Dr Philippe Bourget
email: philippe.bourget@nck.aphp.fr

Alexandre Amin

Fabrice Vidal

Christophe Merlette

Frédéric Lagarce

Raman spectra Fluorouracil compounded in portable infusion pump *Graphical

Highlights

 We compare the performance of HPLC to Raman spectroscopy.

 The two methods were validated for trueness, precision and accuracy.

 There is a statistical correlation between Raman Spectroscopy and HPLC.

 Raman Spectroscopy is effective for analytical quality control of 5-fluorouracil.

 Raman Spectroscopy contribute to protect caregivers and their working environment.

This study compares the performance of a reference method of HPLC to Raman spectroscopy (RS) for the analytical quality control (AQC) of complex therapeutic objects. We assessed a model consisting of a widely used anticancer drug, i.e., 5-fluorouracil, which was compounded in a complex medical device, i.e., an elastomeric portable infusion pump. In view of the main objective, the two methods provided excellent results for the analytical validation key criteria, i.e., trueness, precision and accuracy, ranging from 7.5 to 50 mg/mL and in either isotonic sodium or 5% dextrose. The Spearman and Kendall correlation tests (p-value < 1.10 -15 ) and the statistical studies performed on the graphs confirm a strong correlation in the results between RS and the standard HPLC under the experimental conditions. The selection of a spectral interval between 700 and 1400 cm -1 for both the characterization and quantification by RS was the result of a gradual process optimization, combining matrix and packaging responses. In this new application, we demonstrate at least eight benefits of RS: a) operator safety, b) elimination of disposables, c) elimination of analysis waste, which contributes to the protection of the environment, d) a fast analytical response of less than two minutes, e) the ability to identify the solubilizing phase, f) reduction of the risk of errors because no intrusion or dilution are needed, g) negligible maintenance costs and h) a reduction in the budget dedicated to technician training. Overall, we indicate the potential of non-intrusive AQC performed by RS, especially when the analysis is not possible using the usual techniques, and the technique's high potential as a contributor to the safety of medication.

. Background and purpose

In France, central IV admixtures of chemotherapy treatments (CT) are required by law [START_REF]relatif au contrat de bon usage des médicaments et des produits et prestations mentionné à l'article L.162-22-7 du code de la sécurité sociale[END_REF]. This process is currently performed under pharmaceutical liability, especially at hospitals. This requirement represents an important step forward in terms of both the quality and safety of care [START_REF] Dahan | Sécurisation du circuit du médicament à l'Assistance Publique-Hôpitaux de Paris (AP-HP)[END_REF], as well as a) a strong contribution to the standardization of prescribing practices, b) a lower exposure of caregivers to chemicals, c) an improved organization of caregiver workloads and d) a substantial cost savings [START_REF] Martin | Prevention of preparation errors of cytotoxic drugs in centralized units: from epidemiology to quality assurance[END_REF]. However, we see a) an increasing number of combined therapies, b) an increasing number of patients and c) more individualized and more complex therapeutic regimens. In this multifactorial context, the development of effective tools for the quality control of therapeutic objects (TO)* is highly relevant [START_REF] Martin | Prevention of preparation errors of cytotoxic drugs in centralized units: from epidemiology to quality assurance[END_REF]. Our goal is to ensure a high and stable quality in our pharmaceutical preparations for the benefit of patients, caregivers and the environment. Furthermore, a systematic analysis of the production process reveals several critical points; these abnormalities may dangerously weaken the validity of the process. In the course of pioneering studies started 12 years ago at the Gustave-Roussy Institute (Villejuif 94805 cedex, France), we demonstrated the importance of linking the physical product resulting from a compounding process, which we call TO, to the flow of information [START_REF] Bourget | Place et spectre fonctionnel de l'HPTLC dans un programme d'assurance qualité pharmaceutique hospitalier[END_REF][START_REF] Bourget | Contribution of high-performance thin-layer chromatography to a pharmaceutical quality assurance programme in a hospital chemotherapy manufacturing unit[END_REF][6][START_REF] Bouligand | Quality control and stability study using HPTLC: applications to cyclophosphamide in various pharmaceutical products[END_REF][START_REF] Gravel | Fluorescence detection combined with either high performance liquid chromatography (HPLC) or high performance thin-layer chromatography (HPTLC) for pharmaceutical quality control in a hospital chemotherapy production unit: application to Camptothecine derivatives[END_REF]. This idea occurred to us long before the recent and serious health accidents that were highly publicized in the French media. We designed an analytical quality control (AQC) process that we applied, as systematically as possible, to the three following key parameters: identity, purity and nominal concentration of an active pharmaceutical ingredient (API) in solution or in suspension in a sterile medium. However, experience indicates that a TO cannot be reduced to the API. Under these conditions, the following question is important: is it possible to offer an analytical solution, ideally non-intrusive, that could manage the entire TO, i.e., API, solubilizing matrix and its container?

