-C Trelea

M Doyennette
email: mariondoyennette@grignon.inra.fr

C De Loubens

I Déléris

I Souchon

I C Trelea

Mechanisms explaining the role of viscosity and postdeglutitive pharyngeal residue on in vivo aroma release: a combined experimental and modeling study

Keywords: Flavor release, saliva dilution, swallowing, dynamic modeling, rheology

Mechanisms explaining the role of viscosity and post-deglutitive pharyngeal residue on in vivo aroma release: A combined experimental and modeling study

Introduction

Aroma compound release and perception determine the aromatic quality of food products and contribute to consumer choices and preferences. During consumption, flavor delivery is particularly determined by product properties (structure and composition) and individual physiology.

Understanding the key mechanisms of release is of great practical interest for rational food design and formulation (Linforth & Taylor, 2000).

In the present work, the focus has been placed on the effect of matrix viscosity. This subject has already been discussed in the literature but there appears to be no consensus. On the one hand, some authors observed no effect of product viscosity on aroma release kinetics [START_REF] Cook | Oral shear stress predicts flavour perception in viscous solutions[END_REF][START_REF] Hollowood | The effect of viscosity on the perception of flavour[END_REF][START_REF] Weel | New device to simulate swallowing and in vivo aroma release[END_REF]. These authors studied solutions viscosified with hydrocolloids. Their analysis may have been biased by the fact that the concentration of the viscosifying agent modified both rheological and physico-chemical properties. On the other hand, some authors found an impact of viscosity on aroma release [START_REF] Saint-Eve | Flavored yogurt complex viscosity influences real-time aroma release in the mouth and sensory properties[END_REF]. They obtained different rheological properties by a mechanical treatment that does not modify the product composition and that therefore leaves physico-chemical properties such as air/product partition coefficients unchanged [START_REF] Kora | Composition rather than viscosity modifies the aroma compound retention of flavored stirred yogurt[END_REF]. In that way, authors were able to uncouple rheological and physico-chemical properties in their study. [START_REF] Saint-Eve | Flavored yogurt complex viscosity influences real-time aroma release in the mouth and sensory properties[END_REF] showed a strong influence of yogurt complex viscosity on aroma release and hypothesized that these differences were due to different mechanical behaviors of the products in the mouth or in the pharynx.

However, yogurts present complex rheological properties such as viscoelasticity and yield stress.

These complex behaviors, leading to different experimental conditions when compared with the other studies, could explain the conflicting results.

In this context, the objective of this study was to analyze the Newtonian viscosity effects on the aroma release kinetics of the products. To this end, we measured in vivo aroma release kinetics by Proton Transfer Reaction Mass Spectrometry (PTR-MS) after the ingestion of glucose syrup solutions. These solutions were Newtonian liquids for which a wide range of viscosities could be obtained.

Increasing the carbohydrate concentration of the solutions increased the Newtonian viscosity but modified the air/product partition and mass transfer coefficients as well. In order to quantify these effects independently, we developed a mechanistic model that described aroma release during consumption of a liquid and semi-liquid food. Most of the model parameters related to the products or to the subjects were measured experimentally. Comparing the model predictions under different assumptions with the experimental data allowed us to understand the influence of viscosity on aroma release.

The mechanistic model describing aroma release in the present study was developed on the basis of the work described by Trelea, Atlan, Deleris, Saint-Eve, [START_REF] Trelea | Mechanistic mathematical model for in vivo aroma release during eating of semiliquid foods[END_REF]. The sensitivity analysis of the previous model highlighted the parameters that have a major influence on aroma release kinetics. For example, the residual product layer thickness reduction in the pharynx accelerates the volatile compound depletion by the breath flow rate, whereas its increase induces a longer persistence effect. The breath flow rate also influences the aromatic persistence. In addition, increasing the equilibrium partition coefficient or the mass transfer coefficient increases the aroma concentration in the nasal cavity.

Most of these key parameters can be determined experimentally or evaluated from the literature.

However, the residual thickness of a product is an unknown parameter that should depend both on the product viscosity and on the individual physiology. Due to the presence of saliva on the pharyngeal mucosa, two hypotheses can be formulated about the nature of this post-deglutitive pharyngeal residue. The first one considers that the initial saliva thickness in the pharynx is very thin compared to the deposited thickness of the product, or is swept out during swallowing: a pure product layer coats the mucosa. In the second hypothesis, we consider that the amount of saliva on the mucosa is large: the deposited residue layer is a mix of saliva and the product. These two assumptions were tested successively. In order to do this, the present work was carried out in successive steps. First, a model of aroma release during ingestion was developed. In parallel, relevant physico-chemical and physiological parameters were measured using in vitro or in vivo experiments, or were calculated from the literature or experimental data. Finally, model predictions under the two hypotheses were compared to measured in vivo release data. [START_REF] Trelea | Mechanistic mathematical model for in vivo aroma release during eating of semiliquid foods[END_REF]. It is based on a physiological representation of the deglutition process as described by [START_REF] Buettner | Observation of the swallowing process by application of videofluoroscopy and real-time magnetic resonance imaging-consequences for retronasal aroma stimulation[END_REF]. A schematic representation of the various compartments involved in the modeling design, as well as their connections, is given in Fig. 1A. We considered that the oral cavity (index O), the pharynx (index F) and the nasal cavity (index N) were interconnected compartments containing product and/or air phase.

In the present study, two main simplifications were performed with the aim of eliminating parameters that have little impact on model predictions and which are difficult to determine experimentally.

The first simplification concerns the number of swallowing steps. In the original model, the product consumption process was decomposed into a series of four steps. Three of them concerned the deglutition event. However, they were very short and quite difficult to validate experimentally.

Therefore, the new version of the model considers only three steps: product residence in the mouth, swallowing and release after swallowing. The swallowing step includes simultaneous contraction of the oral cavity and of the pharynx, leading to air and product expulsion, followed by relaxation and filling with fresh air. Figure 1B shows the successive steps modeled in the present work.

The second simplification of the model consisted in neglecting the aroma compound transfer resistance in the air at the gas/product interface compared to the resistance in the product.

