Merwan Barlier
email: merwan.barlier@orange.com

Romain Laroche
email: romain.laroche@orange.com

Olivier Pietquin
email: olivier.pietquin@univ-lille1.fr

LEARNING DIALOGUE DYNAMICS WITH THE METHOD OF MOMENTS

In this paper, we introduce a novel framework to encode the dynamics of dialogues into a probabilistic graphical model. Traditionally, Hidden Markov Models (HMMs) would be used to address this problem, involving a first step of handcrafting to build a dialogue model (e.g. defining potential hidden states) followed by applying expectation-maximisation (EM) algorithms to refine it. Recently, an alternative class of algorithms based on the Method of Moments (MoM) has proven successful in avoiding issues of the EM-like algorithms such as convergence towards local optima, tractability issues, initialization issues or the lack of theoretical guarantees. In this work, we show that dialogues may be modeled by SP-RFA, a class of graphical models efficiently learnable within the MoM and directly usable in planning algorithms (such as reinforcement learning). Experiments are led on the Ubuntu corpus and dialogues are considered as sequences of dialogue acts, represented by their Latent Dirichlet Allocation (LDA) and Latent Semantic Analysis (LSA). We show that a MoM-based algorithm can learn a compact model of sequences of such acts.

INTRODUCTION

The ability to provide models of spontaneous human-human dialogue is an important step in understanding dialogue, leading to applications such as goal-oriented human-machine dialogue [START_REF] Lemon | Data-Driven Methods for Adaptive Spoken Dialogue Systems: Computational Learning for Conversational Interfaces[END_REF], chatbots [START_REF] Iulian V Serban | Building end-toend dialogue systems using generative hierarchical neural network models[END_REF] computer-aided human-human dialogue [START_REF] Barlier | A stochastic model for computer-aided human-human dialogue[END_REF]. Hidden Markov Models [START_REF] Lawrence R Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF] are the traditional framework addressing this problem [START_REF] Stolcke | Dialogue act modeling for automatic tagging and recognition of conversational speech[END_REF]. According to this framework, dialogue is seen as a stochastic process transiting through non-observable states, called dialogue states, and emitting an observable symbol, an utterance, while transiting. Since dialogue states are, by definition, not directly observable, monitoring the dialogue progress is made by maintaining a probability distribution over those states [START_REF] Williams | The dialog state tracking challenge series: A review[END_REF].

Previous work addressing the problem of learning the latent structure of dialogues [START_REF] Alexandersson | Learning dialogue structures from a corpus[END_REF] adopt the following strategy: a first model is handcrafted, its parameters are then adjusted using data by maximizing the likelihood of the model with algorithms such as Markov Chain Monte-Carlo or Baum-Welch/Expectation-Maximization (EM) [START_REF] Bangalore | Learning the structure of task-driven human-human dialogs[END_REF][START_REF] Michael | Mixed membership markov models for unsupervised conversation modeling[END_REF][START_REF] Zhai | Discovering latent structure in task-oriented dialogues[END_REF]. Those algorithms rely on a alternation between optimization and update steps. However, three problems arise naturally from this strategy. First, it requires to know what may be the different hidden states in order to build the first model. This state design is generally handcrafted. Models are therefore strongly domain dependent and may suffer from human modeling errors. Second, the EM and MCMC algorithms are iterative procedures converging towards local optima. Finally, those algorithms do not scale well with the number of samples and the number of hidden states.

In this work, we show how these problems can be efficiently handled by modeling dialogue as a Multiplicity Automaton and using the Method-of-Moments.

Multiplicity Automata (MA), introduced in [START_REF] Paul | On the definition of a family of automata[END_REF], are a general class of graphical models, including HMMs, able to compute a large variety of functions, including probability distributions. Modeling probability distributions as MA allow inference within spectral algorithms [START_REF] Hsu | A spectral algorithm for learning hidden markov models[END_REF][START_REF] Bailly | Grammatical inference as a principal component analysis problem[END_REF], which are a class of methods based on the Method-of-Moments which learns the representation of a distribution. Their first interest is that the representation learned by the algorithm is expressed in terms of observable variables, avoiding directly modeling errors. More precisely, in this case, hidden states may be understood as possible futures. Those algorithms also distinguish from EM algorithms by being extremely fast and often coming with theoretical guarantees. They have also shown their efficiency on a wide variety of Natural Language Processing tasks such as learning Latent Dirichlet Allocation (LDA) [START_REF] Anandkumar | A spectral algorithm for latent dirichlet allocation[END_REF], Probabilistic Context Free Grammars [START_REF] Shay B Cohen | Experiments with spectral learning of latent-variable pcfgs[END_REF], distributed representations [START_REF] Belanger | A linear dynamical system model for text[END_REF] or parsing [START_REF] Franco M Luque | Spectral learning for nondeterministic dependency parsing[END_REF].

However, a well-known problem of these algorithms is that in the case of HMMs, they are not able to provide valid parameter estimates. This problem is of major importance since in that case, the learned model is not directly usable for planning algorithms, which rely at the heart of dialogue systems since [START_REF] Levin | A stochastic model of computer-human interaction for learning dialogue strategies[END_REF] . In this work, we show that it is possible to bypass this difficulty by casting dialogue as a particular type of multiplicity automaton, called Probabilistic Residual Finite Automaton (PRFA), which is efficiently learnable [START_REF] Glaude | Pac learning of probabilistic automaton based on the method of moments[END_REF].

This paper is organized as follows: in Section 2, we briefly recall the Hidden Markov Model framework and formally introduce the class of Probabilistic Finite Automata; in Section 3, we show how dialogue model learning may be cast as a PRFA learning problem; in Section 4, we show the efficiency of our approach by learning dialogue models for the Ubuntu Corpus.

BACKGROUND

Hidden Markov Models

From the point of view of an external observer, a dialogue may be seen as a generator of symbols, or observations o, drawn from a set Σ. Depending on the observer, those observations may be utterances, dialogue acts or words. One fundamental task when studying such phenomena is to perform inference, ie. to predict what may be the next observations given the past. Formally, one assumes that each observation is drawn according to some distribution p:

p(o 0 , o 1 , ...) = p(o 0 ) t>0 p(o t |h t ),
where h t = {o 0 , ..., o t-1 } is called history. Computing this distribution for all possible histories is often intractable, a problem known as the curse of history. A compression of those histories called states are often introduced. In a dialogue context, those states often contains the last utterance and some relevant information about the past [START_REF] Larsson | Information state and dialogue management in the trindi dialogue move engine toolkit[END_REF]. This relevant information is however not precisely defined and in practice, it is often handcrafted and strongly domaindependent. Furthermore, when spoken dialogues are listened by a machine, the correspondence between states and observations may be fuzzy, since speech recognition and spoken language understanding may be error-prone. This problem is commonly addressed within the Hidden Markov Models (HMM) paradigm. Formally, Definition 2.1. An HMM is an uncontrolled Markov Process or a tuple {Q, Σ, T, O, b 0 } where:

• Q = (s 1 , . . . , s n ) is a finite set of states • Σ is a finite set of observations • T = [T i,j ] i,j∈Q is the transition matrix • O = [O o,i ] o∈Σ,i∈Q is the observation matrix • b 0 = [b 0 (i)]
i∈Q is the initial belief vector, representing the initial distributions over states.

It is often impossible to know exactly what is the current state of the process. But in a wide variety of applications, such as control and thus human-machine dialogue, it is sufficient to maintain a distribution over the different states. This distribution forms a vector called belief state. This belief is updated thanks to the update equation, which requires to know the parameters of the HMMs. Those parameters may be learned thanks to algorithms such as Baum-Welch, MCMC... However, it is known that those algorithms need a lot of computational resource and slowly converge towards bad local optima (or require strong prior assumptions).

In the remainder of this section, we will present a new paradigm addressing the inference problem, surpassing this traditional model on a large variety of points.

Stochastic Processes and Hankel Matrices

In the remainder of the paper, we will adopt the following terminology and notations. Let Σ be the set, called alphabet, containing all the possible observations. The concatenation between two elements x and y of Σ will be noted xy. A sequence of observations is called a word. The set of words over the alphabet Σ is denoted by Σ * . The empty word will be denoted by . Words will be written by variables with bars. The cardinal of a set Q will be denoted by |Q|.

A function p : Σ * → K, with K = R or R + is called a formal series. The function p characterizing dialogue defined in the last section is a particular type of formal series called stochastic process.

Definition 2.2. [21] A stochastic process is a function p : Σ * → [0, 1] that satisfies • p( ) = 1 • ∀x ∈ Σ * : p(x) = x∈Σ f (xx)
A stochastic process p defines then probabilities of initial observation sequences.

Given a stochastic process p : Σ

* → R + , one defines its Hankel matrix H ∈ R Σ * ×Σ * + as the bi-infinite matrix H = [p(xy)] x,y∈Σ * : H =        p( ) p(a) p(b) p(aa) . . . p(a) p(aa) p(ab) p(aaa) . . . p(b) p(ba) p(bb) p(baa) . . . p(aa) p(aaa) p(aab) p(aaaa) . . . . . . . . . . . . . . . . . .       
Rows (resp. columns) of this matrix correspond thus to prefixes (resp. suffixes) of the words which will be taken as arguments of the formal series p.

It is important to notice that the Hankel matrix is not a model of the stochastic process but an equivalent representation. The ability to compute H gives thus the complete knowledge of p. Since both representations are indifferently interchangeable, one may define the rank of the stochastic process as the rank of H: rank(p) := rank(H). A remarkable feature of the Hankel matrix is that it contains all the information concerning the stochastic process but is defined only over observable elements. No hidden state is therefore introduced.

In the next section, we present Multiplicity Automata, a particular class of graphical models closely related to the Hankel matrix, which will allow its computation.

