Soheil Borhani

Reza Abiri

Jabril Ibrahim Muhammad

Yang Jiang

Xiaopeng Zhao

EEG-based Visual Attentional State Decoding Using Convolutional Neural Network

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Maintaining sustained visual attention to a cognitive task is of high importance [START_REF] Abiri | Real-Time Neurofeedback for Attention Training: Brainwave-Based Brain-Computer Interface, Organization for Human Brain Mapping[END_REF]. Recent studies in Brain-Computer Interface (BCI) using electroencephalography (EEG) shows a promising capability to reveal moment-to-moment attentional states [START_REF] Jiang | Tuning Up the Old Brain with New Tricks: Attention Training via Neurofeedback[END_REF]. A number of studies highlight the implication of Event-Related Potentials (ERPs) such as N170 or P300, yet some other studies identified the significance of alpha and beta bands elicited from specific parts of human scalp in spotting level of attention. In the present study, we developed a deep learning approach to analyzing the neurophysiological signals collected during a visual attention task. An individualized EEG-based classifier was developed to probe and extract underlying subjectspecific features of early visual attention.

Experiment Setup

The BCI platform will consist of a wireless EEG headset, a workstation computer with dual monitors, data acquisition, and analysis software.

A flexible Graphical User Interface (GUI) has been developed to allow the experimenter to conveniently administer the experimental protocols. The data collection protocol is borrowed and adapted from a fMRI study [32]. Simulink is adopted as the data acquisition engine; the signal processing, feature extraction, classification, presenting the images, and recording behavioral responses were all carried out within MATLAB. The participants were be primed into the subcategories throughout the experiment by asking their overt response during each trial.

Data

Thirty-eight healthy participants (11 females; 21.3±1.9 years and 27 males; 23.1±5.2 years) were recruited to conduct tasks on visual attentional state evaluation. The participants were exposed to 8 blocks of 50 trials. Each trial is a single image followed by a black screen. Each block starts with a 1000ms cue texture that guides participants on the requested behavioral response. Then, it continues with showing single images randomly selected from scene subcategories (Indoor scene & outdoor scene) or face subcategories (male face & female face) with a black screen between images. Each image will be shown for 1000ms and the black screen for 1000ms to 1500ms.

We also collected the behavioral response via keyboard button presses.

Method

Information is reflected in the EEG as dynamical changes in time, frequency, and space. Among various time-frequency analysis methods, Wavelet transform stands out for the efficiency. This technique brings multi-resolution analysis to analyze EEG at different scales. EEG records for each block were divided into 50 epochs. Each epoch includes EEG records when subjects exposed to an image plus one second EEG record during the successive blank image.

Results

Rectified Linear Unit (ReLU) activation function was used as a nonlinear function. We also used Adam optimizer to adapt the learning rate while preventing the fluctuations of the gradient descent. On average, a dropout with a probability of 0.2 (Keep Prob = 0.8) in the fully connected layers resulted in higher accuracy over the dataset. Overall, the first approach achieved an average accuracy of 55% and the second approach achieved an average accuracy of 73%.

Two different representations were studied. The spatio-spectral representations lead to more accurate results compared to spatiotemporal representations. The size and architecture of the model are designed in a way that training the model would be considerably fast ( less that 1 minute for each participant's dataset using a workstation equipped with a Titan Xp GPU, an 8-core i7 CPU, and 32 GB RAM) and enable it to run on small machines.

Conclusion

This study shows that EEG signal can be used to distinguish attentional state using visual stimuli. The proposed deep learning approach has advantages over the conventional selective visual attention decoding procedures [START_REF] Bashivan | Learning representations from EEG with deep recurrent-convolutional neural networks[END_REF]; instead of using engineered features of the EEG, we developed a classifier based on the convolutional neural network using learned features.

We are also interested in more complex snapshot-based models such as VGGNet and ResNet. The temporal correlation between samples of EEG suggests that Recurrent Neural Network (RNN) may result in a higher accuracy. We aim to apply a sequential model in the future. The findings of this study may be beneficial to people with attention deficit and attention disorder. Also, the platform may improve the understanding of the causal attributes of human visual attention.

Figure 2 : 3 :

 23 Figure 2: An illustration of the experimental data collection protocol Figure 3: A flowchart of EEG data representation A Convolutional Neural Network (CNN) classifier inspired by AlexNet has been developed. Two different representations of the EEG data were used as input to the CNN classifier. The first approach utilizes a spatio-temporal representation and the second one utilizes a spatiospectral representation. We also used Adam optimizer to adapt the learning rate while preventing the fluctuations of the gradient descent.

Figure 1 :Figure 5 :Figure 6 :Figure 7 :

 1567 Figure 1: A schematic of the data collection


Stéphane Pesce
email: stephane.pesce@irstea.fr

Olivier Perceval

Chloé Bonnineau

C Casado Martinez

Aymeric Dabrin

Emilie Lyautey

Emmanuel Naffrechoux

Benoit J D Ferrari
email: benoit.ferrari@centreecotox.ch

Carmen Casado-Martinez

Looking at biological community level to improve ecotoxicological assessment of freshwater sediments: Report on a First French-Swiss Workshop

Keywords: Sediment ecotoxicity, Environmental Risk Assessment, Structural and Functional effects, Sediment exposure, Bioavailability, Microbial ecotoxicology, Invertebrates

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Context

Among the different compartments of aquatic habitats, sediments play a critical role in biogeochemical cycling and in the maintenance of the biodiversity, and benthic processes often support the base of aquatic food chains. However, sediments are often polluted with contaminants introduced into surface waters as these latter bind predominantly to fine particulate matter settling in "storage habitats", i.e. the porous matrix and fine deposits, along the river continuum or in lakes and reservoirs. The subsequent accumulation of contaminated sediment can represent a risk for benthic

Author-produced version of the article published in Environmental Science and Pollution Research, 2018;25 (1): [970][971][972][973][974] The original publication is available at https://link.springer.com/article/10.1007%2Fs11356-017-0620-z doi : 10.1007/s11356-017-0620-z communities of micro-and macro-organisms and thereby disturb the functioning of the ecosystem, even if no signs of pollution are apparent in the water column [START_REF] Lafont | Refinement of biomonitoring of urban water courses by combining descriptive and ecohydrological approaches[END_REF]. Moreover, sediments can also act as a source of contaminants which can be transferred to higher trophic levels via the food chain, or be remobilized during sediment resuspension episodes or by re-dissolution from sediment and diffusion from pore water following changes in redox conditions. It is therefore crucial that this complex compartment is evaluated properly following an appropriate methodological framework in order to identify its impact on aquatic ecosystem health.

At the European level, the sediment compartment has, until recently, been neglected in the Water Framework Directive (DCE 2000/60/EC). However, several successive amendments to that directive have permitted the progressive consideration of sediments in this piece of legislation essential for the protection of aquatic environments [START_REF] Förstner | Sediments and priority substances in river basins[END_REF]. These include the amendment of the 16 th December, 2008 (2008/105/EC), defining the need to "monitor sediment […] at an adequate frequency to provide sufficient data for a reliable long-term trend analysis of those priority substances that tend to accumulate in sediment", or the publication of the guidance document on chemical monitoring of sediment (European Commission, 2010) in line with the above amendment. However, and as reported several years ago [START_REF] De Deckere | Development of sediment quality guidelines for freshwater ecosystems[END_REF][START_REF] Flück | Surveillance de la qualité des sédiments. État actuel des méthodes disponibles et mise en place de recommandations[END_REF], there is still a lack of adequate recommendations on the strategies and methods to better evaluate the ecotoxicological impact of chemical substances which accumulate in sediments on associated benthic communities and the resulting effects on ecosystem functioning. Such questions remain meaningful, both in France and in Switzerland, emphasizing the need to facilitate the dialogue between researchers and environmental stakeholders and managers from these two countries in order to implement joint research actions and monitoring programs.

One way to integrate an ecological dimension into ecotoxicological approaches is to perform studies at the community level, applying community ecology concepts [START_REF] Clements | Community responses to contaminants: using basic ecological principles to predict ecotoxicological effects[END_REF][START_REF] Gessner | Fostering integration of freshwater ecology with ecotoxicology[END_REF]. Indeed, the propagation of ecotoxicological effects along the successive levels of biological organization (from cells to communities) does not follow a linear trend thus limiting the extrapolation from results obtained at cellular, individual or population levels to the community level [START_REF] Segner | Ecotoxicology -how to assess the impact of toxicants in a multifactorial environment[END_REF]. Communities represent the intermediate level between populations and ecosystems.

