Magalie Ochs

Roxane Bertrand

Aurélie Goujon

Deirdre Bolger

Anne-Sophie Dubarry

Philippe Blache

The Brain-IHM Dataset: a New Resource for Studying the Brain Basis of Human-Human and Human-Machine Conversations

Keywords: Feedbacks, multimodality, human-human/human-machine parallel corpus, brain basis of feedback, perception study, EEG, brain

This paper presents an original dataset of controlled interactions, focusing on the study of feedback items. It consists on recordings of different conversations between a doctor and a patient, played by actors. In this corpus, the patient is mainly a listener and produces different feedbacks, some of them being (voluntary) incongruent. Moreover, these conversations have been re-synthesized in a virtual reality context, in which the patient is played by an artificial agent. The final corpus is made of different movies of human-human conversations plus the same conversations replayed in a human-machine context, resulting in the first humanhuman/human-machine parallel corpus. The corpus is then enriched with different multimodal annotations at the verbal and nonverbal levels. Moreover, and this is the first dataset of this type, we have designed an experiment during which different participants had to watch the movies and give an evaluation of the interaction. During this task, we recorded participant's brain signal. The Brain-IHM dataset is then conceived with a triple purpose: 1/ studying feedbacks by comparing congruent vs. incongruent feedbacks 2/ comparing human-human and human-machine production of feedbacks 3/ studying the brain basis of feedback perception.

Introduction

One of the main issues is the understanding of how interaction between two humans can be successful based on the behaviour of the different interlocutors during a conversation. In particular, among the parameters guaranteeing the quality and success of an interaction, the attitude of the participant when listening to the main speaker (nodding, facial expressions, etc.) is crucial: an absence of reaction or an inappropriate reaction leads to a loss of the speaker's engagement and therefore a failure of the interaction [START_REF] Gratch | Virtual rapport[END_REF][START_REF] Bevacqua | A listening agent exhibiting variable behaviour[END_REF]. These attitudes of the interlocutor while listening are often conveyed by feedbacks. As highlighted in [START_REF] Allwood | On the semantics and pragmatics of linguistic feedback[END_REF], "The raison d'être of linguistic feedback mechanisms is the need to elicit and give information about the basic communicative functions, i.e. continued contact, perception, understanding and emotional/attitudinal reaction, in a sufficiently unobtrusive way to allow communication to serve as an instrument for pursuing various human activities". Feedbacks are very frequent, generally short and, multimodal (verbal and/or non-verbal). They ensure cohesion between interlocutors: they are a sign that the conversation is followed, understood, accepted and are therefore essential for natural interaction [START_REF] Schegloff | Discourse as an interactional achievement: some uses of ''uhhuh" and other things that come between sentences[END_REF]Alwood et al. 1992).

This question is crucial in the field of human-machine interaction based on Embodied Conversational Agent (ECA) and constitute a condition in our ability to develop environments in which the human participant perceives the behaviour of the artificial agent as believable and engaging. This question is also of deep importance when trying to determine the differences of perception of the other participant behaviours between human-human and humanmachine situations. At the brain level, several works have been done to analyze the cerebral activities of users interacting or observing artificial agents (ECA or robots). For instance, in [START_REF] Urgen | Uncanny valley as a window into predictive processing in the social brain[END_REF], users' EEG activities are analysed and compared depending on the level of realism of the robot, revealing a correlation between eventrelated brain potential and incongruent appearance and motions. In [START_REF] Rauchbauer | Brain activity during reciprocal social interaction investigated using conversational robots as control condition[END_REF], the cerebral activities of users have been recorded in fMRI and compared depending on whether the participant interacts with a robot or a human.

The problem is that only few resources exist to compare human-human and human-machine interaction in general and the behavioral and neurophysiological users' activities in particular. One of the reasons explaining this lack of resources is the difficulty to create comparable (or even better parallel) corpora with human-human and humanmachine interaction, with exactly the same context and the same dynamics in the interaction. In particular, the behaviour of the artificial agent should be comparable to a human, taking into consideration the virtual agent's expressive capacities (e.g. fluidity of the gesture, caricatured appearance).

In this paper, we first describe a method for creating a parallel corpus of human-human and human-machine conversation. In a second part, we describe how this method has been used for creating the Brain-IHM dataset. This resource is made of different conversations between a doctor and a patient. In these conversations, the doctor delivers bad news to the patient who listen and produces regularly feedbacks. The patient is played by a human actor and then re-played by an artificial agent. This corpus also comes with an original information: the brain activity of a participant watching the conversation.

The Brain-IHM dataset constitutes a unique resource for studying two types of questions:

• Feedback perception, including at the brain level • Human-human vs. human machine interaction

The Brain-IHM dataset presented in this article aims more specifically at studying the feedback in general, the related cerebral activities during their perception, and to compare feedbacks produced by a human or a virtual agent. We propose in the last section of this paper a study done starting from the Brain-IHM dataset, trying to understand whether feedbacks are processed automatically. Today, most of the existing methods to assess artificial agent are based on subjective evaluations through questionnaires filled by the users after their interaction with the virtual agent. This work makes it possible to develop an objective measure of the virtual agent's believability, based on electroencephalography (EEG). The user's EEG activity related to the perception of virtual agent's feedback could constitute objective index of the perceived believability of the agent's behaviour.

Feedbacks

Types of feedback

In this project, we focus on two types of prototypical feedbacks [START_REF] Schegloff | Discourse as an interactional achievement: some uses of ''uhhuh" and other things that come between sentences[END_REF]: continuer (nods, yes, mhmh, ok, etc.) and assessment feedback (agreement, surprise, emotion, etc.). Continuer feedbacks generally appear within 200 ms after the speaker's statement and are performed more automatically without translating a semantic evaluation of the speech, unlike assessment feedbacks which generally appear later (beyond 200 ms after the speaker's statement). We provide for each of them a precise identification of their multimodal parameters (auditory and visual).

During a natural conversation, participants are expected to adopt typical responses. As for listeners, appropriate feedbacks are required for a successful interactional achievement. The appropriateness of feedback responses depends on different criteria such as their localization or their semantic value. For example, Bavelas et al. (2000) have shown that continuers, which help to show the construction of shared knowledge, are appropriate responses when they occur in the beginning of storytelling while assessments, which display an evaluative function concerning the events described, are rather provided in the end. The appropriateness of a feedback can also depend on its semantic value that can be identified with scalar attributes related to certainty/uncertainty, understanding/non-understanding for example (Prevot et al., 2016). In this paper, we consider the appropriateness of feedback according to this criterion of semantic value.

Note that we deliberately focus, in this first study, on these two types of feedbacks (continuers and assessments) since they have the advantages to be characterized (among other things) by two factors (semantic value and localization), that we can easily manipulate to create congruent and incongruent feedbacks.

Among the different feedbacks produced by the participants in the collected corpus, 3 types have been manipulated. Let's underline that the corpus has been collected in French, but the methodology as well as the type of modelling applied here can be applied to other languages.

Target feedbacks with corresponding functions and semantic axis:

• tout à fait ("sure") corresponding to a feedback of confirmation on the semantic axis expected / unexpected • oh non ("oh no") reflecting disappointment on the axis expected/unexpected • ah bon ("really", "oh") reflecting surprise on the semantic axis uncertainty/ certainty Congruent feedback deal with items expressing the appropriate semantic value projected by the previous utterance while incongruent feedback deal with those expressing an inappropriate one. The three studied feedback types are multimodal, i.e. they are expressed through verbal and non-verbal signals. For instance, the feedback "Tout à fait" (sure) is associated with a head nod to strengthen the semantic value of confirmation in the face-to-face conversation. The feedback "ah bon" (really?) is produced with raised eyebrows to underline the semantic function of surprise. The feedback "oh non" is produced with frown eyebrows in order to reinforce the disappointment. Note that the incongruency considered in this study is the semantic incongruency, i.e. the use of a feedback with a specific function (for instance surprise) in a situation in which a feedback with another function is expected (for instance confirmation or disconfirmation). We do not consider incongruence in terms of contradiction between the verbal and non-verbal signal in the expression of a feedback (e.g. feedback with a verbal response "Tout à fait" (sure) and with a facial expression of surprise).

