Julien Velcin
email: julien.velcin@univ-lyon2.fr

Antoine Gourru
email: antoine.gourru@univ-lyon2.fr

Erwan Giry-Fouquet
email: erwan.giry-fouquet@univ-lyon2.fr

Christophe Gravier
email: christophe.gravier@univ-st-etienne.fr

Mathieu Roche
email: mathieu.roche@cirad.fr

Pascal Poncelet
email: pascal.poncelet@lirmm.fr

Readitopics: Make Your Topic Models Readable via Labeling and Browsing

Readitopics provides a new tool for browsing a textual corpus that showcases several recent work for labeling topic models and estimating topic coherence. We will demonstrate the potential of these techniques to get a deeper understanding of the topics that structure different kinds of datasets. This tool is provided as a Web demo but it can be easily installed to experiment with your own dataset. It can be further extended to deal with more advanced topic modeling techniques.

Introduction

Topic Modeling is a powerful tool for monitoring information flow [Allan, 2012]. It is therefore a cornerstone for visualization platforms, allowing users to browse huge volumes of textual data. Interpreting and understanding them is usually left to the human on the basis of a ranked list of likely words. To address this issue, automatic topic labeling [START_REF] Mei | [END_REF] emerged as a task of the utmost practical interest -that is, to provide a textual expression sufficient to quickly grasp the topic informational content.

In parallel, several work designed automatic measures to assess the quality of topics, in particular by evaluating their semantic coherence [START_REF] Röder | [END_REF]. Several visualization tools have been designed on top of topic models [Chaney and Blei, 2012;[START_REF] Liu | [END_REF][START_REF] Sievert | [END_REF] but even recent work such as [START_REF] Kim | [END_REF] do not integrate an advanced topic labeling tool for providing a deep understanding of the underlying topic meaning, or the possibility to estimate their coherence.

In this paper we showcase Readitopics, a Web interface to grasp topic informational contents via topic labeling (Section 2) and browsing (Section 3). Readitopics gives the opportunity for users to get a better understanding of the underlying meaning of the topics that pervade their corpus. We experiment on several case studies with the well-known LDA model [START_REF] Blei | [END_REF] since it has been observed that it leads to "concise and coherent topics" outperforming SVD and NMF [START_REF] Stevens | [END_REF]. However, our system is intended to be compatible with any kind of (flat) topic models and it can be easily extended to document clustering. Be-sides, we released the sources of Readitopics so that the user can experiment with her own data.

Topic Labeling and Coherence

Topic labeling aims at finding a relevant label or title that provides a better understanding of what constitutes the homogeneity of a given topic [START_REF] Mei | [END_REF][START_REF] Danilevsky | [END_REF]. In the following we consider that a given topic z is associated to a distribution p(w|z) over a vocabulary of words w, among which we can extract the top k words, and every document d is associated to a distribution p(z|d) over topics.

Several measures have been proposed to associate either a term or a phrase based on the top-k words with a given topic. [START_REF] Lau | [END_REF] and [START_REF] Bhatia | [END_REF] used external resources (e.g., Wikipedia) to find a title and introduced some supervision. [Kou et al., 2015] explored new solutions relying on letter trigram vectors and word embeddings. Another option is to use multiple measures to increase the chance to find the correct phrase [Gourru et al., 2018].

Using representative sentences has been successfully integrated into topic-modeling oriented applications [START_REF] El-Assady | [END_REF]. The system we present in this demo lets the user select the best possible labels built by a selected number of (unsupervised) labeling techniques. We focus on techniques based on n-gram scoring, such as the 0-order (see Section 3.2), since it has been shown that keyphrases are more understandable than word lists or even images [Aletras et al., 2017].

Topics are not equal when it comes to their relevance with respect to the global informational content of the entire corpus. We therefore integrated a set of coherence measures for each topic, serving as a relevance metric. For a given topic z, DBT measures the distance of p(w|z) from the background word distribution: a small value means a broad topic with general (contextual) words [START_REF] Alsumait | [END_REF]. UCI [START_REF] Newman | [END_REF] measures the quality by calculating the average Pointwise Mutual Information (PMI) of the top words on an external corpus (in our case, a dump of Wikipedia). UMass [START_REF] Mimno | [END_REF] estimates the quality based on document frequencies of the original documents used for learning the topics. We showcase that these metrics are marginally correlated, which leaves topic coherence still an open field of research. 3 Browsing a Corpus With Readitopics

Studied Datasets

We showcase Readitopics on four different corpora: scientific articles (SA), news articles (NA) Harry Potter (HP) and a song of ice and fire book series (ASOIAF). SA is a set of 18,465 scientific abstracts gathered by [START_REF] Tang | [END_REF] over a period of 16 years ; NA is a set of 12,067 news we gathered automatically from the Huffington Post RSS feeds (US version). This set spans a period of 3 months (from June the 20th until Sept. the 8th, 2016) ; HP and ASOIAF are two sets of paragraphs extracted from the book series Harry Potter, by J.K. Rowling, and As Song Of Ice And Fire, by J.R.R. Martin. It includes a total of 38,997 paragraphs for 7 books and 40,831 paragraphs for 5 books, respectively, taken from the previous work of [START_REF] Waumans | [END_REF].

Demonstration Overview

The conference attendees will go through five different main tasks that can be performed on Readitopics interface (see Fig. 1). The features introduced by Readitopics and not available in publicly available web interfaces counterparts are prefixed with a star (*).

-Choose a dataset and a topic among the full list (a) or via the (partial) topic graph (b). We can see in (c) the topic's k words (k can be customized) and the top p documents (d).

Each document is provided with the top 5 topics (e) and the words associated to the current topic are highlighted.

-Move from one topic to another by following the correlation between documents, such as in [Liu et al., 2014]. The graph edges in (b) are sorted by their score in term of Pearson correlation between topics i and j. The number of top correlated topics can be customized. Once a topic is selected on the right side, we can click on the blue arrow to resume the browsing experience.

(*) Look at the documents at the frontier of two topics (blue circles over the edges), i.e. documents that maximize the use of two topics at the same time (e.g., 47 and 91 for (f)). The top documents in (d) targets two topics now.

(*) Choose recommended labels in (g) to explicit the meaning of a topic. Suggested labels given in (h) are based on n-grams scored by different measures, such as the 0-order and 1-order of [START_REF] Mei | [END_REF] and C-order of [Gourru et al., 2018]. For instance, 0-order scores a set of label candidates (in our case, selected by the term identification tool of [START_REF] Lossio-Ventura | [END_REF]) by considering the sum of log probabilities of the words composing the term. Besides, extracted sentences are presented at the very bottom of (h) to help the user to figure out the meaning of a given topic (see [Gourru et al., 2018] for technical details).

(*) See in (i) the coherence of the topic as calculated by several state-of-the-art measures. These measures, such as Umass or UCI mentioned earlier, are calculated with the Palmetto library provided by [START_REF] Röder | [END_REF]. Based on this information, Readitopics allows the user to hide a subset of topics (j).

Overall, the demonstration will focus on showing how i) all this information makes it easier for the human to quickly grasp the topic informational content, and ii) the open challenges in topic labeling and topic coherence. The full sources are available online through a git repository1 .

Additional Requested Information

Type of Demonstration

We choose to present Readitopics in a traditional way. In addition to give an overview of our software at a demonstration booth, we can help the attendees to install it on their computer if it is equipped with Java 8 or above.

List of Requirements

For presenting Readitopics, we only need a table with a couple of chairs. The demonstration can be done on a simple laptop.

Figure 1 :

 1 Figure 1: Overview of Readitopics (online demo available at http://mediamining.univ-lyon2.fr/readitopics/)

https://github.com/Erwangf/readitopics


Antoine Gourru
email: antoine.gourru@univ-lyon2.frjulien.velcin@univ-lyon2.fr

Julien Velcin

Mathieu Roche
email: mathieu.roche@teledetection.fr

Christophe Gravier
email: christophe.gravier@univ-st-etienne.fr

Pascal Poncelet
email: pascal.poncelet@lirmm.fr

United we stand: Using multiple strategies for topic labeling

Topic labeling aims at providing a sound, possibly multiwords, label that depicts a topic drawn from a topic model. This is of the utmost practical interest in order to quickly grasp a topic informational content -the usual ranked list of words that maximizes a topic presents limitations for this task. In this paper, we introduce three new unsupervised n-gram topic labelers that achieve comparable results than the existing unsupervised topic labelers but following di↵erent assumptions. We demonstrate that combining topic labelers -even only twomakes it possible to target a 64% improvement with respect to single topic labeler approaches and therefore opens research in that direction. Finally, we introduce a fourth topic labeler that extracts representative sentences, using Dirichlet smoothing to add contextual information. This sentence-based labeler provides strong surrogate candidates when n-gram topic labelers fall short on providing relevant labels, leading up to 94% topic covering.

Introduction

With the ever-growing information flow, we are facing unprecedented di culties to quickly grasp the informational content on large streams of textual documents. This happens in our daily life when we are browsing social media or syndicated contents, but also in professional processes for which the stakes are to categorize and understand large chunks of documents in an unsupervised setting. Topic models are a solution to tackle this issue. They have been successfully applied to many situations, including historical record analysis, machine translation, sentiment analysis, to name a few [START_REF] Boyd-Graber | Applications of topic models[END_REF]. While topic models make it possible to build sound representations of the di↵erent main topics discussed in the corpus they are draw from, they hardly provide human-friendly outputs. As a consequence, gaining a quick understanding of topics content is a cumbersome task. Interactive topic visualization [START_REF] Kim | Refinery: An open source topic modeling web platform[END_REF] does help in this matter, though they require an in-depth and time-consuming cognitive e↵ort to grasp each topic informational content. This is the compelling rationale for the advent of topic models based on n-grams [START_REF] Wang | Topical n-grams: Phrase and topic discovery, with an application to information retrieval[END_REF] and topic labeling techniques [START_REF] Mei | Automatic labeling of multinomial topic models[END_REF][START_REF] Jey | Automatic labelling of topic models[END_REF]. Such techniques aim at providing a topic label, which means a single or multi-word title that is relevant to represent the informational content being discussed in the documents falling into that topic.

