to that particular class.

 Knowing both the true and noisy labels, we can calculate the AUC ROC of this algorithm for each class, and the global AUC ROC along all the samples.

Finally, we can compare the performance of many outlier detection methods with various hyperparameters, on different noise and sparsity levels, with data produced by Contrastive learning.

IV. RESULTS

A. Robust training under label noise on CIFAR10

For the first experiment, we use contrastive learning with a ResNet18 encoder to produce representations of CIFAR10 images in a 512 dimensions vector, with a projection head of size 128 and a batch size of 256. We also choose the temperature parameter of the NCE loss to be 0.5, and we train for 600 epochs. Fig. 2 shows that Contrastive Learning creates globally well separated representations of the CIFAR10 images in the latent space, except for the labels cats and dogs where there is no distinct separation. It also seems that the clusters are intuitively organized in the sense that animals are separated from vehicles, cars, and trucks are close to each other, as well as for cats and dogs, and in the middle, birds are not so far from planes.

For further experiments, we trained this model for 2000 epochs. t-SNE representations [START_REF] Van Der Maaten | Visualizing data using t-SNE[END_REF] and contrastive losses over epochs can be seen in Appendix B. We use the resulting ResNet18 encoder to represent every image of the CIFAR10 dataset in the latent space, creating a dataset of embeddings on which a simple Multilayer Perceptron (MLP) can be trained. As a first step, we used the Cross-Entropy loss and trained the network on the embeddings in a supervised way, given the noisy labels gener ated in II.B. Furthermore, we also trained this network with the noise robust loss function called Early Learning Regularization (ELR) [START_REF] Liu | Early-learning regularization prevents memorization of noisy labels[END_REF], which prevents memorization effect of neural networks by capitalizing on the early learning phase. The use of this loss significantly improve accuracy in almost all noise configurations compared with Cross-Entropy, as Table 1 shows. For comparison, we use as baselines a ResNet18 with Cross-Entropy loss, and a ResNet18 with ELR loss (See Appendix C).

As intended, training an MLP on top of the encoder significantly improves performance compared to the baselines approaches. One may also notice that the method is not robust to sparsity under high-level noise.

A promising future work would be to push the algorithm further by using deeper models, larger batches, and to train for more epochs to observe the resulting representations. This should increase the accuracies, and may help for the errors' detection methodology described in III.B. B. Clusterization of the latent space Fig. 3 presents the t-SNE representations of the CIFAR10 images, obtained via Contrastive Learning with a ResNet18 after 2000 epochs. The representations seem to separate classes, but to generate out-of-distribution clusters as well. In particular, we circled two remarkable small clusters. The red circle indicates an out-of-distribution cluster of cars, while the blue circle is a group of samples that are close to each other but do not belong to the same class. This could be a side effect of applying t-SNE for visualization, or an intrinsic behavior of the learned representations of the Contrastive Learning algorithm. Fig. 4 shows the images inside the two clusters. We are now better able to understand how the model generates representations. The red cluster contains similar cars with the same color and the same background, and the blue cluster contains images from different classes on a black background.

Having a cluster of samples from the same class is not a problem since a classifier will easily match it to the associated label. However, clusters like the blue one raise a problem and can be hard to identify for a classifier. To overcome this phenomenon, an option is to change data augmentations applied to original samples. Adding stronger color distortion may help to avoid focusing on the background of certain images and improve performance. In general, Contrastive Learning is highly dependent on the data augmentations used [START_REF] Tian | What makes for good views for contrastive learning?[END_REF], and the quality of the set of augmentations is very specific to the dataset itself.

C. Finding errors and outliers

Fig. 5 reports AUC ROC scores computed on the predictions of eight different outlier detection methods with various hyperparameters, on a particular noise and sparsity setting (0.3 / 0.2). We take the average scores across the five seeds to get a representative value, instead of over-interpreting scores from one noise configuration. Results with other noise and sparsity settings are in Appendix D.

The first observation we can make is that the Kernel Density Estimation (KDE) technique outperforms every other methods when comparing the global AUC ROC score (0.97), while keeping a relatively narrow distribution of scores along the ten classes. Still, we can see that it struggles more with the "bird" class. In contrast, KNN-based methods also perform well when the number of neighbors is high enough. For the "maxknn_k1000", which takes the maximum distance to the 1000 nearest neighbors in the class, the global AUC ROC is still high, but the scores of all classes are closer together. In other words, this method does not "sacrifice" any class.

Similarly, the Auto-Encoder performs well, even though we did not tune any hyperparameters. It might need some parameters tuning to perform to its full potential, but still got an AUC ROC around 0.95.

Conversely, the ECOD and COPOD methods do not perform well. The LOF model neither, whereas some combinations of hyperparameters made the IsolationForest algorithm reach an AUC ROC of 0.87.

To compare the difficulties in finding labeling errors inside the classes of CIFAR10, we took the five KDE models of various bandwidths and plotted in Fig. 6 the distributions of AUC ROC for all noises. Unsurprisingly, for all classes, the scores globally drop with the increase of label noise. What is more interesting is the disparity between the classes of when this drop occurs. This dissimilarity might come from a particular disposition of noise matrices, or from an intrinsic difficulty for the algorithm to detect labeling errors in this class. Plots using KNN-based models and all models are in Appendix D.

V. CONCLUSION Data cleaning can be used as a preprocessing step to train robust AI models. In this paper, we investigate how to use embedding spaces learned through a contrastive learning approach to detect anomalous data. To evaluate several anomaly detection methods, we controlled the noise associated to each class.

