Philippe Bruneton

Frédéric Lechenault
email: frederic.lechenault@phys.ens.fr

Adèle Douin

Samuel Poincloux

Jean-Philippe Bruneton

Assessing seismic-like events prediction in model knits with unsupervised machine learning

Keywords: crackling noise, knitted fabric, seismicity, machine learning

published or not. The documents may come

Assessing seismic-like events prediction in model knits with unsupervised machine learning

Adèle Douin, Samuel Poincloux, Jean-

Introduction

A few years ago, the scientific community seemed outdistanced by the tremendous achievements of corporate machine learning research eg. in games [START_REF] Silver | Mastering chess and shogi by self-play with a general reinforcement learning algorithm[END_REF][START_REF] Mnih | Playing atari with deep reinforcement learning[END_REF][START_REF] Vinyals | Grandmaster level in starcraft ii using multi-agent reinforcement learning[END_REF] or in natural language processing [START_REF] Devlin | Pre-training of deep bidirectional transformers for language understanding[END_REF][START_REF] Li | Deep reinforcement learning for dialogue generation[END_REF]. Yet the momentum impulsed by these early developments has now galvanized a growing number of fields into the use of deep learning in particular. Ranging through robotics and computer vision [START_REF] Ruiz-Del Solar | Applications of deep learning in robot vision[END_REF], exoplanet search [START_REF] Shallue | Identifying exoplanets with deep learning: A five-planet resonant chain around kepler-80 and an eighth planet around kepler-90[END_REF], particle physics [START_REF] Radovic | Machine learning at the energy and intensity frontiers of particle physics[END_REF], cancer detection [START_REF] Ribli | Detecting and classifying lesions in mammograms with deep learning[END_REF], protein folding [START_REF] Senior | Improved protein structure prediction using potentials from deep learning[END_REF], drug design [START_REF] Jing | Deep learning for drug design: an artificial intelligence paradigm for drug discovery in the big data era[END_REF], recent use has many times demonstrated super-human scientific abilities. As potentially every field can benefit one way or another from these revolutionary tools, it is natural to actively explore their reach within physics laboratories, which are prolific data sources.

The geophysics community has been an early adopter of these approaches [START_REF] Panakkat | Neural network models for earthquake magnitude prediction using multiple seismicity indicators[END_REF], with many teams now working on earthquake prediction in the lab [START_REF] Rouet-Leduc | Machine Learning Predicts Laboratory Earthquakes[END_REF][START_REF] Johnson | Laboratory earthquake forecasting: A machine learning competition[END_REF] and in the field [START_REF] Asim | Earthquake magnitude prediction in Hindukush region using machine learning techniques[END_REF][START_REF] Mohankumar | A study on earthquake prediction using neural network algorithms[END_REF][START_REF] Corbi | Machine Learning Can Predict the Timing and Size of Analog Earthquakes[END_REF][START_REF] Huang | Large earthquake magnitude prediction in taiwan based on deep learning neural network[END_REF][START_REF] Rouet-Leduc | Probing slow earthquakes with deep learning[END_REF][START_REF] Mallouhy | Major earthquake event prediction using various machine learning algorithms[END_REF][START_REF] Yousefzadeh | Spatiotemporally explicit earthquake prediction using deep neural network[END_REF], and they have recently been invoked in the more general context of plasticity and crackling noise prediction [START_REF] Salmenjoki | Machine learning plastic deformation of crystals[END_REF][START_REF] Papanikolaou | Learning local, quenched disorder in plasticity and other crackling noise phenomena[END_REF].

In practice though, even if a given predictor achieves a reasonable accuracy, it remains unclear how to take advantage of this edge in a practical situation: on the one hand, accuracy assigns every target with the same importance regardless of their relative relevance to a specific problem, and on the other, it doesn't allow direct comparison of similar problems with different targets, i.e. from one publication to another.

Here we propose an operational solution to overcome this challenge, based on the idea that the accuracy in the prediction of a specific quantity should be evaluated in light of how informative it is to the associated underlying question, in our case risk management. First, we introduce a range of scalar targets to be predicted from analogue seismic signals emitted during the experimental deformation of knitted fabric, and train a generic neural network at these predictions. Then we define a risk-based metric balancing the impact of political decisions in an imaginary city living on our system: evacuating the city results in a given social cost, but failing to evacuate might result in casualties. Finally, we train an agent to design a policy by minimizing this penalty over time through reinforcement learning, while having access only to the predictions of the different forecasters. This bias-free, autonomous decision making process allows us to quantitatively compare the various targets and associated parameters, and to give physical meaning to the notion of accuracy within this context. Finally, we discuss the resulting ranking in terms of past and future time scales, assessing in particular the relevance of the initial forecasting endeavor.

Materials and methods

Experimental set up

In order to gather time series of seismic-like activity, we collect experimental data while mechanically cycling a nylon thread, loose Stockinette knit, which was recently shown [START_REF] Poincloux | Crackling Dynamics in the Mechanical Response of Knitted Fabrics[END_REF] to display a rich, seismic-like response. We use a setup similar to that reported in [START_REF] Poincloux | Geometry and Elasticity of a Knitted Fabric[END_REF]. We perform a tensile test, consisting in varying cyclically the elongation L of the fabric, mesuring the mechanical response during the stretching phase: the force signal and the stitches field displacement. This protocol yields a value of the force every time step of 0.04s, with a cycle duration of 2000s, leading to 50000 points of mechanical response per cycle, and 400 pictures. We collected dedicated data from 20 experiments of approximately 30 cycles each, which corresponds to roughly to 25 millions force points. The raw data for one cycle is shown in Fig. 1.

<F(L)> = b + aL f(L) = F(L) -<F(L)>

A B

Figure 1: A: mechanical response of the fabric for one complete cycle of elongation followed by a compression between L i and L f . The knitted fabric becomes entirely 2D around L = 195mm. The slow velocity part between 210 and 220 mm is zoomed in the upper left corner, and the affine response is highlighted in red. B Picture of the full knitted fabric taken during an experiment, decorated by the non-affine part of the stitch displacement field (see [START_REF] Poincloux | Crackling Dynamics in the Mechanical Response of Knitted Fabrics[END_REF] for more details). The color encodes the corresponding vorticity in arbitrary units.

Data preprocessing

Upon stretching, the mechanical response of the fabric displays large fluctuations around an affine response that is removed by a linear detrending (Fig. 1). The amplitude of these fluctuations is however non-stationary over the cycles, signaling the wear of the fabric over time. In order to build a robust normalization of this signal, we first remove the temporal mean of the data and scale it by its standard deviation, these quantities being different from one cycle to the next. Furthermore, within a given cycle, we observe that the amplitude of the fluctuations increases linearly with the extension. We thus apply a second such normalization, where the statistics are collected over a sliding time window across all cycles, which achieves a signal f with a stationary distribution.

Event statistics : a seismic analogue system

Upon closer inspection, the normalized fluctuations f exhibit a complex, "stick-slip"-like behavior, with linear loading phases interrupted by abrupt drops, as can be seen in Fig. 2 A. These force drops, or "slip-events", were shown in [START_REF] Poincloux | Crackling Dynamics in the Mechanical Response of Knitted Fabrics[END_REF] to be concomitant and correlated in amplitude with timeintermittent, spatially extended fault-like plastic events like those shown in Fig. 1 B (see Appendix B for morphological aspects of this analogy).

They are thus very reminiscent of the seismic "quakes" that threaten populations, and are as such at the heart of our prediction endeavor. We therefore define the quantity δf at each time step t by:

δf (t) = ∆f if t is the beginning of a drop 0 else. ( 1
)
where we characterize each drop by its amplitude ∆f (see Fig. 2A). Following this construction, more than 93% of δf 's values are zeros. The distribution of the events ∆f displays three different regimes: noisy structureless at low amplitude, a scale-invariant regime that extends over slightly more than 3 decades with an exponent of -1.3, and an exponential cut-off for very large and rare events. This distribution is characteristic of the avalanching dynamics found in seismic activity (see [START_REF] Ramos | Avalanche Prediction in a Self-Organized Pile of Beads[END_REF] and references within). This long-tailed statistics suggests defining classes of event severity in a logarithmic scale. As an illustrative example, we will pick either N= 5 classes centered on the decimal magnitudes in the event number count distribution, or N=2 classes with two different thresholds a and b, isolating either the The thresholds a and b used for two-class learning separate respectively the noise from the events, and "small" from "large" events. The figures correspond to the relative proportion of events in each of the five class.

noise or the large events, as shown in Fig. 2B. Class zero events correspond to noise, extended to a small event class 1. Then medium-sized events (class 2) and large events (class 3) potentially qualify as non-severe and severe respectively, while class 4 corresponds to very rare, catastrophic quakes.

Results

Predicting extreme events throught supervised machine learning

In this section we describe in detail the machine learning procedure we designed in order to predict various notions of danger imminence based on past measurements. We tackle time series forecasting using an artificial neural network whose architecture is detailed below.

Because most of the δf 's are zeros, the NN would only learn to predict zero without a proper rebalancing of the dataset. We deal with this issue by introducing a future horizon window of size τ (in time steps) and predicting the severity of future events within that window. We consider three strategies for aggregating the events in the near future:

• Target 1:

T 1(t) = max t ∈[t,t+τ ] δf (t ) (2)
This target focuses only on the largest event in the near future discarding the temporal information,

• Target 2:

T 2(t) = Σ t =t+τ t =t δf (t ) (3)
aggregates the amplitudes of events in the near future,

• Target 3:

T 3(t) = Σ t =t+τ t =t e -(t -t) (τ /3) δf (t ) (4)
confers more weight to more imminent events.