With the existing topic labeling techniques that we will discuss in Section 2, the popular approach for topic labeling is to rely on a single topic labeling technique. This implies a single measure to rank label candidates -therefore assuming the hypothesis that a single measure exists that befits any kind of topic regardless their number, their informational content type, their size, etc. While a single strategy may be overall satisfactory, reaching about 2.0 on average on a 0-3 Likert scale in a unsupervised setting [START_REF] Kou | Automatic labelling of topic models using word vectors and letter trigram vectors[END_REF], it also leaves many topics with very poor labels (0 or 1 on such scale).

In this paper, we investigate how to improve topic labeling. In this context, a new multi-strategy method is proposed with two main functions.

First, we propose in Section 3 three new n-gram topic labeling techniques, called M-Order, T-Order, and document-based labelers. M-Order and T-Order both leverage the odds for label candidates to be generated by the other topics as a background distribution as a penalty, while T-order also demotes label candidates with high score when they are nested in another significant candidate. Document-based labeler investigates the possibility that the best label may be found in a very few number of documents that are central to the category. We discuss how each labeler performs but also how they complement each other by showing that it is possible to reach a 64% improvement when using at least 2 labelers.

The second function of our multi-strategy approach (see Section 4) consists in surrogating labels using sentence information retrieval and showing that they provide a complementary approach for some topics that cannot find a proper fit with n-gram labels. Section 5 concludes and provides further lines of research.

Related work

Topic labeling aims at finding a good label or title to provide a better understanding of what constitutes the homogeneity of a given topic [START_REF] Mei | Automatic labeling of multinomial topic models[END_REF]. Several measures have been proposed to associate either a term or a phrase that roughly summarizes the top-K words associated to a given topic. More recently, [START_REF] Kou | Automatic labelling of topic models using word vectors and letter trigram vectors[END_REF] explored new solutions relying on letter trigram vectors and word embeddings.

Both information-based topic labeling strategies [START_REF] Mei | Automatic labeling of multinomial topic models[END_REF][START_REF] Danilevsky | Automatic construction and ranking of topical keyphrases on collections of short documents[END_REF] and those based on external semantic resources [START_REF] Jey | Automatic labelling of topic models[END_REF][START_REF] Magatti | Automatic labeling of topics[END_REF] only provide a satisfactory labeling e ciency in a subset of topics in a corpus. On a 0-3 Likert scale, [START_REF] Jey | Automatic labelling of topic models[END_REF] achieves 2.03 at best while [START_REF] Kou | Automatic labelling of topic models using word vectors and letter trigram vectors[END_REF] reaches 2.13 at best -and less than 2 in most of the cases. It does not mean that every topic finds a good match (score 2), but that a set of topics achieves 3 whereas another set achieves 1 or even 0. This has been confirmed in our own experiments that show standard deviations from 0.74 to 0.88 (see Table 2). We demonstrate in this paper that in an unsupervised setting, without the need of external semantic resources or user supervision, it is nonetheless possible to achieve results that let most of the topics be associated to a good label.

Another option is to work with representative sentences, which has been successfully integrated into topic-modeling oriented applications [START_REF] El-Assady | Progressive learning of topic modeling parameters: A visual analytics framework[END_REF]. However, their usefulness in how the topic is understood has not been evaluated yet. In particular, in this paper we evaluate to which extent the sentences can complement the n-gram labels.

Other work investigated the use of other modalities for topic labeling, such as images. It turns out that previous work proved that labels based on n-grams showed the best performances when evaluated by human beings [START_REF] Aletras | Evaluating topic representations for exploring document collections[END_REF]. This explains why we focus on n-gram labeling here, with an additional interest in the possibility to enhance topic understanding with sentences as a surrogate.

Topic labeling based on n-grams

First, our multi-strategy approach proposes several labels (i.e., phrases) by using di↵erent statistical ranking measures. In what follows, we score a candidate term t that is a sequence of p consecutive words, also called n-grams: t = (w 1 , w 2 . . . w p ). We consider these candidates as possible labels for a given topic using di↵erent new proposed measures. The probability p(w/z) of word w given topic z and the probability p(z/d) of topic z given document d are given by the topic modeling algorithm (here, LDA).

T-order, M-order and document-based labelers

M-order labeler. Our first contribution aims at improving the 0-order measure [START_REF] Mei | Automatic labeling of multinomial topic models[END_REF] that is computed by P p i=1 log p(wi|z) p(z) . Instead of normalizing by the marginal probability, we use the odds for the candidate to be generated by the other topics as a background distribution. With p (w i |z) the probability for the topic z to generate the ith word of t, we define a first score of relevance M order as follows:

M order(t, z) = p X i=1 log p (w i |z) 1 |Z| 1 P z 0 6 =z p (w i |z 0 )
with Z the set of extracted topics. The denominator penalize the candidates that are also likely to be generated by the other topics than topic z.

T-order labeler. To introduce the notion of "termhood" [START_REF] Katerina T Frantzi | The c-value/nc-value method of automatic recognition for multi-word terms[END_REF], we define that a term t is a short term if it is nested in a longer term t 0 that has a bigger value for some base measure of termhood (e.g., c-value). For example, in a computer science corpus, "Gibbs" would be a short term, because it is usually nested in "Gibbs Sampling" that has a higher termhood. In this case, the term t can be ignored. This post-processing method is akin to the "completeness" measure usage in [START_REF] Danilevsky | Automatic construction and ranking of topical keyphrases on collections of short documents[END_REF]. Finally, the score is divided by the length len of the candidate. We can now define our new measure:

T order(t, z) = ⇢ 0 i f t is a short term 1 len(t) • M order(t, z) else
The score adds a notion of distance maximization between topics to 0-order, and dividing by the term length prevents from favoring long terms too much. The use of a termhood base measure prevents the labels to be terms that are not semantically relevant.

Document-based labeler. In some cases, the best label can be found in a very few number of documents that are central to the category. We define our second new measure by averaging the importance of the set of documents featuring a given term:

Doc Based(t, z) = ⇣ Y d2Dt imp z (d) ⌘ 1 |D t |
where D t is the set of documents in which the term t can be found and imp z (d) stands for the importance of document d in z. We decided to estimate

imp z (d) in two ways. First, doc-based u (d, z) is based on p(z/d) with a natural bias towards short documents. The second measure doc-based n (d, z) is based on p(d/z) / p(z/d) ⇤ p(d)
for a given z. We decided to approximate p(d) by the ratio between the length of d and the total length of the corpus. The rationale of the new measure is therefore to find terms very specific to the topic although they exhibit moderate topic covering.

Evaluation

Methodology. We experiment on two case studies with the LDA model [START_REF] David M Blei | Latent dirichlet allocation[END_REF] and a fixed number of topics k = 100. The maximum number of iteration is set to 2000 and the hyperparameters ↵ and are automatically tuned as explained in [START_REF] Hanna M Wallach | Rethinking lda: Why priors matter[END_REF]. We may do other choices, such as using other topic learning algorithms or setting k to other values. However, we think that the following experimental design is su cient for supporting the claim of this paper.

Datasets. Topic models are drawn from the following datasets:

• Sc-art: a set of 18 465 scientific abstracts gathered by [START_REF] Tang | Cross-domain collaboration recommendation[END_REF] over a period of 16 years. Many contributions in topic visualization and labeling techniques have been applied on similar datasets, on which n-grams seem to provide very relevant labels.

• News-US: a set of 12 067 news we gathered automatically from the Hu ngton Post RSS feeds (US version). This set spans a period of almost 3 months (from June the 20th until Sept. the 8th, 2016). Monitoring news feed is another case study of the utmost practical interest.

After learning topic models, we perform standard post-processing that is removing the topics that present a poor homogeneity. Actually, topics of poor quality would bias our experiments since no labeler will be capable of finding a satisfactory solution. To this end, we compute the Normalized Pointwise Mutual Information (NPMI) of the top 10 words, and we eventually remove the topics with a negative score, as it is shown in [START_REF] Aletras | Evaluating topic coherence using distributional semantics[END_REF] that this score is correlated with human measure of the topic coherence. Therefore, we keep 145 topics (on 200 initial topics) and every annotator had 48 or 49 tasks to complete (2 annotators ⇥ 145 topics / 6). Each task corresponds to the evaluation of two types of elements: (i) evaluation of candidate labels (i.e. words and/or phrases), (ii) evaluation of representative sentences.

As in previous works, the evaluation consists in measuring how well an ngram candidate labels the topic on a Likert scale. A scale of five points is used in [START_REF] Danilevsky | Automatic construction and ranking of topical keyphrases on collections of short documents[END_REF] and four in [START_REF] Li | Labeling clusters from both linguistic and statistical perspectives: A hybrid approach[END_REF][START_REF] Kou | Automatic labelling of topic models using word vectors and letter trigram vectors[END_REF]. Our four points scale is presented on Table 1; it was constructed so that we can easily compare our results to the literature. We called six computer scientists as human annotators. The annotation task aims at evaluating the three main n-gram labels provided by the di↵erent labelers for a given tuple (dataset, topic). For any given tuple to annotate candidates were ranked randomly and the annotators were blind to the kind of labeler which generated each label. Each annotation was given to two annotators in order to calculate an agreement score. For a given annotation task, we provided five documents that maximize p(d|z), three documents that maximize p(z|d), plus the thirty top words with their associated probabilities, as in [START_REF] Li | Labeling clusters from both linguistic and statistical perspectives: A hybrid approach[END_REF].

The three most highly ranked labels were evaluated, either they have been computed by the basic measures of [START_REF] Mei | Automatic labeling of multinomial topic models[END_REF] or by our own measures presented in Section 3.1. The 0-order was computed with both uniform and frequency-based background distribution. The T-order was computed using the LIDF-value from [START_REF] Antonio | Biomedical term extraction: overview and a new methodology[END_REF] as a termhood measure, which seems to provide better results than the other termhood scoring measures after a preliminary screening. We choose not to limit the labeling candidate to be a bigram set, but to keep any length for the labels. The candidate generation was performed using the BioTex API6 [START_REF] Antonio | Biomedical term extraction: overview and a new methodology[END_REF].

