Eddy El

Eddy El Tabach
email: eddy.el-tabach@univ-9orleans.fr

Leyla Adishirinli

Nicolas Gascoin

Guillaume Fau

Prediction of transient chemistry effect during fuel pyrolysis on 1 the pressure drop through porous material using artificial neural 2 networks 3

teaching and research institutions in France or abroad, or from public or private research centers.

Prediction of transient chemistry effect during fuel pyrolysis on the pressure drop through porous material using artificial neural networks

pores of the material and thus strongly affect the cooling efficiency. The pressure drop is one [START_REF] Zhou | Thermolytic reactions of dodecane[END_REF] of the indicator to monitor the modification of the through-flow and thus of the cooling. 17

Introduction 36

The development of hypersonic vehicles for future access to space or civil transport 37 applications leads to an important heating of the engine and air frame. At flight speeds near 38 Mach 4 and above, the air taken on board these vehicles will be too hot to cool the engines 39 and airframe. Therefore, using fuel within regenerative cooling technique may be applicable 40 [START_REF] Kuhn | Application of transpiration cooling for hot structures, RESPACE: 308 Key Technologies for Reusable Space Systems[END_REF]. To do so, it will be necessary to study and develop adapted light weight and high-41 temperature materials whose characteristics in terms of permeability and porosity are well 42 defined. Among the materials the composite ones made of Ceramic Matrix (e.g. silicon based 43 matrix) with carbon fibers are particularly interesting. For the lowest speed regime, metallic 44 materials may also be used [START_REF] Gascoin | High temperature and pressure reactive flows through porous media[END_REF]. The aero-thermal loads must be thus addressed to quantify 45 permeability/porosity fluctuations of materials as a function of operating conditions. 46

In the literature, different studies are found in relationship with this need, experimentally 47 [START_REF] Langener | Experimental investigations on transpiration 313 cooling for scramjet applications using different coolants[END_REF][START_REF] Gascoin | Comparaison of two 316 permeation test benches and two determination methods for Darcy's and Forchheimer's 317 permeabilities[END_REF][START_REF] Zhang | On Temperature 319 and Strain Rate Dependent Strain Localization Behavior in Ti-6[END_REF] or numerically [START_REF] Romagnosi | Pyrolysis 322 in Porous Media: Part 1. Numerical model and parametric study[END_REF][START_REF] Tabach | Neural-Network Metamodelling for the Prediction 325 of the Pressure Drop of a Fluid Passing Through Metallic Porous Medium[END_REF]; even mathematically [START_REF] Zhou | Theoretical Investigation on Mechanical and Thermal 328 Properties of a Promising Thermal Barrier Material: Yb 3 Al 5 O 12[END_REF]. Such studies are not only dedicated to 48 the flow description but also to the heat transfers [START_REF] Ji | Effect of Temperature on 331 Material Transfer Behavior at Different Stages of Friction Stir Welded 7075[END_REF][START_REF] Fau | Fuel pyrolysis through porous 334 media: Coke formation and coupled effect on permeability[END_REF][START_REF] Herbinet | Thermal decomposition of 337 n-dodecane: Experiments and kinetic modeling[END_REF]. The flows in porous materials are 49 widely studied under common operating conditions. 50

The problem becomes more difficult when the coolant can react with the materials or 51 within the material (local coking) [START_REF] Gascoin | High temperature and pressure reactive flows through porous media[END_REF]. In case of chemical reaction, the formation of carbon 52 deposit on the surface and inside the porosities can impact the physical properties of the 53 material (lowering the permeability and the porosity) and thus the cooling efficiency. These 54 reactions can be due to the thermal fluid decomposition and to the degradation of the material 55 itself. The degree of decomposition is highly dependent on the operating conditions 56 (temperature, pressure, type of flow, nature of reactor) [START_REF] Fau | Fuel pyrolysis through porous 334 media: Coke formation and coupled effect on permeability[END_REF][START_REF] Billaud | Thermal coupling of methane in a tabular flow 340 reactor: parametric study[END_REF][START_REF] Murphy | Analysis of products of high-temperature 342 pyrolysis of various hydrocarbons[END_REF][START_REF] Liu | Supercritical thermal cracking of N-344 dodecane in presence of several initiative additives: products distribution and kinetics[END_REF][START_REF] Fau | Hydrocarbon pyrolysis with a methane focus: A review 347 on the catalytic effect and the coke production[END_REF]. Thermal cracking of 57 hydrocarbons have been widely studied in petrochemical industry [START_REF] Zhou | Thermolytic reactions of dodecane[END_REF][START_REF] Aribike | Thermal cracking of n-Butane and a light hydrocarbon 351 mixture[END_REF][START_REF] Wauters | Computer generation of a network of elementary steps for coke 353 formation during the thermal cracking of hydrocarbons[END_REF][START_REF] Chakraborty | High pressure pyrolysis of n-heptane[END_REF][START_REF] Sadrameli | Thermal/catalytic cracking of hydrocarbons for the production of 358 olefins: A state-of-the-art review 1: Thermal cracking review[END_REF] and in the context 58 of chemical vapor infiltration for the preparation of carbon/carbon composites [START_REF] Marinkovic | Carbon/carbon composites prepared by chemical vapor infiltration-15 361 years later[END_REF][START_REF] Li | Densification of unidirectional carbon-carbon 363 composites by isothermal chemical vapor infiltration[END_REF][START_REF] Wu | Kinetics of thermal gradient chemical vapor 365 infiltration of large-size carbon/carbon composites with vaporized kerosene[END_REF][START_REF] Deng | Densification behavior and 368 microstructure of carbon/carbon composites prepared by chemical vapor infiltration 369 from xylene at temperatures between 900 and 1250[END_REF][START_REF] Ren | Preparation of carbon/carbon composite by 371 pyrolysis of ethanol and methane[END_REF]. It 4/19 appears than the bigger the molecule, the higher the number of reactions which occur. 60

Considering dodecane pyrolysis, the number of reactions largely overpasses 1000 [START_REF] Herbinet | Thermal decomposition of 337 n-dodecane: Experiments and kinetic modeling[END_REF]. This 61 implies very complex phenomena (heat and mass transfers with chemistry). 62 A lot of studies, often under high pressure (up to 2MPa) are available for ambient to 63 average temperature conditions (under 800K) [START_REF] Langener | Experimental investigations on transpiration 313 cooling for scramjet applications using different coolants[END_REF] or for low pressure and high temperatures 64 [START_REF] Kuhn | Application of transpiration cooling for hot structures, RESPACE: 308 Key Technologies for Reusable Space Systems[END_REF]. But only few are dedicated to both high temperature and high pressure conditions in case 65 of reactive fluid. Numerous equations (derived from Brinkman's equation) which relate the 66 pressure drop (ΔP=P in -P out ) through the porous material to the through-flow velocity have 67 been published [START_REF] Gascoin | Comparaison of two 316 permeation test benches and two determination methods for Darcy's and Forchheimer's 317 permeabilities[END_REF][START_REF] Romagnosi | Pyrolysis 322 in Porous Media: Part 1. Numerical model and parametric study[END_REF]. They are based on coefficients, whose physical meaning is not evident 68 [START_REF] Gascoin | Comparaison of two 316 permeation test benches and two determination methods for Darcy's and Forchheimer's 317 permeabilities[END_REF]. One of the complexities of such configuration is due to the fact that along the chemical 69 reactor (cooling channel of the hot vehicle), the fluid is supercritical [START_REF] Gascoin | High temperature and pressure reactive flows through porous media[END_REF]. Multi-species flow 70 is found due to fuel degradation during which heavy compounds (coke particles) are formed 71 and produce solid particles that can block the pore within the porous medium where they are 72 flowing [START_REF] Fau | Fuel pyrolysis through porous 334 media: Coke formation and coupled effect on permeability[END_REF][START_REF] Gascoin | Charaterisation of coking activity 373 during supercritical hydrocarbon pyrolysis[END_REF]. Due to these large and open difficulties, CFD calculations may not be 73 relevant and experimental tests are costly and they cannot cover the entire range of test 74 conditions/material variety, fluid nature. 75