After these model simplifications, the number of physicochemical and physiological parameters that needs to be known is reduced from 24 to 16. A comparison of the new model with the previous one shows that these simplifications do not change the predictions in any significant way.

Therefore, the model simulates the relative concentration of a specific aroma compound in the nose space of the subject. Aroma compound concentrations in all compartments (oral cavity, pharynx and nasal cavity) were calculated using mass transfer equations and mass balances. Isothermal conditions were assumed. Moreover, aroma compounds have a strong preference for the aqueous phase compared to the air, and the contact area between air and lungs is very large (~100 m 2 ) [START_REF] Menache | Upper respiratory tract surface areas and volumes of laboratory animals and humans: Considerations for dosimetry models[END_REF]. Thus, it seems reasonable to assume that aroma compounds are quickly absorbed into the lungs. It was therefore assumed that the air coming from the trachea (i.e., the lungs) would be aroma-free. If we take a closer look at the anatomy of the nose, we can subdivide the nasal cavity into the nasal vestibule, the anterior turbinate and the posterior turbinate with different volumes and airflow rates (Wen, Inthavong, Tu & Wang, 2008). Similarly, it could be possible to take aroma compound-mucosa interactions into account. These additional phenomena were tentatively incorporated into a provisional model but were not retained in the final model, as will be explained below in the Results and Discussion section.

Moreover, concerning the presence of saliva on the pharyngeal mucosa, two different hypotheses about the nature of the bolus that coats the pharyngeal mucosa after swallowing were considered. The first one (H1) assumes that a pure product layer is deposited on the pharyngeal mucosa. The second one (H2) assumes that the product coating the pharyngeal mucosa is significantly diluted with saliva.

In that case, contrarily to the first hypothesis, the physico-chemical parameters of the bolus have to be recalculated on the basis of the dilution rate.

Mathematical model description

Step 1: product residence in the mouth

 Product in the oral cavity

The mouth is closed during this step and does not exchange aroma compounds with other compartments. The volume of the product in the oral cavity V op increases due to dilution by saliva.

S OP Q dt t dV = ) ( (1)
The volatile mass flux φ OPA is given by the difference between the product concentration (C OP ) and the interfacial concentration (C * OP ):

)

) ( ) ( ( ) ( * t C t C k A t OP OP P OAP OPA - × × = φ (2)
where k P is the mass transfer coefficient of the aroma compound in the product.

The variation of the aroma concentration present in the product C OP is due to release to the air in the mouth (transfer through the product-air interface A OAP ) and to dilution by saliva flow Q S :

) ( ) ( ) ( ) ( t C Q t dt t dC t V OP S OPA OP OP × - - = × φ (3)

 Air in the oral cavity

The variation of aroma concentration in the air C OA is due to the volatile flux from the product in the mouth φ OPA :

) ( ) ( t dt t dC V OPA OA OA φ = × (4)

 Interfacial conditions

The interfacial aroma compound concentration on the product side was calculated using the partition conditions at the interface [START_REF] Cussler | Diffusion: Mass Transfer in Fluid Systems[END_REF]. Since transfer resistance on the air side was assumed to be negligible, the interfacial air concentration is the same as the bulk air concentration:

) ( ) ( * t C t C K OP OA AP = (5)
where K AP is the air/product partition coefficient.

Initial conditions for

Step 1: product residence in the mouth At the beginning of Step 1, the product introduced into the mouth (C OPini ) is the only compartment containing aroma compounds. Hence, the initial conditions are:

C OP (t 0 ) = C OPini (6) C OA (t 0 ) = C FP (t 0 ) = C FA (t 0 ) = C NA (t 0 ) =0 (7)
Step 2: Swallowing

The deglutition step is very short compared to the mouth residence step. The main modeling implication is that the transfer to the gaseous phase is negligible during deglutition.

To describe this sequence of very quick contraction and relaxation events, the following notation is used (Fig. 1B):

• t deg-corresponds to the product and air status immediately before the oral and pharyngeal contraction begins. It is the end of Step 1;

• t deg corresponds to the status between the end of the contraction and the subsequent relaxation of the pharynx and mouth;

• t deg+ corresponds to the moment just after pharynx and mouth relaxation. This is the end of

Step 2 and the beginning of Step 3.

 Product in the oral cavity

After the oral cavity contraction, the residual amount of product is assumed to be equal to the usual residual amount of saliva:

es O OP V t V Pr deg ) ( = (8)
Since

Step 2 is very short, the aroma compound concentration in the oral cavity is unchanged during deglutition (negligible dilution by saliva and transfer to air):

) ( ) ( ) ( deg deg deg - + = = t C t C t C OP OP OP (9)  Product in the pharynx
During deglutition, it is assumed under hypothesis (H1) that the saliva film in the pharynx is swept out by the large amount of product coming from the mouth:

) ( ) ( deg deg - + = t C t C OP FP (10)
Under hypothesis (H2), only a small part of the product coming from the mouth is mixed with the saliva film in the pharynx. This corresponds to the dilution factor discussed below.

 Air in nasal cavity, pharynx and mouth

Assuming that during the contraction, the expelled air is well mixed in the mouth, pharynx and nose, the intermediate aroma compound concentration in the nasal cavity, after contraction, is given by the total mass divided by the total volume:

NA FA OA NA NA FA FA OA OA NA V V V t C V t C V t C V t C + + × + × + × = - - - ) ( ) ( ) ( ) ( deg deg deg deg (11)
After the contraction, the amount of aroma compound present in the upper airway is

) ( deg t C V NA NA × .
After relaxation, this amount is diluted by ambient air. Assuming good mixing, the final concentrations will be:

NA FA OA NA NA OA FA NA V V V t C V t C t C t C + + × = = = + + + ) ( ) ( ) ( ) ( deg deg deg deg (12)
Step 3: Release after swallowing

The initial conditions of Step 3 are the final values of Step 2 (at t deg+ ).