First, we found that when the dataset contained labeling errors, classifiers trained on embedding spaces performed better than classifiers trained directly on the data input. It would be interesting to compute a confidence statistic from the embedding of a data point in future work. This confidence statistic could be used to weight the loss accordingly during the learning phase of the classifier.

Second, we can identify groups of data points inside the embedding space that share a strong intrinsic similarity with each other but are less similar to data points of their own class. Based on this observation, we compared the projection of data points with and without noise to evaluate anomaly detection algorithms. We observed that the performance of anomaly detection algorithms depends strongly on the initial parameters. The more robust methods scales with high hyperparameters values such as KNN or KDE (k=1000 or bandwidth=0.5). The performances also vary inter-classes, with "cat", "bird" and "plane" being the most difficult classes to separate from input noise.

Further work is required to evaluate how to train an embedding space using contrastive learning, taking into account the properties of the available dataset. Ideally, one should be able to choose the learning parameters based on properties such as batch size and embedding dimension to optimize the projection. We could test deeper models, such as ResNet50, to see if the performances of the anomaly detection methods applied to the embedding space scale by the size of the network. Similarly, large batch size might affect the outcome of the embedding space.

Another direction could be the addition of a constraint on the loss of the embedding space, such as a spherical embedding or decision boundary to learn a confidence score Fig. 6. Class by class distributions of AUC ROC scores computed by KDE models in all noise configurations. i.e. for the class "plane", the subplot on the upper left shows, for every noise rate of this class, the distribution of all the AUC ROC computed by KDE models (five models with various bandwidth parameter) associated with the data heterogeneity with respect to the dataset.

A. Noise matrices used in our experiments

We generated noise matrices with noises in (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7) and sparsities in (0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7), Fig. 5 presents these noise matrices.

Fig. 1 .

 1 Fig. 1. Simple representation of the contrastive learning algorithm. Two different data augmentations (t and t' from the same family of augmentations) are applied to each data example to obtain two correlated views. The encoder 𝑓(. ) and the projection head 𝑔(. ) are trained to minimize the contrastive loss. After the training is completed, we discard the projection head and keep the encoder and representations ℎ for downstream tasks.

Fig. 2 .

 2 Fig.2. The representations of CIFAR10 images obtained via contrastive learning, represented as 2 dimensions points thanks to t-SNE[START_REF] Van Der Maaten | Visualizing data using t-SNE[END_REF] dimensionality reduction. Each color correspond to a true label.

Fig. 3 .

 3 Fig. 3. The t-SNE representations of CIFAR10 images with ResNet18 encoder for 2000 epochs. Each color correspond to a true label.

Fig. 4 .

 4 Fig.4. On the left, 16 randomly chosen CIFAR10 images from the cluster circled in red in Fig.3. On the right, 16 randomly chosen images from the cluster circled in Blue in Fig.3.

Fig. 7 .

 7 Fig. 7. Noise matrices with seed 0.

Fig. 8 .

 8 Fig. 8. Evolution of the loss function of Contrastive learning with ResNet18 encoder with batches of 256 over 2000 epochs.

Fig. 9 .

 9 Fig. 9. Evolution of the loss function of Contrastive learning with ResNet18 encoder over 2000 epochs.

Fig. 9

 9 Fig.9shows the evolution of the t-SNE representations, and we can clearly see how the Contrastive Learning algorithm is splitting the dataset of representations into more and more clusters that globally correspond to their true class.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Class by class distributions of AUC ROC scores computed by all models in all noise configurations

Table 1 .

 1 Top-1 accuracies of the MLP on different noise and sparsity levels, using the Cross-Entropy loss in the first table, and a noise robust loss (ELR) in the second table, with ResNet18 as encoder.

					Sparsity
	Noise
		0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7
				With Cross-Entropy loss
	0.0	90.72
	0.1	90.56	90.66	90.54	90.75	90.53	90.57	90.64	90.53
	0.2	89.58	89.98	89.50	89.78	90.50	90.16	89.89	88.87
	0.3	89.51	89.37	88.61	89.67	89.40	89.00	85.55	87.46
	0.4	87.69	87.03	86.89	86.05	83.44	77.43	72.44	66.90
	0.5	82.57	76.90	69.32	73.06	62.79	65.75	54.60	56.49
	0.6	65.82	61.80	58.96	54.00	51.47	50.22	45.11	40.44
	0.7	41.26	35.35	34.00	36.86	35.46	26.20	27.23	28.54
				With ELR loss
	0.0	91.31
	0.1	91.02	91.22	91.00	91.04	91.01	91.10	90.90	90.95
	0.2	90.51	90.63	90.63	90.63	90.57	90.54	90.69	90.64
	0.3	90.16	90.02	90.41	90.43	90.70	90.21	89.91	90.29
	0.4	89.80	88.79	87.15	89.85	85.75	82.42	79.96	71.97
	0.5	85.78	80.83	68.11	73.55	64.44	74.17	46.91	56.21
	0.6	70.89	73.67	57.21	64.93	42.39	57.36	40.77	40.24
	0.7	42.43	36.48	29.71	42.23	40.52	31.17	23.40	21.10


Pour Le Diplôme D'état De Docteur

E N Médecine

Imagerie Radiologie

Par M Médicale

Beaudoin Pierre

Soutenue Thèse

Publiquement

Mme Le Pr

Ivan Bricault

Charlotte Costentin

M Le Dr

Alexandre Bellier

Mme Le Dr Bleuenn

Brusset M Le Dr

Julien Ghelfi

COULD CISTERNA CHYLI NON-DILATATION BE PREDICTIVE OF SURVIVAL IN PATIENTS WITH PORTAL HYPERTENSION? THÈSE

AVERTISSEMENT

Ce document est le fruit d'un long travail approuvé par le jury de soutenance.

