Julien Delaunay
email: julien.delaunay@irisa.fr

Luis Galárraga
email: luis.galarraga@inria.fr

Christine Largouët
email: christine.largouet@irisa.fr

Improving Anchor-based Explanations

Keywords: Explainable AI, Machine Learning, Rule Mining, Discretization

Rule-based explanations are a popular method to understand the rationale behind the answers of complex machine learning (ML) classifiers. Recent approaches, such as Anchors, focus on local explanations based on if-then rules that are applicable in the vicinity of a target instance. This has proved effective at producing faithful explanations, yet anchor-based explanations are not free of limitations. These include long overly specific rules as well as explanations of low fidelity. This work presents two simple methods that can mitigate such issues on tabular and textual data. The first approach proposes a careful selection of the discretization method for numerical attributes in tabular datasets. The second one applies the notion of pertinent negatives to explanations on textual data. Our experimental evaluation shows the positive impact of our contributions on the quality of anchor-based explanations.

INTRODUCTION

Explanations based on logical rules are a popular strategy to explain the logic of complex black-box machine learning (ML) classifiers. However, approximating a complex model with human-readable rules incurs an inevitable trade-off: Fidelity can only be achieved at the expense of complexity, and complex explanations miss the whole point of explainable ML. For this reason recent approaches, such as Anchors [START_REF] Túlio Ribeiro | Anchors: High-Precision Model-Agnostic Explanations[END_REF], focus on explanations of local scope. These are if-then rules -also called anchors -that mimic the black box in the vicinity of a target instance. This strategy relies on the assumption that the black-box classifier is simpler to approximate when we focus on a particular region of the space.

While local rule-based explanations yield and simple and locally faithful explanations, their quality can still be very sensitive to Authors' addresses: Julien Delaunay, Inria/IRISA, France, julien.delaunay@irisa.fr; Luis Galárraga, Inria/IRISA, France, luis.galarraga@inria.fr; Christine Largouët, Agrocampus Ouest/IRISA, France, christine.largouet@irisa.fr.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. © 2018 Association for Computing Machinery. 0730-0301/2018/8-ART111 $15.00 https://doi.org/10.1145/1122445.1122456 some design factors. One of such factors is the discretization of the numerical attributes for tabular data. Figure 1 illustrates the anchors obtained for the same dataset with two discretization methods. When running Anchors with a suitable discretization method on the left-hand side of the figure, we obtain the anchor 𝑥 > -5.78 ⇒ Red that matches the black box's behavior more faithfully than the anchor obtained by another discretization method on the righthand side. Another factor that can impact the quality of an anchor is the training set used to learn the explanation. Anchors [START_REF] Túlio Ribeiro | Anchors: High-Precision Model-Agnostic Explanations[END_REF] generates training samples by perturbing the instance of interest according to a neighborhood generation strategy. Figure 2 shows the average anchor length (number of conditions on the rule's antecedent) and precision across 10 instances of three explanations learned with different neighborhood generation methods. The strategy in dark blue (pertinent negatives explained later) provides the explanation with the best trade-off between rule length and precision.

In this work we study the impact of discretization and neighborhood generation on the different metrics that define the quality of anchor-based explanations. Our contributions focus on the tabular and text variants of Anchors and include (i) the application of MDLP [START_REF] Usama | Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning[END_REF] to discretize the numerical attributes on tabular data, and (ii) the definition of pertinent negatives on text classifiers. Before elaborating on our contributions, we provide a proper introduction to Anchors in the next section.

ANCHORS

Consider a black-box classifier 𝑓 : X 𝑑 → Y that maps instances 𝑥 ∈ X 𝑑 to a set Y of classes. Each instance 𝑥 is a vector of 𝑑 attributes that can be either categorical or numerical, and 𝑥 [ 𝑗] denotes the value of 𝑥 for the 𝑗-th attribute. [START_REF] Túlio Ribeiro | Anchors: High-Precision Model-Agnostic Explanations[END_REF] defines an anchor as a logical rule 𝑅 that explains a black-box 𝑓 . The generated rule has the form:

𝑅 : B ⇒ 𝑓 (𝜂 -1 (𝑧)) = 𝑓 (𝑥) with B = 𝑗 ∈𝐹 ⊆ {1,...,𝑑 ′ } 𝑧 [ 𝑗]
The left-hand side (or antecedent) of the rule is a conjunction of conditions that predicts 𝑓 (𝑥), i.e., the class of the target instance 𝑥 according to the black box. An example is the rule age ∈ [28, 37]∧ workclass="private" ⇒ "well-paid" (for simplicity we write only the predicted value on the right-hand side). For tabular data, the interpretable space can be obtained by discretizing the numerical variables -to turn them categorical -and then binarizing the resulting conditions. For text classifiers, the surrogate space is usually defined on the presence or absence of words.

The method proposed by [START_REF] Túlio Ribeiro | Anchors: High-Precision Model-Agnostic Explanations[END_REF]], learns rule-based explanations from the answers of the black box 𝑓 on a randomly generated neighborhood Z ⊆ {0, 1} 𝑑 ′ constructed around 𝑧 = 𝜂 (𝑥) ∈ Z. Anchors applies principles of depth-first search and multi-armed bandit theory to output the shortest anchor with the largest coverage that satisfies the precision guarantee prec(𝑅) = 𝑃 (𝑓 (𝜂 -1 (𝑧)) = 𝑓 (𝑥) | B ∧ 𝑧 ∈ Z) ≥ 𝜏 for a user-defined precision threshold 𝜏. The coverage of an anchor is the ratio of instances in Z that match the anchor's antecedent, i.e., cov(𝑅) = 𝑃 (B | 𝑧 ∈ Z).

The next two sections present our contributions that highlight some of the limitations of Anchors and propose improvements.

IMPACT OF DISCRETIZATION ON TABULAR DATA

The variant of Anchors for tabular data assumes we have access to the black box's training dataset D ⊆ X 𝑑 . Tabular Anchors uses D to discretize the numerical attributes properly according to the data distribution. It supports three discretization methods. Two of them, decile and quartile, are based on classical quantile discretization. In contrast, the entropy discretization method splits the domain of an attribute 𝑗 in a dataset D (denoted by D [ 𝑗]) so that the information entropy of 𝑓 (𝑥) -for 𝑥 ∈ D and black box 𝑓 -is minimized. Anchors' entropy-based discretization outperforms quantile-based discretization in terms of coverage, precision, and anchor length. However, as we show later in this section, it can still lead to relatively long anchors. On these grounds we investigate the performance of two new discretization methods. Its key heuristic lies in the selection of the "best" cut points.

New Discretization Methods

Experimental Evaluation

We evaluate the quality of Anchors when used with five discretization methods. This includes the three methods already supported, i.e., quartile (Q), decile (D), entropy (E), and the methods proposed in this work, i.e., MDLP (M) and k-means (K). The precision threshold 𝜏 (Section 2) is set to the default value, that is, 𝜏 = 0.95.

Metrics.

The quality of an anchor is defined by its coverage, precision, and length. Shorter anchors with high coverage and precision are preferred. We highlight that the coverage of an anchor is almost analogous to the recall: It defines a trade-off with the precision. The only difference with respect to recall is that coverage is not necessarily bounded by 1. To account for this issue, we define the normalized coverage ncov(R) of an anchor 𝑅 as follows:

ncov(𝑅) = cov(𝑅) 𝑃 (𝑓 (𝜂 -1 (𝑧)) = 𝑓 (𝑥) | 𝑧 ∈ Z)
That is, the standard coverage is now normalized by the maximal attainable coverage of an anchor that explains the class given by 𝑓 (𝑥). With this formulation we can define the F1 measure of an anchor as the harmonic mean of the precision and the normalized coverage. This score provides a trade-off between coverage and precision.

3.2.2 Datasets. We use three synthetic and two real datasets for our evaluation. The synthetic datasets were generated by drawing 10k instances with the functions make_blobs, make_moons, and make_circles available in scikit-learn 1 . The real datasets comprise (i) Titanic2 , where the goal is to predict if a passenger of the Titanic survived based on her age, sex, class, etc., and (ii) Adult3 where we aim at predicting if a person earns more than 50k USD also based on personal characteristics.

Support Vector Machines Logistic Regression Multilayer Perceptron

Random Forest K M D Q E K M D Q E K M D Q E K M D Q E Blobs 0.
M D Q E K M D Q E K M D Q E K M D Q E Blobs 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Results

Table 1 summarizes the F1 performance of Anchors for a set of instances 4 of each dataset for all the studied black-box models and discretization methods. The labels K, M, D, Q, and E denote k-means, MDLP, decile, quartile, and entropy respectively. We observe that MDLP achieves overall the best F1, followed by quartile and entropy.

In particular, MDLP and quartile split the domain of attributes into fewer intervals, leading to less specific conditions with potentially higher coverage. The use of the black-box labels for binning gives MDLP a significant advantage over a simple quartile discretization.

Besides, the focus on compression minimality makes MDLP output fewer intervals than the entropy strategy. Table 2 confirms our intuitions as we observe that MDLP yields on average the shortest anchors. All discretization methods obtain a good performance on the highly structured dataset Blobs (depicted in Figure 1). An example of an anchor using MDLP in the Adult dataset is age ≤ 22 ∧ relationship = "own-child" ⇒ < 50kUSD.

