Clément De Loubens
email: cdeloubens@grignon.inra.fr

Albert Magnin
email: magnin@ujf-grenoble.fr

Eric Verin
email: eric.verin@chu-rouen.fr

Ioan Marion Doyennette

Cristian Tréléa

Isabelle Souchon
email: souchon@grignon.inra.fr

A lubrication analysis of pharyngeal peristalsis: Application to flavour release

Keywords: biomechanics, swallowing, aroma, viscosity, pharynx, saliva, food bolus 2.3

After eating a liquid or a semi-liquid food product, a thin lm responsible for the dynamic prole of aroma release coats the pharyngeal mucosa. The aim of this article was to analyze the uid mechanics of pharyngeal peristalsis and to develop a simple biomechanical model in order to understand the role of saliva and food bolus viscosity on the coating of pharyngeal mucosa. We began by analysing the physiology and the biomechanics of swallowing in order to determine relevant model assumptions. This analysis of the literature claried the types of mechanical solicitations applied on the food bolus. Moreover, we showed that the pharyngeal peristalsis in the most occluded region is equivalent to a forward roll coating process, the originality of which is lubrication by a lm of saliva. A model based on the lubrication theory for Newtonian liquids was developed in dimensionless form. The parametric study showed the strong inuence of relative saliva thickness on the food bolus coating. A specic experimental device was designed that conrms the model predictions. Two sets of conditions that depend on the relative thickness of saliva were distinguished. The rst is characterised by a relatively thin lm of saliva: food bolus viscosity has a strong impact on mucosa coating. These phenomena are well represented by the model developed here. The second is obtained when the saliva lm is relatively thick: hydrodynamic mixing with saliva, interdiusion or instabilities may govern mucosa coating. Finally, these results were extrapolated to determine the

Introduction

Increasing attention has been given to the analysis and modelling of biomechanical phenomena related to oral food processing over the last ve years. More and more studies have been dedicated to integrating physiological and biomechanical constraints into the formulation of food to improve care for dysphagia patients [13] as well as into the formulation of health food with control of avour and texture perception [410]. Improving the nutritional quality of foods without modifying their organoleptic properties is a real challenge that requires more knowledge about the mechanisms involved in sensorial stimulus release in terms of both products and consumers.

After eating a liquid or a semi-liquid food product, a thin lm responsible for the dynamic prole of aroma release coats the pharyngeal mucosa [START_REF] Levine | Radiology of the esophagus[END_REF][START_REF] Buettner | Observation of the swallowing process by application of videouoroscopy and real-time magnetic resonance imaging-consequences for retronasal aroma stimulation[END_REF]. The phenomena governing pharyngeal mucosa coating are insuciently understood. Many studies hypothesize that the rheological properties of the food bolus modify the coating and, subsequently, the dynamic prole of avour release [1316]. However, there is no consensus on the role played by physical eects such as pharyngeal mucosa coating and that of sensory interactions between texture and aroma. For example, the complex viscosity of avoured yogurts has a direct inuence on both the perception and dynamic prole of avour release [START_REF] Saint-Eve | Flavored yogurt complex viscosity inuences real-time aroma release in the mouth and sensory properties[END_REF], while the viscosity of avoured hydrocolloid solutions inuences perception but not the dynamic prole of avour release [13,[START_REF] Cook | Eects of hydrocolloid thickeners on the perception of savory avors[END_REF]. Moreover, investigations of the inuence of viscosity on postdeglutitive pharyngeal residue are not in agreement [1820]. The relationship between viscosity and post-deglutitive pharyngeal residue is not clear. Residue was evaluated by dierent techniques such as scintigraphy or breoptic endoscopic evaluation. The retention of products on mucosa can be analysed by uorescence as well [START_REF] Pivk | Assessing lipid coating of the human oral cavity after ingestion of fatty foods[END_REF]. Results seem to be dependent on the method chosen and probably on the individual. We therefore need to develop other approaches to analyse and understand the phenomena governing pharyngeal mucosa coating.

For this purpose, Weel et al. [START_REF] Weel | New device to simulate swallowing and in vivo aroma release in the throat from liquid and semiliquid food systems[END_REF] developed an articial throat in which liquids were poured down a tube and a thin lm coated the tube wall. Their results conrmed the importance of coating for aroma release, but the ow was governed by gravity, whereas in vivo, the liquid is forced by pharyngeal peristalsis.

The aim of this study was to develop a simple biomechanical model of pharyngeal peristalsis that focuses on the food bolus coating of the mucosa. We rst analysed the physiology and the biomechanics of swallowing in order to determine relevant model assumptions. On the basis of this analysis, we considered that the physiological process is equivalent to a forward roll coating process, the originality of which is lubrication by saliva. Second, a mathematical model based on a lubrication analysis for Newtonian liquids was developed. A specic experimental device was designed to conrm model predictions. The inuence of food bolus viscosity and lubrication by saliva on mucosa coating and the forces generated was then shown. Finally, the results obtained were applied in order to assess the impact of food bolus viscosity on avour release.

The physiology of swallowing and biomechanical analysis 2.1. Anatomy

The pharynx extends from the nasal cavity to the pharyngoesophageal segment [START_REF] Donner | Anatomy and physiology of the pharynx[END_REF]. It can be divided into three parts: the naso-, the oro-and the hypopharynx (Figure 1). The oropharynx, that extends from the palate to the tongue base at the level of the epiglottis and is at the croosroads where the residual product and the breath ow come in contact. It is therefore a key element in avour release.

Swallowing sequences

After being chewed and mixed with saliva, the food bolus is propelled by the tongue into the oropharynx (Figure 2: phase 1). Several succesive phenomena are observed: i-the pharynx riszes, ii-the bolus tail enters the pharynx, iii-the upper oesophageal sphincter opens and the tongue base and the pharyngeal constrictors generate a peristaltic wave (Figure 2: phase 2). Bolus propulsion is due to the opposition of the tongue base with constrictors and the progressive forward movement of the posterior pharyngeal wall [START_REF] Jones | Radiographic evaluation of motility of mouth and pharynx[END_REF]. It is mediated by an involuntary reex [START_REF] Goyal | Physiology of oral, pharyngeal, and esophageal motility[END_REF]. The wave velocity is between 0.1 and 0.5 m/s [START_REF] Chang | Mathematical modeling of normal pharyngeal bolus transport: A preliminary study[END_REF][START_REF] Meng | Computer simulation of the pharyngeal bolus transport of Newtonian and non-Newtonian uids[END_REF][START_REF] Goyal | Physiology of oral, pharyngeal, and esophageal motility[END_REF][START_REF] Dantas | Eect of swallowed bolus variables on oral and pharyngeal phases of swallowing[END_REF]. During this phase, the highest frictional forces are generated in the most occluded region of the constriction [START_REF] Pal | Intrabolus pressure gradient identies pathological constriction in the upper esophageal sphincter during ow[END_REF]. Visualisation by X-rays attests to the existence of a thin lm of product coating the oropharyngeal mucosa [START_REF] Levine | Radiology of the esophagus[END_REF] that can be explained by a reux of the food bolus in the opposite direction of the peristaltic wave (Figure 2). waves but not in coating phenomena resulting from a single wave. Numerical models have already been proposed to simulate the swallowing of a liquid bolus [START_REF] Chang | Mathematical modeling of normal pharyngeal bolus transport: A preliminary study[END_REF][START_REF] Meng | Computer simulation of the pharyngeal bolus transport of Newtonian and non-Newtonian uids[END_REF] and a gelled bolus [START_REF] Mizunuma | Numerical modeling and simulation on the swallowing of jelly[END_REF] in order to calculate the evolution of pressure and ow rates. The length scale used is the oropharynx width (∼30 mm) that does not permit us to observe local phenomena such as coating (∼10 µm).

In order to model this phenomenon, in the present study, we only considered the most occluded region of the wave. Firstly, this is the zone where there may be a reux: a weak amount of food bolus ows in the opposite direction of the peristaltic wave that leads to coating of the mucosa.

Secondly, as analysed by Pal et al. [START_REF] Pal | Intrabolus pressure gradient identies pathological constriction in the upper esophageal sphincter during ow[END_REF], the strongest frictional forces are generated in this zone.

We considered a peristaltic wave (Figure 3) and its associated frame of reference. Within this framework and near the most occluded point, the two pharyngeal walls are in rotation, each one in relation to the other. Thus, two forward roll cylinders can simplify the peristaltic movement. The two rolling cylinders represent the contact between the tongue-base and the posterior pharyngeal wall in the oropharynx. This simplication is not a complete representation of the swallowing, but only a physiological realistic schematisation of the phenomena that permit to generate a thin lm of product after swallowing. In the physiological case of swallowing, a thin saliva lm lubricates the mucosa. From a tribological point of view, we made the hypothesis that we are always in a hydrodynamic regime, in other words, the lm generated is thick enough to avoid contact between the two walls [START_REF] Hamrock | Fundamentals of uid lm lubrication[END_REF]. If this was not the case, it would lead to a boundary regime (walls in contact): friction would be great and the mucosa could be damaged. In order to model the uid dynamics of such a problem, the main challenge is to determine the kind of mechanical solicitations applied by the pharyngeal constrictors and by the base of the tongue and to determine boundary conditions that are consistent with physiology.

Mechanical solicitations

Contraction of pharyngeal constrictors is due to the active shortening of the muscles bres by the eects of nerves [START_REF] Gregersen | Biomechanics of the gastrointestinal tract[END_REF]. It results from this shortening a distribution of stress and strain in the muscles that is transmitted to the uid through boundary conditions, but the uid sets against this contraction by the generation of opposite forces. The type of solicitations imposed by the pharyngeal constrictors and by the base of the tongue remains an open question. The nerve simulation is like the same state of stress or strain is always imposed to the uid? What governs the velocity of the wave? Are these solicitations stationary or are they dependent on the position?