A c c e p t e d M a n u s c r i p t 4 In this context, the purpose of this study was to develop and validate a Raman spectroscopy (RS) method as an effective tool for the non-intrusive AQC of geometrically complex TO(s). We studied the model of elastomeric portable infusion pumps filled with fluorouracil (5-FU) either in a normal saline solution or in a 5% dextrose solution. This protocol was compared to a reference HPLC method. We also examined how the use of one analytical method vs. another contributes to the security and safety of the administration of medication at the hospital. * We call Therapeutic Object(s) (TO(s)) the product resulting from a compounding process, performed by specialized staff, i.e., a) an active principle in solution or in suspension in an appropriate medium, usually normal saline or 5% dextrose solution, and b) an immediately labeled package, possibly pre-connected to an infusion set. The presence of secondary packaging may complete the definition.

Analytical quality control and Raman Spectroscopy

Ideally, the purpose of AQC is to allow the analytical certification of the TO prior to its administration to a patient. In terms of hospital organization, the AQC should be fast, reliable, and fully integrated into the production process and treatment. This is particularly relevant for day care units. However, the need to withdraw a fraction of a TO for analysis purposes should also be considered in terms of security and safety, for both operators and their working environment. For some TOs, withdrawal is difficult, even impossible, e.g., small syringes, autonomous infusion devices (elastomeric portable infusion pumps), and PCA devices. The most frequently used analytical techniques are: a) chromatographic methods coupled with appropriate detection systems, b) HPTLC (high performance thin layer chromatography) methods, and c) coupling of UV/visible light spectroscopic techniques to a Fourier transform infrared spectroscopy detector. Chromatographic methods are powerful, but their implementation is costly and sometimes tedious. They also require specialized skills. We will not A c c e p t e d M a n u s c r i p t 5 detail the strengths and weaknesses of this reference option. According to our criteria, and despite substantial technical improvements, chromatographic methods are not suitable to highthroughput AQC. RS allows for the qualitative and quantitative characterization of an API and its solubilization matrix, without any risk of alteration. However, among the characterization parameters, both the specificity and reliability of the technique must be demonstrated through experimentation; furthermore, some molecules are structurally similar [START_REF] Moriceau | Proceedings of the 8th GERPAC European Conference[END_REF]. Finally, we must systematically study the spectral behavior of packaging layers (of varying number and thickness), their contents, and the possible interferences of their respective signatures. For these reasons, the term -contextual analysis‖ by RS will be used. It is worth to note that quantitative Raman studies of APIs in injectable are very rare [START_REF] Mazurek | Quantitative determination of diclofenac sodium and aminophylline in injection solutions by FT-Raman spectroscopy[END_REF][START_REF] Bourget | The Raman Spectroscopy (RS): A new tool for the analytical quality control of injectable in health settings. Comparison of RS technique versus HPLC and UV/Vis-FTIR, applied to anthracyclines as anticancer drugs[END_REF].

Material and Methods

Choosing a suitable API and working conditions

In brief, fluorouracil is a pyrimidine analogue that has been used for more than 40 years. This drug is widely used in the treatment of many forms of cancer and often in combination with other anticancer drugs. Some of its main indications are in colorectal and pancreatic cancer. It is also used in the treatment of inflammatory breast cancer, an aggressive form of breast cancer [START_REF] Perry | The chemotherapy source book[END_REF]. Most of the protocols involving 5-FU are listed in Table 1. 5-FU is administered at therapeutic concentrations from 12.5 to 50 mg/mL, either in saline or 5% dextrose; the analytical comparison was performed within these two values and in both solvents. To test the analytical performance of RS vs. HPLC and to build robust calibration models, we expanded the range of concentrations from 1.5 mg/L, leading to the production of a large number of calibration TOs and external validation TOs.