As a consequence in this paper, we have used an approach based on the artificial neural 76 networks (ANN) for simulating the transient changes of the pressure drop of n-dodecane 77 (reactive fluid) passing through the porous material (Stainless Steel) by taking into account 78 both high temperature and high pressure conditions. This work intends to indirectly predict 79 the chemical effect of fuel pyrolysis, of coking and of clogging on the permeation process 80 which directly controls the cooling efficiency. The description of the same numerical 81 approach applied to another set of gas mixture (inert) and flow conditions can be found in a 82 previous study [START_REF] Tabach | Neural-Network Metamodelling for the Prediction 325 of the Pressure Drop of a Fluid Passing Through Metallic Porous Medium[END_REF]. Over the last two decades, ANN have been successfully used by many 83 researchers for a wide range of engineering applications [START_REF] Tabach | Use of artificial neural network 376 simulation metamodelling to assess groundwater contamination in a road project[END_REF][START_REF] Arumugam | Ultimate 379 Strength Prediction of Carbon/Epoxy Tensile Specimens from Acoustic Emission Data[END_REF][START_REF] Nazari | Computer-aided Prediction of the ZrO 2 Nanoparticles Effects on 382 Tensile Strength and Percentage of Water Absorption of Concrete Specimens[END_REF]. ANN is based on the 5/19 substitution of the complex simulation model by an approximation of the input-output 85 relationship. ANN has the advantage over regression that the form of the model needs not to 86 be pre-determined [START_REF] Kleijnen | Kriging metamodeling in simulation: A review[END_REF]. In addition, ANN can theoretically approximate any function to any 87 level of accuracy, which is very interesting when the governing physical mechanisms are 88 non-linear like in high velocity fluid flow in porous materials. The database was built with 89 four input parameters (experiment time, inlet fuel mass flow rate, inlet operating pressure and 90 the uniform temperature) and with the outlet fuel pressure as the output parameter. The 91 results obtained experimentally are used to construct, to optimize and to validate the model. 92

This artificial neural network has been trained and tested on this database using the error 93 backpropagation algorithm and cross validation. The performance of the ANN model is 94 compared with a multilinear regression approximation method. 95

Material 96 2.1 Experimental permeation bench 97

The COMPARER pyrolysis test bench (Fig. [START_REF] Kuhn | Application of transpiration cooling for hot structures, RESPACE: 308 Key Technologies for Reusable Space Systems[END_REF]) is used to pressurize and to heat the fuel 98 under flow conditions [START_REF] Gascoin | Comparaison of two 316 permeation test benches and two determination methods for Darcy's and Forchheimer's 317 permeabilities[END_REF]. Its main characteristics are the following: 99 Maximum operating conditions: 1800K, 8MPa, 0.0006 kg.s -1 for liquid fuel and 100 0.006 kg.s -1 for gas. 101 Sensors: 5 pressure transducers, 5 mass flow rates, over 10 K-type and R-type 102 thermocouples with data acquisition system (16 bits, 48 channels, 0.1 Hz). 103

A permeation test cell contains the porous sample (Fig. 1). This cell is inserted inside the 104 furnace of the COMPARER bench and it is connected to the fluid supply system and to the 105 suitable sensors. The permeable material bounds the cell in two high and low pressure 106 chambers (upstream and downstream to the porous material respectively). An inlet pipe 107 provides the fuel into the system. This cell is connected to a dynamic sampling system to get 108 6/19 hot pressurized samples at three location points in the cell. Despite its small size (external 109 diameter of 40mm), it enables measuring the temperature, pressure and mass flow rate on 110 each side of the porous sample. 111

In the present work, an isotropic stainless steel material is preferred to composite one to 112 avoid considering complex microstructure (fibres, layers). It is characterized by a porosity 113 around 30 %, a grain diameter of 14.1 μm and a pore diameter of 4.1 μm. Further geometrical 114 information can be found in Gascoin et al. [START_REF] Gascoin | Comparaison of two 316 permeation test benches and two determination methods for Darcy's and Forchheimer's 317 permeabilities[END_REF]. 115 The experimental protocol is achieved with constant mass flow rate and given 125 downstream pressure (P out ). The upstream pressure (P in ) increases due to coking and 126 clogging of the porous medium; which makes the pressure drop to increase as a 127 function of the test time. 128 Monitoring of the chemical species: transiently thanks to a FTIR spectrometer for 5 129 gaseous species (methane, ethane, ethylene, propane, propylene) and during the three 130 thermal plateaus by using a dedicated sampling system [START_REF] Fau | Fuel pyrolysis through porous 334 media: Coke formation and coupled effect on permeability[END_REF] coupled with a 131 GC/TCD/FID/MS apparatus (more than 40 species analysed). 132 7/19

Experimental results 133

We present in this section an experimental test result obtained for T=725K. As shown in 134 Fig. 2, the measured pressure drop (Measured P in -P out ) varies as a function of experimental 135 time (t) and the measured fuel mass flow rate (q in ) when the fuel (dodecane) temperature is 136 kept constant (T=725K). Other obtained experimental results [START_REF] Fau | Fuel pyrolysis through porous 334 media: Coke formation and coupled effect on permeability[END_REF] showed that the 137 temperature has a major effect on the measured pressure drop. Further details on the 138 experimental results can be found in previous work [START_REF] Fau | Fuel pyrolysis through porous 334 media: Coke formation and coupled effect on permeability[END_REF]. Globally, based on the overall 139 obtained experimental results, we can conclude that there are three parameters (t, q in and T) 140 that have a great influence on the measurements of the pressure drop. ANN models learn the relationship between the input and the output parameters as a 149 result of training with previously recorded data. The database was built using experimental 150 data which are obtained from the developed experimental bench with input parameters: test 151 time (t), operating inlet pressure (P in ), inlet fuel mass flow rate (q in ) and temperature (T) 152 varying in a range of representative values: between 0 and 858s for t; between 3.3MPa and 153 3.8MPa for P in ; between 0.000033 kg/s and 0.0001 kg/s for q in and 725K, 765K and 810K for 154 T. Totally, the database contains an appreciable size of 979 experimental test points.