Virtual agent's feedbacks

The feedback described above have been reproduced on the Embodied Conversational Agent Greta of the platform VIB [START_REF] Pelachaud | Studies on gesture expressivity for a virtual agent[END_REF]. In this platform, the communicative signals, such as feedback, are described through an XMLbased languages called FML (Function Markup Language) and BML (Behaviour Markup Language) of the SAIBA international framework [START_REF] Vilhjálmsson | The behavior markup language: Recent developments and challenges[END_REF]. In order to simulate the identified feedbacks, we have enriched the library of the ECA with a set of files describing exactly the multimodal behaviour corresponding to the feedback.

Figure 1: Two different feedbacks produced by the ECA

To replicate the feedbacks on the ECA, linguists, experts on this phenomenon, have observed the feedbacks expressed by humans during the recordings of films (section 3) and have manipulated the prosody, gestures, head movements, and facial expressions of the ECA to obtain similar expressions. Figure 1 illustrates two examples of feedback. Finally, we have created 6 ECA's feedback corresponding to the needs. In addition to the 3 types of feedbacks studied, we have created 3 common feedbacks -"D'accord (I agree)", "Ok", "Oui (yes)" -to ensure a variability in the patient's behaviour and naturalness in the conversation. Note that the brain activity of the observer is not analyzed for these three feedbacks.

Creation of a parallel corpus (humanhuman and human-machine)

The Brain-IHM dataset has been designed to explore the question of feedback production in a controlled context by studying their perception by a third-party participant (hereafter the observer). Our first hypothesis is that the observer's perception of a feedback is comparable to that of the conversation's participants. In other words, when somebody hears (and sees) a conversation without attending to it, she/he will process the different elements of the dialogue in the same way as for the interlocutors. If this hypothesis is true, it broadens the possibilities of investigation. In particular, it becomes possible to study the brain's reactions of feedback perception.

Studying the brain signal of a conversation interlocutor in a natural environment is a very complex task, the signal being extremely noisy due to muscular activity, moves, etc. The idea of this Brain-IHM dataset has been then to record a dialogue between two actors reproducing a specific conversation, in which one of the interlocutors is the main speaker, the other producing regularly feedback.

Dialog scenarios and films recording

The theme chosen in this study is a medical context in which a doctor has to break bad news to a patient. Such a context is particularly suitable to the study of feedbacks since the patient is mainly in a listener position. We have first elaborated 3 scenarios, in collaboration with doctor partners of the project: intestinal perforation following endoscopy, regurgitation of gastric fluid during an operation, respiratory arrest during an operation. Each scenario led to the creation of a prototypical dialogue in which the doctor's turn taking are fully specified and followed by feedbacks produced by the listener. The dialogs have been validated by real doctors, used to be faced with such situations. The following step was to train two actors, playing the role of each dialogue interlocutors (doctor and patient). The doctor had to follow strictly the general content of each turn, but with the possibility to adapt the way the content has been expressed. The patient had to produce exactly the feedback stipulated in the scenario.

In each dialog, the patient produced several feedbacks (at least one at each turn end), among which 18 are studied. In order to compare the perception of the different types of feedbacks, we asked the actors to play the same scenario (and then the same dialogue) twice: one in which all feedbacks are congruent, the second with 50% of incongruent feedbacks (with semantic incongruency as described Section 2.1)

Example of incongruent feedback:

Doctor: Do you have any questions? Patient: Really?

Note that in the incongruent condition, some feedbacks are produced canonically (i.e. with incongruency) in order to avoid an unnatural dialog. Moreover, in the perspective of varying the patient's production, we also integrated a lexicalized turn for the patient, in response to a question of the doctor. Two doctor-actors and two patient-actors played these scenarios, for about 3 minutes each.

Each scenario led to several films, varying the doctor/patient pair. Figure 2 illustrates the set-up for the recording. In addition, for each scenario, we established specific dialogs in which patients produced incongruent feedback (e. g. a surprise feedback in place of a confirmation feedback).

From this first collection of films, we selected the best ones. They were selected by external experts in human-human interaction, evaluating the most realistic interactions. Finally, two films have been chosen for each scenario (6 films in total): one in which the patient produces congruent feedbacks, a second in which he/she produces congruent and incongruent feedbacks.

Human-human and human-virtual agents videos

Each film has been edited, allowing the patient be seen as illustrated in Figure 3.b. The goal is to make it possible for the observer to perceive as clearly as possible the feedbacks produced by the actors (virtual or real).

In order to create the parallel corpus with the virtual actor, we have annotated the video of human-human interaction described in the previous section using ELAN to identify precisely the timing (begin, end, duration) and the type of the feedbacks expressed by the actor-patient (Figure 3.a). The annotation consists in specifying the FML file in the library of multimodal feedbacks produced by the virtual agent (see section 2.2) corresponding to the feedbacks expressed by the patient in the film. Moreover, the annotation specifies the timing and the duration of the feedbacks (Figure 3.a). A tool has been developed to then generate automatically from the annotation file the animation of the virtual agent expressing the feedbacks at the exact timing. The tool takes as input the annotated files (Figure 3.a) and generates the film corresponding to the animation of the virtual patient with the appropriate feedbacks described in FML (Section 2.2) at the indicated moment and with the corresponding duration specified in the ELAN file. By this way, the feedback behaviour of the virtual agent is the same as the feedback behaviour of the actor-patient.

Moreover, the conversations were integrated into a virtual environment designed in Unity and validated by doctors to represent a recovery room where the breaking of bad news generally takes place in hospitals. In total, we obtain a corpus of 12 films, 4 per scenario. For each scenario, we have:

• two human-human films, one in which the actorpatient produces congruent feedbacks, another with congruent and incongruent feedbacks • two human/virtual agent films, one in which the artificial patient produces congruent feedbacks (the same feedbacks produced by the actor-patient and at the same time) plus a second with congruent and incongruent feedbacks (similar to the actor-patient) It is interesting to note the triple originality of the Brain-IHM dataset: 1/ it is the first corpus with controlled production of feedback 2/ it contains parallel humanhuman and human-virtual agent conversations 3/ it contains both verbal, non-verbal and electro-physiological information

Verbal and non-verbal annotations

The fact that the production is almost fully controlled facilitates annotations. At the verbal level, in particular the transcription of the dialogue is aligned onto the signal, using SPASS [START_REF] Bigi | SPPAS -Multi-lingual Approaches to the Automatic Annotation of Speech[END_REF]. This is done at the phoneme level, offering a precise segmentation in phonemes, syllables and tokens. The POS tagging is also provided, as well as a mid-level syntactic segmentation within the turns. The quality of the signal recording also offers the possibility to apply automatic prosodic analyzers.

The non-verbal level is only concerned with face attitudes: both actors were asked to be static, the listener only produced different facial expressions (nods, eyebrow raises, smiles, etc.). This information is directly annotated without using any tool, thanks to the specifications of the scenarios.

Beside these annotations, the main originality of the corpus is that it comes with two other types of information: one concerning the subjective evaluation of the virtual patient, the second with the recording of the brain signal of the participant watching the films. This two information are described in the next section.

Experimental Set-up and Design

The brain signal has been acquired thanks to a specific design. Each participant has to watch movies of the dialogue in 4 different conditions: human/human, human/virtual agent, with only canonical (congruent) or canonical and incongruent feedbacks. These conditions make it possible to do different comparisons: human vs. machine communication and congruent vs. incongruent productions. More precisely, the idea is first to confirm the hypothesis that no difference can be observed in the perception of feedbacks by human or virtual agent. This done, it becomes possible to explore the specific effects observed at the brain level.

Thirty-six participants (27 females and 9 males) have been recruited for the experiment; all participants signed a consent form at the start of the experiment and were remunerated for their participation. Subject recruited had between 18 and 40 years old.

