C Julcour

R V Chaudhari

J M Le Lann

A M Wilhelm

H Delmas
email: henri.delmas@ensigct.fr

Dynamic modeling of three-phase upflow fixed-bed reactor including pore diffusion

Keywords: fixed-bed reactor, dynamic modeling, internal diffusion, multistep hydrogenation

The dynamics of a three-phase upflow fixed-bed reactor are investigated using a non-isothermal heterogeneous model including gas-liquid and liquid-solid mass transfer and diffusion / reaction phenomena inside the catalyst. The partial differential and algebraic equations (PDAE) involving three integration variables (time and two space coordinates) are solved via discretization of the spatial coordinates coupled with the Gear method. For a multistep hydrogenation on a shell catalyst the model exhibits significant effects of the external and above all internal resistance to hydrogen transfer but also non trivial internal hydrocarbons concentration profiles. A simplified model is compared to the extended one and to experimental data in transient regime. In the investigated conditions -hydrocarbons in large excess -the diffusion of hydrocarbons appears to be actually not limiting, so that the simplest model predicts accurately the transient reactor behavior.

INTRODUCTION

In order to improve the performances of three-phase fixed-bed reactors, several recent papers have studied unsteady-state ways to operate, for instance by imposing periodical variations on the gas or the liquid flow rate (Lange et al. [START_REF] Lange | Investigations of periodically operated trickle-bed reactors[END_REF] and Gabarain et al. [START_REF] Gabarain | Analysis of rate enhancement in a periodically operated trickle-bed reactor[END_REF]). For that purpose, models investigating the dynamic behavior of the reactor are useful, as well as to assess the reliability of the model parameters in limit cases (such as hot spot or runaway). However corresponding literature is quite sparse. Visser et al. [START_REF] Visser | Dynamic operation of a three-phase upflow reactor for the hydrogenation of phenylacetylene[END_REF] and Lange et al. [START_REF] Lange | Forced periodic operation of a trickle bed reactor[END_REF] used dynamic models to evaluate conversion and/or selectivity improvements due to forced periodical variations of the gas composition or the liquid flow rate. Wärna et al. [START_REF] Wärna | Dynamic modelling of catalytic three phase reactors[END_REF] simulated the start-up period of fixed-bed reactors in nonisothermal conditions. In a previous article (Julcour et al. [START_REF] Julcour | Dynamics of a three-phase upflow fixed-bed catalytic reactor[END_REF]) we also examined numerically transient concentration and temperature profiles obtained during the start-up of a co-current upflow reactor or consecutive to flow rate steps. All those models considered the catalyst pellet as a gradientless volume and did not investigate the effects of internal diffusion on the reactor dynamics.

The objective of this work is to examine in details the transient concentration (and temperature) profiles at the pellet and reactor scale for a reaction highly limited by the diffusion of the gaseous reactant: the hydrogenation of 1,5,9-cyclododecatriene on a 0.5 % Pd/Al 2 O 3 shell catalyst. In this model we will consider both the transient diffusion of hydrogen and hydrocarbons inside the pellet (inert support and active layer) and we will investigate their respective roles. The results at the reactor scale will be compared to the predictions of the model developed in the previous article and to experimental measurements obtained with a co-current upflow reactor.

EXPERIMENTAL

INVESTIGATED REACTION

The partial hydrogenation of cyclododecatriene (CDT) in cyclododecene (CDE) was selected as a complex reaction involving constraints of exothermicity and selectivity. The cyclododecatriene used in this work was found to contain three isomers: more than 97% cis,trans,trans-CDT, around 2% trans,trans,trans-CDT and 0.5% cis,cis,trans-CDT. The products of the reaction are respectively: cyclododecadiene (CDD), cyclododecene and cyclododecane (CDA). A simplified reaction scheme lumping isomers may be written as follows:

CDT CDD CDE CDA H 2 r 1 H 2 r 2 H 2 r 3  →    →    →   (1)
Cylindrical alumina pellets of 3.1 mm diameter coated with palladium over a depth of 250 µm (Degussa, E263/D, 0.5% Pd) were used as a catalyst.

The experimental investigation of the kinetics was performed by Stüber et al. [START_REF] Stüber | Partial hydrogenation of 1,5,9cyclododecatriene in three phase catalytic reactors[END_REF] and more details can be found in the related paper.

For the intrinsic kinetics (measured with crushed pellets of mean diameter less than 10 µm), an Eley-Rideal model was selected:

∑ = = = + = 3 1 j j j H i j i j i i C K 1 C C K k R i α 2 ( 2
)
where i is the reaction number, and j is the component number ( j = 1: CDT, 2: CDD, 3: CDE). The Arrhenius and Van't Hoff laws define the rate constants k i and adsorption constants K j :

( ) ( ) k k exp E RT and K K exp A RT i i,0 i j j,0 j = - = - .
The corresponding kinetic parameters are given in Julcour et al. [START_REF] Julcour | Dynamics of internal diffusion during the hydrogenation of 1,5,9-cyclododecatriene on Pd/Al 2 O 3[END_REF].

The same type of model was found to be suitable to describe the apparent kinetic law i ' r measured with 3.1 mm diameter pellets. The parameters of apparent kinetics are reported in table 1.

CDE CDE CDD CDD CDT CDT α H i j i j i i C K C K C K 1 C C K k r' i 2 + + + = = = (kmol/kg cat /s) Frequency factor (kmol 1-α ×m L 3α /s/ kg cat ) Activation energy (kJ/kmol) Adsorption constant (m L 3 /kmol) k 1,0 = 13.187 α 1 = 1 E 1 = 34.9×10 3 K CDT = 100 k 2,0 = 7.016 α 2 = 1 E 2 = 30.4×10 3 K CDD = 22.81 k 3,0 = 2.049 α 3 = 1.312 E 3 = 25.4×10 3 K CDE = 10.80

FIXED-BED EXPERIMENTS

The experimental results mentioned below were obtained in a jacketed packed bed reactor (D R = 0.026 m, L R = 1.5 m), filled with the Pd/Al 2 O 3 pellets and operating in co-current upflow mode. Pt100 probes located along the reactor provided axial temperature profiles. Liquid samples were also taken at different heights and analyzed by gas chromatography to measure axial concentration profiles. The complete experimental unit and the start-up procedure were described in a previous paper (Julcour et al. [START_REF] Julcour | Dynamics of a three-phase upflow fixed-bed catalytic reactor[END_REF]). Experimental runs were performed at a pressure of 4 bars and at high temperatures (above 433 K). Liquid velocity varied from 3×10 -4 to 10 -3 m/s, and gas velocity from 0.03 to 0.12 m/s: according to the flow pattern established by Stüber [START_REF] Stüber | Sélectivité en réacteur catalytique triphasique : analyse expérimentale et théorique d'hydrogénations consécutives en lit fixe catalytique à co-courant ascendant de gaz et de liquide[END_REF] with the same reagents and reactor, those conditions correspond to the pulsing regime.

DYNAMIC MODELING OF THE THREE-PHASE CATALYTIC UPFLOW REACTOR

Non-isothermal heterogeneous models were chosen to account for both mass and heat transfer limitations at the gas-liquid and liquid-solid interfaces and the heat exchanges through the reactor walls, including the thermal balance of the cooling fluid.

FUNDAMENTAL ASSUMPTIONS

The dynamic modeling of the fixed-bed reactor is based on the following assumptions:

1. Radial gradients are negligible: the ratio of reactor diameter (0.026 m) to reactor length (1.5 m) is indeed very small, and this hypothesis has been confirmed by radial temperature measurements.

2. Plug flow is assumed for the gas phase, but liquid axial dispersion effects are taken into account.

3. The vaporization of the hydrocarbons is not considered due to their very low vapor pressures (a thermal balance on the whole reactor shows that the heat flux generated by vaporization is less than 5% of the one produced by the reaction in standard operating conditions). The dissolution enthalpy of hydrogen is totally negligible.

4. Heat transfer to the inner jacket wall is assumed to occur through the liquid phase only.

The outer jacket wall is supposed to be perfectly insulated. Walls are assumed to be at a uniform average temperature.

5. The catalyst wetting is complete.

6. In the investigated conditions the effective reaction rate is drastically reduced by the diffusion of hydrogen (limiting reagent) inside the catalyst pores. The effectiveness factor, ratio of the actual reaction rate to the intrinsic one (without diffusion limitation), is about 1%.

In order to take into account this diffusion limitation, two approaches are proposed:

-the first one (model I) describes the transient mass balances for each component inside the catalyst pores. Two zones have to be accounted for: the active layer (impregnated with palladium over 250 µm) and the inactive support which can play a significant role as a supply of reagents. This complete model involves three integration variables: a time coordinate (t), a coordinate along the reactor axis (z) and a coordinate along the catalyst radius (r); -the second one (model II), already examined in a previous article (Julcour et al. [START_REF] Julcour | Dynamics of a three-phase upflow fixed-bed catalytic reactor[END_REF]), assumes the pellet to be a gradientless volume for the hydrocarbon concentration (CDT, CDD, CDE and CDA). This assumption is fully justified when steady state is reached since the concentration of CDT is very high compared to hydrogen solubility. In the transient regime it supposes that the dynamics of pore diffusion is very fast compared to the evolution of concentrations in the external liquid phase. These considerations allow to simplify the terms describing mass accumulation inside the pellet: a uniform concentration of hydrocarbons and a negligible concentration of hydrogen (thus no accumulation) are assumed.

In both models the catalyst pellet is supposed to be isothermal and the variations of the amount of reactants adsorbed on the solid phase is neglected.

EQUATIONS OF THE MODEL

Based on the assumptions described above, the dynamic model is given by the following set of equations:

Mass balances

Liquid phase (plug flow with axial dispersion)

( ) ( ) 2 j LS, j GL, j L, zLi Lext j L, j L, Lext H CDA, CDE, CDD, CDT, j N N z C D ε z z F C ε t = - +         ∂ ∂ ∂ ∂ + ∂ ∂ - = ∂ ∂ ( 3
)
with N GL,k = 0 k = CDT, CDD, CDE, CDA since hydrogen only is present in the gas phase N GL,H2 = k L a (C * L,H2 -C L,H2 ) and N LS,j = (k LS a LS ) j (C L,j -C S,j )

Catalyst phase

• Model I takes into account diffusion and reaction phenomena inside the catalyst pores, for both the active layer and the inert support. The catalyst pellet is described as a long cylinder, for which only radial flux are considered (however an equivalent pellet length is estimated to keep the actual active volume V a ). Thus model I leads to:

δ r r 0 r C' r 1 r C' D t C' ε p j 2 j 2 j e j p - < <         ∂ ∂ + ∂ ∂ = ∂ ∂ in the inactive part (4.1a) p p i i ij j 2 j 2 j e j p r r r R r C r 1 r C D t C < < δ - ∑ ν +         ∂ ∂ + ∂ ∂ = ∂ ∂ ε
in the active layer (R i is the intrinsic reaction rate per unit volume of active layer)

with the following boundary conditions:

∀ t, r = 0 0 r C' j = ∂ ∂ (condition for symmetry) ∀ t, r = r p -δ      = ∂ ∂ = ∂ ∂ j j j j C' C r C' r C ∀ t, r = r p j S, r r j C C p = = p r r j p a p j e B j LS, r C V V ρ δ D ρ N 0 = ∂ ∂ × × - = (4.1b)
• Model II neglects the hydrogen amount inside the pellet and assumes a flat concentration profile for hydrocarbons. In order to take into account the effect of internal diffusion in the reaction term, an apparent kinetic law is then used to describe the consecutive hydrogenations ( i ' r per unit of catalyst weight). This apparent kinetic law has been determined by measurements made with the 3.1 mm diameter pellets.