These scalar targets are then mapped to discrete labels for classification, denoted Y(t) in the following, first with two classes separated by two different thresholds, one separating the noise from the events, denoted as a, and the second one separating significant against unsignificant events, denoted as b, and then with 5 classes matching the events statistics discussed earlier. We have tested different choices of τ = 20, 40, 60 time steps, which roughly coincide with the average time delay between events from class 1 to 3. The class rebalancing achieved by all targets for τ = 20 is displayed in Table 1. Note that our approach is somewhat hybrid (via the use of τ ) with respect to other choices of the literature, where, eg. the prediction task focused on either time to failure regardless of amplitude [START_REF] Rouet-Leduc | Machine Learning Predicts Laboratory Earthquakes[END_REF] or amplitude of next event regardless of when it happens [START_REF] Mallouhy | Major earthquake event prediction using various machine learning algorithms[END_REF].

The input of the NN is built by stacking together three 1D arrays: • (f (t -n -1), . . . , f (t -1)),

• (δf (t -n -1), . . . , δf (t -1)),

• (Y (t -n -τ -1), . . . , Y (t -τ -1)).
Here, n is a past horizon that we set to 256 time steps. We investigated different NN architectures and found that convolutionalbased NNs achieved the best results. We will thus only report the results obtained with a ResNet18 [START_REF] He | Deep residual learning for image recognition[END_REF] (see Appendix G for details). The whole dataset of 27M sequences was split into 22M of them for training, 2.5M for the validation, and 2.5M for testing. The training sequences are then subsampled in order to enforce equiprobability of the associated labels. The test set is however not subsampled since we want to probe our model's abilities on realistic data.

We would like to be able to compare our results with those found in the literature [START_REF] Rouet-Leduc | Machine Learning Predicts Laboratory Earthquakes[END_REF][START_REF] Johnson | Laboratory earthquake forecasting: A machine learning competition[END_REF][START_REF] Asim | Earthquake magnitude prediction in Hindukush region using machine learning techniques[END_REF][START_REF] Mohankumar | A study on earthquake prediction using neural network algorithms[END_REF][START_REF] Corbi | Machine Learning Can Predict the Timing and Size of Analog Earthquakes[END_REF][START_REF] Huang | Large earthquake magnitude prediction in taiwan based on deep learning neural network[END_REF][START_REF] Rouet-Leduc | Probing slow earthquakes with deep learning[END_REF][START_REF] Mallouhy | Major earthquake event prediction using various machine learning algorithms[END_REF][START_REF] Yousefzadeh | Spatiotemporally explicit earthquake prediction using deep neural network[END_REF], but the choice in machine learning strategy makes this comparison difficult, even counter intuitive. Indeed, the two-class models preferred in the literature present the best accuracy, whereas we find it not very helpful to predict extreme events only. Moreover, for N=5, the accuracy value alone fails to qualify that ability, due in particular to the proportion of events in each class being highly imbalanced in the test set.

We thus also report the F1-score, which is the harmonic mean of recall and precision, two additional and complementary metrics [START_REF] Mallouhy | Major earthquake event prediction using various machine learning algorithms[END_REF] (see Appendix C for definitions), which more precisely qualifies the ratio of true positives and true negatives for each class. Both these indicators, normalized by the value they would assume with a random prediction, are displayed in Fig. 3A: the NN is indeed able to learn and generalize from the training set, and increasing the number of classes or the future horizon τ typically leads to better performance. The target T 2, which is simply the sum of the slip amplitudes in the future horizon, also seems to be mildly favored.

This result is confirmed by the direct study of false positive and false negative rates restricted to the two edge classes, noise versus extreme events only, as seen in Fig. 3B: increasing the number of event classes greatly reduces both the risk of predicting low class events when a major event is in fact going to happen, and the risk of overestimating the danger.

Furthermore, although these false positive and negative rates may seem very low (around 1% for the best model in the bottom left corner of Fig. 3B), this is still far from being perfect because extreme events have themselves an even lower occurrence rate (around ten times smaller).

As stated in the introduction, these predictions are not handy to read or use, and a quantitative assessment of their differential quality is still lacking at this point. One way around these difficulties consists in defining exactly what we mean by a useful prediction: within the georisk context, a prediction is useful if it allows policy-makers to make better informed decisions, in order in particular to save more lives while sparing the local economic activity as much as possible. In the next section we thus describe a second layer of (reinforcement) learning meant to design a risk-management policy based on the predictions of this first layer. We may on the one hand be able to compare the different models in terms of a single risk-based metric. On the other, upon inspection of the past predictions of the model, we may be able to improve the decisions with respect to some naive policy by taking advantage of the dynamics of the past predictions of event severity.

Assessment of the results: Game Theoretical Framework

In this section, we introduce KnitCity, a virtual city that is subjected to "quakes" based on the crackling dynamics extracted from the mechanical response of the knitted fabric. KnitCity laboratory keeps track of all past seismic data, and has access to all past predictions of one of the previously designed model.

At each time step, the mayor must decide whether to evacuate the city or not based on these predictions. Such a decision is a trade-off between the risk of exposing citizens to catastrophic quakes, resulting in a severe human loss, and the risk of evacuating the city for nothing, to which we may associate a "social cost", related to the corresponding economic loss for example. Such a social cost will be denoted λ for each day spent out of the city.

On the other hand, we model the human cost with the following weights corresponding respectively to events from class 0 to 4:

damage = µ [0, 0, 0, 1, 10] ( 5
)
where µ is a free parameter. Such a modeling choice reflects the fact that for actual earthquakes, there is a threshold "magnitude" below which human cost vanishes. Also, increasing by an order of magnitude the damages caused by class 4 events with respect to class 3 events reflects the fact that amplitude drops, which embody the events severity, increase exponentially with class labels. Since the ratio µ/λ is the only parameter that drives the trade-off between casualties and time out, λ can be arbitrarily set to 1. There are then two limiting behaviors: if µ goes to infinity, the optimal choice is to always stay out of the city, and to always stay in if µ goes to zero, though µ cannot be estimated a priori since it is based on social considerations. Using Eq. ( 5) and the event statistics, we may estimate typical values of µ by requiring that a random policy that evacuates the city p percent of the time yields a social cost of the same order of magnitude as the human cost. Values of p around 0.2 for example (see results section below) led to the order of magnitude: µ = O [START_REF] Mallouhy | Major earthquake event prediction using various machine learning algorithms[END_REF]. The influence of µ on the following results is discussed in Appendix E.

A decision policy π can be evaluated by a reward given by the sum over an episode: R = t∈episode s(a(t)) + h(a(t), δf (t))

where s (0 or -1) is the social cost determined by action a at time t, and h is the human cost that depends on both the action and the actual event δf :

s(a) = -λ if action: leave 0 if action: stay. (7)
h(a, δf ) = 0 if action: leave -damage(δf ) if action: stay.

In the following, we shall also use two more quantities in order to represent policy performances. We define η = 1 -actual casualties following the policy maximum casualties [START_REF] Ribli | Detecting and classifying lesions in mammograms with deep learning[END_REF] the life saving rate averaged over episodes and κ = 1 -number of steps where we evacuate number of steps in the episode [START_REF] Senior | Improved protein structure prediction using potentials from deep learning[END_REF] the population retention rate averaged over episodes: the policy consisting of always staying in the city has coordinates (0, 1) in the (η, κ) plane, while the policy consisting in always evacuating the city has coordinates (1, 0) (see Fig. 4A). An agent that randomly evacuates the city at some rate p should on average expect casualties proportional to 1 -p and thus the set of all possible random policies must lie on average on the y = 1 -x straight line. The optimal policy that consists in evacuating the city only when the damages are larger than the social cost can be evaluated by simply looking into the future: we find η = 1 and κ also very close to 1 since dangerous events are very scarce. If we moreover add that the evacuation rate is fixed and continuously varying from 0 to 1, then we may define "an optimal frontier" as being the green straight lines in Fig. 4A.

The average reward by time step can also be mapped as r = r(κ, η) = -A 1 + κ + A 2 η via the previous equations, for two constants A 1 and A 2 that can be computed given the signal statistics and µ. Models can thus be ranked with respect to the average reward per time step; constant rewards are decreasing straight lines in that space, see e.g. Fig. 4A. The relationships between r, R, η, κ, A1 and A2 is discussed in Appendix D.

Using the NN's predictions discussed above, we first manually define a naive policy based only the last available prediction, where we evacuate at every alert beyond the threshold λ, ie. every time an event of class 3 or 4 is predicted:

π naive = leave if damage(prediction) > λ stay else. ( 11
)
Results of such a naive policy are shown in Fig. 4A. The natural question is then whether we can go beyond the naive policy by leveraging the sequence of past NN's predictions through the training of a reinforcement learning agent.

We therefore trained an unsupervised model consisting in a Categorical Deep-Q-Learner [START_REF] Bellemare | A Distributional Perspective on Reinforcement Learning[END_REF] belonging to the wide class of Reinforcement Learning (RL) Agents that have achieved remarkable performance in many areas that need the time component and memory to be taken into account : from games to control, auto-pilots, etc. Such a network learns the probability distribution function of the expected rewards for a given action and a current state, and acts by sampling it. Details about the chosen hyperparameters are explained in Appendix H. We trained multiple RL agents that had access to a varying number of past predictions. We set µ = 20 and train the RL agent for the 27 models obtained in the previous section, with either 1, 4 or 16 past predictions made available to the RL agent. We will denote RL(1), RL(4) and RL( 16) these models. In terms of the average reward per step, the results in Fig. 4 clearly shows that RL agents improve upon the naive policy. Notice also that some of the models converge to the "always in" policy (especially RL(1) models).

