Pierre Brigode
email: pierre.brigode@upmc.fr

Ludovic Oudin

Charles Perrin

Hydrological model parameter instability: A source of additional uncertainty in estimating the hydrological impacts of climate change?

Keywords: Climate change, rainfall-runoff modelling, hydrological model calibration, uncertainty, robustness

This paper investigates the uncertainty of hydrological predictions due to rainfall-runoff model parameters in the context of climate change impact studies. Two sources of uncertainty were considered: (i) the dependence of the optimal parameter set on the climate characteristics of the calibration period and (ii) the use of several posterior parameter sets over a given calibration period. The first source of uncertainty often refers to the lack of model robustness, while the second one refers to parameter uncertainty estimation based on Bayesian inference. Two rainfall-runoff models were tested on 89 catchments in northern and central France. The two sources of uncertainty were assessed in the past observed period and in future climate conditions. The results show that, given the evaluation approach followed here, the lack of robustness was the major source of variability in streamflow projections in future climate conditions for the two models tested. The hydrological projections generated by an ensemble of posterior parameter sets are close to those associated with the optimal set. Therefore, it seems that greater effort should be invested in improving the robustness of models for climate change impact studies, especially by developing more suitable model structures and proposing calibration procedures that increase their robustness.

INTRODUCTION

Hydrological projections under climate change and their associated uncertainties

The impacts of climate change on catchment behaviour have been extensively investigated over the last few decades (see e.g. for Europe Arnell, 1999a, Arnell, 1999b; for Australia Vaze et al., 2011 andVaze andTeng, 2011). Quantitatively assessing the uncertainties associated with hydrological projections is a difficult task, even if qualitatively it is now recognised that these uncertainties are considerable. They stem from the methods used to generate climate projections as well as from hydrological modelling. Moreover, the relative importance of the various uncertainty sources is not easy to assess. [START_REF] Wilby | A framework for assessing uncertainties in climate change impacts: Low-flow scenarios for the River Thames, UK[END_REF] proposed a framework to assess the relative weights of the sources of uncertainty in future low flows for the River Thames. They consider that uncertainty sources should be ranked in decreasing order as follows: Global Circulation Models (GCMs) > (empirical) downscaling method > hydrological model structure > hydrological model parameters > emission scenario. However, this conclusion was obtained using only two rainfall-runoff models applied to a single catchment. [START_REF] Wilby | Uncertainty in water resource model parameters used for climate change impact assessment[END_REF] noted that depending on the rainfall-runoff model used (and possibly the catchment studied), the uncertainties associated with hydrological modelling may predominate. More recently, [START_REF] Chen | Overall uncertainty study of the hydrological impacts of climate change for a Canadian watershed[END_REF] showed on a Canadian catchment that the choices of GCMs and downscaling techniques are the greatest uncertainty sources in hydrological projection estimations, followed by emission scenarios and hydrological model structures, and last hydrological model parameter estimation. On several southeastern Australian catchments, [START_REF] Teng | Estimating the Relative Uncertainties Sourced from GCMs and Hydrological Models in Modeling Climate Change Impact on Runoff[END_REF] also showed that uncertainties stemming from fifteen GCM outputs are much greater than the uncertainties stemming from five hydrological models. Focusing on future hydrological trends in the UK, [START_REF] Arnell | Uncertainty in the relationship between climate forcing and hydrological response in UK catchments[END_REF] showed that "uncertainty in response between climate model patterns is considerably greater than the range due to uncertainty in hydrological model parameterization." These results show that the uncertainties generated by the hydrological modelling step, though generally lower than that generated by the climate modelling step, can be significant in some cases and should not be ignored in climate change impact studies.

The common sources of uncertainty in hydrological modelling in stationary conditions (in terms of climate conditions and/or physical characteristics) include errors in model structure, problems in the calibration procedure, and errors in the data used for calibration. In nonstationary conditions, as in climate change studies, additional uncertainties may come from parameter instability due to the possible changes in the physical catchment characteristics and in the dominant processes. In both cases, model structure errors and the identification of model parameters can generally be considered as the two main sources of uncertainty in the hydrological modelling step. Several methods exist for studying uncertainties due to model structure (see e.g. [START_REF] Refsgaard | A framework for dealing with uncertainty due to model structure error[END_REF]. In climate change impact studies, the errors stemming from the model structure are usually assessed using several rainfall-runoff models and quantifying the range of their outputs [START_REF] Booij | Impact of climate change on river flooding assessed with different spatial model resolutions[END_REF][START_REF] Wilby | Uncertainty in water resource model parameters used for climate change impact assessment[END_REF][START_REF] Wilby | A framework for assessing uncertainties in climate change impacts: Low-flow scenarios for the River Thames, UK[END_REF][START_REF] Jiang | Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin, South China[END_REF]. The problem of parameter identification has been widely investigated and many methods to quantify the associated uncertainty have been proposed (see e.g. Matott et al., 2009, for a review). In a recent study, [START_REF] Bastola | The role of hydrological modelling uncertainties in climate change impact assessments of Irish river catchments[END_REF] attempted to quantify these two hydrological uncertainty sources (model structure and parameter sets) in a climate change context using a multi-model approach combining multiple emission scenarios and GCMs, four conceptual rainfall-runoff models and two parameter uncertainty evaluation methods (Generalized Likelihood Uncertainty Estimation and Bayesian Model Averaging). The authors concluded that "the role of hydrological model uncertainty is remarkably high and should therefore be routinely considered in impact studies." Note that the type of hydrological model used (physically-based or conceptual, lumped or distributed, etc.) may also be considered as an uncertain choice, in both stationary and non-stationary conditions. It is often considered that the physical basis of process descriptions is indispensable to maintain the predictive power of hydrological models in a changing climate (see e.g. [START_REF] Ludwig | The role of hydrological model complexity and uncertainty in climate change impact assessment[END_REF].

A few studies have covered this issue by considering both conceptual and physically-based models (see e.g. [START_REF] Poulin | Uncertainty of hydrological modelling in climate change impact studies in a Canadian, snowdominated river basin[END_REF]. The RExHySS project [START_REF] Ducharne | Impact du changement climatique sur les Ressources en eau et les Extrêmes Hydrologiques dans les bassins de la Seine et la Somme[END_REF][START_REF] Ducharne | Evolution potentielle du régime des crues de la Seine sous changement climatique[END_REF] addressed this issue on the Seine River basin (France) by considering seven hydrological models, including distributed (predominantly) physically-based models, semidistributed physically-based models and lumped conceptual models. Interestingly, the results showed that the conceptualisation of the models was not the main source of variability in hydrological projections among the model simulations since large differences were found between models with similar conceptualisations.

Can model parameter instability be a major source of uncertainty?

Other studies have investigated the dependence of the model parameters on the characteristics of the record period used for calibration. In climate change impact studies, the record period used to calibrate the model differs from the projected period. Since rainfall-runoff model parameters must be calibrated using the available data sets, they will partially account for the errors contained in these data (see e.g. [START_REF] Yapo | Automatic calibration of conceptual rainfallrunoff models: sensitivity to calibration data[END_REF]Oudin et al., 2006a) and/or their specific climate characteristics (see e.g. [START_REF] Gan | An assessment of a conceptual rainfall-runoff model"s ability to represent the dynamics of small hypothetical catchments, 2: hydrologic responses for normal and extreme rainfall[END_REF]. This is a well-known issue for conceptual rainfall-runoff models but physically-based models are also affected by this problem (see e.g. [START_REF] Rosero | Quantifying parameter sensitivity, interaction, and transferability in hydrologically enhanced versions of the Noah land surface model over transition zones during the warm season[END_REF]. Model parameters are the integrators of the data"s information content. Different time periods used for calibration may provide quite different optimum parameter sets, depending on whether the period is dry or wet, for example, thus providing an estimation of parameter uncertainty with respect to their lack of robustness. Here [START_REF] Beven | Prophecy, reality and uncertainty in distributed hydrological modelling[END_REF] states that "it is easy to show that if the same model is "optimised" on two different periods of record, two different optimum parameter sets will be produced. Extension to multiple calibration periods, if the data were available, would yield multiple optimum parameter sets. The resulting parameter distributions would reflect the uncertainty in the parameter estimates and the interaction between the individual parameters." As stressed by [START_REF] Gan | An assessment of a conceptual rainfall-runoff model"s ability to represent the dynamics of small hypothetical catchments, 2: hydrologic responses for normal and extreme rainfall[END_REF], this obviously "should be heeded by modelers who use calibrated conceptual models to explore hydrologic consequences of climate change." As a consequence, and without clear guidelines on how the model should be calibrated for climate change impact studies, most hydrologists calibrate their models with all the available data (e.g. Vaze and Teng, 2011) or with the longest observed period they consider representative of the current hydro-climatology conditions (e.g. [START_REF] Poulin | Uncertainty of hydrological modelling in climate change impact studies in a Canadian, snowdominated river basin[END_REF], generally considering a priori that "the longer the calibration period, the more robust the parameter set."