( ) ( )

        ∑ ν ρ + = ∂ ∂ ε - ε i i ik B k LS, k S, p ' r N C t 1 k = CDT, CDD, CDE, CDA         ∑ ν ρ + = i i iH2 B H2 LS, ' r N 0 (4.2)
Gas phase (plug flow)

( ) H2 GL, H2 G, H2 G, Gext N z F C ε t - ∂ ∂ - = ∂ ∂ ( 5
)

Energy balances

The heat exchanges through the walls of the jacket are represented in figure 1. As already mentioned, both dissolution enthalpy of hydrogen and liquid vaporization are ignored in the energy balance equations.

Q 1 = h 1 A 1 (T L -T W1 ) Q 2 = h 2 A 1 (T M -T W1 ) Q 3 = h 3 A 2 (T M -T W2 ) Cooling oil (T M ) Liquid (T L ) Wall 2 (A 2 , T W2 ) Wall 1 (A 1 , T W1 ) Q 1 Q 3 Q 2

Liquid phase

( ) ( ) ( )( ) ( )( ) ( ) W1 L R 1 1 L S LS LS L G GL L zL j j L, j L, L Lext T T V A h T T a h T T a h z T Λ z ' H F z H ε t - - - + - +         ∂ ∂ ∂ ∂ +         ∂ ∂ - = ∂ ∂ ∑ (6)

Catalyst phase

• Model I: According to stoichiometry:

( ) ( )( ) p r r H2 p a p H2 e R B L S LS LS S r C V V ρ δ D H ∆ ρ T T a h t H ε 1 = ∂ ∂ × × - - - = ∂ ∂ - (7.1)
assuming identical heats of reaction for the consecutive hydrogenations (∆H R1 = ∆H R2 = ∆H R3 = ∆H R ).

• Model II:

( ) ( )( )         ∑ ∆ ρ - - - = ∂ ∂ ε - i i i R B L S LS LS S r' H T T a h t H 1 (7.2)
Gas phase (hydrogen only)

( ) ( ) ( )( ) L G GL G H2 G, G Gext T T a h ' H F z H ε t - - ∂ ∂ - = ∂ ∂ ( 8
)
Cooling oil (in the jacket)

( ) ( ) ( ) W2 M an 2 3 M W1 an 1 2 M M M T T V A h T T V A h H' F z t H - - - + ∂ ∂ - = ∂ ∂ (9) Wall 1 ( ) ( ) M W1 1 2 W1 L 1 1 W1 st P, st W1 T T A h T T A h t T C' ρ V - - - = ∂ ∂ ( 10
)

Wall 2

As the external reactor wall is assumed to be perfectly insulated:

( )

W2 M 2 3 W2 st P, st W2 T T A h t T C' ρ V - = ∂ ∂ (11)

Pressure drop

The pressure drop is supposed to be negligible:

P -P inlet = 0 (12)
Description of liquid holdup and enthalpies In order to lighten the equations structure and to make easier the introduction of new correlations, liquid holdup and enthalpies are treated as independent variables respecting the following algebraic equations:

ε Lext -mε Lext = 0
with mε Lext the model for the external liquid holdup (13) Note that liquid hold-up variations (mainly due to the gas flow rate) are not considered here, and the overall liquid flow rate is assumed to remain constant during the stepwise changes of the gas flow rate

H L -mH L = 0 ( ) dT T C' ρ H TL Tref L P, L L ∫ = m ( 14
)
(Where an average specific heat for the liquid is used , as no significant differences exist between the specific heats of the organic reactants) H S -mH S = 0 (15) For the catalyst phase enthalpy calculation, both the enthalpy of the solid and the enthalpy of the liquid contained in the pores are considered:

( ) ( ) ( )dT T C' ρ ε T C' ρ H S T Tref Lp P, Lp p p P, p S ∫ + = m H G -mH G = 0 ( ) mH C C T dT G G,H2 P,G H2 Tref TG = ∫ (16)
(Since the liquid vapor pressure (0.16 bar at 433K) is negligible compared to the gas pressure (4 bars), vaporized liquid reactants can be neglected in the gas enthalpy).

H M -mH M = 0 ( )dT T C' ρ H TM Tref M P, M M ∫ = m (17) 0 M ρ C H2 H2 G, H2 G, = - (18)
Initial and boundary conditions

Initial conditions

The liquid phase contains CDT saturated with H 2 . The concentrations on the catalyst surface equal the concentrations in the liquid phase. The catalyst pores are filled with CDT.

The hydrogen flow rate is uniform along the reactor.

The temperatures of the gas, liquid and catalyst phases are all equal to the inlet temperature of the gas-liquid mixture (low temperature to prevent any reaction prior to t = 0). Time t = 0 corresponds to the pre-heated cooling oil entering the reactor jacket, which starts the reaction.

Boundary conditions

For the liquid phase, Danckwerts' conditions are used: at z = 0 and ∀t

( ) ( ) inlet j L, 0 z j L, j L, zLi Lext F F z C D - = ∂ ∂ ε = j = CDT, CDD, CDE, CDA, H 2 (19) ( ) ( ) inlet L 0 z L L L L P, L zL T T z T u C' ρ Λ - = ∂ ∂         = (20) at z = L R and ∀t 0 z C j L, = ∂ ∂ (21) 0 z T L = ∂ ∂ ( 22
)
MODEL PARAMETERS Except kinetic data, models involve more than ten parameters to be determined from the literature or by specific experiments.

The effective diffusivity D ej is obtained from the molecular diffusivity by: j m j e D D τ ε = with ε the porosity (ε = 0.45) and τ the tortuosity factor (τ = 7.2) of the catalyst particles. D mj is calculated from the correlation of Diaz et al. [START_REF] Diaz | Correlation for the estimation of gas-liquid diffusivity[END_REF] for hydrogen and from the correlation of Wilke and Chang (cf. Reid et al. [START_REF] Reid | The properties of gases and liquids. 4 th Edition[END_REF]) for CDT and its derivatives. The tortuosity factor has been estimated by comparing initial consumption rates of hydrogen measured with 3.1 mm diameter pellets and crushed particles and assuming a first order reaction kinetics. For the calculation of the liquid holdup ε Lext , the gas-liquid mass transfer coefficient k L a, the liquid-solid mass transfer coefficient of hydrogen (k LS ) H2 , and the wall heat transfer coefficient h 1 , empirical relations have been established using the same reaction and reactor system (Stüber [START_REF] Stüber | Sélectivité en réacteur catalytique triphasique : analyse expérimentale et théorique d'hydrogénations consécutives en lit fixe catalytique à co-courant ascendant de gaz et de liquide[END_REF]): they depend above all on the gas flow rate. The correlation of Specchia et al. [START_REF] Specchia | Solid-liquid mass transfer in concurrent two-phase flow through packed beds[END_REF] is used to calculate the liquid-solid mass transfer coefficients of hydrocarbons. Models are found not to be sensitive to this parameter in its usual range, so that its accuracy is not very important. Axial dispersion is estimated from Stüber [START_REF] Stüber | Sélectivité en réacteur catalytique triphasique : analyse expérimentale et théorique d'hydrogénations consécutives en lit fixe catalytique à co-courant ascendant de gaz et de liquide[END_REF]. The axial thermal conductivity is deduced from the analogy between mass and heat transfer: Pe mL = Pe tL . In fact this analogy underestimates the axial conductivity, as the solid contributes directly to heat conduction but indirectly to dispersion. For the gas-liquid heat transfer, a high coefficient has been used, based on the assumption that the temperatures of both gas and liquid phases are the same. In the absence of reliable relations for the upflow reactor, the liquid-solid heat transfer coefficient is deduced from the well known Kunii and Levenspiel equation derived in single phase fixed beds: Nu = 2 +1.8 Re p 1/2 Pr 1/3 The heat transfer coefficient is then probably underestimated, nevertheless calculated heat effects remain very low.

Preliminary simulations made with a steady state model derived from model II have put into evidence that three of the parameters mentioned above have a great influence on the concentration and temperature axial profiles:

-gas-liquid and the liquid-solid mass transfer coefficients of hydrogen (concentration profiles), -wall heat transfer coefficient (temperature profile).

The sensitivity of the predictions to these parameters is reported in the following table. Experimental steady state profiles have been used to adjust the sensitive parameters: slight corrections (less than 25%) were needed to fit the experimental data.

NUMERICAL TREATMENT

REDUCTION OF THE PDAE SYSTEMS

Model I and II lead to a set of partial differential and algebraic equations (PDAE).

In order to keep a system structure close to the original one (to make easier future developments), the set of equations was reduced by the method of lines: the PDAE were converted to DAE by discretization of the spatial derivatives (z-derivatives and also rderivatives for model I) with finite differences. Then the resultant DAE systems were solved by the software package DISCo (Sargousse et al. [START_REF] Sargousse | DISCo : Un nouvel environnement de simulation orienté -objet[END_REF] and Le Lann [START_REF] Le Lann | Internal Report, User Manual[END_REF]).

Model II was first tested for the plug flow mode by comparing its predictions when steady state conditions are reached with the results of a steady state model where spatial derivatives are integrated by the Gear method.

From a number of spatial divisions equal to 10, model II was checked to give the same axial concentration profiles as the steady state model. However in order to describe more precisely the axial temperature profile (which is relatively steep close to the reactor inlet), 40 divisions were used to discretize the reactor. At the pellet scale (model I), the mesh size was chosen to make coincide one of the discretization points and the interface between the inert support and the active layer. The catalyst pellet was then parted in 31 elements. The last element adjacent to the liquid-solid interface was itself parted into 50 divisions for a more accurate calculation of the mass flux.