Results. Table 2 shows the average score (from 0 to 3) of the top-3 results of the labeling systems. Max-Score is the upper bound, which corresponds to selecting the score of the system that achieves the highest score for every topic. As it was presented earlier, the annotator was able to give some qualitative information when rating with 2: "it is too broad" or "it is too precise". The distribution by labeler is provided in Table 2. The kappa shows a fair agreement (0.34,0.49,0.51) that allows us to look for an automated labeling recommender system. One first observation is that the simple 0-order unif orm is clearly better than the others for the Sc-Art dataset (1.63 against 1.24), but the T-order measure outperforms it for the News-US dataset (1.27 against 1.1). As it is well illustrated in Table 2, labeling systems are not always good (maximum 1.36 on average), but there is (almost) always a labeling system that is able to provide a good label (2.33/3 on average). This means that we can expect an improvement of about 64% in the labeling task. Tables 3 and4 give a more concrete illustration of that idea on a selected set of topics.

An important result is that with 90% of the evaluated topic, a good label (meaning rated 2 or 3) is found. We name this amount as the covering of the labeling strategy. When we reduce the labels to those produced by the T-order and the 0 order unif orm only, there is a good label 83% of the time. A labeler alone can only achieve a good score at best for 63% (0 order unif orm ) and 62% (T order) of all topics.

Discussion. The presented results mean that even with a very small set of proposed labels, one can access the inner semantic content of a given topic. In the case of the two datasets we experiment on, we only need six labels (meaning, Table 4: The words in bold where rated 3, the others 1. We see that for some topics the 0-order is able to find a good label whereas it is the T-order for other topics.

three labels produced by two labelers, if there is no overlap). On average, among these six labels, 15% are rated as unrelated, 46% as related, 29% as good label and 9%as perfect label, 1% have been rated "I don't know".

If we consider 2 and 3 as good labeling scores, the precision is about 38% (29%+9%), even though the other answers are not totally wrong. For instance, the topic 3 presented in Table 3 gets the following labels (0-order followed by Torder labels): "bipolar disorder, depression, anxiety, national suicide prevention lifeline, mental health disorder, mental health care".

The presented results can be thought as over-optimistic: they need further experiment on other various datasets (e.g., book series or blog posts) and we know that within the labels given to the users there is still unrelated/non relevant items (in our case, about 15% of the proposed labels). This is the reason why we need to find advanced strategies to a) improve the quality of the recommended T-order+0 order unif orm 83

Table 5: Performance of the labeling systems, meaning the percent of a least one good label (rated 2 or 3) in the top-3 labels labels, b) complete the labels when the n-gram based approach is not su cient to fully capture the inner semantics. Regarding (a), we can naturally think at integrating other features than the relation between topic-word probabilities and the candidate label. For instance, we can add features related to the topic (importance of the topic, skewness of the word distribution, etc.) or to the dataset (for instance, longer n-grams can be favored in scientific datasets). We can also follow the work of Lau et al. [START_REF] Jey | Automatic labelling of topic models[END_REF] in leveraging more supervision in the labeling process.

Regarding (b), it seems that for some cases, the n-gram labelers can never achieve a satisfactory output. This is the reason why we propose, in the next section, to leverage information retrieval techniques to find relevant sentences.

Topic-relevant sentence extraction

In the second function of our multi-strategy approach, di↵erent representative sentences are proposed in order to identify the semantic content of the topics.

Rationale

Would no n-gram labeler yields an acceptable label candidate, looking for representative sentences from the corpus is another solution to label a topic. For example, the labels returned by all the n-gram based systems for the two topics in Table 6 were rated low (the maximum score being 0 for the first and 1 for the second). But we can find sentences that were well rated, as shown in Table 7.

Sentence extraction solution

With this fourth new labeling technique, we assume that an information retrieval procedure can be used to post-process the top documents (considered as the "context") and look for representative sentences. The top documents, i.e. the documents that maximize p(d/z), are split into sentences. We propose to use a Dirichlet smoothing to add contextual information. We define , the context distribution of a document collection, by:

w = c(w, C) P w2V c(w, C) (1)
where c(w, C) counts the frequency of word w in the context C. With µ as a positive real number, we obtain the following language model:

✓ x w = c(w, x) + µ w len(x) + µ (2)
where c(w, x) stands for the frequency of word w in the candidate sentence x.

We can then compute di↵erent distance measures between the sentence vector representation and the topic. We choose to compute a negative Kullback-Leibler distance, like [START_REF] Mei | Automatic labeling of multinomial topic models[END_REF], and a simple cosine similarity. If µ = 0, the ✓ x w calculated is a simple TF representation of the sentence. The greater µ is, the more importance we give to the context (the top documents). Our model is parameterized by: (more precisely, the number of top documents | | we choose to keep) and µ (the amount of context we want to take into account).

Evaluation

We experiment with the same models and datasets than the n-gram evaluation of the previous section. We choose to ask the following question: "Does the sentence give a clear understanding of the topic content?". Then, the rater could choose between "yes", "no", or "don't know". The systems are presented in Table 9. We choose to compare our systems with random sentences, extracted from documents that do not maximize p(d/z). We call Rand this system based on random sentences. As for the n-grams evaluation in previous section, a weighted Kappa was computed for every annotator pair. The results are similar: it is not really high (0,23, 0.36, 0.04), but su cient for a significant agreement. Table 9 presents the average proportion of extracted sentences tagged as 1 (answer "yes" to the question: "Does the sentence give a clear understanding of the topic content?"). It shows that a simple cosine based on a TF vector using the top 10 documents is better, without the need of smoothing. However, a closer look shows that B20 0.1 (meaning a really small smoothing) is slightly better for News-US.

We can now wonder whether sentences can be combined with n-gram labels to improve the overall topic understanding. For instance, we can estimate the proportion of topics for which we can find at least one good n-gram label (with 0-order or T-order) and, if we cannot, one sentence otherwise. The performance goes from 83% covering up to 93% with the COS 15 labeler. This improvement can be seen even with no agreement among the last annotator pair. If we ignore the annotations attributed by the last annotator pair (weighted Kappa of only 0.04), the covering goes even until 94%.

Conclusion

Finding a suitable textual description of the output of a statistical model is still a di cult task that can be related to interpretable machine learning. In this paper, we introduced three new n-gram topic labelers that are at least on par with the existing labeling technique. A key observation is that those new labelers are complementary labelers to the best known so far (0-order labeler) so that when one of them is combined with the 0-order labeler, the resulting combined labeler provides labels scoring 2 or more on a 0-3 Likert scale. A direct application of this consists in a simple recommender system that suggests a limited set of labels (e.g., the labels produced by T-order and 0 order unif orm ) that are mostly of good quality. When expanding such a combined n-gram labeler with extracted sentences from the corpus as surrogate labels for di cult labeling cases, it is possible to reach the same performance for 94% of the topics to label.

There is still room for future research. First of all, we can consider the covering we get as a good recall, but the precision (meaning, the proportion of really good labels among the labels returned by the system) needs to be improved. If we are able to automatically choose the perfect labeler for each case, this will constitute an important improvement 7 . If we assume that the user can still have di culties for selecting the best labels for some topics, we might adopt a semisupervised system following [START_REF] Jey | Automatic labelling of topic models[END_REF]. Another track would be to define a label as a combination of n-grams and sentences that are complementary for they propose di↵erent views over the targeted topic. The must would be to generate a small paragraph that summarizes the underlying topic semantics.

Topic 1 (

 1 News-US) Topic 2(Sc-Art) Topic 3(News-US) Topic 4(Sc-Art)

Topic 5 (

 5 photo facebook posted media 2016 social pdt online jul app 39 internet instagram video aug google jun users 34 site

Table 1 :

 1 Our Likert Scale

	Score Description
	3 Yes, Perfectly
	2.a Yes, but it is too broad
	2.b Yes, but it is too precise
	1 It is related, but not relevant
	0 No, it is unrelated

Table 2 :

 2 Average score for the top-3 labels proposed on a Likert scale from 0 (unrelated) to 3 (perfect). details the average standard deviations for the two datasets.

	Top-3	News-US Sc-Art All
	Max-Score	2.23	2.40 2.33	Too Broad Too Precise
	T-order	1.27	1.24 1.26 0.81	13%	15%
	M-order	1.25	1.20 1.22 0.8	13%	14%
	doc basedn	0.98	1.12 1.05 0.74	4%	16%
	doc basedu	1.03	1.17 1.10 0.75	4%	17%
	1-order	1.07	1.31 1.19 0.84	8%	16%
	0 order unif orm	1.10	1.63 1.36 0.82	7%	24%
	0 order f requence	1.18	1.23 1.20 0.88	9%	17%

Table 6 :

 6 Example of two topics badly labeled by n-grams.

	Topic Example of sentence returned by our systems
	5	Aphoto posted by Laura Izumikawa Choi (@lauraiz) on Jun 17, 2016 at
		11:05am PDT
	6	So 'follow' or 'Like' them on social media sites like Twitter, Facebook,
		LinkedIn, Google + and Pinterest

Table 7 :

 7 Two extracted sentences that can help the user capturing the meaning of topics 5 and 6 given in Tab. 6 (words occurring in top words are highlighted in bold).

Table 8 :

 8 Evaluated systems with di↵erent parameters' values.

	name	similarity	µ	| |
	COS10	cosine	0	10
	COS15	cosine	0	15
	COSIDF 15	cosine	0 (IDF weighted) 15
	B100,1	negative KL divergence	0.1	10
	B1010	negative KL divergence	10	10
	B101000 negative KL divergence	1000	10
	B200,1	negative KL divergence	0.1	20
	B2010	negative KL divergence	10	20
	B201000 negative KL divergence	1000	20

Table 9 :

 9 Percent of relevance, meaning the proportion of topics correctly illustrated by the sentence.

	System News-US Sc-Art All	System News-US Sc-Art All
	Rand	1%	6%	4%	B1010	34%	38% 36%
	COS10	34%	46% 41%	B101000	25%	28% 27%
	COS15	35%	45% 40%	B200.1	40%	31% 35%
	COSIDF 15	22%	30% 26%	B2010	34%	37% 36%
	B100.1	38%	33% 35%	B201000	25%	26% 26%

http://tubo.lirmm.fr/biotex/

Acknowledgments: This work is partially funded by the SONGES project (Occitanie and FEDER).