Zooming in on the best performing models with a reward per time step |r| below 0.4, we can return a list of best models. Irrespective of the number of past data fed to the RL agent, the best model is systematically the one that uses N = 5 classes with target T3 and a future horizon of 20 or 40. Exploring further our results, we now fix the model (target 3 and N = 5), and vary τ in the range [START_REF] Silver | Mastering chess and shogi by self-play with a general reinforcement learning algorithm[END_REF][START_REF] Mallouhy | Major earthquake event prediction using various machine learning algorithms[END_REF]40,60) and for [START_REF] Silver | Mastering chess and shogi by self-play with a general reinforcement learning algorithm[END_REF][START_REF] Mnih | Playing atari with deep reinforcement learning[END_REF][START_REF] Devlin | Pre-training of deep bidirectional transformers for language understanding[END_REF][START_REF] Radovic | Machine learning at the energy and intensity frontiers of particle physics[END_REF][START_REF] Mohankumar | A study on earthquake prediction using neural network algorithms[END_REF]32) past predictions made available to the RL agent. The results, displayed in Fig. 4B, show that RL(4) and τ = 20 are the best hyperparameters to use.

Discussion

In an effort to gain insights into the immediate future crackling activity in the dynamometric signal of a knitted fabric, we have established a general framework, applicable de facto to any time series prediction for which a clear motivation can be rationalized, in which we can on the one hand compare through a common rating the predictive power of the predictor, and on the other explicitly construct a step by step action plan answering the initial motivation by efficiently exploiting the predictions. This development allows in particular to rank the relevance of the various targets with past and future horizons used in neural network predictors for the risk management in a model seismic environment. Our strategy, which consists in balancing instantaneous deleterious events with a time integrated quantity spontaneously produces interesting policies, can be extended to real-world situations when the cost function can be estimated, i.e. geological or climatic hazard. Encouragingly, our analysis clearly shows that these predictors yield some valuable information about the future.

Of course many challenges remain to be tackled within our approach. Extensive optimization of hyperparameters would certainly allow substantial refinement both in the quality of the predictor and that of the decisionmaking agent: our work only provides a proof of concept of the type of insights that can be obtained within the model environment of KnitCity, and was not fully fine-tuned. Building on our findings, it would be worth further investigating the role of the number of output classes, even going to the regression limit.

Furthermore, our dataset allows for spatially resolved predictions [START_REF] Poincloux | Crackling Dynamics in the Mechanical Response of Knitted Fabrics[END_REF] which would of course also be beneficial within the geoseismic context as satellite imaging enables such analysis: this approach is high on our list of future priorities. However, establishing a quantitative correspondence between the space and time scales in our system and those in the geophysical context would be required if we were to export the machinery introduced above to real-world situations, and this preoccupation will be at the heart of our future work on spatially resolved prediction.

(25 Hz) during the stretching phase on a shorter elongation range, between L m = 210 mm and L f , and pictures of the knit are taken every L f = 5 s. To approach the quasi-static deformation limit in the interval [L m , L f ], we impose a constant loading speed and set it at a small value v = 5 µm/s. To reduce the duration of the experiment, we fix v = 5 mm/s outside this measurement window. To strengthen our argument that the slip events display a deep similarity with earthquakes and fault slips, we describe in more details the spatial morphology of the shear lines inducing the slip events. In Fig. B.6 A, we can clearly distinguish an extended shear on both sides of the fault line, strongly reminiscent of GPS displacement data obtained across active geophysical faults, such as that shown in [START_REF] Fialko | The complete (3-D) surface displacement field in the epicentral area of the 1999 MW7.1 Hector Mine Earthquake, California, from space geodetic observations[END_REF].

Appendix B. Event Morphology

In Fig. B.6 B, we measure the displacement of the stitches with a fast camera (Photron APX RS 3000) at different time steps from a reference frame, and compute the corresponding vorticity field for each time step. We compute the position Y of each stitch along the fault direction e Y . The profile of the fault is then obtained by summing for each position Y the vorticity of the corresponding stitches. Each profile line in the plot is separated by 50 ms, which corresponds to an elongation of the fabric of 37.5 µm as it is loaded at a constant speed of 0.75 mm for this specific experiment. Two snapshots, where each pixel represents a stitch and is colored by its vorticity value, are also shown. We observe that a fault is growing progressively from a point (first snapshot), but then seems to trigger another event as the growth develops from another position. This observation is compatible with propagating faults and avalanching events.

In While the less extended events seem to present a peaked profile, extended ones like number 4 show multimodal profiles. This multi-modality is very reminiscent of that measured in geophysical faults, which are usually constituted of several interacting faults, producing distinct displacement maxima, as observed for example in [START_REF] Willemse | Three-dimensional analyses of slip distributions on normal fault arrays with consequences for fault scaling[END_REF].

Appendix C. Supervised Learning Metrics

We recall the definition of standard classification metrics for reference. Our models are all evaluated on the same set of episodes, over which the κ and η metrics are averaged. We can then express the maximum casualties, over this set, as a function of the probabilities of occurence of the events, such as damage(δf ) = 0 : p d3 = P(δf ∈ class3) and p d4 = P(δf ∈ class4).

Figure 2 :

 2 Figure 2: A: Zoom on the normalized fluctuation signal displaying "stick" phases in blue, and "slip" phases in red. A scalar event ∆f is defined by the (positive) amplitude of a "slip" phase. B: Number count distribution function of force drops amplitudes in the normalized force fluctuations. It displays a power law regime with exponent -1.3. The division into five classes is arbitrary and based on the decimal magnitude of the force drops.The thresholds a and b used for two-class learning separate respectively the noise from the events, and "small" from "large" events. The figures correspond to the relative proportion of events in each of the five class.

Figure 3 :

 3 Figure 3: A: Accuracy and F1-score for all models with respect to a random prediction. B: Learning performance in the false positive (x-axis) and false-negative (y-axis) space between noise and extreme events only for all models.

Figure 4 :

 4 Figure 4: A: Ranking of learned policies with an RL agent compared to the naive policy for the 27 different models trained in the previous section. Also shown are the lines of constant reward per time-step. B: Ranking of learned policies for the model defined with N = 5 classes and target T 3. The largest impact on the results comes from the size of the future horizon, with τ around 20 being clearly favored. The number of past predictions fed to the RL agent is less sensitive, although we find a best model for n = 4 past predictions, and a slight decrease of learning performance if we feed too many of them. Here the reward per step is plotted in absolute value, and best models have the lowest |r| values.

Figure B. 6 :

 6 Figure B.6: Color. A: Non-affine part of the stitches displacement field surrounding an isolated event. Each stitch is colored by the norm of its displacement (arbitrary scale). B: The emergence and propagation of a fault line observed with a high-speed camera. C: Picture of the a full knitted fabric with stitches colored by their vorticity values. D: Corresponding vorticity profile of each event (1 to 4) highlighted in C.

  Fig.B.6 C, 4 events, colored by their vorticity values, can be detected in the knitted fabric, and are labeled from 1 to 4. The corresponding vorticity profile of each event is shown in Fig.B.6 D.

  predicitons in class i number of elements predicted in class i (C.5) recall(i) = number of true predicitons in class i number of elements in class i (C.6) Appendix D. Relations between parameters in the Game Theoritical Framework

4 )

 4 maximum casualties = T * µ * (d 3 p d3 + d 4 p d4 ) (D.1) with T being the number of time step in an episode, d 3 = damage(δf ∈ class3) and d 4 = damage(δf ∈ class4). Thus, we can write the average reward by episode < R > as a function of η and κ: R = t∈episode s(a(t)) + h(a(t), δf (t))⇒ < R > = T * {-λ * (1 -κ) -µ * (d 3 p d3 + d 4 p d4 )(1 -η)} (D.2)To eliminate the dependency on the number of steps per episode, we define the average reward by step, over all the episodes of the set, by:r = < R > T = -1 -µ * (d 3 * p d3 + d 4 * p d4 ) + κ + µ * (d 3 * p d3 + d 4 * p d4 ) * η (D.3) which is indeed of the form r = -A1 + κ + A2η where A 1 = -1 -µ * (d 3 * p d3 + d 4 * p d4 ) and A 2 = µ * (d 3 * p d3 + d 4 * p d4) being the constants we refer to in the main text. In particular, the relation between r and < R > follows from the definition of η and κ.To relate η and p, we must first define the probability of staying while an event of class 3 occurs: P(action = stay ∩ δf ∈ class3), and the probability of staying while an event of class 4 occurs : P(action = stay ∩ δf ∈ class4). Then we can write casualties following the policy as casualties = T * µ * (d 3 * P(action = stay ∩ δf ∈ class3) + d 4 * P(action = stay ∩ δf ∈ class4)) (D.5)where P(action = stay ∩ δf ∈ class3) and P(action = stay ∩ δf ∈ class4) have a non trivial relation to p. However, in the particular case when p is chosen randomly, P (action = stay) = 1 -p and P (δf ∈ class3) or P (δf ∈ class4) become independent, allowing us to simplify the expressions (D.5) and (9), leading to η = p and κ = 1 -η.

Figure E. 7 :

 7 Figure E.7: Color. Typical positions of optimal learned policies in the η, κ space when µ is varied; for models with T 3 , N = 5 classes and τ in the tuple (20, 40, 60), and different number of past predictions. Colored lines are iso-r associated to each value of µ.

Table 1 :

 1

	Target Class 0 Class 1 Class 2 Class 3 Class 4
	δf	94%	2.2%	2.3%	1.42% 0.08%
	T1	33.5%	13%	26%	26%	1.5%
	T2	33.2%	11%	25%	29%	1.8%
	T3	49%	15.8%	23%	12%	0.2%

Example of class rebalancing: percentage of the data -raw δf and the 3 targets evaluated for τ = 20 -falling in the 5 classes defined in the text.

Acknowledgements

We thank Sebastien Moulinet for his assistance in controlling the experiment, and Florent Krzakala for numerical equipment. We acknowledge the PaRisArtificial Intelligence Research InstitutE (PRAIRIE) for financial support. https://github.com/adeledouin/KnitQuakesForecast open/.