One way to evaluate the capacity of models to represent the hydrological behaviour of a catchment in a changing climate is to apply the differential split-sample test, introduced by [START_REF] Klemeš | Operational testing of hydrological simulation models[END_REF]. In this testing scheme, two contrasted periods are identified in the available record and the split-sample test is performed using these two periods. If the model is intended to simulate streamflow under wetter climate conditions, then it should be calibrated on a dry period selected in the available record and validated on a wet period. Conversely, if it is intended to simulate flows under drier climatic conditions, the reverse should be done. The model should demonstrate its ability to perform well in these contrasted conditions. Despite the simplicity of the test, relatively few authors have followed the differential split-sample test in the past (see e.g. [START_REF] Jakeman | Assessing uncertainties in hydrological response to climate at large scale[END_REF][START_REF] Refsgaard | Operational validation and intercomparison of different types of hydrological models[END_REF][START_REF] Donnelly-Makowecki | Hierarchical testing of three rainfall-runoff models in small forested catchments[END_REF][START_REF] Seibert | Reliability of model predictions outside calibration conditions[END_REF][START_REF] Wilby | Uncertainty in water resource model parameters used for climate change impact assessment[END_REF]. More recently, [START_REF] Merz | Time stability of catchment model parameters: Implications for climate impact analyses[END_REF] applied the test to a large set of 273 catchments in Austria and found that the parameters of the hydrological model controlling snow and soil moisture processes were significantly related to the climatic conditions of the calibration period. Consequently, the performance of the model was particularly affected if the calibration and the validation periods differed substantially. [START_REF] Vaze | Climate nonstationarity -Validity of calibrated rainfall-runoff models for use in climate change studies[END_REF] also applied the differential split-sample test to 61 catchments in southeast Australia with four conceptual hydrological models. They found that the performance of these models was relatively dependent on the climatic conditions of the calibration period. On 216 southeastern Australian catchments, [START_REF] Coron | Crash Testing Hydrological Models in Contrasted Climate Conditions: An Experiment on 216 Australian Catchments[END_REF] highlighted the same lack of robustness of three hydrological models tested in climatic conditions different from those used for parameter calibration. [START_REF] Vaze | Climate nonstationarity -Validity of calibrated rainfall-runoff models for use in climate change studies[END_REF] therefore suggest that it would be wiser to calibrate model parameters on a portion of the record with conditions similar to those of the future period to simulate. This idea was also put forward by [START_REF] Vos | Diagnostic evaluation of conceptual rainfall-runoff models using temporal clustering[END_REF], who proposed dynamically re-calibrating model parameters for each temporal cluster by finding analogous periods in the historical record. Following similar motivations, [START_REF] Luo | Effects of conditional parameterization on performance of rainfall-runoff model regarding hydrologic non-stationarity[END_REF] showed that more consistent model predictions on specific hydrological years are obtained if a selection of calibration periods is performed, and [START_REF] Singh | A trading-space-fortime approach to probabilistic continuous streamflow predictions in a changing climateaccounting for changing watershed behavior[END_REF] used adjusted parameter values depending on the aridity of the catchment considered for improving model prediction. These methodologies could be applied for simulating future hydrological conditions, but unfortunately, as stated by [START_REF] Prudhomme | Assessing uncertainties in climate change impact analyses on the river flow regimes in the UK. Part 2: future climate[END_REF], long records that include climatic conditions similar to what could be expected in the future are lacking. This makes it difficult to identify a set of parameters specific to such future conditions. Note that in some regions, climate changes have occurred in the past and it is therefore possible to objectively assess the potential of hydrological models to cope with changing climate. This is the case for Central and Western Africa, affected by a marked reduction in rainfall and runoff from the year 1970 onwards. Using different models on different catchments in this region, [START_REF] Niel | Study of parameter stability of a lumped hydrologic model in a context of climatic variability[END_REF] and Le [START_REF] Lay | Exploring the relationship between hydroclimatic stationarity and rainfall-runoff model parameter stability: A case study in West Africa[END_REF] showed no evidence that non-stationarity in climate would incur model parameter instability.

Scope of the paper

This paper intends to investigate the uncertainty of hydrological predictions for the future climate. To this aim, we followed Klemeš"s differential split-sample test and assessed the corresponding variability of the simulated hydrological impacts of projected climate when considering alternatively (i) the dependence of the optimal parameter set on the calibration period characteristics and (ii) an ensemble of posterior parameter sets obtained on a given calibration period. Each source of uncertainty was already studied in the context of changing climate, but their relative importance has not been assessed so far. Besides, most studies focusing on the parameter"s dependency on climate conditions did not assess the consequences of choosing various calibration strategies on future hydrological projections.

Here we will attempt to assess the long-term effects of these two sources of uncertainty in future conditions.

DATA AND MODELS

Catchment set

A set of 89 catchments located in northern and central France was used, namely the Somme River at Abbeville, 22 sub-catchments of the Loire River basin and 66 sub-catchments of the Seine River basin (see Figure 1). Catchment area ranges from 32 to 109,930 km², runoff yield ranges from 0.11 to 0.69 and the aridity index (here defined as the ratio of mean annual [START_REF] Penman | Natural Evaporation from Open Water, Bare Soil and Grass[END_REF] potential evapotranspiration to mean annual rainfall) ranges from 0.64 to 1.39.

Compared to the Seine basin sub-catchments, the sub-catchments of the Loire River basin add diversity in terms of physiographic characteristics (with generally larger areas, higher elevations, and a different geological context), and hydro-climatic characteristics (with generally higher runoff yields). None of the catchments studied is strongly influenced by upstream dams.

FIGURE 1: Location and distribution of various characteristics of the 89 catchments used.

The boxplots show the 0.10, 0.25, 0.50, 0.75 and 0.90 percentiles (67 is the number of catchments in the Seine and Somme basins, 22 in the Loire basin).

Hydro-meteorological data

The hydrological models tested here require only daily time series of potential evapotranspiration (PE) and rainfall (P) as input data. We used climate data from the SAFRAN meteorological reanalysis [START_REF] Quintana-Segui | Analysis of near-surface atmospheric variables: Validation of the SAFRAN analysis over France[END_REF][START_REF] Vidal | A 50year high-resolution atmospheric reanalysis over France with the Safran system[END_REF], which provides daily series of Penman PE and P from 1970 to 2007 at a mesoscale (on an 8 × 8 km grid). These data were aggregated for each catchment in order to estimate mean areal inputs.

Besides daily streamflow (Q), time series were used to calibrate the models and assess their performance.

Since it is not within the scope of this paper to discuss the uncertainties related to climate projections, the outputs of a single general circulation model (GFDL CM2.1) driven by the A1B emissions scenario [START_REF] Ipcc | Climate change 2007: the physical science basis, 4th Assessment Report[END_REF] were chosen as climate projections. These outputs were regionalised using a statistical downscaling method based on weather types [START_REF] Boé | A simple statistical-dynamical downscaling scheme based on weather types and conditional resampling[END_REF], producing a database at the same spatial resolution as the SAFRAN database (8 × 8 km).

Three time slices with continuous daily series of PE and P were used in this study:

 1980-2000, referred to as "present time" and noted PT hereafter;  2045-2065, referred to as "mid-century" and noted MC hereafter;  2080-2100, referred to as "end-of-century" and noted EC hereafter. This scenario was tested on the Seine and the Somme basins within the RExHySS project [START_REF] Ducharne | Impact du changement climatique sur les Ressources en eau et les Extrêmes Hydrologiques dans les bassins de la Seine et la Somme[END_REF][START_REF] Ducharne | Evolution potentielle du régime des crues de la Seine sous changement climatique[END_REF] and on the Loire River basin within the ICC-Hydroqual project [START_REF] Moatar | La Loire à l"épreuve du changement climatique[END_REF]. For the Seine and the Somme basins, the downscaled projection simulates an increase in mean annual air temperature of 1.8°C by MC and 3.1°C by EC, a decrease in mean annual precipitation of 5% by MC and 10% by EC (with an increase of winter precipitation and a decrease of summer precipitation) and an increase in potential evapotranspiration of 16% by MC and 26% by EC. These predictions are close to the mean trends estimated with up to 14 climate projections used in the RExHySS and ICC-Hydroqual projects, making the scenario used in this study an in-between scenario.

Rainfall-runoff models

Two daily continuous lumped rainfall-runoff models were used to avoid providing modelspecific conclusions:

 The GR4J rainfall-runoff model, an efficient and parsimonious (four free parameters) model described in detail by [START_REF] Perrin | Improvement of a parsimonious model for streamflow simulation[END_REF];  The TOPMO model (six free parameters), inspired by TOPMODEL [START_REF] Beven | A physically based, variable contributing area model of basin hydrology[END_REF][START_REF] Michel | The exponential store: a correct formulation for rainfall-runoff modelling[END_REF], already tested on large data sets. This lumped model is quite different from GR4J but has comparable performance (see e.g. Oudin et al., 2006b). Here the distribution of the topographic index is parameterised and optimised, and not calculated from a digital elevation model. This was found to have only a limited impact on model efficiency, as shown by [START_REF] Franchini | Physical interpretation and sensitivity analysis of the TOPMODEL[END_REF] and this eases the application of the model when it is tested on a large set of catchments.

Note that we did not explicitly investigate the uncertainties stemming from hydrological model structures. This was analysed e.g. by [START_REF] Seiller | Multimodel evaluation of twenty lumped hydrological models under contrasted climate conditions[END_REF] using a multi-model approach in a climate change perspective.

Model parameterisation

The optimisation algorithm used to calibrate parameter values is the Differential Evolution Adaptive Metropolis (DREAM) algorithm [START_REF] Vrugt | Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling[END_REF]. DREAM optimises model parameters on a given period and additionally infers the posterior probability distribution of model parameter values through Markov Chain Monte Carlo (MCMC) sampling.

As an objective function, we used the formal Generalized Likelihood function described by [START_REF] Schoups | A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors[END_REF], which considers correlated, heteroscedastic, and non-Gaussian errors (noted GL hereafter). The results in validation are analysed with the Nash and Sutcliffe (1970) efficiency criterion, which is still widely used in modelling studies. It was computed on root square transformed flows (noted NSEsq hereafter), which makes it possible to assess model efficiency for both high and low flows (Oudin et al. 2006b).

METHODOLOGY FOR INVESTIGATING PARAMETER UNCERTAINTY IN A CHANGING CLIMATE

General methodology

The building blocks of the method originate from the differential split-sample test recommended by [START_REF] Klemeš | Operational testing of hydrological simulation models[END_REF] and the methodology followed by [START_REF] Wilby | Uncertainty in water resource model parameters used for climate change impact assessment[END_REF]. The parameter uncertainty associated with the changing climate is characterised by the variability of the parameters across calibration sub-periods with varying hydroclimatic characteristics.

The methodology is carried out in three steps (see Figure 2 Note that a similar methodology was used in the RheinBlick project [START_REF] Görgen | Assessment of Climate Change Impacts on Discharge in the Rhine River Basin: Results of the RheinBlick2050 Project[END_REF] for quantifying uncertainties due to the parameters of hydrological models in a climate change perspective on the Rhine basin.