Multiplicity Automata

Multiplicity Automaton (MA), introduced in [START_REF] Paul | On the definition of a family of automata[END_REF], are a a class of graphical models realizing formal series. Formally,

Definition 2.3. A K-Multiplicity Automata (K-MA) is a tu- ple {Σ, Q, (A o ) o∈Σ , α 0 , α ∞ } where: • Σ is an alphabet • Q a set of states • α 0 ∈ K |Q| the initialization vector • A o ∈ K |Q|×|Q| the transition matrices • α ∞ ∈ K |Q| the termination vector
The dimension of the MA is defined by d = |Q|. Let A be a K-MA realizing a formal serie f A : Σ * → K defined by:

∀u ∈ Σ * , f A (u) = α 0 A u α ∞ = α 0 A u1 . . . A un α ∞ SP-NFA are R + -MA
realizing a stochastic process. In the general case, no assumption is made on the weights. If K = R + , ignoring a normalization factor, weights may be interpreted as transition probabilities. But if K = R, they lose this probabilistic interpretation. Furthermore, it has been shown [START_REF] Dupont | Links between probabilistic automata and hidden markov models: probability distributions, learning models and induction algorithms[END_REF][START_REF] Jaeger | Discrete Time, Discrete Valued Observable Operator Models: A Tutorial[END_REF] that every HMM with d hidden states may be converted into a K-MA with dimensions at most d while conversely, a d-dimensional SP-NFA may not be represented by a finite-state HMM. A first advantage of both SP-NFA and OOM over HMMs models is that they are thus as expressive as HMM while being at least as compact.

The following theorem gives sufficient constraints on the parameters of an R + -MA to define a SP-NFA [START_REF] Dupont | Links between probabilistic automata and hidden markov models: probability distributions, learning models and induction algorithms[END_REF]:

Theorem 2.1. An R + -MA such that α T 0 1 = 1, o∈Σ A o 1 = 1 and α T ∞ 1 = 1
realizes a stochastic process. MA are linked with Hankel matrices thanks to the following theorem [START_REF] Carlyle | Realizations by stochastic finite automata[END_REF]: Theorem 2.2. Let f A be a formal series realized by an MA with n states, then rank(H f A ) = n. Conversely, if the Hankel matrix H f of a formal series f has rank n, then f can be realized by an MA with n states, but not less.

This theorem states that every formal series (including stochastic processes) may be realized by an MA with a number of states equals to the rank of the formal series.

In the next section, we show how one can learn such MA (and thus our distribution p) from a batch of data.

LEARNING STOCHASTIC PROCESSES WITH THE METHOD-OF-MOMENTS

The Method-of-Moments

Algorithms based on the Methods-of-Moments (MoM) attempt to learn the parameters of an automata realizing a stochastic process by identifying them with the empirical moments of the stochastic process. Those algorithms mainly rely on the Spectral Value Decomposition (SVD) of the Hankel matrix, they are hence often called Spectral algorithms. Those algorithms may be decomposed into the following procedure:

Input : Batch trajectories Output: An K-MA approximating p 1. Find a basis B of the Hankel matrix H p 2. Find an MA with |B| states, verifying constraints of theorem 2.1 and realizing p However, these algorithms have an important drawback. They are improper, which means that even if the learned automaton may be arbitrarily close from the original one, they do not need to belong to the same class. In fact, applying this method often leads to automata with negative weights. Thus, the automaton will not be usable for planning. This problem is called Negative Probability Problem (NPP).

To avoid the NPP, constraints have to be inserted into the second step of the previous procedure. In the case of HMMs however, it has been shown [START_REF] Esposito | Contribution à linférence dautomates probabilistes[END_REF] that the number of constraints necessary to return an SP-NFA was infinite. This is why in this work, we consider SP-RFA, a smaller class of automata, which is efficiently learnable within the MoM and adapted to model dialogues.

SP-RFA

SP-RFA are a class of automata realizing stochastic processes slightly less general than SP-NFA but efficiently learnable. Formally, Definition 3.1. An SP-RFA is an SP-NFA {Σ, Q, α 0 , (A o ) o∈Σ , α ∞ } realizing a distribution p such that for all states q ∈ Q, there exists a word u ∈ Σ * such that α 0 A u = 1 q . SP-RFA may be understood as stochastic processes whose generality lies between n-th order Markov chains and HMMs. In a dialogue context, if we assume that SP-RFA models a conversation, it means that whatever the dialogue state may be, there will be a sequence of utterances which leads to this dialogue state with probability one. This is a reasonable assumption since one often considers that the dialogue state depends only on the noiseless history.

As [START_REF] Glaude | Pac learning of probabilistic automaton based on the method of moments[END_REF] show, SP-RFA may be characterized by a finite set of constraints. It is thus possible to design an algorithm based on the MoM which will output an SP-NFA.

To characterize those constraints, one first needs to define the following operators. Let p be a formal series and o ∈ Σ a symbol. The function . op is the formal series such that ∀u ∈ Σ, . op(u) = p(ou). Then, for all u ∈ Σ such that p(uΣ * ) > 0, one defines p u as the formal series p u = . up p(uΣ * ) , where uΣ * is the set of all words beginning by u. One may thus understand p u (x) as the conditional probability of x given the prefix u.

The first property gives sufficient conditions on the coefficients of an MA to realize a SP-RFA. Property 3.1. Let p be a distribution, if there exists a set of words R and two associated sets of non-negative reals {a v u,o } u,v∈R,o∈Σ and {a v } v∈R such that ∀u ∈ R, p(u) > 0 and

∀u ∈ R, o ∈ Σ, . op u = v∈R a v u,o p v and p = v∈R a v p v then, {Σ, S, (A o ) o∈Σ , α 0 , α ∞ } defines a SP-RFA realizing p, where Q = R, α 0 = (a u ) u∈R ∀u, v ∈ R, A o [u, v] = a v u,o .
Conversely, the second property assures the existence of these coefficients for SP-RFA: Property 3.2. Let {Σ, Q, (A o ) o∈Σ , α 0 , α ∞ } be a SP-RFA and p the distribution it realizes, then there exists a set of words R such that:

∀u ∈ R,p(u) > 0 p ∈ u∈R α u p u α u ∈ R + ∀u ∈ R, o ∈ Σ, . op u ∈ v∈R α v p v α v ∈ R +
The sets { e∈E α e e|α e ∈ R + } are called conical hull of the set E. From now on, they will be denoted as coni(E).

Learning SP-RFA

In this section, we present the algorithm CH-SP-RFA (Algorithm 2) of [START_REF] Glaude | Pac learning of probabilistic automaton based on the method of moments[END_REF] which, given a stochastic process p generated by an SP-RFA, learns an automaton realizing p with proper probabilities as weights, and being as such directly usable to initialize Baum-Welch algorithm or to use planning algorithm.

The algorithm takes as input a basis B = (P, S) and works as follows.

First, one estimates the formal series p and . op (where p denotes the vectorial representation of p). They will be used to learn the coefficients of the Proposition 3.1.

Second, since by assumption data have been generated by a SP-RFA, one looks for the conical hull of Proposition 3.2 in which lies our distribution. This conical hull may be found by a Non-Negative Matrix Factorization algorithm. Following the advice of [START_REF] Glaude | Spectral learning with proper probabilities for finite state automaton[END_REF], in our experiments, we used the Successive Projection Algorithm [START_REF] Gillis | Semidefinite programming based preconditioning for more robust near-separable nonnegative matrix factorization[END_REF].

Third, one regresses the coefficients given by Property 3.1 in the previous conical hull conditioned on the constraints of Theorem 2.1 to return a stochastic process.

One may notice that the MA returned by the algorithm is not necessarily a SP-RFA. It has been assumed that the formal series we try to learn is one but in practice, one only needs to compute a stochastic process.

Input : A target dimension d, a separable complete basis B = (P, S), and a training set.

Output: A SP-NFA {Σ, S, (A o ) o∈Σ , α 0 , α ∞ } for u ∈ P do Estimate pu and . op u from the training set du ← (p u . o 1 p u . . . . o |Σ| p u ) end Find R a subset of d prefixes of P such that ∀u ∈ R, du > 0 and d ∈ coni( du |u ∈ R) for u ∈ R do {â v u,o } ← argmin a v u,o o∈Σ . op u - v∈ R a v u,o pv 2 st v∈ R,o∈Σ a v u,o . o = 1, pu 1 = 1 and a v u,o ≥ 0 end {â u } ← argmin {a u } p - u∈ R a u 2 st u∈ R a u = 1 and a u ≥ 0 α 0 ← (â u ) u∈R for o ∈ Σ do Âo ← (a v u,o ) u,v∈ R end Algorithm 1: CH-SP-RFA Algorithm 4. EXPERIMENTAL SETTING

The Ubuntu Dialogue Corpus

Experiments were led on the Ubuntu dialogue corpus [START_REF] Lowe | The ubuntu dialogue corpus: A large dataset for research in unstructured multi-turn dialogue systems[END_REF], which consists of 1 million dyadic chat dialogues of 3 turns or more extracted from the Ubuntu IRC channel logs. Dialogues in this dataset always follow the same structure: a user asks first the chatroom some question, which is then answered by another user. Pre-processing steps have then been applied on the corpus. First, utterances were tokenised using the twokenize tokeniser 1 . Then, stemming and lemmatising were applied using the NLTK toolkit [START_REF] Bird | Nltk: the natural language toolkit[END_REF]. Finally, stopwords from NLTK and words appearing less than 10 times were removed.

We used 2 different representations of utterances which will be described in the following sections: Latent Dirichlet Allocation and Latent Semantic Analysis, all of them computed with the Gensim library [START_REF] Rehurek | Software framework for topic modelling with large corpora[END_REF]. Additionally, we kept the End of turn token and add another one End of dialogue at the end of each dialogue.

Representation of utterances

Latent Dirichlet Allocation

Latent Dirichlet Allocation (LDA) [START_REF] David M Blei | Latent dirichlet allocation[END_REF] represents the utterances as a mixture of topics and that each word in this utterance is generated by one of these topics. More precisely, LDA supposes that each word in an utterance is generated according to the following procedure:

Input : LDA of an utterance -Size of the utterance Output: Utterance as a Bag-of-Words 1. Draw a topic from the LDA 2. Draw a word from the distribution induced by the topic In the following experiments, LDA vectors are a mixture over 30 topics.