Appendix A. Knitted Fabric and Experimental Protocol

The knits were crafted using a Toyota KS858 single bed knitting machine with nylon mono-filament (Stroft ® GTM) of diameter d = 150 µm and length 25.4 m. All samples are 83 × 83 stitches with an average lateral and longitudinal stitch size of, respectively, 3.9 and 2.8 mm. The yarn Young's modulus E ≈ 5.1 GPa was measured in a standard tensile test. The knit is clamped on its upper and lower rows by means of screws holding each stitch individually, imposing a constant spacing between them along the corresponding rows. Starting from an initial configuration with height L i = 170 mm and width L c = 360 mm, we perform the tensile test using an Instron ® (model 5965) dynamometer mounted with a 50 N load cell. The elongation L of the fabric between the jaws is varied cyclically between L i and L f = 220 mm. The force signal is recorded at high frequency

L c

Appendix E. Effects of µ

We report on the effect of varying the parameter µ, summarized in Fig. E.7. Points here are trained models grouped by values of µ. This allows to see a smooth evolution from always-in (low µ) to always-out (high µ) policies as expected. Again, this figure emphasizes that there is no unique way to define an optimal policy when predictions are not perfect; instead we get a family of trained decisional agents that are µ dependent. However the point is that the framework we introduced now provides with both quantitative and qualitative tools to explore and rank decision policies, and most importantly it allows to compare predictions of possibly completely different nature.

Appendix F. Data and materials availability

All raw and processed data are available under CC-By licence at https://osf.io/nf847/ in the KnitQuakesForecast Project (DOI 10.17605/OSF.IO/NF847). The source code of the data analysis can be found at https://github.com/adeledouin/ KnitAnalyse open/, and is plug and play with the above data set.

Appendix G. Machine learning neural net

The Neural Network used in this work is a ResNet18 -inspired by the one coded in

Appendix H. Reinforcement learning environment and model

We developed a Gym environment, and used a Categorical Deep-Q-Learner from the prfl package that can be found at https://github.com/pfnet/pfrl/. We use a distributional Q-function with discrete action of 51 atoms, with 2 hidden layers of 64 neurons. As optimizer we use Adam with an 1.10 -3 rate, and a discounting factor γ of 0.95. We subsampled the test set of the previous Section 3.1.2 in a set of 75 episodes, or "games" of 5000 time steps each (such that on average, two major events of class 4 are present in each game), and validate on unseen data grouped in 50 episodes of 5000 steps. All models are then tested on 180 new unseen episodes of the same number of steps. The code source can be found at


Natacha Fourny
email: natacha.fourny@etu.univ-amu.fr

Carole Lan
email: carole.lan@univ-amu.fr

Frank Kober
email: frank.kober@univ-amu.fr

Doria Boulghobra
email: doriaboulghobra@gmail.com

Jordan Bresciani
email: jordan.bresciani@etu.univ-amu.fr

Cyril Reboul
email: cyril.reboul@univ-avignon.fr

Monique Bernard
email: monique.bernard@univ-amu.fr

Martine Desrois
email: martine.desrois@univ-amu.fr

Cardiac remodeling and higher

Keywords: Prediabetes, High-fat high-sucrose diet, Female gender, Cardiac MRI, Ischemiareperfusion, Oxidative stress

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Type 2 diabetes is worldwide recognized as a public healthcare issue affecting 425 million of people [1]. The leading cause of mortality and morbidity in type 2 diabetic patients remains cardiovascular (CV) complications. Interestingly, type 2 diabetes leads to CV complications [2] and mortality [START_REF] Wannamethee | Do women exhibit greater differences in established and novel risk factors between diabetes and non-diabetes than men? The British Regional Heart Study and British Women's Heart Health Study[END_REF] more frequently in women than men. The risk of myocardial infarction is indeed 5 times higher in diabetic women than in non-diabetic women, whereas this risk increases only twice in men [2]. However, until now, only a small number of studies focus on female sex.

Prediabetes, a condition characterized by increased fasting plasma glucose and/or intolerance to glucose, is also related to an increase of type 2 diabetes and CV risk [START_REF] Grundy | Pre-diabetes, metabolic syndrome, and cardiovascular risk[END_REF]. Recently, the Maastricht study showed that there are already sex differences in CV risk before the onset of type 2 diabetes, with more adverse cardiometabolic profile in prediabetic women [START_REF] Veugen | 1 -5[END_REF]. During the transition from normoglycemia to impaired fasting glucose and type 2 diabetes, women present higher levels of endothelial factors and fibrinolytic / thrombotic factors than men, leading to greater endothelial dysfunction and insulin resistance [START_REF] Donahue | Impaired fasting glucose and recurrent cardiovascular disease among survivors of a first acute myocardial infarction: evidence of a sex difference? The Western New York experience. Nutrition, metabolism, and cardiovascular diseases[END_REF]. The risk of heart and coronary disease is also higher at lower glucose levels in women [START_REF] Levitzky | Impact of impaired fasting glucose on cardiovascular disease: the Framingham Heart Study[END_REF]. Factors such as oxidative stress, inflammation, dyslipidemia and mitochondrial dysfunction can contribute to endothelial dysfunction, to microvascular and macrovascular damage, leading to CV complications [START_REF] Huang | Macrovascular Complications in Patients with Diabetes and Prediabetes[END_REF]. Prediabetes is often associated with other risk factors of type 2 diabetes and CV diseases, such as abdominal obesity, hypertriglyceridemia, low HDL-cholesterol and raised blood pressure, clustered as metabolic syndrome (MetS) [START_REF] Alberti | Harmonizing the Metabolic Syndrome: A Joint Interim Statement of the International Diabetes Federation Task Force on Epidemiology and Prevention; National Heart, Lung, and Blood Institute; American Heart Association; World Heart Federation; International Atherosclerosis Society; and International Association for the Study of Obesity[END_REF]. MetS is a strong predictor of the onset of type 2 diabetes with a higher risk of 52%. MetS could be responsible for 17% of CV events and 7 % of death by CV disease [START_REF] Ford | Risks for all-cause mortality, cardiovascular disease, and diabetes associated with the metabolic syndrome: a summary of the evidence[END_REF] and contributes to the increase by 78% of CV risk and death in MetS patients [START_REF] Hu | Prevalence of the metabolic syndrome and its relation to all-cause and cardiovascular mortality in nondiabetic European men and women. -PubMed -NCBI[END_REF]. Therefore, more studies are needed to better understand prediabetic and metabolic syndrome conditions leading to higher CV risk in type 2 diabetes, particularly in women. As prediabetes and metabolic syndrome are strongly associated with obesity [START_REF] Mainous | Prevalence of Prediabetes and Abdominal Obesity Among Healthy-Weight Adults: 18-Year Trend[END_REF], it becomes clear that our environment and life habits play an important role in the disease pathogenesis. The increased intake of western diet and the decrease of physical activity combined with genetic predisposition have strongly contributed to appearance and spreading of MetS [START_REF] Wagner | Sedentary behaviour, physical activity and dietary patterns are independently associated with the metabolic syndrome[END_REF].Thus, energy-dense-diet-induced animal model could help us explore CV complications of prediabetes and MetS conditions.

The first objective of our study was to investigate the effect of a high-fat high-sucrose diet on cardiac morphology and function in parallel to the development of prediabetes in female rats, with a longitudinal follow-up in vivo using magnetic resonance imaging (MRI) and spectroscopy (MRS). The second objective was to assess the impact of high-fat high-sucrose diet on the sensitivity of heart during an ischemia-reperfusion injury, in which we combined measurement of myocardial and endothelial function with simultaneous evaluation of energy metabolism using 31 P MRS. Finally, at the end of the experiments, we have explored cellular integrity, nitric oxide (NO) pathway, apoptosis and oxidative stress in the myocardial tissue to probe further into the molecular mechanisms induced by high-fat high-sucrose diet. To our knowledge, this is the first study to consider cardiac longitudinal follow-up and tolerance to ischemic insult in prediabetic female rats under high-fat high-sucrose diet, using MRI and MRS combined with biochemical analyses.

Materials and Methods

For details, see Supplementary Material.

Animal model

Seven-week-old female Wistar rats (around 170 g, Charles River, France) (n=20) were housed in a ventilated rack cabinet, with controlled temperature (22-24°C) and multiple environmental enrichments. All procedures involving animals were approved by the Animal experiment ethic committee of the University (APAFIS#10547-2017071009112930) and were performed in conformity with the Directive 2010/63/EU of the European Parliament on the protection of animals used for scientific purposes. Animals had access to food and water ad libitum. Female Wistar rats were divided randomly in two groups of 10: The control group (CTRL) was fed with standard diet (SAFE, A04C-10); and the HFS group was fed with highfat high-sucrose diet (SAFE, U8978 v19; composition detailed in Table 1). Rats received diets for five months, and weight and food intake were measured every week. Food efficiency was calculated as the ratio of weight gain on food intake over the 5 months of diet.

Study design

The experimental protocol is summarized in Figure 1. At 7 weeks of age, twenty female rats underwent an initial MRI/MRS investigation (T0). They were randomized into two groups (CTRL and HFS), and an MRI/MRS exam was performed on all rats every month. After 5 months of diet, they underwent an intraperitoneal glucose tolerance test (IPGTT) to evaluate their metabolic status, and arterial blood pressure (BP) was measured. After sacrificing the animals, ex vivo experiments on isolated perfused heart were performed to assess myocardial function and tolerance to ischemia-reperfusion injury. At the end of the experiments, hearts were freeze-clamped for biochemical analyses.

Magnetic Resonance Imaging (MRI) and Spectroscopy (MRS) investigations

The MRI and MRS examinations were performed to evaluate in vivo cardiac morphology, cardiac function, myocardial perfusion, cardiac and hepatic triglycerides (TG) content and the amount of visceral (VAT) and subcutaneous (SCAT) adipose tissue in the body. All acquisitions were performed using a Bruker Biospec Avance MR system equipped with a 4.7

Tesla magnet (Bruker, Ettlingen, Germany) and a proton volume resonator (diameter 60 mm; homogeneous length 80 mm).