Electroencephalography (EEG) data were recorded in a using the Biosemi Active2 64-electrode system, which amplifies the signal at the level of the participant's head via an AD-box, a DC amplifier. In this EEG system, the ground is replaced by two electrodes, the CMS (Common Mode Sense) and the DRL (Driven Right Leg), which ensure that the participant's average potential is as near as possible to the ADC voltage of the Biosemi AD-box. Signals were recorded at a rate of 2048Hz and the left mastoid was defined as the reference online. This sample rate was especially high because the same system was used to trig auditory and visual feedbacks. External electrodes were positioned on the face to record both horizontal and vertical eye movements to facilitate their offline processing During EEG recording, the participants passively watched the 4 different movies while comfortably seated in front of a computer screen in a Faraday cage. Before beginning the presentation of the movies, a very short video with sound was presented to regulate the sound level of the videos. A free-field mode of sound presentation was used via loud speakers positioned to the left and right of the screen. Participants were instructed to passively watch the 4 videos; the task did not involve any response on their part. Each movie lasted approximately 5 minutes and, between each, there was a short break during which the participant responded to an online questionnaire based on the preceding movie.

This questionnaire was composed of 7 questions or affirmations on the participants perception of the patient (virtual or real depending on the video just watched): the believability of the patient ("In your opinion, how believable is the patient compared to real patients?"), the participant's appreciation of the patient ("You like the patient"), the reactivity of the patient ("Did you find the patient responsive to what the doctor said?"), the naturalness of the conversation ("Have you found the natural conversation between the patient and the doctor?"), the perceived understanding of the patient ("Did you get the impression that the patient understood what the doctor said?"), the perceived performance of the doctor in the task of delivering the bad news ("Do you think the doctor well explained the problem and what was going to happen to the patient?" and "Do you think the doctor had difficulty telling the patient the bad news?"). The participants respond to the questions or indicate her/his level of agreement to the affirmation through a 5-point Likert scale.

The analysis of the responses to the questions on the perceived believability of the agent and of the naturalness of the conversation enables us to validate the two different conditions, either with only congruent feedbacks (congruent condition) or with congruent and incongruent feedbacks (incongruent condition). In both conditions, for the human-human and the human-virtual agent conversation, the participants have significantly perceived the conversation with incongruent feedbacks as less natural with an agent less believable than the conversation with only congruent feedbacks. Figure 4 illustrates the average responses of the participants to the question on the believability of the patient ("In your opinion, how believable is the patient compared to real patients?") on a Likert scale of 5 points. The results of the T-test show that the actor-patient expressing only congruent feedbacks (HHC) has been perceived significantly more believable than when she expressed incongruent feedbacks (HHI) (p<0.05). In the same way, virtual agent expressing only congruent feedbacks (HAC condition) has been perceived significantly more believable than when she expresses incongruent feedbacks (HAI condition) (p<0.001).

Figure 4: Mean of the responses (between 0 to 5) of the question "In your opinion, how believable is the patient compared to real patients?" for each condition.

Figure 5 illustrates the average response of the participants to the question on the naturalness of the conversation ("Have you found the natural conversation between the patient and the doctor?") on a Likert scale of 5 points. The results of the T-test show a significant difference on the perception of the naturalness of the conversation depending on the feedbacks expressed: the conversations were perceived significantly more natural when the actors (virtual or real) expressed congruent feedback than when they expressed incongruent one.

Figure 5: Mean of the responses (between 0 to 5) of the question "In your opinion, how believable is the patient compared to real patients?" for each condition.

Note that the results of the questionnaire are far from surprising but enable us to validate that the incongruent feedbacks have been perceived as such.

The presentation of the 4 types of videos (human-human congruent, human-human incongruent, human-virtual agent congruent and human-virtual agent incongruent) was counterbalanced across participants to avoid the possibility of confounds due to the order of presentation of the different scenarios. Crucially, to synchronize the onset of each feedback, auditory and visual, and the EEG signal, we integrated 2 small black squares into each video, one for auditory and one for visual feedbacks, which changed from black to white at the onset of each feedback. The change in luminosity of each colored square was detected by photodiodes positioned against the screen and the photodiode signals was recorded as two auxiliary EEG channels via the ERGO1 and ERGO2 inputs of the Biosemi AD-box (Figure 6). In addition, to ensure that the different feedback types could be distinguished offline, the duration of the colour change varied for visual and auditory feedbacks and for each of 4 video thus types yielding a different photodiode signal for each video type (Human-Human, Human-Virtual Agent), feedback modality (auditory and visual) and feedback type (congruent and incongruent). Thus, each feedback corresponds to a step function whose t0 is the onset of the feedback and the type of feedback can be determined by calculating the duration of the step function.

Application: the brain basis of feedback perception

Feedbacks can be considered at the lower level as discourse markers (more instructional than referential) or on the opposite as full linguistic objects. In the first case, feedbacks can be considered as automatic reactions to the discourse of the main speaker. Some studies have shown that such feedbacks can be predicted only from the time course [START_REF] Penteado | Evaluating Temporal Predictive Features for Virtual Patients Feedbacks[END_REF]: the occurrence of a feedback seems to be mainly dependent on the realization of the previous one (see also [START_REF] Ward | Prosodic features which cue back-channel feedback in english and japanese[END_REF]. However, some other works have also shown that feedbacks are dependent from different linguistic features such as prosody (in particular breaks) but also from morpho-syntactic information (some adverbs in the main speaker's discourse can increase the probability of a backchannel realization by the hearer [START_REF] Bertrand | Prosodic cues of back-channel signals in French conversational speech[END_REF][START_REF] Bertrand | Backchannels revisited from a multimodal perspective[END_REF]. Such a contextual behaviour indicates that a certain type of linguistic processing has to be done by the hearer. Finally, some types of feedbacks (in particular assessment feedback) require a certain understanding of the main speaker's production, or in other words a form of semantic processing, which is the higher linguistic level. Feedbacks can be then considered very differently, depending on their relationship with the previous context. In some cases, they seem to be at the lowest level, produced almost automatically where in some other cases, they seem to require deeper linguistic processing. In sum, the main question of this study is to uncover whether feedbacks are processed automatically or not.

Our first hypothesis in this study is that feedback perception relies both on automatic and deep mechanisms.

We propose for doing that to analyze the brain signal in response to the production of feedbacks. Our hypothesis is that verbal and non-verbal feedbacks elicit specific Event-Related Potentials (ERP) depending on the way they are processed. Previous works have shown that a larger early posterior negativity (EPN) can be associated with the perception of facial expression, modulating the amplitude of the N170 and P100 components [START_REF] Eimer | The Face-Sensitive N170 Component of the Event-Related Brain Potential[END_REF][START_REF] Herrmann | Early stages (P100) of face perception in humans as measured with event-related potentials (ERPs)[END_REF][START_REF] Sprengelmeyer | Event related potentials and the perception of intensity in facial expressions[END_REF][START_REF] Krombholz | Modification of N170 by different emotional expression of schematic faces[END_REF][START_REF] Righart | Context influences early perceptual analysis of faces: An electrophysiological study[END_REF]. In the same vein, some works have uncovered similar effects in the perception of emotional words (Wang et al., 2014) and more precisely the sensibility of the N170 component to emotions and their intensity [START_REF] Sprengelmeyer | Event related potentials and the perception of intensity in facial expressions[END_REF][START_REF] Krombholz | Modification of N170 by different emotional expression of schematic faces[END_REF][START_REF] Righart | Context influences early perceptual analysis of faces: An electrophysiological study[END_REF]. These effects can be associated to a certain kind of automatic processing. The hypothesis in this experiment is that feedback perception is in a certain way made up of mechanisms including facial and emotional recognition. If so, it should be the case that feedback perception would elicit comparable early components such as N170 and P100. The second aspect of this experiment is to look for traces of deep mechanisms, involving in particular a certain level of semantic processing. The way we propose to approach this question is to study the effect of incongruity in feedback perception, The idea is that incongruent feedbacks, as described in the previous section, elicit similar effect as semantic incongruity. Such a phenomenon is associated with a strong negative wave elicited 400ms after stimulus onset, known as the N400 effect [START_REF] Besson | An Event-Related Potential (ERP) Analysis of Semantic Congruity and Repetition Effects in Sentences[END_REF][START_REF] Kutas | Reading senseless sentences: brain potentials reflect semantic incongruity[END_REF][START_REF] Eimer | The Face-Sensitive N170 Component of the Event-Related Brain Potential[END_REF], that can also be observed in the case of emotional incongruity [START_REF] Leuthold | The on-line processing of socio-emotional information in prototypical scenarios: inferences from brain potentials[END_REF][START_REF] Bartholow | A psychophysiological examination of cognitive processing of and affective responses to social expectancy violations[END_REF]. We also expect that the amplitude of the N400 could be correlated with the level of incongruity of the feedback (as observed with semantic incongruity)

Our second hypothesis is that there is no difference in the perception of feedbacks produced by a human or by a virtual agent, the signal signature of the brain activity should be the same. This hypothesis is important for different reasons. First, it is necessary to study more precisely the type of mechanisms that occur at the brain level when communicating with a human or with an avatar. For example, we know that facial expressions are processed in the same way, being them produced by an avatar or a human [START_REF] Dyck | Recognition profile of emotions in natural and virtual faces[END_REF]. The Brain-IHM dataset will open new possibilities to compare human and machine communication. Moreover, at the methodological level, such type of resource and the way they are built also offer new possibilities to explore the role of some specific features in feedback production (e.g. the delay, prosody, verbal/non-verbal synchrony, etc.) that cannot be controlled easily or even produced by a human.