Latent Semantic Analysis

Latent Semantic Analysis (LSA) [START_REF] Deerwester | Indexing by latent semantic analysis[END_REF] projects utterances into a concept space where two documents about the same concept are close to each other.

LSA achieves this by performing an SVD on the termdocument matrix, which is defined as the matrix containing word counts of each document. To improve the efficiency of the LSA, we did not fill the term-document matrix with word counts but with their tf-idf values which penalizes frequent words and advantages rare ones.

We chose in the experiments to define the LSA over 100 concepts.

Computing the estimated Hankel matrix

The Hankel matrix was estimated with the suffix-history algorithm [START_REF] Wolfe | Learning predictive state representations in dynamical systems without reset[END_REF]. This algorithm considers all n-grams (with n a parameter of the algorithm) as if they were separate training In the experiments, we considered 4-grams.

Results

To compare the performances of the CH-SP-RFA and Baum-Welch algorithms, we chose the negative-log-likelihood metric and execution times. First, we kept from the Ubuntu dialogue corpus only the dialogues of at least 15 turns, leading to a train (resp. test) set of 257 659 (resp. 4516) dialogues. In order to map continuous LDA and LSA vectors into a set of discrete observations, they were clustered into 30 and 50 categories respectively, leading to alphabets of size 32 and 52 (since End of turn and End of dialogue tokens have to be learned).

In order to avoid getting stuck in local optima, we used 3 random restarts for the Baum-Welch algorithm. Fig. 1 and Fig. 2 show the negative-log-likelihood for LDA and LSA respectively. In both of the experiments, the belief is initialized on the first 10 turns of dialogue and the likelihood is then computed on the prediction of the next observations. We did not computed the Baum-Welch algorithm for models with a dimension bigger than 30 due to a long computation time. We observe that in both experiments, results of Baum-Welch algorithms are better than the ones of CH-SP-RFA, even though Fig. 3. Performance with the LDA representation we observe the order of magnitude is the same. On the LDA representation, one may notice that performances of Baum-Welch also decrease with the size of the model, indicating a tendency to overfit.

However for comparables performances, Fig. 3 shows that the running time of CH-SP-RFA is drastically smaller than the one of Baum-Welch. This can be explained by the fact that the sample complexity is linear for CH-SP-RFA since one needs to browse data only once when constructing the Hankel matrix, whereas Baum-Welch has to browse all the data at each iteration of the algorithm. Furthermore, due to local convergence problems, Baum-Welch has to be run several time with different initial models. Finally, the Hankel matrix has to be computed only once for all the experiments, this step being by far the longest of the CH-SP-RFA algorithm and lasting 197 seconds.

Finally, one observes that small models perform almost as well as bigger ones. This may be explained by the fact that the chosen representations are not rich enough to completely catch the meaning of utterances. More sophisticated representations could have been used but it would have lead to bigger alphabet and in that case, Baum-Welch would have been totally intractable.

For these scalability issues, we conclude that spectral algorithms and more especially CH-SP-RFA, by providing almost equivalent results while being order of magnitudes faster, are a good alternative to the Baum-Welch algorithm which is unable to deal with large amounts of data or large alphabets.

FURTHER WORK AND CONCLUSION

In this work, we suggest the use of spectral methods for learning linear dialogue models. We justified that modeling dialogue as a SP-RFA was reasonable which allowed us to use the CH-SP-RFA algorithm in order to learn a dialogue model from the Ubuntu dialogue corpus. We experimentally showed that the performance of CH-SP-RFA was in this case comparable to the one of Baum-Welch algorithm while being considerably faster.

This work opens the door to a wide range of extensions. First, we would like to generalize the setting to the continuous observation case [START_REF] Boots | Hilbert space embeddings of predictive state representations[END_REF] in order to work with more expressive features such as distributed representation of utterances [START_REF] Kalchbrenner | Recurrent convolutional neural networks for discourse compositionality[END_REF][START_REF] Wieting | Towards universal paraphrastic sentence embeddings[END_REF]. We also want to extend this work for controlled processes [START_REF] Azizzadenesheli | Reinforcement learning of pomdps using spectral methods[END_REF] in order to apply it to human-machine dialogue and computer-aided human-human dialogue. Finally, we would like to apply those set of techniques for Inverse Reinforcement Learning in partially observable environments [START_REF] Choi | Inverse reinforcement learning in partially observable environments[END_REF] in order to learn the preferences of a dialogue system's user.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Computation time for LDA representation (in seconds)


Julien Dupas

Emilie Verneuil

Maxime Van Landeghem

Bruno Bresson

Laurent Forny

Marco Ramaioli

Francois Lequeux

Laurence Talini

Maxime Van Landeghem

Glass Transition Accelerates the Spreading of Polar Solvents on a Soluble Polymer

come

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Poor dissolution of powders leading to lump formation is a common experience in industrial processes as well as in everyday life, however its causes remain poorly understood. It is generally admitted that wetting of powders by a liquid is the first step for dispersing powders in that liquid, and that it often constitutes the rate controlling process, rather than the following steps of imbibition and final dispersion [START_REF] Schubert | FOOD INGREDIENTS EUROPE, CON-FERENCE PROCEEDINGS 1993[END_REF]. In the past decades, a large experimental and theoretical effort has been devoted to the understanding of the wetting of non soluble substrates [START_REF] De Gennes | Gouttes, bulles[END_REF][START_REF] Bonn | [END_REF], including polymeric substrates [4], but wetting by their solvent of soluble materials has been investigated only recently [5][6][7]. A straightforward experiment consists in depositing a droplet of solvent on a soluble substrate, and in simultaneously measuring the wetting angle and contact line velocity of the spreading droplet. Complex wetting behaviors have been reported in that simple geometry; in particular, a counter-intuitive effect is observed with polar solvents: large dynamic wetting angles can be measured although the substrate is soluble [5,6,8]. That behavior has been attributed to the exhibition of the material apolar groups to the interface with air [8]. Since the affinity of the solvent for the substrate increases as the substrate gets solvated, the wetting dynamics is controlled by the solvent content in the substrate [9]. Furthermore, analyses of the different solvent transfer processes from the droplet to the substrate have shown the major role of transport through the vapor phase [5,8,10]. In the course of a spreading experiment, the solvent content in the substrate ahead the contact line increases, owing mostly to condensation of the solvent evaporated from the droplet; as a consequence, the wetting angle strongly decreases together with the contact line velocity during spreading [6,7,10]. Solvent sorption is therefore a crucial parameter for the wetting of soluble materials, and the non-linearities in the sorption isotherm exhibited by polymeric substrates and their solvents can result in complex behaviors [7]. The solvoscopy, i.e. uptake of solvent versus vapor concentration increase, plays a critical role. Many polymers involved in dissolution processes are in a glassy state at room temperature since amorphous forms generally have faster dissolution rates compared to their crystalline counterparts [11]. Nevertheless, when their solvent volume fraction increases, they can undergo a plasticization, i.e. a glass transition in solvent content, and reach a melt state. Glass transition is expected to strongly influence the wetting dynamics since it induces large variations of the solvent diffusion coefficient and solvent uptake in the polymer, as well as drastic changes in the mechanical behaviour (see Fig. 1). Within a small range of solvent content, the polymer evolves from a rigid solid, poorly solvoscopic and in which the solvent has a small diffusion coefficient, to a soft viscoelastic material, highly solvoscopic with a large solvent diffusion coefficient. The influence of the mechanical properties of the substrate on wetting dynamics has been established in the case of non soluble substrates: when soft and viscoelastic, the substrate is locally deformed at the contact line and the viscoelastic dissipation in the substrate may be larger than the viscous dissipation in the liquid [12][13][14] thus substantially impeding wetting. In the present work, we investigate the case of a substrate undergoing glass transition during the course of spreading, the transition resulting from the transfer of solvent from the spreading droplet to the substrate at room temperature. We show that the wetting angle of a polar solvent on an initially glassy polymer film abruptly decreases during spreading. We demonstrate how that effect results from glass transition, and we develop a model to quantitatively predict the velocity at which glass transition plays a role. We confirm the validity of our predictions with experiments performed with polar solvents of different volatilities. The experiments were performed in a well controlled geometry: a 3 µL-droplet of solvent spontaneously spreads on a layer of polymer (maltodextrin, molecular mass 2500 g.mol -1 ). The polymer layers are formed by either spin-coating or dip-coating maltodextrin solutions on silicon wafers. The thickness e of the resulting layer ranges from 100 nm to 3.6 mm. In order to control the initial water volume fraction in the substrate φ 0 , the samples are equilibrated in a sealed chamber of controlled humidity and the experiments are performed in the same chamber. The contact line is monitored from the side and the top by two synchronized video cameras. The recorded views allow for the simultaneous determination of the contact angle of the spreading droplet θ and its instantaneous velocity U . We check that quasi-stationary conditions hold. For sub-micron thick polymer films, interferences build up between the light reflected at the polymer/air and polymer/silicon interfaces. The resulting hue on the color images, recorded by the top video camera, is a function of the product the local average refraction index and thickness of the polymer layer ne [7], a change of hue therefore indicates a local thickness change. The sorption isotherm of maltodextrin in water was measured by thermogravimetric analysis. Figure 1a shows the variation of water activity a w as a function of the water volume fraction in the polymer φ. As for most pairs of polymer and solvent, the sorption isotherm follows a Flory equation [START_REF] Rubinstein | Polymer Physics[END_REF] and is strongly non-linear: at low humidity the polymer is poorly hygroscopic, whereas it becomes hygroscopic at large humidities. The self-diffusion coefficient of water in maltodextrin D self at different water volume fractions φ was measured using a NMR technique [START_REF] Van Landeghem | [END_REF][START_REF] Johnson | Diffusion measurements by magnetic field gradient methods[END_REF][START_REF] Kimmich | [END_REF] (See the Supplemental Material [19]) . We further computed the mutual diffusion coefficient, which is the relevant quantity, using the Flory isotherm for φ < 0.6:

D = D self ∂ ln(aw)
∂ ln(φ) . As shown in Fig. 1a, the diffusion coefficient drops down by two orders of magnitude between φ =0.4 and a few percents. Large variations are also observed for the viscosity of maltodextrin solutions (Fig. 1b) that were measured using a strain-controlled rheometer. Finally, the water volume fraction at glass transition φ g was deduced from Differential Scanning Calorimetry (DSC) experiments made with samples of different initial water content. From the DSC and NMR data, the range of water content corresponding to glass transition spans φ g ∼ [0.14; 0.22], corresponding to a g w ∼ [0.5; 0.65] at room temperature. Less volatile solvents of maltodextrin were used in the spreading experiments: 1,3propanediol, DMSO, and 2,3butanediol of respective saturation concentrations 4.24, 1.75 and 1.18 g.m -3 , whereas it is 23 g.m -3 for water.