 Product in the pharynx

The residual product in the pharynx releases aroma compounds into the adjacent air. The volatile flux φ FPA is given by: )

) ( ) ( ( ) ( * t C t C k A t FP FP P FAP FPA - × × = φ (13)
The mass balance of the aroma compound in the product layer gives:

) ( ) ( t dt t dC V FPA FP FP φ - = × (14)
The product volume in the pharynx V FP can be expressed as the product of the residual layer thickness e and the pharynx area FAP A , i.e. e A V FAP FP × =

. The previous equation can be further simplified to:

)) ( ) ( ( ) ( * t C t C e k dt t dC FP FP p FP - × - = (15)

 Air in the pharynx

The air in the pharynx exchanges aroma compounds with the residual product coating the pharynx walls and with the airflow Q NA from the nasal cavity (inhalation) or the lungs (expiration).

   < - × - ≥ - × + = × n) (expiratio 0 (t) Q if )) ( 0 ( ) ( n) (inhalatio 0 (t) Q if )) ( ) ( ( ) ( ) ( ) ( NA NA t C t Q t C t C t Q t dt t dC V FA NA FA NA NA FPA FA FA φ (16)

 Air in the nasal cavity

The concentration of aroma compounds in the nasal cavity results from a dilution with the ambient air during inhalation and with air coming from the pharynx during expiration:

   < - × - ≥ - × = × n) (expiratio 0 (t) Q if )) ( ) ( ( ) ( n) (inhalatio 0 (t) Q if )) ( 0 ( ) ( ) ( NA NA t C t C t Q t C t Q dt t dC V NA FA NA NA NA NA NA (17)

 Interfacial conditions

Similarly to what happens in the oral cavity (Equation ( 5)), the interfacial air concentration in the pharynx is the same as the bulk air concentration:

) ( ) ( * t C t C K FP FA AP = (18)

 Calculation of the respiratory flow rate

We based our calculation of the airflow rate Q NA on the assumption that the volume of air inhaled and exhaled by the panelist had a sinusoidal shape. The tidal volume V T and the respiratory frequency F R were required for this calculation (Section 2.6 for details about this data acquisition).

The time shift (t -t deg ) was introduced to ensure that the deglutition event is always followed by expiration, as physiologically observed. This is referred to as a swallow breath.

Assuming that lung volume variation is as follows:

)) ( 2 cos( 2 ) ( deg t t F V const t V R T lung - × × × × + = π (19)
where the constant accounts for the average air volume in the lungs, the expression of Q NA will be:

)) ( 2 sin( ) ( ) ( deg t t F V F dt t dV t Q R T R lung NA - × × × × × × - = = π π (20)

Model parameters

Model parameters can be related to the product, the consumer or the interaction between them.

Parameters related to the product

These parameters include the initial aroma compound concentration, the air/product partition coefficient and the mass transfer coefficient. The first parameter above is directly calculated from the product flavoring protocol (Section 2.2), and the second one is estimated via the non linear phase ratio variation method described in [START_REF] Atlan | Processing gas chromatographic data and confidence interval calculation for partition coefficients determined by the phase ratio variation method[END_REF]. The mass transfer coefficient was measured with the headspace method [START_REF] Lauverjat | Rapid determination of partition and diffusion properties for salt and aroma compounds in complex food matrices[END_REF]. Experimental protocols are described in detail in Section 2.4.

Parameters related to consumer anatomy and physiology

These parameters include the areas and volumes of the various compartments of the oro-nasalpharyngeal sphere, as well as the saliva and airflow rates. Data collection protocols are described in detail in the Section 2.6.

Parameters related to product-consumer interaction

These parameters are the residual amounts of the product and the air/product contact areas (both in the mouth and in the pharynx). Residual product left in the mouth after swallowing was arbitrarily set to 1% of the initial volume of product in the oral cavity. The air/product contact areas of the mouth and pharynx were calculated as detailed in Appendix A. The thickness of the post-deglutitive pharyngeal residue coating the pharynx was the degree of freedom of the model. Since it only affected the part of the curve related to the persistence of aroma, it was determined so that the model fitted the decay time of the experimental curve for each panelist, product and replicate.

The effects of these parameters on model prediction were investigated and are presented in the "Results and Discussion" section.

Preparation of flavored products

Seven solutions were prepared with a glucose syrup (C*Sweet M01623, Cerestar, Europe) and mineral water (Evian). The dry matters of final solutions varied from 0 g/100 g to 70 g/100 g. All preparations presented a Newtonian behavior, i.e., viscosity was constant regardless of the shearing rate applied.

Viscosities were measured with Physica MCR301 rheometer (Anton Paar Germany GmbH, Ostfildern, Germany) and were between 0.7 and 405 mPa s at 35°C. The characteristics of the solutions are summarized in Table 1. The solutions investigated in this paper were labeled according to their approximate percentage of dry matter (for example, G60 had a dry matter of 61.11g/100g). These solutions were flavored with diacetyl and ethyl hexanoate, which had been previously dissolved in 99.46% of propylene glycol (Aldrich, France). Final concentrations of diacetyl and ethyl hexanoate in the solutions studied were approximately 20 mg/L and 88 mg/L, respectively, for the in vivo experiments, 140 mg/L and 8.3 mg/L, respectively, for the in vitro determination of air/product partition coefficients, and 1.5 mg/L and 0.85 mg/L, respectively, for the in vitro determination of mass transfer coefficients.

For the rest of this work, we focused on the diacetyl results. Data concerning ethyl hexanoate will be used for the validation step.

Measurement of in vitro and in vivo aroma release by Proton Transfer

Reaction-Mass Spectrometry

The dynamic release of aroma compounds for in vitro and in vivo experiments was measured online using a Proton Transfer Reaction Mass Spectrometer (PTR-MS, Ionicon, Innsbruck, Austria).