Assessing ecotoxicological effects on communities, which are composed of several species, gives the opportunity to consider the notion of specific and functional biodiversity in ecotoxicology thus offering the possibility to further develop innovative approaches to assess the impact of toxicants on the biological and functional integrity of ecosystems [START_REF] Ghiglione | Microbial ecotoxicology: an emerging discipline facing contemporary environmental threats[END_REF].

In this context, it is therefore necessary to strengthen the existing methodological framework for sediment quality assessment and to develop new tools and approaches to better take into account benthic communities (especially microorganisms and invertebrates) in sediment ecotoxicology. These scientific developments should allow the design and the implementation of improved procedures for assessing the quality of aquatic environments through the study of the ecotoxicological impacts of toxicants in contaminated sediments (following the accumulation of toxicants) and/or the ecological gain resulting from the improvement of sediment chemical quality (following a decrease in toxicant concentrations).

Objectives

The first French-Swiss workshop on ecotoxicology of freshwater sediment communities The primary aim of the meeting was to encourage fruitful discussions in different sessions between scientists (ecotoxicologists, ecologists, environmental chemists…), environmental stakeholders and managers, as well as economic players.

Forty-five participants attended the workshop (Fig. 1). About two-thirds of them were researchers, lecturers and professors from various research laboratories and universities in the Auvergne-Rhône- The objectives of the different sessions were to present the state of the art of research in exposure assessment of contaminated sediments and in the evaluation of the impact of such contamination on associated biological communities as well as to give an overview of the French and Swiss regulations dealing with those questions. The ultimate goal of the workshop was to collectively identify the main needs and barriers as well as to highlight ways to improve the ecotoxicological assessment of the quality of sediments in freshwater environments by developing approaches at biological community level.

Workshop sessions: highlights and outcomes

On the first day, after a brief introduction by the main organizers to recall the objectives of the workshop and to give an overview of the tools and methods that are currently used to assess the sediment quality, four plenary sessions followed.

In the first session, representatives from the AFB and the OFEV presented an overview of the French and Swiss regulations dealing with the chemical and chemical and ecotoxicological assessment of sediment quality and described current practices regarding the management of polluted sediments in force in these two countries. Another presentation was given by the Ecotox Centre Eawag-EPFL to describe the MODSED project which aims at providing a new module for the sediment compartment within the modular stepwise procedure for quality assessment of surface water bodies in Switzerland.

Altogether, these three talks clearly highlighted the specificities of the strategies and approaches developed in France and Switzerland, which are highly influenced by their respective regulatory frameworks. In addition, specific issues at both practical (e.g. how to define an optimal sampling technique to characterize sediment contamination?) and theoretical (e.g. how to define quality criteria for the sediment compartment?) levels were pointed out by environmental stakeholders and managers.

A discussion was also initiated concerning the pivotal role of institutions such as the Ecotox Centre Eawag-EPFL in Switzerland and the AFB in France. They play a leading role in narrowing the gap between water science, policy and management in the field of ecotoxicology, by facilitating knowledge and technology transfers and providing expertise to governmental bodies and academic groups. The second session focused on environmental chemistry with presentations on innovative tools and technologies recently developed to i) identify the source and origin of contaminants which are detected in freshwater sediments (by using geochemical and isotopic signatures), and to ii) better estimate the potential availability of organic and inorganic contaminants in the sediment compartment (using passive samplers) and predict the bioaccumulation of these contaminants in benthic organisms (by using modelling approaches based on biodynamic and trait-based models). The first question is of primary interest to distinguish between natural inputs and anthropogenic pollution and then to contribute to the implementation of environmental measures to reduce anthropogenic sources of emission and/or contaminants transfers to the sediment compartment. Characterizing and predicting the potential availability of the various classes of contaminants in sediments is also an issue in community ecotoxicology and environmental risk assessment, as shown by the progressive inclusion of the concept of bioavailability in regulatory frameworks. The development of the described innovative analytical tools and modelling approaches should thus facilitate the assessment of sediment communities' exposure levels to contaminants to better establish the causality link between sediment contamination and community responses.

Author-produced version of the article published in Environmental Science and Pollution Research, 2018; 25 (1):970-974

The original publication is available at https://link.springer.com/article/10.1007%2Fs11356-017-0620-z doi : 10.1007/s11356-017-0620-z

The third session was dedicated to the methods that are specifically used to evaluate the effects of contaminants on microbial and macro-invertebrate communities in aquatic ecosystems. The first talk illustrated the relevance of studying microbial adaptation to contaminants (e.g. pollution induced community tolerance or increase in biodegradation potential following in situ chronic exposure) as an ecological indicator to monitor contamination in water and sediment and for assessing consequent ecological effects. The second presentation showed that among the potential indicators of biodiversity, oligochaete indices as well as those based on the functional traits of invertebrates could be particularly adapted to assess the ecotoxicological effects of contaminants on sediment invertebrate communities.

Recent results also demonstrated that the generalization of such approaches, which currently require a high level of morphological and taxonomical expertise, should be enhanced by the development of molecular barcoding methods. Finally, the last talk pleaded for the development and implementation of functional approaches to appraise the effects of contaminants on the main ecological functions supported by the sediment communities, such as organic matter consumption and decomposition, biodegradation or nutrient cycling. This session also highlighted current limits in understanding how structural and functional ecotoxicological effects observed at community level can inform about the biological and functional integrity of ecosystems, preventing for the moment the generalization of community responses at ecosystem scale.

In the fourth session, innovative tools and approaches that could be used to implement biomonitoring surveys in sediments at large spatio-temporal scales were presented. Indeed, the two first presentations introduced molecular methods, which offer the possibility to analyze many biological samples simultaneously. Some of these methods aim at assessing biological diversity, using next-generation sequencing to perform molecular diagnostics. This was notably illustrated by the presentation of the French-Swiss Interreg project SYNAQUA, which proposes to develop genetic tools based on the recognition of bio-indicator species (focusing on diatoms and oligochaetes) that are present in the aquatic environment directly from their DNA. Molecular functional approaches used to detect and quantify the occurrence of functional genes or their expression level, were also described and the potential of such approaches to establish a causal relationship between microbial community exposure to chemicals and the molecular response was exemplified by several successful studies performed in Finally, a half-day workshop session was organized to collectively identify the main needs and perspectives to improve the ecotoxicological assessment of sediment quality in freshwater ecosystems.

First of all, all participants were invited to write down (on post-it notes) both needs and suggestions to better characterize i) the exposure of natural benthic communities to contaminants in sediments and ii)

the resulting ecotoxicological effects on those communities and on the ecological quality of sediments.

These notes initiated a productive discussion allowing to identify relevant actions to be supported and/or implemented in order to contribute to a better evaluation of the ecotoxicological quality of sediments.

The main outcomes and recommendations from these discussions are covered by the points below:

Better adapt the sampling strategy according to the addressed question and the ecosystem assessed:

• Which kind of sediment should be considered? This choice should be made according to various factors such as the depth, the grain size distribution and the organic matter content

• Which temporal and/or geographical scale? The question needs to take into account the hydrology and the associated sediment dynamics.

Better consider the various modes of exposure of organisms to toxicants in the sediment compartment as well as the diversity of contaminants, including metabolites (notion of "exposome").

Author-produced version of the article published in Environmental Science and Pollution Research, 2018;25 (1):970-974

The original publication is available at https://link.springer.com/article/10.1007%2Fs11356-017-0620-z doi : 10.1007/s11356-017-0620-z

Develop modeling and predicting tools to evaluate the exposure risks according, among others, to the source and origin of contaminants and their dispersion and distribution in aquatic environments and in the trophic chain.

Evaluate the relevance of existing ecotoxicological tools at sediment community level to be used as in-situ diagnostic tools and develop new approaches based on the structural and functional study of microbial and invertebrate sediment communities.

Initiate transfer of knowledges to environmental managers by proposing operational guidelines, including standardized protocols and threshold values allowing a relevant and easy interpretation of ecotoxicological effects.

These points underline the necessity to develop pluridisciplinary approaches to better explore the relationship between contaminant exposure and ecological effects in sediments and to propose models and operational tools that could be used to improve the chemical and ecotoxicological assessment of the quality of freshwater sediments in France and Switzerland.