La propriété intellectuelle du document reste entièrement celle du ou des auteurs. Les utilisateurs doivent respecter le droit d'auteur selon la législation en vigueur, et sont soumis aux règles habituelles du bon usage, comme pour les publications sur papier : respect des travaux originaux, citation, interdiction du pillage intellectuel, etc.

Il est mis à disposition de toute personne intéressée par l'intermédiaire de l'archive ouverte DUMAS (Dépôt Universitaire de Mémoires Après Soutenance).

Si vous désirez contacter son ou ses auteurs, nous vous

REMERCIEMENTS

Au professeur Ivan Bricault pour avoir accepté de présider le jury de cette thèse, et pour tout ce que tu auras eu l'occasion de m'apprendre en échographie, au scanner, en IRM et en angiographie.

Au docteur Alexandre Bellier, pour ton aide inestimable sur la partie statistique de ce travail, et ce malgré mes multiples demandes d'analyses complémentaires.

Au professeur Charlotte Costentin et au docteur Bleuenn Brusset, pour avoir accepté de juger ce travail et ainsi y apporter un regard clinique complémentaire de grande valeur.

Au docteur Julien Ghelfi, pour avoir accepté de me guider sur le chemin de la thèse, malgré mon absence de destinée pour la radiologie interventionnelle digestive et mon caractère plus que novice dans la recherche et la rédaction d'article ainsi que dans le système lymphatique, et l'avoir fait, tout comme ce que tu m'as appris en diagnostique et en interventionnel, avec une véritable bienveillance. J'espère t'avoir rendu fier de mon travail.

A l'ensemble de l'équipe du CH Annecy Genevois, médecins, manipulateurs, secrétaires et agents logistiques, qui m'ont accueilli comme une famille dès mon premier semestre, et ont contribué à me faire sentir à la maison à 600 km de chez moi au milieu des montagnes quand j'étais encore un amiénois un peu perdu, et pour votre accueil chaleureux pour mes retours en milieu et fin d'internat. Et notamment A Charles, pour m'avoir tenu la main (métaphoriquement) lors de mes premières échographies et scanners, et avoir continué à tant m'apprendre à chacune de nos rencontres, dans la bonne humeur perpétuelle qui te caractérise.

A Thibaut et Raphael, pour les premiers pas tâtonnant dans l'imagerie ostéo articulaire, que ce soit sur des épaules de patients comme sur ma cheville.

A Nicolas et Fabrice, pour mes premiers pas en radiologie interventionnelle, et à Vincent et Alexandre, pour les derniers en date.

A l'ensemble de l'équipe du CH de Chambéry, malgré une fin de semestre en demi-teinte dans un contexte de pandémie Covid 19 débutante.

A l'ensemble de l'équipe de manipulateurs du CHU de Grenoble, en neuroradiologie, radiologie centrale et en radiopédiatrie, pour les longues vacations (et nuits) d'échographie, de scanner, d'IRM et d'angio, toujours dans la bonne humeur.

A toute l'équipe de Sud, pour m'avoir accueilli sur mon semestre chez vous, et au plaisir de vous retrouver pour plus longtemps dès le prochain.

A tous les cointernes qui ont partagé une partie de ma route jusqu'ici.

A Claire, Kevin, Paul, Emeric et Corentin, les copains de la promo que je n'aurais pas toujours côtoyés avec la même fréquence que d'autres, mais que j'ai et aurais toujours plaisir à croiser et partager une garde ou un relai H, et je l'espère quelques aventures en montagne.

A mes cointernes de périph'.

Lucie, qui m'a appris les premières ficelles de la radiologie quand je n'étais encore qu'un vieil externe débarqué au bord du lac.

A Marion, pour avoir essayé de te transmettre le peu de mes connaissances à l'époque et tenter d'apprendre de toi ton regard clinique sur les situations rencontrées.

A Ebru et Vanina, pour les repas et les cocas partagés pendant l'été, entre nos transmissions du bip d'écho.

A Joachim, pour les moments partagés en écho, en salle de pause et surtout assis sur du carbone à roues, et on aura l'occasion de poursuivre les aventures sur le carbone qui glisse une fois que la neige sera revenue.

A tous les autres cointernes, pour un ou plusieurs semestres ensemble ou simplement une garde ou un échange de bip, toujours dans la bonne humeur et l'entraide, et surtout les moments partagés en dehors de l'hôpital.

Au cointernes devenus chefs, Thomas, Pauline, Charlotte, Alexandre, Nicolas, Maxime, Lucie, et tous ceux que je n'ai pas connu avant, Pierre, Yann, Fabien, Hélène, Marie, Léa, pour avoir corrigé toutes mes bêtises en relecture, et pour tous les avis éclairés que vous avez pu me donner et toutes les connaissances que vous avez pu me transmettre (et ce n'est pas fini, malheureusement pour vous).

A l'ensemble des radiologues du CHU, et notamment à ceux des services de neuroradiologie et d'imagerie digestive que j'aurais eu l'occasion de côtoyer plus fréquemment lors de mes stages de ces surspécialités, merci pour tout ce que vous avez pu me transmettre et m'apprendre, que ce soit au cours de vacations dédiées et répétées ou simplement de relectures, de questions posées et d'avis demandés, et je tacherais de continuer d'apprendre de vous et d'employer au mieux ces connaissances pour ma pratique future.

Aux vieux copains.