Figure 2a shows the contact angle vs. contact line velocity curves of a water droplet spreading on polymer layers with different initial water volume fractions φ 0 . On the initially melt layer (φ 0 > φ g ), the initial value of the spreading angle is larger than 30 o , and both velocity and contact angle further decrease with time as already observed in previous works [7]. That decrease results from hydration of the layer during spreading by water evaporation from the droplet and its further condensation on the substrate. When the substrate is initially glassy (φ 0 < φ g ), a decrease of both θ and U is also observed during spreading. However, at high velocities, the slope of the θ-U curve is smaller than the one on the melt layer, and at intermediate velocity values, the θ-U curve exhibits a kink that corresponds to an abrupt change of the spreading angle. This change of regime is observed with all the solvents tested provided the polymer is initially glassy and its thickness is in a range which is detailed later. The coordinates of the kink are denoted U g and θ g . We show in the following that the observed kink results from the transition from a glassy to a melt state undergone by the polymer layer in the vicinity of the contact line. We emphasize that although glass transition is characterized by rather smooth variations of the properties, the steep θ variations result from the simultaneous change of solvent sorption, solvent coefficient diffusion and mechanical properties of the substrate. Qualitatively, for U > U g the substrate is poorly solvated and behaves as a poorly solvoscopic rigid material, dissipation therefore mainly occurs in the spreading liquid; as the substrate gets solvated, it turns to a highly solvoscopic soft viscoelastic material that is deformed at the contact line for U smaller than but close to U g ; dissipation then mostly occurs in the substate. The degree of hydration can be observed during spreading through the Newton hues that appear close to the droplet on the top views. Figure 2c indeed shows that the substrate is weakly swollen before glass transition, whereas it is significantly swollen over distances from the contact line close to 1 mm when in a melt state (Fig. 2b). As discussed later, the observed swelling results from the solvatation of the substrate, its deformation at the contact line occurring over distances too small to be visible on Figure 2b.

For a non soluble substrate, it has been shown that, if the substrate is rigid, dissipation occurs in the spreading liquid, and the wetting angle and contact line velocity are related through [20][21][22] :

U = θγ l (cos θ e -cos θ) 3η l ln r (1)
Where γ l is the liquid/air surface tension, θ e the static wetting angle, η l the liquid viscosity, and r the ratio of a macroscopic length scale (the droplet radius) and a microscopic cut off length κ, such that ln r ≈ 10 [13]. the substrate is a soft viscoelastic material of elastic modulus G ′ , it deforms at the contact line, owing to the vertical component of the capillary force γ l sin θ [12,13]. The vertical displacement is γ l sin θ/G ′ , and can reach several microns for a gel of elastic modulus G ′ =1kPa. The deformed zone extends away from the contact line over a distance which is as well of a few microns, since it is given by the elastocapillary length γ l /G ′ . In that frame, the relation between wetting angle θ and contact line velocity U on a non soluble soft substrate can be derived, provided a rheological model is chosen to describe the mechanical properties of the substrate. The Chasset-Thirion model used in ref. [13] is well suited to describe the behaviour of concentrated maltodextrin solutions [23]; the relaxation modulus writes

G(t) = G 0 (1 + ( t τ ) -m )
, where G 0 is an elastic modulus, τ a relaxation time and m an exponent. In that frame, a new U vs. θ relation arises [13]:

U = [ γ s (cos θ e -cos θ) γ l sin 2 θ ] 1/m γ s G 0 τ (2)
where γ s is the air/substrate surface tension. Both equations 1 and 2 are represented in Fig. 2 for given values of the equilibrium angle θ e , surface tensions γ s and γ l , and mechanical parameters τ , m and G 0 . Although they are in qualitative agreement with the experimental data that exhibits larger slopes for U U g than for U > U g , those expressions do not provide a quantitative description for wetting on a soluble substrate. Indeed, in that case the volume fraction in the vicinity of the contact line varies with the velocity, but also with the distance to the contact line for a given velocity. This complexity prevents any further quantitative analysis. Equation 2 nevertheless provides an order of magnitude of the velocity U g . Since the term to the power 1/m is of the order of 1, and since η ≈ G 0 τ , equ. 2 actually yields η U ≈ γ s . For γ s ≈ 0.1N.m -1 , the velocity U g = 2.10 -5 m.s -1 measured in the experiment of Fig. 2 corresponds to η ≈ 5.10 3 P a.s, which is a good order of magnitude of the viscosity of maltodextrin with water volume fraction just above φ g . As explained earlier, the solvent volume fraction close to the contact line mainly results from condensation of the solvent evaporated from the droplet. As a consequence, the solvent volume fraction in the vicinity of the contact line may not only depend on the velocity, but also on the ability of the polymer layer to uptake water, and thus on its thickness. The θ-U curves of Fig. 3 obtained with different substrate thicknesses exhibit a thickness dependence for thin enough substrates. For the two thickest layers and U > U g , the contact angle is identical within the experimental uncertainty whereas it is strongly thickness-dependent in all the other cases. In- deed, the thinner the layer, the larger the solvent volume fraction is for a given solvent uptake. Consequently, the thinnest layers (e = 100nm and e = 250nm) are solvated within a very short time and are observed to behave as melt layers although they are initially glassy. Oppositely, the thickest layer (e = 3.6mm) is never solvated enough during the experimental time to observe a change in wetting regime. Remarkably, for layers of intermediate thicknesses, the contact angle at which the wetting regime changes remains roughly constant at θ g ∼ 20 ± 5 for water droplets. That result is consistent with a change in wetting regime coinciding with glass transition: the wetting angle only depends on the water volume fraction in the substrate at the contact line, and thus θ g = θ(φ g ). A simple scaling of the θ vs. U variations when U < U g can be inferred. At small velocity values and far enough from the contact line, solvent equilibrates along the film thickness within a time scale that is short compared to the other time scales. The substrate is then homogeneously solvated along the vertical direction. The distance from the contact line at which such a condition holds is given by [24] : x c = U 2 e/D. If x c is smaller than a microscopic cut off length κ, the problem can be described with a 1D model, the only spatial coordinate being the distance to the contact line. The water concentration then depends on the substrate thickness e and velocity U through the product eU only. In that simple description, it is in particular possible to compute the water volume fraction in the substrate as it is reached by the contact line, φ c [9, 24]:

φ c = φ 0 + 1 U e D v c sat ρ ln r (3)
Therefore, the wetting angle, which only depends on the water volume fraction φ c , is expected to be a function of eU only. That result is well verified for all the data of Fig. 3 corresponding to velocities U < U g since they collapse on a master curve whatever the substrate thickness. Although the deviation from the master curve grows very slowly as the thickness increases, owing to the poor solvent sorption in that case, the scaling is not verified for U > U g . Therefore, at U = U g , the solvent has uniformly diffused over the substrate thickness at horizontal distances from the contact line larger than κ, and equ. 3 can be used to predict the value of φ c . Since velocity U g is actually reached when the water volume fraction at the contact line equals the water volume fraction at glass transition φ c = φ g , it yields for U g :

U g = 1 φ g -φ 0 1 e D v c sat ρ ln r (4)
That expression is compared to the experimental data in Fig. 4 where the measured values of U g are shown as a function of the substrate thickness e for water droplets and different humidities. We find that U g varies as 1/e in agreement with Eq.4. The expression for U g was also tested with other solvents of maltodextrin. Those solvents present similar values of diffusion coefficients in air D v , and volume fractions at glass transition φ g but very different saturation concentrations c sat . Thus in equ. 4, most of the U g solvent dependence, originates in the saturation concentration c sat that strongly varies according to the solvent. As expected, we observe a good collapse on the same curve of all the values of the quantity U g (φ g -φ 0 )/(D v c sat ) for different solvents. We therefore conclude that the mechanism of solvent evaporation from the droplet and its further condensation in the substrate ahead the contact line governs whether the substrate experiences or not a glass transition, and that glass transition is responsible for deep changes in the wetting dynamics. In conclusion, we demonstrate that a glassy polymer substrate, when wetted by a polar solvent, may melt ahead the contact line, at contact line velocity smaller than a critical value, which depends on the layer thickness. Glass transition of the substrate results in a sharp decrease of the wetting angle, controlled by the substrate deformation induced by the contact line pulling.

FIG. 1 .

 1 FIG. 1. (a) (left axis) Water activity aw in the atmosphere and (right axis) mutual diffusion coefficient versus volume fraction of water in the polymer at equilibrium. Dashed line: D extrapolates to D self of the polymer for φ = 1. Sorption isotherm aw(φ) (gray squares) is fit to a Flory equation with Flory parameter χ=0.5 (grey line). (b) Viscosity of maltodextrin solutions as a function of measured water volume fraction (symbols).

FIG. 2 .

 2 FIG. 2. (color online) (a) Contact angle as a function of contact line velocity of a water droplet spontaneously spreading on a 2.7 µm thick layer of maltodextrin. The experimental data (dots) was obtained at two different initial humidities. The gray line represents Eq. 1 with θe = 16 o , γ l =0.07 N.m -1 , η = 10 -3 Pa.s and ln(r)=10 and the dashed black line Eq. 2 with θe = 5 o , γs=0.1 N.m -1 , m = 0.75 and G0τ = 2×10 3 Pa.s. Inset: side view of a spreading droplet. (b,c) Color images from the top of a droplet of DMSO spreading onto a 550-nm thick layer of maltodextrin. (b) U < Ug; (c) U > Ug. The scale bar represents 2 mm.