Main conclusions

The The original publication is available at https://link.springer.com/article/10.1007%2Fs11356-017-0620-z doi : 10.1007/s11356-017-0620-z of aquatic environments) around the main issues identified. To this end, a first step will be the drafting of a technical article, intended for both environmental managers and scientists, describing the main needs and perspectives in sediment ecotoxicology and the resulting proposed strategies to improve the quality assessment of sediment in freshwater ecosystems. The original publication is available at https://link.springer.com/article/10.1007%2Fs11356-017-0620-z doi : 10.1007/s11356-017-0620-z

  Author-produced version of the article published in EnvironmentalScience and Pollution Research, 2018; 25 (1):970-974 The original publication is available at https://link.springer.com/article/10.1007%2Fs11356-017-0620-z doi : 10.1007/s11356-017-0620-z different contaminated ecosystems. The last presentation focused on the soil quality monitoring network for French soils (RMQS;[START_REF] Ranjard | Biogeography of soil microbial communities: a review and a description of the ongoing french national initiative[END_REF] in order to initiate a reflection on the possible development of joint integrated chemical and biomonitoring strategies in sediments from differentFrench and Swiss aquatic ecosystems. The implementation of such monitoring programs could be technically supported by the involvement of platforms such as those proposed by the infrastructure for the analysis and experimentation on ecosystems (AnaEE; http://www.anaee.com/).

  presentations and discussions carried out during the SediCommuTOX workshop highlighted the relevance of bringing together actors from different spheres (scientific, operational, economic…) and representing different disciplines. It was also particularly interesting to present, compare and discuss the specific features of each regulatory framework and the different approaches implemented in France and in Switzerland for the management of polluted sediments. The sharing of ideas and of experiences and knowledge made it possible to collectively propose a wide range of possible actions to improve the ecotoxicological assessment of the quality of sediments in freshwater environments. These actions are characterized by variable operational levels, from fundamental research to large-scale implementation. Based on the conclusions of the SediCommuTOX workshop, we aim at mobilizing stakeholders (involved in the monitoring and management of the chemical, ecological and ecotoxicological quality Author-produced version of the article published in Environmental Science and Pollution Research, 2018; 25 (1):970-974

Figure 1 :

 1 Figure 1: Group picture of most of the participants of the first French-Swiss workshop on

research group of the French Research Institute of Science and Technology

	(SediCommuTOX), which was co-organized and co-chaired by Drs. Stéphane Pesce (leader of the
	Aquatic Microbial Ecotoxicology

for Environment and Agriculture, Irstea) and Benoît Ferrari (leader of the Soil and Sediment Ecotoxicology group of the Swiss Centre for Applied Ecotoxicology, Ecotox Centre EAWAG-EPFL) took place on 27 th -28 th April, 2017 in Villié-Morgon (Beaujolais Region, France).

  Numerous scientific disciplines were thus represented, including, but not limited to, ecology, ecotoxicology, hydrobiology, environmental chemistry, microbiology, genetic and molecular biology, geochemistry, modelling… The French Agency for Biodiversity (AFB) and the Swiss Federal Office for the Environment (OFEV), as well as several Swiss cantons (e.g. Vaud, Fribourg) were also represented to promote the dialogue between scientists and environmental stakeholders and managers during the meeting. Given its pivotal and unifying role in the field of environmental toxicology and ecotoxicology, the Rovaltain Foundation Took part in the discussions. Finally, it seemed important for us to complete the panel of participants by also involving representatives of French and Swiss private

Alpes region (e.g. Irstea Lyon-Villeurbanne Center, University Savoie Mont Blanc, INRA CARRTEL joint research Unit, Grenoble Alps University) and in Switzerland (e.g. EPFL, University of Geneva, EAWAG). sectors including start-ups in environmental and molecular diagnostics (e.g. Enoveo, ID-Genes) and environmental consulting firms (e.g. Burgeap, Soluval Santiago, Biol'Eau) as well as public technical platforms for environmental analysis (AnaEE France Biochem-Env and GenoSol platforms).

  Author-produced version of the article published in Environmental Science and Pollution Research, 2018; 25 (1):970-974The original publication is available at https://link.springer.com/article/10.1007%2Fs11356-017-0620-z doi : 10.1007/s11356-017-0620-z

Author-produced version of the article published in Environmental Science and Pollution Research, 2018; 25 (1):970-974The original publication is available at https://link.springer.com/article/10.1007%2Fs11356-017-0620-z doi : 10.1007/s11356-017-0620-z

Acknowledgments

This workshop benefited from funding from the Auvergne-Rhône-Alpes Region, the French Research Institute of Science and Technology for Environment and Agriculture (Irstea) and the Swiss Centre for Applied Ecotoxicology (Ecotox Centre Eawag-EPFL). We would like to thank the Municipality of Villié-Morgon for granting us the space to host our workshop and our colleagues from Irstea who were closely involved in the workshop organization: Vanessa Aburegaiba, Catherine Ambroise-Rendu, Anaïs Charton and Bernard Motte. We are also grateful to Dr. Inge Werner for her careful reading of and valuable comments on the manuscript.

The first French-Swiss organized by the French Research Institute of Science and Technology for Environment and Agriculture (Irstea) and the Swiss Centre for


Dorian Vogel

Ashesh Shah

Fabiola Alonso

Jean-Jacques Lemaire

Jerome Coste

Karin Wårdell

Simone Hemm

Co

Co-registering Thalamus for Analysis of Patient-specific Intra-operative Improvement Maps in DBS

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

Co-registering Thalamus for Analysis of Patient-specific Intraoperative Improvement Maps in DBS

ESSFN 2018 | Poster P094 Movement Disorders Dorian VOGEL (Speaker), Ashesh SHAH, Fabiola ALONSO, Jean-Jacques LEMAIRE, Jérôme COSTE, Karin WÅRDELL, Simone HEMM Deep brain stimulation (DBS) is used for symptomatic treatment of movement disorders. In many centers, the optimal DBS position is identified by intra-operative stimulation tests, which are performed at several positions along the planned trajectories toward the target structure with various stimulation amplitudes. ). A conductivity model of each patient's brain was derived from the intensity values of the T1 image. Finite element simulations were performed using these models for the positions and amplitudes (between 0 and 3 mA) with the best improvement. A 0.2 V/mm isolevel [START_REF] Åström | Relationship between Neural Activation and Electric Field Distribution during Deep Brain Stimulation[END_REF] was used to visualize the electric field. Improvement maps of each patient's brain were visualized by affecting to each voxel in simulation results the maximum improvement measured. These maps were further enhanced by 14 subthalamic structures per side labeled by the neurosurgeon [START_REF] Lemaire | Anatomy of the Human Thalamus Based on Spontaneous Contrast and Microscopic Voxels in High-Field Magnetic Resonance Imaging[END_REF]. The resulting Improvement Map was visualized together with the patients' anatomy and the implant position providing a summary of the intraoperative testing [START_REF] Shah | Improving DBS targeting using 3D visualization of intraoperative stimulation tests[END_REF]. An example view of this visualization is presented in Figure 1. In order to proceed to group analysis, a normalization pipeline for the improvement maps was designed as a two-step process: the first step uses the MNI152 template [START_REF] Grabner | Symmetric Atlasing and Model Based Segmentation: An Application to the Hippocampus in Older Adults[END_REF] and tools from FSL [START_REF] Smith | Advances in functional and structural MR image analysis and implementation as FSL[END_REF] to proceed to an initial linear registration. The T1 image for each patient was aligned and then registered to the MNI template. The WAIR image was then aligned to the aligned T1 and the registration transformation was applied. Both transforms were also applied to the anatomical structures. A result of this first normalization is presented in Figure 2 for the ventro intermediate nucleus (Vim). Those results show the necessity of a finer registration step, allowing local displacement of voxels in order to provide a better definition of the anatomical labels after normalization. In the second step, several normalization templates as well as non-linear group registration tools were evaluated in order to obtain the best probabilistic definition of the labeled sub-thalamic structures after application of the disformation field. Future work will focus on transferring the improvement values and spatial distribution of the electric field to the anatomical atlas to create an improvement atlas, and select appropriate statistical methods to visualize it. The atlas will present a summary of the complete patient pool, to be used as an assistance tool during planning. As the number of patient increases, this type of atlas will help analzing the mechanisms of action.