TREATMENT OF THE RESULTANT DAE SYSTEMS (DISCo)

According to the reduction method and the number of discretization points chosen, the resultant system associated to model II involves nearly 1000 differential and algebraic equations (while model I leads to more than 16000 equations). So the corresponding dynamic operators exhibit a banded structure with a high void degree.

The DAE solver applied here -DISCo -has been developed from a modified version of the LSODI package based on the Gear method (Hindmarsh [START_REF] Hindmarsh | LSODE and LSODI, two initial value ordinary differential equation solvers[END_REF]). It has been improved in robustness and reliability in order to solve problems typically encountered in the chemical engineering field, characterised by rapid transient phenomena, stiffness, large scale systems, high non linearity, external and intrinsic discontinuities. More particularly this software allows different treatments of the jacobian matrix to increase storage and calculation efficiency: full, banded or sparse mode. For instance, in the case of model II, twice less computation time is needed when sparse mode is used instead of banded mode. A fortiori sparse treatment was applied to model I, allowing the program to simulate 200 minutes of operation during the reactor start-up in about 25 minutes CPU 1 .

RESULTS AND DISCUSSION

START-UP OF THE REACTOR

Models were first applied to describe the start-up of the fixed-bed reactor for various flow rate conditions. Transient axial temperature and concentration profiles were compared with the experimental values.

Concentration profiles at the pellet scale

Along the reactor axis, model I gives transient concentration profiles in all the different phases, especially in the catalyst pores. Figure 2 exhibits hydrogen and CDT concentration profiles at the reactor outlet, one hour after the reaction has begun.

The figure puts into evidence the existence of great resistance at the gas-liquid and liquidsolid interfaces (hydrogen concentration at the catalyst surface is less than 10% of hydrogen solubility). This phenomenon is all the more marked since gas flow rate, then k L a is low. It is also shown that the internal resistance in the catalyst pores is even more significant, as hydrogen concentration falls steeply to zero in the pellet.

After one hour of operation, the concentration of CDT is higher at the pellet center than at its surface, revealing a slow diffusion of the hydrocarbon from the inert support (initially filled with CDT) to the reaction zone at the catalyst surface. When steady state is reached (inside the external liquid phase and the catalyst pores), CDT concentration profile in the pellet is nearly flat as expected, since the concentration of CDT is very high compared to hydrogen solubility. (defined either as the ratio of the hydrogen concentration to the solubility or the ratio of the CDT concentration to the sum of the hydrocarbon concentrations).

Concentration and temperature profiles at the reactor scale

Figures 3 and4 illustrate two examples of axial concentration profiles calculated by models I and II at different times during the start-up of the reactor. Before steady state conditions the observed differences between the predictions of the two models can be explained by their distinct description of the pellet dynamics:

-model I introduces a slow diffusion of the non-volatile components inside the catalyst pores (so that pores are still filled with CDT, whereas a high amount of this reagent has already been consumed in the liquid bulk), -model II assumes that, at any time, hydrocarbon concentrations in the catalyst pores equal bulk concentrations. That is why smaller differences are observed (figure 3a) if effective diffusivities of hydrocarbons are multiplied by a factor 5 (this multiplying factor would largely compensate for a probable overestimation of the tortuosity factor). When steady state conditions are reached (figure 3c and4c), results are -as expectedsimilar whatever the applied model -intrinsic kinetics coupled with internal diffusion (model I) or apparent kinetic law (model II).

When model predictions are compared to experimental measurements, it appears that actually the diffusion time of hydrocarbons should be fast compared to the bulk concentration evolution. It must be mentioned that model I underestimates diffusion efficiency as only radial flux are taken into account in the pellet model. Moreover the real nature of the active layer (homogeneity of the catalytic deposit, depth, tortuosity factor) should be more complex than described in model I. This may explain why model II predictions are surprisingly in a better agreement with the experimental data.

Simulations also exhibit a minimum for the concentration of CDT, which was experimentally checked. This minimum moves towards the top of the reactor when time increases and disappears when steady state conditions are reached (cf. figures 3c and4c). This phenomenon results from the complex coupling between hydrodynamics and initial conditions (at t = 0 the column is full of cyclododecatriene saturated with hydrogen at a low temperature): the liquid phase leaving the reactor during the transient regime has only reacted on a fraction of the bed height and moreover with a reduced hydrogen gas flow (leading to a lower external mass transfer). Figure 5 shows that the axial concentration profile of hydrogen in the liquid phase forms rapidly (in less that 10 minutes, order of magnitude of the time needed to get steady temperatures), imposing a decreasing profile of reaction rate. It results in an increasing concentration of CDT towards the top of the reactor, as long as the liquid has not been renewed by the convective flux. A typical axial temperature profile in steady state conditions is given in figure 6: it exhibits a maximum near the reactor inlet, due to the heat flux generated by the exothermic reaction (at its maximum near the inlet) and to the high heat transfer at the reactor wall.

RESPONSE TO A CHANGE IN OPERATING CONDITIONS

In order to investigate further the reliability of the dynamic model II, it was used to predict the influence of a step change in the gas or liquid flow rate. For that purpose techniques for discontinuity treatment were applied, such as the use of a cubic polynomial function to simulate the valve opening (or closing).

Stepwise changes of the flow rates (up to 100 %) were imposed to the reactor and the predicted time-concentration curves were compared to experimental responses. Figures 7 and8 give typical responses of the system to such a sudden increase in the gas flow rate. The numerical results fit well the observed transient behavior: it is seen that the conversion increases to reach the second steady state profile after a period of 25 minutes, representing nearly twice the estimated residence time. Indeed a rise of the gas velocity increases the reaction rate by accelerating gas-liquid and liquid-solid mass transfer (figure 7). Moreover it goes with a less efficient heat dissipation, as the wall heat transfer coefficient is a decreasing function of gas velocity in pulse flow regime, leading to an increase of overall reactor temperature (figure 8). This latter figure reveals also that thermal dynamics is significantly faster than concentration evolution.

Fig. 1 .

 1 Fig. 1. Schematic drawing of the heat exchanges through the walls of the jacket.

Fig. 2 .

 2 Fig. 2. Dimensionless concentration profiles at the reactor outlet.

Fig. 3 -

 3 Fig. 3 -Concentration profiles during the start-up. P=4 bars, T inlet =313 K, u L,inlet =0.52×10 -3 m/s , u G,inlet =0.050 m/s, T M,inlet = 150°C.

Fig. 4 -

 4 Fig. 4 -Concentration profiles during the start-up. P=4 bars, T inlet =323 K, u L,inlet =0.34×10 -3 m/s , u G,inlet =0.027 m/s, T M,inlet = 150°C.

Fig. 5 -

 5 Fig. 5 -Axial concentration profile of hydrogen in the liquid phase during the start-up. P=4 bars, T inlet =323 K, u L,inlet =0.4×10 -3 m/s , u G,inlet =0.027 m/s, T M,inlet =150°C.

Fig. 6 -

 6 Fig.6-Axial temperature profile in steady state conditions. P=4 bars, T inlet =313 K, u L,inlet =0.52×10 -3 m/s , u G,inlet =0.050 m/s, T M,inlet =150°C.

Fig. 7 -Fig. 8 -

 78 Fig.7-Concentration evolution at Z = 1.065 m when increasing u G,inlet from 0.04 to 0.06 m/s at t=120 min (u L,inlet =0.55×10 -3 m/s, P=4 bars, T M,inlet =150°C).

Table 1 -

 1 Parameters of apparent kinetics.

Table 2 -

 2 Sensitivity of the concentration and temperature profiles on several parameters.

	Parameter	Concentration profiles	Temperature profile
	k L a	+ + + + +	+ + + +
	(k LS ) H2	+ + + +	+ + +
	(k LS ) hydrocarbons	-	-
	h 1	+ +	+ + + + +

IBM RS6000, 390, 66 MHz

Acknowledgments

The authors would wish to thank IFCPAR (Indo-French Center for the Promotion of Advanced Research) for the financial support of this work.

CONCLUSION

In this paper two ways of describing the phenomena at the pellet scale for the dynamic modeling of a three-phase fixed-bed reactor were compared: a detailed one coupling intrinsic kinetics with internal diffusion and a simplified one assuming flat hydrocarbon concentration profiles inside the catalyst pores and using an apparent kinetic law. The resulting PDAE systems were solved by using both discretization techniques and a DAE solver based on the Gear method (DISCo): this numerical treatment proved to be reliable and quite efficient (the simplest model needs less than one minute CPU 1 to simulate 200 minutes of operation including a flow rate change). The models were assessed for the hydrogenation of 1,5,9-cyclododecatriene on Pd/Al 2 O 3 by comparing their results to experimental measurements performed in an upflow reactor. The extended model put into evidence the role of hydrocarbon diffusion on the whole reactor dynamics, as well as the effect of external and internal resistance to hydrogen transfer on the observed reaction rate. However in the investigated conditions, this extended model does not improve the prediction of the reactor transient behavior, as the hydrocarbon diffusion is not limiting. Its description of pore diffusion appears to need still improvement, by accounting for the real pellet geometry and maybe also including transient adsorption phenomena. Nevertheless such a sophisticated model is useful to better understand how the dynamics of the whole reactor is influenced by the transient phenomena at different scales, and specially for reactions much more sensitive to hydrocarbon concentrations -remember a quasi zero order is observed here. Moreover thanks to improved numerical techniques and computer tools it does not require much CPU time. In case of non limiting hydrocarbon diffusion, the simplified model proved its reliability to describe the start-up of the reaction as well as the response to a gas or liquid flow rate variation in standard working conditions. It can be then regarded as a first step to the optimization of the reactor performances in the transient regime.