Step 1: Identification of climatically contrasted sub-periods

For each catchment, four climatically contrasted 3-year sub-periods were identified in the available record: a wet sub-period, two dry ones and an intermediate one. The driest subperiod will be used as the validation period (hereafter noted dry validation sub-periods) and the three others will be used as calibration sub-periods. This choice was made because the selected climate projection indicates that future conditions will be drier and warmer on the test basins. The aridity index (here defined as the ratio of mean Penman potential evapotranspiration to mean precipitation) was used to characterise the climatic specificity of each sub-period: the wet sub-period corresponds to the three contiguous hydrological years with the lowest aridity index (here a hydrological year starts on September 1 and ends on August 31). The choice of this index is rather arbitrary and may influence the results obtained hereafter. However, since it is solely based on climate characteristics, this makes it possible to assess the climatic specificity of the chosen sub-periods compared to the projected future climate. Obviously, it was not possible to use a criterion based on observed streamflows, as done by [START_REF] Seibert | Reliability of model predictions outside calibration conditions[END_REF] on observed data, since future flow observations by definition do not exist.

The choice of the length of the record sub-period to consider is not straightforward since it is based on a trade-off between two opposite expectations: (i) the longer the sub-periods, the more robust the set of parameters should be and (ii) the shorter the sub-periods, the more climatically contrasted sub-periods can be found in the record period. A review of the literature (see e.g. the review proposed by [START_REF] Perrin | Impact of limited streamflow data on the efficiency and the parameters of rainfallrunoff models[END_REF] shows that there is no clear consensus on the minimum length of calibration period for rainfall-runoff models, which is probably attributable to the specificity of the catchments and models used in those studies.

Specifically for the two parsimonious models used in this paper, [START_REF] Anctil | Impact of the length of observed records on the performance of ANN and of conceptual parsimonious rainfall-runoff forecasting models[END_REF] obtained good GR4J performance with 3-to 5-year calibration periods and [START_REF] Perrin | Impact of limited streamflow data on the efficiency and the parameters of rainfallrunoff models[END_REF] showed that the calibration of the GR4J and TOPMO models with the equivalent of only 1 year of data can provide acceptable performance. Thus, it seems that 3-year periods can yield acceptable parameter sets. Those relatively short sub-periods allow representing significantly contrasted climatic conditions. Interestingly, Figure 3 shows that the contrast between the aridity indexes of the different calibration sub-periods is similar to the contrast between the aridity indexes of the observed record and future climate projection. However, it should be noted here that the climate projection simulates systematically drier conditions than the dry validation sub-periods. This means that whatever the selected calibration sub-period, the model is applied in extrapolation in future climate conditions. Note that the aridity index does not reflect seasonal variability of precipitation and potential evapotranspiration: two subperiods with similar values of the aridity index may be quite different in terms of climate seasonality. This means that seasonal indexes would be useful to consider as additional criteria for period selection if seasonal contrasts were under study.

Step 2: Model calibrations on the specific periods

For each catchment, the two hydrological models were calibrated using the three climatically contrasted sub-periods (i.e. the wet, mean and dry sub-periods) and the whole record period (except the dry validation sub-periods, which are used for model validation in step 3). A 1year warm-up period was considered for each simulation.

The DREAM algorithm was used to infer the most likely parameter set and its underlying posterior probability distribution. We selected for each calibration run (i) the optimal parameter set defined as the parameter set maximising the GL objective function and (ii) an ensemble of 2000 posterior parameter sets representing the posterior probability distribution of parameter sets. For each catchment and each calibration period, we checked that the DREAM algorithm converged to the stationary distribution representing the model"s posterior distribution by analysing the Gelman-Rubin convergence statistics.

Note that additional model calibrations were also performed on the dry validation sub-periods.

The corresponding calibration performance was used as a reference to evaluate the performance of models validated on these dry validation sub-periods after calibration on other periods.

Step 3: Model simulations with different parameter sets

At this stage of the methodology, four optimal parameter sets corresponding to the four calibration periods and an ensemble of 2000 posterior parameter sets identified throughout the record period (except the dry validation sub-periods) are available for each catchment.

All these parameter sets were used for each catchment to simulate the streamflow time series over the dry validation sub-periods (illustrated as grey hydrographs in the first line of the third For each catchment and each model, the four ensembles of parameter sets were tested first on the dry validation sub-periods. We analysed the dependence of model performance on the climatic specificity of the calibration period. Furthermore, the biases between the observed and the simulated streamflow characteristics were assessed. Second, the variability of the future streamflow simulations obtained using various calibration conditions was analysed for each future time slice. To differentiate the impacts stemming from the specificity of the calibration period from those associated with the "classical" parameter uncertainty approach based on Bayesian inference on the whole record period, the results are presented step by step hereafter.

RESULTS

Calibration performance results

In this section, the general calibration performance of the two models are analysed. Figure 4 presents the distributions of the GL function evaluations and the distributions of the Nash-Sutcliffe efficiencies computed on root square transformed flows (NSEsq) obtained by the GR4J and TOPMO models on the catchment set. The distributions were obtained with (i) the calibration efficiencies over the whole record without the dry validation sub-periods obtained with optimal parameter sets, i.e. 89 values for each model (white boxplots, noted OPT) and (ii) calibration performance over the same record periods obtained with the 2000 posterior parameter sets identified for each of the 89 catchments, i.e. 178,000 values for each model (grey boxplots, noted POS). The distributions of the GL objective function values highlight that optimal parameter sets present similar general calibration efficiency to the calibration efficiency obtained using the populations of posterior parameter sets. Considering populations of posterior parameter sets thus adds a limited variability in terms of calibration performance over the whole record periods (without dry validation sub-periods) for the two models. For GR4J, the distributions of the NSEsq efficiencies similarly show that the optimal parameter identified with the DREAM algorithm and with the GL objective function have similar general performance as the posterior parameter sets. The performance losses when considering populations of posterior parameter sets instead of optimal parameter sets are more significant for TOPMO than for GR4J, with median NSEsq moving from 0.86 with optimal parameter sets to 0.84 with posterior parameter sets. Calibration performance results for the other calibration sub-periods (wet, mean and dry 3-year calibration sub-periods) show the same general tendencies (not shown here). The difference between the two models might stem from the number of free parameters, higher for TOPMO (six free parameters) than for GR4J (four free parameters). Thus, the calibrated parameter values of TOPMO may show greater sensitivity to the choice of the objective function. Finally, note that the general performance of both models is quite reasonable, with half of the catchments studied presenting calibration performance obtained with optimal parameter sets on the whole record periods (without the dry validation sub-periods) greater than 0.85 for the two models.

Sensitivity to the climate characteristics of the calibration period

In this section, the model outputs are analysed considering different calibration periods. First the efficiency of the model on the dry validation sub-periods is discussed in terms of NSEsq and simulation of standard streamflow characteristics. Second, we analyse the resulting spread of the simulated streamflows for the future time slices.

 Efficiency on dry validation sub-periods:

Figure 5 shows the distributions of the NSEsq values on the catchment set obtained by the two models in (i) calibration over the dry validation sub-periods and (ii) validation over the dry validation sub-periods using the other four calibration sub-periods considered (wet, mean, dry, and whole record periods). Models calibrated over different sub-periods generally encountered similar difficulties simulating flows on the dry validation sub-periods since the validation efficiencies are clearly reduced compared to the calibration efficiencies on this subperiod. The differences between the four calibration strategies (over a wet, a mean, a dry subperiod or a long period) are limited but, for both models, using the wettest sub-periods for calibration appears particularly detrimental to simulating the dry validation sub-periods. GR4J and TOPMO obtained marginally better validation results using dry and mean conditions for calibration, respectively. Interestingly, calibrating the models on the whole record period (except the dry validation sub-periods, resulting in 20 years of record on average) does not warrant a particularly robust estimation of optimal parameter sets, since the validation efficiencies are generally similar to those obtained with 3-year calibration periods. This is not consistent with the wide-spread idea that the longer the calibration period, the more robust the parameter set. Figure 6 summarises the results of the models' sensitivity to the climatic specificity of the calibration period on the observed dry validation sub-periods. This figure is organised as a table with two columns and three rows: each column represents a hydrological model (left: GR4J; right: TOPMO) and each row represents a specific characteristic of the simulated flow series (from top to bottom: Q 95 , Q MA and Q 05 ). For each model and for each streamflow characteristic, the plot on the left shows the observed versus simulated value for each catchment, each dot representing the mean of simulated values obtained with the four optimal parameter sets and each bar representing the range of simulated values when using the four optimal parameter sets. Ideally, all range bars should be centred on the 1:1 line, meaning that streamflow simulated by parameter sets originating from different calibration sub-periods are all equal to the observed streamflow. The boxplots on the right represent the distributions of the relative errors on the flow characteristic on the dry validation sub-periods over the 89 catchments when considering the four calibration sub-periods. These relative errors were estimated as the ratio of the difference between simulated and observed flow characteristics to the observed flow characteristics. Ideally, all the boxplots should be centred on a null value of the bias between the observed and the simulated streamflow.

The first main result is that the two rainfall-runoff models present similar overall efficiency in simulating the flow characteristics on the dry validation sub-periods (graphs on the left). This efficiency is rather limited since the median absolute bias is greater than 0.1 for both models.

Even for the estimation of mean annual flow (Q MA ), none of the four calibration strategies yields a median absolute bias lower than 0.1. The second main result is that the impact of the climatic specificity of the calibration sub-periods on the modelled flow characteristics is not straightforward (graphs on the right). For GR4J, it seems that the 3-year dry calibration subperiods provide the least biased estimations of the three streamflow characteristics of the dry validation sub-periods. Using wet and mean 3-year calibration sub-periods tends to yield overestimated flow simulations on the dry validation sub-periods. Conversely, TOPMO tends to underestimate flows of the dry validation sub-periods. The mean 3-year calibration subperiods seems to provide less biased estimation of the streamflow characteristics on the dry validation sub-periods. Finally, using 3-year calibration sub-periods (dry ones for GR4J and mean ones for TOPMO) yields less biased predictions than when considering the whole available records for calibration for both hydrological models and for the three streamflow characteristics studied here, which corroborates the validation performance illustrated in Figure 5. Note, however, that all calibration periods produce highly biased predictions and that the differences between the calibration strategies are relatively limited compared to these biases. The boxplots are constructed with the 0.10, 0.25, 0.50, 0.75 and 0.90 percentiles.