Alexia Audebert

Sylvie Beaufils

Valérie Lechevalier-Datin

Cécile Le Floch-Fouéré

Arnaud Saint-Jalmes

Stephane Pezennec
email: stephane.pezennec@inra.fr

Valérie Lechevalier

Arnaud Saint- Jalmes

Stéphane Pezennec

How foam stability against drainage is affected by conditions of prior whey protein powder storage and dry-heating: A multidimensional experimental approach

Keywords: Dry-heating, Whey protein powder, Foam stability, Water activity, pH, Lactose

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Liquid foams are concentrated dispersions of gas bubbles in a liquid continuous phase. They are thermodynamically unstable, due to destabilisation processes such as liquid drainage, disproportionation and coalescence. Foam drainage is the flow of liquid under the influence of gravity. It leads to foam drying, which promotes the rupture of thin liquid films separating adjacent bubbles, namely coalescence events. Disproportionation is the surface-tension-driven gas exchange from small to large bubbles due to the difference in internal pressure (Laplace's law), favouring the growth of the average bubble size with time. Their limitation is crucial to obtain a better foam stability [START_REF] Cantat | Foams: Structure and Dynamics[END_REF].

Due to their amphiphilic nature, proteins adsorb to hydrophobic interfaces. At the air-water interface and in aqueous foams, they can reduce surface tension and form a visco-elastic interfacial film surrounding the gas bubbles, thus helping the formation and stabilisation of foams. Protein foam formation depends on their surface activity and their adsorption kinetics, while foam stability depends on the film mechanical properties [START_REF] Narsimhan | Role of Proteins on Formation, Drainage, and Stability of Liquid Food Foams[END_REF]. Protein foam structure can be described at different length scales. First, an adsorbed protein layer (≈10 -10 -10 -8 m) separates the solution from air. Second, neighbouring bubbles are separated by a liquid film, or lamellae (≈10 -8 -10 -6 m), with two air-water interfaces. Third, three films junction forms a canal called Plateau border (≈10 - 6 -10 -4 m) [START_REF] Cantat | Foams: Structure and Dynamics[END_REF].

In food sciences, measurements of protein foam stability generally integrate the consequences of all the instability mechanisms in a global stability, such as the time at which the first drop drains or the cumulative weight of drained liquid as a function of time [START_REF] Nicorescu | Comparative effect of thermal treatment on the physicochemical properties of whey and egg white protein foams[END_REF]. In the present study, we developed an original methodology to characterise in more details the protein foam stability against drainage, by transposition of a foam physics approach. More precisely, we analysed whole time and height profiles of liquid fraction in foams, in conditions where drainage is the prominent destabilisation mechanism. Multivariate statistics were used to extract essential information from the whole data set.

After cheese and casein manufacturing, a fluid called whey remains, mainly composed of water, lactose (4.8 %) and protein (0.7 %). Whey is processed by separation technologies and dried into food ingredients such as whey protein isolates (WPI) (>90 % of protein). In WPI, the main proteins are βlactoglobulin (β-lg) and α-lactalbumin (α-la) [START_REF] Ortega-Requena | Retracted Article: Bigger data open innovation: potential applications of value-added products from milk and sustainable valorization of by-products from the dairy industry[END_REF]. Whey proteins have attracted considerable interest because of their high nutritive value and functional properties. Their use in food formulation is based on their aptitude to increase viscosity, gelling, water binding, emulsion or foam stability [START_REF] Ortega-Requena | Retracted Article: Bigger data open innovation: potential applications of value-added products from milk and sustainable valorization of by-products from the dairy industry[END_REF]. They are found in a large diversity of aerated food products like aerated desserts, whipped cream, and cappuccino foam [START_REF] Narsimhan | Role of Proteins on Formation, Drainage, and Stability of Liquid Food Foams[END_REF].

Whey protein heating is a commonly used processing operation for changing techno-functionalities. Heating denatures proteins which enhances the exposition of buried hydrophobic amino acid residues. Then, aggregation of proteins can occur by covalent bonding and hydrophobic interactions [START_REF] Anema | Chapter 9 -The Whey Proteins in Milk: Thermal Denaturation, Physical Interactions, and Effects on the Functional Properties of Milk[END_REF]. The coexistence of non-aggregated and aggregated proteins is important for foaming properties. Non-aggregated proteins contribute to the foam formation because they adsorb quickly at the interface. Aggregated proteins, depending on the structure and the size, can modify the bulk rheology and slow down the drainage by their presence in the Plateau borders [START_REF] Fameau | Effect of particles and aggregated structures on the foam stability and aging[END_REF]. In the case of in-solution heating of WPI, [START_REF] Schmitt | Bulk self-aggregation drives foam stabilization properties of whey protein microgels[END_REF]; [START_REF] Lazidis | Whey protein fluid gels for the stabilisation of foams[END_REF] have

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3 demonstrated that specific aggregates, called microgels, greatly increase foams stability through a reduced drainage, by increasing the bulk viscosity. Aggregates may also contribute to interfacial layer properties [START_REF] Fameau | Effect of particles and aggregated structures on the foam stability and aging[END_REF]. Indeed, interfacial rheology is a key factor in foam stability [START_REF] Narsimhan | Role of Proteins on Formation, Drainage, and Stability of Liquid Food Foams[END_REF].

Dry-heating of egg white powder is commonly applied to maintain the microbiological quality and improve foaming and gelling properties [START_REF] Boreddy | Novel Radiofrequency-Assisted Thermal Processing Improves the Gelling Properties of Standard Egg White Powder[END_REF]. In comparison with heating of liquid solutions, dry-heating of protein powders is a way to disconnect proteins denaturation and aggregation and also to obtain different protein structural modifications [START_REF] Desfougères | Strong Improvement of Interfacial Properties Can Result from Slight Structural Modifications of Proteins: The Case of Native and Dry-Heated Lysozyme[END_REF][START_REF] Gulzar | Influence of pH on the dry heat-induced denaturation/aggregation of whey proteins[END_REF][START_REF] Povey | Investigating variables and mechanisms that influence protein integrity in low water content amorphous carbohydrate matrices[END_REF]. Indeed, [START_REF] Desfougères | Strong Improvement of Interfacial Properties Can Result from Slight Structural Modifications of Proteins: The Case of Native and Dry-Heated Lysozyme[END_REF] showed that slight structural modifications of lysozyme are sufficient to greatly improve interfacial properties and foam stability. Usually, molecular motion is reduced in powders because of their amorphous glassy state at room temperature. Consequently, reaction kinetics are considerably slowed. The powder water activity (a w ) is a crucial parameter. As an example, the denaturation temperature of proteins in a WPI powder is 175°C, 163°C and 132°C at different a w 0.11, 0.23, 0.53 respectively (Zhou and Labuza, 2007). Dryheating time and pH prior to dehydration also affect both the type and kinetics of reactions in a WPI powder, and its gelling [START_REF] Gulzar | Influence of pH on the dry heat-induced denaturation/aggregation of whey proteins[END_REF][START_REF] Gulzar | The physicochemical parameters during dry heating strongly influence the gelling properties of whey proteins[END_REF]. The lactose content in WPI also plays a key role in functional properties [START_REF] Guyomarc'h | Current ways to modify the structure of whey proteins for specific functionalities-a review[END_REF]. The Maillard reaction occurs in dairy products subjected to heat treatment, drying or storage. The first step is the lactosylation: lactose condenses with a protein amino groups to form a Schiff base. In a later stage, a complex form of non-enzymatic browning is produced [START_REF] Arena | Dairy products and the Maillard reaction: A promising future for extensive food characterization by integrated proteomics studies[END_REF].

Dry-heating could be a way to improve the techno-functionality of WPI. However, only a few investigations on the foaming properties of dry-heated whey proteins have been reported. Some report that the effect of dry-heating on the foaming properties of WPI powder strongly depends on the dryheating conditions (time, temperature, a w ) [START_REF] Team ; Radwan | Improvement of the Surface Functional Properties of β-Lactoglobulin and α-Lactalbumin by Heating in a Dry State[END_REF]Norwood et al.,2016). The effect of dry-heating of β-lg powder with sugars on foam stability depends also on the sugar nature [START_REF] Medrano | The effect of glycation on foam and structural properties of β-lactoglobulin[END_REF][START_REF] Corzo-Martínez | Interfacial and foaming properties of bovine β-lactoglobulin: Galactose Maillard conjugates[END_REF]. Thus, in this study, we examined the effect of parameters like time, a w , pH prior to dehydration and lactose content on the WPI foaming properties. Our multifactorial experimental design allowed us to highlight the complex interactions between parameters.

The originality of our experimental approach consist of i) the multifactorial experimental design, ii) the bi-dimensional monitoring of foam stability as a function of both time and height and iii) the multivariate statistical analysis of the data set.