Conclusion

This paper presents a new and original dataset of controlled interactions, focusing on the study of feedbacks and more particularly two types of multimodal feedbacks: the continuer and the assessment. A parallel corpus of video of both human-human and human-virtual agent conversations have been created. A specific methodology has been developed to create such a corpus with a virtual agent's behaviour replicating the actor's behaviour but considering the expressive capacity of the virtual agent. In this article, we have particularly focus on the feedbacks in a French conversation between a doctor and a patient in the context of breaking bad news but the methodology could be replicated to analyse others multimodal behaviours in other language. This kind of corpus enables one to compare the perception of human-human versus human-machine interaction. Moreover, we have proposed a specific experimental setup and design to record the brain activities of the observers of the interaction.

In conclusion, the Brain-IHM dataset constitutes the first resource of this type, providing a controlled production of feedbacks, a parallel human-human/human-machine corpus, completely annotated at the verbal and non-verbal level and a set of EEG data making it possible to study the perceptive level.

•••••

  Examples: Doctor: Je suis votre médecin anesthésiste c'est moi qui vous ai endormi, vous vous en souvenez ? (I'm your anesthesiologist, I put you to sleep, do you remember?) Patient: Congruent feedback: Tout à fait • Incongruent feedback: oh non -----------Doctor: C'est un médicament qui permet de relâcher les muscles (It's a drug that relaxes muscles) Patient: Congruent feedback: Ah bon • Incongruent feedback: Tout à fait -----------Doctor: Ça a dû être un moment très pénible pour vous. (It must have been a very difficult time for you.) Patient: Congruent feedback: tout à fait • Incongruent feedback: ah bon -----------Doctor: Vous éprouvez toujours des difficultés à respirer ?( Still having trouble breathing?) Patient: Congruent feedback: tout à fait • Incongruent feedback: ah bon -----------Doctor: Avez-vous des questions ? (Do you have any questions?) Patient: Congruent feedback: tout à fait • Incongruent feedback: ah bon

Figure 2 :

 2 Figure 2: Set-up for the recording of the doctor-actor and patient-actor dialog. A green background has been used to enable us to integrate the scene in a virtual environment.

Figure 3

 3 Figure 3.a: Screenshot of the annotation of the patient's feedbacks in ELAN.

Figure 3

 3 Figure 3.b: Screenshots of the video of the Brain-IHM dataset (left, simulation of a actor-doctor /actor-patient interaction, right, re-synthesis of the same multimodal behaviour of the actor-patient on the virtual agent)

Figure 6 :

 6 Figure 6: A graphical overview of the experimental setup and protocol.

Acknowledgements

This work has been funded by the CNRS (PEPS Brain-IHM) and supported by grants ANR-16-CONV-0002 (ILCB), ANR-11-LABX-0036 (BLRI) and ANR-11-IDEX-0001-02 (A*MIDEX).4

Language Resource References

The Brain-IHM Dataset is available from the ORTOLANG DataWarehouse.


Victor Pozzobon

Perré Patrick

Lgpm

Centralesupélec

Multiscale numerical workflow describing microalgae motion and light pattern incidence towards population growth in a photobioreactor

Keywords: Photobioreactor, Growth, Light/dark cycles, Han's model, CFD

In this article, a numerical workflow describing the microalgal growth inside of a photobioreactor is proposed. CFD is used to compute reactor internal hydrodynamics taking into account marine impeller rotation and sparged bubbles motion. Lagrangian approach is used to track microalgae motion inside of the culture vessel. The illumination across the reactor is obtained using the classical Beer-Lambert's law. The combination of light field and cell motion allows to reconstruct the light history of each microalgae. These histories are then supplied to Han's model which predicts individual growth rate and experienced photodamages. Once computed, several thousands of trajectories are agglomerated at the population level yielding the photobioreactor performances. After having ensured properties convergence, this procedure is applied to a large range of optical density (0 to 4.0), i.e. cell concentration, and incident light intensities (0 to 2 000 µmolPhoton/m 2 /s). From this exploration, it is possible to determine the photobioreactor response surfaces in terms of growth rate and photodamages. These are latter used to propose an optimal lighting strategy for biomass production -reducing photobioreactor operation time by 16 % compared to classical two-step procedure -and assist light induced stress with the aim of triggering secondary metabolites production.

Introduction

Nowadays, microalgae are seen as a promising way to produces high added-value molecules such as pigments, essential fatty acids, specific carbohydrates, antioxidants [START_REF] Rizwan | Exploring the potential of microalgae for new biotechnology applications and beyond: A review[END_REF]. Being living organisms, triggering the desired molecules production usually requires a fine control over the culture. This culture commonly undergoes a two stage process: biomass production followed by a stress phase, inducing production of the molecule of interest [START_REF] Pancha | Nitrogen stress triggered biochemical and morphological changes in the microalgae Scenedesmus sp[END_REF].

In order to achieve the required level of control, the vessels are often closed and well regulated. pH, temperature and dissolved gases are usually set to desired fixed values through mechanical stirring or bubble induced mixing. Yet light patterns experienced by the cell cannot be made uniform. As microalgae are photosynthetic organisms, this may have an impact on their response to the culture protocol. As pointed by numerous authors, and reviewed by Abu-Ghosh [START_REF] Abu-Ghosh | Flashing light in microalgae biotechnology[END_REF], cells are being shuttled from high to low light intensity areas, and vice-versa. These light/dark cycles have been shown to have an important, adverse or beneficial, impact on algae growth. The most known effect being the flashing light effect -i.e. for a same total amount of light energy, growth can be promoted by taking advantage proper light/dark phases alternation [START_REF] Degen | A novel airlift photobioreactor with baffles for improved light utilization through the flashing light effect[END_REF][START_REF] Vejrazka | Photosynthetic efficiency of Chlamydomonas reinhardtii in flashing light[END_REF][START_REF] Wang | Microalgae cultivation in photobioreactors: An overview of light characteristics[END_REF][START_REF] Levasseur | Impact of seconds to minutes photoperiods on Chlorella vulgaris growth rate and chlorophyll a and b content[END_REF].

Being able to assess the impact of this phenomena during the photobioreactor design stage would save both time and effort to engineers. That is why several attempts to acquire beforehand light/dark cycles have been led [START_REF] Giannelli | A Numerical Model for the Quantification of Light/Dark Cycles in Microalgal Cultures: Air-Lift and Bubble-Column Photobioreactor Analysis by Means of Computational Fluid Dynamics[END_REF][START_REF] Sato | Development of virtual photobioreactor for microalgae culture considering turbulent flow and flashing light effect[END_REF]. To do so, authors usually rely on computational fluid dynamics as it can yield tracers motion all around a reactor [START_REF] Bitog | Application of computational fluid dynamics for modeling and designing photobioreactors for microalgae production: A review[END_REF]. For example, this was done to investigate the economical relevance of the addition of static mixer in tubular reactors [START_REF] Qin | Influence of successive and independent arrangement of Kenics mixer units on light/dark cycle and energy consumption in a tubular microalgae photobioreactor[END_REF][START_REF] Perner-Nochta | Simulations of light intensity variation in photobioreactors[END_REF]. The key parameters is usually the light/dark cycle frequencies. Sadly, few authors have linked cell positions -and experienced light patterns -to a proper microalgae growth model.