Emile Devillers

Michel Hecquet

Xavier Cimetière

Jean-Philippe Lecointe

Jean Le Besnerais

Thierry Lubin

Experimental Benchmark for Magnetic Noise and Vibrations Analysis in Electrical Machines

Keywords: Electric machines, Magnetic forces, Noise, Vibrations, Experimental, Test bench

This article presents an experimental setup dedicated to the analysis of magnetic noise and vibrations in radial flux electrical machines. Both electromagnetic excitation and structural response of the electrical machine are simplified to provide the first benchmark of the phenomenon of electromagnetically-excited noise and vibrations. The test bench properties as well as the magnetic, vibration and acoustic upcoming extensive measurements are shared to the scientific community, providing a clear reference case to compare different modeling and simulation approaches.

I. INTRODUCTION

The vibro-acoustic performances of an electrical machine at variable-speed is a key factor in its design along electromechanical and thermal performances. Including the emitted noise and vibrations level in the design process requires a dedicated multi-physics simulation which weakly couples electromagnetic, structural mechanics and acoustic models [START_REF] Gieras | Noise of polyphase electric motors[END_REF], as shown in Figure 1. In particular, both electromagnetic and mechanical models have to be finely detailed to accurately compute the time and space distribution of the electromagnetic forces and the resulting vibration level of the machine's structure. Besides, for variable-speed machines such as traction machines, the simulation has to be performed for several points of the speed cycle to assert potential resonance issues between magnetic forces and structural modes of the machine [START_REF] Boesing | Exploring a Vibration Synthesis Process for the Acoustic Characterization of Electric Drives[END_REF], [START_REF] Besnerais | Prediction of Audible Magnetic Noise Radiated by Adjustable-Speed Drive Induction Machines[END_REF].

Therefore, this multi-physics modeling often requires a high level of discretization over time, space and speed operating points. Even if numerical models enable to accurately predict noise and vibrations levels, they are too much timeconsuming to be systematically used at early design stages [START_REF] Pellerey | Coupled Numerical Simulation Between Electromagnetic and Structural Models. Influence of the Supply Harmonics for Synchronous Machine Vibrations[END_REF], especially in presence of high frequency phenomenon such as Pulse Width Modulation (PWM) [START_REF] Besnerais | Characterization and Reduction of Audible Magnetic Noise Due to PWM Supply in Induction Machines[END_REF], [START_REF] Boesing | Modeling spatial harmonics and switching frequencies in PM synchronous machines and their electromagnetic forces[END_REF]. Hence, E.Devillers is with the L2EP laboratory, Univ. Lille, Centrale Lille, Arts et Metiers ParisTech, HEI, EA 2697, F-59000 Lille, FRANCE. He is also with the EOMYS ENGINEERING company, 59260 Hellemmes, FRANCE (email: emile.devillers@phd.centralelille.fr).

M.Hecquet is with the L2EP (email : michel.hecquet@centralelille.fr). X.Cimetière is with the L2EP (email : xavier.cimetiere@centralelille.fr). J-P.Lecointe is with the LSEE laboratory, Univ. Artois, EA 4025, F-62400 Bthune, FRANCE (email : jphilippe.lecointe@univ-artois.fr).

J.Le Besnerais is with EOMYS ENGINEERING (email : jean.lebesnerais@eomys.com).

T.Lubin is with the GREEN laboratory, Univ. Lorraine, EA 4366, F-54500 Vanduvre-ls-Nancy, FRANCE (email : thierry.lubin@univ-lorraine.fr). Fig. 1. Multi-physics modeling for noise and vibration assertion in electrical machines [START_REF] Manatee | Magnetic Acoustic Noise Analysis Tool for Electrical Engineering[END_REF]. analytical and semi-analytical models have been developed to quickly and accurately estimate the vibro-acoustic behavior of electrical machines [START_REF] Besnerais | Fast prediction of variable-speed acoustic noise due to magnetic forces in electrical machines[END_REF]. The main (semi-) analytical electromagnetic models are the Permeance-MagnetoMotive Force model (PMMF) [START_REF] Timar | Noise and vibration of electrical machines[END_REF] and the SubDomain Model (SDM) [START_REF] Boisson | Analytical approach for magnetic and acoustic modeling of flux-switching permanent-magnet motors: Application to geometrical optimization[END_REF], followed by the Magnetic Equivalent Circuit (MEC) model. PMMF, SDM, MEC and Finite-Elements (FE) models are qualitatively compared in Table I [START_REF] Devillers | A review of subdomain modeling techniques in electrical machines: Performances and applications[END_REF].

Concerning the structural mechanics, many analytical models are applicable to predict the dynamic response of the machine's external structure. They mostly consist in representing the structure as an equivalent isotropic thin cylindrical shell or thick cylinder whose mass and stiffness have been pondered to include teeth and windings effect [START_REF] Gieras | Noise of polyphase electric motors[END_REF], [START_REF] Timar | Noise and vibration of electrical machines[END_REF], [START_REF] Jordan | Electric motor silencer-formation and elimination of the noises in the electric motors[END_REF], [START_REF] Verez | Natural Frequencies Analytical Modeling of Small Industrial Radial Flux Permanent Magnet Motors[END_REF]. The mechanical behavior of the equivalent structure is assumed to be linear. Then the dynamic response is obtained using Electromagnetic Vibration Synthesis (EVS), which consists in the superposition of the contribution of each harmonic of force pondered by its Frequency Response Function (FRF) [START_REF] Boesing | Noise and Vibration Synthesis based on Force Response Superposition[END_REF]. The FRF are previously computed using analytical unit-magnitude rotating force waves [START_REF] Roivainen | Unit-wave response-based modeling of electromechanical noise and vibration of electrical machines[END_REF]. The noise level is finally asserted based on the vibration velocity and the radiation factor of machine's external surface [START_REF] Gieras | Noise of polyphase electric motors[END_REF].

However, several key aspects of the multi-physics modeling are still under investigation in the literature, such as:

1) the interaction between radial and tangential air gap forces and their influence on yoke's radial vibrations [START_REF] Devillers | Tangential effects on magnetic vibrations and acoustic noise of induction machines using subdomain method and electromagnetic vibration synthesis[END_REF], especially for electrical machines with few teeth and a large tooth length to yoke thickness ratio. In many analytical studies the tangential forces are neglected as their magnitude in much smaller than the one of radial forces [START_REF] Gieras | Noise of polyphase electric motors[END_REF], [START_REF] Besnerais | Prediction of Audible Magnetic Noise Radiated by Adjustable-Speed Drive Induction Machines[END_REF]. 2) the spatial sampling effect of tooth on the air gap magnetic field. In case of under-sampling, force harmonics with high spatial orders may excite lower structural modes due to aliasing effect. This phenomenon exists in topologies where the number of teeth is close to the number of poles [START_REF] Fang | Modulation Effect of Slotted Structure on Vibration Response in Electrical Machines[END_REF]; 3) the computation of magnetic forces applied to a slotted structure, regarding the method formulation which depends on the electromagnetic model (mainly Virtual Work Principle for FEM [START_REF] Coulomb | Finite Element implementation of Virtual Work Principal for magnetic or electric force and torque computation[END_REF] versus Maxwell Stress Tensor for (semi-) analytical models [START_REF] Gieras | Noise of polyphase electric motors[END_REF], [START_REF] Devillers | A review of subdomain modeling techniques in electrical machines: Performances and applications[END_REF]) and also on the modeling assumption (either local (or nodal) forces applied everywhere on the surface or lumped forces (resultant) applied on each tooth) whose equivalence is still under discussion [START_REF] Pile | Comparison of main magnetic forces computation methods for vibro-acoustic in electrical machines[END_REF]. 4) the noise and vibrations reduction strategies including passive reduction (such as rotor and/or stator skewing [START_REF] Blum | Investigation of the segment order in step-skewed synchronous machines on noise and vibration[END_REF], [START_REF] Yang | Acoustic Noise/Vibration Reduction of a Single-Phase SRM Using Skewed Stator and Rotor[END_REF], rotor and/or stator notching [START_REF] Zhou | Rotor Notching for Electromagnetic Noise Reduction of Induction Motors[END_REF], [START_REF] Lan | Influence of dummy slots on noise and vibration performance in permanent magnet synchronous machines[END_REF], magnetic wedges [START_REF] Besnerais | Fast prediction of variable-speed acoustic noise due to magnetic forces in electrical machines[END_REF], flux barriers [START_REF] Dajaku | A novel 12-teeth/10-poles PM machine with flux barriers in stator yoke[END_REF], etc.) and active reduction through control strategy (current injection [START_REF] Cassoret | Magnetic noise reduction of induction machines[END_REF], [START_REF] Franck | Active reduction of audible noise exciting radial forcedensity waves in induction motors[END_REF], effect of stator current load angle [START_REF] Zhu | On the effect of stator excitation on radial and tangential flux and force densities in a permanent magnet synchronous machine[END_REF], damper winding [START_REF] Bauw | Damper winding for noise and vibration reduction of PWM-fed induction machines[END_REF], etc.).

Therefore, this paper deals with the design of an electrical machine prototype which aims at illustrating and answering all of the above research axes about noise and vibrations due to magnetic forces in electrical machines. This is the first part of a benchmark project on vibro-acoustics of electrical machines which wishes to improve the scientific comprehension on the topic by sharing publicly all data (including design, materials etc.) and deeply discussing the results.

As a first part of the project, this paper mainly focuses on the choice of the prototype's design to achieve the benchmark purposes. The adopted design is a Surface-mounted Permanent Magnet Synchronous Machine (SPMSM) with 12 stator slots and 5 pole pairs (12s10p). This choice results from several considerations on how to generate noise and vibrations in electrical machines, resulting from a pre-design based on the analytical multi-physics modeling presented in the introduction.

Then, all the prototype's characteristics are detailed including geometry and materials properties. The final design is validated with a simulation study performed on MANA-TEE [START_REF] Manatee | Magnetic Acoustic Noise Analysis Tool for Electrical Engineering[END_REF], a simulation software specialized in the integrated electromagnetic and vibro-acoustic design of electrical machines. The last section describes the test bench and the different steps of the experimental benchmark, including magnetic, vibration and noise measurements.