Before the experiments, rats were sedated by inhalation of 3.5% isoflurane. During MRI/MRS investigations, anesthesia was maintained at 1.5-2.5% isoflurane in 1 L/min pure oxygen-flow to obtain regular breathing at a rate of around 70 breaths per minute. Respiration, ECG signal and temperature were monitored during the whole procedure.

Every month, an ECG-gated gradient-echo cine-MRI sequence (cine-FLASH) was used for the assessment of myocardial mass and function [START_REF] Kober | Cine-MRI assessment of cardiac function in mice anesthetized with ketamine/xylazine and isoflurane[END_REF]. In vivo myocardial perfusion was quantified using the Arterial Spin Labeling (ASL) technique [START_REF] Kober | High-resolution myocardial perfusion mapping in small animals in vivo by spin-labeling gradient-echo imaging[END_REF]. At 5 months, cardiac and hepatic 1 H MR spectra were acquired for TG assessment using an ECG-and respiratory-gated Point-Resolved Spectroscopy (PRESS) sequence [START_REF] Gaborit | Assessment of epicardial fat volume and myocardial triglyceride content in severely obese subjects: relationship to metabolic profile, cardiac function and visceral fat[END_REF]. The TG/water signal ratio was calculated to obtain TG concentration. For a quantitative map of adipose tissue distribution, whole-body scanning was performed. Sixty-four contiguous axial imaging slices were selected across the animal body length excluding the tail [START_REF] Abdesselam | Time course of cardiometabolic alterations in a high fat high sucrose diet mice model and improvement after GLP-1 analog treatment using multimodal cardiovascular magnetic resonance[END_REF][START_REF] Mattei | Segmentation of fascias, fat and muscle from magnetic resonance images in humans: the DISPIMAG software[END_REF]. After each experiment, animals were kept alone under infrared light during wakefulness.

Intra-peritoneal Glucose Tolerance Test (IPGTT) and Blood Pressure assessment at

T5 months

An IPGTT was performed after 6 hours of fasting to evaluate glucose homeostasis. Glycemia was measured before and 15, 30, 60, 90, 120 minutes after injection of a bolus of glucose, using ACCU-CHEK Performa Nano Glucometer (Roche, Switzerland).

BP was recorded non-invasively by the tail cuff method (Bioseb, Chaville, France) [START_REF] Achard | Immediate Postnatal Overfeeding in Rats Programs Aortic Wall Structure Alterations and Metalloproteinases Dysregulation in Adulthood[END_REF].

Isolated perfused heart preparation and tolerance to ischemia-reperfusion injury

Rats were anesthetized by intraperitoneal injection of 90mg/kg pentobarbital sodium. Hearts were cannulated and perfused in the Langendorff mode at constant pressure as described previously [START_REF] Desrois | Upregulation of eNOS and unchanged energy metabolism in increased susceptibility of the aging type 2 diabetic GK rat heart to ischemic injury[END_REF].

Experimental protocol

After stabilization, hearts were perfused for 24 minutes with a physiological Krebs-Henseleit buffer containing 0.4 mM palmitate, 3% albumin, 11 mM glucose, 3U/L insulin, 0.8 mM lactate and 0.2 mM pyruvate. Before low-flow ischemia, they were perfused with physiological Krebs-Henseleit buffer containing 1.2 mM palmitate and then underwent a lowflow ischemia (0.5 mL/min/g wet wt) of 32 minutes with the same buffer. A higher concentration of palmitate (1.2 mM) was provided during ischemia to cause maximal damage during ischemia and reperfusion [START_REF] Lopaschuk | Alterations in fatty acid oxidation during reperfusion of the heart after myocardial ischemia[END_REF]. Finally, flow was restored entirely for 32 minutes with the physiological Krebs-Henseleit buffer containing 0.4 mM palmitate. This protocol was previously reported to provide sufficient level of ischemia in a type 2 diabetic animal model [START_REF] Desrois | Upregulation of eNOS and unchanged energy metabolism in increased susceptibility of the aging type 2 diabetic GK rat heart to ischemic injury[END_REF].

Evaluation of myocardial function and energy metabolism

A water-filled latex balloon was inserted in the left ventricle to record developed left ventricular pressure (DP) and heart rate (HR) [START_REF] Desrois | Reduced up-regulation of the nitric oxide pathway and impaired endothelial and smooth muscle functions in the female type 2 diabetic goto-kakizaki rat heart[END_REF]. The product of DP and HR (in mmHg/min) was used as an index of myocardial function. Coronary flow (CF) was measured by collection of coronary effluent before and after ischemia (at 20 minutes and 80 minutes of protocol). CF is expressed in mL/min/g wet weight.

Energy metabolism was evaluated as previously described [START_REF] Desrois | L-arginine during long-term ischemia: effects on cardiac function, energetic metabolism and endothelial damage[END_REF]. Briefly, perfused rat hearts were placed in a 20-mm magnetic resonance sample tube and inserted in a 4.7 Tesla magnet (Oxford instruments, Oxford, UK) interfaced with a Bruker-Nicolet Avance WP-200 spectrometer (Bruker, Karlsruhe, Germany). A series of eight 31 P NMR spectra were recorded during every period of the experimental protocol to quantify phosphorus metabolite signals (ATP, PCr and Pi) and intracellular pH.

Dissection and collection of samples

VAT, SCAT, tibia and blood were collected for evaluation of physiological parameters. At the end of the experiments, hearts were freeze-clamped in liquid nitrogen with a Wollenberger clamp and kept at -80°C for subsequent analysis.

Biochemical analyses

In plasma, assay kits were used to determine glucose (Randox Laboratories, Crumlin, Antrim UK), Free Fatty Acids (FFAs) (NEFA kit; Roche Diagnostics, Roche Applied Science, Mannheim, Germany), TG (Abcam, ab 65336), HDL-and LDL-Cholesterol (Abcam, ab 65390).

In freeze-clamped hearts, cellular integrity was evaluated by measurement of creatine kinase (CK) (CK-NAC, Randox Laboratories, Crumlin, UK) and lactate dehydrogenase (LDH) activities [START_REF] Desrois | L-arginine during long-term ischemia: effects on cardiac function, energetic metabolism and endothelial damage[END_REF]; apoptosis with expression of cleaved caspase-3 by Western Blot [START_REF] Huffman | Coronary effluent from a preconditioned heart activates the JAK-STAT pathway and induces cardioprotection in a donor heart[END_REF]; NO pathway with the expression of total eNOS (endothelial NO synthase), P-eNOS (phosphorylated on Ser1177) and eNOS dimer-to-monomer ratio (eNOS d/m) by Western Blot [START_REF] Farah | Exerciseinduced cardioprotection: a role for eNOS uncoupling and NO metabolites[END_REF][START_REF] Kleindienst | Exercise does not activate the β3 adrenergic receptor-eNOS pathway, but reduces inducible NOS expression to protect the heart of obese diabetic mice[END_REF]; proteins post-translational modification with evaluation of S-Glutathionylation by Western Blot; and oxidative stress with assessment of Malondialdehyde (MDA), an index of lipid peroxidation, with the lipid peroxidation assay kit (MAK085, Sigma-Aldrich, St Louis, USA).

Expression of results and statistical analyses

Data are graphically provided as mean ± SEM of absolute values. Graph Pad Prism software 5.0 (La Jolla, CA) was used for all statistical processing. Significant differences between groups were determined using two-way analysis of variance (ANOVA) with repeated measures over time for the time-dependent variables followed by Bonferroni post-hoc test. An unpaired Student's t-test was used for the other parameters. Correlation analyses were also performed between imaging and other parameters. A p value of less than or equal to 0.05 was considered to indicate significant difference.

Results

Effect of high-fat high-sucrose diet on physiological parameters

Physiological parameters are summarized in Table 1. Food intake was significantly lower in HFS versus CTRL during the whole diet (p<0.0001), while calorie intake and food efficiency were significantly increased (respectively p<0.001 and p<0.01). After 5 months of diet, the weight and the lean mass of animals was not different between groups, and neither systolic or diastolic arterial blood pressure. However, fat mass percentage was significantly higher in HFS vs. CTRL. Amount of VAT and SCAT measured by MRI was significantly higher at T5 (p=0.014 and p=0.01, respectively), as well as VAT measured by dissection (p<0.05 vs. CTRL; p=0.08 for SCAT) in HFS vs. CTRL. Measurement by MRI and dissection were strongly correlated (VAT, r=0.98; SCAT, r=0.90). The percentage of cardiac TG was not different between groups, but the percentage of hepatic TG was significantly higher in HFS vs. CTRL at T5 (p<0.001). Heart weight-to-tibia-length ratio was similar in both groups.

Plasma FFAs and fasting plasma glucose were significantly higher in HFS compared with CTRL (p<0.05 and p<0.01 respectively). No difference was found in plasma TG and HDL-Cholesterol, but LDL-Cholesterol was significantly higher in HFS compared with CTRL (p<0.05). The IPGTT highlighted a significant glucose intolerance in HFS compared with CTRL (p<0.01).

Effect of high-fat high-sucrose diet on cardiac morphology, perfusion and function

The effects of high-fat high-sucrose diet on cardiac parameters are shown in Figure 2. The high-fat high-sucrose diet led to thickening of the myocardial wall in both diastole (p<0.01, Figure 2A) and systole (p<0.01, Figure 2B), and to increased left ventricular mass (p<0.05, Figure 2C) starting at the 3 rd month of diet in HFS vs. CTRL. Myocardial perfusion (Figure 2D) was significantly increased in HFS (p<0.01) from T2 month vs. CTRL. However, the high-fat high-sucrose diet had no effect on cardiac function parameters (supplemental material) compared to CTRL.