To do so, a cell level mechanistic model is required as pointed out by Bechet in his extensive review of light models predicting microalgal growth [START_REF] Béchet | Modeling the effects of light and temperature on algae growth: State of the art and critical assessment for productivity prediction during outdoor cultivation[END_REF]. This is the purpose of Han's model which links perceived illumination over time and cell growth. This approach also raises the question of the quality of the light field prediction. Improved methodologies have been delivered by some authors [START_REF] Franco-Lara | Model-supported optimization of phototrophic growth in a stirredtank photobioreactor[END_REF]. Yet they used the obtained high quality light maps as input of averaged growth rate models. This highlights the complexity of properly predicting algae motion, experienced light/dark cycles and subsequent growth.

Nevertheless, this modeling approach has successfully been led for raceway open ponds [START_REF] Hartmann | Growth Rate Estimation of algae in Raceway Ponds: A novel Approach[END_REF], as light distribution inside of the vessel is obtained in a straightforward manner. Yet these reactors are usually placed outdoor, moderately controlled and do not offer as many ways to modify light/dark cycles as closed vessels. Applying the same approach to indoor photobioreactor is the aim of this work. Indeed, given the wide range of parameters one can control on this kind of reactor -aeration, stirrers speeds, external light intensity -, it would paves the way to improving the benefits drawn from the flashing light effect at the photobioreactor scale, as pointed out by Gao in his recent review [START_REF] Gao | Simulation of algal photobioreactors: recent developments and challenges[END_REF]. Among the few available studies, none produced a response surface of the photobioreactor, nor dealt with impellers. Our work aims at boarding the community capabilities in these two aspects. As the first one is key for proper batch operation given the fact that the culture evolves with time. As for the second, it has been highlighted in recent work [START_REF] Luzi | Comparison between different strategies for the realization of flashing-light effects -Pneumatic mixing and flashing illumination[END_REF] that pneumatic mixing alone cannot achieve efficient flashing light effect. Indeed it restricts average achievable light/dark cycles frequencies and prevents the use of high diameter culture vessels because of low efficiency radial mixing.

In this work, the CFD-light-biological model coupling is applied to a 5 liter lab scale photobioreactor hosting a Porphyridium sp. culture (Fig. 1). The design is quite common: a cylindrical shape with a spherical lower end. Light is supplied externally by LEDs placed in an enclosure all around the reactor (not shown on the picture). CO2-enriched air is bubbled by a cylindrical sparger to supply carbon to the culture. Stirring is ensured by a marine impeller. Finally, probes are immersed in the growth medium to allow for continuous monitoring. The whole system behavior is investigated numerically for different cell concentrations, light intensities and stirring speeds, to assess both growth and photodamages.

Mathematical model

In order to model the behavior of a whole photobioreactor, different submodels are coupled. First of all, a classical two phase flow model is used to predict internal hydrodynamic. Then, microalgae motion is tracked using Lagrangian approach. Illumination along the microalgae trajectories is obtained using cylindrical Beer-Lambert law. Finally, these information are supplied to Han's model in order to compute individual, and, by averaging, population growth rate.

Fluid dynamics model

The hydrodynamic features three different phases: the growth medium, considered as a continuum, the bubbles, considered as a dispersed gaseous phase and the microalgae considered as a dispersed solid phase. The dispersed phases are described as Lagrangian particles. They will be governed by the same equations, yet with different physical parameters.

Continuum description

The liquid flow is modeled using classical incompressible Navier Stokes equations, considering the growth medium as a Newtonian fluid. While valid for low concentration cultures, this assumption could be discussed for high density ones. Here, for the sake of simplicity, it will be maintained throughout this work. The stirrer motion is described using Multiple Reference Frame approach. This method approximates the rotary flow pattern around the impeller. To do so, the impeller shape is added to the case geometry, yet it will be kept stationary. Besides, a source term inducing a rotational flow is added into the Navier Stokes momentum equation (Coriolis force: αsρ f ω × u f ). This way, the main fluid structures can be reproduced. This approach is commonly used for the prediction of stirred tank hydrodynamics [START_REF] Deglon | CFD modelling of stirred tanks: Numerical considerations[END_REF][START_REF] Wang | Evaluation of the Multiple Reference Frame (MRF) Model in a Truck Fan Simulation[END_REF][START_REF] Bujalski | CFD Study of Homogenization with Dual Rushton Turbines-Comparison with Experimental Results: Part II: The Multiple Reference Frame[END_REF], provided the tank diameter is twice the one of the impeller [START_REF] Oshinowo | Chapter 35 -Predicting the tangential velocity field in stirred tanks using the Multiple Reference Frames (MRF) model with validation by LDA measurements[END_REF]. Its main advantage is to avoid the computation of a CPU intensive mesh deformation. In our case, a source term corresponding to a 100 rpm rotation speed is located in the volume in the vicinity of the impeller (where αs = 1 over 1.1 times the impeller diameter, 8 cm, 0 elsewhere). Furthermore, from a biological perspective, this rotation speed represents an impeller tip velocity of 0.64 m/s which is not harmful to Porphyridium sp. (damages being induced from 2.45 m/s [START_REF] Sobczuk | Effects of agitation on the microalgae Phaeodactylum tricornutum and Porphyridium cruentum[END_REF]).

Bubbles are also contributing to the continuum motion. As they are traced using a Lagrangian approach (Sec. 2.1.2), the forces they apply on the liquid can directly be accounted for in the momentum balance equation ( 1Vc n i=1 m i=1 F i t ). In addition to the aforementionned phenomena, turbulence matters in the way the liquid moves around the reactor. In our case, the RNG-k-model is chosen to model it, as it proved to perform well in stirred tanks configurations [START_REF] Zakrzewska | CFD Modeling of Turbulent Jacket Heat Transfer in a Rushton Turbine Stirred Vessel[END_REF][START_REF] Ammar | Numerical investigation of turbulent flow generated in baffled stirred vessels equipped with three different turbines in one and two-stage system[END_REF][START_REF] Aubin | Modeling turbulent flow in stirred tanks with CFD: the influence of the modeling approach, turbulence model and numerical scheme[END_REF]. As fine computation of the shear stress induced pressure drop is not of interest here, walls interactions are described using high Reynolds approach, i.e. neglecting viscous sub-layer contribution.

Finally the continuum motion is governed by the following equation:

∂ ∂t (ρ f u f ) + ∇ • (ρ f u f u f ) = -∇p + ∇ • (µ + µt) ∇ u f + ∇ u f T - 2 3 ρ f kI - 1 Vc n i=1 m i=1 F i t -αsρ f ω × u f + ρ f g (1)
Liquid properties are taken as those of 20 °C water (density: 998 kg/m 3 , viscosity: 1.0 10 -3 Pa.s, air-water surface tension: 72 mN/m).

Lagrangian phases description

Dispersed phases motion (bubbles and microalgae) is described using a Lagrangian approach. With this method the tracers trajectories are the results of a force balance. This balance sums the contribution of: virtual mass, drag and buoyancy (Eq. 2).

ρpVp d up dt = m j=1 F i p = -Cmρ f Vp d up dt + 1 2 ρ f C d Sp u f + ut -up ( u f + ut -up) + Vp g(ρ f -ρp) ( 2
)
Where Cm is the virtual mass coefficient, C d is the drag coefficient, and ut the turbulent velocity fluctuation expressed as the two thirds of the square root of the turbulent kinetic energy supported by a randomly oriented (U[0, 4π]) vector with a randomly drawn magnitude (U[0, 1]) (Eq. 3).

ut = 2 3 √ k Λ (3)
Potential tracers-walls collision are described using elastic shock model with no energy dissipation. The same description is used for cell-cell collisions. Bubble-bubble collisions are described with a 0.5 probability of coalescence provided their merging would yield a stable bubble [START_REF]Shapes and velocities of single drops and bubbles moving freely through immiscible liquids[END_REF]. Furthermore, cells are considered spherical with a uniform diameter of 12 µm. Bubbles are also described as spherical as the sparger holes low diameter (0.5 mm) ensures the formation of small spherical bubbles. The bubble individual diameter is drawn from a Gaussian distribution, centered around 3.40 mm, the diameter that balance the sparger diameter using 2πRsσ = 4 3 πR 3 b g(ρ f -ρ b ). The distribution standard deviation is taken as 10 % of the mean value. The coefficients describing the two Lagrangian populations are taken from literature and summarized in Table 1.