The PTR-MS inlet was connected to samples or to the subject's nose via a 1/16" PEEK tube maintained at 60°C. The PTR-MS instrument drift tube was thermally controlled (Tdrift = 60°C) and operated at Pdrift = 200 Pa with a voltage set of Udrift = 600 V. Measurements were performed with the multiple ion detection mode on specific masses with a dwell time of 50 ms per mass. Diacetyl was monitored with m/z 87 (molecular ion). For in vivo experiments, m/z 59 (acetone) was also monitored as a breath marker, as described in [START_REF] Normand | Modeling the kinetics of flavour release during drinking[END_REF] and [START_REF] Trelea | Mechanistic mathematical model for in vivo aroma release during eating of semiliquid foods[END_REF].

In addition, masses m/z 21 (signal for H 3 18 O + ) and m/z 37 (signal for water clusters H 2 O-H 3 O + ) were monitored with a dwell time of 100 ms to check the instrument performances and cluster ion formation. m/z 21 intensity was (1.34±0.51) x 10 4 cps for in vitro experiments and (9.46±0. 035) x 10 3 cps for in vivo experiments. In both cases, the ratio of intensities of m/z 37 and 21 variation was lower than 5%. These differences were considered sufficiently small to ensure accurate PTR-MS measurements. For both in vitro and in vivo measurements, a minimum of three replicates were preformed for each condition studied.

Air was sampled from the subject's nose at a flow rate of 35 cm 3 /min. Nose space air was sampled via two inlets of a stainless nosepiece placed in both of the assessor's nostrils.

Determination of physicochemical parameters of diacetyl

Determination of air/product partition coefficients

The air/product partition coefficient of diacetyl K AP was measured for each solution with the Phase Ratio Method using headspace gas chromatography [START_REF] Ettre | Determination of gas-liquid partition coefficients by automatic equilibrium headspace-gas chromatography utilizing the phase ratio variation method[END_REF]. A known amount of solution was placed in vials (22.4 cm 3 , Chromacol, France) and incubated at 35°C for 5 hours. After this equilibration time, 2 cm 3 of the headspace above the product was sampled and injected with an automatic HS CombiPal sampler (CTC Analytics, Switzerland) into a gas chromatograph HP (GC-FID HP6890, Germany) equipped with an HP-INNOWax polyethylene glycol semi-capillary column J&W Scientific (30 m x 0.53 mm, with a 1 µm-thick film) and a flame ionization detector. The temperatures of the gas chromatograph injector and detector (GC-FID HP6890, Germany) were both set at 250°C.

The oven program was 12 min long, starting at 40°C, for 5°C/min up to 60°C, then for 10°C/min up to 120°C, and 2 min at 120°C. The carrier gas was helium (flow rate: 8.4 cm 3 /min, corresponding to a 57 cm/s average velocity at 50°C). Peak areas were measured using Hewlett-Packard Chemstation integration software.

A non-linear regression was performed on the data set as described in [START_REF] Atlan | Processing gas chromatographic data and confidence interval calculation for partition coefficients determined by the phase ratio variation method[END_REF]. A minimum of three replicates were performed for each solution tested.

Determination of mass transfer coefficients

The method used for mass transfer coefficient measurements was based on two studies: the Static Equilibrium and Headspace Dilution Analysis [START_REF] Marin | Volatile Release from Aqueous Solutions under Dynamic Headspace Dilution Conditions[END_REF] and the Volatile Air

Stripping Kinetic (VASK) method [START_REF] Lauverjat | Rapid determination of partition and diffusion properties for salt and aroma compounds in complex food matrices[END_REF].

Five g of solution were poured into 134.8-cm 3 vials (three replicates/solution). The samples were left for a minimum of 12 h at 35°C to establish thermodynamic equilibrium. The headspace was then stripped by a gaseous flow at a controlled rate of 1.45 cm 3 /s (Brooks Digital Mass Flow Meter, Brooks Instrument 5860s). The evolution over time of headspace concentration of these vials was measured by PTR-MS for 25 minutes. The experiment time had to be longer than four times the characteristic time of the headspace stripping

Q V

, where V is the volume of the headspace, and Q the stripping airflow rate. In fact, when the experiment time is shorter than Q V , the headspace concentration is mainly governed by dilution with the airflow rate and not by the transfer from the product to the air.

Fitting the diacetyl release model (Appendix B for detailed equations) to experimental data made it possible to determine the mass transfer coefficient of this aroma compound in the solutions.

2.5. In-nose measurements of aroma release and data processing

Five panelists (three females and two males, all Caucasian) aged between 25 and 38 years old were recruited for this study. Only the four solutions presenting the widest range of viscosities (G0, G40, G60 and G70) were investigated in vivo. The 10-cm 3 samples were first left at 35°C for 2 hours to allow thermal equilibrium. Panelists were then instructed to pour the sample into their mouth, keep it while they were connecting to the PTR-MS (1-2 seconds) and to then swallow. Subjects had to continue to breathe normally through the nose (and with their mouth closed) for approximately one minute, during which time the nose-space PTR-MS signal was recorded. Each experiment was repeated three times.

An additional protocol consumption was applied for G0: panelists had to suck up a mouthful of the headspace vial with a straw, swallow it and continue to breathe normally through the nose.

On the basis of data treatment observed in the literature, the aroma release curve is rarely analyzed in its entirety. In the modeling studies of [START_REF] Buffo | Persistence of aroma compounds in human breath after consuming an aqueous model aroma mixture[END_REF] and Linforth et al.

(2000) on aroma compound persistence in human breath, analyses were performed on the ratio between the corresponding intensities of the second and the first expirations after swallowing for each subject and each aroma compound investigated. [START_REF] Hodgson | Aroma release and delivery following the consumption of beverages[END_REF] proceeded differently and calculated the decay exponent of the maximum intensity of the second and subsequent breath peaks plotted against time (setting apart the first aroma release peak).

Figure 2 represents the data processing results of our experimental aroma release kinetics for one panelist and one solution. Each kinetic presented a sinusoidal pattern due to the cyclic shape of the breath. For clarity, we smoothed the breath-by-breath aroma release profiles by plotting a curve linking the maxima of the sinusoids (referred to as the "peak curve" in Fig. 2), including the swallowbreath peak. Then, for each product, each panelist and for the three replicates, a mean curve and an envelope curve were built based on the peak lines. This last one represents the standard deviation of the replicates and, as a result, the intra-individual variability.