1 )FIG. 3 .

 13 FIG.3. Contact angle as a function of contact line velocity for water droplets spreading on maltodextrin of different thicknesses e. From top to bottom: e = 3.6mm (open symbols), 8µm, 2.7µm, 1.1µm, 550nm, 250nm and 100nm. Insert: same data plotted vs. the product eU .

FIG. 4 .

 4 FIG.4. Ug(φg -φ0)/(Dvcsat) as a function of polymer film thickness e for water at water activities: 0.11 (circles), 0.43 (triangles); 0.58 (diamonds) and for solvents at aw = 0 (hollow circles: DMSO, stars: 2,3-butanediol, squares: 1,3propanediol). The dotted line represents 1/e variations. Insert: velocity Ug from the same experimental data. All data fit to 1/e.


Keywords: Microbleeds, Magnetic susceptibility, Phase MRI, SWI

Introduction/Purpose: In vivo detection of cerebral microbleeds (CMBs) from T2* gradient recalled echo (GRE) magnitude image suffers from low specificity, modest inter-rater reproducibility and is biased by its sensitivity to acquisition parameters. New methods were proposed for improving this identification, but they mostly rely on 3D acquisitions, not always feasible in clinical practice. A fast 2D phase processing technique for computing internal field maps (IFM) has been shown to make it possible to characterize CMBs through their magnetic signature in routine clinical setting, based on 2D multi-slice acquisitions. However, its clinical interest for CMBs identification with respect to more common images remained to be assessed. To do so, systematic experiments were undertaken to compare the ratings obtained by trained observers with several image types, T2* magnitude, Susceptibility Weighted Imaging reconstructions (SWI) and IFM built from the same T2*-weighted acquisition.

Materials/Methods: 15 participants from the MEMENTO multi-center cohort were selected: six subjects with numerous CMBs (20+/-6 CMBs), five subjects with a few CMBs (2 +/-1 CMBs) and four subjects without CMB. 2D multi-slice T2* GRE sequences were acquired on Philips and Siemens 3T systems. After pilot experiments, T2* magnitude, Susceptibility Weighted Imaging (SWI) minimum intensity projection (mIP) on three slices and IFM were considered for the rating experiments. A graphical user interface (GUI) was designed in order to consistently display images in random order. Six raters of various background and expertise independently selected "definite" or "possible" CMBs. Rating results were compared with respect to a specific consensus reference, on both lesion and subject type points of view.

Results: IFM yielded increased sensitivity and decreased false positives rate (FPR) for CMBs identification compared to T2* magnitude and SWI-mIP images. Inter-rater variability was decreased with IFM when identifying subjects with numerous lesions, with only a limited increase in rating time.

IFM thus appears as an interesting candidate to improve CMBs identification in clinical setting.

A C C E P T E D M A N U S C R I P T Introduction

Cerebral microbleeds (CMBs), described as small foci of chronic blood products within brain parenchyma [START_REF] Greenberg | Cerebral Microbleeds: A Guide to Detection and Interpretation[END_REF], were first seen in patients with small vessel diseases on specific MRI sequences that are sensitive to magnetic susceptibility. Correlation of these radiological findings with histopathological studies has generated considerable interest [START_REF] Cordonnier | Brain Microbleeds: More Evidence, but Still a Clinical Dilemma[END_REF]. CMBs are now commonly reported in the general population as well as in patients with specific disorders [START_REF] Conijn | Cerebral Microbleeds on MR Imaging: Comparison between 1.5 and 7T[END_REF]. CMBs' prevalence is highly variable among reports: from 47% to 80% in patients with intra-cerebral hemorrhage [START_REF] Lee | Cerebral Microbleeds Are Regionally Associated with Intracerebral Hemorrhage[END_REF][START_REF] Naka | Frequency of Asymptomatic Microbleeds on T2*-Weighted MR Images of Patients with Recurrent Stroke: Association with Combination of Stroke Subtypes and Leukoaraiosis[END_REF], from 8% to 71% in patients with ischemic stroke [START_REF] Naka | Frequency of Asymptomatic Microbleeds on T2*-Weighted MR Images of Patients with Recurrent Stroke: Association with Combination of Stroke Subtypes and Leukoaraiosis[END_REF][START_REF] Tsushima | Brain Microhemorrhages Detected on T2*-Weighted Gradient-Echo MR Images[END_REF], from 17% to 46% in patients with cognitive decline and dementia (C. [START_REF] Cordonnier | Prevalence and Severity of Microbleeds in a Memory Clinic Setting[END_REF][START_REF] Hilal | Cerebral Microbleeds and Cognition: The Epidemiology of Dementia in Singapore Study[END_REF]) and about 20% in healthy elderly population [START_REF] Cordonnier | Brain Microbleeds: More Evidence, but Still a Clinical Dilemma[END_REF]. Deep brain CMBs are associated with hypertensive arteriopathy (HTA), while those close to the cortex are associated with cerebral amyloid angiopathy (CAA), although they may also be present in patients with isolated cerebral small vessel disease [START_REF] Park | Pathogenesis of Cerebral Microbleeds: In Vivo Imaging of Amyloid and Subcortical Ischemic Small Vessel Disease in 226 Individuals with Cognitive Impairment[END_REF].

CMBs identification using MRI remains complicated [START_REF] Cordonnier | Brain Microbleeds: More Evidence, but Still a Clinical Dilemma[END_REF][START_REF] Greenberg | Cerebral Microbleeds: A Guide to Detection and Interpretation[END_REF]). As made of hemosiderin, they can be described as strongly super paramagnetic iron-storage complexes [START_REF] Cordonnier | Brain Microbleeds: More Evidence, but Still a Clinical Dilemma[END_REF], whereas the surrounding brain parenchyma is diamagnetic. Thus, this magnetic susceptibility difference with surrounding brain parenchyma makes CMBs appear as magnetic inclusions, causing a local magnetic field inhomogeneity similar to the one that would be created by a unit dipole. At the voxel level, this inhomogeneity leads to intra-voxel phase dispersion and strong T2*-contrast. CMBs' detection is thus commonly based on Gradient Recalled Echo (GRE) T2*weighted magnitude images, in which they appear as areas of signal loss. However, their appearance on these sequences is sensitive to imaging parameters such as echo time (TE) and B 0 field strength.

Furthermore, blood vessels and cerebral micro-calcifications (CMCs) also have strong T2* effects and can be misidentified as CMBs. Physiologic calcifications commonly found in specific areas (e.g.

pineal gland, choroid plexus, basal ganglia) can easily be identified but smaller calcifications at unexpected localization sometimes require a CT scan [START_REF] Yamada | Intracranial Calcification on Gradient-Echo Phase Image: Depiction of Diamagnetic Susceptibility[END_REF].

Specific GRE-based solutions have been proposed to address these issues or related ones, including different acquisition protocols and/or different signal processing methods such as Susceptibility weighted imaging (SWI) [START_REF] Cheng | Susceptibility-Weighted Imaging Is More Reliable than T2*-Weighted Gradient-Recalled Echo MRI for Detecting Microbleeds[END_REF][START_REF] Goos | Clinical Relevance of Improved Microbleed Detection by Susceptibility-Weighted Magnetic Resonance Imaging[END_REF][START_REF] Nandigam | MR Imaging Detection of Cerebral Microbleeds: Effect of Susceptibility-Weighted Imaging, Section Thickness, and Field Strength[END_REF][START_REF] Vernooij | Cerebral Microbleeds: Accelerated 3D T2*-Weighted GRE MR Imaging versus Conventional 2D T2*-Weighted GRE MR Imaging for Detection[END_REF], Enhanced Susceptibility weighted angiography (ESWAN) [START_REF] Guo | Quantification of Phase Values of Cerebral Microbleeds in Hypertensive Patients Using ESWAN MRI[END_REF], Quantitative susceptibility mapping (QSM) [START_REF] Klohs | Detection of Cerebral Microbleeds with Quantitative Susceptibility Mapping in the ArcAbeta Mouse Model of Cerebral Amyloidosis[END_REF][START_REF] Liu | Cerebral Microbleeds: Burden Assessment by Using Quantitative Susceptibility Mapping[END_REF][START_REF] Mcauley | Quantification of Punctate Iron Sources Using Magnetic Resonance Phase[END_REF], internal field maps (IFM) [START_REF] Guo | Quantification of Phase Values of Cerebral Microbleeds in Hypertensive Patients Using ESWAN MRI[END_REF][START_REF] Kaaouana | 2D Harmonic Filtering of MR Phase Images in Multicenter Clinical Setting: Toward a Magnetic Signature of Cerebral Microbleeds[END_REF]. SWI has already been considered for the diagnosis of CMBs. It is based on combining phase and magnitude images from 3D high resolution GRE acquisitions and aims at increasing detection sensitivity for paramagnetic structures such as veins

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or hemorrhages [START_REF] Goos | Clinical Relevance of Improved Microbleed Detection by Susceptibility-Weighted Magnetic Resonance Imaging[END_REF][START_REF] Haacke | Susceptibility-Weighted Imaging: Technical Aspects and Clinical Applications[END_REF][START_REF] Haacke | Susceptibility Weighted Imaging in MRI: Basic Concepts and Clinical Applications[END_REF][START_REF] Nandigam | MR Imaging Detection of Cerebral Microbleeds: Effect of Susceptibility-Weighted Imaging, Section Thickness, and Field Strength[END_REF][START_REF] Reichenbach | Small Vessels in the Human Brain: MR Venography with Deoxyhemoglobin as an Intrinsic Contrast Agent[END_REF]. A comparison between SWI and GRE T2* reported that conventional GRE T2* magnitude missed 67% of CMBs compared to SWI [START_REF] Nandigam | MR Imaging Detection of Cerebral Microbleeds: Effect of Susceptibility-Weighted Imaging, Section Thickness, and Field Strength[END_REF][START_REF] Cheng | Susceptibility-Weighted Imaging Is More Reliable than T2*-Weighted Gradient-Recalled Echo MRI for Detecting Microbleeds[END_REF][START_REF] Vernooij | Cerebral Microbleeds: Accelerated 3D T2*-Weighted GRE MR Imaging versus Conventional 2D T2*-Weighted GRE MR Imaging for Detection[END_REF]. The QSM reconstruction technique, aiming at quantifying susceptibility, should make it possible to estimate the real lesion load. A validation study on 3D multi-echo GRE T2* acquisitions on ten patients suspected of having experienced a stroke reported that the total susceptibility (TS) of CMBs was more consistent than CMBs size measurement [START_REF] Liu | Cerebral Microbleeds: Burden Assessment by Using Quantitative Susceptibility Mapping[END_REF]). Nevertheless, SWI, ESWAN and QSM techniques have been designed and evaluated with 3D multi-echo GRE T2* acquisitions which may not be available in large cohorts. Internal field maps (IFM) can be computed with standard parameters from phase images of routine 2D T2* GRE single echo acquisitions. A method based on 2D harmonic filtering (2DHF) [START_REF] Kaaouana | 2D Harmonic Filtering of MR Phase Images in Multicenter Clinical Setting: Toward a Magnetic Signature of Cerebral Microbleeds[END_REF] has been shown to allow generating appropriate internal field maps for discriminating CMBs and visualizing the dipole field patterns created by CMBs; this magnetic signature could be used in CMBs' characterization.