Fabien Lotte
email: fabien.lotte@inria.fr

Josef Faller
email: josef.faller@tugraz.at

Christoph Guger
email: guger@gtec.at

Yann Renard
email: yann.renard@aliceadsl.fr

Gert Pfurtscheller
email: pfurtscheller@tugraz.at

Anatole Lécuyer
email: anatole.lecuyer@inria.fr

Robert Leeb
email: robert.leeb@epfl.ch

Combining BCI with Virtual Reality: Towards New Applications and Improved BCI

Introduction

Historically, the main goal of Brain-Computer Interface (BCI) research was, and still is, to design communication, control and motor substitution applications for patients with severe disabilities [START_REF] Wolpaw | Brain-computer interfaces for communication and control[END_REF]. These last years have indeed seen tremendous advances in these areas with a number of groups having achieved BCI control of prosthetics, wheelchairs and spellers, among other [START_REF] Millán | Combining Brain-Computer Interfaces and Assistive Technologies: State-of-the-Art and Challenges[END_REF]. More recently, new applications of BCI have emerged that can be of benefit to both patients and healthy users alike, notably in the areas of multimedia and entertainment [START_REF] Nijholt | Turning shortcomings into challenges: Braincomputer interfaces for games[END_REF]. In this context, combining BCI with Virtual Reality (VR) technologies has rapidly been envisioned as very promising [START_REF] Lécuyer | Brain-computer interfaces, virtual reality and videogames[END_REF][START_REF] Leeb | Walking by thinking: the brainwaves are crucial, not the muscles! Presence[END_REF]. Such a combination is generally achieved by designing a system that provides the user with immersive 3D graphics and feedback with which it can interact in real-time by using the BCI. The promising potential of this BCI-VR combination is visible at two levels. On one hand, BCI is seen by the VR community as a new input device that may completely change the way to interact with Virtual Environments (VE) [START_REF] Lécuyer | Brain-computer interfaces, virtual reality and videogames[END_REF]. Moreover, BCI might also be more intuitive to use than traditional devices. In this sense, BCI can be seen as following a path similar to that of haptic devices a few years ago [START_REF] Burdea | Force and touch feedback for virtual reality[END_REF], that led to new ways of conceiving VR interaction. On the other hand, VR technologies also appear as useful tools for BCI research. VE can indeed be a richer and more motivating feedback for BCI users than traditional feedbacks that are usually in the form of a simple 2D bar displayed on screen. Therefore a VR feedback could enhance the learnability of the system, i.e., reduce the amount of time needed to learn the BCI skill as well as increase the mental state classification performance [START_REF] Leeb | Walking by thinking: the brainwaves are crucial, not the muscles! Presence[END_REF][START_REF] Ron-Angevin | Brain-computer interface: Changes in performance using virtual reality technique[END_REF]. VE can also be used as a safe, cost-effective and flexible training and testing ground for prototypes of BCI applications. For instance, it could be used to train a patient to control a wheelchair with a BCI [START_REF] Leeb | Selfpaced (asynchronous) BCI control of a wheelchair in virtual environments: a case study with a tetraplegics[END_REF] and to test various designs for the wheelchair control, all of this without any physical risk and with a very limited cost. As such, VR can be used as an intermediary step before using BCI applications in real-life. Finally, VR could be the basis of new applications of BCI, such as 3D video games and artistic creation for both patients and healthy users, as well as virtual visits (cities, museums . . . ) and virtual online communities for patients, in order to address their social needs 1 .

Designing a system combining BCI and VR comes with several important challenges. First, the BCI being used as an input device, it should be, ideally, as convenient and intuitive to use as other VR input devices. This means that [START_REF] Allison | Towards an independent brain-computer interface using steady state visual evoked potentials[END_REF] the BCI should provide the user with several commands for the application; [START_REF] Ammon | Transcranial magnetic stimulation can influence the selection of motor programmes[END_REF] the user should be able to send these commands at anytime, at will, i.e., the BCI should be self-paced (a.k.a. asynchronous); [START_REF] Bayliss | Use of the evoked potential P3 component for control in a virtual apartment[END_REF] the mapping between the mental states used and the commands (i.e., the interaction technique) should be intuitive, efficient, and not lead to too much fatigue for the user. This last point is particularly challenging since current BCI are usually based on a very small number of mental states, typically only 2 or 3, whereas the number of interaction tasks that can be performed on a typical VE is very large, usually much larger than 3. From the point of view of the VE design and rendering, the challenges include [START_REF] Allison | Towards an independent brain-computer interface using steady state visual evoked potentials[END_REF] to provide a meaningful VR feedback to the user, in order to enable him to control the BCI; [START_REF] Ammon | Transcranial magnetic stimulation can influence the selection of motor programmes[END_REF] to integrate the stimuli needed for BCI based on evoked potentials as tightly and seamlessly as possible in order not to deteriorate the credibility and thus the immersiveness of the VE and (3) to design a VR application that is useful and usable despite the huge differences between a typical VE and the standard BCI training protocols.

This chapter presents an overview of the research works that have combined BCI and VR and addressed these challenges. As such, [START_REF] Allison | Towards an independent brain-computer interface using steady state visual evoked potentials[END_REF] it surveys recent works that use BCI to interact with VE, (2) it highlights the critical aspects and solutions for the design of BCI-based VR applications and (3) it discusses the related perspectives. It is organized as follows: Section 2 provides some introductory material on VR and the way to interact with VE using a BCI. Then, Section 3 reviews existing BCIbased VR applications according to the different neurophysiological signals used to drive the BCI. More particularly, Section 3.1 discusses VR applications controlled with a motor imagery (MI)-based BCI, Section 3.2 those based on Steady State Visual Evoked Potentials (SSVEP) and Section 3.3 those exploiting a P300-based BCI. Then, Section 4 elaborates on the impact of VR on BCI use, notably in terms of BCI performance and user experience. Finally, Section 5 concludes the chapter.

Basic principles behind VR and BCI control

This section gives some insights about how VE can be controlled with a BCI. In the first subsection, VR is defined and the typical interaction tasks are described. The suitability of the different BCI neurophysioligical signals (MI, P300, SSVEP) for each interaction task is also briefly mentioned. In the second subsection, a general architecture for BCI-based VR applications is proposed. This architecture is illustrated with examples of existing VR applications using BCI as input device.

Definition of Virtual Reality

A VR environment can be defined as an immersive system that provides the user with a sense of presence (the feeling of "being there" in the virtual world [START_REF] Burdea | Virtual Reality Technology[END_REF]) by means of plausible interactions with a real-time simulated synthetic world [START_REF] Lécuyer | Using eyes, hands, and brain for 3D interaction with virtual environments: A perception-based approach[END_REF]. Such plausible interaction is made possible thanks to two categories of devices: input and output devices. First, the user must be able to interact with the virtual world in real time. This is achieved by using input devices such as game pads, data gloves, motion tracking systems or, as described in this chapter, BCI. Second, the user must be provided with real time feedback about the virtual world state. To this end, various output devices are generally used to render the virtual world content, such as visual displays, spatial sound systems or haptic devices.

According to Bowman et al [START_REF] Bowman | 3D User Interfaces: Theory and Practice[END_REF] typical interaction tasks with a 3D-VE can be described as belonging to one of the following categories:

• Object selection: it consists in selecting an object among those available in the virtual world, typically in order to subsequently manipulate it.

• Object manipulation: it consists in changing attributes of an object in the virtual world, typically its position and orientation or other properties such as appearance and size. • Navigation: it consists in modifying the user's own position and orientation in the virtual world in order to explore it. In other words, navigation can be defined as moving around the VE and changing the current point of view.

• Application control: it consists in issuing commands to the application, to change the system mode or to activate various functionalities, for instance.

All these categories of interaction tasks can be performed with a BCI. However, each BCI paradigm is more or less suitable for each category of interaction task. For instance, MI and SSVEP-based BCI are more suitable for navigation tasks and possibly object manipulation because they can issue commands continuously and potentially in a self-paced way. On the other hand, P300-based BCI let the user pick one item among a list of usually at least four, such command being issued in a discrete and synchronous way. For this reason, they are more suitable for object selection tasks. The suitability of each BCI paradigm is discussed more in details and illustrated in Sections 3.1, 3.2 and 3.3 respectively.

General architecture of BCI-based VR applications

Implementing a BCI control for a VR system can be seen as using the BCI as an input device to interact with the VE. Therefore, it consists in providing the user with a way to act on the virtual world only by means of brain activity, and using the available output devices to provide a meaningful feedback to the user. So far, only visual feedback has been deeply investigated in the context of BCI-based VR applications, but other modalities, in particular audio and haptics, would also be worth studying in the future. A BCI-based VR setup typically involves two independent softwares: 1) a BCI software to record brain signals, process them to extract relevant features and classify mental states in real-time in order to generate commands, and 2) a VR software to simulate and render a virtual world, provide feedback to user and process the received commands. Therefore, these two softwares must be able to communicate in order to exchange information and commands. Figure 1 provides a schematic representation of BCI control of a VR application.

In addition to these software considerations, there are also several hardware related issues that must be considered when using a BCI system in a VE: (1) the biosignal amplifiers must be able to work in such a noisy environment, (2) the recordings should ideally be done without wires to avoid collisions and irritations within the environment, (3) the BCI system must be coupled with the VR system to exchange information fast enough for real-time experiments and (4) in the case of CAVE systems, users mostly want to move around and therefore active EEG electrodes should be used to avoid movement artifacts.

In order to illustrate this general architecture implementation and propose a complete setup, we can mention two softwares which are devoted to BCI and VR as an example: OpenViBE and Ogre3D. OpenViBE2 is a free software platform to design, test and use BCI [START_REF] Renard | OpenViBE: An open-source software platform to design, test and use brain-computer interfaces in real and virtual environments[END_REF]. OpenViBE has been successfully used for the three major families of BCI: Motor Imagery [START_REF] Lotte | Exploring large virtual environments by thoughts using a brain-computer interface based on motor imagery and high-level commands[END_REF], P300 [START_REF] Congedo | Brain Invaders": a prototype of an open-source P300-based video game working with the OpenViBE platform[END_REF] and SSVEP [START_REF] Legény | Navigating in virtual worlds using a self-paced SSVEP-based brain-computer interface with integrated stimulation and real-time feedback[END_REF]. Ogre3D 3 Fig. 1 General architecture of a BCI-based VR application: the user generates specific brain activity patterns that are processed by the BCI system and sent as command to the VR application. In return, the VR application provides meaningful feedback to the user, this feedback being potentially any combination of visual, audio or haptic feedback forms. This combination of "control on the VE" and "feedback from the VE" can elicit the sense of presence. is a scene-oriented, flexible 3D engine that is capable of producing realistic representations of virtual worlds in real time. Ogre3D also includes extensions for spatial sound, physics simulation, etc. Moreover, it has been successfully used to simulate VE on equipments ranging from basic laptops to fully immersive systems such as CAVE systems [START_REF] Cruz-Neira | The CAVE : audio visual experience automatic virtual environment[END_REF]. These two softwares can communicate and exchange information, commands and responses using the Virtual Reality Peripheral Network (VRPN), a widely used library proposing an abstraction of VR devices [START_REF] Taylor | VRPN: a deviceindependent, network-transparent VR peripheral system[END_REF]. Since both OpenViBE and Ogre3D have VRPN support, either natively or through contributions, they are able to communicate efficiently in order to design BCI-based VR applications. Those softwares have been used to design BCI-based VR applications such as those described in [START_REF] Lotte | Exploring large virtual environments by thoughts using a brain-computer interface based on motor imagery and high-level commands[END_REF][START_REF] Legény | Navigating in virtual worlds using a self-paced SSVEP-based brain-computer interface with integrated stimulation and real-time feedback[END_REF][START_REF] Lotte | Self-paced brain-computer interaction with virtual worlds: a qualitative and quantitative study 'out-of-the-lab[END_REF]. Generally not only VRPN, but any other interface (like proprietary TCP, UDP connections) can be used to communicate with existing VR systems.