8/19

The present database was subdivided in three subsets. A first subset (490 experimental 156 tests) is used to train the networks. A second one (245 experimental tests) is used to test the 157 ANN models to determine when to stop the training stage. The third subset (244 experimental 158 tests) is used to validate the performance of the selected model on unseen cases. 159

Each input or output parameter has been normalized relative to its minimum and 160 maximum values observed in the data (according to Eq. ( 1)) to make the training procedure 161 more efficient. 162

min max min norm X X X X X (1) 163
where X is an arbitrary parameter, X norm is the normalized value, and X max and X min are the 164 maximum and minimum values of X. 165

Architecture and learning process of ANN models 166

An artificial neural network model is composed of interconnected group of artificial 167 neurons or nodes. The most frequently utilized network is the multilayer backpropagation 168 neural network (BPNN) which is used in the present study. The BPNN structure consists of 169 three layers, an input layer which receive data; an output layer which sends computed 170 information; and one or more hidden layers to link input and output layer. All the neurons 171 (nodes) in a layer are connected with all the neurons of the previous and the next layer. In 172 general, the number of the nodes in the input and output layer are determined by the nature of 173 the problem. The architecture of a typical 3-layer backpropagation neural network is shown 174 in Fig. 3. 175 Mathematically, a 3-layer BPNN with n, m, and p the number of input, hidden and output 178 neurons respectively, can be formulated as in the following: 179

1 1 m j jk n i i ij j k k W X W b f b f O (2) 180
where X i the input values of the network and O k are the output values; b j , the hidden unit 181 biases; b k , output nodes biases; W ij , the connection weights between the input layer and the 182 hidden layer; W jk , the connection weights between the hidden layer and the output layer; f is a 183 transfer function. The sigmoid transfer function (Eq. ( 3)) was used in the present study. 184 This process (forward-backward) is repeated until predicted outputs and target answers 193 coincide within a given tolerance [START_REF] Duda | Pattern Classification[END_REF]. 194

The commonest convergence criterion is the average squared error (ASE) defined as: 195 The determination of the ANN architecture constitutes one of the major tasks in the use of 209 the ANN. The overall performance of an ANN is dependent on the numbers of hidden layers 210 and hidden nodes. In the usual case of a 3-layer BPNN, the optimum number of hidden nodes 211 can be determined by cross-validation in the same way as the optimum number of training 212 cycles (Fig. 4). 213

In the present article, a neural network relating inputs {X 1 , X 2 , …, X n } to outputs {O 1 , O 2 , 214 …, O p } and containing one hidden layer with m hidden nodes will be noted: 215

{O 1 , O 2 , …, O p } = ANN n n m p {X 1 , X 2 , …, X n } ( 5

) 216

In our case, the outlet operating pressure (P out ) is sought as a function of t, P in , q in and T. So, 217 it is possible to compute P out by using a BPNN model with one node in the output layer (Eq.

11 /19 In this present study, the choice of the outlet pressure is preferred to limit the impact of 221 experimental uncertainties due to the two pressure transducers (which are generally 222 multiplied if compared to a single transducer). In addition, since the upstream pressure is an 223 inlet parameter, looking at the pressure drop or at the pressure outlet is equivalent when 224 focusing on the behaviour of the ANN model. As can be observed in Fig. 5, the optimal value 225 of ASE was calculated while using 9 nodes in the hidden layer for our model. 226

{P out } = ANN 4-9-1 {t, P in , q in , T} (6) 227
The ASE values for the training, testing and validation phases for the optimal artificial 228 neural network model (ANN 4-9-1 ) are respectively 0.000114, 0.000101 and 0.000132. 229 through the origin is also plotted and the coefficient of determination R 2 for this line is 237 computed according to Eq. ( 7): 238 system should be designed to furnish this increasing need for upstream pressure if outlet 290 pressure should remain constant. 291

N i i i N i i i Y Y N Y Y N R 1 2 1 2 2

Conclusion 292

In this article, an artificial neural networks tool has been used to simulate the transient 293 pressure drop of n-dodecane under pyrolysis conditions and crossing a metallic porous 294 material (Stainless steel). Based on experimental data, the optimum architecture of artificial 295 neural network was trained and validated, in order to generalise the prediction of the pressure 296 drop under clogging configurations not included in the database for difficult access reasons. 297

The validation showed excellent performance of this ANN model for the prediction of 298 dodecane transfer in the porous material (R²>0.983). An example of application was 299 presented to detect the temperature at which chemistry starts to strongly impact the fluid flow 300 within the porous medium. It was found that a turning point around 760 K-770K has to be 301 expected in terms of clogging when using n-dodecane at 3.6 MPa in stainless steel medium. 302

This study is a contribution to the growing evidence of the benefits of ANN models in 303 Aeronautical engineering. This important result may be applied to automate pressure drop 304 estimations, which are used in space flight applications, without prior knowledge of material 305 parameters and particularly for materials with transient changing properties. 306 19/19

Highlights :

We modeled the transient pressure drop of n-dodecane under pyrolysis conditions.

We found a good agreement between the numerical results and the experimental data.

We found that the developed model is able to reproduce physical variations.

The model has been applied successfully on a series of examples.

*Highlights (for review)

  Having a tool to predict these variations is of practical and theoretical interest for a better 18 management of the complex chemical and physical phenomena. This paper presents a model 19 based on artificial neural networks (ANN) for estimating the transient changes of the pressure 20 drop of a reactive fluid (n-dodecane) under pyrolysis conditions passing through porous 21 *Manuscript Click here to view linked References 2/19 metal material. The ANN is developed using experimental data obtained from an 22 experimental bench, which assures the monitoring of fluid mass flow rate, pressure and 23 temperature in stationary and transient conditions. For each case, the fluid pressure which 24 crosses the metallic porous material is measured as a function of test time, inlet operating 25 pressure, temperature and fuel mass flow rate. The optimal ANN architecture with error 26 backpropagation (BPNN) was determined by the cross validation method. The ANN 27 architecture having 9 hidden neurons gives the best choice. Comparing the simulated values 28 by ANN with the experimental data indicates that the ANN model give correct results. The 29 performance of the ANN model is compared with the multiple linear regression model. This 30 work is expected to be used for later prediction of pressure drop under a wide range of 31 clogging conditions. 32 KEYWORDS: Pyrolysis; Artificial neural networks; Modelling; Permeation; Coke;

Figure 1

 1 Figure 1 should be placed here 116

Figure 2 should be placed here 146 4 .

 24 Figure 2 should be placed here 146

Figure 3

 3 Figure 3 should be placed here 176

  x is the excitation. 186 The learning process of BPNN is based on a series of connection weight adjustments in 187 order to minimize the gap (global error) between the outputs of the BPNN and the target 188 values [31]. Initially, all biases and connection weights are initialized to random values in the 189 range of [-1, +1]. Inputs are first propagated forward through each layer of the ANN. Errors 190 between outputs and target values are then propagated backwards and the connection weights 191 are modified according to a specific learning algorithm (delta rule) to reduce the overall error. 192

Figure 4 should be placed here 206 5 .