In order to validate model prediction against experimental measurements, simulated data were also represented as a peak line. For ease of comparison among different release curves, the deglutition event was always synchronized at time zero.

In the "Results and Discussion" section, two main characteristics of the curves were analyzed during in vivo/simulation comparison: the intensity of the first peak after swallowing, and the decay time of the curve (which is representative of the aroma persistency and related to the thickness of the postdeglutitive residue in the pharynx).

Determination of physiological parameters

Volumes of oral, nasal and pharyngeal cavities were measured with the Eccovision Acoustic Rhinopharyngometer from Eccovision (Sleep Group Solutions, North Miami Beach, FL 33162). The air/product contact areas in the mouth and in the pharynx were calculated for each panelist as described in Appendix A. However, for the air/product contact area in the mouth, we only took 60% of the calculated value, since we estimated that the brief in-mouth product residence did not allow the subjects to spread the product over the full surface of the mouth before swallowing.

The volume of solution introduced into the mouth was fixed by the experimental protocol at 10 cm 3 , which corresponds to a realistic "mouthful". In-mouth saliva volume was set at 1.1 cm 3 based on data from [START_REF] Dawes | Salivary flow patterns and the health of hard and soft oral tissues[END_REF], and stimulated saliva flow rate was measured for each panelist (under a parafilm stimulation).

The tidal volume of each panelist was measured with a spirometer (SpeeDyn from Dyn'R group) and the respiratory frequency was calculated from the acetone signal measured by PTRMS during the resting time preceding each experiment.

Prior to their participation in the experiments, a written consent was obtained from all participants after a full explanation of the purpose and nature of the study.

Results and Discussion

3.1. Experimental data

Air/product partition coefficients of diacetyl

Results from PRV experiments are shown in Table 2. The diacetyl air/product partition coefficient for the pure water at 35°C was 1.28 x 10 -3 . This value is quite close to the ones obtained by [START_REF] Bakker | Dynamic release of diacetyl from liquid gelatin in the headspace[END_REF] at 37°C, ranging between 1.16 x 10 -3 and 1.78 x 10 -3 . Additional values of the diacetyl partition coefficient for pure water can be found in the literature, but mostly for experiments performed at 25°C or below. By using the Arrhenius law on data obtained by [START_REF] Atlan | Processing gas chromatographic data and confidence interval calculation for partition coefficients determined by the phase ratio variation method[END_REF], it is possible to calculate an activation energy of 40.7°kJ/mol and to extrapolate a partition coefficient value of 1.18x10 -3 at 35°C, which is very close to the value found in the present work.

We can observe that the air/product partition coefficient increases with the dry matter for values greater than 5% of dry matter solution. Values range from 0.57 x 10 -3 for G5 up to 2.5 x 10 -3 for G70.

Most of the data available in the literature are for sucrose. For example, [START_REF] Friel | An empirical model to predict the headspace concentration of volatile compounds above solutions containing sucrose[END_REF] showed a similar trend in the air/product partition coefficient for diacetyl for a variation of sucrose concentrations. These phenomena could be explained by a loss of free water due to hydration of sugar molecules. Increasing the sucrose concentration makes the solvent character of a solution more hydrophobic. Therefore, for a hydrophilic aroma compound such as diacetyl, its affinity for the product would be reduced [START_REF] Nahon | Flavor release from mixtures of sodium cyclamate, sucrose, and an orange aroma[END_REF][START_REF] Nawar | Some variables affecting composition of headspace aroma[END_REF][START_REF] Thanh | Interactions between volatile and non-volatile compounds in the presence of water[END_REF].

Mass transfer coefficients of diacetyl

The mass transfer coefficients calculated with the headspace dilution method are presented in Table 2.

They ranged between 1.1x10 -6 m/s (pure water) and 3.31x10 -8 m/s (G70) at 35°C. We observe a decrease in the mass transfer coefficient of diacetyl with the dry matter content of the solution. [START_REF] Nahon | Modeling Flavor Release from Aqueous Sucrose Solutions, Using Mass Transfer and Partition Coefficients[END_REF] reported similar results within a range of 0 to 60% w/w of sucrose concentration. [START_REF] Marin | Volatile Release from Aqueous Solutions under Dynamic Headspace Dilution Conditions[END_REF] measured a mass transfer coefficient for diacetyl at 35°C of 2 x 10 -6 m/s for an aqueous solution. [START_REF] Bakker | Dynamic release of diacetyl from liquid gelatin in the headspace[END_REF] found a value of 2.7 x 10 -6 m/s at 37°C for pure water and showed that an increase in viscosity induced a decrease in the mass transfer coefficient, similarly to our work.

Physiological parameters

In order to make the model as accurate as possible, all of the physiological parameters (except the thickness of the product layer coating the pharynx) were measured for each panelist. The variation ranges of the physiological parameters are presented in Table 3.

We observe that all physiological parameters present a wide range of variation. For example, the volumes of oral cavity, nasal cavity and pharynx obtained by rhinopharyngometry are about 37±8, 11±4 and 29±9 cm 3 , respectively. The contact areas in the oral cavity and the pharynx are 102±14 cm² and 60±13 cm², respectively.

Typical experimental results

We observed that the aroma release curve ("single repetition" curve in Fig. 2) has a sinusoidal shape, and is synchronized with breath (data not shown): when a subject exhales, he/she brings aroma to his/her nasal cavity (corresponding to the rising part of the sinusoid pattern), whereas during inhalation, fresh air is delivered to the nose (decreasing part of the sinusoid pattern). We can also observe that the first breath peak of the aroma release is the highest and corresponds to the delivery that occurs immediately after the first swallow. The aroma concentration then gradually decreases, and secondary peaks are due to the continuous aroma release induced by the flavored post-deglutitive film coating the pharynx, which is permanently in contact with the breath airflow.

Figure 3 represents the mean peak curves of aroma release for the four solutions consumed by one panelist. The global shapes of the kinetics are the same, regardless of the panelist or the product.