 Impacts on simulated flow evolutions:

Then we assessed the change in future simulated streamflow characteristics when considering the variability stemming from the climatic specificity of the calibration periods. Figure 7 shows the models" outputs on future time slices when using the sets of model parameters obtained on the four different calibration periods considered so far. The range of streamflow characteristics simulated for future time slices (mid-century (MC) and end-of-century (EC)) with the four parameter sets are plotted against those simulated for the present time slice (PT).

In the following, we assume that a model simulates a significant hydrological change on a catchment if the range bar is completely above or below the 1:1 line, meaning that the change can be considered beyond the variability generated by the climate specificity of the calibration periods considered. For example, a decreasing trend of Q 05 between PT and MC is assumed for a particular catchment if a model calibrated over the four different sub-periods simulates four Q 05 values lower in MC than in PT.

Considering the range across centres, the two models suggest a rather similar decreasing trend for the values of the three streamflow characteristics from PT to EC. This trend is not observed for the MC time slice. The Q 05 streamflow characteristic (high flows) increases for this time slice, before decreasing more sharply by the end of the century. Some catchments show particularly large range bars. An analysis of these catchments (not shown here) indicates that the calibration performance is particularly poor for at least one calibration sub-period.

This shows that a model with poor performance in current conditions will add substantial uncertainty to future predictions. The sensitivity of the two models to the climatic specificity of the calibration periods is of the same magnitude for all three time slices considered, meaning that the sensitivity to the calibration periods is relatively stable in the future time slices. Figure 8 synthesises the results of these trends (e.g. a decreasing trend of Q 05 between PT and MC is assumed for a particular catchment when a model calibrated over the four different sub-periods simulates four Q 05 values lower in MC than in PT), showing the proportion of catchments where hydrological trends between present (PT) and future (MC and EC) time slices have been simulated considering different calibration sub-periods for the two hydrological models. It also compares the information given by a hydrological model calibrated over a long period (here the entire available record without the dry validation sub-periods) and the information given using the four different calibration periods. These results confirm the previously obtained general trend of a decrease in the three streamflow characteristic values from PT to EC, with a particular increasing trend for high flows (Q 05 ) from PT to MC. Nevertheless, when considering the four different calibration periods, a number of catchments show no clear trends for the MC time slice, which attenuates the general trends highlighted when using the whole record periods as the only calibration periods. Last, differences between the two models can be observed: when considering only the whole record for calibration, GR4J seems to simulate a more regionally homogeneous decrease in low-to medium-flow characteristics (Q 95 and Q MA ), since the percentage of catchments with a decrease in flow is larger than for TOPMO. Considering the four calibration periods, the two models yield more homogeneous simulations for the catchment set.

Sensitivity to the use of a posterior ensemble of parameter sets

In this section, the model outputs are analysed considering 2000 posterior parameter sets obtained on the whole record period for each catchment and for each model. First, we discuss the efficiency of these ensembles of posterior parameter sets on the dry validation sub-periods in terms of NSEsq and simulation of the three streamflow characteristics (Q 95 , Q MA and Q 05 ).

Second, we analyse the resulting variability of the simulated streamflow characteristics for the future climate conditions.

 Efficiency on dry validation sub-periods:

Figure 9 shows the distribution of NSEsq values obtained by the two models illustrating (i) the calibration performance of the optimal parameter sets over the dry validation sub-periods (i.e. 89 NSEsq values for each model) and (ii) the validation performance over the dry validation sub-periods using optimal parameter sets (i.e. 89 NSEsq values for each model) and posterior parameter sets (i.e. 178,000 NSEsq values for each model) identified on the whole record periods without the dry validation sub-periods. For GR4J, the validation performance obtained by posterior parameter sets is very similar to that produced by the individual optimal parameter sets presented in Figure 5, meaning that for the catchments studied, the DREAM algorithm produces posterior parameter sets yielding efficiency close to the value obtained by optimal parameter sets over the dry validation sub-periods. The NSEsq performance distributions obtained with optimal and posterior parameter sets are not similar for TOPMO: the optimal parameter sets appear to be less efficient than the posterior parameter sets in terms of NSEsq validation performance. This means that rather different optima exist when using the GL function and a likelihood function based on a standard least squares errors scheme (NSEsq here). Nevertheless, differences between optimal parameter set performance and posterior parameter set performance are less significant in the validation step than in the calibration step, as shown in Figure 4. It should be remembered that the NSEsq was not used as an objective function.

FIGURE 9: Distribution of NSEsq values obtained by the two models illustrating (i)

calibration performance of the optimal parameter sets over the dry-validation sub-periods (black "OPT" boxplots) and (ii) validation performance over the dry validation sub-periods using optimal (white "OPT" boxplots) and posterior (grey "POS" boxplots) parameter sets identified on the whole record periods without the dry validation sub-periods. Results are shown for GR4J (left) and TOPMO (right). The boxplots show the 0.10, 0.25, 0.50, 0.75 and 0.90. The first major result is that considering posterior parameter sets does not significantly increase the variability of the simulated flows. The biases between observed flows and flows simulated by the ensembles of posterior parameter sets (grey boxplots) are close to those obtained with the ensembles of optimal parameter sets (white boxplots). Moreover, this variability is very limited compared to the variability observed when considering the four climate-specific parameter sets (see Figure 6). Here, the hydrological responses associated with 2000 posterior parameter sets are similar to those associated with optimal parameter sets.

The flow characteristics obtained by TOPMO present generally greater uncertainty than those obtained by GR4J. These predictive uncertainty values are again probably due to the larger number of free parameters for TOPMO. Note, however, that the predictive uncertainty for TOPMO is often consistent with the observed biases for the validation sub-periods since the estimation range often encompasses the observed flow value. increase in the number of catchments for which no clear trend is observed, particularly between the MC and the PT. Nevertheless, the future trends are similar to those observed without taking into account the ensembles of posterior parameter sets, i.e. when using only the optimal parameter sets. There is a sharp decrease in all streamflow characteristics by the EC and a slight but significant increase in the high-flow characteristic for the MC.

DISCUSSION AND CONCLUSION

This paper attempted to investigate the uncertainty of hydrological predictions for the future climate when considering either (i) the dependence of the optimal parameter set on calibration period specificity or (ii) the use of several posterior parameter sets over a given calibration period. The first aspect often refers to the robustness of model parameters, while the second often refers to parameter uncertainty estimation based on Bayesian inference.

The two conceptual hydrological models tested here were sensitive to the use of climatically contrasted calibration sub-periods. This sensitivity was highlighted by a wide range of possible simulated streamflows for both the dry observed validation sub-periods and the future climate time slices. Even if general future changes can be observed when considering four optimal parameter sets (obtained with the calibration on three sub-periods and the whole record periods except the dry validation sub-periods) for each catchment, the proportion of catchments showing clear changes is much lower than when considering a unique parameter set (obtained by calibration on the whole record periods except the dry validation subperiods). However, the impact of the calibration period climate specificity on the simulated streamflows is not straightforward since for a majority of the catchments studied, using a wet calibration sub-period for a dry validation sub-period does not systematically generate a larger bias between observed and simulated flows than when using a dry calibration sub-period.

Moreover, considering long periods for model calibration does not generate more robust simulation than using 3-year sub-periods, which is not consistent with the common belief that "the longer the calibration period, the more robust the parameter set". Since the use of two different hydrological models did not provide equivalent results, the relation between the model considered and the impact of the climatic specificity of the calibration period on calibration and validation performance should be further investigated.

Concerning the "classical" parameter uncertainty assessment followed in this study, it seems that the prediction bounds obtained from the ensembles of posterior parameter sets are considerably thinner than what would be expected, especially for the GR4J model.

Nevertheless, it is important to note that these results are dependent to some extent on the method used (the DREAM algorithm [START_REF] Vrugt | Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling[END_REF] and the GL objective function [START_REF] Schoups | A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors[END_REF]), the catchments studied and the models considered. It appeared that DREAM provided posterior parameter sets that were close to the optimal ones in terms of Nash-Sutcliffe validation efficiency over the dry validation sub-periods. Other methods to quantify parameter uncertainty could produce posterior parameter sets with greater differences than the optimal ones and thus yield larger uncertainty bounds. Considering the ensembles of 2000 posterior parameter sets yields a slight increase in the number of catchments for which no clear trend is observed, especially for TOPMO. The results obtained by the two conceptual models were found to be relatively consistent. The main differences were the larger uncertainty bounds observed for TOPMO. This is probably attributable to the larger number of degrees of freedom of TOPMO, which has six free parameters, compared to the four free parameters of GR4J. TOPMO"s calibrated parameters are thus likely to depend more on the choice of the calibration period and the objective function used during the optimisation process. Still, further research is needed to confirm these hypotheses.

Our results show that, given the evaluation approach followed here, model robustness was the major source of variability in streamflow projections in future climate conditions. They corroborate the previous findings of [START_REF] Vaze | Climate nonstationarity -Validity of calibrated rainfall-runoff models for use in climate change studies[END_REF], [START_REF] Merz | Time stability of catchment model parameters: Implications for climate impact analyses[END_REF] and [START_REF] Coron | Crash Testing Hydrological Models in Contrasted Climate Conditions: An Experiment on 216 Australian Catchments[END_REF] obtained with different catchment sets and models, emphasising the lack of robustness of conceptual rainfall-runoff models when the climatic context between calibration and validation periods are different. Note that for these three studies, long-term regional nonstationarities were observed on the catchments studied: southeastern Australian catchments suffered from long drought periods while Austrian catchments experienced a significant increase in temperature over the last few decades, generating a shift in the hydrological regimes, particularly for snow-affected catchments. These situations allow testing the hydrological models on long as well as significantly different sub-periods in terms of climatic conditions. Even if these actual non-stationarities were not observed everywhere, it seems possible to test the sensitivity of models" calibration on climatically contrasted sub-periods. Thus, from these results, it seems difficult to provide general guidelines for calibrating hydrological models for climate change studies. The robustness issue should be investigated more thoroughly, by proposing and testing calibration procedures that increase this robustness. For example, [START_REF] Coron | Crash Testing Hydrological Models in Contrasted Climate Conditions: An Experiment on 216 Australian Catchments[END_REF] proposed the Generalized Split Sample Test procedure, which aims at testing all possible combinations of calibration-validation periods and thus studying the capability of the tested model to be used in different climatic contexts.