A Romain, tu resteras pour toujours un des meilleurs amis que j'ai eu la chance d'avoir, et même si je ne te le dis pas forcément, je te remercierais toujours au fond de moi d'avoir choisi de venir trifouiller des boites crâniennes et des rachis au milieu de mes montagnes, pour tout ce qu'on a partagé jusqu'ici et tout ce qu'il nous reste à partager ensemble pour les nombreuses années à venir.

A Rivière, Raguin, Delville, Panero et Ben.

Une nouvelle famille de copains qui m'a intégré sur le tard à bras ouvert, je vous aime de tout mon coeur, et même si l'internat nous a catapulté aux 4 coins de la France, je suis toujours très heureux d'avoir de vos nouvelles et encore plus de vous voir, et j'espère que j'aurais l'occasion de vous faire partager la beauté de ma nouvelle région en été comme en hiver, et de découvrir les vôtres. Nos aventures ne font que commencer.

A Nicolas. Peu de semaines s'écoulent sans que je ne pense à toi, une tristesse profonde de t'avoir perdu mais j'espère que tu es enfin en paix.

A Gabriel, autant nouveau que vieux copain, un plaisir de partager les chemins avec toi, pour une heure au bord du lac comme pour quinze au fond de la Vanoise, titubant pendant que tu te balade sur tes jambes d'acier. Je ne te rattraperai surement jamais mais je fais de mon mieux, pour toutes nos prochaines balades ensemble.

A Félix, pour les après-midis de passes et de discussion sans fin ni thème spécifique partagées à Jean Rostand, j'espère que quand ta carrière politico associative te laissera plus de temps libre on aura l'occasion d'aller se balader dans la neige ensemble et continuer à bavarder sans fin.

A tous les copains d'Amiens que je ne saurais citer, du lycée, de la fac de médecine, du SUAPS et d'ailleurs. La vie et le goût de la montagne m'ont éloigné de vous, mais j'ai toujours un grand plaisir à partager mes retours au pays avec vous, et ma porte ici vous est toujours grande ouverte.

Aux nouveaux copains.

A Aymeric, le moins radio de mes cointernes de radio, tu es devenu un de mes meilleurs amis.

Pour tous les moments passés ensemble dans les montagnes, et tous les prochains, vivement que tu rejoignes la brigade du carbone.

A Guillaume et Hélène, les meilleurs colocataires. Il aurait fallu me payer pour vivre dans une coloc avant ça, et pourtant j'ai partagé des moments extraordinaires avec vous et ce fut une des meilleures expériences de ma vie. Entre les levers à 5h pour la Féclaz et les soirées ensemble, encore plus pendant le confinement, je vous aime énormément et j'espère qu'on réussira à se voir plus souvent.

Aux copains de l'internat de mon premier hiver à Annecy, Alexandre, Kevin, Pierre et Théo, j'ai toujours plaisir à vous croiser aux détours des couloirs du CHU.

A Elora, qui a fait se raccourcir la grande rue de la Tronche de 800m pour un semestre, j'ai toujours beaucoup de plaisir à discuter avec toi et à te voir (brièvement malheureusement) au gré de tes passages par mes montagnes (quelle idée de partir à Limoges).

A tous les nouveaux copains rencontrés au cours de l'internat, à l'hôpital comme en dehors, A Elia. Toujours à mes côtés dans les bons moments comme dans les autres. Je ne pourrais jamais assez te remercier pour toutes ces années à mes côtés, et qui me donnent l'impression qu'on se connait depuis dix fois plus longtemps. Et ce n'est que le début.

ABSTRACT Purpose

Portal hypertension is responsible for congestion of the central lymphatic system to reabsorb excess fluid from the interstitial sector. This congestion is visible on CT scan by a dilatation of the cisterna chyli (CC). However, central lymphatic system is not dilated in 25 to 42% of cirrhotic patients with portal hypertension. It has been suggested that cirrhotic patients undergoing transjugular intrahepatic portosystemic shunt (TIPS) insertion without CC dilatation on CT scan have a poorer prognosis. The hypothesis made was that the absence of CC dilatation and thus of central lymphatic system congestion prevent buffering of portal hypertension variation.

Objectives

The main objective of this study was to evaluate the association of CC dilatation with overall survival of patients with portal hypertension undergoing TIPS or transjugular liver biopsy (TJLB) with hepatic venous pressure gradient (HVPG) measurement. Secondary objectives were to evaluate the correlation between CC diameter with HVPG and portal pressure measurements in the total cohort as well as in the subgroup of patients without large venous collaterals (≥ 6 mm on CT scanner) that could partially absorb portal hypertension, and to investigate predictive factors of CC non-dilatation (non-detectable or < 5 mm of axial diameter on CT scan).

Materials and methods

It was a monocentric retrospective study, including patients who had undergone TIPS insertion or TJLB with HVPG from January 2011 to December 2021. Exclusion criteria were the absence of CT scan pre TIPS and pre or post TJLB, and the absence of portal hypertension (defined as HVPG < 5 mm). The diameter of the CC was measured on strict axial slices.

Results

138 patients were included in this study with a mean age of 61.8 years ± 12.1. Among them 115 patients were men (83.3%) and 130 patients had cirrhosis (94.2%). CC was dilated in 97 patients (70.3%), with a mean diameter of 8.9 ± 4.4 mm. Overall survival was not different between patients with dilated CC versus patients without (p=0.454). There was no correlation between diameter of the CC and HVPG, in the total cohort (r=0.025; p=0.804) and in the subgroup without large venous collaterals (r=0.033; p=0.906), or between diameter of the CC and portal pressure, in the full cohort (r=0.148; p=0.196) and in the subgroup without large venous collaterals (r=0.446; p=0.110). No predictive factors for non-dilatation of CC were found, including the Child-Pugh score (p=0.387).