Naturally, various other software and hardware can also be used to design BCIbased VR applications, such as Matlab/Simulink for real-time EEG signal processing and XVR (eXtremeVR 3D software, VRMedia, Italy) for VE design and applications [START_REF] Guger | Control of a smart home with a brain-computer interface[END_REF][START_REF] Guger | Recent Advances in Brain-Computer Interface Systems, chap[END_REF]. Furthermore, simple projection walls with Qt4 application framework (Nokia Corporation, Finland), or stereoscopic presentation techniques such as head-mounted display (HMD) with VRjuggler, or even in fully-immersive multi-projection stereo-based and head tracked VE systems (commonly known as a "CAVE" [START_REF] Cruz-Neira | The CAVE : audio visual experience automatic virtual environment[END_REF] using DIVE software, or "DAVE" [START_REF] Fellner | Dave -eine neue technologie zur preiswerten und hochqualitativen immersiven 3d-darstellung[END_REF]) with the scene graph library OpenSG were already used and combined with a MATLAB based BCI [START_REF] Leeb | Brain-computer communication: the motivation, aim, and impact of virtual feedback[END_REF]. On the EEG hardware part, we can mention the gMOBIlab+5 (g.tec, Austria) which is a mobile EEG recording device that has been sucessfully used in VE (e.g., see [START_REF] Groenegress | Effects of P300-based BCI use on reported presence in a virtual environment[END_REF]).

Review of BCI-controlled VR applications

This section reviews works that have used BCI to interact with VR applications. These works are arranged according to the neurophysiological signal used to drive the BCI: Motor Imagery (Section 3.1), SSVEP (Section 3.2) and P300 (Section 3.3). It should be mentioned that Section 3.1 describes more works than the other two sections, since more groups have used MI as the input signal to BCI-based VR applications. This is probably due to the fact that MI is a popular and well-studied neurophysiological signal for BCI [START_REF] Pfurtscheller | Motor imagery and direct brain-computer communication[END_REF], and that, contrary to SSVEP and P300, MI does not require any external stimulus which could be more convenient and natural for the the user of a VR application.

Motor imagery controlled VR environments

In this section we will focus on BCI based on MI, meaning on the analysis and classification of sensorimotor electroencephalographic (EEG) patterns generated during the imagination of specific movements (MI of left and right hand) [START_REF] Pfurtscheller | Motor imagery and direct brain-computer communication[END_REF][START_REF] Pfurtscheller | 15 years of BCI research at Graz University of Technology: current projects[END_REF]. The imagination of different types of movements results in a characteristic change of the EEG over the sensorimotor cortex which is called event-related de-/synchronisation [START_REF] Pfurtscheller | Event-related EEG/MEG synchronization and desynchronization: basic principles[END_REF]. After the computer learned the user-specific patterns, they can be used to control the movement of a bar to the right or left, just by imagining right or left hand movements. The same principle can be used to control simple movements in VEs.

The progress and comparison of MI-BCI controlled VR was first shown by Leeb and Pfurtscheller, by increasing the complexity of their studies from controlling a simple bar feedback in a synchronous manner till a self-paced (asynchronous) BCI in highly immersive VE [START_REF] Leeb | Brain-computer communication: the motivation, aim, and impact of virtual feedback[END_REF]. In their first work, users perceived the feeling of rotating with constant speed to the right and left depending on the imagined hand movement (see Figure 2.a), while the rotation information was integrated over one trial [START_REF] Leeb | Combining BCI and virtual reality: scouting virtual worlds[END_REF]. Interestingly, no differences between HMD and CAVE feedback could be found, but all users performed better compared to standard bar feedback. The reason for the same VE performance was that users lost the spatial orientation while rotating, which disturbed them. In a similar experiment the imagination of foot movement was used to walk forward in a virtual street [START_REF] Leeb | Walking by thinking: the brainwaves are crucial, not the muscles! Presence[END_REF][START_REF] Pfurtscheller | Walking from thought[END_REF]. Correct classification of foot motor imagery was accompanied by forward movement at constant speed, whereas a correct classification of hand motor imagery stopped the motion.

Incorrect classification of hand motor imagery resulted in backward motion (same speed) and incorrect foot in halting. The walking distance was scored as a "cumulative achieved mileage" (CAM, [START_REF] Leeb | Walking by thinking: the brainwaves are crucial, not the muscles! Presence[END_REF]), which was the integrated forward/backward distance covered during foot movement imagination and was used as performance measurement. All users achieved their best results within the CAVE and the worst in the standard BCI condition, so we can assume that the use of VR as feedback stimulated the participant's performances. The results indicate that foot motor imagery is a suitable mental strategy to control events within the VEs, because the imagination of feet movement is a mental task which comes very close to that of natural walking. It was observed that in the CAVE condition (highest immersion) the performance variation were stronger than in the control condition. One possible interpretation is that VR feedback amplifies both positive and negative feedback effects on the performance. The wrong behaving rich visual feedback can modify the EEG activity and thereby results in a further deterioration of performance [START_REF] Leeb | Walking by thinking: the brainwaves are crucial, not the muscles! Presence[END_REF].

The next important step was to overcome the cue-based interactions and to incorporate free will decisions (intentional control). Thereby users could navigate freely through a virtual apartment (see Figure 2.b), whereby at every junction the users could decide by their own, how they wanted to explore the VE [START_REF] Leeb | Brain-computer communication: motivation, aim and impact of exploring a virtual apartment[END_REF]. The apartment (maze like) was designed similar to a real world application, with a goal-oriented task (predefined target room), a high mental workload and a variable decision period for the user. For comparison reasons, synchronous BCI sessions with a standard BCI bar feedback have been performed before and after the sessions with the virtual apartment, whereby the experiments with the virtual apartment were performed both in front of a normal TFT monitor and in an immersive VE. The users noted that the task in the apartment was much harder compared to the prior feedback training, because it was necessary not only to perform the "correct" imagination, but also the shortest way through the apartment had to be found. Therefore the cognitive load was much higher compared to the standard BCI paradigm. According to the hypothesis, it was found that the performance improves (decrease of error) over the sessions and the statistically significant lowest error could be found during the sessions with virtual feedback [START_REF] Leeb | Brain-computer communication: motivation, aim and impact of exploring a virtual apartment[END_REF].

Giving the user the full control over timing and speed, was demonstrated in a study where users had to explore the Austrian National Library (see Figure 2.c). The participants were navigating down the library hall at their own pace but had to stop at several specific points (e.g. statue, column) [START_REF] Leeb | Self-paced exploring of the Austrian National Library through thoughts[END_REF]. After a variable pause time (between 20-95 seconds) the experimenter gave the command to restart moving. Navigating always happened when the users performed foot motor imagery. Seven users accomplished the study with a very small number of false positive. Most interestingly in this study are the extremely long periods (up to 1.5min) of pause times, where the user intentionally delivered no commands.

In their final study a tetraplegic patient used the imagination of his paralyzed feet to control forward movement of his wheelchair in VR [START_REF] Leeb | Selfpaced (asynchronous) BCI control of a wheelchair in virtual environments: a case study with a tetraplegics[END_REF]. The task was to go / move down a virtual street and stop at every avatar which was lined up along the street (see Figure 2.d). The patient achieved in some runs 100 % performance and in average 90 %. This work demonstrated for the first time that a tetraplegic user, sitting in a wheel chair, could control his movements in a VE by the usage of a self-paced BCI based on one single EEG recording. It has to be mentioned that VEs are especially attractive for a person who is wheelchair-bound. First, simply using a VE can give such persons access to experiences that may be long forgotten (or which they have never had). The fact that the user could still perform feet motor imagery, years after an injury that rendered him unable to use his feet, is a testament to the plasticity of the human brain (similar to [START_REF] Kuebler | Patients with ALS can use sensorimotor rhythms to operate a brain-computer interface[END_REF]).

Another BCI controlled wheelchair study was performed by Grychtol et al [START_REF] Grychtol | Human behavior integration improves classification rates in real-time bci[END_REF] with healthy users. Their results confirmed how voluntary behavioral modification brought about by VR feedback can help to improve the performance of a BCI system. VR feedback played an important role in the users' ability to learn and perform the activity well. While these applications are already very impressive and innovative, one could argue that most of them provide the user with only a single or two commands. This could be inconvenient for the user and restrict the range of possible VE the user could interact with. This has motivated some researchers to explore BCI-based VR applications providing a larger number of commands to the user. For instance, Scherer et al [START_REF] Scherer | Towards self-paced brain-computer communication: Navigation through virtual worlds[END_REF] proposed a 3-class self-paced BCI to freely navigate in a VE. With this BCI, the user could turn left, turn right or move forward by imagining a left hand, right hand or foot movement, respectively. While this proves to work and to be convenient for the user, this also highlighted some limitations of BCI-based interaction with VR. First, it stressed the well known performance problem of BCI, the performance being generally modest and decreasing when the number of classes to be identified increases [START_REF] Kronegg | EEG-based synchronized braincomputer interfaces: A model for optimizing the number of mental tasks[END_REF]. Second, it suggested that performing navigation tasks in VR with a BCI can be tiring, especially when the user has to perform mental tasks continuously to go for one point to another or to keep the imagination over very long periods [START_REF] Leeb | Self-paced exploring of the Austrian National Library through thoughts[END_REF].

Some groups have recently proposed solutions to alleviate these issues, based on the use of specific interaction techniques. To address the limited classification performances of BCI system, the DIANA6 group proposed to navigate VE using a self-paced BCI based on 1 or 2 motor imagery tasks only [START_REF] Ron-Angevin | A two-class brain computer interface to freely navigate through virtual worlds[END_REF][START_REF] Velasco-Álvarez | Free virtual navigation using motor imagery through an asynchronous brain-computer interface[END_REF]. Indeed, with a number of classes as small as possible, the classification performances of the BCI are much more likely to be high. In order to still provide the user with 3 or more commands (in order to go forward, turn left or turn right) despite the BCI recognizing only 1 or 2 motor imagery states, they proposed specific interaction techniques. These techniques are based on a scanning principle (similar to the hex-o-spell [START_REF] Williamson | Designing for uncertain, asymmetric control: Interaction design for brain-computer interfaces[END_REF]). This means that to select a given interaction command, the user had to perform a motor imagery task during a given time frame, each frame being associated to a different command. Their evaluations showed that, with this approach, users can actually freely navigate in a VE with a simple brain-switch [START_REF] Velasco-Álvarez | Free virtual navigation using motor imagery through an asynchronous brain-computer interface[END_REF].