Other tests could be performed, inspired by the methodology defined in this work.

This study also stresses that hydrological models do not efficiently reproduce streamflow characteristics, even if the NSEsq coefficient estimated after calibration is quite high. The median bias obtained for mean annual flow was generally greater than 10%. This is a considerable limitation for the use of hydrological models to simulate extreme high or low flows in a changing climate. To cope with this notable failure, one could suggest using multiobjective calibration procedures and/or adapting the objective function to the estimated flow characteristic. performance of the optimal parameter sets over the dry-validation subperiods (black ""OPT"" boxplots) and (ii) validation performance over the dry validation sub-periods using optimal (white ""OPT"" boxplots) and posterior (grey ""POS"" boxplots) parameter sets identified on the whole record periods without the dry validation sub-periods. Results are shown for GR4J (left) and TOPMO (right). The boxplots show the 0.10, 0.25, 0.50, 0.75 and 0.90.

FIGURES



  ): Step 1: identification of test periods.  Step 2: model parameter calibration and identification of posterior parameter sets.  Step 3: model validation and simulation, and parameter uncertainty quantification. These three steps are further detailed hereafter.

FIGURE 2 :

 2 FIGURE 2: Illustration of the three-step methodology used for investigating parameter

FIGURE 3 :

 3 FIGURE 3: Comparison of Aridity Index (AI) values for the different calibration and

  step of Figure 2) and on the three time slices (PT, MC and EC) (illustrated as grey envelops on the flow duration curves plotted in the second line of the third step of Figure 2). Three typical streamflow characteristics were analysed:  The 95th flow exceedance percentile of the flow duration curve, Q 95 (mm/day), describing low flows;  The mean annual streamflow, Q MA (mm/y), indicating the overall water availability;  The 5th flow percentile, Q 05 (mm/day), describing high flows.

FIGURE 4 :

 4 FIGURE 4: Distributions of the GL objective function values (top) and of the NSEsq values

  These results corroborate the previous findings of[START_REF] Vaze | Climate nonstationarity -Validity of calibrated rainfall-runoff models for use in climate change studies[END_REF],[START_REF] Merz | Time stability of catchment model parameters: Implications for climate impact analyses[END_REF] and[START_REF] Coron | Crash Testing Hydrological Models in Contrasted Climate Conditions: An Experiment on 216 Australian Catchments[END_REF] obtained with different catchments and models, emphasising the lack of robustness of conceptual rainfall-runoff models when the climatic settings between calibration and validation periods are different.

FIGURE 5 :

 5 FIGURE 5: Distributions of the NSEsq values obtained by the two models illustrating (i)

FIGURE 6 :

 6 FIGURE 6: Sensitivity of the simulated flow characteristics (from top to bottom: Q 95 , Q MA

FIGURE 7 :

 7 FIGURE 7: Comparison of the simulations of three streamflow characteristics (from top to

FIGURE 8 :

 8 FIGURE 8: Proportions of catchments showing (or not) hydrological trends between present

Figure 10

 10 Figure10shows the variability of the models" outputs on the dry validation sub-periods when

FIGURE 10 :

 10 FIGURE 10: Sensitivity of the simulated flow characteristics (from top to bottom: Q 95 , Q MA

FIGURE 11 :

 11 FIGURE 11: Comparison of the simulations of three streamflow characteristics (from top to

Figure 12

 12 Figure 12 illustrates the proportion of catchments showing (or not showing) clear changes

FIGURE 12 :

 12 FIGURE 12: Proportion of catchments showing (or not showing) hydrological trends

Fig. 1 .

 1 Fig. 1. Location and distribution of various characteristics of the 89 catchments used. The boxplots show the 0.10, 0.25, 0.50, 0.75 and 0.90 percentiles (67 is the number of catchments in the Seine and Somme basins, 22 in the Loire basin).

  Fig. 10. Sensitivity of the simulated flow characteristics (from top to bottom: Q95, QMA and Q05) on the dry validation sub-periods using the 2000 posterior parameter sets determined on the whole record periods without the dry validation sub-periods for the two hydrological models (left: GR4J; right: TOPMO). The Q-Q plots show the observed versus simulated value for each catchment, each dot representing the mean of simulated values when using the 2000 posterior parameter sets and each bar representing the range of simulated values when using the 2000 posterior parameter sets. The boxplots on the right represent the distributions of the relative errors on the flow characteristic on the dry validation sub-periods over the 89 catchments when considering the 2000 posterior parameter sets. The boxplots are constructed with the 0.10, 0.25, 0.50, 0.75 and 0.90 percentiles.

ACKNOWLEDGMENTS

All hydro-meteorological data were provided by two research programs that addressed the potential impacts of climate change: the RexHySS project [START_REF] Ducharne | Impact du changement climatique sur les Ressources en eau et les Extrêmes Hydrologiques dans les bassins de la Seine et la Somme[END_REF][START_REF] Ducharne | Evolution potentielle du régime des crues de la Seine sous changement climatique[END_REF]) on the Seine and the Somme basins and the ICC-Hydroqual [START_REF] Moatar | La Loire à l"épreuve du changement climatique[END_REF] project on the Loire basin.

The authors thank the reviewers who provided constructive comments on an earlier version of the manuscript, which helped clarify the text. Among them, Jasper Vrugt is thanked for providing the codes to implement the optimisation approach he advised. Finally, François Bourgin (IRSTEA) is also acknowledged for his comments and suggestions.


Dr Laurent Lemaire
email: laurent.lemaire@univ-angers.fr

G Bastiat

F Franconi

N Lautram

T Duong

Thi Dan

E Garcion

P Saulnier

J P Benoit

PERFLUOROCARBON-LOADED LIPID NANOCAPSULES AS OXYGEN SENSORS FOR TUMOR TISSUE PO 2 ASSESSMENT

Keywords: Lipid nanocapsules, 19F-MRI, Fluorocarbon, Oxygenation, tumor

The assessment of tumor oxygenation is a crucial factor in cancer therapy and may be carried out using fluorine MRI once fluorine probes have been distributed within the tumor.

However, the deposit of those highly fluorinated compounds often jeopardizes anatomical image quality and requires emulsification of the probes. Due to the high density and the high lipophilicity of perfluorocarbons, nanoemulsion of these molecules usually requires high energy processes. In the present work, we discuss the synthesis and the physico-chemical characterization of perfluorocarbon nanocapsules using a low-energy phase-inversion process.

The nanocapsules were tested on a mouse tumor brain model to assess oxygenation.

INTRODUCTION

Hypoxia is a characteristic feature of locally-advanced solid tumors resulting from an imbalance between oxygen supply and consumption [START_REF] Vaupel | Treatment resistance of solid tumors: role of hypoxia and anemia[END_REF] . Hypoxia has been shown to play a key role in tumor resistance to radiation therapy [START_REF] Nordsmark | The relationship between tumor oxygenation and cell proliferation in human soft tissue sarcomas[END_REF] and also in decreasing the efficacy of certain cytotoxic drugs [START_REF] Selvendiran | Hypoxia induces chemoresistance in ovarian cancer cells by activation of signal transducer and activator of transcription 3[END_REF]. Numerous studies have demonstrated that tumor hypoxia, in addition to diminishing therapeutic efficacy, plays a major role in malignant progression [START_REF] Hockel | Association between tumor hypoxia and malignant progression in advanced cancer of the uterine cervix[END_REF].

Methods to determine tumor oxygenation are therefore of crucial importance for the prediction of therapeutic outcomes. Many current methods, such as Eppendorf electrodes [START_REF] Kavanagh | A comparison in individual murine tumors of techniques for measuring oxygen levels[END_REF], near-infrared spectroscopy [START_REF] Xia | Tumour oxygen dynamics measured simultaneously by near-infrared spectroscopy and 19F magnetic resonance imaging in rats[END_REF], electron paramagnetic resonance imaging [START_REF] Meenakshisundaram | Oxygen sensitivity and biocompatibility of an implantable paramagnetic probe for repeated measurements of tissue oxygenation[END_REF], susceptibility magnetic resonance imaging based methods [START_REF] Ogawa | Brain magnetic resonance imaging with contrast dependent on blood oxygenation[END_REF] or 19 F magnetic resonance imaging oximetry [START_REF] Xia | Tumour oxygen dynamics measured simultaneously by near-infrared spectroscopy and 19F magnetic resonance imaging in rats[END_REF][START_REF] Diepart | In vivo mapping of tumor oxygen consumption using (19)F MRI relaxometry[END_REF] have been used in preclinical studies but have either been highly invasive, nonquantitative, or have lacked spatial resolution. As far as clinically available devices are concerned, MR-based techniques may be of interest, whereby, proton-based-imaging can be used to access blood oxygen change using the BOLD (Blood Oxygen Level-Dependent) sequence [START_REF] Ogawa | Brain magnetic resonance imaging with contrast dependent on blood oxygenation[END_REF], currently widely used in clinics for functional magnetic resonance imaging (fMRI) studies. Nevertheless, this imaging technique is based on relaxivity changes that allow the depiction of oxygenation variations, but it does not enable the quantitative assessment of oxygen concentration [START_REF] Baudelet | How does blood oxygen level-dependent (BOLD) contrast correlate with oxygen partial pressure (pO(2)) inside tumors?[END_REF]. However, recent studies have shown a high correlation between oxygen changes assessed using BOLD-imaging and oxygen levels measured using 19 F-MRI of a fluorinated oxygen probe in a preclinical model [START_REF] Zhao | Comparison of 1H blood oxygen leveldependent (BOLD) and 19F MRI to investigate tumor oxygenation[END_REF].