Effect of high-fat high-sucrose diet on myocardial tolerance to ischemia-reperfusion injury

Ex vivo myocardial function and coronary flow

Myocardial function (Figure 3A) evaluated by the product of DP and HR was significantly lower in baseline conditions (p<0.05) and during reperfusion (p<0.01) in HFS vs. CTRL. The percentage of recovery, expressed as percentage of control values, was significantly lower in HFS compared with CTRL (53 % ± 6 % vs. 29 % ± 6 %; p<0.05) during reperfusion. CF was not different between groups in baseline conditions (Figure 3B). However, CF was significantly lower in HFS vs. CTRL during reperfusion (p<0.05) (Figure 3C).

Ex vivo energy metabolism and intracellular pH (pHi)

Figure 4 shows kinetics of PCr (A), ATP (B), Pi (C) and pHi (D) during the ischemiareperfusion protocol. During the control period, no difference in PCr, ATP and Pi content was found between the two groups. During ischemia, PCr and ATP were significantly decreased in HFS compared with CTRL (p<0.05) and Pi was similar in both groups. During reperfusion, PCr and ATP were significantly decreased, and Pi was significantly increased in HFS vs. CTRL (respectively p<0.01, p<0.05 and p<0.05). pHi was similar in both groups during the whole protocol.

Biochemical analyses in freeze-clamped hearts

At the end of the ex vivo experiments, we studied NO pathway involved in the endothelial function. The expression of total eNOS and P-eNOS (Figures 5A and5B) was similar between CTRL and HFS. However, we found an increase of uncoupled eNOS (inactive form) in HFS, characterized by significantly lower eNOS dimer-to-monomer ratio (Figure 5C) in comparison to CTRL (p<0.01), indicating an impaired endothelial function. Total S-Glutathionylation (Figure 5D) of proteins was decreased (p=0.052) in HFS compared with CTRL, indicating a potentially diminished protection against oxidative stress. S-Glutathionylation of eNOS (Figure 5E) was similar between groups. Malondialdehyde, a lipid peroxidation marker, was significantly increased in HFS vs. CTRL (p<0.05; 90.4 ± 6.3 vs.

± 4.7 nmol/g).

Myocardial CK and LDH activities as markers of cellular integrity were similar in CTRL (11.03 ± 0.44 and 3.97 ± 0.28 U/mg protein) and HFS (10.65 ± 0.55 and 3.97 ± 0.25 U/mg protein) groups after ischemia-reperfusion injury. In both groups, the active form of caspase-3 protein, was not expressed in hearts (data not shown) suggesting absence of apoptosis.

Correlation analyses

Correlation analyses are shown in Figure 6. FFAs, intrahepatic TG and percentage of functional recovery during reperfusion were correlated with the amount of VAT measured by MRI (respectively r²=0.68; r²=0.88 and r²=0.46).

Discussion

The aim of this study was to investigate the effects of long-term high-fat high-sucrose dietfeeding i) on the development of prediabetes and/or metabolic syndrome (MetS), ii) on cardiac parameters and iii) on myocardial tolerance to ischemia-reperfusion injury in female Wistar rats. Here, the emergence of a prediabetic state combined with metabolic disturbances has led to cardiac remodeling characterized by thickening of the myocardial wall, and to increased myocardial perfusion. High-fat high-sucrose diet also decreased the sensitivity of the heart to ischemia-reperfusion injury characterized by an impairment of cardiac function, energy metabolism and endothelial function. Finally, biochemical analyses in heart tissue highlighted eNOS uncoupling, decreased S-Glutathionylation of proteins and increased MDA in HFS compared with CTRL, indicating exacerbated oxidative stress.

Diet-induced models appear to be one of the best strategies to study prediabetic and MetS conditions associated with CV complications. In 2016, Wong et al. reviewed the different existing types of diet [START_REF] Wong | Animal models of metabolic syndrome: a review[END_REF]. To get closer to human disease, Panchal et al. suggested to use a combination of fat-and carbohydrate-enriched diet, which groups a maximum of criteria and leads to cardiac dysfunction and hypertrophy in rats after 16 weeks of diet [START_REF] Panchal | Rodent models for metabolic syndrome research[END_REF]. Here we used high-fat high-sucrose diet containing 19.4% of protein, 35.8% of fat and 32.1% of carbohydrate. After five months of diet, animals displayed the typical characteristics for diagnosis of prediabetes (higher fasting glucose and lower glucose tolerance), which were associated with metabolic disturbances that could lead to MetS and type 2 diabetes. While many studies [START_REF] Poudyal | Olive leaf extract attenuates cardiac, hepatic, and metabolic changes in high carbohydrate-, high fat-fed rats[END_REF] showed increased body weight in animals under various high-fat diets, we found that the weight of female HFS rats was not significantly increased in comparison with the control group. Aubin et al. reported the same observation in their study on female Sprague Dawley rats fed with HFD for 8 weeks [START_REF] Aubin | Female rats fed a high-fat diet were associated with vascular dysfunction and cardiac fibrosis in the absence of overt obesity and hyperlipidemia: therapeutic potential of resveratrol[END_REF]. Nishikawa et al. suggested that the female sex could be more resistant to high-fat diet-induced obesity, which could explain our results [START_REF] Nishikawa | Involvement of sex, strain and age factors in high fat diet-induced obesity in C57BL/6J and BALB/cA mice[END_REF]. Also, food intake was lower in HFS rats, possibly because the high-fat high-sucrose diet was more caloric. Consistent with this explanation, an increase of serum leptin, the hormone regulating satiety, has been previously reported in rats under high-fat diet [START_REF] Balasubramanian | High fat diet affects reproductive functions in female dietinduced obese and dietary resistant rats[END_REF]. Despite a possible regulatory mechanism via leptin, HFS animals had a higher caloric intake leading to abdominal obesity. Indeed, HFS rats did not display weight gain but MRI and dissection highlighted an abdominal obesity with significant increase of fat mass percentage (of both VAT and SCAT). Multiple human studies have shown that waist circumference, an indicator of abdominal obesity, is more representative of total body fat than BMI [START_REF] Wilner | Dynamic Relation of Changes in Weight and Indices of Fat Distribution With Cardiac Structure and Function: The Dallas Heart Study[END_REF]. Interestingly, the amount of VAT was correlated with changes in plasma FFAs and hepatic TG content.

Moreover, VAT was also correlated to the percentage of functional recovery after ischemiareperfusion injury. These observations confirm that the anatomical distribution of excess fat is closely related to the occurrence of cardiovascular and metabolic complications [START_REF] Mantatzis | Abdominal adipose tissue distribution on MRI and diabetes[END_REF], even in subject with normal weight [START_REF] De Larochellière | Visceral/epicardial adiposity in nonobese and apparently healthy young adults: association with the cardiometabolic profile[END_REF]. Expansion and dysfunction of visceral adipose tissue both result in the release of fatty acids into the circulation and in ectopic fat deposition in organs like heart, liver or pancreas [START_REF] Després | Abdominal obesity and the metabolic syndrome: contribution to global cardiometabolic risk[END_REF]. Here, we found an increase in plasma free fatty acids and LDL-cholesterol associated with an increase in intrahepatic TG content. The increase in myocardial TG content seems to occur later than the increase of hepatic TG content, as shown in male mice under high-fat high-sucrose diet [START_REF] Abdesselam | Time course of cardiometabolic alterations in a high fat high sucrose diet mice model and improvement after GLP-1 analog treatment using multimodal cardiovascular magnetic resonance[END_REF]. This may explain why we found no difference between groups regarding cardiac TG content in this study. Finally, in this model we would expect an increase in arterial blood pressure, as described by Aubin et al. in female high-fat fed rats [START_REF] Aubin | Female rats fed a high-fat diet were associated with vascular dysfunction and cardiac fibrosis in the absence of overt obesity and hyperlipidemia: therapeutic potential of resveratrol[END_REF]. Here, only a non-significant tendency to elevated systolic and diastolic blood pressures was observed in the HFS group, warranting further investigation on a larger animal group.

The combination of these risk factors predisposes women to CV complications. As shown by Levitzky et al. the risk of CV disease at lower glucose levels is higher in women than in men [START_REF] Levitzky | Impact of impaired fasting glucose on cardiovascular disease: the Framingham Heart Study[END_REF]. However, the mechanisms involved are not yet fully understood, and literature studies on female sex are scarce. Here, we followed female rats over months using cardiac MRI and observed multiple cardiac abnormalities. First, cardiac morphology was modified starting at the third month of diet with an increased myocardial wall thickness in systole and diastole.

Left ventricular mass evaluated by MRI was increased at three and four months of high-fat high-sucrose diet. Concentric remodeling may occur, for example, as a result of pressure overload (such as high blood pressure or aortic stenosis) whether or not there is ventricular hypertrophy (defined as an increase in mass) [START_REF] Panchal | Highcarbohydrate, high-fat diet-induced metabolic syndrome and cardiovascular remodeling in rats[END_REF]. Cardiomyocyte hypertrophy and cardiac fibrosis [START_REF] Panchal | Highcarbohydrate, high-fat diet-induced metabolic syndrome and cardiovascular remodeling in rats[END_REF] could also explain the cardiac remodeling found here. However, we note that heart weight to tibia length ratio obtained ex vivo was not significantly higher in HFS compared to CTRL. We attribute this apparent inconsistency to the difference in methodology of measurement in vivo and ex vivo. MRI evaluation of hypertrophy was based on an ellipsoid model [START_REF] Kober | Cine-MRI assessment of cardiac function in mice anesthetized with ketamine/xylazine and isoflurane[END_REF] evaluating the left ventricle only. Ex vivo, we measured the weight of the entire heart just before cannulation, i.e. without potential biases by blood pressure and circulation.