Conclusion

Non-dilatation of CC does not seem to be correlated with overall survival in patients with portal hypertension undergoing TIPS or TJLB.

TABLE OF CONTENTS

INTRODUCTION

Hepatic cirrhosis is a common chronic disease, affecting more than 112 million people in the world [START_REF] Sepanlou | The global, regional, and national burden of cirrhosis by cause in 195 countries and territories, 1990-2017: a systematic analysis for the Global Burden of Disease Study 2017[END_REF]. It leads to portal hypertension, which can be responsible for the occurrence of digestive bleeding and ascites, worsening the disease's prognosis. The importance of lymphatic drainage has been known for a long time in portal hypertension (2-4). Starling's law governs the exchanges between vascular and interstitial sectors, and the increase of hydrostatic pressure in portal hypertension results in a transfer of fluid to the interstitial sector [START_REF] Witte | Lymph Protein in Hepatic Cirrhosis and Experimental Hepatic and Portal Venous Hypertension[END_REF][START_REF] Levick | Capillary filtration-absorption balance reconsidered in light of dynamic extravascular factors[END_REF]. The lymphatic system is the main way to evacuate this fluid excess. Liver lymphatics vessels drain into the cisterna chyli (CC) and then to the thoracic duct (TD), ending up in the central venous system at the left venous angle [START_REF] Hsu | Lymphatic Anatomy[END_REF]. The lymphatic flow in the TD is increased three to six fold in cirrhotic patients, as compared to general population [START_REF] Dumont | Flow Rate and Composition of Thoracic-Duct Lymph in Patients with Cirrhosis[END_REF]. When the lymphatic system is overwhelmed, excess fluid reaches the extracellular space, responsible for the onset of ascites [START_REF] Chung | The lymphatic vascular system in liver diseases: its role in ascites formation[END_REF].

The dilatation of the CC and TD on CT scan illustrate this central lymphatic congestion [START_REF] Kumar | Lymphatic dysfunction in advanced cirrhosis: Contextual perspective and clinical implications[END_REF]. However, literature data remains scarce and contradictory, some authors correlating TD diameter with cirrhosis grade [START_REF] Hwang | Evaluation of the left neck distal thoracic duct in cirrhosis with computed tomography[END_REF][START_REF] Park | Clinical implications of thoracic duct dilatation in patients with chronic liver disease[END_REF], while other do not find significant association with clinical data [START_REF] Pieper | Impact of transjugular intrahepatic portosystemic shunt creation on the central lymphatic system in liver cirrhosis[END_REF][START_REF] Porret | Evolution of Thoracic Duct Congestion after Portal Decompression by TIPS in Cirrhotic Patients[END_REF]. Also, the absence of central lymphatic vessels congestion in 20 to 42 % of cirrhotic patients [START_REF] Kiyonaga | Thoracic duct and cisterna chyli: evaluation with multidetector row CT[END_REF] suggests an alteration of the central lymphatic drainage [START_REF] Sarin | Deeper insights into the relevance of lymphatic circulation in cirrhosis of the liver: A trojan horse or the holy grail?[END_REF].

Recently, a study including 93 patients with portal hypertension reported a decrease in size of CC after transjugular intrahepatic portosystemic shunt (TIPS) insertion. The authors also described that the non-visibility of the CC prior to TIPS insertion was associated with shorter overall survival [START_REF] Pieper | Impact of transjugular intrahepatic portosystemic shunt creation on the central lymphatic system in liver cirrhosis[END_REF], suggesting that this may be responsible for a poorer capacity to adapt to surges of portal hypertension [START_REF] Ready | Morbidity and Mortality of Portal Hypertension[END_REF]. It was also mentioned that the absence of large venous collaterals, acting like a physiological pressure relief system [START_REF] Arora | Spectrum of hepatofugal collateral pathways in portal hypertension: an illustrated radiological review[END_REF][START_REF] Bandali | Portal hypertension: Imaging of portosystemic collateral pathways and associated image-guided therapy[END_REF], was responsible for a direct transfer of portal hypertension to the lymphatic system [START_REF] Porret | Evolution of Thoracic Duct Congestion after Portal Decompression by TIPS in Cirrhotic Patients[END_REF], and thus a correlation between portal pressure and CC diameter in this subgroup of patients.

The purpose of this study was to confirm these recent findings and then to evaluate the association between the absence of central lymphatic congestion and overall survival in patients with portal hypertension undergoing TIPS insertion or transjugular liver biopsy (TJLB) with hepatic venous pressure gradient (HVPG) measurement.

MATERIALS AND METHODS

Study design and patients

This study was approved by a national review board and a non-opposition notice was given to all patients. All consecutive patients of 18 years and older who underwent HVPG measurement either by TIPS insertion or TJLB at our academic center between January 2011 and December 2021 were retrospectively included in this study.

Exclusion criteria were the absence of portal hypertension, defined by a HVPG of at least 5 mm Hg [START_REF] Kumar | Hepatic venous pressure gradient measurement: time to learn! Indian[END_REF], and the absence of pre TIPS abdominopelvic CT scan in case of TIPS insertion and pre or post procedure for patients undergoing TJLB.

Imaging data collection

All patients had at least one abdominopelvic CT scan before TIPS insertion or before or after TJLB. If more were available, the closest to the procedure was selected for the study.

Measurements and imaging analysis were done on a dedicated PACS software from AGFA Enterprise Imaging 8.1.2 SP4 HF5 (AGFA Healthcare, Mortsel, Belgium), and included the maximal CC diameter in millimeters in axial slices, the spleen long axis in coronal slices, the presence of large portosystemic collaterals (defined as ≥ 6 mm in axial slices [START_REF] Pieper | Impact of transjugular intrahepatic portosystemic shunt creation on the central lymphatic system in liver cirrhosis[END_REF]), the presence of ascites and the azygos vein diameter in millimeter in axial slices.