II. DESIGN APPROACH AND SPECIFICATIONS

The main design constraint imposed to the prototype is the ability to magnetically excite several modes of the external structure in the audible frequencies. The different modes should occur at distant natural frequencies so that each resonance phenomenon can be clearly isolated and identified.

Another constraint concerns the magnetic forces production. For the sake of clarity, the prototype's design is intentionally simplified to only tackle the intrinsic complexity of magnetic forces and structural interaction. As said previously, this complexity mostly resides in the computation, projection and superposition of magnetic forces on a slotted structure including tangential and under-sampling effects (see objectives 1)-3) in the Introduction). It is easier to study these physical aspects if the harmonic content of the magnetic forces is finite, discrete, sparse and unambiguously identifiable.

Then, the slots must be sufficiently deep and large to place accelerometers on the teeth sides to observe tangential vibrations. In fact, this constraint agrees with the objective of observing tangential effects, as long teeth should emphasize the yoke displacement due to the tooth bending induced by tangential forces. Likewise, assuming large slots naturally limits the maximum number of slots hence it increases the under-sampling effect for a given number of poles.

Besides, the air gap has to be large enough to insert a network of eddy-current coil sensors and measure the time and space distribution of the air-gap flux density. To the author's knowledge, such measurement has not been carried out yet inside the air gap of electrical machines and is one of the benchmark's main original features. The influence of a large air gap on the previous constraints is mitigated. The larger is the air gap, the more spatial harmonics with high wavenumbers are filtered, but the lower are the tangential forces applied on teeth, as a direct consequence of filtering slotting harmonics.

Finally, the chosen design must comply with the assumptions of the (semi-)analytical magnetic and acoustic models presented in the introduction, in particular:

• the SubDomain Method (SDM) for electromagnetic field computation, which implies polar geometry and magnetic linearity of ferromagnetic parts ; • acoustic analytical radiation factor including the radiation of the support frame ;

Concerning the structural modeling, investigating the interaction between magnetic forces and slotted structures is obviously contradictory with validating the structural models based on slotless equivalent cylinders. Hence the main contribution on the structural side consists in investigating and pushing the limits of the analytical structural models to estimate natural frequencies and tangential effects.

The next section explains the choice of the SPMSM 12s10p topology based on a pre-design using the classic analytical structural regarding the previous constraints. The predesign follows a reverse engineering methodology, starting from the vibro-acoustics considerations, deducing the best electromagnetic excitation thus giving the final topology.

III. DISCUSSION ON THE PROTOTYPE DESIGN

A. Magnetic Forces Specifications

In this analytical pre-design, the slotted structure is transformed into an equivalent cylindrical structure. As the magnetic force is continuously applied on the interface between the air gap and the cylinder, the excitation can be equivalently seen as a force or a pressure. Furthermore, the tangential pressure is neglected as it cannot induce a radial displacement of the cylinder. The harmonic content of time and space distribution of the radial magnetic pressure p rad (t, θ) is determined by performing a 2D Fourier Transform :

p rad (t, θ) = ( n=+∞ n=-∞ r=+∞ r=-∞ P rad n,r e j(2πnf t-rθ) ) (1)
where:

• P rad n,r is the complex magnitude of the harmonic (nf, r), with the magnitude: P rad n,r = | P rad n,r | and the phase: φ n,r = arg( P rad n,r ). As p rad (t, θ) is a real signal, conj( P rad n,r ) = -P rad -n,-r which reduces the relevant harmonic content only to the positive frequencies.

• (nf, r) is the couple of frequency and wavenumber for each harmonic. f is the synchronous frequency. n is a positive integer for synchronous machines and is real positive for induction machines. r is a relative integer; ¡ Fig. 2 shows the first spatial harmonics of the air gap radial pressure at a specific instant, for the adopted SPMSM topology. The real slotted geometry is represented in blue dotted line and the equivalent cylinder is the continuous external black ring. It can be seen that the main spatial harmonics of pressure are at r = 0, r = 2p = 10 and r = Z s = 12. However, these pressure harmonics interact differently with the structure. In fact, the induced vibration level generally depends more on the frequency order and the wavenumber of the pressure harmonic than on its magnitude in case of resonance effect. The next subsection qualitatively explains the influence of the mode order and the geometrical parameters on the induced vibration level.

B. Vibration Specifications

The complex vibration level V d n at a given frequency derives from the dynamic displacement Ū d n of the external structure:

V d n = j2πnf Ū d n (2)
The dynamic displacement Ū d n is obtained from the Electromagnetic Vibration Synthesis (EVS), which consists in summing each harmonic of pressure P rad n,r=m weighted by the corresponding spatial FRF of mode order m:

Ū d n = r=+∞ r=-∞ F RF (nf, r) P rad n,r=m (3)
The Frequency Response Function (FRF) can be actually defined as the dynamic displacement of the external structure subject to a unit-magnitude rotating force waves (meaning P rad n,r=m = 1) with a certain frequency nf and wavenumber r. The FRF can be computed using analytical models of equivalent cylinders [START_REF] Besnerais | Prediction of Audible Magnetic Noise Radiated by Adjustable-Speed Drive Induction Machines[END_REF], [START_REF] Jordan | Electric motor silencer-formation and elimination of the noises in the electric motors[END_REF], finite-element models [START_REF] Boesing | Vibration Synthesis for Electrical Machines Based on Force Response Superposition[END_REF] or experimental modal analysis. The FRF accounts for potential resonances between each force harmonic P rad n,r=m = 1 and structural modes of order m associated to their natural frequency f m . Under the common assumption of neglecting under-sampling effect, the resonance occurs when:

r = m & nf ≈ f m (4)
For m ≥ 2, the classical analytical models as in [START_REF] Besnerais | Prediction of Audible Magnetic Noise Radiated by Adjustable-Speed Drive Induction Machines[END_REF] show that natural frequencies increase according to the mode order m at the power of 2. f 0 and f 1 are usually much higher than the first natural frequencies f m , due to the cylinder's stiffness. Natural frequencies also increase with the dimensionless geometrical ratio R sy /h sy , where R sy is the cylinder outer radius and h sy its thickness.

An analytical study also enables to show the influence on mode order and geometry parameters on the FRF. FRF maximum peak increases with the dimensionless geometrical ratio R sy /h sy and decreases with the mode order at the power of 4 for mode orders m ≥ 2. The structure acts like a lowpass filter on the wavenumbers, as displacements for m = 10 and m = 12 are much smaller than for low modes such as m = 0 ("breathing mode") and m = 2 ("ovalization mode"). The FRF for m = 0 and m = 1 have naturally their maximum peak higher than for low modes as they appear around their corresponding natural frequency.

It is worth mentioning that mode m = 1 can be excited in presence of Unbalanced Magnetic Pull (UMP), due to the existence of force harmonics with wavenumber r = 1 (induced by eccentricity, irregular magnetization, fractional winding etc.). Exciting this mode should be avoided for the prototype because it creates mechanical eccentricity and lots of parasitic forces.

As a conclusion, the prototype should generate noise and vibrations due to the excitation of low-order structural modes, in order to increase the vibration level and have the lowest values of natural frequencies. The ovalization mode (for m = 2) has the lowest natural frequency and is the easiest one to be excited for the benchmark purposes. Its naturally frequency can be adjusted in the audible range by setting properly the stator dimensions. Consequently, the magnetic field should create force harmonics of wavenumber r = 2 to excite the ovalization mode.

C. Magnetic Field Specifications

The aim is to produce force harmonics of wavenumber r = 2. The magnetic force waves are created by the interaction of rotating magnetic field waves. In fact, a single rotating field wave is sufficient to create a rotating force wave and excite the structure as it is shown thereafter. The pressure distribution is given by the Maxwell Stress Tensor, such as:

p rad (t, θ) = B rad (t, θ) 2 -B tan (t, θ) 2 2µ 0 [N.m -2 ] (5) p tan (t, θ) = B rad (t, θ)B tan (t, θ) µ 0 [N.m -2 ] (6)
where p rad and p tan are the radial and tangential components of the magnetic pressure, B rad and B tan are the radial and tangential components of the flux density and µ 0 is the void magnetic permeability.

The same Fourier transform as in Eq. ( 1) can be done to the tangential forces and tangential flux density distributions. It is worth mentioning that both components have the same harmonic content, only the complex magnitudes differ [START_REF] Devillers | Tangential effects on magnetic vibrations and acoustic noise of induction machines using subdomain method and electromagnetic vibration synthesis[END_REF]. For the numerical computation of Fourier transform, the series are truncated to a finite number of frequency and wavenumber values, respectively N and R. Using the convolution approach, the complex magnitude of the exciting pressures is related to those of the radial and tangential flux densities as follows [START_REF] Rothe | Convolution approach for analysis of magnetic forces in electrical machines[END_REF]:

P rad n,r = Brad n,r * Brad n,r -Btan n,r * Btan n,r 2µ 0 ( 7
)
P tan n,r = Brad n,r * Btan n,r µ 0 ( 8
)
where P tan n,r is the complex magnitude of the tangential force harmonics, Brad n,r and Btan n,r are the complex magnitude of the radial and tangential flux density harmonics and * is the convolution operator such as:

Xn,r * Ȳn,r = 1 4N R l=N l=-N k=R k=-R Xl,k * Ȳn-l,r-k (9)
In conclusion, due to the convolution product, a flux density harmonic either interacts with itself if X = Y , l = n -l and k = r -k, or it interacts with another harmonic with different frequency order and wavenumber. A force harmonic with a low non-null wavenumber is obtained as soon as two different flux density harmonics with close wavenumbers combine themselves, even if they are flux density harmonics with high wavenumbers. This implies that the flux density spectrum should not actually be sparse to have harmonics with close wavenumbers.

Besides, force harmonics with odd wavenumbers only exist if there are both even and odd wavenumbers in the flux density spectrum. Therefore, the flux density spectrum should exclusively contain either even or odd wavenumbers to avoid exciting odd orders of structural mode, in particular m = 1.