 45 Figure 4 should be placed here 206

Figure 5 should be placed here 230 5 . 2

 552 Figure 5 should be placed here 230

Fig. 2

 2 Fig. 2 Measured pressure drop variations with the measured fuel mass flow rate and 397

Fig. 3 Fig. 4 Fig. 5

 345 Fig. 3 Architecture of a typical multilayer BPNN. 399

Fig. 6 Fig. 7

 67 Fig.[START_REF] Romagnosi | Pyrolysis 322 in Porous Media: Part 1. Numerical model and parametric study[END_REF] Comparison between target and predicted values for P out using BPNN (model 1) and 403

Figure 3 Click here to download high resolution image Figure 4 Click here to download high resolution image Figure 5 Click here to download high resolution image Figure 6 Click here to download high resolution image Figure 7

 34567 Figure 3 Click here to download high resolution image

256 257 Figure 6 should be placed here 258 259 Table 1 should be placed here 260

  is the mean of the N target values. R 2 coefficients close to unity indicate a high degree 241 12/19 of linearity between predicted and target values. Associated with a best fit line slope close to 242 unity, it indicates a high model prediction accuracy. 243 A basis of comparison for BPNN performance is usually sought in multiple linear 244 regression [33], a more ubiquitous prediction tool in fluid flow through porous material 245 research. Least square parameter fitting for a linear model expressing P out as a function of t, 246 P in , q in , and T (model 2) is performed on the same training database subset as for BPNN 247 model. This model is tested to predict the never-seen data from the BPNN validation database 248 subset. The lowest R 2 value is obtained for multiple linear regression model. It is also noted 249 that the trend line deviates somewhat from the 1:1 line in the case of model 2. The 250 coefficients of determination (R 2 ) for model 1 and model 2 are given in Table 1. The model 2 251seems to be less efficient than model 1 for predicting the variations of P out . This result is 252 expected: the physical phenomena captured in the database are complex and non-linear. In 253 ANN non-linearity is accounted for by the use of transfer functions (Eq. (3)), while 254 complexity can be controlled by varying the number of hidden nodes. In the present case, the 255 artificial neural networks provide good and realistic predictions. It should be noticed that fixing arbitrarily the inlet pressure imposes the 264 outlet pressure to decrease, which simulate the pressure drop increase. The evolution of the 265 predicted outlet pressure (P out ) using BPNN as a function of time and temperature inside the

	1 where N is the number of data, Y i is the target value, i 1 1 1 Y is the value predicted by the model (7) and i An application of ANN is now proposed in the following part. Considering a constant inlet pressure at 3.6 MPa, it is now possible to investigate the chemical effect within the Y 261 239 240 262 263 range of 725K-810K. 14/19

Table 1

 1 R 2 values between target and predicted outputs for all models. 394 395 Fig.1Schematic of the permeation test cell with porous material and associated measures. 396

Table 1

 1 R 2 values between target and predicted outputs for all models.

	R 2	Neural network (model 1)	Multiple linear regression (model 2)
	Training phase	0.986	0.897
	Testing phase	0.986	0.878
	Validation phase	0.983	0.891

Table 1 Figure 1 Click here to download high resolution image Figure 2 Click here to download high resolution image

 1

[START_REF] Romagnosi | Pyrolysis 322 in Porous Media: Part 1. Numerical model and parametric study[END_REF]). It could be noticed that usually the pressure drop through the porous medium is

investigated as a function of the through-flow rate.

Multiphas. Flow, 2011, 37,24-35.


Keywords: Tourisme médical, comportement post-consommation, qualité du médecin, valeur perçue du prix, segmentation Medical tourism, post-consumption behaviors, doctor quality, price value, segmentation

Une étude exploratoire de la satisfaction et des intentions de comportement du touristepatient dans le cadre du tourisme médical : segmentation Post-hoc Résumé Cette étude explore l'influence de la qualité perçue du médecin et la valeur perçue du prix sur la satisfaction du touriste-patient et ses intentions de comportement envers une destination médicale. Le modèle proposé est analysé par l'approche PLS des équations structurelles. Celle-ci étant adaptée aux échantillons de petite taille et n'exige pas la normalité des données. Les résultats obtenus au niveau du modèle global montrent l'existence d'une hétérogénéité dans les réponses obtenus. Par conséquent une analyse par REBUS-PLS a été effectuée afin de détecter les éventuels segments latents. Les résultats de cette recherche apportent un éclairage nouveau sur le comportement post-consommation du touriste-patient. Ils sont discutés à la fin de cet article ainsi que leurs implications théoriques et managériales.

An exploratory study of Tourist-patient satisfaction and behavioral intentions in medical tourism: Post-hoc segmentation

Introduction

Medical tourism is to travel to a foreign country, in order to diagnose or treat illness, or for esthetic treatment or surgery [START_REF] Carrera | Globalization and healthcare: understanding health and medical tourism[END_REF][START_REF] Mugomba | Medical Tourism and its Entrepreneurial Opportunities-A conceptual framework for entry into the industry[END_REF][START_REF] Conrady | Trends and issues in global tourism[END_REF]. This can be associated with conventional tourism services such as transport and accommodation [START_REF] Mugomba | Medical Tourism and its Entrepreneurial Opportunities-A conceptual framework for entry into the industry[END_REF]. In this sense, it is a subcategory of health tourism, which in turn integrates all forms of tourism related to health and wellbeing [START_REF] Mugomba | Medical Tourism and its Entrepreneurial Opportunities-A conceptual framework for entry into the industry[END_REF][START_REF] Smith | Health and wellness tourism[END_REF]. Therefore, the main specificity of the medical tourism consists in the medical intervention (Connell, 2013). This firstly implies the exclusive intervention of doctors and medical staff for the treatment of patients. Moreover, such practice allows purely medical establishments that consist in hospitals, clinics and medical offices.

In recent years, this market has been growing for many reasons: excessive price of medical intervention, unavailability of certain treatment, lack of insurance, long waiting list, etc [START_REF] Peter | A survey of medical tourisme service provider[END_REF]. However, according to Connell (2013), little is yet known about the touristpatient's behavior and about the results of such travel experience. Meanwhile the understanding of such determinants related to tourist-patient satisfaction and those of his intentions toward the medical destination could bring advantages for both government and practitioners to improve their communication and marketing strategy and develop their market share. This research seeks to advance knowledge in these directions by understanding the international tourist-patients' behavior across different medical destinations. Unlike the previous researches in this context, they have been broadly focused on behavioral intentions toward hospital/clinic or medical treatment at a particular destination [START_REF] Mechinda | An examination of tourist's loyalty towards of medical tourism in Pattaya[END_REF][START_REF] Lertwannawit | International tourist's service quality perception and behavioral loyalty to medical tourism in Bangkok metropolitan area[END_REF]Han.H & Hyun.SS, 2015) especially the Asiatic ones (Connell 2013).

The cognitive-affective model of consumer behavior is the most commonly applied approach in tourism and medical service studies [START_REF] Giese | Defining consumer satisfaction[END_REF][START_REF] Gill | A critical review of patient satisfaction[END_REF]. Moreover, results often highlight the positive relation between quality, satisfaction and behavioral intentions (ex. [START_REF] Dagger | A hierarchical model of health service quality scale development and investigation of an integrated model[END_REF]. In this research, we proposed an extension of this model adapted to medical tourism context by inferring perceived price. The main objective of this study is to determine the significant determinants of both tourist-patient satisfaction and his behavioral intentions toward a medical destination. Specifically we tend to explore whether the perception of doctor quality and price value which are considered by many authors as "pull motivations factor" in medical destination choice (Doshi, 2008;Connell, 2013), may lead to a positive behavioral intentions such as intention to recommend and to revisit the medical destination for other treatment or also for pleasure. Such findings can lead to a behavioral segmentation of the tourist-patients and may have consequently an impact on the destination's marketing strategy.

Literature background

Zeithaml (1988) defined perceived quality as the judgments of excellence or superiority of the service provided. According to [START_REF] Parasuraman | A Conceptual model of service quality and its implications for futur research[END_REF], perceived quality is a result of the perceived difference between consumer expectations and their perceptions of service performance. For many authors, quality assessment may precede the act of consumption since it can be the result of disclosures word-of-mouth (WOM), or company's communications, unlike the satisfaction concept that is a post-consumption evaluation state [START_REF] Parasuraman | A Conceptual model of service quality and its implications for futur research[END_REF]Oliver R. L., 2010). Consequently, they represent two distinct concepts [START_REF] Parasuraman | A Conceptual model of service quality and its implications for futur research[END_REF].