Overall, CMBs' detection has limited reproducibility and is observer dependent [START_REF] De Bresser | Visual Cerebral Microbleed Detection on 7T MR Imaging: Reliability and Effects of Image Processing[END_REF][START_REF] Charidimou | Cerebral Microbleeds on Magnetic Resonance Imaging and Anticoagulant-Associated Intracerebral Hemorrhage Risk[END_REF]. This can be explained by confounding structures and artifacts as well differences in acquisition settings between studies. Previous studies comparing rating performance for advanced images vs standard magnitude images did in fact combine the advantages of 3D acquisitions with those of the new pre-processing techniques. Here, we aimed at evaluating the specific advantages of advanced image processing technique for CMB's identification by trained raters. In fact, 3D GRE T2*-weighted acquisitions may not always be feasible in clinical setting and 2D acquisitions make it possible to ensure uniformity in multi-center clinical studies while guaranteeing reasonable acquisition time. Thus, routine 2D multi-slice GRE acquisitions were used as inputs in this study from which several types of reconstructions were derived: magnitude images, SWI-like images, and preprocessed phase images (IFM).

The paper is organized as follows. In the first part, the dataset used for this comparison study is presented, followed by a description of the advanced pre-processing techniques and comparison experiments. Results are then detailed in the second part, regarding the reliability of the reference built specifically for this study and the performance of the method on both "single lesion" and "subject" points of view.

Material and Methods

Evaluation dataset

The evaluation dataset was extracted from data acquired for the ongoing French national cohort named MEMENTO [START_REF] Chene | MEMENTO: A NATIONAL COHORT ON DETERMINANTS AND BIOMARKERS OF ALZHEIMER'S DISEASE AND ASSOCIATED DISORDERS[END_REF] The acquisition protocol was described in [START_REF] Kaaouana | 2D Harmonic Filtering of MR Phase Images in Multicenter Clinical Setting: Toward a Magnetic Signature of Cerebral Microbleeds[END_REF].

Methods

CMBs are made of hemosiderin and are detected on GRE images because of the local magnetic susceptibility variation they yield. Besides, GRE phase images are proportional to magnetic field variations and thus sensitive to local susceptibility variations. Both magnitude and phase images will thus be considered in this study.

However, phase image analysis for local field variations is not straightforward. In fact, phase wraps appear on the images because phase is defined in the [ -π , π ] interval and local variations are hidden in large scale field variations resulting from background effects, dominated by the magnetic susceptibility sharp edge of air-tissue interfaces.

The extraction of relevant internal field information thus requires two preliminary steps: phase unwrapping and background field removal (E. Mark [START_REF] Haacke | Susceptibility Weighted Imaging in MRI: Basic Concepts and Clinical Applications[END_REF]. These two preprocessing steps are embedded in the two methods chosen for this study, SWI and IFM, as described below.

Susceptibility Weighted Imaging (SWI)

SWI relies on combining phase and magnitude images (E. Mark Haacke and Reichenbach 2011), phase information being used to enhance blood-related contrast on magnitude image (e.g. veins).

Phase images are first high-pass filtered (HPF) to extract local information and then transformed in a phase mask with values in the interval. In this study, the HPF phase image was obtained through the following steps. The complex-valued image was first generated from magnitude and phase images.

It was then low-pass filtered slice by slice with a two dimensional Gaussian filter in Fourier domain.

The HPF phase image was then estimated as the phase component of the ratio between complexvalued and low-pass-filtered images. The HPF phase image was then transformed in a consistent phase mask which was then applied N times on the original magnitude image to highlight voxels with a high

Internal Field Map (IFM)

A 2D-based method for phase unwrapping and harmonic filtering, based on solving Poisson equation [START_REF] Song | Phase Unwrapping of MR Phase Images Using Poisson Equation[END_REF], has been proposed as an efficient mean for obtaining the IFM [START_REF] Kaaouana | 2D Harmonic Filtering of MR Phase Images in Multicenter Clinical Setting: Toward a Magnetic Signature of Cerebral Microbleeds[END_REF]) on 2D acquisitions. This method was shown to solve the potential slice-to-slice phase inconsistency that may occur in 2D multi-slice T2* GRE datasets. The magnetic field observed inside the brain, B , can be decomposed as the sum of the magnetic field due to internal sources, B in , and the one induced by external sources, B out . From Maxwell's equations, B out is harmonic inside the brain (ΔB out =0), resulting in ΔB=ΔB in ( Δ denotes the Laplacian). Consequently, field variations due to external sources can be filtered out through a second order derivative, followed by a second order integration using adequate boundary conditions. In the process, the Laplacian of the field B in , which locally depends on susceptibility distribution, is set to 0 outside the brain to remove external susceptibility effects. Paramagnetic dot-like inclusions such as CMBs appear as a dipolar field on the resulting IFM (see Figure 1 and [START_REF] Kaaouana | 2D Harmonic Filtering of MR Phase Images in Multicenter Clinical Setting: Toward a Magnetic Signature of Cerebral Microbleeds[END_REF]). CMBs can be better discriminated by this magnetic signature.

Evaluation experiments

In order to determine the influence of the type of image for CMBs' identification, rating was performed by several raters in different conditions. A pilot experiment was first carried-out in order to determine the optimal settings for the rating experiments (see appendix 1 for more details). Three types of images were finally considered as good candidates for CMBs rating in clinical setting: T2* magnitude image, SWI-mIP image (mIP being done on three slices with a resulting slab thickness of 7.5 mm) and IFM image.

Experiment

Rating was performed independently by six raters (one session each) with various levels of expertise:

a trained clinical research assistant, a trained engineer, two junior neuroradiologists and two senior neuroradiologists. For each rater, all scans were scored in a single session. All observers were blind to image type, clinical information and other ratings. In order to facilitate detection, interactive

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visualization tuning was embedded in a specific Graphical User Interface (GUI) built with GUIDE in MATLAB (see Figure 6 appendix 1). As in MARS (S. M. [START_REF] Gregoire | The Microbleed Anatomical Rating Scale (MARS): Reliability of a Tool to Map Brain Microbleeds[END_REF]) and BOMBS (Charlotte Cordonnier et al. 2009) rating scales, a certainty score was included and CMBs could be categorized as "definite" or "possible". The aim of this categorization was both to facilitate the rating in case of uncertainty and to differentiate the amount of variability that came from clear and dubious CMBs. CMBs were defined as small round areas of signal loss on axial slices without 3D connectivity that would characterize vessels on sequences that are sensitive to magnetic susceptibility. Their size may vary from 2 to 10 mm [START_REF] Greenberg | Cerebral Microbleeds: A Guide to Detection and Interpretation[END_REF].

Building-up of the reference

After the series of ratings was completed, a reference was built by two trained neuroradiologists, one of whom did not participate to the comparison experiments. All the CMBs that were detected by any rater on any image during comparison experiments were reassessed independently by each trained neuroradiologist. Here, the three image types were displayed simultaneously through a specific GUI (reference GUI). The resulting two sets of 15 reference images were then combined to create a set of 15 consensus images using a given explicit scoring rule (Table 1). Briefly, if a lesion was identified by both observers and at least one observer considers it as definite, then it was rated as "definite CMB" in the consensus. If it was identified by only one observer as "possible" then it was discarded from the reference. If it was identified by only one observer as "definite", then it was considered as a "possible CMB". Because of the well-known inter-rater variability when rating CMBs, the reliability of the consensus reference needed to be evaluated, to ensure that the consensus rating could be considered as a meaningful reference. Rating experiments were then analyzed on a lesion-based point of view by comparing the decision of each rater for each lesion in the reference. Two types of identification were analyzed: 1. all detected CMBs (either definite or possible); 2. CMBs detected as definite only.

Exp

Furthermore, in order to assess clinical usefulness, ratings and reproducibility analyses were carried out on a subject-type point of view, by classifying patients in three groups: no CMB (G1), few CMBs (G2, less than 10 CMBs) and numerous CMBs (G3, more than 10 CMBs). Finally, rating durations

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT
were also analyzed, in order to evaluate clinical feasibility of IFM-based rating with respect to more standard T2* magnitude and SWI-mIP.

Results

The specificity (defined as ) cannot be determined since TN (true negatives) is not a meaningful measure in CMBs detection. Here, the performance of each rater is characterized through the false positives (FP) rate (FPR), false negatives (FN) and true positives (TP). Dice coefficients which combines TP, FP and FN, were also calculated for each rater.

Reference

In order to evaluate the reliability of the consensus reference, detected CMBs were compared between expert raters. Results are given in Cohen's kappa coefficient was computed to compare between raters the number of CMBs detected for each subject. When considering all lesions, the kappa value was 0.5 (p-value=0.01) and for definite lesions only, the kappa value was 0.54 (p-value=0.02).