Finally, Eq. ( 9) also shows that X non-null harmonics of flux density create exactly 2X -1 components in the pressure's spectrum. Therefore, reducing the harmonic content of the flux density reduces twice as much the one of the magnetic forces.

D. Topology Specifications

In real machines, the flux density's harmonics content is mainly due to the following factors:

• the discretization of the magnetic sources along the air gap (winding distribution, magnetization pattern etc.) which produces non-sinusoidal spatial MMF; • the variation of the air gap permeance due to stator and rotor slotting effects, saturation, pole shaping etc. which modulates the MMF in time and space; • the voltage control (such as PWM) which generates additional time harmonics in the stator current waveform. • fault situations or manufacturing tolerances, such as demagnetization, eccentricities, broken bar etc. Then, the sparsity of the flux density spectrum depends on the periodicity of the time and space distribution of the flux density. The spatial periodicity depends on the main topology's parameters: number of poles, phases, stator and rotor slots. The time periodicity depends on the AC supply periodicity. It also depends on if the rotor mechanical speed is synchronous or not. In induction machines, the mechanical slip generates asynchronous harmonics which coexists with synchronous ones and causes spectral leakage, except for particular values of slip. Besides, there are naturally more harmonics in induction machines than synchronous machines at variable speed due to rotor slotting and local saturation. Due to these drawbacks, induction machines are eliminated from the available topologies.

Thus the prototype is chosen among the different topologies of synchronous machines, which actually mostly differ on the rotor topology: Surface PM, Interior PM, Wound Rotor (WR), Synchro-Reluctant (SyRM). The main advantage of PM and wound rotors compared with SyRM is the ability to excite the stator only with the rotor field, hence mechanically separate the magnetic excitation from the excited structure. Besides, it does not require PWM to generate a rotating field at variable frequency, which would add many new harmonics of force. However, the rotor has to be driven by an external motor which increases the cost and the technical complexity of the test bench. Indeed, the driving machine must be vibro-acoustically isolated from the prototype to cancel any perturbations on the prototype's measurements.

The SPM rotor topology is finally retained as it is free from rotor slotting and saturation effects at no-load, which is not the case of IPM and WR.

The last step of the pre-design consists in choosing the number of pole pairs p and stator slots Z s of the SPMSM prototype, which automatically sets the spatial periodicity of the magnetic field and forces. They must be chosen in oder to produce at least force harmonics of wavenumber r = 2 and excite the ovalization mode. In SPMSM at no-load, the lowest non-zero wavenumber r min is given by the well-known GCD rule:

r min = GCD(Z s , 2p) = 2 (10)
If Z s is even and p = 1, r min = GCD(Z s , 2) = 2 so the condition is fulfilled. However, it disagrees with the constraint of choosing a close number of poles and stator teeth, which is required to study the under-sampling effect. Besides, increasing the number of poles enables to reduce the rotating speed N of the driving machine and therefore the mechanical tolerances of the test bench. The 12s10p design is finally retained because it is a realistic topology which is also known to be particularly noisy.

With this topology, there are two harmonics of order r = 2 at 8f and 10f which can excite the ovalization mode between N = 2000 and 5000 RPM, depending on the natural frequency. However, these are not the highest excitation harmonics of order r = 2. The highest one is the first stator slot harmonic at (2f, Z s -2p). It excites the ovalization mode if 2f ≈ f 2 , meaning N = 60f /p ≈ 6f 2 RPM, which requires a high speed driving machine.

IV. TEST BENCH PROPERTIES AND MEASUREMENTS

A. Setup and parameters

The main parameters of the prototype are detailed in Fig. 3 and Table II. The air gap measures 2.5 mm in order to setup the air gap flux density sensor. The slot is sufficient wide to stuck tri-axis accelerometers on the side of the tooth in order to measure radial and tangential vibrations at tooth tips. The lamination stack is pressurized by two lateral rings joined by four bolts. The lateral rings have holes to enable passing of instrumentation wires. The test bench including the prototype and the driving machine is illustrated on Fig. 4. The driving machine is a DC machine for the easy variable speed command. Both machines are coupled with an axial flux magnetic coupling to limit the direct torque and axial force ripple transmission. They are fixed on two independent T-slot tables which are fixed on a common base frame. Silent blocks are screwed between T-slot tables and the base frame to reduce the vibration transmission through the base frame. Hence the test bench is robust to shaft eccentricity and misalignment between the two machines and the prototype is vibrationally isolated from the driving machine.

B. Magnetic simulation and experimental validation

The flux density is computed using the Subdomain method (SDM) including ferromagnetic parts with linear finite permeability [START_REF] Dubas | New Scientic Contribution on the 2-D Subdomain Technique in Polar Coordinates: Taking into Account of Iron Parts[END_REF], as shown on Fig. 5. SDM is validated with finite-element analysis and experimentation. First, the real magnetization pattern is checked by measuring the flux density on all the rotor surface using a Hall effect probe and compared with 3D FEA (not shown in this article). Then, the flux density in each tooth is experimentally obtained by measuring the induced voltage in coils surrounding each tooth (represented on Fig. 5). The comparison is shown on Fig. 6 for the first tooth at 500RP M and a good agreement is found between experiment and simulation.

C. Stator modal analysis

The stator experimental modal analysis is performed in the test bench condition. The lamination stack is pressurized by four bolts with a tightening torque of 7N.m. The tightening torque has an effect on natural frequencies (not illustrated here) and must be known to fit with simulation models. The mode m = 0, 2, 3, 4 respectively appear at f 0 = 7536Hz, f 2 = 720Hz, f 3 = 1495Hz, f 4 = 2424Hz. The ovalization mode m = 2 is easily excitable with the surface PM rotor as explained in Section III-D. The global FRF including all structural modes is illustrated on Fig. 7 and the experimental modal shapes are reconstructed on Fig. 8. Other peaks appear between f 4 and f 0 due to resonance with both circumferential and longitudinal modes.

V. CONCLUSION AND PERSPECTIVES

This article presents a test bench for the experimental study of noise and vibrations due to magnetic forces in electrical machines. The test bench aims at clearly illustrating the electromagnetic and structural interactions in electrical machines, including tangential effects and low-mode vibration generation due to teeth under-sampling effects. The second purpose is to create the first benchmark of electromagnetic and vibro-acoustic analysis in electrical machines. This benchmark consists in comparing and validating the analytical and numerical multi-physics simulations with the test bench experimental results. In perspectives, the following measurements will carried out:

• Electromagnetic air gap flux density measurement ;

• Operational modal analysis of the test bench;

• Vibration measurement including teeth radial and tangential vibrations compared with yoke vibrations; • Acoustic and sound directivity measurement in semianechoic chamber; • Transfer path analysis of the vibrations in the machine and its structure.

Fig. 2 .

 2 Fig.2. Spatial harmonics of the air gap radial pressure for the adopted SPMSM 12s10p topology at no-load and computed with SDM.

Fig. 3 .

 3 Fig. 3. Prototype SPMSM 12s10p topology description

Fig. 4 .

 4 Fig. 4. Benchmark prototype (without stator) on the right and driving DC machine on the left. Twelve mono-axis accelerometers are placed on the stator surface to capture modal and operational deflection shapes.

Fig. 5 .

 5 Fig. 5. Flux density and flux lines at no-load using subdomain model.

Fig. 6 .

 6 Fig. 6. Induced voltage comparison between SDM and experimentation.

Fig. 7 .

 7 Fig. 7. Global FRF including all structural modes of the stator prototype.

Fig. 8 .

 8 Fig. 8. Experimental modal shapes.

TABLE I QUALITATIVE

 I COMPARISON ON PERFORMANCES CRITERIA.

		PMMF SDM MEC FEM
	Tangential component	-	+	+	+
	Accuracy versus computation time	++	+	+-	--
	Local saturation	-	-	+	++
	Adaptability to complex geometries	-	+-	+-	++
	3D Effects (skewing, end-effect)	-	+-	+-	+

TABLE II BENCHMARK

 II PROTOTYPE PARAMETERS.

	Parameter	Symbol	Value
	Number of poles	p	10
	Number of stator teeth	Zs	12
	Air gap length	g	2.5 [mm]
	Stator lamination		M 400 -50A
	Stator bore radius	R sbo	48 [mm]
	Stator yoke height	Hsy	5 [mm]
	Stator tooth length	H tooth	20 [mm]
	Stator outer radius	Rsy	73 [mm]
	Stator stack length	L st1	140 [mm]
	Stator slot width	Ws	18 [degrees]
	Permanent magnet		N dF eB(N 42)
	Magnet width	Wmag	36 [degrees]
	Magnet top radius	Rmag	45 [mm]
	Magnet height	Hmag	5 [mm]
	Magnet length	Lmag	70 [mm]
	Magnet sleeve height		0.5 [mm]
	Magnetization orientation		parallel []
	Rotor steel		C22(XC18)
	Rotor bore radius	R rbo	40 [mm]
	Rotor shaft radius	Rry	20 [mm]
	Rotor length	L st2	140 [mm]


Ali Gharaviri

Matthias Zink

Mark Potse

Simone Pezzuto

Stef Zeemering

Rolf Krause

Angelo Auricchio

Ulrich Schotten

Acute Changes in P-Wave Morphology by Pulmonary Vein Isolation in Atrial Fibrillation Patients

Keywords:

Pulmonary vein (PV) plays an important role in atrial fibrillation (AF) initiation, progression, and stability. Successful PV isolation (PVI), either by radiofrequency catheter or Cryoballoon ablation, may terminate AF and prevent its recurrence. Whereas, incomplete PV isolation or reconnection of isolated PVs underlies mechanisms of AF recurrence. Hence, defining parameters able to predict a successful PVI and detect reconnections can assist clinicians in treatment of AF patients. Here, we developed a highly detailed human atrial model to simulate PVI and its acute effect on the P-wave morphology. Afterwards, the simulation results were compared and validated by recorded ECGs from patients before and after PVI procedure. In both simulation data and clinical recordings, we observed morphological changes in Pwave after PVI. More importantly our simulation helped us to find electrode positions, in which the differences in P-wave morphology before and after PVI were more pronounced.