The CC was identified as a tubular structure, isodense to water and located in the retrocrural space, right of the aorta, extending cranially to the TD (Figure 1). It was measured at its largest diameter on strict axial slices of 2.5 mm. The CC was stated as dilated when its axial greatest diameter was ≥ 5 mm [START_REF] Ito | Cisterna chyli in patients with portal hypertension: Evaluation with MR imaging[END_REF].

Imaging data were analyzed in a blinded fashion by two radiologists with 4 and 6 years of experience. Discrepancy of more than 1 mm leaded to a new analysis for agreement on a common value.

Figure 1. Cisterna chyli vizualisation on CT scan. A : non dilated cisterna chyli, axial slice ; B : dilated cisterna chyli, axial slice, C : dilated cisterna chyli, coronal slice.

Objectives

The main objective of this study was to investigate the association between non-dilatation of central lymphatic system on CT scan and overall survival in patients with portal hypertension undergoing TIPS insertion or TJLB with HVPG measurements. Overall survival of patients with non-visible CC or CC diameter < 5 mm on axial slice was compared to survival of patients with CC diameter ≥ 5 mm in the full cohort and in the subgroups of patients who had TIPS creation for refractory ascites or bleeding.

Secondary objectives were to evaluate the correlation between the CC diameter and HVPG measurements, in the full cohort and in the subgroup of patients without large venous collaterals, between the CC diameter and the Child-Pugh score, the MELD score, the CT scan signs of portal hypertension (splenomegaly, presence of large portosystemic collaterals, ascites and azygos vein diameter) and the TIPS clinical success. The last secondary objective was to evaluate predictive factors for non-congestion of central lymphatic system (i.e., nonvisible CC or CC diameter <5mm on CT scan).

Statistical analysis

Summary statistics for qualitative variables were reported as number and percentage while quantitative variables are expressed as mean and Standard Deviation (SD). Inclusion characteristics were described for the entire sample. Univariate analyses were performed to compare patient characteristics according to the patient's vital status (primary endpoint) using Student's t test or a Mann-Whitney test depending on the distribution of the quantitative variable, as well as an ANOVA or Kruskal-Wallis test and a Pearson's Chi-squared test or Fisher exact test depending on the validity conditions. The secondary endpoints were analyzed using the same strategy in univariate analysis. Correlations were calculated using a Pearson test or a Spearman test if validity conditions were not satisfied. Descriptive analysis were conducted using Kaplan-Meier survival analysis with analysis in sub-groups according to the defined objectives. Two-sided p-values of <0.05 were considered statistically significant. All analyses were performed using RStudio (Version 1.0.143 ©).

RESULTS

Patients' inclusion

From January 2011 to December 2021, 372 patients had TIPS insertion or TJLB with HVPG measurements. Among them, 193 patients (51.9%) without CT scan data available and 41 patients (11.0%) without portal hypertension on HVPG measurement were excluded. The remaining 138 patients (37.1 %) were included in this study (Figure 2). CC diameter (if visible), mean (± SD) 8.9 (4.4) Splenomegaly, n (%) 83 (60.1) Azygos vein diameter in mm, mean (± SD) 8.9 (1.9) Large portosystemic collaterals > 6 mm, n (%) 102 (73.9) Portal pressure in mm Hg, mean (± SD) 30.4 (9.9) HVPG in mm Hg. mean (± SD) 16.8 (8.1) n : number ; SD : standard deviation ; MELD : model for endstage liver disease ; TIPS : transjugular intrahepatic portosystemic shunt ; TJLB : transjugular liver biopsy ; PR : prothrombin ratio ; CC : cisterna chyli

Overall survival and non-dilatation of central lymphatic system

The CC was detectable and dilated (diameter ≥5 mm) in 97 patients (70.3%), with a mean diameter of 8.9 mm (±4.4). In the group of patients who underwent TIPS insertion, mean CC diameter was 10.0 mm (±7.1) in the ascites group and 8.2 mm (±4.1) in the digestive bleeding group (p=0.258).

Mean overall survival was 33.7 months (±34.6) in patients with a dilated CC vs 27.9 months (±30.8) in patients without dilatation of the CC (p=0.454) (Figure 3A). There was no difference in overall survival in the subgroups according to the indication of TIPS insertion, such as digestive bleeding (p=0.282) (Figure 3B), with a mean survival of 22.8 months (±26.5) without CC dilatation and 31 months (±33.9) with a dilated CC, and ascites (p=0.518) (Figure 3C), with a mean survival of 34.3 months (±39.8) without CC dilatation and 38.5 months (±37.5) with a dilated CC.

Figure 3. Log-rank overall survival curves segregating the cohorts of patients according to CC dilatation in full cohort (A), subgroup of patients with TIPS insertion for digestive bleeding (B) and subgroup of patients with TIPS insertion for ascites (C):

Cisterna chyli and correlation with portal hypertension

The CC diameter was not correlated with HVPG (r=0.025; p=0.804) or with portal pressure (r=0.148; p=0.196) in the full cohort (Table 2), in the subgroup of patients without large venous collaterals (r=0.033; p=0.906 and r=0.446; p=0.110), and in the subgroups according to TIPS indication (digestive bleeding and ascites). There was also no correlation between the CC diameter and the Child-Pugh score (p=0.490), the MELD cirrhosis score (p=0.149) and with clinical success of TIPS (p=0.368).