Currently, the major limitations of 19 F -oximetry is the lack of equipment of clinical MR to perform fluorine imaging. However, such a limitation can easily be removed since it only requires the acquisition of a specific 19 F -tuned probe. Fluorine oximetry is based on the influence of oxygen tension on the relaxivity of certain fluorinated probes. In the early 80's Clark et al. [START_REF] Clark | Perfluorinated organic liquids and emulsions as biocompatible NMR imaging agents for 19F and dissolved oxygen[END_REF] showed a linear relation between longitudinal relaxivity of fluorinated probes with oxygen tension; this opened the field for MR oximetry [START_REF] Sotak | A new perfluorocarbon for use in fluorine-19 magnetic resonance imaging and spectroscopy[END_REF][START_REF] Mason | Perfluorocarbon imaging in vivo: a 19F MRI study in tumor-bearing mice[END_REF][START_REF] Gowland | Accurate measurement of T1 in vivo in less than 3 seconds using echo-planar imaging[END_REF]. Numerous fluorine probes were tested as oxygen sensors and numerous protocols have been proposed to optimize the injection of the fluorinated probes. Zhao et al. proposed a multiple deposit of the probe along 3 orthogonal directions in order to ensure that the interrogated regions are representative of the whole tumor [START_REF] Zhao | Measuring changes in tumor oxygenation[END_REF]. However, as reported by these authors [START_REF] Zhao | Comparison of 1H blood oxygen leveldependent (BOLD) and 19F MRI to investigate tumor oxygenation[END_REF], the deposit induced signal voids on the anatomical proton images that can jeopardize the information that can be extracted from the anatomical data set.

To overcome this drawback, we propose the development of lipid nanocapsules to carry the fluorinated probe. Lipid nanocapsules are engineered using FDA-approved constituents (i.e. Solutol and Lipoid) that are prepared by a solvent-free and low -energy process [START_REF] Heurtault | A novel phase inversionbased process for the preparation of lipid nanocarriers[END_REF], they are able to deliver drugs to a target [START_REF] Huynh | Lipid nanocapsules: a new platform for nanomedicine[END_REF] and, amazingly, they are characterized by an intrinsic effect on Multi-Drug-Resistance via the inhibition of P-gp [START_REF] Garcion | A new generation of anticancer, drug-loaded, colloidal vectors reverses multidrug resistance in glioma and reduces tumor progression in rats[END_REF].

According to the preparation process used, this nano-scaled platform can encapsulate hydrophilic [START_REF] Vonarbourg | The encapsulation of DNA molecules within biomimetic lipid nanocapsules[END_REF] and lipophilic [START_REF] Allard | 188Re-loaded lipid nanocapsules as a promising radiopharmaceutical carrier for internal radiotherapy of malignant gliomas[END_REF] compounds and therefore can encapsulate the lipophilic fluorinated O 2 probe, the perfluoro-15-crown-5-ether (C 10 F 20 O 5 ) in this case. This compound was chosen since all twenty fluorines are MR equivalent and therefore provide a single and intense resonance [START_REF] Srinivas | Customizable, multi-functional fluorocarbon nanoparticles for quantitative in vivo imaging using (19)F MRI and optical imaging[END_REF]. The second advantage of lipid nanocapsules is that they can be efficiently and homogeneously infused in tumors using the convection-enhanced delivery (CED) technique [START_REF] Vanpouille-Box | Tumor eradication in rat glioma and bypass of immunosuppressive barriers using internal radiation with (188)Re-lipid nanocapsules[END_REF], a technique initially introduced in the early 90's [START_REF] Bobo | Convection-enhanced delivery of macromolecules in the brain[END_REF] to deliver macromolecules to the brain but which is nowadays used in clinics to improve tumor therapy [START_REF] Noble | Novel nanoliposomal CPT-11 infused by convectionenhanced delivery in intracranial tumors: pharmacology and efficacy[END_REF].

EXPERIMENTAL

Materials

Lipoïd ® S75-3 (soybean lecithin -69% phosphatidylcholine and 10% phosphatidylethanolamine) and Solutol ® HS15 were supplied by Lipoïd GmbH (Ludwigshafen, Germany) and BASF (Ludwigshafen, Germany), respectively. Perfluoro-15crown-5-ether (C 10 F 20 O 5 ) was provided by Chemos GmbH (Regenstauf, Germany). NaCl was purchased from Prolabo (Fontenay-sous-bois, France). Deionized water was obtained from a Milli-Q plus ® system (Millipore, Bilerica, USA). I 2 and KI were supplied by Sigma Aldrich Chemie GmbH (Steinheim, Germany). The abbreviations Lipoïd, Solutol, PEG, PEG-HS and PFCE are used for Lipoïd ® S75-3, Solutol ® HS15, polyethylene glycol, polyethylene glycol hydroxystearate, and perfluoro-15-crown-5-ether, respectively.

Formulation process

The quantities of PFCE (oil phase), water and NaCl (aqueous phase), Solutol ® HS15 and Lipoïd (surfactants) were precisely weighed: m PFCE = 2g, m Solutol = 0.846g, m Lipoïd = 0.075g, m Water = 2g and m NaCl = 0.1 g. A four step process was tested to obtain PFCE nanocapsules (PFCE-LNC). After an increase of temperature from room temperature to 95°C to dissolve the Lipoïd, a 1 min-sonication of the mixture with the power of 3, 5 or 10 W using a Microson XL2007 (Misonix, Farmingdale, USA) sonication probe was performed prior to three heating and cooling cycles from 25°C to 95°C. During the final cooling, when the temperature reaches 70°C, a rapid cold dilution was performed by adding 3.5 volumes of cold milli-Q water.

The influence of the formulation composition on PFCE-LNC synthesis was assessed when the process used included the 1minute sonication period at 10W.

Interface characterization -Drop tensiometer.

Adsorption kinetics measurements were carried out at the oil-water interface by means of a pendant drop method [START_REF] Benjamins | Viscoelastic properties of triacylglycerol/water interfaces covered by proteins[END_REF] (Tracker, IT Concept, Longessaigne, France). A drop was formed with an Exmire microsyringe (Prolabo, Paris, France) into an optical glass cell (Hellma, Paris, France) containing the other phase. In our case, a pendant drop of PFCE was formed in aqueous solution containing Solutol at various concentrations (from 0 to 400mg.L -1 ). The cell was maintained at room temperature. The axial symmetric shape (Laplacian profile) of the drop was analyzed using a video camera connected to a computer. In this study, the volume of the drop was 5µL and the Laplacian shape of the drop was always checked. From the analysis of the numerical image of the drop using the Laplace equation and integrating the points of the drop profile, the interfacial tension, interfacial area and volume of the drop were derived in real time (five measurements per second). The experiment was stopped once the interfacial tension remained constant for 30 minutes.

Electrophoretic measurements.

Dialysis of PFCE-LNC (5 mL) was performed (Spectra/Por ® Biotech Cellulose Ester Dialysis Membrane, MWCO = 50 kDa) for one week against pure water (obtained through a milli-Q apparatus, Millipore, Saint Quentin en Yvelines, France), changing the water twice a day. At the end of dialysis and after size verification (similar to hydrodynamic diameter as before dialysis), the PFCE-LNCs were diluted with saline (dilution factors: 60, 600 and 6,000) to obtain different ionic strengths (from 2.5 to 50mM). An electrophoretic mobility test was performed using a Malvern Zetasizer ® (Nano Series DTS 1060). Three different PFCE-LNC batches were prepared to obtain the mean value of electrophoretic mobility  standard deviation (SD) vs. NaCl concentrations.

The surface properties of the nanoparticles were studied by soft-particle analysis using the Ohshima theory [START_REF] Ohshima | Electrophoretic mobility of soft particles[END_REF][START_REF] Ohshima | On the General Expression for the Electrophoretic Mobility of a Soft Particle[END_REF]. Ohshima showed that the electrophoresis mobility of a soft particle depended on the volume charge density distributed in the polyelectrolyte layer, on the frictional forces exerted by the polymer segments on the liquid flow in the polyelectrolyte layer, on the particle size, and on the frequency of the applied oscillating electric field. The theoretical curve (Eq. 1) represents the dependence of electrophoretic mobility () as a function of the charge number density (n), used to evaluate Km, the Debye-Hückel parameter of the shell, , the reciprocal of the Debye length,  DON , the Donnan potential (unequal distribution of diffusible ions between two ionic solutions) and  0 , the potential at the boundary between the surface region and the solution: This method allows the calculation of ZN and  which characterize the electric properties of the surface of particles; ZN represents the spatial charge density in the polyelectrolyte region and  is a physical constant characterizing the degree of resistance to liquid flow in the polyelectrolyte region. The reciprocal of , which is 1/, has the dimension of length and can be regarded as the "softness" parameter of the NP surface. All electrophoretic mobilitiy and softness values reported were the mean of three measurements with separately prepared batches.

Polyethylene glycol titration.

The dialysis of PFCE-LNCs (5mL) was performed (Spectra/Por ® Biotech Cellulose Ester Dialysis Membrane, MWCO = 50 kDa) against 100mL of pure water (obtained through a milli-Q apparatus, Millipore, Saint Quentin en Yvelines France) at room temperature under magnetic stirring, to remove PEG chains (from Solutol) not associated to PFCE-LNC. The PEG concentration was determined by the use of a colorimetric method, based on the complex formation between PEG and iodine [START_REF] Sims | A method for the estimation of polyethylene glycol in plasma protein fractions[END_REF]. 100µL aliquots were collected vs. time (from 0 to 120-h) in the dialysis external medium and immediately replaced with 100µL of pure water.

To this 100-µL aliquot was added 25µL of KI/I 2 (0.01 and 0.02-g.mL -1 for I 2 and KI, respectively), and absorbance was measured at 492nm, 5 minutes after the addition. The calibration curve was assessed using Solutol solutions. Experiments were performed in triplicate.