Accommodation quality, tourist-patient satisfaction and behavioral intentions

According to Baker and Crompton (2000), quality is a measure of provider outcome, whereas level of satisfaction measures a tourist's outcome. Furthermore, they considered perceived quality as an antecedent of satisfaction and have a direct and positive effect on it. In marketing, many studies have confirmed this correlation [START_REF] Cronin | Measuring service quality: a reexamination and extension[END_REF][START_REF] Bei | An integrated model for the effects ofperceived product, perceived service quality and price fairness on consumer satisfaction and loyalty[END_REF].

In tourism context, Žabkar and al (2010) found that a positive perceived quality of destination product could enhance the level of tourist satisfaction. In addition, Chen and Chen (2010) in heritage tourism supported the positive effect of perceived quality of experience on tourist satisfaction. This result is similar to that found by Loureiro and González (2008) in the rural tourism context and that found by [START_REF] Bigné | Tourism image, evaluation variables and after purchase behaviour:inter-relationship[END_REF].

In this research, we consider that the more the tourist-patient (TP) has a positive judgment about the quality of accommodation, the more he perceives that this trip experience is comfortable and more he expresses a higher level of satisfaction and behavioral intentions toward this destination. Therefore, we posit:

Doctor quality, tourist-patient satisfaction and behavioral intentions

In healthcare research, some studies have also corroborated the positive correlation between perceived quality of healthcare service and patient satisfaction. For instance, [START_REF] Dagger | A hierarchical model of health service quality scale development and investigation of an integrated model[END_REF] showed that healthcare quality has a positive impact on patient satisfaction and his behavioral intentions toward both the clinic and the treatment.

According to [START_REF] Crow | The measurement of satisfaction with healthcare: implications for practice from a systematic review of the literature[END_REF], doctor-patient interrelationship and disclosed information about the process of medical care, are the most important dimensions of medical service that affect patient satisfaction. This result is supported by many other studies related to different cultures (ex. Japan, India, UAE, Ethiopia, Turkey, etc.) [START_REF] Andreani | Trends in marketing of Services and Implications for Health Sector. 5th Congress of Marketing Trends in Europe[END_REF]Xiao & Barber, 2008;[START_REF] Badri | Healthcare quality and moderators of patient satisfaction: testing for causality[END_REF][START_REF] Birhanu | Determinants of satisfaction with health care provider interactions at health centres in central Ethiopia: a cross sectional study[END_REF][START_REF] Camgöz-Akdag | Quality of health care and patient satisfaction: an exploratory investigation of the 5Qs model at Turkey[END_REF]. As an example, Xiao and Barber (2008) found that listening to a patient is determinant in his satisfaction with medical provider. Similarly, [START_REF] Birhanu | Determinants of satisfaction with health care provider interactions at health centres in central Ethiopia: a cross sectional study[END_REF], found that verbal and non-verbal communications are important determinants of patient satisfaction. Elleuch (2008) found that quickness of service provided and interaction with medical staff are the most important determinants of the Japanese patients' satisfaction. However, Yu -Chi Tung and G-Ming Chang (2009) found that a patient's overall satisfaction is more influenced by a doctor's technical skill than by his interpersonal skill. They concluded that compared to the other dimensions of healthcare service quality (doctor's interpersonal skill, staff care and access), the technical skill of the doctor is the most important factor in overall satisfaction and plays a critical role in patient recommendation of a clinic to his friends and relatives. [START_REF] Lertwannawit | International tourist's service quality perception and behavioral loyalty to medical tourism in Bangkok metropolitan area[END_REF] found that perceived quality of medical service is a direct and positive antecedent of tourist-patient satisfaction in Bangkok. In quasi similar context Wanlanai (2011), found that perceived quality of medical staff has a positive influence on satisfaction with treatment, satisfaction with hospital and satisfaction with trip, while tangible dimensions do not influence tourist-patient satisfaction. In addition, he found a significative correlation between quality of medical staff and positive WOM. Rad, Som, & Zainuddin (2010), showed that equipment and staff appearance do not affect tourist-patient satisfaction while, all other dimensions of the medical service including staff's empathy directly and positively influence it. They also found a significative indirect relation between service quality and behavioral intentions through satisfaction.

Resulting in literature developed previously, we consider that:

H3: Perceived quality of doctor has a positive and direct effect on satisfaction with trip experience H4: Perceived quality of doctor has a positive and direct effect on intentions behavior a. Perceived quality of doctor has a positive and direct effect on intentions behavior with medical purpose b. Perceived quality has a positive and direct effect on intention to revisit the medical destination for pleasure

Price value, tourist-patient satisfaction and intentions behavior

Price is a determinant factor in medical destination choice (Connell, 2013). In fact, many patients undergo medical treatment abroad to avoid the expensive prices of such treatment in their own country. This price represents the perceived cost of destination package or medical provider offer. However, in this research we are interested in perceived price by the touristpatient after medical intervention. According to Zeithaml (1988), perceived price is an encoded price that reflects monetary and non-monetary sacrifices made to obtain the product or service.

In this research we share the point of view of [START_REF] Bolton | A Dynamic Model of Customers' Usage of Services: Usage as an antecedent and consequence of Satisfaction[END_REF] who have defined price value as a perception of paiement equity. Consequently , we consider that price value is the tourist-patient's perception that the price paid is fair, compared to what he received as medical service in the host destination. This definition refers also to the notion of «price fairness».

This terminology was previously used by many researchers in consumer behavior models [START_REF] Martins | Perceived Price Fairness: a New Look At an Old Construct[END_REF][START_REF] Bei | An integrated model for the effects ofperceived product, perceived service quality and price fairness on consumer satisfaction and loyalty[END_REF]Xia, Kent, & Cox, 2004;Diller, 2008). It indicates that the medical intervention made abroad is a « good deal » or the price is "acceptable" with regard to the service received [START_REF] Bei | An integrated model for the effects ofperceived product, perceived service quality and price fairness on consumer satisfaction and loyalty[END_REF]. Previous studies have established a positive and direct relation between perceived price fairness and satisfaction [START_REF] Bolton | A Dynamic Model of Customers' Usage of Services: Usage as an antecedent and consequence of Satisfaction[END_REF][START_REF] Bei | An integrated model for the effects ofperceived product, perceived service quality and price fairness on consumer satisfaction and loyalty[END_REF][START_REF] Andreas | The influence of price fairness on customer satisfaction[END_REF]. The direct and positive relation between perceived price fairness and intentions behavior has also been found [START_REF] Bei | An integrated model for the effects ofperceived product, perceived service quality and price fairness on consumer satisfaction and loyalty[END_REF]Varki & Colgate, 2001). In addition, the negative perception of price could lead to a negative reaction from the consumer such as lower shopping intentions as demonstrated by Cambell (1999).