Materials and Methods

Powder characterisation

A unique batch of whey protein isolate (WPI) powder was used for all the experiments. It was obtained by spray-drying a whey protein concentrate isolated from milk microfiltrate by ultrafiltration and diafiltration, as described by [START_REF] Chevallier | Increasing the heat stability of whey protein-rich emulsions by combining the functional role of WPM and caseins[END_REF].The nitrogen content (TN), non-protein nitrogen (NPN) and non-casein nitrogen (NCN) of the powder were determined by the Kjeldahl method [START_REF] Schuck | Analytical Methods for Food and Dairy Powders[END_REF]. The protein content was calculated by (TN-NPN) × 6.38 (eq. 1). The amount of casein or insoluble proteins at pH 4.6 was measured by (TN-NPN-NCN) × 6.38 (eq. 2). Free lactose in the WPI powder was measured by ion-exchange high performance liquid

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4 chromatography (HPLC, Dionex, Germering, Germany) using an Aminex A-6 column (Biorad, St Louis Mo., USA) and a differential refractometer (model RI 2031 plus, Jasco).The oven was kept at 60°C and the elution flow was 0.4 mL•min -1 using a 5 mM H 2 SO 4 buffer.

The WPI powder contained 95.0 ± 0.2 % (w/w) of proteins (calculated from eq. 1), among which 9.40 ± 0.04 % (w/w) of caseins or insoluble proteins at pH 4.6 (calculated from eq. 2), and 2.00 ± 0.02 % (w/w) of free lactose.

Preparation of dry heated powders

Sample preparation

Spray-dried WPI was dissolved in 15 mΩ resistivity osmosed water at a 7 % protein concentration. A part of samples (name prefixed with "D" in the following) was dialysed against water to reach 0.2 % (w/w) of lactose (10-fold reduction) (Fig. 1). The other part of samples (name prefixed with "L") was kept at their initial lactose content 2 % (w/w). Each sample was adjusted at pH 4.6 with 12 N HCl and centrifuged for 30 min at 9000×g. The supernatant contained a residual amount of caseins and proteins insoluble at pH 4.6 of 5.89 % (w/w) calculated from eq. 2. Then, the pH of the solution was adjusted to 3.5, 5.0 or 6.5 using 12 N HCl or 12 N NaOH, and then lyophilised. Lyophilised powders were adjusted to water activities of 0.12, 0.23, or 0.52 by storage for two weeks at room temperature in desiccators containing saturated LiCl, MgCl 2 or Mg(NO 3 ) 2 solutions, respectively. Water activity of commercial dairy powders is usually close to 0.23. The water activity of powders before and after dry-heating was checked using an a w -meter (Novasina, Axair Ltd, Switzerland). Powders were then dry-heated at 70°C for 0, 1, 5, 25 or 125 h in hermetically sealed bottles. Control samples were evaluated at intermediate stages of sample preparation (Fig. 1). Sample (1) underwent only the precipitation at pH 4.6. Samples (2) and (3) were also freeze-dried at pH 3.5 and 6.5, respectively.

Experimental design

A multifactorial experimental design was built with pH, a w and dry-heating time as variables. Since the complete design would need 45 combinations (3 pH × 3 a w × 5 time periods), a fractional design of 20 conditions were selected by a backward selection algorithm, based on the maximisation of the information matrix determinant (D-efficiency), with the Statgraphics software (Statgraphics Technologies, Inc).

To focus on samples adjusted at pH 3.5, and to obtain a complete design in this condition, 8 trials were added to the formerly described fractional design. The resulting overall design consisted of 28 trials. This design was used with and without lactose separately, leading to 56 conditions (including 30 conditions at pH 3.5). For all of them, experiments have been at least duplicated. For some of them, experiments have been repeated 3 times or more. Including repetitions, 143 foams have been studied.

Foam generation and drainage rate

Powders were dissolved in ultrapure water at a protein concentration of 1.9 g•L -1 . Each solution was then dialysed against water, in order to suppress ionic strength differences between samples. During dialysis, pH drifted toward the average isoelectric point of whey proteins, close to 5.0 ± 0.2. After dialysis, pH was adjusted to 7.0 (NaOH 1N).

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5 Foams were obtained by bubbling air into the protein solution (40 mL) through a porous glass disk placed at the bottom of a column until contact of the foam with the top e01 electrode (Fig. 2). The foaming time was lower than 1 min. The mean foam bubble diameter was smaller than 1 mm (Fig. 3). The conductivity of a freshly-produced foam was measured by an impedance meter operating at a frequency of 1 kHz and voltage level of 1.0 V. The liquid volume fraction ( = liquid / foam) at each electrode position was measured using the empirical relationship of [START_REF] Feitosa | Electrical conductivity of dispersions: from dry foams to dilute suspensions[END_REF]:

(eq 3) =
where was the relative conductivity σ foam /σ solution .

The liquid fraction in the foam was monitored for each electrode (at different column heights) as a function of time (Fig. 4). Liquid drained from the top to the bottom of the foam because of gravity. Thus, a gradient of liquid fraction took place along the height of the foam column and the foam was dryer at the top. In this situation, called free drainage, the evolution of the liquid fraction at a given height finally reached a power-law regime, on timescales much longer than the initial foaming time [START_REF] Koehler | A Generalized View of Foam Drainage: Experiment and Theory[END_REF][START_REF] Saint-Jalmes | Time evolution of aqueous foams: drainage and coarsening[END_REF]:

(eq 4) ∝
where α is the free-drainage exponent.

When t tends to the foaming time, there is a cut-off and tends to its initial value.

In other words, when drainage was the only instability phenomena occurring in the foam, the liquid fraction evolved linearly with time in log-log representation. The exponent α describes the drainage rate (Fig. 4). The lower α, the higher the foam stability against drainage. Among the electrodes pairs, only e03, e04, e05, e06 and e07 were selected for data analysis. e01, e02, e08, e09 and e10 were excluded because of boundary conditions (capillary liquid holdup at the bottom and finite size effects on the top of the foam) (Saint-Jalmes, 2006).

Statistical analysis

Principal Component Analysis

Principal component analysis (PCA) is a multivariate statistical method used to extract the main information from a data set, based on correlations between variables. New orthogonal variables, consisting in linear combinations of the initial variables and called principal components (PC), are computed together with the values of these new variables (scores) for each observation. Principal components are usually ordered by decreasing order of variance, in such a way that the first few principal components provide a summary of variability in the data set. Scores of observations on principal components allow to draw similarity maps where each observation is represented by a point [START_REF] Abdi | Principal component analysis[END_REF].

In the input of PCA, observations were foams and each foam was described by its liquid fraction measured as a function of electrode (i.e., height) and time (Fig. 4). Liquid fraction was measured every 6 seconds for 1422 s, at electrodes e03 to e07. All the data were converted into log values in order to compare the drainage exponents for different samples [START_REF] Koehler | A Generalized View of Foam Drainage: Experiment and Theory[END_REF][START_REF] Saint-Jalmes | Time evolution of aqueous foams: drainage and coarsening[END_REF].

PCA was performed separately on the data set obtained from the fractional design (143 foams corresponding to 56 combinations of pH, a w , heating time and lactose) and on the complete design at pH 3.5 (76 foams corresponding to 30 combinations of a w , heating time and lactose).

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Analysis of Variance

Analysis of variance (ANOVA) was used to test the effects of parameters (pH prior to dehydration, a w of powders, dry-heating times and lactose content), treated as qualitative, categorical variables, on foam coordinates (scores) on the first two principal components PC1 and PC2. The normal distribution of the data and the homoscedasticity of the samples were checked. Main effects and second order interactions have been taken into account. Only effects significant at the p<0.01 level have been considered and will be discussed. ANOVA was performed using the R software package (R Core Team, 2017).

Results

3.1 A new approach for proteins foams properties Fig. 4a and4b show typical log-log plots of conductivity in foams, converted to liquid volume fraction, as a function of time, for different electrodes (i.e., heights). For a given electrode, the initial steep increase indicates that the foam formed by air bubbling in the protein solution reached the height of the electrode. The bottom electrode (e07) detects the foam first, the top electrode (e03) detects the foam last. When bubbling is stopped, the liquid fraction reaches a maximum. The higher the electrode, the lower the maximum liquid fraction: this is due to liquid drainage occurring already during the foam formation and upward progression. In the case of Fig. 4a, the maximum liquid fractions range between 0.13 and 0.23.