Azygos vein diameter was the only CT scan sign of portal hypertension weakly correlated with the CC diameter (r=0.285; p=0.005).

Inter observer correlation

Correlation between the two readers was excellent with ICC = 0.971 [CI95: 0.785;0.997] for CC diameter measurements. Differences over 1 mm were noted in 32 patients and required a supplementary evaluation to obtain an agreement.

Predictive factors of CC non-dilatation

No predictive factor for CC non-dilatation was found in the population of patients with portal hypertension. In particular, CC non-dilatation was not associated with Child-Pugh score in the full cohort (p=0.387) and in the subgroup of patients with visible CC (p=0.803) (Table 3).

DISCUSSION

This study found no difference in overall survival between patients with dilated and non-dilated CC. In addition, portal pressure and HVPG were not correlated with CC diameter, notably in patients without large venous collaterals.

The results of this study do not confirm those recently reported by Pieper et al. [START_REF] Pieper | Impact of transjugular intrahepatic portosystemic shunt creation on the central lymphatic system in liver cirrhosis[END_REF] regarding the absence of CC dilatation as a poor prognostic factor for survival. In their study, no difference was made according to the indication for TIPS creation, whereas patients with TIPS for digestive bleeding had a worse early prognosis (21) than those with refractory ascites. In the subgroup analyses, we did not find any difference either. The main limitation of this approach is that a TIPS creation leads to the lifting of portal hypertension [START_REF] García-Pagán | Early Use of TIPS in Patients with Cirrhosis and Variceal Bleeding[END_REF] and thus the importance of the lymphatic system in buffering portal hypertension decreases. This factor could make us consider a similar study in cirrhotic patients excluding patients with TIPS insertion and liver transplant, to better evaluate the impact of central lymphatic congestion in patients with persistent portal hypertension. Another study that could be conducted would be to investigate the survival and digestive bleeding of patients with TIPS thrombosis based on CC dilatation before TIPS to see if central lymphatic congestion would absorb the abrupt surge of portal hypertension in these patients. Another explanation for the negative results in this study could come from the anatomical variability of the lymphatic system. Indeed, hepatic drainage is mainly towards the TD, but anterior and intercostal thoracic chains may also be involved and are not detectable on CT scans in routine practice [START_REF] Lengelé | Anatomical bases for the radiological delineation of lymph node areas. Upper limbs, chest and abdomen[END_REF]. The lack of CC dilatation could be compensated by drainage through these accessory channels.

There was also no difference of CC diameter between the subgroups of patients with and without large venous collaterals (p=0.258), as well as no correlation between the CC diameters and portal pressure (r=0.446; p=0.110) or HVPG (r=0.033; p=0.906) in patients without voluminous venous collaterals, contrary to a previous report [START_REF] Pieper | Impact of transjugular intrahepatic portosystemic shunt creation on the central lymphatic system in liver cirrhosis[END_REF]. If these large venous portosystemic collaterals can be considered as a way to partially lift the portal hypertension, acting like a physiological portosystemic shunt, as mentioned by Pieper and al. [START_REF] Pieper | Impact of transjugular intrahepatic portosystemic shunt creation on the central lymphatic system in liver cirrhosis[END_REF], the development of these collaterals is a reflection of an important increase in HVPG as shown in the current study were HVPG was superior in patients with large venous collaterals than in patients without (p=0.020).

Multiple parameters can affect the CC diameter and visibility in CT scan. The CC is a structure with significant anatomical variability, not visible in 20 to 42 % of cirrhotic patients [START_REF] Kiyonaga | Thoracic duct and cisterna chyli: evaluation with multidetector row CT[END_REF], and, like most macroscopic lymphatics vessels, present a high parietal elasticity, explaining that a lot of independent factors might impact its caliber, including position [START_REF] Niggemann | Postural Effect on the Size of the Cisterna Chyli[END_REF], hydration, heart function and central venous pressure [START_REF] Verma | Dilated cisternae chyli: a sign of uncompensated cirrhosis at MR imaging[END_REF][START_REF] Itkin | Pathophysiology of the Lymphatic System in Patients With Heart Failure[END_REF]. It also has a parietal peristaltism, observed during MR imaging [START_REF] Ito | Cisterna chyli in patients with portal hypertension: Evaluation with MR imaging[END_REF], which can impact CT measurements. Nonetheless, our study found detectability (71 %) and dilatation (mean axial diameter of 8.9 mm) in line with those usually described in the cirrhotic population [START_REF] Verma | Dilated cisternae chyli: a sign of uncompensated cirrhosis at MR imaging[END_REF], with an excellent interobserver correlation for the measurement of the CC (ICC=0.971 [CI95: 0.785;0.997]). Furthermore, the absence of correlation between CC diameter and various clinical, biological, imaging and angiographic data stay on track with the discordant results of recent studies in this field [START_REF] Ito | Cisterna chyli in patients with portal hypertension: Evaluation with MR imaging[END_REF][START_REF] Verma | Dilated cisternae chyli: a sign of uncompensated cirrhosis at MR imaging[END_REF]. However, it has to be noted that most of those are mainly focused on the TD end diameter rather that the CC, including the Park and al. study [START_REF] Park | Clinical implications of thoracic duct dilatation in patients with chronic liver disease[END_REF].