In the contact created by the two cylinders, a hydrodynamic pressure prole is generated which that depends on the boundary pressure conditions [START_REF] Hamrock | Fundamentals of uid lm lubrication[END_REF]. The integration of its prole generates a normal force that separates the two cylinders, the lift (or load) L (Figure 3). In order to determine the order of magnitude of this lift, intraluminal manometric data can be used. These measurements are often used during diagnosis and can help in understanding muscle activity, but interpretation remains dicult. Practitioners collect manometric data using a 4-mm-diameter catheter with ten recording points and measure space-time pressure structure during swallowing [START_REF] Williams | Space-time pressure structure of pharyngo-esophageal segment during swallowing[END_REF]. A relevant interpretation makes it possible to estimate the passive and active tension in the hollow organ walls [START_REF] Nicosia | A mathematical model for estimating muscle tension in vivo during esophageal bolus transport[END_REF]. Considering that the catheter does not inuence pharyngeal constrictor response, the pressure prole integration makes it possible to determine the generated lift L in the contact between the catheter and the mucosa. A possible way of determining the type of solicitation imposed by muscles is to change bolus consistency.

Few studies have recorded pressure during swallowing for dierent bolus consistencies. Some authors saw no signicant eects of consistency on the maximal pressure measured in the oropharynx between water, pudding and potatoes [START_REF] Pouderoux | Deglutitive tongue force modulation by volition, volume, and viscosity in humans[END_REF] or between barium boluses with dierent viscosities [START_REF] Dantas | Eect of swallowed bolus variables on oral and pharyngeal phases of swallowing[END_REF][START_REF] Ali | Inuence of mucosal receptors on deglutitive regulation of pharyngeal and upper esophageal sphincter function[END_REF][START_REF] Dantas | Eect of bolus volume and viscosity on the pharyngeal phase of swallowing[END_REF] while others saw dierences between water, pudding and buttered bread [START_REF] Raut | Eect of bolus consistency on swallowing -does altering consistency help?[END_REF]. This maximal pressure depends on the position in the oropharynx [START_REF] Williams | Space-time pressure structure of pharyngo-esophageal segment during swallowing[END_REF][START_REF] Raut | Eect of bolus consistency on swallowing -does altering consistency help?[END_REF]. The values mentioned were between 20 and 30 kPa [START_REF] Dantas | Eect of swallowed bolus variables on oral and pharyngeal phases of swallowing[END_REF][START_REF] Williams | Space-time pressure structure of pharyngo-esophageal segment during swallowing[END_REF]3335]. By integrating the obtained pressure prole measured by Williams et al. [START_REF] Williams | Space-time pressure structure of pharyngo-esophageal segment during swallowing[END_REF], we can estimate a load of about 10-60 N per unit of width.

The second question is to determine whether there is a mechanism that regulates wave velocity.

Tail bolus velocity, which corresponds to the pharyngeal peristalsis wave, has also been compared with consistency, but the results between studies are not coherent. Dantas et al. [START_REF] Dantas | Eect of swallowed bolus variables on oral and pharyngeal phases of swallowing[END_REF] showed that the greater the consistency was, the shorter the wave duration was. Variations range from 0.35 to 0.45 s. Taniguchi et al. [START_REF] Taniguchi | Correspondence between food consistency and suprahyoid muscle activity, tongue pressure, and bolus transit times during the oropharyngeal phase of swallowing[END_REF] noted that the wave is slower for syrups than for water or agar gels.

However the same team [START_REF] Tsukada | Eects of food texture and head posture on oropharyngeal swallowing[END_REF] saw no eects of consistency with the same products. Ali et al. [START_REF] Ali | Inuence of mucosal receptors on deglutitive regulation of pharyngeal and upper esophageal sphincter function[END_REF] showed that the oral and pharyngeal mucosal receptors regulate the duration of the midpharyngeal contraction, which is reduced by 29% by oral-pharyngeal anesthesia. From these observations, we can suppose that the wave velocity is regulated by the pharyngeal mechanoreceptors response. In the contact between the two walls, shear stress acts on the mucosa and hence on the mechanoreceptors. In a shear ow, the order of magnitude of this stress is about μ U /H 0 , where μ is the food bolus viscosity (Pa.s), U the wave velocity (m/s) and H 0 the gap between the mucosa (m).

We can thus hypothesize that the wave velocity is modulated in order to avoid mucosa damage caused by the action of shear stress on the wall mucosa referred to a drag D (in N per unit of width, Figure 3). Although all of the studies are not in agreement, we can reasonably assume that pharyngeal constrictors impose a constant load, and that the velocity is modulated in order not to exceed a constant drag. In this study, we numerically treated the rst case at an imposed gap and velocity.

From a modeling point of view, it is more convenient to set the gap and the velocity and to calculate the load and the drag. In order to carry out qualitative and quantitative applications, rearranging the results obtained allowed us to treat the second case at an imposed load and drag.

Boundary conditions

Boundary conditions consistent with physiology must be dened. The presence of a lm-splitting region at the output contact was taken into account [START_REF] Coyle | Film-splitting ows in forward roll coating[END_REF]. We considered that the contact is fully ooded by food bolus upstream and that the upper oesophageal sphincter is fully open and does not create an overpressure. Manometric recording validates this hypothesis for non-pathological cases [START_REF] Williams | Space-time pressure structure of pharyngo-esophageal segment during swallowing[END_REF]. No wall slip between pharyngeal mucosa and saliva was considered. In this study, we principally investigated the inuence of the viscosity ratio α of the food bolus on saliva and of the initial thickness of saliva t 1 on ow rates and on the generated forces (L and D ). Mucosa deformability is thus ignored in the initial approach. We will discuss of its importance later.

Table 1 summarises the values of the physiological parameters.

Lubrication model of pharyngeal peristalsis

Physical formulation

The thin lm formation is dominated by the phenomena that act in the contact zone between the base of the tongue and the posterior pharyngeal wall. Thus, the characteristic length useful in our problem to dene the Reynolds number Re is the minimum half gap between the walls H 0 (≈10µm) and we have:

Re = ρU H 0 μ ( 1
)
where ρ is the uid density (10 3 kg/m3),U the wave velocity (0.2 m/s) and μ the viscosity that ranges between 10 -3 Pa.s (water) and the innity. So, depending of the uid viscosity, Re is included between 0 and 2. The lubrication approximation is appropiate if the Reynolds number Re is very small compared to the ratio of the the characteristic length of the contact approximately 2R H 0 on the width of the contact H 0 [START_REF] Hamrock | Fundamentals of uid lm lubrication[END_REF]:

Re << 2R H 0 H 0 (2)
The value of the ratio 2R H 0 /H 0 is about 90 and the inertial terms can be neglected compared to the viscous term in the Navieer-Stokes equation.

The time scale of the ow is given by the ratio of the characteristic length of the contact approximately 2R H 0 , -where R is the roll radius (0.04 m)-on the wave velocity U (0.2m/s).

Thus this time scale is about 4 ms and is very short compared to the time scale of the pharyngeal phase (typically 0.5 s) to neglect the non stationary term of the Navier-Stokes equations. Thus, we can use the lubrication approximation to model this ow [START_REF] Hamrock | Fundamentals of uid lm lubrication[END_REF]. Moreover, we suppose that the mechanical solicitations applied by the constrictors are stationary during the pharyngeal phase.

This last assumption could be rened with more experimental data.

The general features of rigid roll coating operations have been described by Coyle et al. [START_REF] Coyle | Film-splitting ows in forward roll coating[END_REF].

They gave analytical solutions for dierent boundary conditions in the monolayer case. Hannachi et Mitsoulis [START_REF] Hannachi | Numerical analysis of multilayer forward roll coating[END_REF] studied the multilayer case applied to the calendering with boundary conditions specic to their problem. The present physical situation was modelled with the lubrication approximation for Newtonian liquids. In addition, the presence of a lubricating saliva lm and of a lm-splitting region at the output contact were taken into account.

The geometry is symmetric (Figure 4). Relative quantities associated with saliva and the food bolus are referred to as noted 1 and 2, respectively. Between the two uid layers, diusion and surface tension eects are ignored. The dimensional values are identied by the symbol . The ow rate of saliva q 1 is known and the ow rate of food bolus q 2 is calculated. μ i refers to the viscosities (Pa.s) and σ 2 to the surface tension of the food bolus with air (N/m).