Choosing the medical device

A c c e p t e d M a n u s c r i p t 6 5-FU is usually administered by IV, by means of either an infusion bag (in this case, gravity is used), or a more or less sophisticated electromechanical pump or, finally, by autonomous elastomeric infusion systems that use a combination of the elastomeric material pressure and Hagen-Poiseuille's law. This last option is of particular interest because: a) these systems are disposable medical devices, b) their physical structure and their geometry are quite complex, c) they are commonly used in both hospitals and in homecare, as well as for ambulatory patients.

We selected a pump model widely used in protocols, such as FOLFOX and FOLFIRI (Table 1), i.e., the Infusor ® SV2 System (Baxter ref 2C1702KD, batch 09C044 2011-12-31); Fig. 1 is a diagram of the device.

HPLC analysis

Chromatographic separation was performed on a Dionex Ultimate ® 3000 series liquid chromatographic system equipped with a quaternary pump, a variable UV/visible detector, and an autosampler (Dionex, 78960 Voisins le Bretonneux, France). Chromatographic separation was performed on Lichrospher ® C18 column (125 mm x 4 mm, dp = 5 m (Merck, 69008 Lyon, France). The mobile phase consisting of a mixture of water for injection and KH 2 PO 4 (40 mmol/L) adjusted to pH 7.0 with NaOH (10% solution in water), was delivered at rate of 0.8 mL per min. The mobile phase was filtered through a 0.45 µm membrane (Millipore, 67120 Molsheim, France) and degassed prior to use. Separation was performed at ambient temperature, i.e., 21°C; detection was performed at 260 nm. The injection volume was 5 L with a run time of 6 min. Data were recorded; the Dionex Chromeleon ® (version 6.80) software was employed for data collection and processing. The chromatographic conditions were based from a HPLC method coupled with UV detection developed by Alanazi et al. [START_REF] Alanazi | Validated highperformance liquid chromatographic technique for determination of 5-fluorouracil: applications to stability studies and simulated colonic media[END_REF].

RS analysis

A c c e p t e d M a n u s c r i p t 7

The RS analysis was performed between 100 and 3400 cm -1 using an RXN1 bench (Kaiser Optical System, Ann Arbor, USA); Fig. 2 is a diagram of the bench. This industrial machine is equipped with a user-safe laser source emitting in the near infrared at 785 nm.

According to the manufacturer's specifications, the rated power of the laser source is 345 mW vs. 210 mW to the end of the probe. The acquisition of signals was performed using a chargecoupled device (CDD detector) through the iC Raman ® Instrument software (Mettler-Toledo AutoChem Inc., Columbia, MD, Version 4.1). The treatment of the signals and the partial least square regression (PLS), first derivative, and mean center were then calculated with the iC Quant ® software (Mettler-Toledo AutoChem Inc., Columbia, MD, Version 4.1). We developed a Raman illumination chamber (RIC) that allows examining examination of TOs of any geometry. This light-tight chamber is equipped with a micrometer focal adjustment system used for accurate fixing and excellent repeatability of the distance between the laser source (the extremity of the probe) and the object, e.g., syringe, pouch, bottle, or portable pump.

Validation protocol

Analytical validation of the methods was conducted in accordance with the recommendations of the Commission of the French Society of Pharmaceutical Science and Technology (SFSTP, 2003) [START_REF] Ph | Harmonization of strategies for the validation of quantitative analytical procedures: a SFSTP proposal-part I[END_REF][START_REF] Ph | Harmonization of strategies for the validation of quantitative analytical procedures: a SFSTP proposal-part II[END_REF]. This guide provides a consensus on the various existing international standards, e.g., the International Conference on Harmonization: Validation of Analytical Procedures Q2 (R1) [START_REF]Validation of analytical procedure: definition and terminology (Q2A), ICH Tech coordination[END_REF][START_REF]Validation of analytical procedure: methodology (Q2B), ICH Tech coordination[END_REF], FDA guidelines: Guidance for Industry, Bioanalytical Method Validation [START_REF]Guidance for industry -bioanalytical method validation‖[END_REF]. It also incorporates ISO terminology. Calculation of both the accuracy profiles and the validation parameters based on the Quality Control (QC) results was performed using the e.noval ® (version 3.0) software (Arlenda, Liège, Belgium). Because the focus of the present study is the AQC of complex therapeutic objects, the acceptance limits were set at ± 10% for the validation, whereas the probability of obtaining results within the tolerance interval was set at 95%. The validation protocol was strictly identical for the 2 techniques comparing HPLC and RS.