If the impact of lymphatic drainage has been clearly established [START_REF] Kumar | Lymphatic dysfunction in advanced cirrhosis: Contextual perspective and clinical implications[END_REF][START_REF] Vollmar | Lymph Vessel Expansion and Function in the Development of Hepatic Fibrosis and[END_REF], analysis methods through imaging are limited to macroscopic pathways. Congestion of the central lymphatics shows us only the final collecting vessel, and histological analysis of the intrahepatic lymphatic vessels could help us locate and better understand the lymphatic congestion in cirrhosis with portal hypertension. One way to further investigate this could be to associate macroscopic analysis through imaging and microscopic analysis in patients who underwent liver biopsy or transplantation [START_REF] Ohtani | Organization and developmental aspects of lymphatic vessels[END_REF][START_REF] Yokomori | Lymphatic marker podoplanin/D2-40 in human advanced cirrhotic liver-Re-evaluations of microlymphatic abnormalities[END_REF].

The first limitation of this study is its monocentric and retrospective design. The inclusion criteria, limited to patients who benefited both from invasive portal pressure measurements and a CT scan close to the procedure were restrictive considering the whole cirrhotic with portal hypertension population. Regarding imaging data analysis, CT scan analysis of CC is limited in this feature-rich anatomical region, without limited contrast even after contrast agents injection, as opposed to the TD, better individualized near the lymphovenous junction in CT scan [START_REF] Hwang | Evaluation of the left neck distal thoracic duct in cirrhosis with computed tomography[END_REF][START_REF] Johnson | The thoracic duct: clinical importance, anatomic variation, imaging, and embolization[END_REF]. MRI better visualize the CC, as shown by Ito and al. who depicted CC in 95 % of patients through hyper weighted T2 imaging, with better characterization between CC, lymph nodes and small vessels [START_REF] Ito | Cisterna chyli in patients with portal hypertension: Evaluation with MR imaging[END_REF], but this imaging method can be limited by loss of signal in patients with abundant ascites, frequent in the decompensated cirrhotic population. Finally, TIPS insertion was a confusing factor in survival evaluation, as well as the divergence in prognosis regarding TIPS indication, as mentioned earlier.

CONCLUSION

Non-dilatation of CC was not predictive of overall survival in patients with portal hypertension undergoing TIPS insertion of TJLB and no predictive factor of non-dilatation of CC was found in this study. Further studies with broader inclusion criteria might be necessary to better investigate the impact and significance of central lymphatic congestion in portal hypertension.

  merci pour votre compagnie et votre partage de l'amour de ces montagnes, Valentine, Guillaume, Camille, Justine, Nans, Clémentine, Nicolas et tous les autres. A ma famille. A Papa et maman pour votre soutien indéfectible après toutes ces années dans la vie, les études, les hobbys et le sport, je vous aime de tout mon coeur et je ne pourrais jamais assez vous remercier pour tout ce que vous avez fait et faites pour moi. Je vous appelle et vous vois trop peu mais vous connaissez ma façon de vous le dire. A Marie Cécile et Julien. Je passerais vous voir plus souvent quand le chat sera au pré et le poney dans le salon. A Mamie Ghislaine et Papy Jean Pierre, après tous ces vendredi midi partagés, merci pour tous les petits mots attentionnés après toutes ces années. A Mamie Monique et Papy Jacques. A Cathy, pour m'avoir accueilli si simplement dans la famille, et nous prêter ta chambre au cours de nos passages à Annecy, bien trop souvent. A Franck et Laura pour m'avoir accueilli dans l'autre versant de la famille.

  INTRODUCTION ................................................................................................................... 19 MATERIALS AND METHODS ............................................................................................. 20 Study design and patients .................................................................................................. 20 Imaging data collection ...................................................................................................... 20 Objectives ............................................................................................................................ 21 Statistical analysis ............................................................................................................... 22 RESULTS ................................................................................................................................ 23 Patients' inclusion ............................................................................................................... 23 Overall survival and non-dilatation of central lymphatic system .................................. 25 Cisterna chyli and correlation with portal hypertension ................................................ 27 Inter observer correlation .................................................................................................. 28 Predictive factors of CC non-dilatation ............................................................................ 28 DISCUSSION .......................................................................................................................... 28 CONCLUSION ........................................................................................................................ 31 REFERENCES ....................................................................................................................... 33

Figure 2 .

 2 Figure 2. Flow chart of the study:

Table 1 )

 1 The mean age of patients included in this study 61.8 years ± 12.1 (age range: 21-86 years),

	including 115 men (83.3%), and 130 patients with cirrhosis (94.2%). In the subgroup of patient
	who underwent TIPS insertion, the TIPS indication was refractory ascites in 49 patients (35.5%)
	and digestive bleeding in 67 patients (48.6%).
	Large venous collaterals were identified in 102 patients (73.9%). Mean HVPG in patients with
	large venous collaterals was 17.8 mmHg (±8.7) versus 14.2 mmHg (±5.3) in patients without
	large collaterals (p=0.020) but mean CC diameter was not different between the two groups

Table 2 . Correlation with CC diameter

 2

	Variables

Table 3 . Predictive factors of CC non-dilatation in patients with portal hypertension:

 3

	Variable	Full cohort (n=138)	Only patients with visible CC (n=97)
	Age	p=0.336	p=0.627
	Sex	p=0.379	p=0.339
	Etiology	p=0.942	p=0.376
	Child-Pugh score	p=0.387	p=0.803
	MELD score	p=0.117	p=0.149
	Ascites	p=0.275	p=0.166
	TIPS indication	p=0.258	p=0.186
	Baseline portal pressure	p=0.622	p=0.196
	Baseline HVPG	p=0.656	p=0.849
	Proteinemia	p=0.489	p=0.191
	Albuminemia	p=0.858	p=0.453
	CC : cisterna chyli ; n : number ; p : p value ; MELD : model for end stage liver disease ;
	TIPS : transjugular intrahepatic portosystemic shunt ; HVPG : hepatic venous pressure
	gradient

ABREVIATIONS