Overall, the agreement on CMBs detection was satisfactory. Apart from one subject (subject 3 with 13 discrepant CMBs), the discrepancy between both raters was negligible (median for "no CMB": 0, "few CMBs": 0 and "numerous CMBs": 2.5). Examples of between-raters discrepancies are illustrated in Figure 2.

Rating results: lesion-based point of view

Blind ratings were analyzed with respect to the consensus reference, in order to evaluate the performance of each image type independently for lesion detection. Because of the large variability in lesion number between subjects, TP, FP and FN were computed for each rater over all the CMBs detected on all subjects. Note that "all" refers to the union of "definite" and "possible" CMBs. The overall count of CMBs detected by each rater is given in Table 3 for the three image types (T2* magnitude, SWI-mIP and IFM). Total numbers of CMBs, TP, FN and FP are detailed for each rater.

IFM yields a slight improvement of the overall ratings with respect to T2* whereas SWI-mIP yields systematic higher numbers of false positives. TP were lower for SWI than for T2* and IFM (78 vs 88-89). Both FN and FP were higher for SWI (FN: 57 vs 48-46, FP: 34 vs 16-9). Furthermore, ranges for TP, FN and FP were narrower for IFM than T2* (TP: 32 vs 54, FN: 32 vs 54, FP: 73 vs 100). Dice coefficients, given for each rater in Table 3, were slightly higher for IFM than T2* and SWI-mIP (0.74 vs 0.69-0.61). When comparing performances between raters, we note that two raters tend to underestimate the number of CMBs (CRA and Exp.Junior1) and one tends to largely overestimate it (Exp.junior2).

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Interestingly, this difference is lessened by the use of IFM with respect to the other two image types (total count range: 99 for IFM vs 150 for T2* and 198 for SWI-mIP).

In order to better understand the detection pattern between raters, ratings for definite CMBs were also analyzed. Detailed results are given in Table 4.

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were also higher for IFM than T2* and SWI-mIP (0.83 vs 0.77-0.66). IFM thus seems to mitigate inter-rater variability for definite lesions (range for total number: 36 vs 55 and 108).

Rating results: subject-type point of view

In order to evaluate the three image types with respect to their clinical usefulness, rating results were evaluated for each subgroup ("no CMB", "few CMBs", "numerous CMBs") (Table 5). The overall trend is confirmed for the subgroups, FPR being decreased by IFM with respect to T2* and SWI-mIP ((0 vs 2 and 2 for G1), (1 vs 4 and 5 G2) and (7 vs 13 and 27 for G3)), even if the performance is more balanced between methods for "no CMB" and "few CMBs" groups.

∑ TP ∑ FN ∑ FP

To investigate clinical relevance, image types were compared regarding to their ability to correctly classify the subjects in the three groups of interest. The number of correctly classified subjects for each rater and each image type is given in Table 6.

G1 (N=4) G2 (N=5) G3 (

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Table 6: Number of correctly classified patients using the three types of images.

Overall T2* magnitude and IFM classify better than SWI-mIP (median value: G1: 3/4 and 4/4 vs 2.5/4, G2: 2/5 and 2/5 vs 2/5, G3: 5.5/6 and 5/6 vs 4.5/6). IFM yields more similar results between raters than T2* magnitude and SWI-mIP (ranges: G1: 2 vs 3 and 3, G2: 2 vs 2 and 1, G3: 1 vs 4 and 4).

Discussion

We presented here a comparison of CMBs detection performance when using three different kinds of images built from the same 2D GRE T2* weighted dataset: T2* magnitude, SWI-mIP and IFM. Blind ratings by six raters were evaluated with respect to a reference built from a reliable consensus between two expert raters. Overall, 2D-dedicated phase processing yielding IFM proved a very promising tool to improve CMB detection in clinical setting. In fact, it yielded increased sensitivity and decreased FPR compared to T2* magnitude and SWI-mIP images for lesion detection. Furthermore, IFM yielded less inter-rater variability when classifying patients with numerous lesions than both other methods, with only a slight increase in rating duration.

One of the main novelties of our work was to compare between ratings performed on images obtained from the same 2D acquisition. Previous studies [START_REF] Vernooij | Cerebral Microbleeds: Accelerated 3D T2*-Weighted GRE MR Imaging versus Conventional 2D T2*-Weighted GRE MR Imaging for Detection[END_REF]) compared 2D T2* magnitude images and 3D SWI; the differences that was obtained in this study may in fact be mainly due to the differences between 2D and 3D acquisitions. Using a unique acquisition was motivated by the fact that 2D GRE multi-slice sequences are more common than 3D multi-echo GRE T2* in large multi-center

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clinical research studies. IFM thus proved an efficient mean to improve CMBs detection. The method we used here, 2DHF, removes 2D acquisition and / or reconstruction artifacts from phase images while keeping fine details with limited border effects.

False positives in CMB detection can be explained by CMBs mimics, which have similar shape and signal properties.

The most frequent source of false positives is linked with blood vessels when not fully embedded in the acquired slice. In fact, when blood vessels are really perpendicular to acquisition plane, they will appear as round hyposignal. In some cases, SWI-mIP may help to differentiate these vascular-related mimics as the projection makes it possible to highlight the 3D tubular shape, as illustrated in Figure 3.

Less frequent false positives originate from susceptibility artifacts and Partial Volume Effect (PVE).

PVE-related mimics are more likely to occur adjacent to the petrous temporal bones, para-nasal sinuses, frontal bones, orbit and occipital bone [START_REF] Werring | Cerebral Microbleeds: Pathophysiology to Clinical Practice[END_REF]; S. M. F. Gregoire 2014; Greenberg et al. 2009). Experienced raters seem to better distinguish between PVE-related mimics and CMBs as they rely more on anatomical criteria. Although the use of SWI with 3D-acquisitions is known to increase the contrast of CMBs, allowing to detect smaller CMBs, here SWI yielded increased FPR on 2D acquisitions. In fact, SWI may enhance flow voids from small blood vessels and hyposignal artifact, thus creating new mimics. Thus, the increased sensitivity with SWI is balanced by a higher FPR. Moreover, the blooming effect is emphasized by SWI compared to magnitude images and could merge close CMBs. Finally, high pass filtering technique has been proven sub-optimal for background field removal, crucial for SWI [START_REF] Kaaouana | 2D Harmonic Filtering of MR Phase Images in Multicenter Clinical Setting: Toward a Magnetic Signature of Cerebral Microbleeds[END_REF]. This could yield an enhancement of some artifactual voxels and increased the FPR.

Undetected CMBs are predominantly small lesions with low contrast with respect to their background.

The criterion based on how much of the CMB is embedded in the parenchyma varies between authors and may lead to miss CMBs very close to sulci. Examples of undetected CMBs are illustrated in The efficient calculation of IFM with the 2DHF method requires expressing boundary conditions to define the "internal" region of interest. These boundary conditions are derived from a mask of the region of interest, calculated using SPM (Statistical Parametric Mapping) software as described in [START_REF] Kaaouana | 2D Harmonic Filtering of MR Phase Images in Multicenter Clinical Setting: Toward a Magnetic Signature of Cerebral Microbleeds[END_REF], and named the brain mask. However, the border of the brain mask co-localizes with areas of strong susceptibility gradients, thus leading to potentially strong border effects. To reduce these border effects, the brain mask was eroded. Theoretically, this may lead to miss little areas of the cortex, and thus cortical CMBs, as shown in the example in Figure 5. The use of both IFM and T2* magnitude images may help solve this issue for CMB detection. Similar to SWI, IFM enhances the contrast of paramagnetic structures (Figure 2), and thus increases sensitivity with respect to T2*-magnitude images. However, compared to SWI, IFM further yields a magnetic signature of CMBs. In fact, these inclusions behave like small magnetic dipoles and thus create magnetic field patterns similar to those of dipoles; this dipolar magnetic field appears as a ringlike effect in the axial plane in IFM. The sign pattern depends on the lesion susceptibility class (paramagnetic or diamagnetic) and allows to discriminate between CMBs and cerebral microcalcifications related mimics [START_REF] Kaaouana | 2D Harmonic Filtering of MR Phase Images in Multicenter Clinical Setting: Toward a Magnetic Signature of Cerebral Microbleeds[END_REF]. Overall, IFM thus improve sensitivity (with respect to magnitude image) and decrease FPR (with respect to SWI-mIP). This results in a better characterization of subjects between "few CMBs" and "numerous CMBs".

Sensitivity and FPR of CMB detection appeared to vary between raters. Three types of rater behaviors were noted: two raters identified less CMBs on all image types and thus tended to under-rate (CRA and Exp.Junior1); one rater largely over-rated (Exp.Junior2); the last three raters had a similar tendency for medium rating (Trained.Ing and the two Exp.Seniors). For the two "under-raters", IFM was more sensitive and more specific than T2* magnitude and SWI-mIP. By contrast, for the "over-

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rater", sensitivity was very high for all image types, but most FPs were identified on SWI-mIP and FPR was twice better for IFM than T2* magnitude and SWI-mIP. For the most experienced raters, all image types were comparable regarding sensitivity but IFM shows lower FPR.

IFM proved to yield only a slight increase in rating duration, even though it was a new image type for all raters. Rating duration may be reduced by making a better use of the magnetic signature in the visualization tool.

Although studies on CMBs are becoming more common, some ambiguity remains on their rating leading in low inter-rater reproducibility. In fact, the main reasons of between-raters discrepancy are low contrast, distance with respect to sulci and lesion size. Better integrating new neuroimaging tools is likely to lead to considerable improvements with respect to these issues.

For reference building-up, consensus was obtained with a specific scoring rule, in order to take into account the intrinsic variability of CMB detection (definite and possible CMBs). In fact, although the two observers reassessed the CMBs by considering all image types simultaneously, agreement was not perfect and a few cases of non-negligible disagreement were noticed. Even though relying on a third observer or consensus meetings may have been more standard approaches, both may suffer from subjective bias, whereas our approach considered both observer equally.