Magnetic resonance imaging protocols

In vitro studies

The in vitro calibration relating the R 1 of perfluoro 15-crown-5 ether encapsulated in lipid nanocapsules to the O 2 partial pressure value were made using three different O 2 concentrations (0, 21 and 100% corresponding to 0, 160 and 760 mmHg, respectively) with balance N 2 . The colloidal suspension was bubbled for 30 minutes to equilibrium at 37°C. 19 F measurements were performed on a Bruker Biospec 70/20 operation at a magnetic field of 7T (Bruker, Wissembourg, France). The resonant circuit of the NMR probe was a 40-mm diameter, double tuned ( 1 H/ 19 F) birdcage. The sequence used was a multi-spin echo sequence (RARE factor =8, mean TE = 21.7ms) with multiple TR (300ms, 800 ms, 1,500ms and 6,000ms). 4 averages were performed. The geometrical parameters were fixed at FOV = 2x2cm, matrix 64x64, slice thickness =4mm. Using Equation 2:

2 * 1 1 pO S A T   (Eq. 2)
The average T1 value of the 3 measurements per oxygen concentration was used for the linear fit of 1/T1 vs. pO2, from which the anoxic intercept A and slope S were derived.

In vivo studies 2.4.2.1. Tumor induction

Animal care and use were in strict accordance with the regulations of the French Ministry of Agriculture. Brain tumors were induced by stereotaxic inoculation of glioma cells as previously described [START_REF] Lemaire | Highfield quantitative transverse relaxation time, magnetization transfer and apparent water diffusion in experimental rat brain tumour[END_REF]. Briefly, 7-8week-old male SCID mice (Charles Rivers, France)

were anesthetized with a mixture of Rompun® (Xylazine, Bayer AG, Leverkusen, Germany)

and Clorketam® (Kétamine, Vétoquinol, Lure, France) before being fixed in a stereotaxic holder. Through a small hole drilled in the skull (anterior -0.5mm, lateral 2mm, depth -3mm according to the bregma), 5μl of a suspension of 50,000 grade IV glioma cells were injected over a 10-minute time period into the caudate putamen of the right hemisphere [START_REF] Bourseau-Guilmain | In vitro expansion of human glioblastoma cells at non-physiological oxygen tension irreversibly alters subsequent in vivo aggressiveness and AC133 expression[END_REF].

Tumor growth control and pO 2 measurement

After 8-10 weeks, the animals were scanned using a Bruker Biospec 70/20 operating at a magnetic field of 7T (Bruker, Wissembourg, France) equipped with a 1 H cryoprobe under isoflurane anesthesia (1.5-0.5%, O 2 0.5L/min) to assess tumor development. Mice body temperature was maintained at 36.5-37.5°C by using a feedback-regulated heating pad during the entire imaging protocol. Rapid anatomical proton images were obtained using a rapid acquisition with relaxation enhancement (RARE) sequence (TR =3,200ms; mean echo time (TEm)=21.3ms; RARE factor=4; FOV=2×2cm; matrix 256×256; nine contiguous slices of 0.5mm, Nex = 1). T1 weighting was introduced in these images by using an inversion pulse prior to the RARE pattern in order to better the depiction of the tumors. The duration of the inversion delay was fixed at 600 ms, enough time to allow the annulation of the normal parenchyma [START_REF] Vonarbourg | Characterization and detection of experimental rat gliomas using magnetic resonance imaging[END_REF].When a tumor was detected, the mice underwent an intratumoral stereotactic injection of 8µL of the PFCE-LNCs using a convection-enhanced delivery protocol [START_REF] Franconi | Susceptibility gradient quantization by MRI signal response mapping (SIRMA) to dephaser[END_REF]. The fluorine acquisitions were performed immediately and could be repeated for at least a week using the same protocol as the one used for the in vitro study. The resonant circuit was a 40mm 1 H/ 19 F coil, and the sequence used was the same as the one used for the in vitro studies.

RESULTS AND DISCUSSION

PFCE-LNC formulation.

The morphology of LNC results in an oily core surrounded by lecithins and a non-ionic surfactant [START_REF] Heurtault | Physico-chemical stability of colloidal lipid particles[END_REF]. The formulation protocol is based on a phase-inversion process due to the specific properties of the non-ionic surfactant, PEG-HS present in Solutol. Then, PEG-HS gives an oil-in-water emulsion (O/W) at room temperature and a water-in-oil emulsion (W/O) at high temperature [START_REF] Heurtault | A novel phase inversionbased process for the preparation of lipid nanocarriers[END_REF].

This inversion process was tested to obtain PFCE nanocapsules (PFCE-LNC), using PFCE as the oil in the formulation. First of all, it appeared that the oil and water phases were not easy to mix due to the high density of PFCE (d ~ 2) and the size of the dispersed droplets produced were large (hydrodynamic diameter (Z-ave) ~ 450nm) with a high polydispersity index (PdI ~ 0.7).

In the literature, sonication in combination with high pressure is often used to obtain PFCE-LNCs [START_REF] Fan | MRI of perfluorocarbon emulsion kinetics in rodent mammary tumours[END_REF][START_REF] Lanza | A novel site-targeted ultrasonic contrast agent with broad biomedical application[END_REF]. In our case, sonication at atmospheric pressure was used to improve the dispersion of the oil and water phases before the phase-inversion process. A first cycle of temperature was added before the sonication step to allow the Lipoïd to melt. Various sonication powers were tested (0, 3, 5 and 10W) prior to the phase-inversion process. Without sonication, no PFCE-LNCs were formulated. When the sonication power was increased, PFCE-LNCs were formulated with sizes ca. 300nm when the power was set to 3W, and ca.

200nm when the power was set to 5 or 10W. The higher sonication power led to a narrowing of the PFCE-LNC population (PdI = 0.14 vs 0.22 for 10W vs 5W).

As a consequence, the formulation process had to include four steps: i) temperature increase of the formulation from room temperature to 95°C to allow the Lipoïd melting; ii) sonication of the formulation to the power of 10-W for 1 minute; iii) 3 temperature cycles from 25°C to 95°C; iv) and finally, during the last temperature decrease, when the temperature reaches 70°C, a rapid cold dilution with deionized water (dilution factor: 3.5).

The composition is however a crucial point for PFCE-LNC formulation using this low-energy process. Indeed, using Fan's formulation composition [START_REF] Fan | MRI of perfluorocarbon emulsion kinetics in rodent mammary tumours[END_REF], i.e. PFCE 2g, Lipoïd 0.12g, glycerin 0.09g and deionized water 2.91g, larger particles were obtained with a hydrodynamic diameter (Z-ave) ~ 250nm and a higher polydispersity index (PdI ~ 0.25). Interestingly, those nanoparticles are however comparable in size with those obtained using the high-energy process described by Fan et al [START_REF] Fan | MRI of perfluorocarbon emulsion kinetics in rodent mammary tumours[END_REF].

Therefore, with respect to the phase-inversion process and the composition used in this work, The PFCE, Solutol and deionized water compositions ranged from 0.1 to 0.55 w/w Total , from 0.05 to 0.35 w/w Total and from 0.25 to 0.80 w/w Total , respectively. The defined process was used for PFCE-LNC formulation and the results are reported on a phase diagram in Figure 1.

A feasibility area was observed, corresponding to PFCE-LNCs with Z-ave < 200 nm and PdI < 0.2. The limits of the domain were : about 0.1 to 0.2 w/w Total for Solutol, about 0.2 to 0.45 w/w Total for PFCE and about 0.4 to 0.6 w/w Total for deionized water. Outside this area, the PFCE-LNC size and the PdI were above 200nm and 0.2, respectively. Whatever the composition inside the feasibility area, a constant value of Z-ave was found, slightly lower than 200nm. For the system with a PFCE core, a size limit was observed while for LNCs with Labrafac core, size was dependent on the oilsurfactant ratio [START_REF] Heurtault | The influence of lipid nanocapsule composition on their size distribution[END_REF].

Figure 2 presents the stability of PFCE-LNC size as a function of time when stored at 4°C.

According to the phase diagram, the formulation was performed using 0.168 w/w Total for Solutol, 0.015 w/w Total for Lipoïd, 0.02 w/w Total for NaCl, 0.398 w/w Total for PFCE and 0.398 w/w Total for deionized water. A slight increase in size and the PdI (about 10%) was observed over a 3 month period of time. In addition, during storage and according to the high density of the oil, sedimentation of the PFCE-LNC was observed but a simple dispersion under stirring allows the material to be recovered without size modification. Interestingly, it should then be possible to concentrate the PFCE-LNCs using the property of sedimentation for these nanocarriers.

PFCE-LNC characterization.

PFCE-LNCs appeared to be different from classical Labrafac-LNCs, at least in terms of size dependency with respect to formulation composition. The density of the PFCE (~2) may account for this observation but the interaction of the surfactant may also be peculiar with this oil. As a consequence, the amphiphilic properties of PEG-HS were carefully examined at a PFCE-water interface. A PFCE pendant drop was formed using a drop tensiometer in a water phase containing various concentrations of Solutol from 0 to 0.4g.L -1 . A significant decrease of the surface tension from 45 to 20mN.m -1 was observed when Solutol concentrations were increased (Figure 3). PEG-HS from Solutol acted as a surfactant at the PFCE-water interface, as it was observed for with Labrafac oil [START_REF] Heurtault | Properties of polyethylene glycol 660 12-hydroxy stearate at a triglyceride/water interface[END_REF]. This may then explain the feasibility of producing lipid nanocapsules with PFCE.

As PFCE-LNC size was larger than those reported for Labrafac-LNC, the quantity of PEG-HS involved in nanoparticles was determined. PFCE-LNC formulation was dialyzed to remove all the free materials after formulation. The PEG chain concentration was obtained using KI/I 2 titration. As observed in Figure 4, about 20% (w/w) of PEG was free after the formation of the LNCs corresponding to the free PEG chains present in commercial Solutol.

Therefore, PEG-HS from Solutol totally participated into the formation of nanoparticle shells.