Introduction

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia with a very high prevalence and associated with severe complications such as stroke [START_REF] Loewe | In-silico assessment of the dynamic effects of amiodarone and dronedarone on human atrial patho-electrophysiology[END_REF][START_REF] Miyasaka | Mortality trends in patients diagnosed with first atrial fibrillation: a 21-year community-based study[END_REF]. The progression of AF from short-lived "paroxysmal" episodes to longer-lasting forms is a hallmark feature of this chronic disease with important clinical implications. Indeed, the longer a patient has been in AF, the more difficult it becomes to restore normal sinus rhythm, and treatment options extremely limited. [START_REF] Calkins | HRS/EHRA/ECAS/APHRS/SOLAECE expert consensus statement on catheter and surgical ablation of atrial fibrillation: Executive summary[END_REF] Therefore, making efficient AF prevention and therapy is a major clinical challenge.

Although mechanisms underlying AF initiation and perpetuation is not well understood, atrial muscle sleeves surrounding the pulmonary veins (PVs) are known to be the most frequent source of focal activities initiating atrial fibrillation (AF). [START_REF] Haissaguerre | Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins[END_REF] As a consequence, pulmonary veins (PVs) play a significant role in atrial fibrillation initiation, progression, and stability. Therefore, PV isolation (PVI) is the therapy choice for patients with paroxysmal AF stubborn to antiarrhythmic therapies and patients with persistent AF. [START_REF] Mcgarry | The anatomical basis of pulmonary vein reconnection after ablation for atrial fibrillation: wounds that never felt a scar?[END_REF] Despite the acute success of PVI in AF termination, specifically in paroxysmal AF patients, AF recurrences are not rare. [START_REF] Verma | Approaches to catheter ablation for persistent atrial fibrillation[END_REF][START_REF] Macle | Adenosine-guided pulmonary vein isolation for the treatment of paroxysmal atrial fibrillation: an international, multicentre, randomised superiority trial[END_REF] More than 40% of patients experience AF recurrence one year after their PVI procedure [START_REF] Calkins | HRS/EHRA/ECAS/APHRS/SOLAECE expert consensus statement on catheter and surgical ablation of atrial fibrillation[END_REF], and in nearly all cases, with AF recurrence, one or more of the PVs is found to have re-established electrical connection to the atria. As a consequence, these patients may require additional catheter ablation [START_REF] Mcgarry | The anatomical basis of pulmonary vein reconnection after ablation for atrial fibrillation: wounds that never felt a scar?[END_REF][START_REF] Callans | Efficacy of repeat pulmonary vein isolation procedures in patients with recurrent atrial fibrillation[END_REF][START_REF] Cappato | Prospective assessment of late conduction recurrence across radiofrequency lesions producing electrical disconnection at the pulmonary vein ostium in patients with atrial fibrillation[END_REF][START_REF] Ouyang | Complete isolation of left atrium surrounding the pulmonary veins: new insights from the double-Lasso technique in paroxysmal atrial fibrillation[END_REF]. This influences patient's quality of life and risk for stroke.

Even though the mechanism underlying PV reconnections is not well understood, it is assumed to be caused by remained gaps in the line of blocks during PVI procedure or failure to generate a complete transmural block line. Therefore, finding non-invasive approach capable of detecting complete PVI and predicting PV reconnections during follow up, is highly desirable in clinical routines. [START_REF] Saha | Changes in P-wave morphology after pulmonary vein isolation: insights from computer simulations[END_REF] Due to the presence of discontinuity in the left atria and PV connections there might be conduction delay between left atria and PV [START_REF] Hamabe | Correlation between anatomy and electrical activation in canine pulmonary veins[END_REF][START_REF] Ogawa | Reduction of P-wave duration and successful pulmonary vein isolation in patients with atrial fibrillation[END_REF]. Therefore, it is possible that the final portion of P-wave reflects electrical activation of the PVs [START_REF] Ogawa | Reduction of P-wave duration and successful pulmonary vein isolation in patients with atrial fibrillation[END_REF]. As a consequence, a successful PVI might be associated with a reduction in P-wave duration. Whereas, unsuccessful PVI might cause little or no changes in the Pwave durations.

In figure 1 an example of recorded ECG of a patient in three consecutive time points (pre PVI, acute post PVI and 3 months after) is illustrated. As it is shown in this figure, there were acute morphological changes in the second half of the P-wave. These morphological changes were stable after three months, and in this period the patient had neither an AF recurrence nor any symptoms related to AF.

Therefore, we hypothesized that morphological changes in the final part of the P-wave could serve as a predictor for a successful PV isolation or presence of reconnections. To test this hypothesis, we developed a highly detailed human atrial model and simulated circumferential PV isolation line. Afterwards, we compared the P-wave in the control simulations (without ablation lines) and PVI simulations.

Method

Human atria computer model

We have developed a highly detailed human atrial model including epicardial layer and all major endocardial bundle structures. One to three layers of realistic fiber orientations were incorporated into the model, corresponding to their location in the atrium. The model consisted of approximately 5 million nodes spaced at 200µm. Ionic currents for each node were described by the Courtemanche-Ramirez-Nattel human atrial cell model. [START_REF] Courtemanche | Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model[END_REF] To simulate the ECG from the simulated atrial electrical activity, we embedded the atrial model in an inhomogeneous torso model. The torso model included lungs and interactivity blood masses. 256 body surface potentials were simulated using a bi-domain equation solved at 1-mm resolution. [START_REF] Potse | Patient-specific modelling of cardiac electrophysiology in heart-failure patients[END_REF] Two transmural ablation lines surrounding PVs positioned on the atrial model based on the documented method and localization of clinical ablation points (see figure 2). Virtual ablation lesions consisted of the tissue volumes within 0.35 cm (i.e., the ablation lesion radius for standard irrigated-tip catheters). [START_REF] Narayan | Treatment of atrial fibrillation by the ablation of localized sources: CONFIRM (Conventional Ablation for Atrial Fibrillation With or Without Focal Impulse and Rotor Modulation) trial[END_REF] Along the ablation line intercellular coupling will be set to zero to avoid any conduction toward the PVs. [START_REF] Dang | Evaluation of ablation patterns using a biophysical model of atrial fibrillation[END_REF][START_REF] Reumann | Preventive ablation strategies in a biophysical model of atrial fibrillation based on realistic anatomical data[END_REF]. In both control (no ablation lines) and post ablation the normal propagation was initiated by injecting intracellular current in the region of the sino-atrial node.

Analysis

For all 256 electrograms, P-wave duration, P-wave amplitude and P-wave area were calculated. P-wave duration was defined as the interval between the stimulus time and the moment that all model elements became repolarized. P-wave amplitude was defined as the maximal vertical peak to peak distance. P-wave area was defined as the time integral of the unfiltered signal between the onset and the end of the P wave.

Result

In the simulated standard 12 lead ECG signals, there were slight morphological changes in the simulated Pwaves in PVI simulation compared with the P-waves in control simulation. These changes occurred at the second half of the P-wave. In figure 3, ECG leads with the largest differences between P-waves in control and PVI simulations is depicted.

For all 256 body surface electrograms in control and PVI simulations, P-wave area and amplitude were calculated. Averaged P-wave area for all 256 leads decreased from 1.3517 ± 0.7193 in control to 1.0832 ± 0.5796 in PVI simulations. The averaged P-wave amplitude decreased as well from 0.0309mV ± 0.0114 in control to 0.0284mV ± 0.0104 in PVI simulations.

Pre-Ablation

Post-Ablation 3 months after ablation Amplitude (mV)

A) B) C) A) B)
In order to quantify morphological differences between P-waves in control and PVI simulations, Euclidean distances between P-waves pre and post ablations were calculated. In figure 4 projected color coded differences on the torso and simulated electrograms on the electrodes with largest differences illustrated. Highest differences were observed in the posterior side of the torso.

Discussion

We have developed a highly detailed computer model of a human atria and torso to simulate PVI. The simulation results showed that a complete PVI led to a decrease in both the amplitude and the area of the P-wave. Notably, differences between P-waves in control and PVI simulations were pronounced more in the posterior side of the torso rather than the anterior side. Recording electrograms from those locations are not considered in the clinical routines. Hence, analyzing those electrograms might be a great tool for clinicians to be sure that the PVI procedure is complete and to detect possible PV reconnections during the follow-up.

Limitations

Although the atrial model contains many details of atrial electrophysiology, the simulated activation sequence of our atrial model may not exactly reflect that of the patients in this study. The simulations were performed only on a generic computer model of the atria and torso, and anatomical variations were not included in this study. Thus, the simulated atrial electrogram morphology may not match the surface ECG of all patients. Finally, presence of fibrosis and slow conduction areas in the atria may cause changes in the atrial activation sequence. Therefore, PVs may not be the latest sites of activation.

Figure 1 .

 1 Figure 1. An example of Lead II ECG of a patient A) Pre-ablation. B) Acute post ablation (the area with a morphological change indicate by a red box). C) 3 months after ablation without AF recurrence after ablation

Figure 2 .

 2 Figure 2. A) Position of ablation lines (white arrows). B) Anterior view of the human atrial model and the pacing location (black flash).

Figure 3 .

 3 Figure 3. P-wave before (blue) and after (red) PVI in lead II, III, aVR, and V6.

Figure 4 .

 4 Figure 4. The Euclidean distance between pre-and postsimulated P-wave, color coded. Red shows the highest differences and blue shows the lowest difference. Top: Anterior view. Bottom: Posterior view.


Mark Potse

Ali Gharaviri

Simone Pezzuto

Angelo Auricchio

Rolf Krause

Sander Verheule

Ulrich Schotten

Anatomically-induced Fibrillation in a 3D model of the Human Atria

Atrial fibrillation (AF) requires both a trigger and a substrate that can maintain a complex reentrant activity. In patients and in experimental models this substrate is provided by both electrical and structural remodeling. Since these processes overlap in time it is impossible to assess their individual contributions to AF maintenance experimentally. Therefore we studied the effect of electrical remodeling alone on AF initiation in a realistic numerical model of the human atria. We attempted to initiate AF by rapid pacing in 10 different locations, both with and without electrical remodeling. The protocols were repeated twice, with small variations in calcium conductivity, so that in total 30 simulations with and 30 simulations without remodeling were performed. In models with electrical remodeling, functional conduction block at structural inhomogeneities induced AF in 27 % of the simulations. In models without electrical remodeling, AF could not be induced. We conclude that in the complex anatomy of the atria electrical remodeling alone increases the probability of AF substantially. This finding supports a mechanism whereby electrical remodeling, which occurs relatively fast, accelerates the slower but irreversible structural remodeling process.