However, similarly to [START_REF] Buffo | Persistence of aroma compounds in human breath after consuming an aqueous model aroma mixture[END_REF] and [START_REF] Linforth | Persistence of Volatile Compounds in the Breath after Their Consumption in Aqueous Solutions[END_REF], we observed differences in PTRMS responses for each subject due to their physiological characteristics. Nevertheless, G0

presents the highest intensity for the swallow-breath peak of aroma compound release for all panelists.

This observation was confirmed by a statistical analysis. Since our data were not normally distributed, we performed a Friedman test (non parametric) with an excel macro developed by P. Georgin et M.

Gouet (available online at www.AnaStats.fr) on the in vivo release data, normalized by the initial aroma concentration in the product, to see if we could observe a solution effect. The three analyzed descriptors of the kinetics were: (1) the normalized area under the curve, (2) the normalized maximum intensity I NAmax /C OPini (first peak intensity), and (3) the decay time of the curve τ. Results show that there is a product effect on the first peak intensity (level of significance 0.05). Confirming the empirical observation in Fig. 3, the classification performed with a multiple comparison test (Bonferroni method with a macro developed by G. Le Page, available online at www.AnaStats.fr) (Table 4) shows that the first diacetyl peak for flavored pure water (G0) is significantly higher than for the other solutions (G40, G60 and G70) (level of significance 0.05).

The normalized area under the curve and the characteristic decay time of the curve were not statistically different between the glucose syrup solutions.

Parameter effects on model predictions

As mentioned in Section 2.1, the simplifications of the model were validated by comparing the kinetics obtained with the current model and the previous one with the same parameters. A sensitivity analysis of the new model was conducted.

We found that an increase in the mass transfer coefficient of the product induced an increase in the aroma concentration in the nasal cavity and a decrease in the characteristic decay time τ.

The post-deglutitive residual thickness layer in the pharynx influences the characteristic decay time of the curve τ. In fact, this time period follows the relationship:

p k e ∝ τ ( 21
)
where e is the residual thickness layer in the pharynx and k p the mass transfer coefficient (Equation ( 15)). Moreover, this parameter has no influence on the height of the first aroma release peak. Last but not least, the lower the respiratory frequency is, the higher the aroma persistence will be.

Comparison of model predictions with experimental data

This section is dedicated to the comparison of model prediction with experimental data. Firstly, we verified that the aroma compound investigated in this study, i.e., diacetyl, does not specifically interact with the mucosa of the different compartments of the oro-pharyngeal sphere and the airways.

Hodgson, Parker, [START_REF] Hodgson | In vivo studies on the longterm persistence of volatiles in the breath[END_REF] stated that while volatile molecules are transferred through the upper airways, they absorb to the nasal mucosa. To check the absence of mucosa interaction, panelists were asked to absorb aroma compounds either in gaseous phase or in liquid phase, as described in the "Material and Methods" section. A typical result of each type of consumption protocol is illustrated in Fig. 4. On the one hand, we observe a curve for the liquid ingestion protocol (solid line) that shows secondary aroma release peaks due to persistence phenomena. On the other hand, the aroma release after inhaling the aroma compound in gaseous phase (dotted line) has only one major peak. This shows that no significant mucosa retention occurred. This is in agreement with the work of [START_REF] Normand | Modeling the kinetics of flavour release during drinking[END_REF], stating that short persistence of the aroma release (less than 1 min, which is the case in our study) is considered to be mainly due to saliva coating, whereas longer persistence is due to volatile adsorption in the mucosa. Therefore, introducing an additional mucosa compartment into the model was unnecessary for this aroma compound.

Secondly, another assumption of the model that was investigated was that complex airflow in the airways could have a significant effect on aroma kinetics. Tentatively, the model was implemented by considering an additional "lung" compartment and/or by subdividing the nasal cavity into several compartments, i.e., the nasal vestibule, the anterior turbinate and the posterior turbinate, with corresponding volumes and airflow fractions [START_REF] Hahn | Velocity profiles measured for airflow through a large-scale model of the human nasal cavity[END_REF]. It appeared that the effect of these additional compartments on model predictions was minor (results not shown).

Therefore, we did not keep those compartments in the final version of the model.

Finally, two different hypotheses concerning the nature of the post-deglutitive residue coating the pharyngeal mucosa after swallowing were developed.

The first hypothesis assumed that a pure product layer is deposited on the pharyngeal mucosa. In this case, the air/product partition coefficients as well as the mass transfer coefficients are those obtained earlier in Section 3.1.

The second hypothesis assumed that the product coating the pharyngeal mucosa is highly diluted with saliva. In that case, the physico-chemical parameters of the bolus need to be recalculated according to the dilution rate.

These two hypotheses will be tested and discussed in the following sections.

Assumption of the pure product layer (H1)

By fitting the model to experimental data, we found a residual thickness layer in the pharynx of 14.6±3.4 µm for G0, and of 2.9±1.1 µm, 2.5±1 µm, and 0.8±0.2 µm for G40, G60 and G70, respectively. In their work, Wright, Hills, [START_REF] Cook | Oral shear stress predicts flavour perception in viscous solutions[END_REF] found a thickness of film saliva (which is equivalent to our post-deglutitive residue) of 55 µm for flavored aqueous solutions with only 2% of sucrose (which is close to our reference G0). Their thickness value is almost four times higher than ours. This difference could result from individual variability or the determination method used.

We then observed that similarly to in vivo measurements (Fig. 3), simulations predicted that the highest peak intensity was reached for G0 (results not shown). The second set of bars in Fig. 5 shows that the model prediction for the first aroma release peak for the aqueous solution is five times higher than for the glucose syrup solutions. These differences are due to the differences that we found in the mass transfer coefficients for the solutions studied. However, the in vivo data (first set of bars) do not reveal such a large gap between the aqueous and the glucose syrup solutions (which reaches between 58% and 83% of G0's Imax, depending on the solution and the panelist). These discrepancies between experimental observations and model predictions led us to consider that the product properties considered in the model (mass transfer and air/product partition coefficients) might be misevaluated due to saliva dilution.