As a result, we consider in our case that the perception of price fairness leads to a positive intentions behavior toward destination and has a positive and direct effect on tourist-patient satisfaction toward this trip experience. Therefore, we posit:

Research design

The empirical survey was conducted through a self-administered questionnaire in two languages (French and English) that was distributed by different means: internet and directly at the departure from the accommodation (Hotel or rented house) at Tunis. On the web, the invitations to participate in the survey were sent by incorporating links on facebook pages related to the medical tourism context, either by emails. The target population was people who traveled abroad to undertake medical intervention (chirurgical, non-chirurgical, esthetic and non-esthetic intervention (related to illness)). For this purpose, we posited at the beginning of the questionnaire, a screening dichotomous question for which response can be either yes or no and that consists in "have you ever traveled abroad for medical or surgical operation/treatment?" ; In total 130 responses were obtained and 101 were selected as valid for analysis.

Sample

The selected sample is constituted from 51% females and 49% males having different categories of ages and nationalities. 42.5% of respondents are adults aged between 26 and 35 years and 43.5% of them belong to a category of middle-aged adults from 36 years to 55 years. The rest are seniors over 55 years. The major responses are patients with African origin from Tunisia, Algeria, Mauritania and Libya (51.48%). In addition, we have 29.7% of respondents from Europe (France and Swiss) and 18 .81% from the U.S.

Measures

All the measures were adapted from previous literature on tourism, medical service and medical tourism. Moreover, they were pretested with convenience sample of 20 touristpatients. The results of their reliability are mentioned below (See the alpha scores in table 1).

In all the questions, we asked the respondent to denote his level of agreement or disagreement with proposed statements in five points Likert from strongly disagree (1) to, strongly agree (5). The questionnaire survey consisted in the following major parts: questions related to the tourist-patients demographics, date and type of medical intervention and the name of the medical destination where the operation/ treatment was undergone. Moreover, there are questions related to measures of the following variables: doctor perceived quality, satisfaction with trip, price value, accommodation quality, and intentions behavior (See table 1).

Variables

Analysis method

The proposed model was tested by using the partial least square path modeling (PLSPM) with XLSTAT2015 Software. This method is adapted to a small sample and/or with non-exigency about the normality of the data (Chin W. W., 1998;Hair, Ringle, & Sarsted, 2011).

According to [START_REF] Assaker | Partial Least Squares Path Modelling (PLSPM):A New Direction for Research in Tourism and Hospitality[END_REF] PLSPM can overcome the difficulties associated with non-normal datasets, complex models and relatively small sample sizes, which are common in tourism research. Therefore, these authors postulated that the use of this method could expand our undestanding of many phenomena including destination competitiveness, satisfaction, and customer loyalty.

The analysis of the PLSPM consists in two steps (Chin W. , 2010) : (1) analysis of outer model and (2) analysis of structural model. The first step is an evaluation of measures. The constructs of this study are reflexives (Mode A). Therefore, their evaluation consists in the analysis of their reliability, unidimensionality, convergent validity and discriminant validity (Chin W. , 2010;[START_REF] Götz | Evaluation of structural equation model[END_REF]. The second step is related to the evaluation of relations between the latent variables and the hypothesis testing. This step consists in the evaluation of the significance of the path coefficients by combining several methods and indicators: student-t test, effect-size (f²) and confident bootstrap interval. The cross validation of the two models (outer and inner) was carried out with the blindfolding procedure, using G=30.

Results and discussions

Measurement model

Before analyzing data with PLSPM, we conduct a principal component analysis (PCA) with

Varimax rotation on doctor quality items. Our objectives are to get factors that may lead to a more comprehensive model of tourist-patient behavior, and to facilitate the interpretation of results. Therefore, we obtain as a solution three principal components and the proportion of explained variance is equal to 78,132%. The first component is "Kindness" which is reflected by the item "QDoctor1: the doctor who treated me is friendly". The second component is coded "Communication/ information" and reflects the ability of the doctor to understand patient expectations, and his ability to establish with him a real dialogue about the medical process. Their related items are: "QDoctor2", "QDoctor3" QDoctor4" and "QDoctor5" (see table1). The latest component refers to technical skills of a doctor and his trustworthiness. In other words, it reflects the "trustworthy behavior" of a doctor and integrates two items:

"QDoctor6 "("inspires confidence") and "QDoctor7" (knows what he/she is doing and does it well") (see table 1).

The tested model is shown in figure 2 below. The Alpha Cronbach (α) and composite reliability (D.G Rho, ρ) of the all multi-items constructs ("communication/information", "trustworthy behavior" and "intentions behavior 1"), are over .7 as indicated in Table 2. This shows a satisfactory internal consistency of these metrics and their unidimensionality

Table 2. Indicators of measurement model quality

The corresponding average variance extracted (AVE) of these variables are also widely over .5 (see table 2). In addition, the loadings of "communication/information" variable ranging from .76 to .854 and of "intentions behavior 1" construct ranging from .843 to .966. They are the narrow ranges. According to Chin (2010, p 674), measures "with both a higher average loadings and narrower range such as from .7 to .9 you would have greater confidence that all items help (i.e., converge) in estimating the underlying construct". Therefore, the convergent validity for these constructs is satisfied.

On the other hand, the discriminant validity, "is supported if a latent variable's AVE is larger than the common variances (squared correlations) of this latent variable with any other of the model's constructs" (Fornell & Larcker, 1981from Götz & al 2010, p 696). In our case, this condition is supported, so the discriminant validity is also confirmed. Therefore, the variables of the proposed model are distinct theoretical constructs (see table 3). Furthermore, "kindness" dimension of doctor quality does not have a significant direct impact on intentions behavior toward a host destination. In contrast, the "communication /information" is a significant direct and positive antecedent of both intentions behavior with medical purpose ( = .330 and p-value=.012 ˂.05) and intention to revisit for pleasure ( = .257 and p-value=.043 ˂.05). "Trustworthy behavior" appears as only a significant and positive antecedent of intention to revisit for pleasure ( = .266 and p-value=.034 ˂.05).

Kindness Com/info TB AQ PV STE IB1 IB2 AVE

Consequently, the hypothesis 4 is partially supported. Concerning the perceived price fairness, results showed that this variable does not have a significant direct impact on all the three dependent variables (see table 4). Therefore, hypothesis 5 and 6 are also not supported.

The blindfolding test (G=30) showed positive scores of average CV-communalities a little below or downright superior to 0.5 that indicate the good quality of measurement model [START_REF] Götz | Evaluation of structural equation model[END_REF]Hair, Ringle, & Sarsted, 2011). However, for the average scores CV-redundancies related to intentions behavior (1) and satisfaction with trip are negative. This indicates that the predictive relevance of these variables is doubtful. In contrast, concerning the "intention behavior 2" , the result of the blindfolding test showed the Q² equal to 0.189 that is larger than zero, which indicates the good predictive relevance of this variable (Chin W. , 2010). Looking closer at these scores, we notice that the intention1

("no regret"), intention2 (intention to recommend), and the intentions 3 (positive WOM) are less predicted by the proposed model because their corresponding CV-redundancy are negative. On the other hand, intention to revisit for other medical intervention (intention 4), and for pleasure (IB2) are well predicted with this model. This obtained result from the REBUS-PLS analysis was performed by the permutation test (number of permutations =1000, α=5%) based on these two classes. This test confirmed the dissimilarity between these groups at the level of inner-model and showed that there is no significant difference between them at the level of measurement model. Especially, the permutation test confirmed the existence of significant difference between them, at the level of three structure relationships as shown in table 6 below. This difference lies not in strength of relations between latent variables which is higher in both segments, but in a sign of these relations. The characteristics of these two segments are as follow:

GoF

Indicators

Class 1: The occasional tourist-patients (n=32)

This class is characterized by a negative relationship between accommodation quality and intention to revisit the destination for pleasure. The effect size of this variable on the structural equation is high (f² = .482 ˃ 0.35) (Chin W. , 2010). In addition, the price fairness has a high negative impact on intentions behavior 1 (β= -.794) and the doctor communication/ information dimension has a high negative impact on satisfaction with the trip (β= -. 391).