In order to alleviate the fatigue caused by BCI-based navigation in VR, as well as to efficiently use the small number of MI tasks recognized by a BCI, INRIA7 also proposed a new interaction technique for BCI-based VR applications [START_REF] Lotte | Exploring large virtual environments by thoughts using a brain-computer interface based on motor imagery and high-level commands[END_REF]. This technique, based on a 3-class self-paced BCI, provides the user with high-level commands, thus leaving the application in charge of performing the complex and tedious details (low-level aspects) of the interaction task. Thus, this can be seen as a form of shared-control [START_REF] Nijholt | Brain-computer interfacing for intelligent systems[END_REF]. The user can explore the VE by selecting points of interest such as navigation points (e.g., junctions, room entrances, etc.) or artworks. Interestingly enough, these navigation points can be generated completely automatically from the geometry of the VE. The user can select these points due to a sequence of binary choices. In addition to the two commands used to perform these binary choices, the user can use a third command to cancel any of his/her choice. Once a navigation point has been selected, the application takes all the necessary actions to perform the interaction task such as moving from the current navigation point to the next selected one. Evaluations, performed in the context of the exploration of a virtual museum (see Figure 3), showed that with this approach, users can navigate from one room to the other nearly twice as fast as with low-level commands, and with less fatigue.

Due to the huge potential of BCI-based VR applications, not only for patients but also for healthy users, it quickly became necessary to evaluate them outside laboratories, in close to real-life conditions. Such an evaluation was performed with the "use-the-force" application [START_REF] Lotte | Self-paced brain-computer interaction with virtual worlds: a qualitative and quantitative study 'out-of-the-lab[END_REF], a BCI-based VR game inspired by the Star Wars TM movie. With this game, users were asked to control the takeoff of a virtual spaceship by using real or imagined foot movements (see Figure 4). The system Fig. 3 Exploring a virtual museum using a BCI and high-level commands [START_REF] Lotte | Exploring large virtual environments by thoughts using a brain-computer interface based on motor imagery and high-level commands[END_REF].

relied on a simple brain switch that detects the beta rebound posterior to the real or imagined foot movement, at electrode Cz. The game was evaluated with 21 naïve users, during a public exhibition dedicated to VR. Despite the simplicity of the BCI design and the noisy environment, results showed that, without training, half the users could control the virtual object's motion by using real foot movements. A quarter of them could do so by using imagined foot movements. Furthermore, the whole application appeared enjoyable and motivating to the users.

Fig. 4 The "Use-the-force" entertaining application [START_REF] Lotte | Self-paced brain-computer interaction with virtual worlds: a qualitative and quantitative study 'out-of-the-lab[END_REF], which enables its users to lift a virtual spaceship by using the BCI ( c Hubert Raguet/Phototheque CNRS).

Another instance of BCI to interact with complex applications was shown by Scherer et al [START_REF] Scherer | The self-paced graz brain-computer interface: methods and applications[END_REF]. The Brainloop interface provides a new way to interact with complex programs like Google Earth TM . Thereby through remapping of commands and options the interface can be customized. In this study, a multi-level selection process and the use of mental tasks in parallel enabled the user to send multiple commands to the application.

Although not based on motor imagery, another BCI-based VR application deserves to be mentioned here since it was also evaluated in public places, outside the lab: the "AlphaWoW" application [START_REF] Nijholt | Turning shortcomings into challenges: Braincomputer interfaces for games[END_REF]. In this game, based on World Of Warcraft R , the player controlled his avatar using a classical keyboard but can turn it from a fragile elf to a powerful bear by using a BCI. More particularly, the avatar shape (bear or elf) depended on the band power in the alpha band (8-12 Hz), the alpha rhythm power being related to the player's state of relaxation. In other words, when the player was stressed the avatar changed into a bear, and he/she has to relax to turn back the avatar into an elf. The evaluations showed that the game was received very positively despite the modest BCI performances, which were considered by the players more as a challenge than as a shortcoming. These different close-toreal-life-studies thus highlight the potential of BCI-based VR application and the need to push research efforts in these directions [START_REF] Nijholt | Turning shortcomings into challenges: Braincomputer interfaces for games[END_REF][START_REF] Lotte | Brain-computer interfaces for 3D games: Hype or hope?[END_REF][START_REF] Scherer | The self-paced graz brain-computer interface: methods and applications[END_REF] 3.1 summarizes the numerous studies presented in this section, by describing some key characteristics of these BCI-based VR applications using MI. Several interesting points come out of this table. First, this table highlights the importance of self-paced BCI design for VR application in general and for navigation tasks in particular. Indeed, navigation is inherently a self-paced task. Moreover, despite the fact that self-paced BCIs are a challenging research topic that is not well explored [START_REF] Mason | Evaluating the performance of self-paced BCI technology[END_REF], most of the aforementioned studies have designed and used such a BCI. Another point to notice is that, although most BCI-based VR applications provide the user with as many commands as MI tasks used, it is possible to provide more commands than MI tasks by using appropriate interaction techniques. Finally, this table stressed that MI has been almost exclusively used to perform navigation tasks in VR. Indeed, MI appears as particularly suitable for such a task since it enables spontaneous and self-paced control, which navigation should be. On the contrary, it is not convenient to perform selection tasks with MI, since MI provides only a few mental states and thus a few commands whereas virtual objects to be selected can be potentially numerous. As based on Evoked Potentials (SSVEP, P300) are more suitable for selection tasks since they can use numerous stimuli and corresponding brain responses.

SSVEP based VR/AR environments

A SSVEP is an electroencephalographic response occurring when a user perceives a visual stimulus flickering at a constant frequency [START_REF] Vialatte | Steady-state visually evoked potentials: Focus on essential paradigms and future perspectives[END_REF]. This response is observed over the visual cortex (occipital electrodes), and consists of an EEG pattern oscillating at the same frequencies that the flickering stimulus and its harmonics. Interestingly enough, SSVEP can be modulated by attention, which means that the SSVEP response to a given stimulus will be stronger (i.e., with a larger amplitude) when the user focuses his/her attention on this stimulus.

Lalor et al [START_REF] Lalor | Steadystate vep-based brain computer interface control in an immersive 3-d gaming environment[END_REF] were the first to use an SSVEP-based BCI to control a character in a 3D gaming environment. In this game, a monster went from platforms to platforms by moving along a tight rope. From time to time, the monster lost its balance, and the user had to restore it by using the BCI. To do so, two flickering checkerboard were placed on each side of the VE, in order to elicit SSVEP at different frequencies. When the system detected that the user was focusing on the left or right checkerboard, it restored the monster's balance towards the left or right respectively. Later, Touyama worked towards more immersive applications based on SSVEP and showed that they could be used to change the point of view towards the left or right in a VE displayed in a CAVE-like system [START_REF] Touyama | Advances in Human Computer Interaction, chap[END_REF].

The works mentioned above proved that SSVEP-based BCI is a suitable and efficient way to interact with VE. One of its limitations though, is that it requires flickering stimuli in order to be used. In the context of VR applications, this has been mainly achieved by relying on flickering squares or checkerboards statically overlayed over the screen. As a consequence, the VE may look unnatural and is unlikely to elicit a strong sense of presence for the user. In order to address these limitations, Faller et al [START_REF] Faller | An application framework for controlling an avatar in a desktop based virtual environment via a software SSVEP braincomputer interface[END_REF] presented a desktop-based virtual environment, where the stimuli were tightly integrated within 3D scenarios that allowed controlling avatar interaction and navigation. In one of the scenarios, seven healthy volunteers successfully controlled an avatar to alternately push one of two buttons in an asynchronous paradigm. The stimuli were fixed to the hands and hence dynamically following every avatar movement.

In another of the presented scenarios [START_REF] Faller | An application framework for controlling an avatar in a desktop based virtual environment via a software SSVEP braincomputer interface[END_REF], five out of seven users successfully navigated an avatar in third person perspective through the same apartment scenario (see Figure 5.a) as presented in Leeb et al [START_REF] Leeb | Brain-computer communication: motivation, aim and impact of exploring a virtual apartment[END_REF]. They could guide the avatar in discrete steps and turns by visually fixating one of three SSVEP stimuli that were fixed to the avatars back. Each successful classification would then trigger one of three associated navigation commands, go one step ahead, turn left 45 • or turn right 45 • (see Figure 5.b). Still dealing with the integration of SSVEP-stimulus within VE, Legeny et al worked towards an even more natural and ecological approach [START_REF] Legény | Navigating in virtual worlds using a self-paced SSVEP-based brain-computer interface with integrated stimulation and real-time feedback[END_REF]. In their work, which aimed at navigating in a virtual forest, the flickering stimuli necessary for SSVEP generation were displayed on butterfly wings. Three of these butterflies were displayed on screen, flying up and down in front of the user (see Figure 6). The user had to focus his/her attention on the left, center or right butterfly in order to go left, forward or right, respectively. The butterflies' antennas were also used to provide feedback to the user. Indeed, the further apart the two antennas of a butterfly were, the more likely this butterfly will be selected by the classifier as the one the user pays attention to. Such stimuli are therefore more naturally incorporated into the VE, and formal evaluations suggested that it indeed increased the subjective preferences and feeling of presence of the users.

Finally, moving beyond traditional VE, Faller et al [START_REF] Faller | A software SSVEP BCI integrating stimuli within motivating and immersive virtual and augmented reality environments[END_REF][START_REF] Faller | Avatar navigation in virtual and augmented reality environments using an SSVEP BCI[END_REF] extended their previous work into a SSVEP BCI system that relies on stimuli that are presented within immersive virtual and more interestingly, in an Augmented Reality (AR) environments. In a pilot study, three healthy volunteers were able to successfully navigate an avatar through an immersive VR slalom scenario based on embedded SSVEP stimuli. The complete scene was presented using a head-mounted display (HMD). Two of these three volunteers also succeeded in the immersive AR condition, where a camera was mounted on the HMD and the slalom scenario 3D graphics were injected into the live, real-world video by tracking fiducial markers (see Figure 7). Fig. 6 Mimetic integration of SSVEP stimulation and feedback in a Virtual Environment [START_REF] Legény | Navigating in virtual worlds using a self-paced SSVEP-based brain-computer interface with integrated stimulation and real-time feedback[END_REF]. The butterfly wings are flickering at different frequencies in order to enable SSVEP-based BCI control, while their antenna positions represent the real-time feedback, i.e., the butterfly the most likely selected by the user according to the classifier. Fig. 7 The middle picture shows a screenshot of how the user saw the scene through the HMD seen in the left picture. The 3D graphics were tracked to the underlying fiducial marker. The participants were instructed to navigate the avatar through the slalom like in the picture on the right [START_REF] Faller | A software SSVEP BCI integrating stimuli within motivating and immersive virtual and augmented reality environments[END_REF][START_REF] Faller | Avatar navigation in virtual and augmented reality environments using an SSVEP BCI[END_REF].