Case setup and solving strategy

The model is applied to the description of a 5 liter cylindrical photobioreactor with a spherical lower end. The culture volume inside of the reactor is 4.5 liters. This reactor features several key technical elements: a gas sparger, providing dissolved CO2 to the microalgae, a marine impeller, preventing them from settling at the bottom of the bioreactor, a pH probe, allowing to monitor the culture online. In the numerical reproduction, the complex geometry induced by these elements is accounted for when meshing the culture volume. Figure 2 provides a schematic view of the numerical setup with the associated boundary conditions.

The CFD model is implemented under OpenFOAM [START_REF] Jasak | OpenFOAM: A C++ Library for Complex Physics Simulations[END_REF] into an homemade solver. The code uses a PISO strategy (Pressure-Implicit with Splitting of Operators) to solve momentum and mass continuity equations. Momentum equation also features a two-way interaction with the bubbles swarm, as Langragian phase volume fraction is around 10 -3 [START_REF] Elghobashi | On predicting particle-laden turbulent flows[END_REF] (or below with around pH probe. Dashed delimited: area where the momentum source term is applied to emulate stirrer motion 100 bubbles present in the reactor at the same time). For every iteration, once the flow is computed, the bubbles and microalgae populations positions are updated. Mirocalgae positions are then extracted, associated illumination and resulting growth are then computed. The mesh is made of about 200 000 cells, with a higher cell refinement near the walls and the solid elements immersed into the culture medium. Figure 3 provides a visualization of the numerical setup after 1 minute of run.

α s = 0 α s = 1
Being initially still, the water is set in motion by the marine impeller and the bubble motion. Yet after a certain time, the hydrodynamic enters into a quasi-steady state (supplementary materials, Sec. 8.1). The transient period should not be taken into account as it is only represent a tiny fraction (few seconds over a week) of the operation of an actual photobioreactor.

Here, this timelap is around 10 seconds. In order to be conservative and to be sure that all the tracers trajectories would not feature artefacts from this transient state, the 60 first seconds are discarded. The code is then run for 10 minutes. Thus the total runtime is 11 minutes, which were produced in about 3 days on a desktop computer (3 threads, Intel(R) Xeon(R) CPU E5-2643 v3 @ 3.40GHz, DDR3 64 Go 2133MHz).

Light and cell growth model

Illumination field inside of the reactor is computed using the cylindrical Beer-Lambert law [START_REF] Katsuda | Light intensity distribution in the externally illuminated cylindrical photo-bioreactor and its application to hydrogen production by Rhodobacter capsulatus[END_REF]. Even though some authors have proposed corrections to this law, in order to take microalgae radiative properties into account [START_REF] Fernández | BIT1%3E3.0.CO%3B[END_REF], they have been shown to be a little influence for concentrated culture -the usual operating condition of a photobioreactor -, at least for cylindrical shapes [START_REF] Qin | Influence of successive and independent arrangement of Kenics mixer units on light/dark cycle and energy consumption in a tubular microalgae photobioreactor[END_REF]. Thus, the unmodified law is used is this work (Sec. 8.2).

From the CFD computation, the position of each tracer is extracted every 0.01 second (Fig. 4). Using the light field computed inside of the reactor, position and perceived illumination are linked for a given optical density (i.e. cell concentration). Because external lighting and cell concentration are assumed to have little impact on reactor hydrodynamic, this procedure can be repeated over a range of conditions. In this work, external light is considered uniform and ranges from 0 to 2 000 µmolPhoton/m 2 /s, while optical density ranges from 0 to 4.0. The optical density is taken as the one that would yield a spectrophotometer mounted with 1.00 cm cuvettes.

Once light histories of all the tracers are built, the individual growth rate is computed using Han's model (Eq. 4, 5, and 6, Fig. 5). This model is now well-established in the community [START_REF] Han | Photosynthesis-Irradiance Response at Physiological Level: a Mechanistic Model[END_REF][START_REF] Han | A Mechanistic Model of Algal Photoinhibition Induced by Photodamage to Photosystem-II[END_REF] and has been shown to perform well given its low number of parameter [START_REF] Rudnicki | A comparative study of photosynthetic unit models for algal growth rate and fluorescence prediction under light/dark cycles[END_REF]. It links together perceived illumination (I) and resulting growth (B state and later µ) and photodamages (C state). In short (Fig. 5), it considers that open photosystems (A state) can convert light into chemicals, with a given photon capture chance (σPSII) and turnover rate (1/τ ). Yet if a processing photosystem is hit before it returned to the open state, it may undergo damages (κ d probability), that will later be repaired (1/κr repair time). In our case, the parameters describing the cell responses are taken from previous work [START_REF] Pozzobon | Han's model parameters for microalgae grown under intermittent illumination: Determined using particle swarm optimization[END_REF] (Tab. 2). It this work the parameters reproducing the light dependence of red marine algae Porphyridium sp. (UTEX637) were determinded using experimenal data [START_REF] Wu | A model integrating fluid dynamics in photosynthesis and photoinhibition processes[END_REF] used as input to a particle swarm optimizer [START_REF] Pozzobon | Han's model parameters for microalgae grown under intermittent illumination: Determined using particle swarm optimization[END_REF]. For those experimental investigations, microalgae were grown under different light intensities, under different light/dark periods and fed with 3% CO2 air bubbling. Thus, our numerical photobioreactor is performing the scale up of this strain under this level of CO2. A point of note, should still be added, in this configuration, cells are considered as individuals. While true for the majority of growth conditions, this assumption can be invalidated under stress conditions. Indeed, as protection mechanism conferring a selective edge, cells can aggregate forming multicelluar stable bodies [START_REF] Ratcliff | Experimental evolution of multicellularity[END_REF][START_REF] Boraas | Phagotrophy by a flagellate selects for colonial prey: A possible origin of multicellularity[END_REF]. The possibility of cell clusters appearance under high light conditions cannot firmly be ruled out, still its investigation lies outside of the scope of this study. The former equations system is integrated for every tracer at each time step. Thus it yields the fraction of open, working and damaged photosystems over the whole simulation. In order to go one step further, it is possible to link the photosystem state to population growth under the assumption that light is the limiting growth factor. With given units, i.e. µ in per hour, τ in seconds and M e in per hour, the equation governing population growth rate can be expressed as Eq. 7:

dA dt = -IσPSIIA + B τ ( 4
)
dB dt = IσPSIIA - B τ + κrC -κ d IσPSIIB (5)
µ = K B τ -M e (7)
Still, in our case, Han's model calls for a comment. Indeed, cell physiological state may vary over the course a culture as they can manage their pigment content to either adapt low or excess light as well as redeploy nitrogen contained in chlorophylls. These variations could be taken into account through adaption of antenna size evolution (σPSII). In addition, cells can sometime aggregate. In this last condition, perceived light may be less for the inner cells than the outer ones. For the sake of simplicity, we considered cells as individuals with constant photosynthetic parameters.

Finally, individual growth rate are averaged into a population level growth rate. The integration procedure is repeated for each couple of light intensity and reactor optical density. In the end, it delivers the response surface of the microalgal population inside of the reactor over a wide range of incident light intensity and optical density.