After bubbling was stopped, typically after less than 1 min, the liquid fraction decreases, reflecting foam destabilisation. If drainage is the main destabilisation process operating, the liquid fraction in foam decreases as a power law of time [START_REF] Koehler | A Generalized View of Foam Drainage: Experiment and Theory[END_REF][START_REF] Saint-Jalmes | Time evolution of aqueous foams: drainage and coarsening[END_REF], illustrated by a linear decrease in log-log representation, and the time exponent reflects the drainage rate. However, after a variable period of time, depending on the electrode and sample, a deviation of this power law regime occurs. In Fig. 4b, for bottom electrodes (e05, e06 and e07), curves have a pronounced rounded shape, followed by a faster liquid fraction decrease. On Fig. 4a, bumps just before 1000 s are visible, corresponding to abrupt water flows from above in the column. So, the drainage is probably coupled with film rupturing (locally popped bubbles and/or disproportionation). Moreover, collective coalescence events, marked by an important decrease of liquid fraction for a very short time, are visible at quite high liquid fraction (1 %) as compared to what is usually found for low molecular weight (LMW) surfactants [START_REF] Carrier | Coalescence in Draining Foams[END_REF]. However, electrodes at the top, such as e03, seem more suitable for drainage rate measurements with weak disruption by other instability mechanisms. Finally, this method displays foam variability along the height of the column and between samples.

In the general case, the dual output of PCA consists of i) principal components, which are loadings of the initial variables in the principal components and depict the main dimensions of variability among observations, and ii) scores, which are the coordinates of observations on principal components, used to draw similarity maps where observations are projected. Fig. 5, Fig. 6 and Fig. 7 show the results of PCA on the first two principal components PC1 and PC2. The cumulated proportion of variance accounted for by PC1 and PC2 is 74.5 % (53.0 % and 21.5 %, respectively). PC3 was not considered because it accounted for less than 10 % of total variance. Fig. 5 and Fig. 6 show projections of

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observations on the map defined by PC1 and PC2, for all the non dry-heated samples (Fig. 5) and only the dry-heated samples (Fig. 6).

To illustrate the respective meanings of PC1 and PC2 as regards foam profiles, we reconstituted imaginary foams located arbitrarily at coordinates (±2×σ1, 0) and (0, ± 2×σ2), where σ1 and σ2 are the standard deviations of the sample scores on PC1 and PC2, respectively. In other words, 95% of the samples are between the imaginary samples A and B (for PC1) or C and D (for PC2), assuming a normal distribution. Comparing the corresponding reconstituted, imaginary foam profiles allow to sensibly interpret location on the factorial maps, i.e. scores on PC1 and PC2 in term of foam stability.

Reconstituted imaginary foams A and B in Fig. 7a correspond to samples with low and high scores, respectively, on PC1 (Fig. 5 and Fig. 6). Whatever the electrode (Fig. 7a), over the whole kinetics, the liquid fraction of sample B, decreases slower than the liquid fraction of sample A. Thus, whatever the electrode (Fig. 7a), sample B is more stable than sample A. In addition, the maximum liquid fraction, right after the end of bubbling, tends to be higher for B than for A: for example, at electrode e07, max B =0.23 while max A =0.20. In other words, higher scores on PC1 are associated with higher stability and higher maximum foam density.

Reconstituted imaginary foams C and D in Fig. 7b correspond to foams with low and high scores on PC2, respectively (Fig. 5 and Fig. 6). Stability profiles along the foam height are not uniform since they depend on the electrode (Fig. 7b). Sample D has a higher stability at the top of the foam column (Fig. 7b). Indeed, at e03 and e04, the decrease in liquid fraction is slower for sample D than for sample C. The corresponding exponents at electrode e03 are α D = 0.80 for D and α C = 1.10 for C. However at the bottom of the foam column (e05, e06, e07), kinetics are less linear than at the top (e03, e04), and differences in stability between C and D are less obvious. Concerning the foam formation, the foam is detected earlier for sample D by a given electrode (t D =61 s and t C =71 s at e03) (Fig. 7b). However, this was attributed to an experimental bias and will not be discussed in the following sections.

Finally, samples with a high score on PC1 (i.e. located on the right side of the factorial map) have a high foam stability and density. Samples with a high score on PC2 (i.e. located on the upper part of the factorial map) have a high foam stability at the top of the foam. Fig. 5 shows the scores on PC1 and PC2 of foams from control samples (1), ( 2) and (3) and of foams from a w -conditioned samples at different pH (i.e., prior to dry-heating). Control samples are grouped on the high-PC1-score side of the map and around the average zero score on PC2. In contrast, a wconditioned samples are spread over the map, showing that the incubation for two weeks at room temperature for a w -conditioning markedly affected the foam behaviour, whatever the pH. However, Fig. 5 does not show any clear preferential location of foams on the PC2 versus PC1 map depending on a w (a) or pH (b). Fig. 6 shows that dry-heating of whey proteins impacts their foaming behaviour with a complex dependence on dry-heating parameters such as pH prior dehydration for example (Fig. 6b). In more details, dry-heating at pH 5.0, whatever the time, results in low scores on PC1 (Fig. 6b), suggesting low foam stability of these samples. On the other hand, dry-heating for 125 h, whatever the pH prior to dehydration, increases score on PC2 (Fig. 6a), suggesting rather high foam stability at the top of the foam. Those results suggest complex interactions between dry-heating parameters. They also show that the effect of powder pre-conditioning (Fig. 5) is in the same order of magnitude as the effect of subsequent dry-heating (Fig. 6). In order to obtain quantitative estimations of the effects of dry-

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8 heating parameters and their interactions on foam stability, analysis of variance (ANOVA) was performed.

Dry-heating parameters effects on foam stability

Table 1 presents the significant main effects and their second order interactions, on the coordinates of the samples on PC1 and PC2. The ANOVA estimates and standard errors are given in supplementary materials (Tables A andB). Taking into account all variables and interactions, the R 2 of the models for PC1 and PC2 are 45.42 % and 60.85 %, respectively. These quite medium R² scores may be due to the significance of higher order interactions that could not be estimated, due to the use of a fractional experimental design. For the same reason, some interaction estimates on PC1 (pH 3.5:1 h, pH 5.0:1 h, pH 5:25 h) and PC2 (pH 3.5:1 h, pH 5.0:1 h, pH 5.0:25 h and pH 5.0:5 h) could not be calculated (supplementary data). Thus, the corresponding experimental conditions, shown as greyed cells in Fig. 8 and Fig. 9, are not discussed.

Fig. 8 shows the values predicted by the model for scores on PC1 (i.e. foam stability) as a function of pH, dry-heating time and lactose content for samples dry-heated at an a w of 0.52. This a w was chosen for data representation because it emphasised the effects of dry-heating. In this case, the optimal foam stability corresponds to no or short dry-heating (0 h or 1 h), whatever the lactose content. However, since the colours are overall lighter for reduced lactose content (Fig. 8a), decreasing the lactose content increases samples scores on PC1, and thus their foam stability. On the opposite, extensive dry-heating (125 h) at pH 5.0 and pH 6.5 decreases the foam stability and the effect strengthens with lactose content (Fig. 8b). In contrast, dry-heating at pH 3.5 preserves or even improves the foam stability for extended dry-heating.

Fig. 9 shows the values predicted by the model for scores on PC2 (i.e. stability at the top of the foam) as a function of a w and heating time at pH 6.5 (a) and pH and heating time at a w 0.52 (b). Fig. 9a shows that decreasing a w of samples dry heated at pH 6.5 (whatever the dry heating time, i.e. even for non-dry heated samples) increases the local stability at the top of the foam. Fig. 9b illustrates that the adjustment of the powder pH to 3.5 (whatever the dry-heating time), or 125 h dry-heating (whatever the pH) also increases the stability at the top of the foam.

The results of ANOVA thus validate the tendencies previously observed on PCA maps (Fig. 5, Fig. 6): they highlight the major role of interactions between pre-conditioning and dry-heating parameters.

Considering the particular results obtained with samples adjusted to pH 3.5 before dry-heating, the experimental design was completed with samples missing at this pH.

Foam stability at pH 3.5

The data about foam stability from the complete experimental design at pH 3.5 were also analysed independently using PCA. The corresponding results are presented in supplementary data (Fig. A).

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9

The first two principal components at pH 3.5 can be interpreted in the same way as in the case of the fractional design (see 3.1), i.e. PC1 as the global stability of the foam and PC2 as the local stability at the top on the foam. In the following section, only the global foam stability will be considered. The proportion of variance accounted for by PC1 is 49.7 %. As in the case of the overall fractional design, increasing scores on PC1 also corresponds to an increase in the global foam stability. The parameter effects on PC1 scores were also evaluated using ANOVA. Table 2 shows significant parameter main effects (a w , time) and interactions (a w :time, time:lactose).