Assumption of the product dilution by saliva (H2)

Under the saliva dilution hypothesis, the aroma release profile of any glucose syrup solution predicted by the model is expected to be closer to the reference solution (G0), as observed in vivo, because the physico-chemical properties of the newly formed mixtures would be closer to the properties of water.

It is difficult to check this assumption in situ and, more specifically, to determine the quantity of saliva present in the pharyngeal junction, as well as the amount of product left in the pharynx after swallowing. Therefore, in order to validate this assumption, additional simulations were performed and compared to in vivo data. Since the sensitivity analysis of the model showed that the residual thickness layer does not have an impact on the first peak intensity of aroma release, we fixed this parameter to the averaged value found for G0, i.e., 14.6 µm. After several tests, a common dilution factor was determined for all solutions such that the model predictions fit the in vivo release data.

Physico-chemical parameters for dilutions not present in Table 2 were interpolated with the formulas indicated below Table 2.

The dilution factor was selected to keep the ratio "Intensity of the first peak for the investigated solution"/"Intensity of the first peak for G0" as close as possible to in vivo experimental observations. Results presented in Fig. 5 (first versus last series of bars in the chart) showed that it was possible to find a common dilution factor that reproduces the intensity ratios observed in vivo.

Results indicated that all glucose syrup solutions were highly diluted in the pharynx (by a factor of 10).

We validated the saliva dilution assumption with an additional aroma compound, ethyl hexanoate. This molecule was chosen for its hydrophobicity, in contrast to diacetyl. Similarly to diacetyl, the absence of retention by mucosa was checked. Since the two molecules were investigated together, we performed simulations with the same residual thickness layer and with the same dilution factor that was previously determined with diacetyl. Due to the introduction of the dilution factor, the physicochemical parameters of ethyl hexanoate in the glucose syrup solutions, G0, G5, G10 and G20, were measured. On the basis of the results presented in Table 5, we can observe that the air/product partition coefficient values for the three glucose syrup solutions are all higher than G0, but very close to each other. For the mass transfer coefficient, we observe an opposite trend: the three glucose syrup solutions values are lower than G0, but also close to each other. Similarly to the diacetyl, interpolations of the experimental points were necessary to perform the simulations. For both the air/product partition and mass transfer coefficients, we decided to use a linear regression between G0 and G5, and to calculate an averaged value between G5 and G20.

Comparison of the ratios "Intensity of the first peak for the investigated solution"/"Intensity of the first peak for G0" between in vivo experiments and model predictions for ethyl hexanoate are presented in Fig. 6. They show that the model provides a satisfactory prediction for all solutions under the saliva dilution assumption, given the wide range of experimental variability (standard deviation bars on Fig. 6).

These results lead to the conclusion that the viscosity of the initial product has a limited effect on aroma release for products with Newtonian properties within the wide range of viscosities studied, and confirm the results of [START_REF] Hollowood | The effect of viscosity on the perception of flavour[END_REF]. The combined modeling and experimental approach conducted in this work suggests a possible explanation for this limited effect: viscous solutions are highly diluted by saliva during the swallowing step and the relevant properties are those of relatively similar product-saliva mixtures.

Conclusions

This work aimed at studying the influence of food viscosity on flavor release during ingestion of a liquid food. The originality of this study was the combination of experimental and modeling approaches that allowed us to gain insights into the aroma compound release mechanisms, based on the example of the diacetyl release from glucose syrup solutions. When considering the consumption of a liquid product, it can be assumed that the saliva dilution is relatively low due to the short residence time in the mouth. Therefore, the hypothesis that a pure product layer was deposited on the pharynx walls after ingestion of a liquid food was stated at first. This assumption was invalidated by the comparison of model predictions to in vivo measurements. This result led us to consider the dilution of the product during swallowing. This new hypothesis, stating that the film coating the pharyngeal walls was a mixture of saliva and product, provided predictions compatible with experimental observations for the aroma compound investigated (diacetyl). Simulations showed that the dilution factors by saliva determined were quite similar, regardless of the initial dry matter of the solution: approximately 10% of the initial solution was kept in the final diluted mixture. With these dilution factors, we tentatively extended the model to a highly hydrophobic molecule (ethyl hexanoate) with satisfactory results.

The formulated hypothesis has to be further confirmed based on the study of the release of other aroma compounds with different physico-chemical characteristics. In parallel, work is in progress on the pharynx mucosa coating to increase the understanding of these phenomena based on a mechanical approach. Combining mechanical and mass transfer studies should help us to gain new insights into the complex phenomena of in vivo aroma compound release. Figure 5. "Imax of a solution/Imax of G0" ratios for diacetyl: comparison of experimental data with the model simulations under the "pure product layer (H1)" and the "saliva dilution (H2)" assumptions. Figure 6. "Imax of a solution/Imax of G0" ratios for ethyl hexanoate: comparison of experimental data with the model simulations under the "saliva dilution (H2)" assumption. Table 1. Characteristics of the analyzed glucose syrup solutions.

Figure legends

Tables

Solutions

25.12±4.97 0.33±0.07 †For G10, G20, G60, 3 replicates were performed. For G0, G5, G30, G40 and G70, 6 replicates were performed ‡Between 3 and 9 replicates were preformed for each solution For Diacetyl air/product partition coefficient (K ap ), the following second-degree polynomial regression curve fits the data (R² = 0.94) and was used for interpolation:

- - - × + × × - × × = g g ap C C K
where C g is the total carbohydrate concentration in g/100g.

For Diacetyl mass transfer coefficient (k p ), the following non-linear regression (exponential type) fits the data (R² = 0.88) and was used for interpolation:

g p C k × - - = 0367 . 0 1549 . 6 ) log(
where Cg is the total carbohydrate concentration in g/100g.