IMPROVING THE QUALITY OF ANCHORS ON TEXT

In some of our experiments with Anchors on text data, it was impossible to attain the default precision threshold 𝜏 = 0.95. This phenomenon makes Anchors output rules with a precision smaller than 𝜏. We argue that the maximal attainable precision of Anchors depends on (i) the distribution of the training neighborhood and the expressiveness of the rule language. In this section we study the performance of Anchors for two different neighborhood generation strategies and propose an extension of the rule language by considering negated conditions, known as pertinent negatives in the explainable AI literature.

4 10k for the synthetic datasets, 100 for Titanic and Adult.

Neighborhood Generation Strategies

The variant of Anchors for text classification converts a textual instance into a surrogate binary vector where each entry defines the absence or presence of a word of the target phrase. Consider, for example, a black-box classifier 𝑓 for sentiment analysis and the target instance "This is a good book". Anchors will convert this instance into a five-component vector, i.e., 11111, and generate neighbors by randomly toggling off bits of this binary representation. Examples are the instances 10101 or 11101. An anchor is induced from that set of neighbors and their class labels according to the black box 𝑓 . However, 𝑓 operates in a different space than Anchors. Hence, the inverse conversion function 𝜂 -1 must map the generated neighbors to actual text instances. The strategy called mask words does so by replacing the words of each zero component with a neutral wildcard unseen before by the black box. In our example the neighbor 11101 becomes "This is a W book" for wildcard W. The strategy called replace words, on the other hand, replaces toggled-off words with random words that have the same syntactic role, i.e., they would be assigned the same part-of-speech tag. For instance the neighbor 11101 could become "This is a great book".

Pertinent Negatives

We highlight that anchors are defined on conjunctions of nonnegated conditions. For text data this entails conditions on the presence of words in phrases. This design decision guarantees simpler rules while keeping the search space under control. On the downside, it imposes limits on the expressiveness of explanations.

Inspired by the work presented by [START_REF] Dhurandhar | Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives[END_REF], we propose to change the language of Anchors and provide explanations on the absence of words. Those words are known as pertinent negatives. We can also see pertinent negatives as counterfactual explanations or words whose presence would change the answer of the black box. Considering the absence of all possible words in the corpus makes the search space for anchors prohibitively large. Hence we apply two mechanisms to alleviate this fact. First, we focus on a limited set of words. This set consists of the top 𝑘 most frequent words that co-occur next to the words of the target instance, stopwords excluded. For our example phrase "This is a good book", our algorithm would consider words such as scientific, interesting, or very as they may often appear with "book" and "good". Second, we set an upper bound 𝑛 in the number of pertinent negatives allowed in explanations.

It follows that a neighborhood generation method purely based on pertinent negatives represents a phrase as a vector of 𝑚 + 𝑝 components where 𝑚 is the number of words in the target phrase and 𝑝 is the number of pertinent negatives. The target instance is mapped to a vector where the first 𝑚 elements are set to 1 and the remaining are set to 0. Neighbors are then generated by randomly toggling on the zero entries of the pertinent negatives, which instructs Anchors to add the word to the phrase. Our goal is to show the potential and viability of pertinent negatives in Anchors, thus we leave as future work the implementation of a hybrid approach that combines pertinent negatives with one of the classical strategies for neighborhood generation based on present words.

Experimental Evaluation

We evaluate the discussed neighborhood generation strategies using the F1 measure and the anchor length as quality criteria. For pertinent negatives we use 𝑛 = 20. 4.3.1 Datasets. Our experimental datasets comprise (i)5 , a set of movie reviews for sentiment analysis, and (ii) Tweets6 , a set of tweets, where the goal is to predict the occurrence of emojis. 4.3.2 Black-box models. We use the same black-box models as in Section 3.2.3. Those models were trained on a vector representation of the phrases based on word counts and provided by the class CountVectorizer of scikit-learn.

Results

We summarize the aggregated results for the F1 measure and the anchor size among 10 randomly selected instances in Tables 3 and4. We first observe that the replace words strategy lies far behind the others in terms of F1 (except for logistic regression on Tweets). While it usually produces anchors of high precision, the coverage of those anchors is very low, in other words, it generates overly specific explanations. This intuition is confirmed by Figure 3, where we can observe that replace words yields, on average, longer anchors than the other strategies. These overly specific anchors are a consequence of the neighborhood generation strategy. By replacing toggled-off words with other words of the same syntactic role, the neighbor instances become very unstable: the addition of a single word can change the meaning of the phrase as well as the black box's answer. We observe this phenomenon to a lesser extent when using the strategy mask words. This happens because replacing a word with the wildcard forces the black box to make a decision on the basis of fewer words. We observe that pertinent negatives achieves the best F1 score and leads to shorter and more stable anchors. This happens because the training set is based on the variation of a small and carefully selected set of features (words) that exhibit a high correlation with the features present in the target phrase. An example of an anchor with pertinent negatives is ¬caring ∧ downpur ⇒ for the tweet "Totally worth getting caught in this evening's downpour. #jacquelineonassisreservoir". The addition of the word "caring" would have made the classifier predict a different emoji.

CONCLUSION

In this work we have studied the impact of two elements in the design of anchor-based explanations, namely the discretization of numerical features for tabular data, and the neighborhood generation strategy for text data. We have shown that by careful adjusting those elements, we can obtain a significant increase in the precision, coverage, and length of anchor-based explanations. As future work, we envision to explore post-hoc discretization methods, i.e., methods that rediscretize the variables of an anchor in order to improve its coverage. We will also consider the combination of the pertinent negatives and mask words strategies in order to provide more expressive and accurate anchors defined both on the presence or absence of words. The code, data, and experimental results are available at https://github.com/juliendelaunay35000/anchors.

Figure 1 :

 1 Figure 1: Two anchors (depicted as green lines) learned with different discretizations of the numerical features. The target instance is marked as a violet star

Figure 2 :

 2 Figure 2: Trade-off between F1 score and anchor length for three neighborhood generation methods

  3.1.1 K-means. We propose a baseline discretization method based on the k-means clustering algorithm [Jain and Dubes 1988]. This method splits the domain D [ 𝑗] of an attribute into 𝑘 clusters that minimize intra-cluster distance while maximizing inter-cluster distance. Distance is based on the absolute difference of the values in D [ 𝑗]. Therefore, and unlike the entropy-based method, our adaptation of k-means does not make use of the labels provided by the black box 𝑓 . The parameter 𝑘 is chosen using the Elbow method [Thorndike 1953]. 3.1.2 MDLP Discretization. [Fayyad and Irani 1993] proposes a method for discretization of continuous-valued attributes into multiple intervals based on the Minimum Description Length Principle (MDLP). Intuitively, MDLP returns the minimal number of "pure" intervals needed to separate instances from distinct classes. Compared to a traditional entropy-based method, MDLP focuses on compression minimality, hence it outputs as few intervals as possible.

Table 1 :

 1 F1 score for Anchors using different discretization methods. MR denotes the mean rank of the method.

		89	1	0.84	0.85	1	0.89	1	0.84	0.85	1	0.89	1	0.84	0.85	1	0.89	1	0.84	0.85	1
	Circles	0.45 0.87 0.43	0.46	0.77	0.45 0.87 0.43	0.46	0.77	0.45 0.87 0.43	0.46	0.77	0.45 0.87 0.43	0.46	0.77
	Moons	0.6	0.7	0.66 0.72 0.68	0.6	0.7	0.66 0.72 0.68	0.6	0.7	0.66 0.72 0.68	0.6	0.7	0.66 0.72 0.68
	Adult	0.66	0.66	0.66 0.98 0.66	0.66	0.96	0.66 0.98 0.66	0.66	0.96	0.66 0.98 0.66	0.66	0.65	0.66 0.98 0.66
	Titanic 0.42 0.93 0.33	0.42	0.42	0.42 0.93 0.33	0.42	0.42	0.42 0.93 0.33	0.42	0.42	0.42 0.93 0.33	0.42	0.42
	MR	3	1.4	3.6	2	2	3.2	1.4	3.8	2	2.2	3.2	1.4	3.8	2	2.2	3	1.6	3.6	2	2
			Support Vector Machines			Logistic Regression			Multilayer Perceptron			Random Forest
		K

Table 2 :

 2 Anchor length using different discretization methods. MR denotes the mean rank of the method.

	1	1	1

3.2.3 Black-box models. We tested our contributions on a variety of black-box classifiers, namely logistic regression, support vector machines, multi-layer perceptron, and random forests.

Table 3 :

 3 Length of textual Anchors for different neighborhood generation strategies.

		Support Vector Machines	Logistic Regression	Multlayer Perceptron	Random Forest
		RW MW	PN	RW MW PN RW MW PN RW MW PN
	Tweets	5.1	4.3	8.1	4.6	6.4	9.1	2.1	4.6	7.2	3.7	5.4	4.2
	Polarity 8.3	7.7	4.9	6.7	3.6 4.5	6.9	6.6 2.3	2	2	2
		Support Vector Machines	Logistic Regression	Multilayer Perceptron	Random Forest
		RW MW	PN	RW MW PN	RW MW PN	RW MW PN
	Tweets 0.63 0.41	0.82	0.56 0.31 0.91 0.85 0.44 0.95 0.57 0.27 0.95
	Polarity 0.35	1	0.87	0.35 0.98 0.86	0.52	1	0.98	0.47	1	0.79

Table 4 :

 4 F1 score of textual Anchors for different neighborhood generation strategies.

https://scikit-learn.org

https://www.kaggle.com/c/titanic/data

https://archive.ics.uci.edu/ml/datasets/adult

http://www.cs.cornell.edu/people/pabo/movie-review-data/

https://competitions.codalab.org/competitions/17344#learn_the_details-data


Bernold Hasenknopf
email: bernold.hasenknopf@sorbonne-universite.fr

How to establish a lasting covid-19 compatible teaching

The sanitary crisis of covid-19 forces universities to provide distance teaching and learning. This paper discusses three approaches: i) replicating existing lectures on video, ii) comodal teaching with the division of student audience into groups for face-toface and distance learning, and iii) blended learning with a redistribution of learning activities.