H (x) refers to the half gap between the two cylinders, H 0 its minimum, h 2 (x) the location of the interface between the food bolus and the saliva, U the cylinder velocity, L the lift per unit of width, D the drag per unit of width, p (x , y ) the pressure eld, R the radius, u 1 (x , z ) the velocity eld in the saliva, u 2 (x , z ) the velocity eld in the food bolus and x m the split point

abscise. The roll surface proles are approximated by parabolas:

H (x) = H 0 + x 2 2R (3)
The dimensionless values dened for imposed velocity and gap are given by:

x = x 2R H 0 z = z H 0 u i = u i U q i = q i U H 0 p i = p i H 0 μ 1 U H 0 2R L = L H 0 μ 1 U 2R D = D H 0 μ 1 U 2R H 0
The dimensionless cylinder prole is given by:

H(x) = 1 + x 2 (4)
The momentum conservation equations are solved in the lubrication approximation in their dimensionless form:

∂p ∂x = ∂ 2 u 1 ∂z 2 (5) ∂p ∂x = α ∂ 2 u 2 ∂z 2 (6) ∂p ∂z = 0 ( 7
)
where α is the viscosity ratio:

α = μ 2 μ 1 (8)
After changing the variables η = z/H(x) and integration, we obtain:

u 1 = H 2 (x) dp dx η 2 2 + A 1 η + B 1 (9)
u 2 = H 2 (x) dp dx η 2 2 + A 2 η + B 2 (10)
where A 1 , B 1 , A 2 , B 2 are integration constants. They are determined by considering no wall slip, continuity of velocity and shear stress at interface between the two uids and symmetry. Dening

β = h 2 (x)/H(x)
, the boundary conditions are:

u 1 (η = 1) = 1 (11) u 1 (η = β) = u 2 (η = β) ( 12
)
∂u 1 ∂η η=β = α ∂u 2 ∂η η=β ( 13
)
∂u 2 ∂η η=0 = 0 (14)
We thus have:

u 1 = H 2 (x) dp dx η 2 -1 + 1 ( 15
)
u 2 = H 2 (x) 2 dp dx η 2 α -1 -β 2 1 α -1 + 1 (16)
After changing the variables θ = arctan(x) and application of mass conservation, we have two equations on ow rates:

q 1 + q 2 - 1 cos 2 (θ) = 1 3 cos 4 (θ) dp dθ β 3 1 - 1 α -1 (17) q 2 - β cos 2 (θ) = 1 2 cos 4 (θ) dp dθ β 3 1 - 2 3α -β (18)
Considering that upstream is fully submerged, we have:

p θ = - π 2 = 0 (19)
We consider that the lm splits at the rst stagnation point, θ m = arctan(x m ) [START_REF] Coyle | Film-splitting ows in forward roll coating[END_REF]:

p (θ m ) = - 1 α.Ca m .r m ( 20
)
where r m is the radius of curvature of the meniscus at the lm-splitting point (Figure 4) and Ca m is a modied capillary number:

Ca m = μ 2 U σ 2 2R H 0 (21)
If the meniscus is modelled as an arc of a circle between parallel plates of radius r m , geometry and mass balance, geometry demands that [START_REF] Coyle | Film-splitting ows in forward roll coating[END_REF]:

q 1 + q 2 + r m = H (θ m ) = 1 + tan 2 (θ m ) (22)

Resolution method

The problem was solved with Matlab7.0. For a set of parameters (q 1 , α, Ca), we iterated on q 2 until the pressure output condition was veried [START_REF] Kelly | Pharyngeal residue across the lifespan: a rst look at what's normal[END_REF]. The ratio of ( 17) and [START_REF] Hamlet | Normal adult swallowing of liquid and viscous material: Scintigraphic data on bolus transit and oropharyngeal residues[END_REF] gives a polynomial equation of order 4 in β independent of the pressure:

0 = 1 -1/α cos 2 (θ) β 4 + q 1 + q 2 - 1 cos 2 (θ) 2 3 - 1 α -q 2 1 - 1 α β 3 + - 3 2 q 1 + q 2 - 1 cos 2 (θ) - 1 cos 2 (θ) β ( 23
)
+ q 2
The space was discretised into 4000 nodes. At each iteration and for each node, we determined the roots of (23) included between 0 and 1. The rst stagnation point θ m weas determined from equation ( 16) where u 2 = 0 for η = 0 and θ > 0. So, we have to nd the node satisfaying the following equation:

0 = 1 2cos(θ m ) 2 dp dθ θ=θm -1 -β (θ m ) 2 1 α -1 + 1 (24)
(22) and ( 20) make it possible to calculate r m and p (θ m ). Finally, we calculated the error ε on p (θ m ):

ε = p (θ m ) -1/Ca m .r m 1/Ca m .r m ( 25
)
We iterated on q 2 until ε < 10 -10 . After resolution of this equation system, the resulting lift and the drag were calculated:

L = π/2 - π/2 p(θ) cos(θ) 2 dθ (26) D = π/2 - π/2 1 cos(θ) 2 dp dθ dθ (27)

Gravity eects in experimental data

For the experimental data, gravity eects could not be avoided but could simply be included in the model. In the experiments, gravity acted from the negative x to the positive x. Considering that uid densities are the same, the momentum conservation equations become:

∂p m ∂x = ∂ 2 u 1 ∂z 2 ( 28
)
∂p m ∂x = α ∂ 2 u 2 ∂z 2 (29)
where p m = p + St (x 0x) is the modied pressure. St is the Stokes number dened by:

St = H 2 0 ρ.g/μ 1 U ( 30
)
where g is the acceleration due to gravity (10 m/s²) and x 0 is the dimensionless free surface abscise from the minimum gap that can be calculated with the relationship

x 0 = x 0 / 2.R.H 0 ,
where x 0 is the dimension value (30 mm in the experiments). The solution method is the same as explained previously, but the pressure p is replaced by the modied pressure p m .

Pharyngeal peristalsis simulator

In order to experimentally analyse the coating phenomena due to the pharyngeal peristalsis, an experimental set-up was developed. It is schematically depicted in Figure 5. It was composed of two rotating cylinders of 40 mm in radius. They are suciently wide to avoid side leakage (2x40 mm in width [START_REF] Hamrock | Fundamentals of uid lm lubrication[END_REF]). The radius value was estimated according to data on the evolution of the pharyngeal chamber geometry during swallowing given by Chang et al. [START_REF] Chang | Mathematical modeling of normal pharyngeal bolus transport: A preliminary study[END_REF]. A weak hydrophobic material for the cylinders was chosen in order to facilitate lubrication by saliva, Nylon6.6. A thin lm of uid simulating saliva was deposited on the cylinders by two slot coaters. The cylinder velocity was xed at 0.2 m/s corresponding to physiological conditions (Table 1). The cylinders were equipped with scrapers and collectors and the gap was controlled with a transducer (0-250 µm). Scrappers were designed in order to carry out a total recovery of the coated bolus on the cylinders.

Newtonian glucose solutions and water were used as test uids for the food bolus and the saliva respectively. In a rst approach, since saliva viscosity is between 1 to 10 mPa.s [START_REF] Schipper | Saliva as research material: Biochemical, physicochemlical and practical aspects[END_REF], water was used to simulate it. To simulate the food bolus, glucose solutions were chosen for their Newtonian behaviour and their wide range of viscosity (2.6 10 -2 and 0.4 Pa.s). The uid temperature was controlled for each experiment. Viscosity was measured with a Physica MCR 301 (Anton Paar) at the experimental temperature (between 20-25°C).

Before a measurement was made, the deposited thickness of water was xed and measured (40 µm). Velocity was imposed and water collected over a given time. The quantity of water allowed collected permited us to determine its ow rate and its thickness.

The glucose ow rate was determined with the measurement of the quantity of uid passing through the contact during a known time (from 20 to 60 s).

Machining defects were measured (± 20 µm). For this, air was the test medium and the two cylinders were put in contact by application of a force (with a spring). The evolution of the distance seprating the axes of the cylinders was measured over several revolutions and provided machining defects. The experimental ow rate was obtained with the measurement of the quantity of glucose syrup passing through the contact m (in kg) during a known time t (in s). This ow rate was then adimensionalized by the velocity and the gap:

q = m 2.ρ.t 1 U .H 0 ( 31
)
where ρ is the density (kg/m 3 ). Considering that the uncertainties were principally due to the measurement of the gap and of the time, the uncertainty aecting the measurment of ow rate is:

Δq q = ΔH 0 H 0 + Δt t ( 32
)
where ΔH 0 = 20 μm and Δt = 1 s.

Results

Parametric study Monolayer case

Numerical solutions were validated by comparing the results in the monolayer case with the analytical solution obtained by Coyle et al. [START_REF] Coyle | Film-splitting ows in forward roll coating[END_REF]. Figure 6 shows that our numerical solutions correspond well to their analytical solutions. The dimensionless ow rate q 1 is independent of the modied capillary number when Ca m > 10 and is equal to 1.3015. For low capillary numbers, Coyle et al. [START_REF] Coyle | Film-splitting ows in forward roll coating[END_REF] showed that the ow rate is overestimated because the free-model surface is crude and there is recirculation occurs before the split region, which is not taken into account by the lubrication theory.

Food bolus ow rates

Figure 7-a shows that viscosity eects have a relatively low impact on food bolus ow rate q 2 . There are two asymptotic cases: when α tends to zero or innity, q 2 tends to two dierent constants depending on q 1 . The variation is about 20%.

Figure 7-b represents the food bolus ow rate q 2 against the saliva ow rate q 1 for dierent values of viscosity ratios α. We observe two asymptotic cases. When there is no saliva at the interface (q 1 = 0), the bolus ow rate is constant regardless of the viscosity and q 2 is equal to 1.3015. When saliva fully oods the contact (q 1 = 1.3015), the bolus does not coat the mucosa (q 2 = 0). For α > 1, we observe that q 2 reaches an maximum for the low values of q 1 . After this maximum, q 2 decreases with q 1 .

Pressure and surface proles

This optimum is due to two antagonistic phenomena. The rst is the fact that the contact obstruction by saliva is greater when q 1 increases and q 2 thus decreases. In fact, Figure 8-a shows the evolution of the interface location between the two uids in the contact. When q 1 increases, the obstruction by saliva is increasingly high. The second is due to the fact that the bolus shears the saliva thickness, especially since its viscosity is considerable, as shown in Figure 8-b, the velocity at the interface between the two uids is faster and q 2 increases. Figure 8-c shows the characteristic pressure prole that is generated in the contact. The pressure steeply increases as the uid is dragged into the narrowing channel, after which the channel widens and the pressure drops. Figure 8-c also reveals how it develops when the saliva ow rate falls.

Flow eld distribution

Figure [START_REF] Trelea | Mechanistic mathematical model for in vivo aroma release during eating of semiliquid foods[END_REF] presents ow eld distributions and the location of the food bolus / saliva interface in the contact between the root of the tongue and the pharyngeal wall for dierent saliva ow rate at α = 100 and Ca m = 10 3 . The velocity steeply increases as the uid is dragged into the narrowing channel, after which the channel widens and the velocity decreases. The velocity is maximal at the axe of symmetry (z = 0) and minimal at the wall (z = H(x)). When the saliva ow rate q 1 increases, the food bolus velocity increases, but the obstruction of the contact by saliva increases too.