The positive results from this first feasibility study suggest that AR SSVEP BCIs have the potential to vastly improve real-world practicality and usability of BCI systems by compensating for some of their traditional shortcomings such as the low bandwidth, by offering a richer, more direct, and intuitive interface. This would allow for a more goal-directed and seamless real-world interaction. In an AR SSVEP BCI system, stimuli targets can be spatially associated to distinct points of interest in the physical world. These may be abstract or may overlap physical objects such as devices, people or controls, which is an elegant and intuitive way of presenting the user with all possible interaction options. These systems could provide patients with a higher degree of self autonomy and functional independence by introducing more intuitive and effective smart home control. Apart from that, AR SSVEP BCIs can further introduce a valuable, additional communication or control channel for user groups that require or benefit from hands free operation like pilots, car-drivers or office workers.

P300 based VR control

One of the first efforts to combine VR and BCI technologies was achieved by Bayliss and Ballard [START_REF] Bayliss | A virtual reality testbed for brain-computer interface research[END_REF][START_REF] Bayliss | Use of the evoked potential P3 component for control in a virtual apartment[END_REF], and made use of the P300 evoked potential. The P300 is a positive waveform occurring roughly 300 ms after a rare and relevant stimulus [START_REF] Wolpaw | Brain-computer interfaces for communication and control[END_REF][START_REF] Elshout | Review of brain-computer interfaces based on the P300 evoked potential[END_REF]. In order to use a P300-based BCI, users have to focus their attention on a given stimulus randomly appearing among many others, each stimulus corresponding to a given command [START_REF] Donchin | The mental prosthesis: assessing the speed of a P300-based brain-computer interface[END_REF]. The appearance of the desired stimulus being rare and relevant, it is expected to trigger a P300 in the user's brain activity. In their study, Bayliss introduced a simple virtual smart home in which users could control different appliances (e.g., a TV or a light) using the P300-based BCI. 3D spheres were randomly appearing over the objects that can be manipulated and the user could turn them on or off simply by counting the number of times a sphere appears over the desired object.

More recently, a more interactive and richer virtual version of a smart home was implemented [START_REF] Groenegress | Effects of P300-based BCI use on reported presence in a virtual environment[END_REF]. This smart home consists of a living room, a kitchen, a sleeping room, a bathroom, a floor and a patio as shown in the right side of Figure 8. Each room has several devices that can be controlled: TV, MP3 player, telephone, lights, doors, etc. Therefore, all the different commands were summarized in 7 control masks: a light mask, a music mask, a phone mask, a temperature mask, a TV mask, a move mask and a go to mask. The left side of figure 8 shows the TV mask and as an example the corresponding XVR image of the living room [START_REF] Edlinger | Goal-oriented control with brain-computer interface[END_REF]. The user can e.g. switch on the TV by looking first at the TV symbol. Then, the station and the volume can be regulated. The bottom row of Figure 8 shows the go to mask with an underlying plan of the smart home. Inside the mask, there are letters indicating the different accessible spots in the smart home which flash during the experiment. Therefore, the user has to focus on the spot where he wants to go. After the decision of the BCI system, the VR program moves to a bird's eye view of the apartment and zooms to the spot that was selected by the user. This is a goal oriented BCI control approach, in contrast to MI navigation task, where each small navigational step is controlled. Experiments with 3 users yielded accuracies of the BCI system between 83 and 100 % and showed that such a BCI system can be used for the smart home control [START_REF] Guger | Brain-computer interface for virtual reality control[END_REF]. For comparison a group study with healthy people with the standard P300 speller gave an average accuracy of 91 % [START_REF] Guger | How many people are able to control a P300-based brain-computer interface (BCI)?[END_REF]. The Virtual Reality approach is a very cost effective way for testing the smart home environment together with the BCI system. Currently the BCI technology is interfaced to real smart home environments within the EC project SM4all 8 . The project aims at studying and developing an innovative middleware platform for inter-working of smart embedded services in immersive and person-centric environments [START_REF] Guger | Recent Advances in Brain-Computer Interface Systems, chap[END_REF]. These different experiments yielded 2 important new facts for P300-based BCIs:

(1) instead of displaying characters and numbers to the user, it appears that different icons can be used as well, (2) the BCI system does not have to be trained on each individual character. The BCI system was trained with EEG data of the spelling experiment and the user specific information was used also for the smart home control. This allows using icons for many different tasks without prior time consuming and boring training of the user on each individual icon. This reduces the training time in contrast to other BCI implementations were hours or even weeks of training are needed [START_REF] Birbaumer | A spelling device for the paralysed[END_REF][START_REF] Guger | Rapid prototyping of an EEG-based brain-computer interface (BCI)[END_REF][START_REF] Vaughan | EEG-based communication: prospects and problems[END_REF], which might be important for locked-in and ALS patients who have problems with the concentration over longer time periods. The P300 concept works also better if more items are presented in the control mask as the P300 response is more pronounced if the likelihood that the target character is highlighted drops down [START_REF] Krusienski | A comparison of classification techniques for the P300 speller[END_REF]. This results of course in a lower information transfer rate, but enables to control almost any device with such a BCI system. Especially applications which require reliable decisions are highly supported. Therefore the P300 based BCI system enables an optimal way for the smart home control. In a further study the P300 smart home control was combined with a head tracker to switch on and off the BCI system. This means if the person was looking at the BCI system then it was switched on and a selection could be done. If the person turned to the VR projected the BCI system was switched off. Recently a hybrid version of a P300 and SSVEP BCI was used for controlling the smart home environment. The P300 BCI was used to select the command and SSVEP was used to switch on and off the BCI system [START_REF] Edlinger | A hybrid brain-computer interface for smart home control[END_REF]. These hybrid BCI systems hence demonstrated that BCI could be used practically to interact with a virtual smart home, hence potentially offering new and promising applications for patients, at home. It is worth mentioning that Groenegress compared the P300-based BCI control with a gaze-based selection method coupled with wand navigation [START_REF] Groenegress | Effects of P300-based BCI use on reported presence in a virtual environment[END_REF]. Results suggested that the P300 BCI gives lower Presence scores which might be due to the lack of motor actions which are relevant for semantic tasks and more breaks in presence.

Impact of Virtual Reality on BCI

In contrast to traditional interfaces like mouse or keypad, BCI systems could potentially promise a more direct and intuitive way of interacting and thereby overcome some limitations of navigating within VEs [START_REF] Slater | Taking steps: the influence of a walking technique on presence in virtual reality[END_REF]. This is especially obvious for stimulus-dependent BCI-VR systems, where users can control appliances in the VE by simply directing their eye gaze and/or focus of attention towards the desired element (e.g., looking at the TV to switch it on, looking at the door to open it [START_REF] Allison | Towards an independent brain-computer interface using steady state visual evoked potentials[END_REF]). On the other hand motor imagery offers an intuitive way of VE control, for example, imagining foot movements for moving forward in a VE [START_REF] Leeb | Self-paced exploring of the Austrian National Library through thoughts[END_REF][START_REF] Pfurtscheller | Walking from thought[END_REF]. This could overcome the problem of the contradictory stimuli while navigating VEs using a hand-held device and the reduced sense of being present in the VE [START_REF] Slater | Taking steps: the influence of a walking technique on presence in virtual reality[END_REF]. On the other hand it is well known that feedback is one of the key components of a BCI, as it provides the user with information about the efficiency of his/her strategy and enables learning. The studies mentioned above show realistic and engaging VR feedback scenarios, which are closely related to the specific target application. However, the processing of such a realistic feedback stimulus may also interfere with the motor imagery task, and thus might impair the development of BCI control [START_REF] Neuper | Motor imagery and action observation: modulation of sensorimotor brain rhythms during mental control of a brain-computer interface[END_REF]. Furthermore, characteristic EEG changes during VE conditions were reported in [START_REF] Pfurtscheller | Walking from thought[END_REF], where a dominant ERS pattern which was permanently present in the CAVE, was less pronounced in the HMD and not existing at all in the normal feedback. Nevertheless, it was presented in Section 3.1 that VR improves the BCI performance; either the users achieved their best results within VR [START_REF] Leeb | Walking by thinking: the brainwaves are crucial, not the muscles! Presence[END_REF][START_REF] Pfurtscheller | Walking from thought[END_REF][START_REF] Grychtol | Human behavior integration improves classification rates in real-time bci[END_REF] compared to normal feedback or even 100 % performance result in VR [START_REF] Leeb | Selfpaced (asynchronous) BCI control of a wheelchair in virtual environments: a case study with a tetraplegics[END_REF] or achieved the lowest error with virtual feedback [START_REF] Leeb | Brain-computer communication: motivation, aim and impact of exploring a virtual apartment[END_REF]. Generally it can be stated that VR feedback amplifies both positive and negative feedback effects on the performance.

Besides BCI performances, other data can also be used to investigate the influence and impact of VR on the BCI. For most of the MI studies mentioned in the beginning of Section 3.1, the electrocardiogram was recorded in addition and questionnaires were conducted. An interesting aspect is that mental simulation of a movement (motor imagery) results in cardiovascular changes explained by two factors: anticipation of movement and central preparation of movement [START_REF] Damen | Changes in heart rate and slow brain potentials related to motor preparation and stimulus anticipation in a time estimation task[END_REF][START_REF] Oishi | Autonomic response specificity during motor imagery[END_REF]. The heart rate (HR) generally decreases during motor imagery in normal BCI conditions (without VR feedback) [START_REF] Leeb | Brain-computer communication: the motivation, aim, and impact of virtual feedback[END_REF][START_REF] Pfurtscheller | Cardiac responses induced during thought-based control of a virtual environment[END_REF] which is similar to that observed during preparation for a voluntary movement. In case of VR feedback, the HR can be increased during effortful imagery [START_REF] Pfurtscheller | Cardiac responses induced during thought-based control of a virtual environment[END_REF][START_REF] Pfurtscheller | Centrally controlled heart rate changes during mental practice in immersive virtual environment: a case study with a tetraplegic[END_REF][START_REF] Leeb | Brain-computer communication: the motivation, aim, and impact of virtual feedback[END_REF]. The heart rate acceleration in the VE is interpreted as effect of an increased mental effort [START_REF] Decety | Vegetative response during imagined movement is proportional to mental effort[END_REF] to move as far as possible in VE. This underlines the importance of VR feedback in modifying emotional experiences and enhances autonomic and visceral responses. The HR changes can be in the order of several beats-per-minute (bpm) and therefore could be used to increase the classification accuracy of an ERD-based BCI when both the EEG and the HR are analyzed simultaneously [START_REF] Pfurtscheller | The hybrid BCI[END_REF].