Mainly we note that if the practitioners make further effort to improve the quality of accommodation or/and the perception of price fairness, they can make this kind of touristpatient as relatively satisfied but they will not obtain from him a positive intentions behavior toward this medical destination such as revisit intentions or recommendation.

Class2: The quality oriented tourist-patients (n=69)

This class is characterized by a weaker influence of perceived price fairness on the three dependent variables. In contrast, it is characterized by a strong positive relationship between the "Communication/information" dimension of perceived doctor quality, and both variables "satisfaction with trip" and "intention to revisit for pleasure" (intention behavior 2). In addition, in this segment of TP, the trustworthiness of doctor has a significant and positive impact on the intentions behavior (1). Quality of accommodation appears also as a significant and positive determinant of satisfaction with trip, intentions behavior (1) and intention behavior (2). As a result, we can note that if the stakeholders in this sector make further efforts to improve quality of services at the destination level, they will make this kind of tourist-patient as satisfied, and at the same time, they will influence positively his intentions behavior with medical purpose and those related to entertainment motives.

According to M.Mehmetoglu 2011, such segmentation is not sufficient for gearing marketingmix activities toward a specific segment, it should be complemented by a follow-up procedure that profiles individuals belonging to different obtained segments in relation to other relevant external variables such a socio-demographic data. Knowing that such a procedure is not available at the moment in Rebus-pls, this author started-up a CHAID analysis (Chisquared automatic interaction detector) which is considered as compatible with PLS-SEM because they both handle the non-normally distributed data. In our case, we choose to undertake the same procedure to determine relevant individual characteristics for each TP segment. Consequently, we run a CHAID analysis in which the dependent variable is the two obtained segments from the REBUS-PLS and the independent variables are : gender, age, country of origin, intervention type and medical destination. The results of this analysis are discussed in the following paragraph.

Profile of both occasional and quality oriented Tourist-patient

The CHAID analysis showed that the gender and intervention type are not pertinent in characterizing both tourist-patient segments. In contrast the other independent variables are more suitable (p-value=.000). Therfore, as shown in the figure 4 below, there is a high percentage of "occasional Tourist-patient" (occasional TP) among American tourist-patients and a higher percentage of "quality oriented tourist-patient" (quality oriented TP) among

European and African tourist-patients. In addition, there is a high percentage of "occasional TP" among seniors (≥56 years) and a high percentage of "quality oriented TP" among touristpatient aged less than or equal to 55 years (see figure 5). And finally, this analysis also reveals that there is a high percentage of "occasionnal TP" among the tourists that had made their medical intervention in the Asiatic destinations such as china, Malysia and India. On the other hand, there is a high percentage of "Quality oriented patient" among those that had made their medical intervention in Tunisia and other countries (ex.Hungary).

Conclusion

The most important finding of this research is the behavioral segmentation of the touristpatients on two groups based on their intentions behavior toward the medical destination.

They consist in the "occasional TP" which is intentionally non-loyal. This group takes the opportunity to make the medical intervention abroad, and that is all. They do not have any intentions to recommend and to speak positively about this destination or to revisit it, even if they have a positive perception of price and services provided. In contrast, the group of "quality oriented TP" is sensible to quality of accommodation, communication and trustworthiness dimensions of doctor quality and may have a positive intention if supplementary efforts were made in these directions.

From the managerial standpoints, these results imply that the main interesting segment in term of profitability for both destination and stakeholders in medical tourism sector which concerns exclusively medical intervention (medical treatment or chirurgical intervention related to illness or for esthetic purposes), may be the group of "the quality oriented TP".

In addition, this study showed that perceived price fairness is a marginal variable in touristpatient satisfaction and his behavioral intentions mainly for "oriented quality TP". In fact this study revealed that whether the perceived price fairness is high, the "occasionnal TP" will not have a positive intention toward the medical destination. On the other hand, this variable is also insignificant in tourist-patient satisfaction and his behavioral intentions for the group of "quality oriented TP". Such result indicates that if the price is a crucial element in marketing strategy to attract the newest tourist-patient (Connell, 2013;Doshi, 2008), it does not constitute a suffuciant element to retain them. These results are similar to those founded by [START_REF] Chaohui | Impact of Tourists′ Perceived Value on Behavioral Intention for Mega Events: Analysis of Inbound and Domestic Tourists at Shanghai World Expo[END_REF] in event tourism context . Furtheremore, these could have a theorotical support in some finding of Cronin, Brady and Hult (2000) study. In fact, these authors concluded that consumers regarding healthcare services, seem to place greater importance on the quality of a service than they do on the costs associated with this acquisition. Consequently, we consider that quality seems to be as key variable in developing strategic and operational marketing in medical tourism market. In addition, these results encourage to establish in medical tourism context, a quality oriented theoretical framework for destinations.

Finally, we note that this study confirmed for the group of "quality oriented TP" that perceived quality is a good predictor of intentions behavior for both medical purpose and pleasure. This showed that a success of such medical experience could tempt the tourist to come to the same destination to see it in a different way and thus experiment in it other tourism products (ex. cultural, wellbeing, etc.). This result implies that further efforts should be made by the different stakeholders including government to enrich such experience and build such intentions behaviors toward a destination. In addition, this result implies that any experience with one destination can influence the attitude and future intentions toward this destination regardless of the product consumed at the level of this destination .

H1:

  Perceived quality of destination accommodation has a direct and positive effect on tourist-patient satisfaction with trip experience. H2: Perceived quality of destination accommodation has a direct and positive effect on behavioral intentions a. Perceived quality of destination accommodation has a positive and direct effect on behavioral intentions with medical purpose b. Perceived quality of destination accommodation has a positive and direct effect intention to revisit the medical destination for pleasure

H5

  Positive perception of price has a direct and positive effect on tourist-patient satisfaction with trip experience H6 Positive perception of price has a direct and positive effect on tourist-patient intentions behavior a. Positive perception of price has a direct and positive effect on tourist-patient intentions behavior with medical purpose b. Positive perception of price has a direct and positive effect on tourist-patient intention to revisit the medical destination for pleasure Finally, we propose the following schema that represents the proposed model of touristpatient satisfaction and his behavioral intentions toward a medical destination. In addition, it summarizes all the hypothesis of research mentioned before.

Figure 1 .

 1 Figure 1. Proposed model of tourist-patient satisfaction and intentions behavior toward medical destination

Figure

  Figure 3. Dendrogram obtained by REBUS-PLS Global n=101

Figure 4 .

 4 Figure 4. Result of CHAID analysis according to nationalities Note. TP= Tourist-Patient; Purity= % of objects corresponding to the dominating class at the node level.

Figure 5 .