Introduction

Atrial fibrillation (AF) requires a substrate and a trigger. The substrate is a stretch of myocardium that can accomodate a reentrant wave. Slow propagation, a tortuous route, and a short refractory period can contribute to such a substrate. The trigger may be an ectopic impulse that arrives during a vulnerable window, or a situation of unidirectional conduction block. Ectopic impulses often arise from the pulmonary veins [START_REF] Haïssaguerre | Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins[END_REF], and may themselves be caused by reentrant activity, on a microscopic scale [START_REF] Hocini | Electrical conduction in canine pulmonary veins: Electrophysiological and anatomic correlation[END_REF].

Rapid ectopic or paced activity in the atria promotes an arrhythmic substrate by inducing both electrical and structural remodeling [START_REF] Schotten | Pathophysiological mechanisms of atrial fibrillation: A translational appraisal[END_REF]. The electrical remodeling process sets in first and involves changes in calcium and potassium currents that shorten the action potential and thus the wavelength. Structural remodeling, consisting mainly of interstitial fibrosis, develops more slowly, and contributes to AF vulnerability by slowing conduction and creating obstacles. Thus, electrical and structural remodeling have a common cause, but it is not as firmly established that electrical remodeling alone can cause AF. For example, apart from initial structural remodeling, repolarization heterogeneity may also play a role [START_REF] Krueger | In-silico modeling of atrial repolarization in normal and atrial fibrillation remodeled state[END_REF][START_REF] Kneller | Cholinergic atrial fibrillation in a computer model of a twodimensional sheet of canine atrial cells with realistic ionic properties[END_REF]. The purpose of this study is therefore to test the effect of homogeneous electrical remodeling alone, in a realistic numerical model of the human atria.

Methods

We used a realistic atrial anatomy prepared by a combination of imaging and literature data, as described previously [START_REF] Potse | P-wave complexity in normal subjects and computer models[END_REF], but with a more realistic multiple-layer fiber structure in the left atrium, posterior inter-atrial bundles, and a few fiber tracts connecting the left atrium with the coronary sinus musculature (figure 2). These features were manually edited based on literature [START_REF] Ho | Atrial structure and fibres: morphologic bases of atrial conduction[END_REF][START_REF] Ho | Left atrial anatomy revisited[END_REF][START_REF] Chauvin | The anatomic basis of connections between the coronary sinus musculature and the left atrium in humans[END_REF]. From these elements, illustrated in figure 2A, a computational mesh was created algorithmically. This mesh consisted of approximately 5 million nodes with 200 µm spacing. Outside the thicker bundles, the atrial wall was between 2 and 3 mm thick, i.e. about 10 to 15 model elements.

Electrical activity was simulated with a monodomain reaction-diffusion equation using the human atrial myocyte model developed by Courtemanche et al. [START_REF] Courtemanche | Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model[END_REF]. While our model uses several different tissue conductivity values (Table 1), the parameters of the ionic model were uniform. Simulations were performed with the Propag-5 code [START_REF] Krause | Hybrid parallelization of a large-scale heart model[END_REF] To simulate normal atria, we used the original parameter values of the ionic model [START_REF] Courtemanche | Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model[END_REF]. To simulate remodeled atria we modified the maximum conductivities of the calcium current, g CaL , and three potassium currents as detailed in Table 2 [START_REF] Gharaviri | How disruption of endoepicardial electrical connections enhances endo-epicardial conduction during atrial fibrillation[END_REF]. To test the sensitivity of our results to small changes in model parameters we repeated the simulations with 101 % and 102 % of the g CaL values given in the table, for both normal and remodeled atria.

In each simulation, 14 stimuli were delivered at the same location with an interval decreasing from 280 to 124 ms. For each parameter set 10 simulations were performed, each with a different stimulus location (figure 2D). The 10 stimulus locations were chosen randomly, but guaranteed to be at least 30 mm apart.

Results

Figure 2 shows an example of a succesful AF initiation. The atria were stimulated from the left atrial appendage (site 1) and g CaL was 101 % of the "remodeled" value (Table 2). A reentry developed due to functional block at the narrow connection between the left atrium and the coronary sinus. Initially the reentry was anatomical, reaching the left atrium through the coronary sinus and returning through the septum and posterior interatrial bundles. However, after 5 cycles the wave found a shortcut at the most inferior of the interatrial bundles and a meandering spiral wave developed near the right inferior pulmonary vein. It A: activation fronts of the last and pre-last stimuli. The pre-last stimulated wave is seen entering the coronary sinus from the left atrium. B: the last stimulated wave blocks at the connection between the left atrium and the coronary sinus and enters the latter through the right atrium. C-G: the wave now crosses retrogradely from the coronary sinus to the left atrium and follows the same circuit 5 times. H-R: A spiral wave develops with its tip meandering near the right inferior pulmonary vein.

remained there during the rest of the simulation.

Variations in g CaL significantly modified the effects of rapid pacing at this site. With 100 % g CaL , the last paced wave did not block at the connection between the left atrium and the coronary sinus and no AF was induced. With 102 % g CaL , AF initiation happened in the same way as in the 101 % case, but after the spiral wave near the left inferior pulmonary vein developed it moved to the right atrium, where it remained near the inferior caval vein. A wave break at the crista terminalis induced a concurrent reentry near the superior caval vein.

Table 3 summarizes the results for all simulations in electrically remodeled atria. The table shows how long activity lasted beyond the last stimulus, which occurred at 2088 ms after the start of the simulation. In 8 of 30 simula-tions (27 %), activity lasted until the end of the simulation. In the others, activity lasted between 533 and 1417 ms after the last pacing pulse.

AF initiation succeeded most frequently with pacing in site 9 (right atrium near the sinus node) and site 1 (left atrial appendage).

In 30 simulations without electrical remodeling, activation never lasted more than 182 ms beyond the last pacing pulse.

Discussion

This study shows that in a structurally heterogeneous model AF can be induced by rapid pacing, demonstrating that intrinsic repolarization heterogeneity is not a require- ment. In addition we found that small changes in g CaL enabled or disabled AF initiation in 4 out of 30 simulations. Altogether, AF was initiated from 5 of the 10 pacing sites for some value of g CaL . However, electrical remodeling, involving a shortening of APD, was necessary: without this remodeling AF could not be induced with the same pacing protocol.

A shortcoming of this study is that the pacing protocol was designed to gently approach the refractory period of the electrically remodeled tissue, so that all stimuli were captured. In the non-remodeled simulations not all stimuli were captured. Thus, we cannot exclude that AF initiation would also be possible without electrical remodeling if a well-tuned pacing protocol is used.

Nevertheless, our results strongly suggest that homogeneous electrical remodeling can contribute to the duration of AF paroxysms and thus accelerate the development of structural remodeling and permanent AF.

The results also demonstrate that the success of an AF induction attempt is highly sensitive to g CaL , in a seemingly random fashion. This suggests that small variations in other physiological factors, such as autonomic tone, can also have a decisive effect on AF induction.

Figure 1 .

 1 Figure 1. A: Imaging-derived outline and manually-edited curves to define bundles and fiber orientations in the atria. The yellow tubes define the crista terminalis, pectinate muscles, and other bundles. Green tubes define posterior interatrial bundles. Red and blue tubes define fiber orientations; dark blue for the inner layer and light blue for the outer layer of the left atrium. B: The resulting thickness variations in the atrial wall. C: The resulting fiber orientations (red, endocardial; blue, epicardial; yellow, bundle). D: The 10 randomly chosen stimulus locations.

  and ran on either 2048 cores of a Bullx cluster machine or on 4096 cores of an IBM BlueGene/Q.

Figure 2 .

 2 Figure 2. Example of AF initiation (pacing site 1, in the left atrial appendage, 101 % g CaL ). The panels show 18 consecutive intervals during the simulation, as indicated on top of each panel in milliseconds from the start of the simulation. Colors show activation times; the color scale labels apply with respect to the start of each interval. The view is posterior.A: activation fronts of the last and pre-last stimuli. The pre-last stimulated wave is seen entering the coronary sinus from the left atrium. B: the last stimulated wave blocks at the connection between the left atrium and the coronary sinus and enters the latter through the right atrium. C-G: the wave now crosses retrogradely from the coronary sinus to the left atrium and follows the same circuit 5 times. H-R: A spiral wave develops with its tip meandering near the right inferior pulmonary vein.

Table 1 .

 1 Tissue

		normal remodeled
	g CaL 0.1238 0.037
	g TO	0.1652 0.026
	g K1	0.09	0.180
	g Ks	0.129	0.1
	g Na	7.8	8.0

conductivities (σ) in mS/cm. The subscript 'i' stands for intracellular, 'e' for extracellular, 'L' for longitudinal, 'T' for transverse (within a tissue sheet) and 'C' for cross-sheet. Most of the model elements had the anisotropic type. The isotropic tissue type was used in a small area between the caval veins.

Table 2 .

 2 Maximum conductivities of ionic currents (nS/pF) for simulations of normal and remodeled atria.

Table 3 .

 3 Duration (in seconds) of activity after the last pacing pulse.

	pacing		g CaL
	site	100 % 101 % 102 %
	1	0.609	> 8	> 8
	2	0.702 0.552 0.536
	3	0.564 0.568	> 8
	4	> 8	1.417 1.398
	5	0.533 0.538 0.543
	6	0.578	> 8	0.572
	7	0.605 0.605 0.603
	8	0.543 0.539 0.550
	9	> 8	> 8	> 8
	10	0.591 0.603 0.591

Acknowledgements

This work was granted access to HPC resources of TGCC-CEA and IDRIS under GENCI allocation 2018-A0030307379. This work was supported by the French National Research Agency, grant reference ANR-10-IAHU04-LIRYC.