Table 2 ANOVA p-values of main effects and interactions for PC1, for the complete experimental design at pH 3.5. For a pvalue higher than 0.05, variables and/or interactions were considered as not significant (NS) and were eliminated. The lactose main effect was kept due to the highly significant time:lactose interaction.

a w time lactose a w :time a w :lactose time:lactose PC1 0,0021 0,0020 0,6985 0,0008 NS <10 -4

The model R 2 is 64.03 %. Fig. 10 illustrates the model predictions for PC1 scores (the estimated effects are provided in supplementary data, Table C).

For short dry-heating (0 and 1 h), lactose enhances foam stability. However, the highest foam stability is obtained after 125 h of dry heating, whatever the lactose content. However, the increase in foam stability is not monotonous, since dry-heating for 5 h with high lactose content strongly decreases the foam stability.

The focus on data at pH 3.5 thus shows that in these conditions, extended dry-heating significantly increases the global foam stability.

Discussion

Principal component analysis of liquid fractions time-and height-profiles allows a detailed comparison of foam stabilities

Monitoring the variation of the liquid fraction by electrical conductivity measurements is reported in the literature for drainage rates [START_REF] Koehler | A Generalized View of Foam Drainage: Experiment and Theory[END_REF][START_REF] Carey | Free drainage of aqueous foams stabilized by mixtures of a nonionic (C12DMPO) and an ionic (C12TAB) surfactant[END_REF][START_REF] Daugelaite | Quantifying liquid drainage in egg-white sucrose foams by resistivity measurements[END_REF] and coalescence events measurements [START_REF] Carrier | Coalescence in Draining Foams[END_REF]. However, it has been mainly applied to low-molecular-weight (LMW) surfactants foams, which are simpler systems than protein foams. The drainage exponents α inform about both flows at the bubble interface and within the Plateau borders. In our experiments, drainage exponents for whey protein are of the order of α≈0.80-1.10 which correspond to immobile interfaces, with slow drainage [START_REF] Koehler | A Generalized View of Foam Drainage: Experiment and Theory[END_REF][START_REF] Saint-Jalmes | Time evolution of aqueous foams: drainage and coarsening[END_REF]. Conversely, LMW surfactants usually provide mobile interface and an exponent of α ≈2 [START_REF] Koehler | A Generalized View of Foam Drainage: Experiment and Theory[END_REF][START_REF] Saint-Jalmes | Time evolution of aqueous foams: drainage and coarsening[END_REF]. Recently, [START_REF] Daugelaite | Quantifying liquid drainage in egg-white sucrose foams by resistivity measurements[END_REF] had the same approach for egg-white protein foams. They also obtained low drainage exponents (α ≈0.5-1).

In contrast with forced drainage experiments, used in some of the above-mentioned works, drainage experiments performed in our study are called "free drainage" because the initial liquid fraction gradient is not counterbalanced by re-wetting from the top [START_REF] Koehler | A Generalized View of Foam Drainage: Experiment and Theory[END_REF]. Consequently, we showed that the liquid fraction time-profiles of whey protein foams are not uniform along the height of the foam column. Indeed, the foam starts draining as soon as it is formed. In addition, as evidenced

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ACCEPTED MANUSCRIPT 10 by non-linear time-profiles (in log-log plots), drainage and coalescence occur simultaneously. Thus, the water flow at any layer of the foam integrates what happens above, and that is why the top electrode pair (e03) generally shows a more linear time-profile than the other ones, which is suitable for a drainage study. Since the time-profiles are not uniform along the height of the foam, it is necessary to study simultaneously the height-and time-profiles of foam liquid fractions. The large amount of resulting data motivates the use of multivariate statistical analysis, such as principal component analysis (PCA).

Interestingly, this approach clearly shows that foam stability has a 'global' dimension (which does not depend on the height), and a 'local' dimension (which distinguishes the time-profiles of top and bottom electrodes). The former is illustrated by our PC1, the latter by our PC2. However the technique we used also give information about foam density and foam formation, which also contribute to PC1 and PC2, making the analysis slightly more difficult.

In the present work, a focus was made on the stability of foams against drainage. Nevertheless collective coalescence events were also observed (Fig. 4). Bubble coalescence represents a process of thin liquid film rupture between two neighboring bubbles. Factors such as disjoining pressure, film lamella thickness or surface elasticity control the foam stability against coalescence [START_REF] Narsimhan | Role of Proteins on Formation, Drainage, and Stability of Liquid Food Foams[END_REF]. In our study, the ionic strength of protein solutions was low. In such conditions, β-lg shows higher film thickness and disjoining pressure, and lower surface elasticity than at high ionic strength [START_REF] Gochev | Electrostatic stabilization of foam films from β-lactoglobulin solutions[END_REF]. This is probably due to unscreened electrostatic repulsions between protein molecules inside the interfacial layer, as well as between the two interfacial layers of the liquid lamella. The occurrence of collective coalescence could then be explained by the low surface elasticity of adsorbed protein films.

4.2 a w pre-conditioning at room temperature significantly impacts foam stability.

To control a w , it was necessary to pre-condition powders at 20 °C for two weeks in the presence of saturated salt solutions. Surprisingly, our results clearly show that this pre-conditioning significantly changed foaming properties, even in the absence of any heat-treatment (Fig. 8, Fig. 9 and Fig. 10).

It has been shown that dairy powders stored under solid state may indeed undergo physico-chemical changes with time, like Maillard reaction and oxidation [START_REF] Rao | Storage Stability of Food Protein Hydrolysates-A Review[END_REF]. These changes occur close to or above the powder glass transition temperatures (Tg), or after long storage time as compared to the time scale of molecular diffusion [START_REF] Rao | Storage Stability of Food Protein Hydrolysates-A Review[END_REF]. The monitoring of a w is crucial since the glass transition temperature Tg of dehydrated milk products decrease from 60°C to 0°C with the increase of a w from 0.1 to 0.5. The temperature Tg also depends on sugar content (Thomas et al., 2004). In our study, powder lactose content was involved in foam stability changes (Fig. 8 and Fig. 10). Thus, since the presence of lactose during the powder storage is known to lead to lactosylation (i.e. condensation between sugar and protein amino groups (glycation)), this chemical modification may be proposed to impact their foaming properties. According to Thomas et al. (2004), nearly all the β-lg is lactosylated after one week of storage (a w 0.45 at 37°C). Even at low temperatures in milk powders, lactosylation occurs especially when storage temperature exceeds 20°C.

However, our statistical analysis revealed that lactose acts differently on foaming properties depending on pH. Indeed, lactose improved foam stability at pH 3.5 but decreased it at pH 6.5 and a w 0.52. Consistently, pH effects on protein powder glycation have already been observed [START_REF] Povey | Investigating variables and mechanisms that influence protein integrity in low water content amorphous carbohydrate matrices[END_REF]Thomsen et al., 2012).

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Moreover, other modifications could be considered during storage of WPI such as copolymer formation of α-La and β-lg due to free sulfhydryl group oxidation and exchange between proteins [START_REF] Alting | Number of thiol groups rather than the size of the aggregates determines the hardness of cold set whey protein gels[END_REF]Thomas et al., 2004).

Finally, complex interactions between the pH, a w and lactose could explain the changes of foaming properties for samples that have not been dry-heated, even at short storage time at 20 °C. Considering, the results of this study, to keep good foaming properties, lactose content of WPI powders should be reduced or, WPI powder pH and/or a w should be decreased. Otherwise, the manufacturers could also store dairy powders at 4°C according to Norwood et al. (2016) in order to preserve protein functional properties. Indeed, the control of whey protein aggregation is perturbed by WPI powder ageing . Up to date, dairy powder ageing remains an industrial concern, responsible for uncontrolled technofunctional variability [START_REF] Haque | Effects of Protein Conformational Modifications, Enthalpy Relaxation, and Interaction with Water on the Solubility of Milk Protein Concentrate Powder[END_REF][START_REF] Nasser | Influence of storage conditions on the functional properties of micellar casein powder[END_REF].

4.3 Dry-heating parameters interactions impacts foam properties.

Our study shows that extensive dry-heating (125 h) leads to a wide range of global foam stability, depending on the powder properties (Fig. 6a). In statistical terms, this is reflected by complex interactions between parameters, especially pH:time.