I. INTRODUCTION

The covid-19 crisis has brought distance teaching into the focus of nearly all universities. Within days or weeks, teaching staff had to modify their practice and use teaching modes that were unfamiliar to most of them. The result, named emergency remote teaching, 1 secured the end of the academic year, but a degradation of the quality was unavoidable. As a relief of the sanitary crisis is still not within short sight, distance teaching becomes the new normalcy in universities. The persons in charge of curricula must therefore decide how to transform the programs to cope with two apparently contradictory values: first, the health and safety of their students and staff; second the quality of teaching and learning. Having been confronted with this dilemma at my university in Paris, France, I share in the following my personal thoughts and arguments to build a lasting covid-19 compatible teaching.

Health regulations require social distancing and can easily be met by distance learning. Although excellent programs entirely remote are developed, distance learning does not fit all type of learners. In particular the average student population who is today at universities is used to face-to-face learning, and is not prepared to stay away from the campus. Their student life and interaction with peers is part of their learning experience and an important factor of their motivation. This is important for all study years, but particularly for freshman years. They come directly from High School where they were neither trained for distance learning, not prepared for autonomous learning. Teaching in universities during the covid-pandemic should therefore, as much as possible, include face-to-face sessions, in addition to remote teaching and learning. The way how to articulate both is challenging, and should be carefully considered. The most straightforward solutions might not be the best ones to maintain efficient learning.

II. VIDEO-LECTURING

A simple way of distancing the teacher and the students is to place a camera and a screen in between.

The teacher is recording or live streaming his lecture, and the students are listening. This is appealing to many teachers because they only have to learn how to use the video equipment, and can then perform as they are used to do. However, by doing so, the quality of the outcome is usually very poor, even if the technical part (sound and image quality) is satisfactory. One factor is fatigue. In our former oncampus teaching, our students had usually different classes that add up to four to eight hours per day in a classroom or lecture theater. The transposition of the sessions with the same length in front of a screen is useless, students will not be able to pay attention over such a long time. This sounds of course evident to every teacher, and nobody would ever ask students to listen to him or her for so many hours. But another consequence is that teachers within a department must cooperate to make sure that on a day when they program a video session, their colleagues don't do the same.

Another drawback of video-lecturing is the lack of interaction. 2 The teacher loses the feedback from the audience, that he usually feels intuitively as a competent professional. This feedback is essential for the teacher to adapt his/her behavior, such as accelerating or slowing down, reexplaining or remotivating. In addition, students are left in the role of the passive receiver of content. Due to the isolation and anonymity in front of their screen, they are often adopting a consumerist attitude. Many are no longer asking questions or giving comments. Students who feel more comfortable to post a question in an online chat than in front of a lecture theater, do exist, but they are not the majority. The teacher must therefore build into his lecture sequences where the students are obliged to react. Audience response systems are a useful tool for that purpose and can bring some improvements. Another possibility is to cut long video lectures into short sequences, and insert quizzes, exercises or other type of work.

III. COMODAL TEACHING

As soon as they recognize the importance of faceto-face teaching, teachers exclude the exclusive use of video lecturing. The idea of comodal teaching appears rapidly. It means that some students are present together with the teacher in a room, and others are following by video, either at the same time (live streaming) or later (recording). [START_REF] Beatty | Hybrid-Flexible Course Design : Implementing student-directd hybrid classes[END_REF] The concept is well established and in use for instance at institutions with more than one campus, or to accommodate student populations with significant commuting. 4 The University of Laval has offered comodal teaching with a free choice by each student. [START_REF] Gobeil-Proulx | What do university students think about hybrid-flexible, or HyFlex courses?[END_REF] They can decide individually if they prefer to come to class, or watch it synchronously or asynchronously from home. Comodal teaching is challenging for the teacher, because it is necessary to consider three different audiences (on site, synchronous at distance, asynchronous at distance). For instance, usually the teacher is the only person with a microphone. Questions from the audience in the classroom are not audible for remote participants, and as a minimum the teacher must repeat them before answering. At the same time, he/she must keep an eye on the broadcasting system to see if any questions come from remote participants. Similarly, a live discussion in class is very interesting for those on site. They can confront their ideas and conceptions with their peers, and the teacher can directly intervene. Remote students will only be able to participate if they are connected in real time, all people in the room use a microphone, and a moderator distributes speech time equally between the on-site and the distant participants. Asynchronous remote students are left behind, because watching a discussion passively does not give the same learning experience.

Teacher who want to switch to comodal teaching are therefore obliged to design a microplanning of their sessions that includes the content of their class, their own activity and what each of the different audiences is supposed to do. This can be done in form of a table as suggested by the University of Laval (Table I. 6 ).

The University of Lausanne, Switzerland, recommends their teachers to include in comodal lectures every 12-15min an activity on Wooclap or similar audience response systems to maintain the engagement and participation of all students. [START_REF] Van De Poel | Centre de Soutien à l'Enseignement[END_REF] The bottom line is that comodal teaching requires more investment from the teacher than setting up equipment for recording and broadcasting. Teaching sequences must be designed carefully beforehand, and some degree of multitasking is required during teaching.

IV. BLENDED LEARNING Instead of dividing the audience into groups that follow on site or at distance, one might think of dividing the lecture into parts to be done face-to-face or remotely. Thus, it comes to blended learning. [START_REF] Keengwe | Blended Learning Pedagogies and Professional Development in Higher Education[END_REF] Despite extensive literature and practice of blended learning, many teachers in higher education have not thought of it before the covid-19 pandemic. Most of us tend to reproduce teaching modes that we experienced and appreciated when we were students, and blended learning was rarely in place when nowadays academics were sitting themselves in the rows of lecture halls. I often witnessed that teachers, when asked to move parts of their lecture to distance learning, were checking which of their chapters they want to keep face-to-face and which one can be done at distance, then looking for tools to efficiently transmit information abroad. This approach does not consider what it needs for the student to be done to acquire that content, i. e. it ignores learning activities. An efficient switch from face-to-face teaching to blended learning must therefore start by going one step back and reconsider the learning outcomes of the class. For each of the learning outcomes, there should be several learning activities possible to achieve them. The teacher should list them, and then categorize them according to where his/her input is the most valuable (supervision / autonomy), and when all students should work together at the same time or individually at their own pace (synchronous / asynchronous). Once this has been done, the teacher can decide what activity should be kept in class, and what can be done at distance. The decision should be made on a pedagogical base, not depending on technical considerations. For example, some learning outcomes can be met by group work. Students can work together in small groups when sitting together around a table in a classroom, but they can also work on a shared document (google docs, sheets and slides are just one example) while sitting each one at home. So, the type of work to be done does not justify in general the decision between face-to-face and distance learning sessions. The teacher must how his/her student population would behave. One might think that Freshman are less used to group

[a] Learning through acquisition is what learners are doing when they are listening to a lecture or podcast, reading from books or websites, and watching demos or videos. [b] Learning through collaboration embraces mainly discussion, practice, and production. Building on investigations and acquisition, it is about taking part in the process of knowledge building itself. [c] Learning through discussion requires the learner to articulate their ideas and questions, and to challenge and respond to the ideas and questions from the teacher, and/or from their peers. [d] Learning through investigation guides the learner to explore, compare and critique the texts, documents and resources that reflect the concepts and ideas being taught. [e] Learning through practice enables the learner to adapt their actions to the task goal, and use the feedback to improve their next action.

Feedback may come from self-reflection, from peers, from the teacher, or from the activity itself, if it shows them how to improve the result of their action in relation to the goal. [f] Learning through production is the way the teacher motivates the learner to consolidate what they have learned by articulating their current conceptual understanding and how they used it in practice.

work on a new subject, and more easily distracted when not in class, whereas in graduate school or vocational training, the students are more autonomous, more self-guided and target oriented and are very well able to organize group work at distance.

In order to break down a course sequence with its set of leaning outcomes into learning activities, one might use the ABC Learning Design 9 that was developed by UCL, London and is now in use by many universities, including my own. 10 Learning activities are organized into six groups of learning types: 11 acquisition, [a] collaboration, [b] discussion, [c] investigation, [d] practice, [e] and production. [f] Within each group coexist learning activities with and without digital technologies. Teaching teams can combine learning activities of different types within a storyboard for their course or curriculum. Although the ABC method can be used for any teaching mode, it is particularly useful when switching from conventional teaching to blended learning. As an example, Figure 1 is showing how to rearrange a science class that originally had a lecture, a tutorial and a laboratory session into distance and face-toface sessions. The overall working time for the student is constant, but the time of face-to-face sessions is reduced. During the covid-19 pandemic, this allows to organize smaller groups and ensure social distancing. After the pandemic, such a blended approach opens new possibilities for the organization of our curricula with less space-time constraints.

The teacher focuses his/her face-to-face interventions on those sessions where they are the most valuable, i. e. for explanations, discussions, or demonstrations. During the distance learning sessions, he/she is not absent, but the input is in form of the organization of the teaching material, and feedback to exercises.