Dedicated histology experiments may help confirm this result in future studies.

Left-ventricular cardiac function parameters evaluated by MRI were not different in female rats submitted to high-fat high-sucrose diet for 5 months compared with CTRL, whereas ex vivo basal cardiac function was significantly weaker. The in vivo cardiac function measurements reflect dynamic volume measurements whereas ex vivo function reflects pressure developed during contraction. Also, ex vivo cardiac function is not submitted to the effective regulations and demands in vivo. A similar difference between in vivo and ex vivo cardiac function was found by Cole et al., who found normal cardiac function in vivo in rats submitted to high-fat diet but 21% decreased cardiac efficiency ex vivo compared with controls [START_REF] Cole | A high fat diet increases mitochondrial fatty acid oxidation and uncoupling to decrease efficiency in rat heart[END_REF]. They related the lower cardiac efficiency to an increase in myocardial oxygen consumption. In our study, along with cardiac function we monitored myocardial perfusion in vivo, which may be linked to oxygen consumption. Interestingly, myocardial perfusion was significantly higher in HFS vs. CTRL, despite normal in vivo cardiac function, consistent with the study by Cole et al. We thus hypothesized that HFS hearts needed higher capillary blood flow to produce the same work indicating decreased cardiac efficiency. Moreover, increased myocardial perfusion might be a transient condition found in prediabetic animals [START_REF] Nagarajan | Obesity paradox in heart failure: a heavy matter[END_REF]. In fact, a previous study in our laboratory showed decreased myocardial perfusion in type 2 diabetic male mice under high-fat high-sucrose diet [START_REF] Abdesselam | Time course of cardiometabolic alterations in a high fat high sucrose diet mice model and improvement after GLP-1 analog treatment using multimodal cardiovascular magnetic resonance[END_REF]. Also, Iltis et al. showed defective myocardial blood flow in 8-13 months type 2 diabetic GK rats [START_REF] Iltis | Defective myocardial blood flow and altered function of the left ventricle in type 2 diabetic rats: a noninvasive in vivo study using perfusion and cine magnetic resonance imaging[END_REF]. Then, it would be interesting to test this diet over a longer period to evaluate whether myocardial perfusion decreases below normal values at later stages in this model as well. Another study in type 1 diabetic patients reported higher myocardial perfusion at rest than in healthy controls [START_REF] Byrne | Myocardial perfusion at rest in patients with Diabetes Mellitus Type 1 compared with healthy controls assessed with Multi Detector Computed Tomography[END_REF]. Finally, it is well known that myocardial perfusion can be modified by isoflurane concentration, temperature or heart rate, and that perfusion values likely reflect partial vasodilation [START_REF] Iltis | In vivo assessment of myocardial blood flow in rat heart using magnetic resonance imaging: effect of anesthesia[END_REF]. However, these parameters were monitored during the MRI exam and were not different between the groups (data not shown).

In summary, 5 months of high-fat high-sucrose diet induced modification of cardiac morphology and efficiency. Using the ischemia-reperfusion ex vivo protocol, we further found higher sensitivity to ischemia-reperfusion injury in HFS compared with CTRL, characterized by a significant decrease in myocardial function and energy metabolism during reperfusion.

Under physiological conditions mitochondria play a fundamental role in oxidative catabolism leading to the production of energy in the form of ATP. Multiple mitochondrial impairments could be responsible for lower energy metabolism. Among these are mitochondrial uncoupling [START_REF] Cole | A high fat diet increases mitochondrial fatty acid oxidation and uncoupling to decrease efficiency in rat heart[END_REF], decreased expression of mitochondrial respiratory chain complex or increased ROS production. Moreover, a loss of nucleotide precursors limiting ATP repletion during reperfusion could contribute to our observation. Because these alterations may be correlated with oxidative stress, we particularly focused on myocardial MDA content as lipid peroxidation marker, which was significantly higher in HFS vs. CTRL. Pakdeechote et al.

have previously reported higher vascular superoxide production as well as higher MDA levels in plasma in metabolic syndrome rats [START_REF] Pakdeechote | Asiatic acid alleviates hemodynamic and metabolic alterations via restoring eNOS/iNOS expression, oxidative stress, and inflammation in dietinduced metabolic syndrome rats[END_REF]. Poudyal et al. also showed lowered capacity to neutralize free radicals characterized by the decrease of anti-oxidant capacity [START_REF] Poudyal | Olive leaf extract attenuates cardiac, hepatic, and metabolic changes in high carbohydrate-, high fat-fed rats[END_REF]. Finally, ischemia and mostly reflow are well-known to induce high oxidative stress, which is exacerbated here by the 5-month high-fat high-sucrose diet. We also assessed the S-Glutathionylation of proteins, which is the reversible addition of glutathione to cysteine residues inactivating the target proteins [START_REF] Belcastro | Regulation of protein function by S-nitrosation and S-glutathionylation: processes and targets in cardiovascular pathophysiology[END_REF], and which could be involved in CV complications [START_REF] Goel | Sexual dimorphism in rabbit aortic endothelial function under acute hyperglycemic conditions and gender-specific responses to acute 17beta-estradiol[END_REF]. Protein S-Glutathionylation occurs mainly at the beginning of reflow in an ischemia-reperfusion protocol and has been shown to be increased in some studies. For example, De Pascali et al. showed an increase in eNOS S-Glutathionylation during ischemiareperfusion injury in endothelial cells [START_REF] Pascali | Hypoxia and reoxygenation induce endothelial nitric oxide synthase uncoupling in endothelial cells through tetrahydrobiopterin depletion and S-glutathionylation[END_REF]. However, Belcastro et al. explained that S-Glutathionylation can also be a protective mechanism coping with irreversible oxidation [START_REF] Goel | Sexual dimorphism in rabbit aortic endothelial function under acute hyperglycemic conditions and gender-specific responses to acute 17beta-estradiol[END_REF].

This would explain the lower rate of S-Glutathionylation found here in HFS vs. CTRL. We have shown that S-Glutathionylation of all the proteins was significantly decreased in HFS compared with CTRL, but we found no difference in specific S-Glutathionylation of eNOS.

Here, we suggest that S-Glutathionylation was decreased by high-fat high-sucrose diet, leading to higher level of damage by oxidative stress in hearts. This result was consistent with the higher MDA heart content mentioned before.

Prediabetes and MetS increase the risk of cardiovascular events and have a deleterious impact on endothelial function with enhanced coronary artery disease prevalence [START_REF] Wilson | Clustering of metabolic factors and coronary heart disease[END_REF]. Altered vasodilatation has been previously described. Poudyal et al. showed lower vascular response to noradrenaline, acetylcholine and sodium nitroprusside in a MetS model [START_REF] Poudyal | Olive leaf extract attenuates cardiac, hepatic, and metabolic changes in high carbohydrate-, high fat-fed rats[END_REF] while Senaphan et al. found decreased eNOS expression in mesenteric arteries [START_REF] Senaphan | Ferulic Acid Alleviates Changes in a Rat Model of Metabolic Syndrome Induced by High-Carbohydrate, High-Fat Diet[END_REF]. Here, no significant difference was found in coronary flow before ischemia. During reperfusion, however, coronary flow was significantly impaired in HFS vs. CTRL, indicating higher sensitivity of coronary arteries to ischemia-reperfusion injury. We found no difference between the groups concerning the expression of total eNOS or its phosphorylated form. However, we found higher eNOS uncoupling in HFS compared with CTRL, with a lower dimeric (active) form of eNOS and a higher monomer form of eNOS in hearts, indicating that high-fat high-sucrose diet impaired eNOS activity. eNOS uncoupling is known to be responsible for the increase in superoxide anion O2 .-production instead of NO [START_REF] Forstermann | Nitric oxide synthases: regulation and function[END_REF]. O2 .-is highly deleterious for the cells and can also react with NO to form peroxynitrite (ONOO -), making it less available for endothelial function. ONOO -has been shown to inhibit mitochondrial respiratory chain complex [START_REF] Brown | Nitric oxide and mitochondrial respiration in the heart[END_REF]. During reperfusion this phenomenon is amplified because the free electrons couple to oxygen to form O2 .-. Moreover, patients with MetS show lower levels of superoxide dismutase able to handle superoxide anion [START_REF] Sabir | Oxidative stress among subjects with metabolic syndrome in Sokoto, North-Western Nigeria[END_REF].

Endothelial function also seems to be a key point in cardiac complications of type 2 diabetes. Desrois et al. showed endothelial impairment in female Goto-Kakizaki rats, with lower coronary flow and reduced up-regulation of the NO pathway [START_REF] Desrois | Reduced up-regulation of the nitric oxide pathway and impaired endothelial and smooth muscle functions in the female type 2 diabetic goto-kakizaki rat heart[END_REF]. Zhang et al. revealed a predisposition of females to vascular lesions after induction of diabetes, in the mesenteric arteries [START_REF] Zhang | Sex differences in mesenteric endothelial function of streptozotocin-induced diabetic rats: a shift in the relative importance of EDRFs[END_REF] and the aorta [START_REF] Han | Sexual dimorphism in rat aortic endothelial function of streptozotocin-induced diabetes: possible involvement of superoxide and nitric oxide production[END_REF]. Thus, endothelial dysfunction found in our model of prediabetes could be related to the higher cardiovascular risk in prediabetic and type 2 diabetic women.

As a perspective, it would be interesting to measure plasma hormones in order to fully elucidate their role in high-fat high-sucrose diet-induced cardiovascular modifications.