Generated forces

Lift and drag are represented in Figures 10-a and b compared to α for dierent values of q 1 .

In the case of a mono-layer of saliva (q 2 = 0 and q 1 = 1.3015), they are 0.32 and 0.9, respectively.

These values correspond to those we can obtain from the analytical equations of Coyle et al. [START_REF] Coyle | Film-splitting ows in forward roll coating[END_REF].

When there is no saliva at the interface (q 1 = 0), we have L = 0.32α and D = 1.9α. When the contact is lubricated by saliva, the forces generated are included between these two asymptotic cases.

Finally, saliva reduces the inuence of bolus viscosity on the generated forces and ow rates.

Experimental results

Experimental data are represented in Figure 11. Glucose syrup ow rate (bolus) is plotted against water ow rate (saliva) for two viscosity levels (2.6 10 -2 Pa.s and 0.4 Pa.s).

The uncertainties are greater when q 1 increases, because these data are obtained for small gaps and the machning defects are considerable compared to the gap (cf. 4). We observe that the non-lubricated points for glucose syrups and water are close to the theoretical value of 1.3. Nonlubricated points for water have been established with a small gap in order to avoid eects of gravity, explaining the high level of uncertainties. Gravity eects cannot be avoided for lubricated data but can simply be included in the model (cf. 3.3). Each data set was modelled and the comparison with experimental data and numerical results are given in Figure 11. The maximal value of the Stokes number St representing gravity eects on viscous eects is 0.58. This observation conrms that gravity could not be ignored in the experiments and that the ow was not dominated by gravity.

Figure 11 show that experimental results are in agreement with model predictions. For high viscosity and high levels of lubrication, the measured ow rates are greater than those predicted. For this data, we observed that a large quantity of water came back up and dissolved the glucose syrups during measurement. In the case of a large gap, the mixing of glucose syrups by water was very low. We can hypothesize that when lubrication is considerable, the ow becomes unstable and recirculations are generated as observed.

Numerical results are therefore in agreement with experimental data when saliva ow rates and viscosity ratios are relatively low. The lubrication theory is thus an eective tool for modeling these phenomena. When they were high, model predictions were underestimated compared to experimental results. We can assume that in these cases instabilities and recirculation could occur because the saliva lm is very conned and sheared. Saliva thickness has a strong inuence on the results and its relative importance could change the nature of the ow.

In conclusion, the experimental results validate the bilayer lubrication model developed in this study.

6. Application to avour release and discussion

Qualitative applications to swallowing

We now qualitatively analyse the inuence of saliva and food bolus viscosity on aroma release.

In the rst section of this article, we concluded that the hypothesis of constrictor muscles working at imposed load and drag is -although speculative -reasonable. The previously results obtained can be easily rearranged in order to consider that a given force is applied to the cylinders. Calculation details are given in the appendix. Figure 12 represents dimensionless residual food bolus thickness t 2 compared to dimensionless initial saliva thickness t 1 for dierent viscosity ratios α at imposed load and drag. When there is no saliva at the interface, bolus thickness is constant regardless of the viscosity (t 2 = 0.036) and when saliva thickness fully oods the contact (t 1 = 0.036) , the bolus does not coat the mucosa. Between these extremes, when saliva thickness and viscosity increase, bolus thickness decreases.

Application to avour release

As mentionned in the introduction, the role of viscosity on avour release has to be claried.

To be perceived, aroma compounds must be released from the food bolus to reach the olfactory receptors. Many authors agree that short term aroma persistence (<1 min) is due to food coating on the pharyngeal mucosa [START_REF] Trelea | Mechanistic mathematical model for in vivo aroma release during eating of semiliquid foods[END_REF][START_REF] Wright | Persistence eects in avour release from liquids in the mouth[END_REF][START_REF] Normand | Modeling the kinetics of avour release during drinking[END_REF]. The goal of this section is to analyse the inuence of viscosity on aroma release from a rheological point of view, independently of other mechanisms, via the product layer thickness.

Considering that the contact is fully ooded by saliva and the food bolus, the area of the deposited lm is constant regardless of the viscosity, and only the lm thickness can vary. The main transport phenomenon of aroma compounds in the thin lm is diusion. In the air, the molecules are stripped by breathing. Based on a dimensional analysis as proposed by Weel at al. [START_REF] Weel | New device to simulate swallowing and in vivo aroma release in the throat from liquid and semiliquid food systems[END_REF], the characteristic time τ (s) of aroma compound depletion in the coating lm is in rst approximation given by τ ∼ t 2 2 /D a , with t 2 the residual food bolus thickness (in m) and D a the aroma diusion coecient in the uid (typically 10 -9 m²/s for aroma compounds in water). Hence, a variation of the product thickness induces a variation of the characteristic time of the depletion that we refer to as the persistence. Figure 13 illustrates the inuence of the thickness on the dynamic prole of aroma release. These data are the predictions of a mechanistic model based on the one developed by Trelea et al. [START_REF] Trelea | Mechanistic mathematical model for in vivo aroma release during eating of semiliquid foods[END_REF] (Doyennette et al., in preparation).

In terms of aroma release, if the contact is not fully ooded by saliva, the decrease of the food bolus thickness with an increase of viscosity (Figure 12) induces a decrease of aroma persistence when viscosity increases independently of physicochemical properties, i.e. D a is constant. For example, the characteristic time of the persistence is divided by 4 between viscosity ratios of 1 and 3 and for a saliva thickness of 0.02. If saliva fully oods the contact (t 1 > 0.036), the coating can be due to interdiusion, mixing or instabilities. Finally two sets of conditions can be distinguished depending on the value of t 1 . The rst is characterised by a relatively thin layer of saliva; food bolus viscosity has a strong inuence on mucosa coating and, therefore, on avour release. The second is obtained when the layer of saliva is relatively thick; the mucosa coating must be due to a hydrodynamic mixing with saliva, diusion or instabilities.

Quantitative application

In this section, the results are quantitatively applied. In the rst part of this article, we gave the order of magnitude of the lift applied by the constrictors and the peristaltic wave velocity, but we have no data on the applied drag (Table 1). Knowing the applied load and the wave velocity, we can estimate the thickness of saliva necessary to fully ood the contact (corresponding to the monolayer case). From the dimensionless expressions of the lift L and the thickness t , we can deduce the following relationship: t = t.μ 1. U .2.R.L/L where U is the wave velocity (= 0.2 m/s), R the radius (= 40mm, estimated from [START_REF] Chang | Mathematical modeling of normal pharyngeal bolus transport: A preliminary study[END_REF]), μ 1 the saliva viscosity (= 5mPa.s) and L the applied load (= 10N/m). The values of t and L are those obtained when the contact is fully ooded by food bolus (1.3 and 0.32 respectively). We observe that the initial thickness of saliva should be lower than 3.3 µm for the bolus to coat the mucosa. This value seems quite small, but no value of saliva thickness coating mucosa is given in the literature to our knowledge. It should be emphasized that the calculations were performed with rigid cylinders that migth result in the underestimation of this thickness. To improve model predictions, it would be interesting to take mucosa deformability into account.

Finally, this type of biomechanical model, combined with a mechanistic model for in vivo aroma release, could be a relevant tool to help formulate food in order to obtain specic dynamic proles of aroma release or products adapted to people who suer from swallowing disorders.

q = q 2R .D 4 /μ 1 L 3
We have two conditions for the dimensionless lift and the drag: L = 1 and D = 1. The values at given gap and velocity and the variables at a given lift and drag are identied by a and b respectively. The dimension ow rate can be expressed in two ways:

q i = U .H 0 .q a i ( 33
)
q i = 2R D 4 μ 1 L 3 q 2 i ( 34
)
By equalising the two relationships and replacing L and D with

L a = L H 0 μ 1 U 2R and D a = D H 0 μ 1 U √ 2R H 0
, we have:

q b i = q a i .L a 3 /D a 4 (35)
In the same way, we determine the cylinder velocity:

U b = U a .L a /D a 2 (36)
where U a = 1. The deposited layer t i is given by the ow rate divided by the cylinder velocity:

t b i = q a i L a D a 2 (37)
On the basis of this relationship, we can easily plot the dimensionless deposited thickness of the food bolus t 2 against the initial thickness of saliva t 1 for dierent viscosity ratios α. However, it should be observed that the modied capillary number is not constant. In fact, the boundary pressure condition at the contact output becomes:

p b (θ m ) = - 1 α.Ca b m .r m with Ca b m = D /σ 2 .
Hence, we obtain a relationship between the modied capillary number at a given velocity and gap an therefore, a given lift and drag :

Ca b m = D a .Ca a m .
Since Ca a has a low impact on the results (cf. 5.1), the fact that C b m is not constant has a little inuence on the results. These manipulations make it possible to supplementary numerical resolution. Dimensionless food bolus ow rate as a function of the viscosity ratioα for dierent saliva ow rates q 1 (a) and as a function of the saliva ow rate q 1 for dierent viscosity ratios α (b) at imposed gap and velocity (Ca m = 1000). . . . . . . . . . . . . . . . . 33 8 Location of the interface between the food bolus and saliva h 2 (a), velocity at the interface between the food bolus and saliva (b), and pressure prole p (c), for dierent dimensionless saliva ow rates q 1 and for a viscosity ratio α of 100 (Ca m = 1000). . 34 9

List of Tables

Example of ow eld distribution (isovalues of velocity) in the contact and saliva / food bolus interface (withe line) for q 1 = 0 and q 2 = 1.30 (a), q 1 = 0.1 and q 2 = 1.41

(b) ,q 1 = 0.

3 and q 2

 2 = 1.20 (c), (α = 100 and Ca m = 1000). . . . . . . . . . . . . . 35 10 Dimensionless lift L (a) and drag D (b) as a function of the viscosity ratio α for dierent saliva ow rates q 1 at imposed gap and velocity (Ca m = 1000). . . . . . . . 36 11 Glucose ow rate as a function of water ow rate for two viscosity levels (solid symbols) at imposed gap and velocity. Each piece of data has been modelled by taking gravity eects into account (hollow symbols). . . . . . . . . . . . . . . . . . . 37

Figure 1 :Figure 2 :Figure 3 :Figure 4 :

 1234 Figure 1: Anatomy of the oral cavity and the pharynx (adapted from [43])

Figure 5 :

 5 Figure 5: Pharyngeal peristalsis simulator: (1) saliva feed, (2) slot coater, (3) food bolus, (4) scraper, (5) collector.

Figure 6 :

 6 Figure 6: Dimensionless ow rate as a function of modied capillary number in the monolayer case. Comparison with the analytical results of Coyle et al. [38].

Figure 7 :

 7 Figure7: Dimensionless food bolus ow rate as a function of the viscosity ratioα for dierent saliva ow rates q 1 (a) and as a function of the saliva ow rate q 1 for dierent viscosity ratios α (b) at imposed gap and velocity (Cam = 1000).

Figure 8 :

 8 Figure8: Location of the interface between the food bolus and saliva h 2 (a), velocity at the interface between the food bolus and saliva (b), and pressure prole p (c), for dierent dimensionless saliva ow rates q 1 and for a viscosity ratio α of 100 (Cam = 1000).

Figure 9 :

 9 Figure9: Example of ow eld distribution (isovalues of velocity) in the contact and saliva / food bolus interface (withe line) for q 1 = 0 and q 2 = 1.30 (a), q 1 = 0.1 and q 2 = 1.41 (b) ,q 1 = 0.3 and q 2 = 1.20 (c), (α = 100 and Cam = 1000).

Figure 10 :

 10 Figure 10: Dimensionless lift L (a) and drag D (b) as a function of the viscosity ratio α for dierent saliva ow rates q 1 at imposed gap and velocity (Cam = 1000).

Figure 11 :

 11 Figure 11: Glucose ow rate as a function of water ow rate for two viscosity levels (solid symbols) at imposed gap and velocity. Each piece of data has been modelled by taking gravity eects into account (hollow symbols).

Figure 12 :

 12 Figure 12: Dimensionless food bolus thickness t 2 as a function of saliva thickness t 1 for dierent viscosity ratio a at a given force (lift and drag).

Figure 13 :

 13 Figure 13: Evolution f the concentration in aroma compound C N in the nasal cavity for dierent residual thicknesses of product t 2 : a decrease of the thickness induces a decrease of the persistence (from Doyennette et al., in preparation).

1

  Physiological variables and approximate corresponding value. . . . . . . . . . . . . . 26

	List of Figures
	1	Anatomy of the oral cavity and the pharynx (adapted from [43]) . . . . . . . . . . . 27
	2	Swallowing sequences. Phase 1: Initiation of swallowing. Phase 2: Pharyngeal
		peristalsis (adapted from [26]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
	3	Scheme of the peristaltic wave and associated study system. Near the most occluded
		point, the pharyngeal walls are in rotation one compared to the other. In black,
		-→ x ,	-→ z represents the laboratory frame, whereas, in grey,	-→ X ,	-→ Z represents the

wave frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4 Schematic diagram of denitions and notations. . . . . . . . . . . . . . . . . . . . . . 30 5 Pharyngeal peristalsis simulator: (1) saliva feed, (2) slot coater, (3) food bolus, (4) scraper, (5) collector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6 Dimensionless ow rate as a function of modied capillary number in the monolayer case. Comparison with the analytical results of Coyle et al. [38]. . . . . . . . . . . . 32 7

Table 1 :

 1 Physiological variables and approximate corresponding value.

	Description	Symbol Typical value References
	Saliva thickness	t 1	no data
	Wave velocity	U	0.1-0.5 m/s	[1, 2, 25]
	Radius	R	40 mm	estimated from [1]
	Load	L	10-60 N/m	estimated from [29]
	Drag	D	no data
	Saliva viscosity	μ 1	1-10 mPa.s	[40]
	Bolus viscosity	μ 2	> 1 mPa.s

Acknowledgements

The authors gratefully acknowledge the French National Research Agency (ANR) project SensIn-Mouth for its nancial support.

Appendix

For a given lift L and drag D ,the dimensionless variables are:


Thomas Leduc
email: thomas.leduc@cerma.archi.fr

Philippe Woloszyn
email: philippe.woloszyn@univ-rennes2.fr

TOWARDS A LANDSCAPE POTENTIAL. A METHOD BASED ON A SYSTEMATIC CHARACTERIZATION OF THE SURROUNDING URBAN FABRIC THROUGH THE VISUAL DYNAMICS OF PEDESTRIANS

Keywords: landscape analysis, open spaces, isovist, sensory Digital Elevation Model, ambio-potential, sociotope

The pedestrian mobility is a way to understand how a person might experience the void in between the buildings (this void defines a space portion as a shape) and therefore the urban fabric itself. The present paper aims to characterize landscape potentialities through pedestrian perception. Our proposal consists in building a set of sort of sensory Digital Elevation Models in which the third dimension is computed based on a measure of the surrounding open spaces using isovists. More precisely, we present three different DEMs: a first one corresponds to the isovist area in each point, the second one corresponds to its drift value (a frequently used indicator in isovist fields) and the third one corresponds to its kurtosis value. At last we combine all these DEMs with different pedestrian pathways so as to obtain corresponding sensory fingerprints.

Introduction

In the manner of the biologists' biotope concept, which is an area of uniform physical environmental conditions providing a living place for a biological community, the sociotope concept has been defined [START_REF] Sandberg | Converging Cognitive Enhancements[END_REF][2] [START_REF] Stahle | Compact sprawl: Exploring public open space and contradictions in urban density[END_REF]. As summarized by [START_REF] Stahle | Sociotope mapping -exploring public open space and its multiple use values in urban and landscape planning practice[END_REF], the sociotope corresponds to the commonly perceived direct use values of a place by a specific culture or group. Even if the aforementioned perception can obviously not be reduced to its visual component, one must admit that the visual field is predominant in the human perception of the urban fabric.

Therefore, [START_REF] Morello | A digital image of the city: 3D isovists in Lynch's urban analysis[END_REF] notices that there were "many attempts to translate visual-perception research into architectural and urban design. The best known contribution in urban-planning studies is perhaps [START_REF] Lynch | The image of the city[END_REF]". In his book, Lynch asserts "We are continuously engaged in the attempt to organize our surroundings, to structure and identify them […] it should be possible to give [cities] a form which facilitates these organizing efforts rather than frustrates them". As explained by [START_REF] Morello | A digital image of the city: 3D isovists in Lynch's urban analysis[END_REF], city mental maps can help to describe a sort of image of the city but also to evaluate the 'legibility' of a built context. Based on this concept of legibility, [START_REF] Lynch | The image of the city[END_REF] introduces the derived notion of "imageability" which is a kind of indicator of the evocation power of an environment.

These two key concepts have been enriched by a third one introduced by the Space Syntax theory. Indeed, [START_REF] Hillier | Space is the machine[END_REF] defines the notion of intelligibility as "the degree to which what we can see from the spaces that make up the system -that is how many other spaces are connected to it -is a good guide to what we cannot see, that is the integration of each space into the system as a whole".

The work [START_REF] Benedikt | cyberspace and the spatiology of information[END_REF] reminds us that "Walls and ceilings, buildings and trees, are positioned in such a way as to modulate experience: not just the experience of those very walls and ceilings (and buildings and trees), but the experience of the people and signs, images and machines, and so on, that move about and populate the room or cityscape". To this end, the "theory of isovists" was developed [START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF].

In [START_REF] Franz | From space syntax to space semantics: a behaviorally and perceptually oriented methodology for the efficient description of the geometry and topology of environments[END_REF], several isovists measures have been translated into basic spatial qualities hypotheses. In its turn the work [START_REF] Meilinger | From isovists via mental representations to behaviour: first steps toward closing the causal chain, Environment and Planning B: Planning and Design[END_REF] addresses the interactions between partial isovists fields and human wayfinding performance. In [START_REF] Leduc | Towards a spatial se-mantics to analyze the visual dynamics of the pedestrian mobility in the urban fabric[END_REF], partial isovists fields have been used to exhibit the fact that it is worth taking strategic visual properties into account in the design of a patrimonial tour in a historic city centre. The work [START_REF] Weitkamp | Capturing the view: a GIS based procedure to assess perceived landscape openness[END_REF] uses isovist to establish the relationship between landscape openness and well-being.

Nevertheless, as noted by [START_REF] Ervin | Landscape visibility computation: necessary, but not sufficient[END_REF], the great advances in understanding the optical physics of intervisibility in urban environments do not suffice to real perceptual understanding. What we see, and what we make of what we see, are questions that drive many, including researchers, planners, designers, computer programmers, cognitive psychologists, and others. We need to consider some of the no trigonometric determinants of perception, including cognitive, cultural, and other psychological factors. That is the reason why [START_REF] Ervin | Landscape visibility computation: necessary, but not sufficient[END_REF] concludes with some 'real' open-ended questions which remain interesting areas for investigation. Thus, [START_REF] Ervin | Landscape visibility computation: necessary, but not sufficient[END_REF] asked for useful metrics -qualitative or quantitative -that can be used to describe visibility from a line or an area, not just from a point: "visibility calculations may be expanded to become more interesting and useful to landscape planners and designers is to consider the ways in which views from not just points, but also from lines, sequences, and areas, may be computed and characterized".

The present paper is an attempt to answer this key question. It exposes a method to synthesize the visibility in the whole of a given urban fabric, using a dedicated digital model.

Shape of the Open-Spaces -Brief Overview of Visibility Analysis

In the 1970s, two main approaches emerge in the visibility analysis context: the concept of viewshed (by analogy to the hydrologic watershed) in terrain and landscape analysis and the concept of isovist in architecture and urban space.

The view-shed analysis is a traditional way of analysing a visibility field. It is defined as the part of terrain visible from a viewpoint (analogous to the outlet of the watershed), and is basically applied to the landscape with terrain and topographic differentiation. As noticed in [START_REF] Yang | Viewsphere: a GIS-based 3D visibility analysis for urban design evaluation[END_REF], view-shed analysis in GIS is rarely applied to urban settings because the operation is based on raster data or TIN (triangular irregular network) data structure, which have problems of accuracy in representing complex geometry of urban form.

An isovist is the set of all points in an environment of opaque surfaces that are visible from a given point (the limit of the isovist is an artificial one functioning something like a horizon in the absence of any other intervening surfaces). This 2D bounded polygon is a useful tool to define the open space concept. From a morphological point of view, open spaces are usually defined as the empty space, the void, between the surrounding buildings. However, although these open spaces are not material components of the physical world, they can be conceived as part and parcel of our urban heritage [START_REF] Teller | A spherical metric for the field-oriented analysis of complex urban open spaces[END_REF]. [START_REF] Batty | Exploring isovist fields: space and shape in architectural and urban morphology[END_REF] puts the emphasis on the fundamental motivations of conducting visibility analysis research. He noticed that the key questions "how far can we see", "how much can we see", and "how much space is enclosed" are relevant to develop good urban design.

Essentially, isovists describe local geometrical properties of spaces with respect to individual observation points and weight all the possible view directions equally (see Fig. 1). An isovist is a 2D horizontal slice of pedestrian's surrounding space.

The Method in Detail

The aim of the present paper is to characterize the landscape potential of a given place, focusing on visibility question. Therefore, the method we need has to evaluate and characterize visibility in a systematic way all over the shape. In order to let this method remain easily and widely repeatable, we want it to be based on "classical" data of vector type (such as the BD Topo®, provided by the French national provider of reference geographic information, IGN). That is why, in the following use case, we present a simulation that is only based on both a polygonal buildings layer and a linear pathways layer.

The simplified schema presented on Figure 2, sums up the whole spatial process we have developed. It is composed of six main tasks. The first task consists in a sampling of the given region of interest into a set of points. Each of them is the node of a regular orthogonal grid that covers the whole of the input shape. The numerous they are (the finer the mesh is), the more accurate the fin al result will be. In the second task, an isovists field computation is performed, based on the one hand on this set of equidistant punctual positions and, on the other hand, on the buildings layer. In the third task, for each isovist, three different indicators are calculated. The first indicator, defined by [START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF], corresponds to the area of the isovist itself. The second one, defined by [START_REF] Conroy Dalton | OmniVista: an application for Isovist field and path analysis[END_REF], is the drift. The drift is the Euclidean-distance between the location from which the isovist is generated (the so-called view-point) and the centre of gravity of the isovist shape. At last, the third indicator, defined by [START_REF] Leduc | Measuring surrounding space to assess the pedestrian visual aperture angle in the urban fabric: towards a kurtosis based isovist indicator[END_REF], is the Kurtosis of the distribution of the radial lengths of each isovist.

The fourth task consists in three join queries between, on the one hand, the set of isovists indicators, and on the other hand, the points of interest. The aim is to provide each of these points with a sort of "elevation" value so as to obtain a so-called Digital Elevation Model (DEM). In this DEM, for each given punctual position, the 3 rd dimension is a measure of the surrounding open spaces using one of the three isovists indicators already mentioned.

With such a DEM-based schematic representation of the city open spaces, we are able to identify not only equipotential curves relative to visual perception criteria (fifth task), but also to extract some "profile plots" all-along pedestrian pathways (sixth task).

Use Case and Result

The study site is a main square in the historic city centre of Nantes. Called Place Royale, it has been designed by the architect Mathurin Crucy in 1788. This square matches the classicism criteria in architecture. It places emphasis on symmetry, proportion, geometry, the regularity of facades and openings. It is of about 80 meters length and 70 meters wide, with a fountain on its east-side (see Fig. 3).

Encompassing the immediate surroundings of the square, the region of interests we focus on, is of exactly 10,000 m². Therefore, because we have decided to handle DEMs with metric accuracy, we have 10,000 points of interest to process. In the three following maps (Figures 4, 5, and6), each pixel corresponds to a 1 m² portion of space. Its colour corresponds to an estimation of the surroundings in the centre of the corresponding location. More precisely, the pixel colour is consecutively given by an estimation of the area of the isovist at this view-point, then by its drift, and, at last, by its Kurtosis.

In the map presented on the Figure 4, the pixel's colour corresponds to an estimation of the area of the visible surroundings, assuming the view-point is located in the centre of the corresponding place (of 1 m²). The hot spots (red coloured) correspond to places where surroundings are wide (from 10,000 to 15,000 m²), intermediate values (from 2,000 to 10,000) are blue coloured, and at last, lowest values are green coloured.

Despite the symmetry of the square, the DEM (based on areas) itself appears asymmetric, with a clear line of highest potential in its south-west side. In each of the corresponding locations, the great value is due to far vantage towards place Graslin square (west side) or towards Orleans' Street (east side). In the map presented on Figure 5, the pixel's colour corresponds to an estimation of the drift of the visible surroundings, assuming the view-point is located in the centre of the corresponding place. The drift, as an Euclidean distance from the view-point to the centre of gravity of the isovist, is a sort of measure of the compliance of the visual environment to the physical surroundings. The greatest this value is, the more far the view point is located from the centre of the corresponding shape.

In the following map (see Fig. 5), a hot-spot (red coloured) corresponds to a place where these two points (the view-point and the shape's centre) are far from each other. On the contrary, a green coloured pixel is a location where they overlap: in this case, the visual impression matches the physical feeling. As may be noticed, the open to Crebillon, de la fosse and d'Orleans main streets, correspond to places with such a coincidence. There is also a green spot in the south part not far from the opening towards the de Gorges Street. In this isle of "centrality", some street performer frequently displays his paints. To illustrate the type of use that we can make from these DEM based representations, we have decided to focus more particularly on three different pedestrian pathways across the square (see Fig. 7). The two first paths are of the same length, 100 meters, while the last one is of about 145 meters. As may be noticed with the profile plots on the Figure 8, even if the second path is quite stable and high valued in term of area values, it varies a lot in term of drift values (twice compared to the two other paths) so as in term of Kurtosis values (twice compared to the two other paths).

Figure 1 .

 1 Figure 1. Isovist symbolic representation[START_REF] Conroy | Spatial Navigation in Immersive Virtual Environments[END_REF]. The observer is comparable to a visual sensor with an aperture angle equal to 360 degrees.Corresponding isovist is the set of all points visible from his given punctual position taking surrounding occluding surfaces into account

Figure 2 .

 2 Figure 2. The geo-processing schema we have adopted. Input maps are 45 degrees wide hatched, intermediate results have no background colour and final output results are grey coloured

Figure 3 .

 3 Figure 3. Four photographic snapshots from the Place Royale square. The first one (top left) corresponds to the beginning of the first pathway (south-east, connected to the Orléans' street).The second one (top right), is the start of the second pathway (connected to the de l'Arche sèche street).The third one (bottom left), is the start of the third pathway (connected to the de la fosse street). At last, the fourth one is a panoramic view of the square. It has been shot from the entrance of the Crebillon's street (output point of the first pathway)

Figure 4 .

 4 Figure 4. A digital "elevation" model in which elevation values have been replaced by measuresof the surroundings (in this case, the area of the isovist in the corresponding view point). Moreover, several isocontour lines have been plotted so as to emphasize some equipotential areas

Figure 5 .Figure 6 .

 56 Figure 5. A digital "elevation" model in which elevation values have been replaced by measuresof the surroundings (in this case, the drift of the isovist in the corresponding view point). Moreover, several isocontour lines have been plotted so as to emphasize some equipotential areas

Figure 7 .

 7 Figure 7. Three different pathways have been identified. They all correspond to classical courses in this central district of Nantes city. The first one (black coloured) is part of a pedestrian tour from 50 hostages main street (and the main tramway stop called Commerce) to the Graslin square through the Crebillon famous shopping street. The second one (green coloured) leads from the car park called Bretagne to the Commerce square.At last, the third one (red coloured), is part of a pedestrian pathway from the multilevel covered street (passage Pommeray) to the town hall

Figure 8 .

 8 Figure 8. Nine different profile plots. One per pathway and per isovist indicator

Acknowledgments

The authors would like to thank F. Gonzalez Cortés (Spain) for all the developments performed on the GearScape GIS. They also would like to thank Professor B. Jiang (Department of Technology and Built Environment, University of Gävle, Sweden) for his relevant comments and proposals during the IF&GIS 2011 workshop.

Concluding Remarks and Outlook

In the current paper, we have tried to give an answer to one of [START_REF] Ervin | Landscape visibility computation: necessary, but not sufficient[END_REF]'s key questions. Indeed, the three DEM representations based on sort of sensory values give us the ability to plot different representations (more anthropocentric) of the urban fabric. To sum up, we have focused on a well-known square in the historical city centre of Nantes, we have sampled it with a fine metric grain and then, in each of the sampling point we have calculated the corresponding isovist.

Even if all these computations still have to do with the optical physics of intervisibility, the resulting maps represent an advanced overview of the complexity and the richness of the urban fabric. Indeed, it combines both a global and systematic method to handle the whole square (zenithal approach) with a set of immersed view-points (tangential approaches).

This study emphasizes the fact that the field oriented analysis of the city (the one that focus on the open-spaces) is a relevant method to model and characterize the urban fabric. It is therefore a promising alternative to the atomist [START_REF] Couclelis | People Manipulate Objects (but Cultivate Fields): Beyond the Raster-Vector Debate in GIS. In: Theories and Methods of Spatio-Temporal Reasoning in Geographic Space[END_REF] based approach (in the atomist conception of space, each item corresponds to a tangible spatial object such as a building). With such a method, we do not emphasize the buildings themselves but the void in-between them. The resulting new urban "objects" are however interesting because they provide a relevant way to describe, analyse, and maybe also partition, the urban fabric.


Philippe Woloszyn
email: philippe.woloszyn@univ-rennes2.fr

Thomas Leduc
email: thomas.leduc@cerma.archi.fr

A LANDSCAPE POTENTIAL CHARACTERIZATION: SPATIAL TEMPLATE OF PEDESTRIAN AMBIENT FIELDS WITHIN THE URBAN FABRIC

Keywords: Landscape analysis, open spaces, isovist, sensory Digital Terrain Model, ambio-potential, sociotope

Through interacting with urban and architectural spaces, pedestrian pathway"s ambient fingerprints delineate ambiences with identifiable characteristics, thus characterizing landscape perception potentialities. Based on a measure of the surrounding open spaces using isovists, our proposal consists in building a sensory Digital Terrain models (DTM) in which the entropy of the function of radial distances is used as a third dimension. As a case study, the distribution of entropy of the Place Royale square in Nantes (France), presented in a dedicated DTM, helps us characterizing the space « intimacy quality » for each observation point. This measure constitutes a relevant indicator of spatial wealth, revealing several perspectives occurrences for a given point of view during an urban walk. This way, this geotopical process establishes a spatial potential, so as to provide to a pedestrian the ability to reach specified townscapes to be contemplated. This sensorial investigation aims to constitute a tool basis for multi-sensorial planning and design process.

Introduction

In the manner of the biologists' biotope concept, which is an area of uniform physical environmental conditions providing a living place for a biological community, the sociotope concept has been defined as a delineated area where use values and social meanings are uniform [START_REF] Sandberg | Converging Cognitive Enhancements[END_REF][2] [START_REF] Stahle | Compact sprawl: Exploring public open space and contradictions in urban density[END_REF].

The word sociotope is used in both anthropology and sociology. The Swedish social psychologist Lars Dencik applied the sociotope concept in 1995 to describe the children social life world [START_REF] Dencik | Children in day care and family life : observations from the BASUN project[END_REF]. The German anthropologist Elisabeth Katching-Fasch in 1998 described "the city as a "sociotope" of multicultural lifestyles" [START_REF] Katsching-Fasch | Die Magie der Bilder: Kulturelle Veränderungen durch die Wiederkehr des Körpers[END_REF]. The German landscape architect Werner Nohl used sociotopes in 2001 to describe social types of urban settings [START_REF] Nohl | Ästhetisches Erlebnis von Windkraftanlagen in der Landschaft[END_REF]: this meaning has been extensively used in Sweden for urban planning practice by Alexander Ståhle [START_REF] Stahle | Compact sprawl: Exploring public open space and contradictions in urban density[END_REF].

As summarized by [START_REF] Stahle | Sociotope mapping -exploring public open space and its multiple use values in urban and landscape planning practice[END_REF], the sociotope corresponds to the commonly perceived direct use values of a place by a specific culture or group. It is shaped by a multiplicity of lifestyles connected to a specific place and it can be categorized as more or less local (or global). This raises questions about the landscape's perception and use characteristics with respect to the physical layout, space, material and furnishing. Questions related to the planning process, land use and conflicts of interest are also raised, in addition to design issues such as space requirements and aesthetic considerations.

The surroundings can be regarded as a perceptual matrix, while the remarkable visual patches, in similarity to the terminology of landscape ecology [START_REF] Forman | Landscape Ecology[END_REF], can be linked together using corridors/paths or stepping stones so that they constitute a connected phenomenon in the city landscape. Such corridors can be used in the urban planning process to plan visual access to parks, green areas, so as to remarkable monuments or areas.

The discourse on the contents and density of the cities [START_REF]Sustainable development in the European Union[END_REF] therefore gets additional arguments against the exploitation of open spaces. Such discourse should, in actual fact, focus on the quality and accessibility of the open spaces [START_REF] Grahn | Landscapes in our mind: people's choice of recreative places in town[END_REF] or remarkable areas.

Even if the aforementioned perception can obviously not be reduced to its visual component, one must admit that the visual field is predominant in the human perception of the urban fabric. Therefore, we will develop specific indicators to improve the visibility access to the "remarkable" items, namely in order to localize amenities access inequalities in a given territory, leading to a "geotropic" environmental enhanced cognitive mapping.

Therefore, [START_REF] Morello | A digital image of the city: 3D isovists in Lynch's urban analysis[END_REF] notices that there were "many attempts to translate visual-perception research into architectural and urban design. The best known contribution in urban-planning studies is perhaps [START_REF] Lynch | The image of the city[END_REF]". In his book, Lynch asserts "We are continuously engaged in the attempt to organize our surroundings, to structure and identify them […] it should be possible to give [cities] a form which facilitates these organizing efforts rather than frustrates them". As explained by [START_REF] Morello | A digital image of the city: 3D isovists in Lynch's urban analysis[END_REF], city mental maps can help to describe a sort of image of the city but also to evaluate the "legibility" of a built context. Based on this concept of legibility, [START_REF] Lynch | The image of the city[END_REF] introduces the derived notion of "imageability" which is a kind of indicator of the evocation power of an environment. These two key concepts have been enriched by a third one introduced by the Space Syntax theory. Indeed, [START_REF] Hillier | Space is the machine[END_REF] defines the notion of intelligibility as "the degree to which what we can see from the spaces that make up the systemthat is how many other spaces are connected to itis a good guide to what we cannot see, that is the integration of each space into the system as a whole". [START_REF] Benedikt | Cityspace, cyberspace and the spatiology of information[END_REF] reminds us that "Walls and ceilings, buildings and trees, are positioned in such a way as to modulate experience: not just the experience of those very walls and ceilings (and buildings and trees), but the experience of the people and signs, images and machines, and so on, that move about and populate the room or cityscape". To this end, the "theory of isovists" was developed [START_REF] Benedikt | To take hold of space: isovists and isovist fields[END_REF].

In [START_REF] Franz | From space syntax to space semantics: a behaviorally and perceptually oriented methodology for the efficient description of the geometry and topology of environments[END_REF], several isovists measures have been translated into basic spatial qualities hypotheses. [START_REF] Meilinger | From isovists via mental representations to behaviour: first steps toward closing the causal chain[END_REF] addresses the interactions between partial isovists fields and human way finding performance. In [START_REF] Leduc | Towards a spatial semantics to analyze the visual dynamics of the pedestrian mobility in the urban fabric[END_REF], partial isovists fields have been used to exhibit the fact that it is worth taking strategic visual properties into account in the design of a patrimonial tour in a historic city center. [START_REF] Weitkamp | Capturing the view: a GIS based procedure to assess perceived landscape openness[END_REF] uses isovist to establish the relationship between landscape openness and wellbeing.

Nevertheless, as noted by [START_REF] Ervin | Landscape visibility computation: necessary, but not sufficient[END_REF], the great advances in understanding the optical physics of intervisibility in urban environments do not suffice to real perceptual understanding. What we see, and what we make of what we see, are questions that drive many, including researchers, planners, designers, computer programmers, cognitive and environmental psychologists, sociologists, geographers and others. We need to consider some of the non-Cartesian determinants of perception, including cognitive, cultural, and other psychological factors. That is the reason why [START_REF] Ervin | Landscape visibility computation: necessary, but not sufficient[END_REF] concludes with some 'real' open-ended questions which remain interesting areas for investigation. Thus, [START_REF] Ervin | Landscape visibility computation: necessary, but not sufficient[END_REF] asked for useful metrics -qualitative or quantitative that can be used to describe visibility from a line or an area, not just from a point: "visibility calculations may be expanded to become more interesting and useful to landscape planners and designers is to consider the ways in which views from not just points, but also from lines, sequences, and areas, may be computed and characterized".

The present paper is an attempt to answer this key question. It exposes a method to synthesize the visibility in the whole of a given urban fabric, using a dedicated digital model.

Shape of the open-spacesbrief overview of visibility analysis

In the 1970s, two main approaches emerge in the visibility analysis context: the concept of viewshed (by analogy to the hydrologic watershed) in terrain and landscape analysis and the concept of isovist in architecture and urban space.

The viewshed analysis is a traditional way of analyzing a visibility field. It is defined as the part of terrain visible from a viewpoint (analogous to the outlet of the watershed), and is basically applied to the landscape with terrain and topographic differentiation. As noticed in [START_REF] Yang | Viewsphere: a GIS-based 3D visibility analysis for urban design evaluation[END_REF], viewshed analysis in GIS is rarely applied to urban settings because the operation is based on raster data or TIN (triangular irregular network) data structure, which have problems of accuracy in representing complex geometry of urban form.

An isovist is the set of all points in an environment of opaque surfaces that are visible from a given point (the limit of the isovist is an artificial one functioning something like a horizon in the absence of any other intervening surfaces). This 2D bounded polygon is a useful tool to define the open space concept. From a morphological point of view, open spaces are usually defined as the empty space, the void, between the surrounding buildings. However, although these open spaces are not material components of the physical world, they can be conceived as part and parcel of our urban heritage [START_REF] Teller | A spherical metric for the field-oriented analysis of complex urban open spaces[END_REF]. [START_REF] Batty | Exploring isovist fields: space and shape in architectural and urban morphology[END_REF] puts the emphasis on the fundamental motivations of conducting visibility analysis research. He noticed that the key questions "how far can we see", "how much can we see", and "how much space is enclosed" are relevant to develop urban design strategies.

Essentially, isovists describe local geometrical properties of spaces with respect to individual observation points and weight all the possible view directions equally (see Fig. 1). An isovist is a 2D horizontal slice of pedestrian's surrounding space.

Figure 1. Isovist symbolic representation [START_REF] Conroy | Spatial Navigation in Immersive Virtual Environments[END_REF]. The observer is comparable to a visual sensor with an aperture angle equal to 360 degrees. Corresponding isovist is the set of all points visible from his given punctual position taking surrounding occluding surfaces into account.

The method in detail

The aim of the present paper is to characterize the landscape potential of a given place, focusing on visibility question. Therefore, the method we need has to evaluate and characterize visibility in a systematic way all over the shape. In order to let this method remain easily and widely repeatable, we want it to be based on "classical" data of vector type (such as the BD Topo®, provided by the French national provider of reference geographic information, IGN). That is why, in the following use case, we present a simulation that is only based on a polygonal buildings layer.

The simplified schema presented in Fig. 2, sums up the whole spatial process we have developed. It is composed of seven main tasks. The first task consists in a sampling of the given region of interest into a set of points. Each of them is the node of a regular orthogonal grid that covers the whole of the input shape. The numerous they are (the finer the mesh is), the more accurate the fin al result will be. In the second task, an isovists field computation is performed, based on the one hand on this set of equidistant punctual positions and, on the other hand, on the buildings layer.

In the third task, for each isovist, a 2π periodic function of radial distances is produced. As described in [START_REF] Leduc | Towards a "typification" of the pedestrian surrounding space: analysis of the isovist using digital signal processing method[END_REF], it corresponds to an angular abscissa sampling process. More precisely, the isovist polygon, which is a complex shape, is transformed into a 1D real-valued function. This reduction of the dimension space is achieved through the discretization of the isovist in polar coordinates with a regular angle.

The fourth task consists in a Shannon entropy computation. In this task, the previously mentioned 1D real-valued function (which is a function of radial distances) is treated as a sequence of independent and identically-distributed random variables. In each viewpoint (for each isovist), a numerical value (the Shannon Entropy) is computed. All these values are combined, in a spatial join query, with the set of points of interest. The aim is to provide each of these points with a sort of "elevation" value so as to obtain a so-called Digital Terrain Model (DTM). In this DTM, for each given punctual position, the 3 rd dimension is a measure of the surrounding open spaces using an isovists indicator based on the information theory (more precisely on the Shannon entropy).

With such a DTM-based schematic representation of the city open spaces, we are able to identify not only equipotential curves relative to visual perception criteria (fifth task), but also to extract some "profile plots" all-along virtual curves (sixth and seventh tasks).

Use case and result

The study site is a main square in the historic city centre of Nantes. Called Place Royale, it has been designed by the architect Mathurin Crucy in 1788. This square matches the classicism criteria in architecture. It places emphasis on symmetry, proportion, geometry, the regularity of facades and openings. It is of about 80 meters length and 70 meters wide, with a fountain on its east-side.

Encompassing the immediate surroundings of the square, the region of interests we focus on, is of exactly 10,000 m². Therefore, because we have decided to handle digital model with metric accuracy, we have 10,000 points of interest to process. In the following map (Fig. 3), each pixel corresponds to a 1 m² portion of space. Its color corresponds to an estimation of the surroundings in the center of the corresponding location. More precisely, the pixel color is consecutively given by an estimation of the entropy value of the isovist fingerprint at this view-point.

Figure 3. In this DTM based representation, the Shannon Entropy of the distribution of the radial lengths of each isovist shape has been plotted, so as several isocontour lines which emphasize equipotential areas.

In the map presented in the Fig. 3, the pixel"s color corresponds to an estimation of the "unpredictability" of the visible surroundings, assuming the view-point is located in the center of the corresponding place (of 1 m²). More precisely, when the entropy value is equal to 1 (when the pixel's color tends to become white), the disorder in the radial distances function is maximal. When the entropy value is equal to 0 (when the pixel"s color tends to become dark), the "signal" is fully predictable and the radial distances function is constant (that is, the corresponding isovist is a disc in which the viewpoint is the center). This proxemy indicator provides an approach of urban space "intimacy quality" of the facades distribution of the Place Royale square in Nantes.

Despite the symmetry of the square, the DTM itself appears asymmetric, with a sort of skeleton in its center. This skeleton joins the points of lowest entropy potential.

Providing information about visual (space) variability for each point of the perceived space (leading to a visual homeostasis quantification), entropy measure constitutes a relevent indicator of spatial wealth, in a perspective viewpoint of the perceived landscape. If high entropy level signs a quasi-uniform perspective for each view angle of an observation point, low-entropy level reveals visual access to many perspectives for a given point of view: this marks a higher choice of spatial occurrences during an urban walk. To illustrate the type of use that we can make from this DTM based representation, we have decided to focus more particularly on five different pedestrian positions across the square (see Fig. 4) and to produce the corresponding panoramic snapshots (see Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9).

As may be noticed, Fig. 5 and 6 exhibit situations of a homogeneous landscape where the viewpoint seems to match the center of the open space. In these two cases, the opaque edges (the buildings) seem to be far from the point of view. In the opposite, Fig. 7, 8, and 9 exhibit situations of inhomogeneous landscape where opaque edges (buildings) are fairly intrusive in the pedestrian viewshed. The profile plot presented in Fig. 10 corresponds to a continuous representation of the Shannon entropy value all along the polyline presented previously in Fig. 4. As may be seen, the two lowest peaks correspond to the locations of 1st and 2nd points whereas the three highest peaks are close to the three other points.

Figure 10. Profile of the polyline presented in the Fig. 4 (using the Shanon entropy measure).

Concluding remarks and outlook

Through the presentation of a visual environment informational analysis, this paper exhibit ambient structural attributes of an urban neighborhood, based on a landscape visual space geo-topical modeling.

In the current paper, we have tried to give an answer to one of [START_REF] Ervin | Landscape visibility computation: necessary, but not sufficient[END_REF]'s key questions. Indeed, the DTM representation based on sort of sensory values gives us the ability to plot different representations (more anthropocentric) of the urban fabric. To sum up, we have focused on a well-known square in the historical city centre of Nantes, we have sampled it with a fine metric grain and then, in each of the sampling point we have calculated the corresponding isovist.

Even if all these computations still have to do with the optical physics of intervisibility, the resulting maps represent an advanced overview of the complexity and the richness of the urban fabric. Indeed, it combines both a global and systematic method to handle the whole square (zenithal approach) with a set of immersed view-points (tangential approaches).

This study emphasizes the fact that the field oriented analysis of the city (the one that focus on the openspaces) is a relevant method to model and characterize the urban fabric. It is therefore a promising alternative to the atomist [START_REF] Couclelis | People Manipulate Objects (but Cultivate Fields): Beyond the Raster-Vector Debate in GIS[END_REF] based approach (in the atomist conception of space, each item corresponds to a tangible spatial object such as a building). With such a method, we do not emphasize the buildings themselves but the void in-between them. The resulting new urban "objects" are however interesting because they provide a relevant way to describe, analyze, and maybe also partition, the urban fabric.

Moreover, this angular perspective variability computation should also provide a spatial potential, allowing a pedestrian to diversify his visual landscape during his walk. This constitutes a main parameter for urban pedestrian itinerary choice, thus implementing the walkthrough complexity at each point of the explored space.

Future challenge is to investigate the inter-sensorial ambient-scape as a basis of a multi-sensory conception in townscape planning and design.

Figure 2 .

 2 Figure 2. The geo-processing schema we have adopted. Input maps are 45 degrees wide hatched, intermediate results have no background color and final output results are gray colored.

Figure 4 .

 4 Figure 4. Five different positions have been identified and joined (from north to south) using a poly-line. They all correspond to credible pedestrian locations in this central district of Nantes city. The two first ones are located in the true middle of the square whereas the three others are much more at the outskirts.

Figure 5 .

 5 Figure 5. Panoramic snapshot at the 1 st position.

Figure 6 .

 6 Figure 6. Panoramic snapshot at the 2 nd position.

Figure 7 .

 7 Figure 7. Panoramic snapshot at the 3 rd position.

Figure 8 .

 8 Figure 8. Panoramic snapshot at the 4 th position.

Figure 9 .

 9 Figure 9. Panoramic snapshot at the 5 th position.

Acknowledgments

The authors would like to thank F Gonzalez Cortés (Spain) for all the developments performed on the GearScape GIS. They also would like to thank Assistant Professor B Suner (from the National School of Architecture of Nantes city, France) for his significant help in the production of the panoramic snapshots.

About the authors

Thomas LEDUC obtained a PhD in Computer Science from Paris VI University (France). He is currently CNRS Research Engineer, in the CERMA Laboratory from the Nantes National School of Architecture. His research activities focus on the urban morphology characterization using the geographic information science and technology. More precisely, he is involved in several projects that aim to describe open spaces morphology, evaluate their impact on the pedestrian mobility in the urban fabric, correlate them with seismic vulnerability, etc. In addition, he is currently co-supervisor of the PhD thesis of R Hamaina.

Philippe WOLOSZYN is CNRS research worker in "Space and Society" ESO laboratory UMR 6590. After his architecture and acoustical engineering diplomas, he gets his degree from University of Nantes (France), with using specific fractal measurements of architectural geometry, coupled with virtual sound restitution. His recent projects develop a synergy between architects, physicians and psychologists in order to model environmental effects of urban ambient surroundings on people, inhabitants and users. He has been expert for the "Transport Energetical and Environmental Assessment" operational research group of the PREDIT (Interministry Terrestrial Transport National Innovation and Research Program), the CSEA (Architectural Teaching Overhead Council), and the CoNRS (Research National Committee). In 2003, the French National Research Centre (CNRS) awarded him the bronze medal for his interdisciplinary contribution to the Architectural and Urban Research Field.