That complexity in parameters effects on foam stability suggest a parallel with the complexity of pH and heating time effects on structural and biochemical changes in WPI: mechanisms and kinetics of aggregation, lactosylation, extent of Maillard reactions [START_REF] Gulzar | The physicochemical parameters during dry heating strongly influence the gelling properties of whey proteins[END_REF][START_REF] Guyomarc'h | Current ways to modify the structure of whey proteins for specific functionalities-a review[END_REF]. Such structural changes and aggregation conditions have been shown to impact foam stability [START_REF] Rullier | Effect of protein aggregates on foaming properties of β-lactoglobulin[END_REF][START_REF] Fameau | Effect of particles and aggregated structures on the foam stability and aging[END_REF].

Fig. 8 shows that extensive dry-heating (125 h) at pH 5.0 and pH 6.5 decreased foam stability, and this effect strengthens with increasing lactose content. On the contrary, dry-heating for 125 h at pH 3.5 with lactose improved foam stability (Fig. 10). This observation suggests the existence of a significant statistical three-way pH:time:lactose interaction, which could not be evaluated due to the choice of a fractional experimental design. Indeed, [START_REF] Guyomarc'h | Current ways to modify the structure of whey proteins for specific functionalities-a review[END_REF] showed that Maillard reaction products are involved in the formation of aggregates differently depending on the WPI pH prior dry-heating. Acidic condition have been shown to limit Maillard reaction, both in powders [START_REF] Guyomarc'h | Current ways to modify the structure of whey proteins for specific functionalities-a review[END_REF] and solution (Wang et al., 2013).

High a w values may favour chemical reactions, promoting both lactosylation and complex Maillard products. It seems that parameters that are favourable to Maillard reaction (lactose, high pH and a w ) decrease foam stability. However, it is worth noting that when this reaction is limited (at pH 3.5), dryheating increases foam stability even with high lactose content and high a w .

Our study also shows that extensive treatment (125 h) improves the local stability against drainage at the top of the foam, as reflected by high scores on PC2. A possible explanation is that aggregates probably act as obstacles to liquid flow during the confinement inside the foam [START_REF] Fameau | Effect of particles and aggregated structures on the foam stability and aging[END_REF].

Still, in our experiments at pH 3.5, even in conditions unfavourable to the formation of aggregates (no or short dry-heating), the local stability was increased. This suggest that interfacial rheology is involved in those observations, as corroborated by the changes in the drainage time exponent, related to interfacial mobility [START_REF] Koehler | A Generalized View of Foam Drainage: Experiment and Theory[END_REF][START_REF] Saint-Jalmes | Time evolution of aqueous foams: drainage and coarsening[END_REF]. Thus, a possible explanation is that the drainage is limited at pH 3.5 because of small structural modification with a large impact on foaming properties.

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Finally, bulk properties, through the presence of aggregates restricting the flow, as well as interfacial properties, through the interfacial rheology, could both explain the extent in the observed variations of the drainage exponent (α).

Thus, WPI dry-heated at pH 3.5 could be used as a foam stabiliser for ice-cream, coffee whitener or meringues applications [START_REF] Suthar | High Protein Milk Ingredients -A Tool for Value-Addition to Dairy and Food Products[END_REF]. Nevertheless, conditions promoting extensive Maillard reaction may also reduce foaming properties, thus justifying a de-sugaring process step, as commonly performed in egg white industrial processing [START_REF] Campbell | Modification of functional properties of egg-white proteins[END_REF].

Conclusions

In the present work, we examined the effect of powder dry-heating time, under controlled physicochemical conditions (a w , pH prior to dehydration and lactose content), on whey protein foam stability. Principal component analysis of the liquid fraction time-and height-profiles of about 150 whey protein foams allows a detailed comparison of foam stabilities. Interestingly, this sensitive approach clearly shows that foam stability has a 'global' dimension (which do not depend of height), and a 'local' dimension (which distinguishes the time-profiles of top and bottom electrodes).

Interactions between pH prior to dehydration, powder a w , lactose content and dry-heating time at 70°C caused complex effects of dry-heating on foam stability. Extensive dry-heating at pH 5.0 and pH 6.5 lower the global foam stability and the effect strengthens with lactose content. Nevertheless, dryheating at pH 3.5 preserves the foam stability, including for extended dry-heating. We propose that pH 3.5 has a protective effect against Maillard reactions, which are detrimental to foam stability, as compared to pH 5.0 and 6.5. Surprisingly, storage of powders for two weeks at room temperature prominently impacted foaming properties. These results suggest that even in the absence of a thermal treatment of the powder, protein structural changes and modifications of interfacial properties may occur. Our findings point at the need for a thorough characterisation of protein structural and biochemical changes in WPI during storage and upon dry-heating. Such a characterisation is in progress. Relating foaming properties to protein features remains a crucial challenge. 2) and (3) were control samples. Sample (1) underwent only the precipitation at pH 4.6. Besides the precipitation, (2) was freeze-dried at pH 3.5 and

(3) at pH 6.5. D samples have a 10 times lower amount of lactose than L samples which keep their native amount in lactose. Figure 10. Graphical representation of the model predictions for PC1 of the PCA performed on the complete factorial design at pH 3.5, as a function of lactose content and dry-heating time at a w 0.52 and pH 3.5. Each cell is coloured according to the predicted score on PC1. The higher the predicted score on PC1 the higher the foam stability.

Figure 1 .

 1 Figure captions

Figure 2 .

 2 Figure 2. Schematic representation of the foam column (height 50 cm and diameter 2 cm) in which 10 pairs of electrodes (e x ) are embedded, facing each other along the height at equal distance.

Figure 3 .

 3 Figure 3. Picture of whey protein foam by CCD camera.

Figure 4 .

 4 Figure4. Typical log-log plots of the liquid fraction of WPI foams as a function of time at different electrodes (e x ). Figure4a and 4bshow two different foams sharing the same parameters (0 h, D, a w 0.52) except their pH prior to dehydration, pH 5.0 and pH 3.5 respectively. The exponent α or drainage rate is represented by a dashed line at e03 as an example.

Figure 5 .

 5 Figure 5. Factorial maps of scores on PC2 vs PC1 of non dry heated samples (42 samples among the 143 used to performed the PCA) represented according to their a w (a) or pH (b).Each circle corresponds to one foam, and the filled colour depends on the value of the indicated parameter. The size of the circles figures the individual projection quality on the map: the larger the circle, the better the projection. Control samples without a w adjustment are represented by numbers surrounded by a black circle, as detailed in section 2.2.1. Samples A, B, C, and D are imaginary samples reconstituted as explained in the text (section 3.1).

Figure 6 .

 6 Figure 6. Factorial maps of scores on PC2 vs PC1 of dry-heated samples (101 samples among the 143 used to performed the PCA) represented according to their dry-heating time (a) or pH (b). Each circle corresponds to one foam, and the filled colour depends on the value of the indicated parameter. The size of the circles figures the individual projection quality on the map: the larger the circle, the better the projection. Samples A, B, C, and D are imaginary samples reconstituted as explained in the text (section 3.1).

Figure 7 .

 7 Figure 7. Liquid fraction profiles calculated for imaginary samples A and B on PC1 (a) and C and D on PC2 (b). A and B (C and D, respectively) are located at plus or minus twice the standard deviations from the mean sample score on PC1 (PC2, respectively), as explained in the text (section 3.1).

Figure 8 .

 8 Figure8. Graphical representations of values predicted by the model for scores on PC1 as a function of pH and heating time at a w 0.52 with (a) a reduced amount of lactose "D" and (b) the initial amount of lactose "L". Each cell is coloured according to the predicted score on PC1. The higher the predicted score on PC1 the higher the foam stability. Greyed cells correspond to missing estimations due to the fractional experimental design.

Figure 9 .

 9 Figure9. Graphical representations of values predicted by the model for scores on PC2 as a function of a w and heating time at pH 6.5 (a) and pH and heating time at a w 0.52 (b). Each cell is coloured according to the predicted score on PC2. The higher the predicted score on PC2

Table 1

 1 ANOVA p-values of the different variables and their significant interactions for PC1 and PC2. For a p-value>0.05 variables and/or interactions were considered as not significant (NS) and were eliminated.

		pH	a w	time	lactose pH:a w	pH:time	a w :time	pH:lactose	a w :lactose time:lactose
	PC1	0,0090 0,0022 0,0001 0,0157 NS	0,0001	NS	0,0032	0,0080	NS
	PC2	0,0901 0,0055 <10 -4	NS	<10 -4	<10 -4	0,0001	NS	NS	NS

Acknowledgements

We are grateful to the Regional councils of Brittany (grant N° 13008651) and Pays de la Loire (grant N°2014-07081) for their financial support as well as INRA for its scientific coordination (J. Leonil) through the interregional project PROFIL, managed by the BBA industrial association.

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