In order to appreciate the softness of PFCE-LNCs, Ohshima's model was applied [START_REF] Ohshima | On the General Expression for the Electrophoretic Mobility of a Soft Particle[END_REF]. This model was used to fit the experimental electrophoretic mobility of PFCE-LNCs, diluted by factors 60, 600 and 6,000, vs. NaCl concentrations (Figure 5 for the dilution factor 600). No difference for the experimental electrophoretic mobility was obtained, whatever the dilution of PFCE-LNCs, and the experimental data points were fitted using the Ohshima model

showing that the PFCE-LNCs could be considered as a charged, hard sphere surrounded by a non-charged, soft-shell. The two fitting parameters were determined: ZN = -0.67 ± 0.21 .10 6

C.m -3 and 1/ = 3.5 ± 1.0nm. The second parameter corresponds to the ion penetration layer around the hard sphere. This penetration layer appeared to be significantly different from the one measured in Labrafac-LNC (~ 0.1nm) [START_REF] Vonarbourg | Electrokinetic properties of noncharged lipid nanocapsules: influence of the dipolar distribution at the interface[END_REF] and suggested that the organization within the PFCE-LNCs shell was unusual.

In order to characterize this peculiar organization of the HS-PEG at the interface PFCE-water in the PFCE-LNCs, the HS-PEG density was calculated. According to Minkov et al. [START_REF] Minkov | Reorganization of lipid nanocapsules at air-water interface -Part 2. Properties of the formed surface film[END_REF],

when HS-PEG molecules are perfectly and compactly organized at the Labrafac-water interface, the surface occupied by one molecule of surfactant is about 1nm². In PFCE-LNC, such a calculation was performed (Appendix 1) and showed that each HS-PEG molecule only occupied 0.1nm². This lower value and therefore higher density can only be reached with a chaotic arrangement of HS-PEG (Figure 6).

Thus, PFCE-LNC can be described as a PFCE spherical core surrounded by lipoïd and PEG-HS whose organization at the interface oil-water is chaotic. The shell layer accessible to ions, calculated using the Ohshima model at 3.5 nm, corresponded to the accessible depth inside this chaotic organization. As it currently is, the thickness of the shell is unknown but has to be above the thickness of the shell in labrafac-LNC. The thickness of the shell and its chaotic organization may then impede the diffusion of O 2 molecules toward the fluorinated sensor, a compulsory phenomenon to assess pO 2 . In order to test this hypothesis, an assessment of relaxivity changes of the PFCE entrapped in the PFCE-LNC as a function of surrounding pO 2 was performed.

PFCE-LNC and MRI.

T1 Measurement of PFCE-loaded nanocapsules in vitro and relationship with pO 2 .

First of all, a comparison between the sensitivity of free PFCE and of encapsulated PFCE with respect to oxygenation was performed. No significant changes were observed. Indeed, T1 measurements performed at 20°C lead to values of 2380ms, 1300ms and 582ms for the free PFCE when the samples were exposed to 0% respectively. The linear regression from R1 (defined as 1/T1) over pO 2 (at 37°C), yielded for the anoxic intercept A, the value 0.6582 ± 0.026 s -1 , and for the slope S, the value 0.0026 ± 0.0001 s -1 mmHg -1 . The calculation of the pO 2 value can then be performed using Equation 3.

0026 . 0 0.6582] - (s)) [(1/T1 ) ( pO 2  mmHg (Eq. 3)
Despite being limited, an effect of temperature is observed on 1/T1 value, which then interferes with the in vivo pO 2 measurements. This error on pO 2 measurements can be calculated from multiple linear regression analysis (Matlab R2011b) of the data presented in Assuming a T1 value of 1,150ms, the pO 2 value at 37, 36 or 35°C is 78, 73 or 67mmHg.

Despite this potential drawback in pO 2 measurements, one may assume that in vivo, the temperature will be constant and therefore, that pO 2 changes will reflect biochemical processes.

PO 2 measurement in vivo

The stereotactic injection of 8µL of the PFCE-loaded nanocapsules suspension was sufficient to allow the detection of a significant fluorine signal (signal-to-noise ratio for TR = 6,000ms was about 20), that can be used to assess tumor pO 2 (Figures 8A&8B). On the images presented, when the mouse was anesthetized for 20 minutes using isoflurane vaporized with pure oxygen (Figure 8A), the tumor pO 2 was calculated on three consecutive sets of images, assuming a tumor temperature of 37°C, at 159, 186 and 177mmHg leading to an average value of 174 ± 14mmHg. When the vaporizing gas was switched to air, the tumor pO 2 dropped below 50mmHg within 10 minutes to tend to values below 10mmHg within 30 minutes in the presented primary grade IV brain tumor model (Figure 8 B). As previously described, the profile of the pO 2 change with time can be fitted with a monoexponential function whose time constant reflect mainly tumor oxygen consumption as perfusion has a limited effect [START_REF] Diepart | In vivo mapping of tumor oxygen consumption using (19)F MRI relaxometry[END_REF][START_REF] Diepart | A New EPR oximetry protocol to estimate the tissue oxygen consumption in vivo[END_REF]. In the type of tumor explored (Figure 8C), this time constant (k) was calculated at k= 0.16 min -1 . This measurement can be repeated over time for at least 10 days in this fast growing tumor model. Currently, the temporal resolution of the pO 2 assessment is ca. 4min, and may be significantly reduced using the SNAP-IR sequence presented by Jordan [START_REF] Jordan | Rapid monitoring of oxygenation by 19F magnetic resonance imaging: Simultaneous comparison with fluorescence quenching[END_REF] assuming that the achievable spatial resolution will be compatible with the small tumors present in the mouse brain. This figure also showed that despite the entrapment of the sensor within the nanocapsules, oxygen molecules can access the PFCE through the constituted surfactant shell.

CONCLUSIONS

Nanoscaled platform capable of measuring brain tumor pO 2 using fluorine MRI was synthesized. Despite the high density and the high lipophilicity of the fluorinated pO 2 sensor, i.e. perfluoro-15-crown-5-ether, the low-energy, phase-inversion process used to produce lipid nanocapsules could be implemented. The resulting nanocapsules are composed of a perfluoro-15-crown-5-ether core surrounded by a chaotic arrangement of polyethylene glycol hydroxystearate that does not interfere with O 2 molecule diffusion toward the oxygenation sensor. Once injected in brain tumors using a convection-enhanced delivery protocol, a pO 2 map of the tumor can then be performed.

where

   is the viscosity of the medium expressed in Pa.s -1 ,  r = 80 (relative permittivity of the electrolyte solution),  0 = 8.85 .10 -23 J.K -1 , e = 1.6 .10 -19 C (elementary electric charge), T is the thermodynamic absolute temperature, k is the Boltzmann constant and n is the bulk concentration of the electrolyte solution, expressed in C.m -3 .

  the phase diagram was explored changing the proportions of deionized water, Solutol and PFCE. The Lipoïd quantity remained constant at 0.075g and the NaCl concentration was maintained at 5% w/w Water . Influences of lipoïd and NaCl on the formulation have been studied previously. Without Lipoïd, PFCE-LNCs were impossible to obtain and a rapid phase separation was observed. The addition of higher Lipoïd quantities led to PFCE-LNCs with larger sizes and larger PdIs. With 0.15g and 0.3g of Lipoïd, the Z-ave values were about 330nm (PdI ~ 0.7) and 220nm (PdI ~ 0.31), respectively. An increase in NaCl concentration did not change the size and PdI of PFCE-LNCs. At an NaCl concentration of 10 % w/w Water , the Z-ave was 197nm and the PdI was 0.115. Changing the temperature of the medium at which the rapid cold dilution occurred did not significantly change the PFCE-LNC parameters. Indeed, when temperatures were 50, 60 and 90°C, the Z-ave values were 189, 196 and 189-nm, respectively, and the PdI were 0.11, 0.11 and 0.10, respectively.

Figure 6

 6 Figure 6 as Equation 4:

2.3. Physico-chemical characterization of PFCE-LNCs

	PFCE, Solutol, Lipoïd, NaCl
	and deionized water, were weighed to obtain a final mixture (about 5g), with PFCE
	composition from 0.10 to 0.55 w/w Total , Solutol composition from 0.05 to 0.35 w/w Total ,
	deionized water composition form 0.25 to 0.80 w/w Total . m Lipoïd and the NaCl concentration
	was fixed at 0.075g and 5 % w/w water .
	These different formulations were stored at 4°C and size stability over the experimental time
	was assessed.
	2.3.1. Size measurement.
	The average hydrodynamic diameter Z-average (Z-ave) and the polydispersity index (PdI) of
	PFCE-LNC were determined by dynamic light scattering using a Malvern Zetasizer ® (Nano
	Series DTS 1060, Malvern Instruments S.A., Worcestershire, UK) fitted with a 633 nm laser
	beam (helium-neon laser, 4 mW) at a fixed scattered angle of 173°. Measurements were made
	at 25°C, with 0.89 cP viscosity and a refractive index of 1.33. The autocorrelation function
	was fitted using the cumulant analysis method to obtain Z-ave and PdI values. The PFCE-
	LNCs were diluted with pure water (dilution factor: 60) before size measurement; each
	measurement was performed three times.

  , 21% or 100% O2 and to values of 2296ms, 1397ms and 607ms for encapsulated PFCE. To characterize the sensitivity of the PFCE-LNCs to oxygenation, T1 values of the suspension of PFCE-loaded nanocapsules after bubbling for 30 min with 100% O 2 , air (21% O 2 ) or 100% N 2 were measured as a function of the suspension temperature. According to Figure 7, at 37°C, T1 values of 376 ± 15ms, 972 ±

	33ms and 1,530 ± 45ms were measured after bubbling in 100% O 2 , air (21% O 2 ) or 100% N 2 ,

ACKNOWLEDGEMENTS

Authors acknowledge financial support from 'Comité Inter-Régional Grand Ouest de La Ligue Contre le Cancer' -CIRGO and 'La Ligue nationale contre le cancer -Equipe Labellisée 2012'. Authors would like to thank Dr. David Rees for editing the manuscript.

BIBLIOGRAPHY: