Sabir Jacquir

S T Éphane Binczak

Jean-Marie Bilbault

Viktor Kazantsev

Vladimir Nekorkin

Synaptic Coupling Between Two Electronic Neurons

Keywords: bifurcation, electronic neuron, FitzHugh-Nagumo model, synaptic coupling MFHN -modified FitzHugh-Nagumo

An electrical circuit is proposed to realize an unidirectional coupling between two cells, mimicking chemical synaptic coupling. Each cell represents the FitzHugh-Nagumo (FHN) model of neuron with a modified exitability (MFHN). We present experimental results on frequency doublings and on the chaotic dynamics depending on the coupling strength in a master-slave configuration. In all experiments, we stress the influence of the coupling strength on the control of the slave neuron.

Introduction

Although the differential equations are used to model the nerve membrane, we suggest describing the overall activity of neurons by one of these models. Moreover, we propose an experimental electronic implementation of it. Indeed in the literature, some electronic neurons, such as the Nagumo's lattice [START_REF] Nagumo | An active impulse transmission line simulating nerve axon[END_REF] and the Neuristor device [START_REF] Scott | Neuroscience: A Mathematical Primer[END_REF], have been realized. In the first section of this paper, the FitzHugh-Nagumo (FHN) equation with modified excitability has been used to conceive the electronic MFHN neuron [START_REF] Binczak | Experimental study of bifurcations in modified FitzHugh-Nagumo cell[END_REF]. Its experimental bifurcation curves in the dimensionless plane (η, ε) is given. This MFHN circuit leads to complex dynamics of traveling waves [START_REF] Dawson | Towards a global classification of excitable reaction-diffusion systems[END_REF][START_REF] Kazantsev | Spiking patterns emerging from wave instabilities in a one-dimensional neural lattice[END_REF] emerging from saddle homoclinic loop bifurcations. In the second section, we use the MFHN circuit as a basic cell to realize a master-slave configuration. Two cells are coupled in an unidirectional manner, which would correspond to two neurons coupled synaptically. After the presentation of the electronic circuit giving this coupling, we discuss the experimental conditions for which the master dynamics controls the excitability of the slave neuron leading to a shift of bifurcation curves, a variation of an eigen interspike frequency or a phenomenon of intermittency route to chaos.

Experimental Description of One Cell

ELECTRICAL CIRCUIT

The nonlinear circuit, as sketched in Figure 1, can be described as follows: Part (A) is a parallel association of three different branches, two of them being resistive and commuted by silicium diodes (V d = 0.6 V ), while the third is a negative resistor obtained with an operational amplifier. Due to diodes' commuting behavior, the resulting I -V characteristic is nonlinear and can be modeled by a cubic polynomial function for an appropriate set of parameters so that

I NL = f (U ) = 1 R 0 U - γ 2 U 3 3 (1)
where U and I NL are respectively the voltage and the corresponding current. The parameters R 0 and γ are obtained by a fitting approximation, e.g. by least mean square method. We obtain a good match between experimental results and Equation (1) by setting R 0 = 1023 and γ = 1.138 V -1 [START_REF] Binczak | Experimental study of bifurcations in modified FitzHugh-Nagumo cell[END_REF]. This nonlinear resistor is in parallel with a capacitance and two branches in parallel including inductances, resistances and voltage sources, one of them being commuted by a silicium diode so that setting the conditions R 6 L 1 = R 7 L 2 , E 2 = -V d, and using a piecewise linear I -V description for diode D 7 , I 2 = 0 if U < 0. Therefore, using Kirchhoff's laws, the system of equations can be expressed in a normalized way by:

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ dV dτ = V - V 3 3 -W dW dτ = ε[g(V ) -W -η] (2)
where V = γ U and W = γ R 0 (I 1 + I 2 ) correspond, in biological terms, to the membrane voltage and the recovery variable;

τ = t R 0 C is a re-scaled time, ε = R 0 R 6 C L 1 the recovery parameter and η = γ R 0 R 6 E 1 a bifurcation parameter. g(V ) is a piecewise linear function, g(V ) = αV if V ≤ 0 and g(V ) = βV if V > 0 where α = R 0 R 6 and β = L 1 +L 2 L 2 R 0
R 6 control the shape and location of the W-nullcline [START_REF] Binczak | Experimental study of bifurcations in modified FitzHugh-Nagumo cell[END_REF].

EXPERIMENTAL BIFURCATION CURVES OF MFHN CIRCUIT

This section presents different dynamics of the MFHN neuron [START_REF] Binczak | Experimental study of bifurcations in modified FitzHugh-Nagumo cell[END_REF]. In the case, α = β = 1, the system corresponds to the standard FHN equation where nullcline can only intersect at a single equilibrium point leading to Andronov-Hopf bifurcations. In the general case α = β, resolving Equation (2), three nullcline points are expected. The phase portrait is very similar to the one occurring from the modified Morris-Lecar Equations [START_REF] Rinzel | Analysis of neural excitability and oscillations[END_REF][START_REF] Koch | Biophysics of Computation: Information Processing in Single Neurons[END_REF] proposed to model barnacle muscle fibres and pyramidal cells. Considering the case α = 0.506 and β = 1.97, an experimental and numerical simulation determination of the bifurcation curves in the parameter plane (η,ε) is proposed in Figure 2.

Several results are to be distinguished depending on the location of the nullcline points and on initial conditions. In domain [START_REF] Nagumo | An active impulse transmission line simulating nerve axon[END_REF], two points are stable and unstable foci, while one point is a saddle, the system responds with an excitation pulse. Domain (2) corresponds to the bistability case characterized by the existence of a stable fixed point and a stable limit cycle that has appeared from a big homoclinic loop bifurcation. Then the model exhibits oscillations if the perturbation is large enough. In domain (3), the fixed point looses stability via a subcritical Andronov-Hopf bifurcation and only those oscillations occur in the model that are similar to the spiking train of pulses. Note that in the region (2), another saddle homoclinic loop bifurcation has taken place, leading to a small unstable limit cycle near the fixed point. Experiments have shown that, contrary to standard FHN, arbitrarily long interspike intervals can be found, as the two lower equilibrium points are merging. Finally, in domain (4), a single unstable fixed point exists, leading to oscillations; See [START_REF] Binczak | Experimental study of bifurcations in modified FitzHugh-Nagumo cell[END_REF] for more details. The existence of these domains has been confirmed with numerical simulations and stability analysis of Equation ( 2). In the following section, we study a specific case of coupling between two cells.

Unidirectional Coupling of Two Cells

The neurons communicate mainly between themselves through specialized devices called synapses via chemical messages. The chemical synapse transmits the impulse unidirectionally. Therefore, it is interesting to conceive and to realize an electrical circuit including the same features as the synaptical coupling. We present in Figure 3 the unidirectional coupling between two cells leading to a master-slave configuration, where N i (i = 1, 2) are described by the circuit of Figure 1.

Let us introduce D, the coupling parameter (synaptic strength). Its circuit, as illustrated in Figure 4, includes an adder-inverter, an inverter and then a follower. U 1 (resp. U 2) is the voltage capacitor of the cell N 1 (resp. N 2). The value of the resistor R is fixed to 100 k , which is large compared to the other components so that the current going though 2R is negligible, R a = 10 k , while R c is a detuning parameter, which allows us to control the coupling parameter value. Note also that the initial condition can be loaded in the neuron via an analogue commutator controlled by V syn . Although it is usual to study a system with normalized variables, it is more convenient to describe electrical circuits with experimental variables. Therefore, we will keep both variables (as normalized V 1 and experimental U 1 ) in the following of this paper. Using Kirchoff's laws, the normalized equations corresponding to the coupling between two MFHN neurons in a master-slave configuration can be expressed by:

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ dV 1 dτ = V 1 - V 3 1 3 -W 1 dW 1 dτ = ε 1 [g(V 1 ) -W 1 -η 1 ] dV 2 dτ = V 2 - V 3 2 3 -W 2 + DV 1 dW 2 dτ = ε 2 [g(V 2 ) -W 2 -η 2 ] (3)
with D = R 0 R c , and where the subscripts 1 and 2 indicate respectively the equations of the master and the slave neuron.

Therefore, the two neurons are coupled so that a part of current weighted by D via R, and generated by N 1 is included in N 2 . The two neurons are initially set to voltage U 1 ini and U 2 ini, due to the analogue commutators controlled by voltage V syn . When the initial conditions are loaded, these commutators are switched off, while the two neurons are connected via a third commutator controlled by V syn . Note that the time delay between the two neurons has not been taken into account in this circuit, a master-slave configuration rendering it unnecessary.

THE MASTER IN A RESTING STATE

When the voltage is so that V 1 is constant (the cell N 1 is in a resting state); it is straightforward to show that the variable W 2 and the bifurcation parameter η 2 of the cell N 2 are given by:

η 2 (V 1 ) = η 2 (V 1 = 0) + DV 1 W 2 (V 1 ) = W 2 (V 1 = 0) -DV 1 (4)
Therefore, it implies a modification of the excitability of the cell N 2 corresponding to a shift in the (η, ε) plane illustrated in Figure 5. The initial conditions are so that, when D = 0, the master neuron N 1 lies in domain (1), while the slave neuron N 2 is in domain (3) and generates a spiking train of pulses. When the unilateral coupling is increased and reaches a critical value, the neuron N 2 ceases to oscillate and stays in the resting state, meaning that the slave neuron has been moved from domain (3) to domain (1) of Figure 2. This ability of neuron N 1 to inhibit neuron N 2 corresponds to the shift predicted by Equation ( 4): As V 1 < 0, increasing D implies to increase η 2 (D, V 1 ) and therefore the bifurcation curves of Figure 2 are translated along abscissa, while the value of η 2 defined by the electrical parameters of neuron N 2 has not been changed. This result suggests that, for a defined activity of a slave neuron, the strength of a unilateral coupling should be above a critical value to give to the master neuron the control on the slave neuron.

In Figure 5, experimental values (D, η[D, V 1 ]) correspond to the shifted bifurcation curve between domains (1) and (3) of the neuron N 2 with ε 2 = 0.01 and when the master neuron N 1 lies in domain (1) in a resting state so that V 1 = -1.05. Comparison shows a good match between experimental results (+) and Equation (4) (continuous line), validating the unilateral coupling circuit.

THE MASTER IN A SPIKING REGIME

In this section, we present some results when the master is in domain (2) and oscillates. As V 1 is varying in time, we cannot express a simple relationship between the parameters of neuron N 2 and V 1 , as in Equation ( 4). Nevertheless, oscillations of neurons N 1 let V 1 be alternatively positive and negative, which implies that the bifurcation curves of neurons are translated along the abscissa in the plane (η, ) in a periodic manner (the position of saddle points of the cell N 2 is moved periodically). Thus, the slave neuron N 2 initially situated in the vicinity of a bifurcation curve may be able to cross sometimes this curve and develop a different dynamical behavior. Therefore, we have investigated the unilateral coupling influence on N 2 , in the case when neuron N 1 is initially (i.e. when D = 0) in domain (3) and oscillating, while the slave neuron N 2 is in domain [START_REF] Nagumo | An active impulse transmission line simulating nerve axon[END_REF].

According to the value of D, several different dynamical behaviors can be identified, as illustrated in Figures 6 and7: -In case (a), the coupling strength is small, leading to subthreshold oscillations of f m frequency, which are not taken into account in Figure 6 but are observable in Figure 7. -In cases (b)-(f), stable periodic oscillations appear whose eigen interspike frequency follows a devil's staircase-like curve. Only specific values of f s / f m are obtainable. Increasing the coupling strength causes the period doubling in the slave cell, that is the period is multiplied by 2, 4, 8, 16, and so on. -In case (g), N 2 is fully synchronized with N 1 . The slave neuron oscillates in the same manner as the master.

The slave neuron shows also a chaotic sequence of spikes resulting with variable interspike intervals. This chaotic regime, corresponding to the dot lines in Figure 6, between the period-doubling plateaus is so that the interspike slave period is varying during the experiments. When the coupling parameter is gradually increased, we firstly proceed from a periodic spiking regime to a chaotic regime via a sequence of period-doubling bifurcations. Finally, it leads to the reappearance of periodic dynamics inserted in the chaotic zones.

The chaotic puffs disturb the periodic spiking regime. Increasing the coupling parameter causes the increase of the frequency disturbances and then the chaos dominates the regime in the slave cell [START_REF] Ott | [END_REF][START_REF] Nayfeh | Applied Nonlinear Dynamics: Analytical,Computational, and Experimental Methods[END_REF]. An illustration of a chaotic signal is given in Figure 8 for D = 0.0535. The corresponding probability of normalized interspike slave frequency f s / f m is presented in Figure 9. This figure shows that in a chaotic regime, the interspike frequencies are distributed widely in the range [0, 0.4 f m ].

These experiments show that the unilateral coupling strength controls the slave neuron, from a silent to a chaotic dynamical behavior.

Conclusion

We have introduced an electrical circuit that allowed an unidirectional coupling without delay between two cells in a master-slave configuration. We have shown that the intervals between successive spikes can be chaotic and depend on the coupling strength. We suggest that this study can be helpful in understanding the different dynamics of potential propagation in brain cells. To complete this work, it would be of interest to study the bidirectional coupling corresponding to the electric synapse case and the influence of the size of the network on the fractal dimension of the information [START_REF] Kazantsev | Selective communication and information processing by excitable systems[END_REF]. This nonlinear electrical circuit cell indeed gives the opportunity to realize a large-scale network.

Figure 1 .

 1 Figure 1. Diagram of the nonlinear circuit.

Figure 2 .

 2 Figure 2. Comparison between experimental results (+, linked by dot line) and numerical simulation (continuous line) in the dimensionless plane (η, ε).

Figure 3 .Figure 4 .

 34 Figure 3. Coupling between two cells N 1 and N 2 .

Figure 5 .

 5 Figure 5. Shifted bifurcation curve of the slave neuron N 2 between domains (1) and (3). Parameters: master neuron N 1 : α 1 = 0.506, β 1 = 1.97, 1 = 0.01, η 1 = 0.01 leading to V 1 = -1.05 (i.e. U 1 = -921 mV). Slave neuron N 2 : α 2 = 0.506, β 2 = 1.97, 2 = 0.01. Comparison between Equation (4) (continuous line) and experimental results (+).

Figure 6 .

 6 Figure 6. Normalized eigen interspike slave frequency f s by interspike master frequency f m versus D with C = 0.001 nF, 1 = 2 = 0.002, η 1 = 0.199 and η 2 = 0.109.

Figure 7 .

 7 Figure 7. Temporal evolution of experimental voltage U 2 for different values of D corresponding to cases (a)-(g) of Figure 6. Voltage of the master neuron N 1 is shown on top. Abscissa: 0.1 ms per division; ordinate: 2 V per division.

Figure 8 .

 8 Figure 8. Chaotic signal in the case where D = 0.0535. Abscissa: 5 μs per division; ordinate: 2 V per division.

Figure 9 .

 9 Figure 9. Normalized distribution of the interspike frequency of N 2 corresponding to the signal in Figure 8.

Acknowledgements

This research has been supported by the Russian-French program of joint research (grant 04610PA), the Russian Foundation for Basic Research (grant 03-02-17135) and INTAS grant (YSF 2001-2/24).


Marc Durand

Jérémie Pourchez
email: pourchez@emse.fr

Bruno Louis

Jean-François Pouget

Daniel Isabey

André Coste

Jean-Michel Prades

Philippe Rusch

Michèle Cottier

Plastinated nasal model: a new concept

Keywords: anatomic model, nasal airway cast, plastination, maxillary sinuses

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

Introduction

Nowadays, nebulization is the preferred route for drug delivery in asthma and chronic obstructive pulmonary disease. As therapeutic agents can be delivered directly to the respiratory tract, the inhaled route offers smaller doses to be used and a more rapid onset of action compared to systemic therapy. In this context, the practice of nasal drug delivery by nebulization is also widely used in otorhinolaryngology, even if there is a lack of reliable data concerning the evaluation of its efficacy [START_REF] Bonfils | L'aérosolthérapie par nebulisation en oto rhino laryngologie[END_REF]. To more accurately define the relevance of nasal drug delivery, a better understanding of the deposition of nebulized drugs in the human nasal cavity is required. Aerosol deposition may be evaluated using different nasal replica.

In broad outline, three main families of human nasal casts can be distinguished: "pipe models" [START_REF] Möller | Ventilation and drug delivery to the paranasal sinuses: studies in a nasal cast using pulsating airflow[END_REF][START_REF] Cakmak | Effects of paranasal sinus ostia and volume on acoustic rhinometry measurements: a model study[END_REF][START_REF] Maniscalco | Sounding airflow enhances aerosol delivery into paranasal sinuses[END_REF], plastic replicas [START_REF] Schreck | Correlation between flow resistance and geometry in a model of the human nose[END_REF][START_REF] Kelly | Detailed flow patterns in the nasal cavity[END_REF] and models obtained from cadavers [START_REF] Hilton | Differential deposition of aerosols in the maxillary sinus of human cadavers by particle size[END_REF]. Unfortunately, these usual experimental casts show specific restrictions: "pipe models" may not adequately mimic the anatomy of the human cavity, plastic replicas can suffer from a lack of thin anatomical details (such as the sinus ostium morphology), and models from cadavers induce issues of time stability and biosecurity. Thus, we propose to create a new concept of functional human plastinated nasal cast.

Plastination permits the preservation of anatomical specimens in a physical state approaching that of the living condition. This technique was introduced by Dr. Gunther von Hagens in the end of 1970s [START_REF] Von Hagens | Impregnation of soft biological specimens with thermosetting resins and elastomer[END_REF]. This process consists in replacing water and lipids in biological tissue by curable polymers. Then, polymers are hardened resulting in dry, odorless and durable anatomic specimen. Nevertheless, plastination is usually restricted to descriptive and topographic studies of anatomy. That is why, the development of a specific plastination protocol is needed in order to create for the first time a plastinated human model devoted to functional studies (e.g. airflow and aerosol deposition experiments). To assess the relevance of our new concept of plastinated nasal models, some preliminary in vitro studies were performed. A first study highlights scintigraphic images of plastinated casts using a technetium (99mTc)-labelled solution to investigate the penetration of aerosols inside maxillary sinuses [START_REF] Durand | Preliminary study of the deposition of aerosol in the maxillary sinuses using a plastinated model[END_REF]. A second one allows to validate the ability of a Computational Fluid Dynamic (CFD) software describing pressure drop and flow [START_REF] Croce | In vitro experiments and numerical simulations of airflow in realistic nasal airway geometry[END_REF].

The technical specifications of the plastinated nasal model to develop are: anatomical features as close as possible to in vivo human airways, time-stability to perform experimental campaign during several years, water-washable to clean the specimen between tests, accessibility of the maxillary sinuses to assess the aerosol deposition, easy handling daily, dry odourless, biologically safe and transportable without restricted constraints. This study presents an original plastination protocol as well as clinical, geometric and aerodynamic characterisation of plastinated nasal airways models using several techniques (endoscopy, CT scans, acoustic rhinometry and rhinomanometry).

Materials and methods

Nasal specimens

Three nasal specimens were successively plastinated. We used adult heads, one female (specimen 1) and two males (specimens 2 and 3). On specimens 2 and 3, we carefully cut away the lateral wall of the maxillary sinuses leading to access inside. Different steps successively occurred (Table 1) during the plastination process: anatomical sampling, section, fixation, dissection, dehydration and degreasing, polymer forced impregnation in a vacuum, and then curing and polymerization.

Fixation and anatomical dissection

The first step of plastination consisted in anatomical sampling from a cadaver donated to the Anatomy Laboratory of Saint-Etienne University. The cadavers were obtained from deceased men or women whose last will and testament documented his wish to leave his body to the Anatomy Laboratory. The cadavers were clinically checked by a qualified ENT specialist prior to begin the anatomical sampling. After freezing the specimen at -80°C, a lateralparamedian section of the cephalic extremity may be carried out. This section allows to access of the maxillary sinuses which nevertheless keep a normal volume and aerodynamic behaviour. Besides, working only with this section offers also a significant time gain during the plastination procedure because of a fast penetration of solvents into the anatomical specimen. During the fixation step, the specimen was embalmed by immersion in a 10 % vol. formaldehyde solution so as to halt decomposition. Long fixation duration, around 3 months, was generally necessary to avoid tissue retraction phenomena during the polymer forced impregnation stage. The temperature was maintained at 5°C during this fixation process.

Dehydration and delipidation

Removal of fat and water from tissues of fixed specimen was the stage in which the specimens were immersed, under freezing conditions at -25°C, in several successive baths of pure acetone. The acetone was used as a degreasing and dehydration agent because this solvent was able to draw out all fats and water and replace them inside the cells. The specimens were passed through several baths of acetone until water and lipids content of the last acetone solution was less than 1%. Therefore, at least 4 baths of pure acetone were required to fully delipidate a cephalic extremity beforehand sectioned. Duration of each acetone bath varied between one and four weeks depending to the volume and tissue content of the specimen to be plastinated as well as the bath number. Between one and two months were generally necessary to satisfactorily dehydrate and degrease a specimen.

Silicon forced impregnation

Polymer forced impregnation under vacuum conditions was the key principle of plastination.

The temperature was always maintained at -25°C. We immersed the specimen in a silicon solution bath (S10 Biodur ® ) placed in a vacuum chamber. We gradually reduced the pressure until acetone boils. At this moment, acetone is vaporized and suctioned out of the tissue, and continuously extracted from the specimen. The resulting negative pressure causes the silicon solution to gradually permeate the tissue. A precise control of the depression applied versus time was therefore absolutely essential and necessitated specific know-how. The duration of the polymer forced impregnation was between 10 and 20 days.

Silicon Curing

After this impregnation, a gas curing takes place to polymerize silicon and thus to keep the polymer inside the specimen tissue. The gas curing was carried out at room temperature in a closed chamber. The hardening product (S6 Biodur ® ) was a liquid containing silicate with a high saturated vapor pressure. It evaporates and builds up a gaseous atmosphere inside the chamber. This active vapor reacts with the silicon at the specimen surface, and then the polymer begins side to side-linkage. Rapidly, the outer surface of the specimen was cured because of silicon polymerization. Over a period of time, the curing gas diffuses into the specimen and polymerization proceeds deeper. After a one month period in contact with the curing gas in a close environment, a final curing step begins. This final curing aimed at totally hardening the center of the specimen.

Anatomical and aerodynamic characterisation of plastinated nasal models

The overall objective of the anatomic and aerodynamic characterisation consisted in:

Checking by nasofiberoscopy the preservation of nasal airway anatomy during the plastination protocol.

Performing CT-scans observations of the final plastinated models to evaluate and improve the quality of the plastination procedure.

Evaluating the reliability of nasal cavity geometry (determined by acoustic rhinometry) and airflow resistance (measured by rhinomanometry) of the final plastinated models compared to in vivo data known from the literature.

The clinical anatomy study by nasofiberoscopic examinations (flexible Machida fiberscope, Japan) were performed in the three specimens during all the plastination process: from the anatomical sampling stage on the cadavers to the final curing step. This monitoring allows to early detect any problem on the specimen during the 6 months duration of the plastination procedure. Plastinated nasal models were also characterized using tomodensitometry (General Electric Prospeed Advantage Scanner with Sun Sparc Solaris console) in the three specimens.

These techniques were performed on plastinated models in order to evaluate the preservation of mucosa in the cast as well as to precisely define the geometrical characteristics of ostia and maxillary sinus cavities.

The geometry of nasal cavities was also characterized using acoustic rhinometry in specimens 2 and 3 [START_REF] Croce | In vitro experiments and numerical simulations of airflow in realistic nasal airway geometry[END_REF][START_REF] Louis | Airway area by acoustic reflexion: the twomicrophone method[END_REF].

Briefly, the device consisted of two microphones (piezoresistive pressure transducers 8510-B; Endevco France, Le Pré Saint-Gervais, France) and a horn driver mounted on a wave tube (inner diameter: 1.2 cm and overall length: 22 cm) connected at one end to a nostril of the model with a nosepiece, allowing tight closure of the nasal entrance.

The horn driver generated an acoustic wave, and the two microphones recorded the resulting pressure. These digitized data were analyzed to obtain the cross-sectional areas of the nasal airway as a function of the distance along the longitudinal axis, with a spatial step increment of ΔL ≈ 0.41 cm. Each nasal fossa of plastinated specimens was separately examined leading to the longitudinal area profiles from the tip of the nostril to the middle meatus region.

Results

Overall observations

In this paper we focused on 3 specimens allowing to exhibit the improvement of the plastination protocol with time (Fig. 1). Moreover, we obviously examined an improvement of subcutaneous and mucosa preservation between specimens 1 and 3. As a matter of fact, the specimen 1 perfectly showed a high tissue retraction because of bad polymer forced impregnation during first tests. On the contrary, the specimen 3 highlighted a very low tissue retraction and an astonishing preservation, certainly the closest possible to living tissue. Thus, these observations appeared as a sign of a significant improvement of the plastination procedure with time.

Nasofiberoscopy

The clinical anatomy study showed that the plastinated nasal specimens 2 and 3 were very similar to living anatomical conditions daily observed by ENT physicians. As a matter of fact, the coloration was clearly checked and all anatomical details were well-preserved. As an example, we clearly put in evidence in the specimen 2 a concha bullosa referring to the pneumatization of the middle turbinates of the right nasal cavity (Fig 2). Endoscopic observations also lead to confirm that the final plastination protocol, corresponding to the elaboration of specimen 3, guarantees an excellent preservation of nasal airways anatomy.

Tomodensitometry

CT scans confirmed the high preservation of nasal airway anatomy of specimen 3. On the one hand, 3D reconstruction and virtual endoscopy from imaging data exhibited high quality of anatomy closed to living conditions (Fig 3). On the other hand, we emphasized a significant increase of the mucosa thickness on the turbinates of the specimen 3 (Fig 3 and4). Thus, the mucosa preservation of the turbinates was higher in the case of specimen 3 thanks to the plastination procedure improvement. Finally, specimen 3 also exhibited very dissimilar maxillary sinus ostium morphologies (Fig 4). Indeed, while the right maxillary sinus ostium appeared as anatomically usual, the left maxillary sinus ostium was doubtless abnormally short and broad. In particular, the diameter of the left maxillary sinus ostium was three times higher compared to the right maxillary sinus ostium.

Acoustic rhinometry

The acoustic rhinometry was found to reasonably resolve the airways geometry of the plastinated casts. Concerning the specimen 2, characterized by pneumatised middle turbinate (i.e. a concha bullosa) in the right nasal cavity, the comparison of areas obtained by acoustic reflexion and by 3D reconstruction and then image analysis were previously described in [START_REF] Cankurtaran | Effects of the nasal valve on acoustic rhinometry measurements: a model study[END_REF].

Both methods provided a relatively good agreement mainly in the anterior part of the nose because of the acoustic method lead to overestimate the area lying beyond the ostium. The specimen 3 was also investigated thanks to this technique (Fig 5). Whatever the plastinated specimen examined, we always found a minimal cross-sectional area around 0.5 cm 2 and a cross-sectional area higher than 1.5 cm 2 from the middle meatus region.

Rhinomanometry

First of all, we measured the resistance of each nasal cavity separately while the opposite nostril was occluded. From the pressure vs flow curves, the unilateral airflow resistances found on specimen 3, for left and right nasal cavities, were perfectly similar at 0.18 Pa.s.cm -3 (i.e. 1.8 cmH 2 O.s.L -1 ). The bilateral airflow resistance was logically measured at a lower value compared to unilateral resistances, around 0.13 Pa.s.cm -3 . A similar investigation of airflow resistance was also performed on specimen 2 (Table 2). We found a rise of airflow resistance for the right nostril (0.21 versus 0.16 Pa.s.cm -3 for the left nasal cavity).

Discussion

Plastinated nasal casts versus living noses

To validate this new concept of anatomical realistic cast, the reliability of plastinated nasal model should be harshly examined by comparison with usual living anatomy as well as in vivo geometric and aerodynamic data of healthy subject. A plastinated model devoted to functional studies needs a specific plastination protocol. In fact, a main challenge consists in a plastination technique enables to ensure a very low degree of tissue retraction. Therefore, high nasal mucosa preservation remains a key point in order to provide conserved specimen with an appearance remaining close to live anatomy. Endoscopic and CT scans observations lead to show a significant improvement of the plastination procedure between the specimen 1 and 3. We also proved that our final plastination protocol, i.e. the elaboration of specimen 3, leads to an excellent conservation of nasal airways anatomy with a high mucosa preservation. We support the conclusion that the improvement of our plastination protocol with time allows to obtain plastinated specimen not too far from live anatomy.

Acoustic rhinometry is frequently used to determine in vivo the nasal cross-sectional areas through acoustic reflexion [START_REF] Louis | Airway area by acoustic reflexion: the twomicrophone method[END_REF]. It is a reliable and non invasive mean in order to assess the first six centimetres of the nasal fossa anatomy [START_REF] Cole | Acoustic rhinometry and rhinomanometry[END_REF]. Although this method has been used in clinical practice, some authors underline its potential limitations in the case of sudden large area changes in the space [START_REF] Tomkinson | acoustic rhinometry: an explanation of some common artefacts associated with nasal decongestion[END_REF], or about the cross-sectional areas posterior to a significant constriction [START_REF] Cankurtaran | Effects of the nasal valve on acoustic rhinometry measurements: a model study[END_REF]. The acoustic rhinometry, performed on specimen 3, emphasized a perfect symmetry of right and left nasal cavities from the nostril to the ostium of maxillary sinus (Fig 5). Moreover, if we compare the acoustic rhinometry results on plastinated models with data performed in vivo, the closest correlations have been noted between the plastinated nasal casts and the geometrical information obtained in healthy subjects after the application of a nasal decongestant. In particular, a good correlation was observed between the cross-sectional areas generated with the plastinated specimens 2 and 3 (Fig. 5) and postdecongested acoustic rhinometry data in healthy subjects described in [START_REF] Corey | A comparison of the nasal crosssectional areas and volumes obtained with acoustic rhinometry and magnetic resonance imaging[END_REF].

Rhinomanometry is a well-established and reliable technique that measures nasal patency in terms of nasal airflow and resistance to airflow [START_REF] Cole | Rhinomanometry 1988 -practice and trends[END_REF][START_REF] Coste | Protruding the tongue improves posterior rhinomanometry in obstructive sleep apnoea syndrome[END_REF]. The unilateral airflow resistances measured on specimen 3, for left and right nasal cavities, were similar. This tendency was consistent with the geometry of nasal cavity investigated by acoustic rhinometry showing identical longitudinal area profile for both left and right nasal cavities (Fig 5). We also emphasized a significant rise of airflow resistance for the right nostril of specimen 2. This asymmetry can easily be explained by the presence of a concha bullosa in the right nasal cavity of specimen 2. Besides, the measured pressure-flow relationship reflects the functional status of the nasal airway. Thus, this technique was usually carried out to measure the nasal resistance before and after surgery for nasal resistance. From the literature a consensus seems to be reached since an unilateral resistance greater than 0.35 Pa.s.cm -3 suggests clinically significant nasal obstruction. As a general rule, the nasal resistance can be categorized into four grades [START_REF] Soga | Upper airways morphology in patients with obstructive sleep apnea syndrome: effects of lateral positioning[END_REF]. From the clinical standpoint, the nasal resistance below 0.19 Pa.s.cm -3 corresponding to grade 1, indicates a subject free from nasal obstruction. Besides, above 4 Pa.s.cm -3 corresponding to grade 4 the airflow resistance indicates a subject suffering from the very severe or complete nasal obstruction. Regarding to this nasal resistance scale, as the unilateral airflow resistances obtained in the specimen 3 was around 0.18 Pa.s.cm -3 , the plastinated replica presents an airflow resistance similar to that of a decongested healthy subject.

Plastinated nasal casts versus other nasal replicas

According to the specific advantages and drawbacks of experimental nasal models found in the literature, we must examine if a human plastinated nasal model leads to a significant scientific breakthrough. To simulate nasal airways, experimental casts with increasing complexity can be used. The "pipe model" [START_REF] Möller | Ventilation and drug delivery to the paranasal sinuses: studies in a nasal cast using pulsating airflow[END_REF][START_REF] Cakmak | Effects of paranasal sinus ostia and volume on acoustic rhinometry measurements: a model study[END_REF][START_REF] Maniscalco | Sounding airflow enhances aerosol delivery into paranasal sinuses[END_REF] is usually a two compartment model where pipes represent nasal and sinus cavities. Following this overall strategy, Moller et al. elaborated a polyoxymethylene replica where sinuses were modelled by cylindrical glass vials [START_REF] Möller | Ventilation and drug delivery to the paranasal sinuses: studies in a nasal cast using pulsating airflow[END_REF]. Cakmak et al. developed a model consisting of a brass pipe with a short neck that branched off and opened into an enclosed cavity [START_REF] Cakmak | Effects of paranasal sinus ostia and volume on acoustic rhinometry measurements: a model study[END_REF]. Maniscalco et al. built a model composed of a syringe (representing the sinus) connected horizontally to a plastic cylinder (representing the nasal cavity) [START_REF] Maniscalco | Sounding airflow enhances aerosol delivery into paranasal sinuses[END_REF]. Although "pipe models" [START_REF] Möller | Ventilation and drug delivery to the paranasal sinuses: studies in a nasal cast using pulsating airflow[END_REF][START_REF] Cakmak | Effects of paranasal sinus ostia and volume on acoustic rhinometry measurements: a model study[END_REF][START_REF] Maniscalco | Sounding airflow enhances aerosol delivery into paranasal sinuses[END_REF] are very useful to collect data in a first approach, it remains unclear how relevant the data are to study in vivo drug delivery. Obviously, "pipe models" may not adequately mimic the complex anatomy of the human nasal cavities in vivo. Especially, these casts may underestimate the difficulty of getting nasally administrated drug beyond the nasal valve and front surfaces of the turbinate because of a lack of anatomical features. As a result, the plastinated nasal cast seems to be very useful to study aerosol depositions and is without doubt preferable to any "pipe model".

To improve biomimetic geometry of the experimental replicas, plastic/silicon models [START_REF] Schreck | Correlation between flow resistance and geometry in a model of the human nose[END_REF][START_REF] Kelly | Detailed flow patterns in the nasal cavity[END_REF] can also be reconstructed from medical imaging data. As example, Schreck et al. used magnetic resonance images (4 mm apart) to make a threefold-enlarged plastic cast of a left nasal cavity [START_REF] Schreck | Correlation between flow resistance and geometry in a model of the human nose[END_REF]. Computed tomography scans coupled with rapid prototyping technique allow to elaborate models such as the silicon right nasal cavity developed by Kelly et al. [START_REF] Kelly | Detailed flow patterns in the nasal cavity[END_REF].

Moreover, the plastic/silicon models [START_REF] Schreck | Correlation between flow resistance and geometry in a model of the human nose[END_REF][START_REF] Kelly | Detailed flow patterns in the nasal cavity[END_REF] reconstructed from imaging data significantly improve the biomimetic geometry of replicas. Some replica was created from a living person (i.e. from CT scans of the nasal cavities of an adult volunteer) and presents both nasal cavities for numerical simulations [START_REF] Pless | Numerical simulation is a method displaying a real environment within a computional model[END_REF]. Nevertheless these plastic/silicon models point out specific restrictions. Besides, the spatial resolution of imaging techniques (around some millimeters) as well as the smoothing procedure imposed by the reconstruction process, could considerably compromise the reliability of the very local anatomical details. Indeed, a three-dimensional reconstruction made from CT scans images too spaced may prevent the capturing of thin anatomical features, such as the maxillary sinus ostium whose internal diameter does not exceed 2-5 mm. Thus, this lack of very thin anatomical details observed in plastic models can strongly affect the replica behaviour especially in term of sinus ventilation or aerosol deposition in sinus cavities.

Finally, it certainly makes more sense to compare plastinated nasal casts with other models which are obtained from cadavers. As a matter of fact, these latter emphasize a high level of anatomical features. Nevertheless, they also induce specific issues of time stability (i.e. a relative short-term use to avoid tissue degradation) and biosecurity (i.e. with reference to handling, transportation, formaldehyde vapours ...) [START_REF] Hilton | Differential deposition of aerosols in the maxillary sinus of human cadavers by particle size[END_REF]. All things considered, to carry out dozens of experimental tests on a relatively long period (e.g. many months or years to develop new prototypes of nebulizers and to assess their aerosol deposition in specific nasal regions of a same human nose), the plastinated nasal cast is a very helpful tool. In other words the plastinated cast appears as an interesting compromise between on the one hand the anatomical quality of models from cadavers, and on the other hand biosecurity, stability and easy-to-use of plastic nasal replicas.

But the plastinated nasal replica exhibits some constraints. It is obvious that the vasoactive role of the mucosa present in living tissue can never be reproduced by plastination technique.

Besides, by contrast with plastic replica, nothing can be temporarily removed from such a plastinated cast (e.g. the inferior turbinate or the uncinate process) to study the effects on flow and cross-sectional. Only addition can be made, for instance to enhance the thickness of the mucosa. However, to assess the impact of some anatomical parameters, "pathologic" nasal specimens (with cartilaginous deviation, functional surgery designed to enlarge the nasal fossa) can be plastinated and thus results are compared to data obtained on "normal" plastinated nasal casts. We must underline that the main drawbacks of plastinated replicas are the high-duration to elaborate one cast (around six months) as well as the specific plastination know-how needing many years of operational experience. Considering this limitation, even if approximately 150 laboratories in the world frequently use the plastination technique, the plastinated nasal cast is not a tool which can be applied easily and quickly without previous experiences on plastination procedures. Nevertheless, the authors build relationships with a wide range of stakeholders and research groups to encourage and promote know-how transfer and experience sharing. We hope that this knowledge dissemination activities dealing with this specific plastination technique will allow the plastinated nasal casts to become more and more accessible. However, even if plastination appears as a tedious and complex technique, we support the conclusion that plastinated human nose casts allow to a significant scientific breakthrough compared to existing experimental nasal replicas.

Conclusion

A novel anatomically realistic nasal cast with bilateral nasal cavities, based on plastination technique, was found suitable. We demonstrate that the nasal plastinated model allow to avoid tissue retraction as well as to well preserve anatomical details. The comparison of the geometric and aerodynamic characteristics of the specimen 3 with in vivo data clearly indicates that the plastinated cast acceptably match a decongestant healthy subject. All things considered, we succeed to develop a cast with similar advantages of models from cadavers (e.g. high anatomical quality, biomimetic airways geometry and airflow resistance) but without theirs specific drawbacks (e.g. low time-stability, biosecurity issues).

By way of conclusion, the development of anatomically realistic plastinated nose models with bilateral nasal cavities is certainly a valuable tool to bring a sound-knowledge of the accurate role of anatomical parameters (ostium morphology, functional endoscopic sinus surgery) to differential deposition of aerosols in the maxillary sinus by particle size, or to validate CFD software which will be used to predict the functional effect of a treatment (e.g. functional surgery designed to enlarge the nasal fossa …).

Finally

  , rhinomanometry was used to provide an objective quantification of nasal airway resistance in specimens 2 and 3. Steady flow was measured with a Fleisch pneumotachograph (Lausanne, Switzerland) coupled to a differential pressure transducer (Validyne DP45, Northridge, CA) by short tubes allowing to estimate the pressure drop. Inspiratory flows for the three different gases were generated by a negative pressure generator made of a turbine rotating at a constant adjustable speed which was connected to the nasopharyngeal extremity of the plastinated airway model. Each nasal cavity was investigated individually. The pressure difference and transnasal airflow were simultaneously measured. The aerodynamic resistance was defined as the ratio of pressure drop across the nose over the volume rate of nasal airflow, when the transnasal pressure reached 1 cmH O. To measure the airflow resistance of the right nasal cavity, maxillary sinus cavity were in "closed" position and the left nostril was 2 occluded.

Figure 1 :

 1 Figure 1

Figure 2 409 410 Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 24102345 Figure 2

Table 1 400 Main stages of the plastination process Keypoints of each stage Global duration of each stage

 1

	Anatomical sampling	Post-mortem deadline within 24 hours	∼ 3 hours
	Lateral section of specimens	Freezing at -80°C	∼ 3 days
	Fixation and dissection	Embalming by immersion at 5°C in a 10 % formaldehyde solution	∼ 3 months
	Dehydration and degreasing	At least 4 successive baths of pure acetone at -25°C	∼ 1-2 months
	Polymer vacuum-forced impregnation	Immersion of the specimen in a silicon bath at -25°C, well-controlled depression applied	∼ 10-20 days
	Polymer hardening	Two step curing process and frequently manicured of the specimen when polymer oozing	∼ 2-3 months
	401

Table 1 :

 1 Overall description of the plastination procedure developed.

Table 2 :

 2 Comparison of airflow resistance investigated by rhinomanometry obtained on specimens 2 and 3.


P Breil

M Lafont

A Vivier

Ph A Namour

L Schmitt

EFFECTS OF COMBINED SEWER OVERFLOWS ON A PERIURBAN STREAM ECOSYSTEM : Methodological approach

Keywords: (Peri)urban development, Combined Sewer Overflows (CSOs), aquatic ecosystem, resilience

Here we develop from a long term field experiment an assessment method of interstitial fauna resilience to combined sewer overflows (CSOs) effect. We address the case of "small water courses" for which the ratio of CSOs to natural flow can be 1 to much more. Biotic material was collected in the benthic and hyporheic layers. Biotic material focussed mainly on oligocheates species whose diversity, species category and abundance are resumed into metrics, called functional traits (FTrs), giving indications on flux dynamics and nutrient bio-assimilation capacity. The biotic resilience is assessed through the analysis of the response time of the biota to CSOs and natural flow characteristics, here called hydrological indices (HIs). In this aim, a series of hydrological indices are defined to reveal varying aspects of the dynamics of CSOs and natural flows. A main result is that CSOs can have both degrading and boosting effects on the biota of a stony stream. Some CSOs characteristics can explain the physical processes supporting these contrasting effects. In particular the geomorphic characteristics of the water course. Management perspectives emerge from the CSOs hydrological indices and resilience of the biota.

INTRODUCTION

The total length of separated and combined sewer network in France is estimated to 250 000 km (OIE, 2006). From this length, 43% are made of combined systems where domestic and urban runoff waters are mixed together during wet weather periods. Combined systems are equipped with CSOs' devices to avoid overflows on streets or house basement during storm events with intense rainfall. Exceeding waters are often directly released to streams or ponds. Combined system was historically developed in France in large towns when separated was lately mainly used in rural areas. Giving the global trend of the urban development throughout the word, and particularly in periurban areas (UNEP, 2003), we can observe that old combined systems must carry more and more waters coming from surrounding areas. It results in an increase of the CSOs impact on receiving waters. At the same time countries of the European Union are expected to manage their water resources in the aim to reach and maintain a good ecological status (EU, Directive 2000). For highly modified water masses like in urban and periurban areas, the objective of a maximal ecological potential must be defined and reached. Concerning CSOs, it exists a range of ecological situations depending on the quality, quantity and frequency of overflows. The CSOs discharges can reach ten folds the receiving stream discharges, that result in a great ecological impact.

The ecological status in water courses (European Union 2000) is related to the water quality, the geomorphic and hydrological features integrity and the biotic quality. Any ecological impact is assumed to result from an alteration of one or some to all of these components of the aquatic ecosystem. CSOs can affect both the water quality (organic and toxic substances) and the physical quality by eroding banks and aquatic habitats. In addition, they are also introducing pathogens in the natural biotope. CSOs water quality, quantity and frequency can vary depending on dry periods durations and human activity (holidays, seasons). In the case of streams, the flow variability can be greatly affected by CSOs, particularly when their discharges is greater than that of the stream. To assess their ecological impact it is necessary to develop a method that enables relating biotic data to their habitat flow conditions.

We consider here small watercourses that can be met around large cities which have been built along large rivers, a common case in Europe. The aim of this paper is to identify constraining flow features when addressing the question of CSOs ecological impact and mitigation in stony periurban streams. Such features can be related to the resilience capacity of the receiving system. Biotic, flow and water quality data come from an experimental reach of a seasonally stream (the Chaudanne) located in the periurban area of Lyon (France). We hypothesize that flow variability is considered as the major driving force governing water fluxes and aquatic habitats (cite references!!).

METHODOLOGICAL APPROACH

Biological assessment

The biological assessment is based on oligochaete assemblages collected in porous habitats (coarse surficial sediments and hyporheic system) (Lafont et al. 2006). Four sites located in a small water course were sampled fourth a year during six years. Site 1 was the reference upstream site next to the source. Site 2 was 50 metres upstream a CSO device. Sites 3 and 4 were located 50 and 500 metres downstream the same CSO device. Surficial (or benthic) sampling are referred later as S3 and S4 and Hyporheic as H3 and H4. The examination of oligochaete assemblages enabled us to distinguish between 4 biotic metrics called functional traits (FTrs). The FTr1 "permeability" is obtained by measuring the proportion (%) of oligochaete species which are indicators of active water exchanges between surface and groundwater (AED species, Lafont & Vivier 2006). The FTr2 is defined by the percentage of pollution-intolerant oligochaete species and is associated with good chemical quality of waters (Lafont et al. 2006). The FTr3 is defined by the percentage of water pollution-tolerant species. It is associated with poor chemical quality and particularly with high nitrate and ammonium salt contents. The FTr4 ("sludge effect") is defined by the percentages of species living in fine sediment and sewage bacterial-bed. It indicates the presence of polluted sludge within sediment interstices, with very high ammonium salt contents, low nitrate concentrations and the significant presence of heavy metals (copper, zinc and lead). The gradient of FTrs has been validated through a range of water courses across France (Vivier, 2007). The association FTr1 + FTr2 is recorded at sites with slight or without pollution (high water exchanges and good chemical quality). The association FTr3 + FTr4 is characteristic of ecological alterations, and the FTr4 strongly predominated in the most impaired situations. FTrs can compensate each other revealing the ecological quality moved along a gradient but this is not systematic because FTr1 is mostly a physical indicator, FTr2 a water chemical when FTr3 and FTr4 are pollution and trophic resource indicators.

Biota response time

Giving the fact that living species can integrate past habitat conditions in their behavior, correlations with instant habitat conditions from the sampling moment are not adapted. This issue was addressed developing a computer routine to calculate a series of antecedent hydrological indices(HIs) into incremented periods backwards from each sampling date. The Preceding Period Duration (PPD) is expressed in day unit. In the aim to scan a range of past aquatic habitat conditions the PPD was incremented with a duration step of 10 days till 120 days before each biotic sampling date. It resulted into 12 PPDs. It allowed us to examine the effect of each hydrological indices from 10 days before to 120 days before the date of biotic sampling. The objective was to identify what hydrological indices in the past were the most able to explain the observed ecological quality. Spearman rank correlation coefficient was calculated for each PPD. Correlations were computed using each functional trait (FTs) as the dependant and each hydrological indices as the independent variable. It resulted in a table of 12 PPDs by 4 FTrs for each of the 4 sampling location S1, S2 , H1 and H2. Such a table was computed for each of the 13 hydrological indices (HIs).

Results were interpreted as follow : only R correlation value over 0.5 with a significance level of 2% were retained for interpretation. The maximum of correlation (when observed) should belong to a series of continuous values to avoid any fortuitous (isolated) correlation with consecutive PPDs. We retained a minimum of 3 consecutive values as a threshold. According to the mentioned conditions we used R versus PPDs plots to asses the biota response time. It was considered to correspond to the maximum R value(Fig. 1). Also the sign of each significant correlation was interpreted in terms of improvement or degradation effect of HIs on FTrs. In the case of a constant R value over several consecutive PPDs two cases were examined. A near constant R value reveals there are only slight changes in some HIs' values when the PPD increases. It happens mainly for HIs corresponding to an extreme flow characteristics that occurs only once over the PPDs. In that case we consider the shorter PPD to be the response time (Fig. 1). Constant R value was also observed for mean (or cumulative) flow characteristics. It indicates that kind of HIs have an homogeneous distribution along the PPDs. The persistence of the corresponding flow conditions can explain the persistence of the correlation value. The response time was then estimated to be the larger PPD value of the constant R sequence.

R

Hydrological indices (HIs)

Natural flow and CSOs time series were computed individually to generate 13 flow characteristics, each being calculated on a same PPD. They are divided into 3 categories:

-8 HIs give CSOs features like magnitude, amount, number, and duration. In this set 5 HIs are dedicated to the greater (in magnitude) observed CSO peak in the PPD. They are Qmax (magnitude), Vmax (the volume of the event), Dmax (the duration), D_qmax (duration between Qmax and date of sampling) and Rmax (log ratio of Qmax to the natural mean flow). This last indicates the diluting capacity of the water course. The maximum CSO event can have both a chemical and a mechanical effect on the biota. It can also be followed by a natural flood in the water course which tends to reinforce its effect. The other 3 HIs of this category tend to resume all CSOs information. They are Vtdo (total CSOs volume), Ttdo ( total duration of CSOs) and Ndo (number of CSOs).

-4 HIs relate to periods without CSOs. They intend to express the "dry weather" effect on the ecological status evolution in the water course because CSOs result from rainfall events. Such dry periods allow the accumulation of pollutants on impervious areas and the development of biofilms in the sewer pipes. It can then can contribute to the ecological impact of CSOs that follow it. It can also support the natural improvement of the ecological status of the water course during the dry period. HIs are Ntsec (number of dry weather periods), Tsec (total dry weather duration), Tsecx (maximum duration of a continuous dry period), Tsecxx (dry weather duration just previous to Qmax),

RESULTS

Biotic metrics

As expected, the oligochaete assemblages exhibited an increasing alteration of the FTr associations from the upstream site 1 top site 4. FTrs moved from FTr1 + FTr2 to progressively FTr3 + FTr4 and last by the large predominance of the sole FTr4 at site 4 (Lafont et al. 2006;[START_REF] Vivier | Effets écologiques de rejets urbains de temps de pluie sur deux cours d'eau périurbains de l'ouest lyonnais et un ruisseau phréatique en plaine d'Alsace[END_REF]. But the ecological effects were surprisingly the most acute at the last site far downstream the CSO and more pronounced in the hyporheic system than in the benthic sediments. Also surprising was the biological quality of the site 3 located 50 m below the CSOs which was not significantly different from that at site 2 (50 m above the CSOs).

For example, the evolution of the FTr4, which is characteristic of heavy ecological alteration in sediments, showed that it was generally more marked in the surface coarse sediments at site 4 only when CSOs occurred during low stream discharge periods (end of June 2000, August and October 2000). But the FTr4 was constantly occurring in the hyporheic system at this site, and not at the site 3 (50 m below the CSOs). In addition, at the site 3, the FTr4 was always low in the hyporheic system and less marked during low stream discharges in surficial sediments than at site 4. As an attempt to give an explanation to those conflicting results, we considered the statistical relations between the various selected hydrological indices and the functional traits at sites 3 and 4.

Hydrological indices (HIs)

Only results for HIs selected under the conditions given in §2.2 are presented. Whether maximum correlation value are not exceeding 0.89, one can argue that trends in correlations are confirmed by (i) the continuity of R values over 0.5 and (ii) that no change along PPDs in the sign of the R correlation coefficient has been observed. This later observation confirms the non ambiguous effect of a given HI on the improvement or degradation of the ecological status. The table 1 gives a synthesis of the R values. Dark and grey cells respectively indicate a positive (+) and a negative (-) correlation sign. The ecological quality improves from FTr4 to FTr1. Hence a positive correlation with FTr1 and FTr2 indicates the corresponding HIs are factors of ecological improvement (and reverse). On the contrary, a positive correlation with FTr3 and FTr4 indicates the corresponding HI is a factor of ecological degradation. FTr2 and FTr3 correspond to a gradient of water quality. They must be interpreted respectively with FTr1 and FTr4. In accordance to remarks from §2.2, the biota response time to flow conditions has been estimated. It is indicated by a cross into cells of table 1. Table 1. Spearman coefficient sign (dark = positive; grey = negative) for the rank correlation of functional traits (FTrs) versus hydrological indices (His). Biota response time estimation (cells with a cross).

In the benthic layer S3 only the FTr1 correlates positively with Rmax and Qmax which are indicators of a maximum CSO event. The ecological quality is improving 20 to 30 days after the event. The associated process can be the renewal, mixing and aeration of the surface sandy substrate during the event.

In the benthic layer S4 the good ecological quality improvement (with FTr1) is again explained by Qmax, Rmax and Vmax. The response time is short only for Rmax (20 days) when it rates 70 days for Qmax and Vmax. FTr2 correlates also positively after 50 days, then before FTr1, with Vmax. Referring to §2.1, this indicates the ecological quality is improving with time. We can argue for the same physical cleaning process than for FTr1 at S3. The poor water chemical quality indicator FTr3 increases with Qbmo, the mean natural flow, since 60 days before the sampling date. At the same time the "polluted sludge" indicator FTr4 regresses also with Qbmo since 70 days before the sampling date. This temporal gradient of ecological and water quality improvement (from FTr4 to FTr3) probably results from the good quality water renewal in S4 during persistent natural flow conditions. Such conditions are related to important rainfalls that can generate great CSOs as the correlation with Qmax, Rmax and Vmax tends to confirm. FTr3 can also regress with Tsecx, the maximum dry sequence observed 50 days before. It globally means that ecological quality at S4 can improve in the absence of CSOs and the persistence of a natural flow.

The hyporheic layers H3 and H4 are all correlated with D_qmax. Correlation signs are negative for FTr1 and FTr2 at H3. It means that longer is the time of the dry sequence before a major CSO, larger is the degradation of the ecological quality. It can be explained by the fact that pollution accumulates on urban surfaces and develops in sewer pipes during dry sequences. Then the amount of pollution a CSO can deliver can be great. Surprisingly, the ecological quality seems to be improved at H4 because larger is the dry sequence smaller is FTr4 and larger is FTr3. In fact, site 4 is a natural deposit site and a long dry sequence seems to improve the ecological quality of this site. Thus H3 seems to be more sensitive to large pollution loads linked to large CSOs and H4 seems to be more sensitive to frequent CSOs with medium pollution load.

In the hyporheic layer H3 improvement of ecological quality is again linked to Qmax, Rmax and Vmax for FTr1 and Vmax, and Ndo for FTr2. The physical effect of maximum CSO has already been discussed. The biota response time for Ftr1 and Tr2 with Vmax again illustrates the gradient of improvement which starts at 50 days for Ftr2 and at 60 days for FTr1. The improving effect of the number of CSOs (Ndo) on H3 can be explained by the associated flow variability. This variability induces variable water head gradients in banks and substrates of the water course not far from the CSO device like for site 3. It would emphasize the exchange of water between the surface and hyporheic layers [START_REF] Breil | Assessing stream bio-assimilation capacity to cope with combined sewer overflows[END_REF]. Then the just downstream CSO receiving waters would benefit from frequent inputs of nutriments but also from an activation of the biotic metabolism in the water course substrates. For TRF3, Ttdo and Ttsec are both correlated for the same PPDs but with opposite signs. This is because these HIs are strictly complementary to the total duration of each PPD. It means the ecological quality is improved as the total duration of CSOs increases. This is in accordance with the effect of Ndo on FTr2 as exposed before. The biota response time is however longer (110 days) than for FTr2 (40 days) which can illustrate the kinetic of cleaning processes in the FTrs. FTr4 is always negatively correlated to Ndo, Qmax and Vmax for this layer. Again the ecological quality is improved when CSOs number increases and large CSOs occur. This is in conformity with other correlated FTrs in this layer.

In the hyporheic layer H4 the ecological quality is again improved by Qmax, Rmax and Vmax both for TFr1 and TFr2. It confirms site 4 requires great CSOs event to be cleaned. Also biota response time is larger than for site 3. A great CSO event is normally followed by a natural flood in the water course. The S4 layer is then cleaned or removed which can reconnect surface and hyporheic waters. This process can explain a longer time of response and improvement of the biota.

DISCUSSION

Mean response time of FTr1, FTr2, FTr3 and FTr4 are respectively of 57, 65, 92 and 81 days. It indicates the most reactive FTrs are FTr1 followed by FTr2 which depend mainly on flow transfer capacity (see §2.1.). Then come FTr4 and FTr3 which take on average 30 days more to be reflected by the biota. An explanation would be that biotic metabolism are slower to reduce pollution than only physical based processes that are inherent to FTr1 and FTr2. The mean response time values of S3, H3, S4 and H4 layers are respectively of 25, 73, 56 and 88 days. It indicates the effect of HIs requires longer time to be reflected by the biota living in the deeper porous media (H3, H4). Several explanations arise : it can result from the lower flow velocity in the deeper layers or from the lower kinetics of the biotic metabolism in these layers or either from the predominance of physical mechanisms, like scouring, in the surficial layers. Also the time of response increases going downstream from site 3 to site 4 when comparing the same layers. This is quite understandable as the pollution can accumulate and be removed from place to place through time. We must also consider the bottom gradient is lower at site 4 than at site 3, which facilitates deposits of pollutants from the water column an transported substrates. As all the TFrs were present in each layer excepted for S3 our result can be interpreted as follow : the resilience capacity of the studied aquatic ecosystem is governed both by physical and biological factors. Two months on average are necessary to get an improvement of the ecological quality when there is only a slight to moderated pollution level. The management of flow dynamics (and water quality) would be sufficient to recover a good ecological quality Three months are required for more impacted situations. In that case, natural metabolism should be give more time to bio-assimilate the pollution load. It would be implemented using a storm water detention tank with adequate management rules.

In stony streams, it is now well-recognized that the dynamics of hydrologic exchanges between surface water and groundwater greatly stimulate the nutrient cycling [START_REF] Jones | Streams and Ground Waters[END_REF][START_REF] Boulton | Rivers as groundwater-dependent ecosystems: a review of degrees of dependency, riverine processes and management implications[END_REF]. When the stream-bed is impervious (artificial concrete bed), the transport of pollutants prevails, but pollutants may be stored in downstream areas. In particular, pollution discharges excessive to the size of the receiving aquatic habitat induce downwellings of surface polluted water and storage of pollutants in the hyporheic layer of gravel streams [START_REF] Ruysschaert | Assessment of the hyporheic fluxes in a headwater stream exposed to combined sewer overflows[END_REF]Lafont et al. 2006;[START_REF] Breil | Assessing stream bio-assimilation capacity to cope with combined sewer overflows[END_REF]Breil et al., in press). Management practices have to account for this pollutant storage, which is a time-bomb triggered off by the occurrence of environmental conditions favourable for pollutant release (e.g., upwellings of polluted hyporheic waters up to the surficial sediments). In addition, the geomorphic context is strongly related to the dynamics of hydrologic exchanges between surface and groundwater, and geomorphic typologies become now essential tools that are integrated in management schemes (Schmitt et al. 2006, Schmitt et al. in press). The already-mentioned conflicting results between sites 3 and 4 of the Chaudanne stream cannot be explained if we do not refer to the hydrological and geomorphic contexts.

The derived management perspectives for stony periurban streams must take into account all those results. All our results tended to demonstrate that it is a simplistic view to consider that the alteration of oligochaete assemblages was only related to the presence of a polluted inflow and that the detrimental effects must be more acute nearby the pollution source. In addition, if one considers the surface sediments only, that is generally the case in current biomonitoring studies, the storage of pollution in the hyporheic layer is not overseen. The monitoring of both surface and hyporheic layers might be an indispensable first step to understand the functioning of streams [START_REF] Boulton | River ecosystem health down under: assessing ecological conditions in riverine groundwater zones in Australia[END_REF][START_REF] Boulton | Imperilled subsurface waters in Australia: Biodiversity, threatening processes and conservation[END_REF], in particular to assess the pollution storage in the hyporheic layer (Lafont & Vivier, 2006;Lafont et al. 2006). This pollution storage is a deleterious "time bomb" for biodiversity, particularly because it is underestimated or even ignored (Lafont et al., in press). An example of those recommendations is given here under : i) preserve or rehabilitate the geomorphic type of each site, the hydrologic connectivity and the dynamics of hydrologic exchanges between surface water and groundwater, ii) prevent pollutant storage in the hyporheic layer: no inflows in areas were downwellings of surface water predominate, either for natural (geomorphic type) or artificial causes (imperviousness of surrounding landscapes, water streaming, alteration of the hydrologic regime…); iii) avoid excessive pollution discharges with respect to the size of the receiving aquatic habitat, a minimum stream discharge must be preserved; which depends on the local hydrologic pattern; iv) where preserved areas exist provide hydrological connections between those areas, v) permit pollution inputs only if the resilience domain is preserved vi) check every year the efficiency of remediation measures and sustainability of the resilience domain by biomonitoring tools that integrate the effects of both physical and chemical alterations, like FTrs.

CONCLUSION

However, the results gained from the study of the Chaudanne stream cannot be strictly extrapolated to other streams because the hydrologic and geomorphic patterns are changing from a stream to another one. On the other hand, general but operational recommendations for management schemes can be derived from the study of the Chaudanne stream [START_REF] Vivier | Effets écologiques de rejets urbains de temps de pluie sur deux cours d'eau périurbains de l'ouest lyonnais et un ruisseau phréatique en plaine d'Alsace[END_REF].

The dorsal bone of the management schemes is to promote that hydrologic and geomorphic backgrounds bear the same importance as chemical inflows, but that the eradication or severe limitation of polluted inflows is the first step that must be performed. After sources of pollution has been eradicated or limited, it becomes necessary to preserve the resilience of the system. A realistic objective might be to define the "resilience domain" (Lafont et al., in press), in which assimilation processes (= nutrient cycling) are most efficient. Within this domain, the system quickly rehabilitates when the pollution load has been severely reduced. The term "quickly" implies that rehabilitation might be achieved over a reasonable time, such as one year after significant pollution reduction [START_REF] Vivier | Effets écologiques de rejets urbains de temps de pluie sur deux cours d'eau périurbains de l'ouest lyonnais et un ruisseau phréatique en plaine d'Alsace[END_REF].

figure 1 :

 1 figure 1: Method to asses the biota response time to past water flux characteristics. Plot of R value versus time before date of sampling (PPD).

  -1 HI corresponds to the mean natural flow of the water course. It relates also to the diluting and cleaning capacity of the water course. Ndo and Ntsec like Ttdo and Ttsec are complementary numbers or durations for a given PPD. It means they should have same R correlation values but with converse signs.

UNESCO Headquarters, Paris, FRA, 12-14 September 2007

Acknowledgements

We thank the Field Observatory in Water Management (http://www.Graie.org./othu/) for providing technical support and data from the experimental site of la Chaudanne. UNESCO also contributed to this work by the way of an international project gathering experts on urban river management.