V. CONCLUSIONS Increasing the part of distance teaching and learning as a response to the sanitary crisis can take different forms. Recording lectures on video is straightforward, but the pedagogical value is very limited. Comodal teaching is appealing, but it requires careful microplanning and places the teacher in the challenging situation to deal with different audiences at once. Blended learning seems to be a better choice. In order to redesign existing lectures, it is important to go back to the learning outcomes, and redistribute learning activities between face-to-face and distance learning, supervised and autonomous learning, synchronous and asynchronous learning. Only when this is done, one should think about the tools, digital or conventional, to be employed. Teaching support centers in higher education institutions therefore must not only provide technical guidance with IT, but also give individual support for learning design to go through the sanitary crisis.

VI. REFERENCES

Last check of all links on 18/10/2020.

Fig. 1 .

 1 Fig. 1. Example of a distribution of learning activities between face-to-face and distance sessions.

FACE

TABLE I .

 I MICROPLANNING OF COMODAL TEACHING SESSION a.

	Time	Content	Teaching and learning activities	Management and
			Teacher	Student	equipment required
		Indicate	Indicate the	In class: Indicate the activity of	Indicate all operations
		learning	activity of the	the student present in class	and productions by teacher
		outcomes of	teacher DURING the	DURING the session	and students, and the
		the session	session	At distance (Synchronous):	equipment required
				Indicate the activity of the remote
				student DURING the session
				At distance (Asynchronous):
				Indicate the activity of the remote
				student DURING the watching of
				the recorded session
				In class:
				At distance (Synchronous):
				At distance (Asynchronous):
				In class:
				At distance (Synchronous):
				At distance (Asynchronous):

a. Translated and adapted from U Laval.

C. Hodges, S. Moore, B. Lockee, T. Trust, A. Bond, "The difference between emergency remote teaching and online learning", https://er.educause.edu/articles/2020/3/the-differencebetween-emergency-remote-teaching-and-online-learning

2 This video demonstrates, with a smile, the need of personal interaction while lecturing: M. Chauvin, R. Fernandez, B.


Bastiaan J Boukens
email: b.j.boukens@amsterdamumc.nl

Mark Potse

Ruben Coronel
email: rubencoronel@gmail.com

Carlo Pappone

Michelle Monasky

Fibrosis and Conduction Abnormalities as Basis for Overlap of Brugada Syndrome and Early Repolarization Syndrome

Keywords: arrhythmias, Brugada syndrome, early repolarization pattern, fibrosis, conduction, repolarization

Brugada syndrome and early repolarization syndrome are both classified as J-wave syndromes, with a similar mechanism of arrhythmogenesis and with the same basis for genesis of the characteristic electrocardiographic features. The Brugada syndrome is now considered a conduction disorder based on subtle structural abnormalities in the right ventricular outflow tract. Recent evidence suggests structural substrate in patients with the early repolarization syndrome as well. We propose a unifying mechanism based on these structural abnormalities explaining both arrhythmogenesis and the electrocardiographic changes. In addition, we speculate that, with increasing technical advances in imaging techniques and their spatial resolution, these syndromes will be reclassified as structural heart diseases or cardiomyopathies.

Introduction

In Brugada syndrome and early repolarization syndrome patients, arrhythmias occur in the absence of gross structural abnormalities [START_REF] Antzelevitch | J-Wave syndromes expert consensus conference report: Emerging concepts and gaps in knowledge[END_REF]. Both syndromes are characterized by abnormal deflections at the end or briefly after the QRS complex, which are referred to as J-waves. Based on these ECG characteristics, Brugada syndrome and early repolarization syndrome are referred to as J-wave syndromes and thought to share a pathophysiological mechanism [START_REF] Antzelevitch | J-Wave syndromes expert consensus conference report: Emerging concepts and gaps in knowledge[END_REF][START_REF] Nademanee | Overlapping risks of early repolarization and brugada syndrome[END_REF][START_REF] Hoogendijk | J-wave syndrome(s)[END_REF].

The initially proposed mechanism underlying the Brugada syndrome involved the existence of regional differences in early repolarization [START_REF] Yan | Cellular basis for the Brugada syndrome and other mechanisms of arrhythmogenesis associated with ST-segment elevation[END_REF]. These differences were initially described in the transmural plane of small blocks of canine ventricular myocardium, in which the subepicardial action potentials repolarize first [START_REF] Lukas | Differences in the electrophysiological response of canine ventricular epicardium and endocardium to ischemia. Role of the transient outward current[END_REF]. The latter could set the stage for "phase-2 reentry" in the presence of a reduced net inward current, a loss-of-function mutation in the sodium or calcium channels, or by a gain-of-function mutation of the channel carrying the transient outward current [START_REF] Krishnan | Flecainide-induced arrhythmia in canine ventricular epicardium: Phase 2 reentry?[END_REF]. This mechanism has been challenged by multiple experimental and clinical studies. These studies have shown that activation in the right ventricular outflow tract (RVOT) is discontinuous and delayed. This predisposes to excitation failure, ST-segment elevation, and the onset of reentry [START_REF] Postema | Slow and discontinuous conduction conspire in Brugada syndrome: A right ventricular mapping and stimulation study[END_REF][START_REF] Coronel | Right ventricular fibrosis and conduction delay in a patient with clinical signs of Brugada syndrome: A combined electrophysiological, genetic, histopathologic, and computational study[END_REF][START_REF] Nademanee | Prevention of ventricular fibrillation episodes in brugada syndrome by catheter ablation over the anterior right ventricular outflow tract epicardium[END_REF][START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF][START_REF] Ten Sande | ST-Segment Elevation and Fractionated Electrograms in Brugada Syndrome Patients Arise from the Same Structurally Abnormal Subepicardial RVOT Area but Have a Different Mechanism[END_REF][START_REF] Hoogendijk | Mechanism of right precordial ST-segment elevation in structural heart disease: Excitation failure by current-to-load mismatch[END_REF]. These findings have led to the now-accepted view that abnormal conduction in the RVOT underlies the Brugada syndrome [START_REF] Blok | Mechanisms of arrhythmias in the brugada syndrome[END_REF][START_REF] Behr | OUP accepted manuscript[END_REF]. This classifies the syndrome as a cardiomyopathy rather than a channelopathy [START_REF] Towbin | HRS expert consensus statement on evaluation, risk stratification, and management of arrhythmogenic cardiomyopathy[END_REF]. For the early repolarization syndrome, the current view is still-as indicated by the name-that the syndrome is caused by enhanced local early repolarization [START_REF] Antzelevitch | J-Wave syndromes expert consensus conference report: Emerging concepts and gaps in knowledge[END_REF]. However, we have recently shown that in a young patient local conduction delay caused by structural abnormalities led to the early repolarization syndrome [START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. Removal of the region containing the abnormalities cured the syndrome, indicating that abnormal conduction may be the mechanism causing early repolarization syndrome similar to the Brugada syndrome.

In this review, we will discuss how abnormal conduction explains the overlap in arrhythmogenic mechanisms in Brugada syndrome and early repolarization syndrome and how differences between the syndromes are explained. We speculate that the J-wave syndromes represent a part of a larger spectrum of cardiomyopathies.

Abnormal Conduction in RVOT in Brugada Syndrome

Structural abnormalities caused by interstitial fibrosis play an essential role in the generation of ST segment elevation and the onset of arrhythmias in Brugada syndrome patients [START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF][START_REF] Frustaci | Cardiac histological substrate in patients with clinical phenotype of Brugada syndrome[END_REF][START_REF] Corrado | Right bundle branch block, right precordial ST-segment elevation, and sudden death in young people[END_REF][START_REF] Martini | Ventricular fibrillation without apparent heart disease: Description of six cases[END_REF]. These structural changes lead to a localized branching and converging myocardial network, very much resembling that of the network of surviving fibers in infarcted myocardium [START_REF] Coronel | Right ventricular fibrosis and conduction delay in a patient with clinical signs of Brugada syndrome: A combined electrophysiological, genetic, histopathologic, and computational study[END_REF][START_REF] De Bakker | Slow conduction in the infarcted human heart[END_REF]. This may cause activation delay at the branching point (Figure 1A) and even excitation failure (Figure 1B) when the depolarizing current generated by the proximal myocardium is too small to activate distal myocardium (current-to-load mismatch) [START_REF] Hoogendijk | ST segment elevation by current-to-load mismatch: An experimental and computational study[END_REF][START_REF] Rohr | Paradoxical improvement of impulse conduction in cardiac tissue by partial cellular uncoupling[END_REF]. The ratio of the current generated and the minimum current required to maintain propagation is referred to as the safety factor for cardiac conduction and is also referred to as conduction reserve [START_REF] Rohr | Paradoxical improvement of impulse conduction in cardiac tissue by partial cellular uncoupling[END_REF][START_REF] Van Rijen | electrical uncoupling, and conduction slowing: Role of conduction reserve[END_REF][START_REF] Kléber | Basic mechanisms of cardiac impulse propagation and associated arrhythmias[END_REF]. Sodium channel blockade decreases the safety for conduction and promotes conduction block at branching sites. This effect of sodium channel blockade forms the basis of the provocation test and explains the increased prevalence of mutations in the gene (SCN5A) encoding the cardiac sodium channel in the population with Brugada syndrome [START_REF] Antzelevitch | Brugada syndrome: Report of the second consensus conference[END_REF]. Conduction block at branching points delays local activation, causes fractionation in local unipolar electrograms [START_REF] De Bakker | The pathophysiologic basis of fractionated and complex electrograms and the impact of recording techniques on their detection and interpretation[END_REF], and may set the stage for reentrant arrhythmias (Figure 1C). Indeed, fractionated local electrograms have been recorded from patients with Brugada syndrome, although the duration of these fractionations does not cover the entire phase of ST-elevation [START_REF] Nademanee | Prevention of ventricular fibrillation episodes in brugada syndrome by catheter ablation over the anterior right ventricular outflow tract epicardium[END_REF][START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF][START_REF] Ten Sande | ST-Segment Elevation and Fractionated Electrograms in Brugada Syndrome Patients Arise from the Same Structurally Abnormal Subepicardial RVOT Area but Have a Different Mechanism[END_REF]. The explanation for this apparent discrepancy is that the tissue beyond the tissue branching points is not activated at all (excitation failure) while being excitable and coupled to the proximal tissue. As a consequence, a potential difference occurs between the unexcited and adjacent activated tissue and generates a systolic current that is visible in the ECG as ST-segment elevation [START_REF] Hoogendijk | Mechanism of right precordial ST-segment elevation in structural heart disease: Excitation failure by current-to-load mismatch[END_REF]. Fractionated potentials as a reflection of late activation thus occur merely at the end of the QRS complex and do not necessarily have to extend throughout the duration of the ST elevation.