Baseline cardiac function differs between sexes in terms of heart rate, systolic output, ejection fraction [START_REF] Parks | Sex differences in mechanisms of cardiac excitationcontraction coupling[END_REF]. Studies on rodents [START_REF] Blenck | The Importance of Biological Sex and Estrogen in Rodent Models of Cardiovascular Health and Disease[END_REF] have shown that cardiac myocytes of male rats contract stronger and faster than the myocytes of female rats. Estrogen receptors (ERα and β) are both found in cardiomyocytes and may have a strong impact on cardiovascular function [START_REF] Murphy | Estrogen signaling and cardiovascular disease[END_REF].

Estrogens have been shown to protect the heart from ischemic injury [START_REF] Knowlton | Estrogen and the female heart[END_REF]. The loss of estrogens also leads to aggravation of mitochondrial dysfunction, inflammation and cardiac remodeling [START_REF] Li | The Role of Estrogen in Cardiac Metabolism and Diastolic Function[END_REF]. Sex hormones could also explain the differences found in endothelial function, as reported by Khalil et al., who showed that estrogen might directly stimulate NO production in women [START_REF] Khalil | Sex hormones as potential modulators of vascular function in hypertension[END_REF]. Interestingly, Al-Mulla et al reported a decrease in estrogens and an increase in testosterone levels in the GK rat model [START_REF] Al-Mulla | Impaired TGF-beta signaling and a defect in resolution of inflammation contribute to delayed wound healing in a female rat model of type 2 diabetes[END_REF]. However, in a model of high-fat diet, Chakraborty et al. reported an increase in estradiol level with high-fat diet [START_REF] Chakraborty | Long-Term High Fat Diet Has a Profound Effect on Body Weight, Hormone Levels, and Estrous Cycle in Mice[END_REF]. In addition, assessing the cytokine profiles in HFS rats could help us understand diet-induced metabolic and structural changes that occur before ischemia-reperfusion injury. Indeed, Pakdeechote et al. reported higher plasma TNFα and increased expression of iNOS in aorta of rat with diet-induced metabolic syndrome [START_REF] Pakdeechote | Asiatic acid alleviates hemodynamic and metabolic alterations via restoring eNOS/iNOS expression, oxidative stress, and inflammation in dietinduced metabolic syndrome rats[END_REF]. In future studies it would also be interesting to have dedicated groups for histology investigations. Previous studies showed that 16 weeks of high-carbohydrate high-fat diet could induce cardiomyocyte hypertrophy, as well as left ventricular interstitial collagen deposition and inflammatory cell infiltration in rat hearts [START_REF] Poudyal | Olive leaf extract attenuates cardiac, hepatic, and metabolic changes in high carbohydrate-, high fat-fed rats[END_REF][START_REF] Panchal | Highcarbohydrate, high-fat diet-induced metabolic syndrome and cardiovascular remodeling in rats[END_REF]62]. Finally, dietary interventions could prevent cardiac changes observed in prediabetic female rats. Abdurrachim et al. showed that intermittent fasting could delay the progression of left ventricular hypertrophy and prevent cardiac dysfunction in prediabetic obese spontaneous hypertensive heart failure rats, by modulating cardiac substrate metabolism [63]. Alam et al. showed for example that chronic L-Arginine treatment improved metabolic, cardiovascular and liver complications in diet-induced obesity in rats [62]. We also believe that an anti-oxidant approach would be of great interest in our context. For example, Resveratrol, a polyphenol, well-known for its anti-oxidant property, can protect the heart of high-fat fed rats [64].

Limitation of the study

One limitation of our study might be the absence of male groups, which could help us demonstrate sex-specific response to high-fat high-sucrose diet on cardiovascular alterations. However, we believe this is an original study on female sex which is little explored in the literature. Indeed, most of the studies use male population only, although type 2 diabetic women have a higher cardiovascular risk than type 2 diabetic men. Here, our objective was to study the female population by performing a longitudinal follow-up at the beginning of the disease and to observe the early adaptation of the heart to prediabetes. It brings new insights on cardiovascular complications in female rats during the development of prediabetes, with increased myocardial perfusion as well as high sensitivity to ischemia-reperfusion injury via impaired energy metabolism, S-Glutathionylation and eNOS uncoupling.

Conclusion

To our knowledge, this is the first study combining a longitudinal cardiac MRI follow-up with an assessment of tolerance to ischemic insult in prediabetic female rats under high-fat highsucrose diet. In female rats, prediabetes led to myocardial adaptation over months characterized by thickening of the myocardial wall and increase in myocardial perfusion. It also led to higher cardiac sensitivity to ischemia-reperfusion injury. Oxidative stress seems to be at the intersection of the pathways elucidated here, as shown in Figure 7. Oxidative stress, induced by ischemia-reperfusion, was exacerbated under high-fat high-sucrose diet. Here, it might be responsible for i) cardiac dysfunction via impaired energy metabolism with altered ATP and PCr production during ischemia-reperfusion injury, ii) endothelial dysfunction via eNOS uncoupling and decreased NO bioavailability leading to lower coronary flow, and iii) decrease of protective protein S-Glutathionylation mechanism. This work provides insights that may contribute to understanding the cardiovascular complications related to prediabetes and type 2 diabetes in the female sex.

Declarations

Author's contribution: All the authors participated substantially in the investigations reported here as indicated : N.F contributed to design, performed the experiments, data [64] Meng C, Liu JL and Du AL. Cardioprotective effect of resveratrol on atherogenic dietfed rats. Int J Clin Exp Pathol 2014;7:7899-906. Western blots were performed to analyze expression of eNOS, P-eNOS, eNOS dimer/monomer, S-Glutathionylation, eNOS S-Glutathionylation and Caspase-3 proteins.

Compounds

Colorimetric assays were performed to assess MDA heart content and activity of creatine kinase and lactate dehydrogenase enzymes.

MRI/MRS T0

Biochemical analysis

In heart tissues

  analysis and wrote the paper; C.L contributed to experiments; F.K contributed to interpretation of the overall study and manuscript writing; D.B, C.R and J.B contributed to [62] Alam MA, Kauter K, Withers K, Sernia C and Brown L. Chronic l-arginine treatment improves metabolic, cardiovascular and liver complications in diet-induced obesity in rats. Food & Function 2013;4:83-91. 10.1039/c2fo30096f. [63] Abdurrachim D, Teo XQ, Woo C-C, Lalic J and Lee P. 54(th) EASD Annual Meeting of the European Association for the Study of Diabetes : Berlin, Germany, 1 -5 October 2018. Diabetologia 2018;61:1-620. 10.1007/s00125-018-4693-0.

Figure 2 :

 2 Figure 2: Monitoring of cardiac morphology and perfusion over time by MRI. Diastolic

Figure 3 :

 3 Figure 3: Ex vivo evaluation of myocardial function. Myocardial function (A) was

Figure 4 :

 4 Figure 4: Ex vivo evaluation of energy metabolism with 31 P-MRS. Kinetics of

Figure 5 :

 5 Figure 5: Biochemical analysis in freeze-clamped hearts at the end of ischemia-

Figure 6 :

 6 Figure 6: Correlation analysis between imaging and outcomes. Plasma FFAs (A) and

Figure 7 :

 7 Figure 7: Potential mechanisms involved in the lower tolerance to ischemia-reperfusion

  Figure 1

  Figure 2

Figure 7

 7 Figure 7

Table 1 : Composition of the high-fat high-sucrose diet (SAFE, U8978)

 1

	%

Table 2 : Physiological characteristics of rats after 5 months of diet.

 2 Data are means ± SEM, two-way ANOVA was used for statistical analysis of IPGTT and t-test was used for all the other parameters. HFS group had lower food intake, higher calorie intake, food efficiency, amount of visceral and subcutaneous adipose tissue, % of fat mass, % of hepatic TG, plasma FFAs, fasting glucose, LDL-Cholesterol and intolerance to glucose. We found no difference between groups for body weight, systolic blood pressure, diastolic blood pressure, cardiac TG content, heart weight-to-tibia length ratio, plasma TG and HDL-Cholesterol. AUC: area under the curve. * p<0.001; † p<0.01 and ‡ p<0.05 vs. CTRL.

	Figure 1: Experimental protocol. At 7 weeks of age, animals (n=20) underwent a first
	MRI/MRS investigation (T0). Female Wistar rats were randomized in two groups (CTRL and
	HFS), and every month an MRI/MRS exam was performed on each rat. The following
	parameters were evaluated: myocardial morphology, function, perfusion, triglyceride content,
	hepatic triglycerides and visceral and subcutaneous adipose tissue amount. After 5 months of
	diet, rats underwent an intraperitoneal glucose tolerance test (IPGTT) to evaluate their
	metabolic status, and arterial blood pressure (BP) was measured. Then, ex vivo experiments
	on isolated perfused heart were performed to evaluate tolerance to ischemia-reperfusion injury
	with simultaneous measurement of myocardial function, energy metabolism and coronary
	flow. At the end of the experiments, hearts were freeze-clamped for biochemical analysis.

Acknowledgements:

We thank Sandrine Gayrard and Sydney Risdon from LaPEC and Dr Michel Grino from NORT for their technical support.

This work was supported by Aix-Marseille Université, CNRS (UMR 7339) and France Life Imaging (ANR-11-INBS-0006). We further acknowledge funding from Agence Nationale de la Recherche (ANR-14-CE17-0016 -COFLORES) and Fondation pour la Recherche Médicale (FRM DBS20140930772).

Funding: This work was supported by Aix-Marseille Université, CNRS (UMR 7339) and France Life Imaging (ANR-11-INBS-0006). We further acknowledge funding from Agence Nationale de la Recherche (ANR-14-CE17-0016 -COFLORES) and Fondation pour la Recherche Médicale (FRM DBS20140930772). Funding was not involved in study design; in collection, analysis and interpretation of data; in the writing of the report; and in the decision to submit the article for publication.

biochemical analyses; M.B and M.D contributed to design, interpretation of the overall study and manuscript writing. All authors read and approved the final manuscript.

Competing interests:

The authors declare that they have no competing interests.

List of abbreviations