 5 Figure 5. Result of CHAID according to ages

Table 1 . Measures and definitions of variables

 1

		Definition	Items
	Doctor quality	The perceived quality of	Alpha de Cronbach = 0.856
		doctor means: his empathy,	QDoctor1:"The doctor who treated me is
	(D'Souza and	his abilities to communicate	friendly"
	Sequeira, 2012;	with patients and to	QDoctor2: "has explained me everything
	Choi& al., 2004)	understand their needs, his	concerning the intervention, the treatment
		technical skill and his	and the consequence of the cure"
		trustworthiness.	QDoctor3: "has allowed me to ask him/
			her as much as I wanted to clear every
			thing"
			QDoctor4: "has carefully considered my
			expectations"
			QDoctor5: "has made me at ease"
			QDoctor6: "inspires confidence"
			QDoctor7: "he/she knows what he /she is
			doing and does it well"
	Satisfaction with	A one-item variable reflects
	trip experience	the overall satisfaction with	STE:"Overall I'm satisfied with my stay"
	(Assaker, Vinzi,	the trip experience lived at
	and O'Connor,	the destination level.
	2011)
	Accommodation	A one-item variable that
	quality	reflects overall perceived
	(Žabkar, Brencic,	quality of accommodation	AQ:"Accommodation is of a good quality"
	and Dmitrovic,	(ex. Hotel, rented house,
	2010)	etc.)
	Price value	A one-item variable that
	(Voss,	reflects the fairness of price
	Parasuraman,and	of medical intervention	PV:"Reasonable price"
	Grewal, 1998; Bei	effected abroad.
	and Chiao, 2001)

Table 3 . Discriminant validity of constructs (AVE˃ square correlations)

 3 higher than .7. However, concerning the "communication/information" dimension, the student test is significant at the level of α=.05, but the corresponding bootstrap interval contains zero. Consequently, we consider that the hypothesis (3) is not supported.

	˃r²

is

Table 4 . PLSPM results: path-coefficients scores and significance

 4

Table 5 . Measurement model results for the global and local models.

 5 Path coefficient is significant at the level of. 05 ** Path coefficient is significant at the level of .001.

		.413	.584	.604
	Satisfaction with trip
	R²	.341	.423	.466
	Doctor quality
	Kindness	-.04	.044	-.001
	Communication /information .275	-.391* .511*
	Trustworthiness	.033	-.245	-.004
	Accommodation quality	.344** .372*	.398**
	Price value	.182	.246	.228*
	Intentions behavior 1
	R²	.191	.604	.582
	Doctor quality
	Kindness	-.072	.137	-.211
	Communication /information .330	.084	.193
	Trustworthiness	.180	.312	.668**

*

Table 6 . The results of permutation test between the two classes.

 6

	Difference	P˂.05

n.s: test not significant p˃.05

Results of the Structural model

The determination coefficient (R²) of the three dependents variables, satisfaction with trip, intentions behavior1 and intention behavior2, are significant and equal respectively to .231, .192 and .239 (figure 2).

Figure 2. The results of PLS-PM structural model

The accommodation quality appears as a significant determinant of satisfaction with the trip experience (β= .344; p-value=.000˂ .001) (See table.4). Nevertheless, it does not constitute a significant determinant of both intentions behavior dimensions. Because the non-significance of corresponding path coefficients: β (AQ→IB1) =.132 with p-value= .180˃ .1, and β(AQ→IB2)= .133 with pvalue= .164˃ .1 .These findings were also confirmed by corresponding effect size scores ( ) that are lower than .02 (See table 4). As a result, these variables do not have a significant impact on these structural equations (Chin W. , 2010;Hair, Ringle, & Sarsted, 2011).

In addition, the bootstrap test resulted in confident intervals that contain zero (see table 4). In consequence, we concluded that the hypothesis (1) of this research is supported. In contrast, the hypothesis (2) is not confirmed. The three dimensions of doctor quality as shown in table 4 below do not have a significant direct and positive effect on satisfaction with trip. The student -t tests for both "Kindness" and "trustworthy" dimensions, are not significant, p-value Concerning the GoF values, we note that the relative GoF; GoF of inner model and of outer model, are above .9 (See figure .2). These indicate the good quality of the proposed model (Vinzi, Trinchera, & Amato, 2010;Chin W. , 2010). However, according to Vinzi and al (2010), in such case and when we have the lower values of R² associated with a higher factor loadings in measurement model (in our case the smallest loadings is equal to .760, see table .2), this could be a sign of possible unobserved heterogeneity in the data. Consequently, we conduct at this level of the study a Rebus-PLS analysis to determine the eventual post-hoc homogenous segments of tourist-patient intentions behavior. This latest variable constitute the key variable in medical tourism context that can be a good predictive of effective loyalty behavior toward a medical destination as were suggested by the theory of planned behavior (Ajzen, 1991). Obtaining such results can improve knowledge of the tourist-patient behavior and as a result help to formulate a suitable product policy for the most attractive segments (M. Mehmetoglu, 2011;Han.H & Hyun.SS, 2015).

Post-hoc segmentation of tourist-patient intentions behavior

Vinzi V. E. and al ( 2008) presented the REBUS-PLS as a newest method to capture unobserved heterogeneity in PLS-PM by detecting the sources of heterogeneity in both the structural and the outer model for all exogenous and endogenous latent variables. This method requires all block of variables to be reflective which is the case of this study (Vinzi V. E., Trinchera, Squillacciotti, & Tenenhaus, 2008;Vinzi, Trinchera, & Amato, 2010). In our case, performing the REBUS-PLS in the global model previously described gave as result automatically two latent classes (see figure 3). We note that the item of "doctor 7" related to latent variable "trustworthy behavior" was eliminated because it was detected by the REBUS-PLS algorithm as constant in class 2.

The table.5 below presents the results of path coefficients for global model (whole sample)

and local models. This solution shows a Group quality index (GQI) equal to .573, which is higher than the absolute GoF of global model (.413). This improvement is higher than 25%, which is a satisfactory result (Trinchera, 2007;Vinzi, Trinchera, & Amato, 2010). For the two groups, the GoF values (relative, inner and outer models) are over .9 (See table 5).

The AVE related to the multi-items variables are over .5. The measurement model is as satisfactory in both segments. In addition, the R² values of the three dependent variables were ameliorated mainly those related to intentions behavior 1 where R² related to class 1 is over .6 and for class 2 is over .5. For the rest, the percentage of explained variance remains little lower than .5.

Limitations and further research directions

The main limit of this study consists in the small sample size and its exploratory character, which cautions any generalization of results. However, it is important to note that the stability of models (inner and outer) was checked out by a Bootstrap method (5000 re-sampling) and it is as satisfactory.

The explained variances of the three dependent variables (satisfaction, intentions (1) and ( 2))

for the two groups are around 0.5 or over 0.6. This indicates that a 0.4 or 0.5 of variance remains not explained. This amounts to the fact that the proposed model does not include all possible variables and elsewhere more research needs to be done in this direction, taking into account the quality of services as main factor. At final, this study provides insight on trends in perceptions and behavioral intentions of the TP through the destinations and nationalities where it is clear that US patients especially the seniors are for the most part the "occasional patients." Consequently, other research with large samples, need to be carried to check these trends by incorporating other destinations and other nationalities in order to consolidate the results found in this study. Xiao, H., & Barber, J. P. (2008). The effect of perceived health status on patient satisfaction.

Value in health , 11, 4, 719-725. Žabkar, Brencic, & Dmitrovic. (2010). Modelling perceived quality, visitor satisfaction and behavioural intentions at the destination level,. Tourism Management ,31,[537][538][539][540][541][542][543][544][545][546]