In Brugada syndrome, arrhythmias are initiated predominantly in the RVOT [START_REF] Haissaguerre | Mapping and ablation of idiopathic ventricular fibrillation[END_REF]. In 2013, we have proposed that the intrinsic conduction reserve in the RVOT is lower than in the remainder of the heart because of its developmental origin, which would facilitate conduction delay and block in the presence of structural abnormalities [START_REF] Boukens | Reduced sodium channel function unmasks residual embryonic slow conduction in the adult right ventricular outflow tract[END_REF][START_REF] Boukens | Developmental Basis for Electrophysiological Heterogeneity in the Ventricular and Outflow Tract Myocardium as a Substrate for Life-Threatening Ventricular Arrhythmias[END_REF]. The RVOT is often the source of arrhythmias, and the initiating premature activation can be the result of the arrhythmogenic substrate as described above [START_REF] Hoogendijk | ST segment elevation by current-to-load mismatch: An experimental and computational study[END_REF]. (A). The structural abnormalities (yellow) in the RVOT separate activation fronts causing fractionated unipolar electrograms. (B). The abnormalities may also set the stage for current-to-load mismatch leaving part of the myocardium unexcited. This myocardium acts as a current sink during systole and receives current from adjacent-excited-tissue causing unipolar electrograms with ST segment elevation (J-point). (C) Current-to-load mismatch may also generate unidirectional block and the onset of reentry. The lighter shade of purple in the RVOT indicates a lower conduction reserve resulting from a distinct embryonic origin [START_REF] Boukens | Reduced sodium channel function unmasks residual embryonic slow conduction in the adult right ventricular outflow tract[END_REF]. RVOT, right ventricular outflow tract; RV, right ventricle; Endo, endocardium; Epi, epicardium.

Overlap in Mechanism of Brugada Syndrome and Early Repolarization Syndrome

Structural Abnormalities and Fractionated Potentials

Structural abnormalities have been reported repeatedly in Brugada syndrome patients [START_REF] Coronel | Right ventricular fibrosis and conduction delay in a patient with clinical signs of Brugada syndrome: A combined electrophysiological, genetic, histopathologic, and computational study[END_REF][START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF][START_REF] Frustaci | Cardiac histological substrate in patients with clinical phenotype of Brugada syndrome[END_REF][START_REF] Martini | Ventricular fibrillation without apparent heart disease: Description of six cases[END_REF]. Fibrosis is found in both the subendocardium [START_REF] Ohkubo | Right ventricular histological substrate and conduction delay in patients with Brugada syndrome[END_REF] and subepicardium [START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF]. Whether fibrosis in Brugada syndrome patients is more prominent in the RVOT than in the remainder of the heart has not yet been thoroughly investigated. However, it has become clear that hearts from Brugada syndrome patients are histologically different from controls [START_REF] Chevalier | Brugada syndrome and myocardial histology: Where may the truth lie?[END_REF]. This suggests that the Brugada syndrome is a structural disease rather than a channelopathy [START_REF] Towbin | HRS expert consensus statement on evaluation, risk stratification, and management of arrhythmogenic cardiomyopathy[END_REF]. In the ECG of patients with a structural heart disease, e.g., arrhythmogenic ventricular cardiomyopathy, Chagas disease, or Uhl's disease, slurring or notching at the end of the QRS complex is often present and is referred to as the early repolarization pattern [START_REF] Nakasuka | QRS alternans due to localized intraventricular block during ventricular tachycardia in Uhl's anomaly: A case report[END_REF][START_REF] Macfarlane | The early repolarization pattern: A consensus paper[END_REF]. The early repolarization pattern is also present in the ECG of some Brugada syndrome patients [START_REF] Nagase | Local Left Ventricular Epicardial J Waves and Late Potentials in Brugada Syndrome Patients with Inferolateral Early Repolarization Pattern[END_REF]. Patients with the early repolarization pattern and with ventricular arrhythmias who, after standard clinical evaluation, appear to have a structurally normal heart are diagnosed with early repolarization syndrome [START_REF] Antzelevitch | J-Wave syndromes expert consensus conference report: Emerging concepts and gaps in knowledge[END_REF]. However, epicardial mapping of these patients often reveals sites with fractionated electrograms [START_REF] Nagase | Local Left Ventricular Epicardial J Waves and Late Potentials in Brugada Syndrome Patients with Inferolateral Early Repolarization Pattern[END_REF][START_REF] Takigawa | Detailed Analysis of the Relation Between Bipolar Electrode Spacing and Far-and Near-Field Electrograms[END_REF], which are indicative of a structural substrate [START_REF] De Bakker | The pathophysiologic basis of fractionated and complex electrograms and the impact of recording techniques on their detection and interpretation[END_REF]. Ablation of these sites prevents ventricular fibrillation, indicating that these regions are required for arrhythmogenesis [START_REF] Nademanee | Prevention of ventricular fibrillation episodes in brugada syndrome by catheter ablation over the anterior right ventricular outflow tract epicardium[END_REF].

We recently reported the first case of early repolarization syndrome in which localized fibrosis in the right ventricular inferior wall caused ventricular fibrillation and the early repolarization pattern in the ECG [START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. Echocardiography and magnetic resonance imaging (MRI) did not reveal gross structural abnormalities in this patient. This leaves room for the possibility that other patients with the early repolarization syndrome have structural abnormalities as well, which have remained undetected so far. Currently, The structural abnormalities (yellow) in the RVOT separate activation fronts causing fractionated unipolar electrograms. (B). The abnormalities may also set the stage for current-to-load mismatch leaving part of the myocardium unexcited. This myocardium acts as a current sink during systole and receives current from adjacent-excited-tissue causing unipolar electrograms with ST segment elevation (J-point). (C) Current-to-load mismatch may also generate unidirectional block and the onset of reentry. The lighter shade of purple in the RVOT indicates a lower conduction reserve resulting from a distinct embryonic origin [START_REF] Boukens | Reduced sodium channel function unmasks residual embryonic slow conduction in the adult right ventricular outflow tract[END_REF]. RVOT, right ventricular outflow tract; RV, right ventricle; Endo, endocardium; Epi, epicardium.

Overlap in Mechanism of Brugada Syndrome and Early Repolarization Syndrome

Structural Abnormalities and Fractionated Potentials

Structural abnormalities have been reported repeatedly in Brugada syndrome patients [START_REF] Coronel | Right ventricular fibrosis and conduction delay in a patient with clinical signs of Brugada syndrome: A combined electrophysiological, genetic, histopathologic, and computational study[END_REF][START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF][START_REF] Frustaci | Cardiac histological substrate in patients with clinical phenotype of Brugada syndrome[END_REF][START_REF] Martini | Ventricular fibrillation without apparent heart disease: Description of six cases[END_REF]. Fibrosis is found in both the subendocardium [START_REF] Ohkubo | Right ventricular histological substrate and conduction delay in patients with Brugada syndrome[END_REF] and subepicardium [START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF]. Whether fibrosis in Brugada syndrome patients is more prominent in the RVOT than in the remainder of the heart has not yet been thoroughly investigated. However, it has become clear that hearts from Brugada syndrome patients are histologically different from controls [START_REF] Chevalier | Brugada syndrome and myocardial histology: Where may the truth lie?[END_REF]. This suggests that the Brugada syndrome is a structural disease rather than a channelopathy [START_REF] Towbin | HRS expert consensus statement on evaluation, risk stratification, and management of arrhythmogenic cardiomyopathy[END_REF]. In the ECG of patients with a structural heart disease, e.g., arrhythmogenic ventricular cardiomyopathy, Chagas disease, or Uhl's disease, slurring or notching at the end of the QRS complex is often present and is referred to as the early repolarization pattern [START_REF] Nakasuka | QRS alternans due to localized intraventricular block during ventricular tachycardia in Uhl's anomaly: A case report[END_REF][START_REF] Macfarlane | The early repolarization pattern: A consensus paper[END_REF]. The early repolarization pattern is also present in the ECG of some Brugada syndrome patients [START_REF] Nagase | Local Left Ventricular Epicardial J Waves and Late Potentials in Brugada Syndrome Patients with Inferolateral Early Repolarization Pattern[END_REF]. Patients with the early repolarization pattern and with ventricular arrhythmias who, after standard clinical evaluation, appear to have a structurally normal heart are diagnosed with early repolarization syndrome [START_REF] Antzelevitch | J-Wave syndromes expert consensus conference report: Emerging concepts and gaps in knowledge[END_REF]. However, epicardial mapping of these patients often reveals sites with fractionated electrograms [START_REF] Nagase | Local Left Ventricular Epicardial J Waves and Late Potentials in Brugada Syndrome Patients with Inferolateral Early Repolarization Pattern[END_REF][START_REF] Takigawa | Detailed Analysis of the Relation Between Bipolar Electrode Spacing and Far-and Near-Field Electrograms[END_REF], which are indicative of a structural substrate [START_REF] De Bakker | The pathophysiologic basis of fractionated and complex electrograms and the impact of recording techniques on their detection and interpretation[END_REF]. Ablation of these sites prevents ventricular fibrillation, indicating that these regions are required for arrhythmogenesis [START_REF] Nademanee | Prevention of ventricular fibrillation episodes in brugada syndrome by catheter ablation over the anterior right ventricular outflow tract epicardium[END_REF].

We recently reported the first case of early repolarization syndrome in which localized fibrosis in the right ventricular inferior wall caused ventricular fibrillation and the early repolarization pattern in the ECG [START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. Echocardiography and magnetic resonance imaging (MRI) did not reveal gross structural abnormalities in this patient. This leaves room for the possibility that other patients with the early repolarization syndrome have structural abnormalities as well, which have remained undetected so far. Currently, echocardio-graphy, computed tomography, and MRI are used to assess structural and functional abnormalities in patients suspected of structural heart disease [START_REF] Towbin | HRS expert consensus statement on evaluation, risk stratification, and management of arrhythmogenic cardiomyopathy[END_REF]. These techniques are presently not sensitive enough to detect transmural fibrosis in Brugada syndrome patients (and also not in the patient with early repolarization syndrome) [START_REF] Coronel | Right ventricular fibrosis and conduction delay in a patient with clinical signs of Brugada syndrome: A combined electrophysiological, genetic, histopathologic, and computational study[END_REF][START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. A biopsy of the myocardium would allow detection of transmural fibrosis by conventional histology using a Picro-Sirius-red or Masson's trichrome staining. Electroanatomic voltage mapping could designate the location for tissue sampling by identifying regions with low-amplitude fractionated potentials [START_REF] Avella | Diagnostic value of endomyocardial biopsy guided by electroanatomic voltage mapping in arrhythmogenic right ventricular cardiomyopathy/dysplasia[END_REF]. Establishing the causal relation between transmural fibrosis and fractionated potentials in patients with the early repolarization syndrome will foster radiofrequency ablation as a future antiarrhythmic therapy in patients with the early repolarization syndrome [START_REF] Nademanee | Mapping and Ablation of Ventricular Fibrillation Associated with Early Repolarization Syndrome[END_REF].

J-Waves in Local Electrograms and Excitation Failure

Late activation appears to be associated with pronounced local J-waves because the notch in the local epicardial action potential in late activated tissue is exposed in the ST segment [START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF][START_REF] Nademanee | Mapping and Ablation of Ventricular Fibrillation Associated with Early Repolarization Syndrome[END_REF][START_REF] Boukens | J-Waves in Epicardial Electrograms Can Guide Ablation of Arrhythmogenic Substrates[END_REF]. This type of electrogram shows large R-waves-indicating late activated myocardium-followed by a positive J-wave as seen in Figure 2A (upper panel). These morphological features are often observed in local electrograms in early repolarization syndrome patients [START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF][START_REF] Boukens | J-Waves in Epicardial Electrograms Can Guide Ablation of Arrhythmogenic Substrates[END_REF]. Similar J-waves that follow an R-wave (in a unipolar electrogram) can be found in Brugada syndrome patients as well, although they are often described following an S-wave [START_REF] Ten Sande | ST-Segment Elevation and Fractionated Electrograms in Brugada Syndrome Patients Arise from the Same Structurally Abnormal Subepicardial RVOT Area but Have a Different Mechanism[END_REF][START_REF] Nagase | Local Left Ventricular Epicardial J Waves and Late Potentials in Brugada Syndrome Patients with Inferolateral Early Repolarization Pattern[END_REF]. Such J-waves may appear in tissue undergoing excitation failure caused by current-to-load mismatch whereby fractionated potentials precede a monophasic potential, imposing as ST elevation in the extracellular electrograms [START_REF] Hoogendijk | ST segment elevation by current-to-load mismatch: An experimental and computational study[END_REF][START_REF] Vigmond | Fractionated electrograms with ST-segment elevation recorded from the human RVOT[END_REF].

Excitation failure in early repolarization syndrome may manifest also in a different manner. Figure 2A shows a simulated electrogram from late-activated subepicardium of the right ventricular free wall before and after excitation failure (gray squares represent tissue with excitation failure). A notching of the QRS complex was seen, although the J-wave disappeared when excitation failure occurred. The same configuration was recorded from the right ventricular wall of a heart of a patient with early repolarization syndrome (Figure 2B). We speculate that in the patients at this location, excitation failure occurred leading to this electrogram morphology.

Generation of the J-Wave in the Electrocardiogram through Structural Abnormalities

If the compromised tissue-distal to the isthmus where excitation failure occurred-is located at the end of the normal activation pathway, it will not be activated at all, even though this tissue is excitable. The RVOT is normally the last part of the heart to be activated. As a consequence, a large systolic intracellular electrotonic "injury" current will flow from the activated tissue towards the unexcited tissue (located in the RVOT) and will generate a monophasic extracellular potential [START_REF] Ten Sande | ST-Segment Elevation and Fractionated Electrograms in Brugada Syndrome Patients Arise from the Same Structurally Abnormal Subepicardial RVOT Area but Have a Different Mechanism[END_REF][START_REF] Vigmond | Fractionated electrograms with ST-segment elevation recorded from the human RVOT[END_REF]. This potential will also be represented on the right precordial leads (or leads placed more cranially) of the ECG in the form of STelevation typical for Brugada syndrome [START_REF] Hoogendijk | Mechanism of right precordial ST-segment elevation in structural heart disease: Excitation failure by current-to-load mismatch[END_REF]. However, if the compromised tissue is located in myocardium that is activated relatively late in the QRS complex but not at the very end of the normal activation pathway (not in the RVOT, but in the LV free wall or RV free wall), the initially unexcited tissue will be activated with a delay through a secondary activation route. As a consequence, a short-lasting systolic intracellular electrotonic current will flow from the activated tissue towards the unexcited tissue that will generate a short-lived positive extracellular potential. This potential will be represented on the according leads of the ECG as a fractionated QRS complex or J-wave in the ECG. This constitutes the typical early repolarization pattern. Simulated activation maps and extracellular potentials during sodium channel reduction (30%) in the absence (upper) and presence (lower) of structural abnormalities. Propagation and extracellular potential were simulated using a similar approach as published previously [START_REF] Hoogendijk | Mechanism of right precordial ST-segment elevation in structural heart disease: Excitation failure by current-to-load mismatch[END_REF]. In brief, propagating action potentials (AP) were simulated with a monodomain reaction-diffusion equation, using software that has been described previously [START_REF] Potse | A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart[END_REF]. Ionic currents were computed with the Ten Tusscher-Noble-Noble-Panfilov model for the human ventricular myocyte [START_REF] Ten Tusscher | A model for human ventricular tissue[END_REF], which distinguishes subendocardial, mid-myocardial, and subepicardial cell types. Computation of extracellular potentials (electrograms) from the simulated membrane potentials was based on the bidomain model for cardiac tissue [START_REF] Vigmond | Solvers for the cardiac bidomain equations[END_REF]. Delayed activation in location a resulted in a pronounced J-wave in the corresponding local electrograms. In the presence of structural abnormalities excitation failure occurred and the local J-wave disappeared. Panel (B) shows the epicardial activation pattern at the right inferior wall measured during open chest mapping [START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. The delayed activated myocardium (in blue) showed unipolar electrograms with (c) and without (d) a local J-wave. We speculate that excitation failure occurred at location d. ERP, early repolarization pattern. Simulated activation maps and extracellular potentials during sodium channel reduction (30%) in the absence (upper) and presence (lower) of structural abnormalities. Propagation and extracellular potential were simulated using a similar approach as published previously [START_REF] Hoogendijk | Mechanism of right precordial ST-segment elevation in structural heart disease: Excitation failure by current-to-load mismatch[END_REF]. In brief, propagating action potentials (AP) were simulated with a monodomain reaction-diffusion equation, using software that has been described previously [START_REF] Potse | A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart[END_REF]. Ionic currents were computed with the Ten Tusscher-Noble-Noble-Panfilov model for the human ventricular myocyte [START_REF] Ten Tusscher | A model for human ventricular tissue[END_REF], which distinguishes subendocardial, mid-myocardial, and subepicardial cell types. Computation of extracellular potentials (electrograms) from the simulated membrane potentials was based on the bidomain model for cardiac tissue [START_REF] Vigmond | Solvers for the cardiac bidomain equations[END_REF]. Delayed activation in location a resulted in a pronounced J-wave in the corresponding local electrograms. In the presence of structural abnormalities excitation failure occurred and the local J-wave disappeared. Panel (B) shows the epicardial activation pattern at the right inferior wall measured during open chest mapping [START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. The delayed activated myocardium (in blue) showed unipolar electrograms with (c) and without (d) a local J-wave. We speculate that excitation failure occurred at location d. ERP, early repolarization pattern.