Error bars on the mass transfer coefficient take into account the uncertainties of the air/solution partition coefficients. Standard protocol (parafilm stimulation) [START_REF] Engelen | The relation between saliva flow after different stimulations and the perception of flavor and texture attributes in custard desserts[END_REF]) [START_REF] Dawes | Salivary flow patterns and the health of hard and soft oral tissues[END_REF] Less than 3.3x10 -2 cm 3 /s; 1.5x10 -2 -2.2 x10 -2 cm 3 /s (parafilm stimulation)

In-mouth saliva volume cm 3 1.1 Literature [START_REF] Dawes | Salivary flow patterns and the health of hard and soft oral tissues[END_REF] 1.1/0.8 (before/after swallowing)

In-mouth air/product contact area cm² 81-120 Calculated (Appendix A) [START_REF] Collins | The Surface Area of the Adult Human Mouth and Thickness of the Salivary Film Covering the Teeth and Oral Mucosa[END_REF] 214.7±12.9

Pharynx

APPENDIX A

Calculation of the area of the mouth and the pharynx

The rhinopharyngometer is an acoustic device that gives a series of cross-section areas of the upper respiratory tract, at various depths, starting from the panelist's front teeth.

The value of interest here is the lateral area of the respiratory tract. It was calculated by assuming that cross-sections are ellipses with a known eccentricity. The eccentricity was graphically estimated from a study of the measurements of airway dimensions of the human oral passage done by [START_REF] Cheng | Measurements of Airway Dimensions and Calculation of Mass Transfer Characteristics of the Human Oral Passage[END_REF].

∑ ∆ = h h Perimeter Area ) ( (A.1)
where dh is the distance between two successive measurements of cross-sectional areas with the rhinopharyngometer (0.43 cm). where k = 7.4 for the mouth, 1.25 for the oropharynx and 1 for the hypopharynx.

The total area of a compartment is therefore the sum of all intermediate areas that have been calculated within the limit of the compartment considered.

APPENDIX B

Model for the determination of the Mass Transfer Coefficient

In the Volatile Air Stripping Kinetic (VASK) method [START_REF] Lauverjat | Rapid determination of partition and diffusion properties for salt and aroma compounds in complex food matrices[END_REF], the product containing the volatile compound is equilibrated with the headspace air in a closed flask. At time t=0, the headspace is stripped with a constant airflow, and the volatile compound concentration in the outlet air is continuously measured by PTR-MS.

The volatile concentrations in the product and in the headspace are given by: ) ( A is the contact area between the air and the product.

Q is the air flow rate stripping the headspace.

Figure 1 .

 1 Figure 1. A. Schematic representation of the nasal cavity, pharynx and oral cavity as interconnected reactors. B. Chronological steps of the consumption of a semi-liquid food.

Figure 2 .

 2 Figure 2. Example of data processing for in vivo aroma release experiments (solution G0, with 16.5mg/L of diacetyl). Dotted line: diacetyl intensity signal recorded by PTR-MS. For clarity, only one single replicate is shown. Solid line: peak curve of the shown replicate. Bold line: mean of the three peak curves for the three replicates of the experiment. Gray area: envelope of the peak curves for the three replicates.

Figure 3 .

 3 Figure 3. Example of in vivo diacetyl release for the four Newtonian solutions (panelist 1).Representation of the mean peak curves.

Figure 4 .

 4 Figure 4. Example of in vivo diacetyl release during two consumption protocols. Solid line: ingestion of aromatized solution; dotted line: aspiration of aromatized air.

  † Values of parameters measured for panelists ‡ sum of the volumes of the nasal valve, the lower and the middle turbinate

  where S is the cross-sectional area measured at a given distance, a the major radius and b the minor radius.Given b a k = as the ratio between the two radii, we obtain:

  volume of the liquid product and of the air, respectively.

  p C and aC are the concentration of aroma in the product and in the air, respectively.The mass transfer coefficient (k p ) is determined by fitting the air concentration predicted by the model to the PTR-MS measurements.

Table 2 .

 2 Diacetyl air/product partition coefficient (K ap ) and mass transfer coefficient (k p ) as a function of the dry matter content for Newtonian glucose syrup solutions at 35°C.

		Dry Matter (g/100g)	Viscosity at 35°C (mPa s)
	G0	0.00	0.7
	G5	5.13±0.19	0.8
	G10	8.99±0.30	1.1
	G20	20.19±0.73	1.5
	G40	45.94±1.70	7.6
	G60	61.11±1.19	25.0
	G70	75.68±2.65	405.0

Table 3 .

 3 Physiological parameter values

			Mean
		Unit	value/range of variation †	Data source	Reference	Value from the literature
	Oral cavity Volume	cm 3	30-45	Rhinopharyngometry	(Xue & Hao, 2006)	32.95±6.10
	Nasal cavity volume	cm 3	4-14	Rhinopharyngometry	Cakmak, 2007) (Cankurtaran, Celik, Coskun, Hizal &	9.11±0.71 ‡
	Pharynx volume	cm 3	20-45	Rhinopharyngometry	(Xue & Hao, 2006)	29.65±6.10
	Residual product thickness in the pharynx	µm	0.8-14.6	Degree of freedom of hypothesis) the model (case of the pure product layer	(Wright & Hills, 2003)	55x10 -3
	Salivary flow rate	cm 3 /s	3x10 -2 -4.7x10 -2

Table 4 .

 4 Statistical analysis of in vivo diacetyl release curves

	Solutions	I NAmax /C OPini (10 5 cps/ppb)
	G0	1.53 A
	G40	1.24 AB
	G60	0.99 B
	G70	0.85 B
	Each letter corresponds to a classification group performed with Bonferroni method (significance
	level=0.05).

Table 5 .

 5 Physicochemical characteristics of glucose syrup solutions aromatized with ethyl hexanoate

		Air/product partition	Mass transfer
	Solutions	coefficient (g/g)	coefficient (m/s)
		x10 -1	x10 -6
	G0	0.82±0.17	8.74±1.63
	G5	1.30±0.51	5.46±1.84
	G10	1.22±0.30	4.27±0.75
	G20	1.33±0.56	5.29±2.07

We refer to the time of product introduction in mouth and the time of deglutition as t 0 and t deg , respectively.

Acknowledgements

The authors gratefully acknowledge the French National Research Agency (ANR) project "SensInMouth" for financial support.

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