Population level convergence

Before producing and commenting results at the photobioreactor scale, it is mandatory to ensure that the produced values are independent of purely numerical parameters. To do so, an increasing amount of tracer (from 1 to 10 000) is integrated over an increasing timelap (from 0.1 to 10 minutes). Population growth rates are computed for all those configurations. This test being computational power consuming, it is carried out for one operating condition: light intensity of 1 000 µmolPhoton/m 2 /s and optical density of 1.0. The response surface is plotted in Figure 6. As one can see, the key numerical parameter is the integration time. Indeed, the number of tracer stops influencing the surface shape from few hundreds of tracers up to 10 000. Quantitatively, going from 3 000 integrated over 4.0 minutes, to 10 000 tracers integrated over 10 minutes conducts to a population growth rate variation below 1 %. From a computational perspective, the CPU-cost is born by the time integration. Increasing the number of integrated tracers has only a minimal effect. Convergence is led for this condition only (1 000 µmolPhoton/m 2 /s and optical density of 1). Thus, in order to be conservative, 4 000 tracers were integrated over 5.0 minutes to produce all the coming results. As one can see, the population growth rate varies tremendously over the explored range of parameters. On the hand, it peaks at 1.35 day -1 for an optical density of 0.025 under 53 µmolPhoton/m 2 /s. On the other hand, it can reach negative value in for high optical density, low illumination conditions, delimited by the dashed line. This is in coherence with what is usually observed, the maximal growth happens for moderate light intensity and diluted cultures. The general trends exhibited response surface can be explicated by combining mutual shading (or optical density) and photodamages (Fig. 7 (b)) concepts. At low incident illumination (e.g. below 50 µmolPhoton/m 2 /s), light cannot trigger extensive photodamages (fraction of C state unit below 5 %), hence the effect of optical density is monotonic and decreasing. The sole shading effect explains the decreasing growth rate with increasing optical density. At moderate incident light (e.g. 500 µmolPhoton/m 2 /s), photodamages dominate first (fraction of C state unit below 25 % for an OD of 0), as a low optical density means that light available everywhere in the photobioreactor at levels likely to trigger photodamages. Increasing the optical density allows then, at first, the averaged growth rate to increase, by mitigating photodamages. The growth rate then reaches a peak before the engaging a downward slope phase due to dominant effect of mutual shading. At high optical density (higher than 2.3), the growth rate eventually becomes negative. At large incident light (e.g. 1500 µmolPhoton/m 2 /s), photodamages are generalized at low optical density and turns into an initial negative averaged growth rate. The optical density must increase significantly for the photodamages to be limited by mutual shading. Then, the growth rate follows a trend similar to the one at 500 µmolPhoton/m 2 /s: peaking before decreasing. The decreasing rate is however much slower as the dark zones receive more light.

Results and discussion

Population level growth rate

A point of note is the existence of a crest path for the maximal growth rate. Indeed, if one is to increase the incident light as the culture grows a high growth rate can be maintained over the photobioreactor operation. This crest path is represented by a solid black line in Figure 7. It starts from 1.35 day -1 (OD 0, light intensity 41 µmolPhoton/m 2 /s) down to 0.82 day -1 for the maximum lighting conditions for an OD of 0.8. This crest path could probably continue further away as it stops when the maximum light intensity explored in this study is reached (2 000 µmolPhoton/m 2 /s).

Constant optical density growth profile

Growing a culture at a given cell concentration (i.e. optical density) is a common procedure -refereed to as turbidostat or PI curve -to study the impact of light intensity on algal growth. Here, it is possible to extract this information at the photobioreactor scale. As example, an optical density of 1.0 is chosen. Figure 8 presents the growth for this optical density over the range of incident light intensities.

The culture exhibits three successive stages. From 0 to 600 µmolPhoton/m 2 /s, the growth rate increases continuously, from negative values to about 0.85 day -1 . This stage corresponds to the affinity phase in which the higher the substrate -here light -the higher the growth rate. It is followed by a plateau phase over which the growth rate is somewhat constant between 95 and 100 % of its maximum value. Within this phase, the increase of photodamages undergone by the cells, when travelling in the most illuminated areas, is balanced by a larger amount of moderate light available in the shaded zones. This plateau comprises the light intensities from 500 to about 1600 µmolPhoton/m 2 /s. Afterwards, the growth rate decreases as the light This behavior is well-known [START_REF] Macintyre | Photoacclimation of Photosynthesis Irradiance Response Curves and Photosynthetic Pigments in Microalgae and Cyanobacteria1[END_REF][START_REF] Geider | A dynamic regulatory model of phytoplanktonic acclimation to light, nutrients, and temperature[END_REF]. The fact that the model is able to reproduce it as an emerging feature at the reactor scale using low level CFD and biological models is a token of its capabilities.

Comparison with static model

Another approach that is commonly used to predict photobioreactor performances is to average growth rates locally computed from the light field but without taking microalgae motion into account. This method is also referred as the second type of light model in [START_REF] Béchet | Modeling the effects of light and temperature on algae growth: State of the art and critical assessment for productivity prediction during outdoor cultivation[END_REF]. From this kind of growth models, the ones yielding to the best prediction are usually inverse of second order polynomial. This can be related to the fact that when on considered Han's model at steady state, the proportion of light processing photosystems follows this kind of law (Eq. 8).

B = IσPSIIτ 1 + IσPSIIτ + κ d κr (IσPSII) 2 τ (8)
In order to better assess the importance of Lagrangian coupling, we compared the two methods (full Lagrangian coupling and static coupling) with the steady-state solution of Han's model (an imaginary photobioreactor with uniform light). Figure 9 reports the population growth rate obtained with these three assumptions under two different optical densities (0.2 (a) and 1.0 (b)). The first comment is that using the incident light intensity as sole guide is unadvisable. Indeed, cylindrical geometries concentrate light on their axis, which is not taken into account by this simplistic approach. The second approach is more sucessful, at least for the low optical density. In this case, this approach captures the trend and is close to absolute values delivered by Han's model coupled with CFD. This can be explained by the fact that light is available in the whole reactor. Hence hydrodynamic has only a minor impact. This illustrates what was pointed out by biologists who pioneered the study of photosynthesis at the population scale: illumination has to be homogeneous throughout the reactor in order to access the intrinsic cell response [START_REF] Kok | Chapter 6, in: Algal culture from laboratory to pilot plant[END_REF][START_REF] Phillips | Growth Rate of Chlorella in Flashing Light. 1[END_REF]. On the opposite, this approach fails to predict reactor performances at higher optical densities. This points out one important feature of algal growth: the time characteristic of photodamages. In the case of a static reactor, cells experience the same light intensity over time. Photodamages therefore completely develop in the highly illuminated zones and growth is completely inhibited in dark zones. For this reason, applying a Han' model without Lagrangian pathways cannot be predictive. Still it could account for the influence of internal hydrodynamics provided the parameters used in Eq. 8 are adjusted, which is a common procedure. Yet, in this case, the model loses its predictive capabilities as these parameters would have to be calibrated again for any change of the culture conditions (geometry, volume, aeration, stirring...). This comments highlighting the added-value of CFD combined Han's model in the prediction of emerging behaviour at the bioreactor level.

Optimal lighting strategy

From the obtained response surface, it is possible to envision an optimal operation procedure for the reactor with the aim of shortening biomass production time. Indeed following the maximum growth crest path would lower the time required to reach the maximal biomass concentration.

Two configurations are compared. • the first one is a culture growing along the crest path until it reaches 2 000 µmolPhoton/m 2 /s. At this point, the light intensity is set constant to this maximum value.

• the second culture is grown under 500 µmolPhoton/m 2 /s until it reaches an optical density of 1.0. Then, the lighting is set at 2 000 µmolPhoton/m 2 /s. The second strategy is what could be done experimentally in order to speed up the growth process, it is referred to as the two steps strategy hereinafter. Even though not optimal, this procedure is not a naive one nonetheless. Indeed, this protocol can be derived from the operation of the reactor as a turbidostat at an optical density of 1.0. This would yield Figure 8 results. From them, the operator could conclude that switching light from 500 to 2 000 µmolPhoton/m 2 /s at an optical density of 1.0 would yield the same growth rate and allow the culture to cope well with high lighting intensity.

Both cultures are starting at an optical density of 0.05. The two predicted scenarii are reported in Figure 10. As one can see, both cultures have similarities: a linear growth phase during which they achieve the same daily productivity (calculated between 10 and 90 %, using the following correlation: Optical Density = 0.4777 × Dry Weight [START_REF] Luo | Airlift column photobioreactors for Porphyridium sp. culturing: Part I. effects of hydrodynamics and reactor geometry[END_REF]) and the same final optical density. This is normal given the fact that the culture is light limited. With the same final amount of light cast over the reactor, the final cell concentration is bound to be the same in both cases. The main difference between two cultures is the lag phase and the subsequent time needed to reach the final concentration. In the case of the optimal lighting strategy, the growth time (to reach 90 % of the final cell concentration) is 5.5 days while it is 6.4 days in the two step light strategy.