These heart rate changes were found in most studies of Section 3.1: (1) In the "walking from thought" study [START_REF] Pfurtscheller | Walking from thought[END_REF], instead of the normal decrease of 3-5 %, an increase of up to 5 % was found. Furthermore, the results provide provisional evidence that moving backwards (negative feedback) resulted in a stronger and longerlasting HR increase than forward moving (positive one) [START_REF] Pfurtscheller | Cardiac responses induced during thought-based control of a virtual environment[END_REF]. [START_REF] Ammon | Transcranial magnetic stimulation can influence the selection of motor programmes[END_REF] In the virtual apartment study [START_REF] Leeb | Brain-computer communication: motivation, aim and impact of exploring a virtual apartment[END_REF] the analysis of the heart rate showed that during the BCI condition a preparatory HR deceleration could be found, which is in line with our prior study [START_REF] Pfurtscheller | Cardiac responses induced during thought-based control of a virtual environment[END_REF] but not in the VE conditions since no preparation cue was provided. Generally, the visible HR deceleration is stronger for good trials than for bad trials in all conditions (with removed preparatory phase). Furthermore, a better classification accuracy was accompanied with a stronger deceleration [START_REF] Leeb | Brain-computer communication: the motivation, aim, and impact of virtual feedback[END_REF]. (3) In contrast to these results, HR increases are observed for two users during VE feedback in study [START_REF] Pfurtscheller | Cardiac responses induced during thought-based control of a virtual environment[END_REF]. Interestingly, the slight HR increase (0.5-1 %) before the cue in the VR feedback conditions could be the effect of the anxiety of the user to find the best and correct way for the next decision. Moreover this increase is more dominant in the immersive VE condition, which correlates with the reported higher motivation. (4) In the case of the self-paced navigating study inside the virtual library [START_REF] Leeb | Self-paced exploring of the Austrian National Library through thoughts[END_REF], a phase relationship between the HR and the EEG could be identified. Movement onset occured during periods of increasing HR, only one user showed a not statistically significant decreasing HR [START_REF] Leeb | Brain-computer communication: the motivation, aim, and impact of virtual feedback[END_REF]. Although the users were participating in a self-paced experiment, the performance was not completely self-paced but aligned with the underlying cardio-vascular pace. [START_REF] Birbaumer | A spelling device for the paralysed[END_REF] Finally, in the study with the tetraplegic patient [START_REF] Leeb | Selfpaced (asynchronous) BCI control of a wheelchair in virtual environments: a case study with a tetraplegics[END_REF], the analysis revealed that the induced beta oscillations were accompanied by a characteristic heart rate (HR) change in form of a preparatory HR acceleration followed by a short-lasting deceleration in the order of 10-20 bpm [START_REF] Pfurtscheller | Centrally controlled heart rate changes during mental practice in immersive virtual environment: a case study with a tetraplegic[END_REF]. This provides evidence that mental practice of motor performance is accompanied not only by activation of cortical structures but also by central commands into the cardiovascular system with its nuclei in the brain stem. Another reason for the observed preparatory HR increase could be that the tetraplegic patient was highly motivated and therefore directed increased attention to "walk" in the immersive environment.

Summing up, the use of VR enhanced the user's BCI and application performances and provided motivation (see [START_REF] Leeb | Walking by thinking: the brainwaves are crucial, not the muscles! Presence[END_REF][START_REF] Pfurtscheller | Walking from thought[END_REF][START_REF] Leeb | Brain-computer communication: the motivation, aim, and impact of virtual feedback[END_REF][START_REF] Ron-Angevin | Brain-computer interface: Changes in performance using virtual reality technique[END_REF][START_REF] Pineda | Learning to control brain rhythms: making a brain-computer interface possible[END_REF]). These findings are supported by the outcome of the questionnaires and heart rate analysis, where the users self-rated their success stronger than their failure and a stronger HR decrease could be found as well for good classification results. Especially the HR outcome, in the case of an asynchronous (self-paced) BCI, was interesting and it can be speculated that the "free will" of the users was affected by processes operating automatically and unconsciously [START_REF] Haggard | Conscious intention and motor cognition[END_REF]. Similar influences on self-paced hand movements without awareness of the participants can be caused by transcranial magnetic stimulation [START_REF] Ammon | Transcranial magnetic stimulation can influence the selection of motor programmes[END_REF].

Conclusion

In this chapter, we have presented and discussed how BCI and VR could be combined and surveyed the related works. As a summary, recent works have shown that BCI could be used to navigate virtual worlds, mostly thanks to motor imagery and SSVEP-based BCI, since these signals enable continuous and self-paced control. BCI could be used to select and manipulate virtual objects as well, for which evoked potentials (P300, SSVEP) seem to be the most used and probably the most appropriate neurophysiological signals. Indeed, such signals enable to select objects simply by paying attention to the corresponding stimulus, and a BCI can deal with numerous such stimuli. On the contrary, MI-based BCI can use only a limited number of mental tasks and are thus less suitable for tasks involving the selection and/or manipulation of numerous virtual objects. These works have also highlighted the challenge in designing BCI-based VR applications, BCI control being usually slow, error-prone and with limited degrees of freedom whereas a VE can be highly interactive and complex. In this context, the design of appropriate interaction techniques and paradigms has shown to be a suitable way to alleviate these limitations and should thus be further studied. Finally, this chapter has highlighted that not only BCI can be a useful interaction device for VE, but that VR could also be a useful technology for BCI. In particular, VR being a rich and motivating environment for the BCI user, it has been shown that this could lead to improved BCI performances, higher motivation and engagement, and reduced human training time in comparison to classical feedback forms. Therefore, BCI and VR can certainly be seen as complementary tools, BCI being useful as an interaction device to enhance the VR experience, and VR being an environment that benefits BCI research and performances.

The various works described in this chapter have also opened the doors to exciting and promising new research topics to further develop the connection between BCI and VR. Indeed, it would be interesting to study how BCI could be used more naturally, transparently and ecologically with virtual environments, in order to make the interactive experience even more immersive. In addition to the classical need for BCI with higher recognition performances, it would be interesting to study whether new mental states and neurophysiological signals could be used to drive a BCI more naturally within a VE. For instance, a study by Plass-Oude Bos et al suggested that visual spatial attention could be detected, to some extent, from EEG signals and could thus be used in the future to naturally look around in a VE [START_REF] Bos | Looking around with your brain in a virtual world[END_REF]. Such kind of research efforts should be encouraged in order to develop the repertoire of mental states that could be used to interact mentally with VE. Similarly, further research in the area of passive BCI [START_REF] George | An overview of research on passive brain-computer interfaces for implicit human-computer interaction[END_REF][START_REF] Zander | Towards passive brain-computer interfaces: applying brain-computer interface technology to human-machine systems in general[END_REF] could help to monitor different mental states of the user (e.g., flow, presence, emotions, attention, etc.) and dynamically adapt the content of the VE accordingly, thus providing an enhanced experience for the user. Since it has been shown that VR could lead to enhanced BCI performances, it would also be interesting to further study the impact of various VR feedback forms (e.g., visual, tactile or audio) on BCI, in order to identify how VR technologies can best optimize the performance and learnability of the system. The specificity of BCI, which do not rely on peripheral nerves and muscles contrary to tradional interfaces, also raise some interesting questions (and maybe answers) related to embodiement and embodied cognition. As such, a system combining BCI and VR might prove a worthy tool and research topic for philosophy and cognitive sciences [START_REF] Clark | Supersizing the mind: Embodiment, action, and cognitive extension[END_REF]. Finally, using BCI to interact with VE has the potential to lead to several practical and useful applications. For patients, BCI-based VR applications could enable them to have access to entertainment (e.g., 3D video games), art and culture (e.g., digital creation of paintings, virtual visits of museums and cities) as well as a better social life (e.g., with virtual online communities), which their disabilities might prevent them from doing. This will enable BCI to be useful beyond restoring mobility and basic communication by addressing other important needs of patients [START_REF] Zickler | Brain computer interaction applications for people with disabilities: Defining user needs and user requirements[END_REF]. For healthy users, BCI-based VR applications could also be useful, in areas such as entertainment as well [START_REF] Nijholt | Turning shortcomings into challenges: Braincomputer interfaces for games[END_REF] -although this may require more improvements in BCI design [START_REF] Lotte | Brain-computer interfaces for 3D games: Hype or hope?[END_REF] and artistic expression [START_REF] Friedman | Neurophysiology-based art in immersive virtual reality[END_REF]. In short, it appears that combining BCI and VR is a promising research topic that is worth being further explored.

Fig. 2

 2 Fig. 2 Pictures of different MI-controlled VE: (a) exploring a virtual pub or (b) an apartment, (c) visiting the national library and (d) walking by thoughts in case of a wheelchair person.

Fig. 5

 5 Fig. 5 Panel (a) shows an overview of the apartment scenario. The users were instructed to navigate the avatar along the path that is depicted by the white arrow. Panel (b) is a screenshot from an actual online scene, where the user navigates the avatar in third person perspective [20].

Fig. 8

 8 Fig. 8 Top left: Smart home control icons for TV, Telephone,. . . Top right: VR representation of the living room [29, 15]. Bottom: Control icons to move to a certain position inside the apartment and corresponding bird eyes view of the apartment.

Table 1

 1 Summary of BCI-based VR applications using Motor Imagery

	interaction number of	number of	synchronous	VE	Reference
	task	MI tasks	commands	or self-paced
	navigation	2	2	synchronous	exploring a	[38]
					virtual pub
	navigation	2	2	synchronous navigating along a [40, 56]
					virtual street
	navigation	2	2	synchronous	navigating	[25]
	navigation	2	2	semi	exploring a	[41]
				synchronous virtual apartment
	navigation	1	1	self-paced	exploring a	[43]
					virtual library
	navigation	1	1	self-paced	moving along a	[39]
					virtual street
	navigation	3	3	self-paced	exploring the	[66]
					"free-space"
	navigation	1-2	4	self-paced exploring a maze [65, 72]
					or park
	navigation	3	more than 3	self-paced	exploring a	[46]
	+ selection		(depends on the VE)		virtual museum
	manipulation	1	1	self-paced	lifting a	[47]
					virtual spaceship
	navigation	3	more than 3	self-paced	controlling	[67]
	+ selection				Google Earth

TM Table

See, for instance, the work achieved as part of the BrainAble project: http://www. brainable.org/

http://openvibe.inria.fr/

http://www.ogre3d.org

http://qt.nokia.com/

http://www.gtec.at

http://www.diana.uma.es

http://www.inria.fr/en/

http://www.sm4all-project.eu

Acknowledgements

This work was supported by the European Union projects PRESENCIA (IST-2001-37927) and PRESENCCIA (IST-2006-27731), furthermore by the French National Research Agency projects OpenViBE (ANR-05-RNTL01601) and OpenViBE2 (ANR-09-CORD-017).