Paradoxical Effect of Sodium Channel Blockade

Sodium channel blockade augments ST elevation in the Brugada syndrome but tends to suppress QRS slurring in the early repolarization syndrome. This paradox could hint towards a separate mechanisms giving rise to the ECG abnormalities in the different syndromes. However, this difference is likely related to the availability of alternative activation routes to the myocardium distal to the conduction block created by sodium channel blockade. In Brugada syndrome, such an alternative route is largely absent in the RVOT and the distal myocardium is, therefore, not excited, although it is excitable [START_REF] Hoogendijk | ST segment elevation by current-to-load mismatch: An experimental and computational study[END_REF]. This creates the characteristic prolonged ST-elevation generated by coupling excited tissue to unexcited tissue (similar to the genesis of a monophasic action potential) [START_REF] Vigmond | The electrophysiological basis of MAP recordings[END_REF]. In the heart with an early repolarization pattern, the structural abnormality is positioned in the free wall of the left or right ventricle, where alternative activation routes to the blocked myocardium are present. The sodium channel blockade, in this case, transforms the delayed activation into activation block. In addition, because the myocardium is not the terminally activated tissue, ajmaline-induced conduction slowing in the rest of the heart may delay activation in the rest of the heart beyond that of the structurally altered tissue. Experimental evidence for this mechanisms has been supported by computer simulations (Figure 3) [START_REF] Meijborg | Reduced sodium current in the lateral ventricular wall induces inferolateral J-waves[END_REF].

wall or RV free wall), the initially unexcited tissue will be activated with a delay through a secondary activation route. As a consequence, a short-lasting systolic intracellular electrotonic current will flow from the activated tissue towards the unexcited tissue that will generate a short-lived positive extracellular potential. This potential will be represented on the according leads of the ECG as a fractionated QRS complex or J-wave in the ECG. This constitutes the typical early repolarization pattern.

Paradoxical Effect of Sodium Channel Blockade

Sodium channel blockade augments ST elevation in the Brugada syndrome but tends to suppress QRS slurring in the early repolarization syndrome. This paradox could hint towards a separate mechanisms giving rise to the ECG abnormalities in the different syndromes. However, this difference is likely related to the availability of alternative activation routes to the myocardium distal to the conduction block created by sodium channel blockade. In Brugada syndrome, such an alternative route is largely absent in the RVOT and the distal myocardium is, therefore, not excited, although it is excitable [START_REF] Hoogendijk | ST segment elevation by current-to-load mismatch: An experimental and computational study[END_REF]. This creates the characteristic prolonged ST-elevation generated by coupling excited tissue to unexcited tissue (similar to the genesis of a monophasic action potential) [START_REF] Vigmond | The electrophysiological basis of MAP recordings[END_REF]. In the heart with an early repolarization pattern, the structural abnormality is positioned in the free wall of the left or right ventricle, where alternative activation routes to the blocked myocardium are present. The sodium channel blockade, in this case, transforms the delayed activation into activation block. In addition, because the myocardium is not the terminally activated tissue, ajmaline-induced conduction slowing in the rest of the heart may delay activation in the rest of the heart beyond that of the structurally altered tissue. Experimental evidence for this mechanisms has been supported by computer simulations (Figure 3) [START_REF] Meijborg | Reduced sodium current in the lateral ventricular wall induces inferolateral J-waves[END_REF]. Inferolateral J waves and their attenuation by sodium channel blockers. The effects of reduced Na current, reduced coupling, and increased transient outward current on inferolateral J waves were evaluated with computer simulations using a detailed model of the human heart and torso [START_REF] Meijborg | Reduced sodium current in the lateral ventricular wall induces inferolateral J-waves[END_REF]. Propagating action potentials were simulated with a monodomain reaction-diffusion model. At 1-ms intervals the simulated transmembrane currents were inserted in a torso model and a static bidomain problem was solved to obtain the electrocardiogram (ECG). Global reduction in Na-channel conductivity deformed and prolonged the QRS complex, masking the inferolateral J-waves. Subtraction of the ECGs with and without local intervention showed that the ECG change associated with the local reduction in Na current was not reduced, but was only hidden by the expanding QRS complex.

Temporal Variability in Signs and Symptoms in Both Syndromes

Patients with Brugada syndrome or with the early repolarization syndrome do not always show the characteristic signs pertaining to the respective syndromes. The typical ST-T changes of Brugada syndrome are not always present and may only be observed after provocation with an intravenous sodium channel blocker (Ajmaline) or after a full-stomach test [START_REF] Ikeda | The full stomach test as a novel diagnostic technique for identifying patients at risk of Brugada syndrome[END_REF]. Even without provocative maneuvers, the symptoms and signs may wax and wane [START_REF] Nademanee | Arrhythmogenic marker for the sudden unexplained death syndrome in Thai men[END_REF]. Similarly, the electrocardiographic changes belonging to the early repolarization pattern are unstable [START_REF] Antzelevitch | J-Wave syndromes expert consensus conference report: Emerging concepts and gaps in knowledge[END_REF] and are modulated by exercise and sodium channel blockade. Small alterations in conduction reserve over time could explain the wax and wane of symptoms.

The reduction in conduction reserve at the site of source-sink mismatch can be modulated by various ionic currents other than the sodium current (I Na ) [START_REF] Boyle | New insights on the cardiac safety factor: Unraveling the relationship between conduction velocity and robustness of propagation[END_REF]. An increase in the density of the transient outward current (I TO ) or a decrease in that of the calcium current (I CaL ) will reduce conduction reserve and hamper conduction across the site of tissue expansion and will exacerbate the conduction abnormality and the consequent ST elevation [START_REF] Hoogendijk | ST segment elevation by current-to-load mismatch: An experimental and computational study[END_REF]. The densities of these currents fluctuate under influence of, e.g., heart rate, autonomic nervous system, diet, and circadian rhythm.

Drugs and compounds other than class I drugs have sodium channel blocker properties. For example, dietary fish oil consumption leads to sodium channel inhibition [START_REF] Xiao | Blocking effects of polyunsaturated fatty acids on Na+ channels of neonatal rat ventricular myocytes[END_REF]. A meal containing fatty fish, therefore, may reduce conduction reserve [START_REF] Den Ruijter | Pro-and antiarrhythmic properties of a diet rich in fish oil[END_REF] and provoke the Brugada sign. We speculate that this contributes to the full stomach effect that has been used as a provocation test for the Brugada sign [START_REF] Ikeda | The full stomach test as a novel diagnostic technique for identifying patients at risk of Brugada syndrome[END_REF]. Certainly, the postprandial parasympathetic surge may also be of importance.

But even without the use of sodium-channel blockers, the sodium channel can have reduced function. The upstroke velocity of the cardiac action potential depends on the resting membrane potential and therefore on the coupling interval between the premature activation and the previous activation. If the premature activation encroaches on the repolarization phase of the previous activation, the take-off potential of the premature beat is less negative, and subsequently fewer ion channels are available. However, if this is related to an increased sympathetic drive the influence of the calcium channel kicks in with contrary effects [START_REF] Meijborg | Stellate ganglion stimulation causes spatiotemporal changes in ventricular repolarization in pig[END_REF].

Hoogendijk et al. have shown in a computer model of a heart with structural abnormalities that a decrease in I CaL also is capable of provoking the Brugada sign [START_REF] Hoogendijk | ST segment elevation by current-to-load mismatch: An experimental and computational study[END_REF]. This effect is based on the observation that in structurally altered myocardium, the potential difference between activated and non-activated tissue may be maintained by the plateau of the action potential [START_REF] Joyner | Unidirectional block between isolated rabbit ventricular cells coupled by a variable resistance[END_REF], if phase 0 has passed, and may even lead to propagation across a region of impaired conduction. Conversely, a temporary decreased calcium current (use of calcium channel blocking drugs and decreased sympathetic tone) may provoke activation block, if structural abnormalities are present.

The simulations by Potse et al. [START_REF] Hoogendijk | ST segment elevation by current-to-load mismatch: An experimental and computational study[END_REF] have also demonstrated the modulatory effect of the transient outward current. If I TO is increased, conduction across a branching structure may be hampered [START_REF] Joyner | Unidirectional block between isolated rabbit ventricular cells coupled by a variable resistance[END_REF], and thus may lead to the Brugada sign. Typical circumstances in which the I TO is increased are a slow heart rate (during sleep, increased parasympathetic tone). Conversely, inhibition of I TO may exert an antiarrhythmic effect or decrease the Brugada sign. Because I TO is particularly highly expressed in the subepicardial myocardium [START_REF] Nabauer | Regional differences in current density and rate-dependent properties of the transient outward current in subepicardial and subendocardial myocytes of human left ventricle[END_REF], the effects of I TO -modulation are expected particularly in the subepicardium.

Conclusions and Future Perspectives

Brugada syndrome is primarily caused by subtle, clinically undetectable, structural abnormalities in the RV and RVOT [START_REF] Towbin | HRS expert consensus statement on evaluation, risk stratification, and management of arrhythmogenic cardiomyopathy[END_REF] and therefore should be considered as a cardiomyopathy. We speculate that at least a subgroup of the patients with the Early Repolarization Syndrome also display similar subtle structural myocardial abnormalities in regions other than the RVOT [START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. The common electrophysiological mechanism is formed by conduction abnormalities, caused by current-to-load mismatch. The modulatory effects of sodium channel inhibition and arrhythmogenesis can be explained by the same mechanism [START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF]. Although we cannot exclude the possibility that some of the patients with early repolarization syndrome have repolarization abnormalities (independent of altered conduction) the definition of J-wave syndromes should not include the criterion of absence of structural abnormalities [START_REF] Antzelevitch | J-Wave syndromes expert consensus conference report: Emerging concepts and gaps in knowledge[END_REF]. The inability to detect these localized structural changes in the clinic is the reason that patients with a J-wave syndrome are thought to have structurally normal hearts [START_REF] Scrocco | Wave Syndromes: Where's the Scar?[END_REF]. Figure 4 shows the relation between the detection method and the diagnosis of various syndromes. We expect that with the increasing extent of the structural abnormalities (by ageing, comorbidities, or possibly by previous cardiac surgery), the J-wave syndromes will eventually become incorporated in the spectrum of structural heart diseases [START_REF] Towbin | HRS expert consensus statement on evaluation, risk stratification, and management of arrhythmogenic cardiomyopathy[END_REF]. Similarly, with the expected increasing resolution of the imaging techniques, we expect that the same patients that are now diagnosed with one of the J-wave syndromes will be diagnosed with structural heart disease in the near future. The latter is relevant for patient management as a structural origin of arrhythmias provides a rationale for radiofrequency ablation as antiarrhythmic treatment [START_REF] Nademanee | Mapping and Ablation of Ventricular Fibrillation Associated with Early Repolarization Syndrome[END_REF].

by the same mechanism [START_REF] Nademanee | Fibrosis, Connexin-43, and Conduction Abnormalities in the Brugada Syndrome[END_REF]. Although we cannot exclude the possibility that some of the patients with early repolarization syndrome have repolarization abnormalities (independent of altered conduction) the definition of J-wave syndromes should not include the criterion of absence of structural abnormalities [START_REF] Antzelevitch | J-Wave syndromes expert consensus conference report: Emerging concepts and gaps in knowledge[END_REF]. The inability to detect these localized structural changes in the clinic is the reason that patients with a J-wave syndrome are thought to have structurally normal hearts [START_REF] Scrocco | Wave Syndromes: Where's the Scar?[END_REF]. Figure 4 shows the relation between the detection method and the diagnosis of various syndromes. We expect that with the increasing extent of the structural abnormalities (by ageing, comorbidities, or possibly by previous cardiac surgery), the J-wave syndromes will eventually become incorporated in the spectrum of structural heart diseases [START_REF] Towbin | HRS expert consensus statement on evaluation, risk stratification, and management of arrhythmogenic cardiomyopathy[END_REF]. Similarly, with the expected increasing resolution of the imaging techniques, we expect that the same patients that are now diagnosed with one of the J-wave syndromes will be diagnosed with structural heart disease in the near future. The latter is relevant for patient management as a structural origin of arrhythmias provides a rationale for radiofrequency ablation as antiarrhythmic treatment [START_REF] Nademanee | Mapping and Ablation of Ventricular Fibrillation Associated with Early Repolarization Syndrome[END_REF].

Figure 1 .

 1 Figure 1. Abnormal conduction in the right ventricular outflow tract (RVOT) as explanation for the Brugada syndrome. (A). The structural abnormalities (yellow) in the RVOT separate activation fronts causing fractionated unipolar electrograms. (B). The abnormalities may also set the stage for current-to-load mismatch leaving part of the myocardium unexcited. This myocardium acts as a current sink during systole and receives current from adjacent-excited-tissue causing unipolar electrograms with ST segment elevation (J-point). (C) Current-to-load mismatch may also generate unidirectional block and the onset of reentry. The lighter shade of purple in the RVOT indicates a lower conduction reserve resulting from a distinct embryonic origin [28]. RVOT, right ventricular outflow tract; RV, right ventricle; Endo, endocardium; Epi, epicardium.

Figure 1 .

 1 Figure 1. Abnormal conduction in the right ventricular outflow tract (RVOT) as explanation for the Brugada syndrome. (A).The structural abnormalities (yellow) in the RVOT separate activation fronts causing fractionated unipolar electrograms. (B). The abnormalities may also set the stage for current-to-load mismatch leaving part of the myocardium unexcited. This myocardium acts as a current sink during systole and receives current from adjacent-excited-tissue causing unipolar electrograms with ST segment elevation (J-point). (C) Current-to-load mismatch may also generate unidirectional block and the onset of reentry. The lighter shade of purple in the RVOT indicates a lower conduction reserve resulting from a distinct embryonic origin[START_REF] Boukens | Reduced sodium channel function unmasks residual embryonic slow conduction in the adult right ventricular outflow tract[END_REF]. RVOT, right ventricular outflow tract; RV, right ventricle; Endo, endocardium; Epi, epicardium.

Figure 2 .

 2 Figure 2. Local J-wave and excitation failure in relation to the early repolarization syndrome. (A).Simulated activation maps and extracellular potentials during sodium channel reduction (30%) in the absence (upper) and presence (lower) of structural abnormalities. Propagation and extracellular potential were simulated using a similar approach as published previously[START_REF] Hoogendijk | Mechanism of right precordial ST-segment elevation in structural heart disease: Excitation failure by current-to-load mismatch[END_REF]. In brief, propagating action potentials (AP) were simulated with a monodomain reaction-diffusion equation, using software that has been described previously[START_REF] Potse | A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart[END_REF]. Ionic currents were computed with the Ten Tusscher-Noble-Noble-Panfilov model for the human ventricular myocyte[START_REF] Ten Tusscher | A model for human ventricular tissue[END_REF], which distinguishes subendocardial, mid-myocardial, and subepicardial cell types. Computation of extracellular potentials (electrograms) from the simulated membrane potentials was based on the bidomain model for cardiac tissue[START_REF] Vigmond | Solvers for the cardiac bidomain equations[END_REF]. Delayed activation in location a resulted in a pronounced J-wave in the corresponding local electrograms. In the presence of structural abnormalities excitation failure occurred and the local J-wave disappeared. Panel (B) shows the epicardial activation pattern at the right inferior wall measured during open chest mapping[START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. The delayed activated myocardium (in blue) showed unipolar electrograms with (c) and without (d) a local J-wave. We speculate that excitation failure occurred at location d. ERP, early repolarization pattern.

Figure 2 .

 2 Figure 2. Local J-wave and excitation failure in relation to the early repolarization syndrome. (A).Simulated activation maps and extracellular potentials during sodium channel reduction (30%) in the absence (upper) and presence (lower) of structural abnormalities. Propagation and extracellular potential were simulated using a similar approach as published previously[START_REF] Hoogendijk | Mechanism of right precordial ST-segment elevation in structural heart disease: Excitation failure by current-to-load mismatch[END_REF]. In brief, propagating action potentials (AP) were simulated with a monodomain reaction-diffusion equation, using software that has been described previously[START_REF] Potse | A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart[END_REF]. Ionic currents were computed with the Ten Tusscher-Noble-Noble-Panfilov model for the human ventricular myocyte[START_REF] Ten Tusscher | A model for human ventricular tissue[END_REF], which distinguishes subendocardial, mid-myocardial, and subepicardial cell types. Computation of extracellular potentials (electrograms) from the simulated membrane potentials was based on the bidomain model for cardiac tissue[START_REF] Vigmond | Solvers for the cardiac bidomain equations[END_REF]. Delayed activation in location a resulted in a pronounced J-wave in the corresponding local electrograms. In the presence of structural abnormalities excitation failure occurred and the local J-wave disappeared. Panel (B) shows the epicardial activation pattern at the right inferior wall measured during open chest mapping[START_REF] Boukens | Structurally Abnormal Myocardium Underlies Ventricular Fibrillation Storms in a Patient Diagnosed with the Early Repolarization Pattern[END_REF]. The delayed activated myocardium (in blue) showed unipolar electrograms with (c) and without (d) a local J-wave. We speculate that excitation failure occurred at location d. ERP, early repolarization pattern.

Figure 3 .

 3 Figure 3.Inferolateral J waves and their attenuation by sodium channel blockers. The effects of reduced Na current, reduced coupling, and increased transient outward current on inferolateral J waves were evaluated with computer simulations using a detailed model of the human heart and torso[START_REF] Meijborg | Reduced sodium current in the lateral ventricular wall induces inferolateral J-waves[END_REF]. Propagating action potentials were simulated with a monodomain reaction-diffusion model. At 1-ms intervals the simulated transmembrane currents were inserted in a torso model and a static bidomain problem was solved to obtain the electrocardiogram (ECG). Global reduction in Na-channel conductivity deformed and prolonged the QRS complex, masking the inferolateral J-waves. Subtraction of the ECGs with and without local intervention showed that the ECG change associated with the local reduction in Na current was not reduced, but was only hidden by the expanding QRS complex.

Figure 4 .

 4 Figure 4. The definition of structural heart disease is based on the ability to detect structural abnormalities. An increased spatial resolution of the detection technique will lead to a leftward shift of the red zone. ERP, early repolarization pattern; BrS, Brugada syndrome; ARVC, arrhythmogenic right ventricular cardiomyopathy; Uhl's, Uhl's disease; MRI, magnetic resonance imaging; Echo, echocardiography. This figure was used with permission from [54].

Figure 4 .

 4 Figure 4. The definition of structural heart disease is based on the ability to detect structural abnormalities. An increased spatial resolution of the detection technique will lead to a leftward shift of the red zone. ERP, early repolarization pattern; BrS, Brugada syndrome; ARVC, arrhythmogenic right ventricular cardiomyopathy; Uhl's, Uhl's disease; MRI, magnetic resonance imaging; Echo, echocardiography. This figure was used with permission from [54].

Funding: RHYTHM (Leducq 16CVD02): This work was supported by the French National Research Agency, grant reference ANR-10-IAHU04-LIRYC. Dutch Heart Foundation (2016T047). Simulations were performed on HPC resources of IDRIS under GENCI allocation x2015037379.

Conflicts of Interest:

The authors declare that there is no conflict of interest.