The determination of the crest path, hence the optimal lighting strategy seems almost impossible experimentally while it is rather easy numerically. Yet this mode of operation yields subsequent benefits: it is less energy intensive and time consuming. From an experimental perspective, following the numerically determined growth rate crest path can easily be achieved. Indeed, it would require the driving the light source by the reading of an immersed optical density probe.

Culture stress

Another possibility offered by the numerical tool is the determination of a light stress zone in the photobioreactor operating conditions. This can be of interest as light stress, in combination with nitrogen limitation or even starvation, is used to trigger high added-value secondary metabolites production by mircoalgae. Here, Han's model yields the amount of photodamaged photosystems, thus this quantity can also be plotted as a surface response (Fig. 7 (b)). As one could have expected, the highest amount of photodamages is achieved for low optical densities, high illumination conditions.

Combining the growth and photodamages response surfaces could yield an operation procedure that would first promote biomass production before triggering secondary metabolites production, through light excess. Yet this may turn out to be challenging. Indeed, it would have to be done by carefully choosing the initial amount of nitrogen in the medium (not accounted for in this study) and anticipating cell pigment composition evolution during the second phase. Furthermore, these operating conditions modifications are likely to induce a variation in cells response to light which would have to be incorporated in the cell biological model. In any case, the proposed numerical workflow would be of help in limiting the time that would require sole experimental approach.

Finally, the proposed numerical can be used to derive some insights about the influence of the stirring speed over induced light stress. Indeed, this parameter can have two opposite effects. On the one hand lowering the stirring speed would allow the cell to spend more time in light intense areas, increasing the amount of experienced photodamages. On the other hand, increasing the stirring speed would lower individual photodamages, yet increase the number of cells experiencing those damages by shuttling more microalgae towards the reactor walls. To investigate theses effects, another numerical trial is produced setting the stirrer speed at 50 rpm. Figure 11 presents population level photodamages at the maximum light intensity (2 000 µmolPhoton/m 2 /s) for the two stirring speeds. Higher stirring speed provides higher intensity photodamages of the whole population, this for both low and high optical densities. This can be explained by the fact that the characteristic time triggering photodamages is shorter than the recovering one. Hence shuttling cells in the highly illuminated zone results in a higher level of photodamages at the culture level. For minimal optical density, the two stirring speeds provide the same damage intensityaround 0.6 -. It is normal given the fact that the culture is translucent and this the photobioreactor is fully illuminated. From this in can be concluded that when stressing a culture, reducing the stirrer speed is not an efficient strategy.

Conclusion

In this article a numerical workflow describing the microalgal growth inside of a photobioreactor is proposed. This tools computes reactor internal hydrodynamics and uses it to track microalgae motion inside of the culture vessel. The illumination across the reactor is obtained using classical Beer-Lambert's law. Afterwards, light histories of the cell are built before being supplied to Han's model. Individual growth rate and experienced photodamages are computed and agglomerated at the population level.

Hence population growth can be computed at the reactor scale. A range of optical density, i.e. cell concentration, and incident light is explored, assuming cell intrinsic response to light does not change with those two parameters. From this exploration, it is possible to determine the photobioreactor response surfaces in terms of growth rate and photodamages. These are latter used to propose an optimal lighting strategy for biomass production -reducing photobioreactor operation time by 16 % compared to classical two-step procedure -and assist light induced stress with the aim of triggering secondary metabolites production.

There are two main possibility of improvement of this work. First, by taking into the evolution of cell response to light with ageing of the culture (e.g. cell pigment content management), or different physiological states (light and/or nitrogen stressed). Second, by confronting models prediction with the actual operation of a photobioreactor.

Figure 1 :

 1 Figure 1: Picture of the actual photobioreactor to be investigated

Figure 2 :

 2 Figure 2: Case geometry with initial and boundary conditions. Aeration: 0.1 vvm, stirring: 100 rpm. 1: stirred, 2: sparger, 3: pH probe. Dashed delimited: area where the momentum source term is applied to emulate stirrer motion

Figure 3 :

 3 Figure 3: Visualization of the photobioreactor. Aeration: 0.1 vvm, stirring: 100 rpm. Lagrangian tracers: 10 000, only 100 represented (randomly drawn). Time: 1 minute. Color legend: blue -bubbles, red -tracers, orange -stirrer, yellow -sparger, purple -pH probe

Figure 4 :Figure 5 :

 45 Figure 4: Radial position of a randomly drawn tracer over the first 3 minutes of computation with a stirrer set at 100 rpm

Figure 6 :

 6 Figure 6: Population level growth rate versus integration time and number of tracers. Optical density: 1.0. Light intensity: 1 000 µmolPhoton/m 2 /s

Figure 7 (

 7 Figure 7 (a) presents the population growth rate as a function of the incident light intensity and the culture optical density. As one can see, the population growth rate varies tremendously over the explored range of parameters. On the hand, it peaks

Figure 7 :

 7 Figure 7: Population level growth rate (a) and experienced photodamages (b) versus optical density and incident light intensity. Continuous line: growth rate crest path. Dashed line: null growth rate. Number of tracer: 4 000. Integration time: 5.0 minutes

Figure 8 :

 8 Figure 8: Population level growth at a given optical density and varying incident light intensity. Optical density: 1.0. A: affinity phase, P: plateau phase, I: inhibition phase. Number of tracer: 4 000. Integration time: 5.0 minutes

Figure 9 :

 9 Figure 9: Population level growth rate at versus incident light intensity, at an OD of 0.2 (a) and 1.0 (b). Solid line: taking cells motion into account, dashed line: Han's model applied locally without taking microalgae motion into account, doted line: Han's model applied only using incident light intensity and without taking microalgae motion into account

Figure 10 :

 10 Figure 10: Predicted microalgal density inside of the reactor. Black line: two steps lighting strategy -500 µmolPhoton/m 2 /s until an optical density of 1.0 is reached, 2 000 afterwards -. Gray line: optimal lighting strategy. Initial optical density: 0.05 / Initial dry weight: 0.1 g/L

Figure 12 :Figure 13 :

 1213 Figure 12: Volume averaged momentum. Aeration: 0.1 vvm, stirring: 100 rpm

Table 1 :

 1 Physical properties of the Lagrangian phases

		Symbol	Property	Ref.
		ρ	1030 kg/m 3	[27]
	Microalgae	C d C m	24 Re (1 + 0.152Re 0.677 ) + 0.5, assumed to behave like solid spheres 0.417 1+5070Re -0.940 , Re < 2 10 5 [28] -
		d	12 µm	[29]
		ρ	1.2 kg/m 3	-
	Bubble	C d C m	24 Re (1 + 0.15Re 0.687 ), Re < 1 000 0.5	[30] [31]
		d	Gaussian distributed (mean 3.40 mm)	-

Table 2 :

 2 Han's model for Porphyridium sp. grown under 3 % CO2-enriched air[START_REF] Pozzobon | Han's model parameters for microalgae grown under intermittent illumination: Determined using particle swarm optimization[END_REF][START_REF] Wu | A model integrating fluid dynamics in photosynthesis and photoinhibition processes[END_REF]

	Parameter	Unit	Value
	σ P SII	m 2 /µmolQuanta 3.85 10 -3
	τ	s	2.81 10 1
	κ d	-	3.95 10 -4
	κ r	1/s	1.32 10 -2
	K	s/h	8.57
	M e	1/h	2.30 10 -1

8 Supplementary materials

Transient timelap assessment

The time required to reach the quasi-steady state is an important parameter of this study. Indeed, the photobioreactor is operated for a long time. Hence only quasi-steady state is relevant, the transient time lap should be discarded. To assess for this time, volume averaged momentum inside of the reactor is monitored (Fig. 12). Volume averaged momentum gets stable after about 10 seconds.

Cylindrical Beer-Lambert law

Figure 13 presents a graph supporting the computation of the illumination at a given radial position inside of a cylindrical photobioreactor. For a given position, light rays comes from a 2π angle (Eq. 9). Yet the distance they travel from the reactor walls varies, hence the amount of attenuation the are submitted to. As a consequence, the wall point distance has to be computed for each step of the integral (Eq. 10).

I(r) =