Two visual scales have been proposed, MARS (The Microbleed Anatomical Rating Scale) (S. M. [START_REF] Gregoire | The Microbleed Anatomical Rating Scale (MARS): Reliability of a Tool to Map Brain Microbleeds[END_REF]) and BOMBS (Brain Observer Microbleed Scale) (Charlotte [START_REF] Cordonnier | Improving Interrater Agreement about Brain Microbleeds: Development of the Brain Observer MicroBleed Scale (BOMBS)[END_REF]). These scales were designed for clinical practice on T2* GRE weighted images and aimed at characterizing the number of CMBs and their distribution in the brain, as the clinical relevance of CMBs has been shown to be related with their localization. Here, a specific GUI was used to record the coordinates of each identified lesion allowing more accurate analysis of agreement or discrepancy cases. Moreover, rating results are embedded within an image with voxels labeled as "definite CMBs" and "possible CMBs" that can be combined either with a registered atlas or with a segmentation method to create an automatic report corresponding to the rating scales.

In this study, we have shown that IFM appears as an interesting add-on to T2*-magnitude image for the detection of CMBs. As expected, it allows discriminating mimics from real CMBs, visible "ring like" effects making it more specific in deep white and grey matter. On the contrary, T2*-magnitude image only and SWI-mIP seemed to increase false positives detection. IFM offers a simple and practical solution to assess the presence, number and distribution of CMBs on standard clinical multicenter dataset. Further clinical studies on more subjects would help better assess the advantages of each type of images with respect to clinical usefulness, together with histological studies in order to infer the physical meaning of the magnetic signature. Finally, a comparison on 3D isotropic datasets would allow a better assessment of advantages of IFM with respect to SWI when these datasets are available.

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Table 8 presents the rating results for all detected CMBs for each subject group (details of Table 5). • Comparison included T2* magnitude, SWI-mIP and IFM images using a specific GUI.

• Rating results showed an improved sensitivity of IFM compared to T2*and SWI-mIP.

• A decreased false positive rate with IFM with respect to T2*and SWI-mIP was proved. • We demonstrate a decreased inter-rater variability with IFM.

  standard-deviation of the Gaussian filter, σ, and the N parameter were empirically chosen in order to optimize the setting for CMBs detection on 2D data. The σ parameter was set to 36 pixels, as recommended in (E. Mark Haacke and Reichenbach 2011), and N was set to 8.

Figure 1 hereFigure 1 :

 11 Figure 1 here

Figure 2 here

 2 Figure 2 hereFigure 2: between-raters discrepancies during reference building-up; First column: magnitude images, second column: SWI-mIP images, third column: internal field map. First two rows: discrepancy cases from subject 3. Lesions shown here by red and green arrows are doubtful due to their shape that can be seen either as two adjacent round CMBs or as a relatively linear structure like a blood vessel. The CMB showed by the yellow arrow is very close to susceptibility artifact. Last two rows: discrepancy cases from subject 14. CMBs pointed by orange and blue arrows may have been ambiguous because of low contrast.

Figure 3 hereFigure 3 :

 33 Figure 3 here

  Figure 4.

FigureFigure 4 :

 4 Figure 4a and 4b here

Figure 5 hereFigure 5 :

 55 Figure 5 here

  Figure 1

Table 1 :

 1

				.1
			no p d
		no no no p
	Exp.2	p no p d
		d	p	d d

Reference consensus building up, scoring rules: "no" for discarded lesion, "p" for "possible CMB" and "d" for "definite CMB".

Table 2

 2 , through the number of CMBs (all or definite CMBs) detected by each of the two expert raters, the number of CMBs detected by both raters (overlap) or by a single rater (discrepancy) and the number of CMBs on the consensus computed by the scoring rules described in Table1.

		expert.1	expert.2	Overlap / discrepancy	consensus
	subject	d	all	d	all	d/d	d/p	d/no	d	all
	2	0	2	0	0	0	0	0	0	0
	12	0	1	0	0	0	0	0	0	0
	13	0	1	0	0	0	0	0	0	0
	15	0	4	0	0	0	0	0	0	0
	6	0	0	1	1	0	0	1	0	1
	5	0	2	1	1	0	1	0	1	1
	10	2	5	2	2	2	0	0	2	2
	1	4	7	1	2	1	1	2	2	4
	8	3	6	4	4	3	1	0	4	4
	9	12	12	12	16	11	0	2	11	13
	11	15	15	15	15	14	0	2	14	16
	7	16	17	12	16	11	3	3	14	17
	3	17	18	15	17	9	1	13	10	23
	4	19	24	16	24	12	6	5	18	24
	14	30	30	12	36	12	18	0	30	30
	Total	118	144	91	134	75	31	28	106	135

Table 2 :

 2 Reference building-up: CMBs detected by expert raters and consensus result. "d" refers to

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	M A N U S C R I P T
	A C C E P T E D

"definite" CMBs and "all" to the sum of definite and possible CMBs. "d/d" is the number of CMBs detected as definite by both raters. "d/p" is the number of CMBs detected as definite by one rater and possible by the other, "d/no" is the number of CMBs detected as "definite" by one observer while not detected by the other.

Table 3 :

 3 Total number of detected CMBs and comparison with the reference: TP, FN, FP and Dice.

		Total number		∑ TP			∑ FN			∑ FP			Dice Coef
		T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM
	CRA	63	70	82	51	42	73	84	93	62	12	28	9	0,52 0.41 0.67
	Exp.Junior1	82	81	89	74	65	86	61	70	49	8	16	3	0,68 0.60 0.77
	Exp.Senior1 132	113	107 99	78	95	36	57	40	33	35	12 0,74 0.63 0.79
	Trained. Ing	100	115	101 83	82	92	52	53	43	17	33	9	0,71 0.66 0.78
	Exp.Senior2 107	119	84	92	78	78	43	57	57	15	41	6	0,76 0.61 0.71
	Exp.Junior2 213	268	181 105	99	105 30	36	30 108	169	76	0,6	0.49 0.66
	Median	104	114	95	88	78	89	48	57	46	16	34	9	0.69 0.61 0.74
	Min	63	70	82	51	42	73	30	36	30	8	16	3	0.52 0.41 0.66
	Max	213	268	181 105	99	105 84	93	62 108	169	76 0.76 0.66 0.97

Table 4 :

 4 Total number of CMBs identified as "definite" and comparison with the reference.

		Total number		∑ TP			∑ FN			∑ FP			Dice Coef
		T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM
	CRA	56	54	66	47	38	62	59	68	44	9	16	4	0.58 0.48 0.72
	Exp.Junior1	72	73	81	67	60	78	39	46	28	5	13	3	0.75 0.67 0.83
	Exp.Senior1 87	74	88	81	66	84	25	40	22	6	8	4	0.84 0.73 0.87
	Trained. Ing	76	87	91	67	65	85	39	41	21	9	22	6	0.74 0.67 0.86
	Exp.Senior2 91	108	74	77	69	70	29	37	36	14	39	4	0.78 0.64 0.78
	Exp.Junior2 111 162 102 86	84	85	20	22	21	25	78	17 0.79 0.63 0.82
	Median	82	81	85	72	66	81	34	41	25	9	19	4	0.77 0.66 0.83
	Min	56	54	66	47	38	62	20	22	21	5	8	3	0.58 0.48 0.72
	Max	111 162 102 86	84	85	59	68	44	25	78	17 0.84 0.73 0.87
	Overall, the results are in accordance with Table 3. More specifically, IFM yields a higher number of
	definite CMBs than the other two image types (81 vs 72 and 66 for T2* and SWI-mIP, respectively)

and smaller number of FN (25 vs 34 and 41) and FP (4 vs 9 and 19). Value ranges follow the same trend (TP: 23 vs 39 and 16, FN: 23 vs 39 and 46, FP: 14 vs 20 and 70). Dice values for definite CMBs

Table 5 :

 5

			T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM T2*	SWI-mIP	IFM
	G1 (N=4)	Median Min Max						2 0 10	2 0 5	0 0 4
	G2 (N=5)	Median Min Max	4 3 8	3 2 5	4 2 6	9 4 9	9 7 10	8 6 10 31 4 0	5 3 7	1 0 19
	G3 (N=6)	Median 82 Min 48 Max 101 96 100 75 76 85 41 38 70 22	48 27 85	38 13 23 5 53 67 160 53 27 7 12 2

Rating results for all detected CMBs for each subject group (see Table

8

in appendix 2 for more details).

Table 7

 7 indicates recorded rating duration. Ratings from IFM took longer in most cases, but the relative difference decreased from participants with no CMBs to participants with numerous CMBs. In the worst case, it took only 1.2 times longer. Interestingly, for all image types, it took less time to do the rating for participants with few CMBs than those with no CMB.

		T2*	SWI-mIP	IFM mean
	G1 (N=4)	70	68	84	74
	G2 (N=5)	58	47	54	53
	G3 (N=6)	172 173 193 179
	mean 100 96 110

Table 7 :

 7 Mean recorded rating durations by image type and subject-type (in seconds).

Table 8 :

 8 Rating results for all detected CMBs for each subject group (details of Table5).

	G1 (N=4)	G2 (N=5)

ACKNOWLEDGMENTS

The research leading to these results has received funding from the program "Investissements d'avenir" ANR-10-IAIHU-06 The Memento study is undertaken through the sponsorship of "Bordeaux CHU" and the financial support of "Fondation Plan Alzheimer". The funding sources had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

Appendix Appendix 1: Pilot experiment

A pilot experiment was first carried-out in order to evaluate the experiment settings: number of subjects, image types and the specifically designed Graphical User Interface (GUI) built with GUIDE in MATLAB. This was conducted by an experienced neuroradiologist who selected the image types to be considered. Possible image types included: T2* magnitude, IFM and SWI minimum intensity projection (mIP) on n slices ( n=[ 2,3,4 ] ). 15 subjects proved feasible and T2* magnitude, SWI-mIP on three slices (slab thickness of 12mm) and IFM were kept for the comparison experiments and the GUI was finalized as in Figure 6. This evaluation GUI allows for displaying the overall 45 images, randomized on subjects and image types in order not to bias the comparison.