Three campaigns were conducted on 3 consecutive days, either in saline or 5% dextrose. To

External validation

An accurately weighed quantity of 5-FU was dissolved in isotonic saline or 5% dextrose. The pH was adjusted to 9.0 by adding a solution of sodium hydroxide at 14.7 mg/mL (VWR, Fontenaysous-Bois, France, ref. to obtain two reference solutions of known concentrations of approximately 50 mg/mL. Two groups of five external validation solutions, i.e., 2.5, 7.5, 15, 30 and 40 mg of 5-FU per mL, were prepared each day in saline and 5% dextrose and transferred into portable infusion pumps (Infusor ® SV2) to obtain the daily external validation set.

Calibration sets

Three independent calibration sets were produced with nine points, 0, 1.5, 2.5, 5, 10, 17.5, 25, 35, and 50 mg/mL, using a ready-to-use commercial solution available at the theoretical nominal concentration of 50 mg of 5-FU per mL (Mylan, 69792 Saint Priest, France) either in isotonic sodium or 5% dextrose according to our compounding protocols. The commercial solution consisted of 5 g of 5-FU in 100 mL of water for injection and sodium hydroxide (pH 8.5 to 9.5).

PLS parameters

Partial least squares (PLS) is the most popular multivariate model for quantitative Raman analysis. PLS uses factor analysis to compress the size of the spectra and to remove redundant information. PLS uses the analyte concentration information along with sample variance in compression process to create factors that are correlated with analyte concentration. More the number of factors increases and more the model will take into account the variance of the set of A c c e p t e d M a n u s c r i p t 9 spectra. However, an excessive number of factors will result in overtraining of the model at the expense of future predictions. The number of factors is therefore crucial for the quality of the calibration model and is determined by cross-validation which allow the calculation of RMSECV (root-mean-square error of cross-validation) whose value must to be minimal.

Validation parameters

The analytical validation steps included the following parameters: a) Linearity, the ability of a method, within a certain concentration range, to give linear and proportional results to the analyte concentration. The parameter was verified by the study of three independent calibration sets and tested on three consecutive days (3 x 3/day) for a total of nine curves per method.

After fitting the linear regression model, i.e., the calculated concentrations vs. actual concentrations, the linearity was verified by the calculation of a correlation coefficient (R²). To demonstrate the linearity of the method, the approach based on the expected tolerance level β, expressed in absolute values, was also used. b) The lower and upper limits of quantification (LLOQ and ULOQ) define the range where an analytical method is able to quantify accurately. These limits are, respectively, the smallest and the highest concentration levels where the expectation tolerance intervals are included within the acceptance limit. c) Accuracy refers to the closeness of agreement between the test result and the accepted reference value, namely the conventionally true value. It is assessed from the accuracy profile and the relative - TOs. f) Uncertainty is a parameter associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurement [START_REF]Uncertainty of measurement: implication of its use in the analytical science[END_REF][START_REF]Eurachem/Citac Guide, Quantifying the Uncertainty in Analytical Measurement[END_REF]. The relative expanded uncertainties lead to a relative interval around the results where the unknown true value can be observed with a confidence level of 95% [START_REF]EA guidelines on the expression of uncertainty in quantitative testing[END_REF][START_REF] Marini | LC method for the determination of R-timolol in a S-timolol maleate: validation of its ability to quantify and uncertainty assessment[END_REF].

Methodological progression

The portable pumps were first analyzed by RS. In a second step, samples were analyzed by HPLC. The need for repeated withdrawals (250 µL per sample) from sealed and closed systems forced us to follow this methodological progression. For HPLC analysis, samples were systematically diluted in the corresponding medium, i.e., 1/50 in normal saline or in 5% dextrose. After characterizing the performance of each instrument, RS was compared to the reference method.

Statistics and correlation study

To study the strength of the relationship between a series of measurements obtained from the two techniques, we used the statistical methodology proposed by Bland and Altman theoretically equal to zero and should be positioned on y-axis (y = 0). Taking into account the repeatability of the two analytical methods, this approach is interesting. However, to give a strong statistical conclusion, and considering that data obtained from the two sequences do not allow for a hypothesis about their underlying distribution, we applied two convergent nonparametric tests of rank, i.e., the Rho (ρ) of Spearman and the Tho (τ) of Kendall. To be applicable, these various tests must be conducted by the two techniques on the same samples.

In this way, the values obtained from each of the three daily independent calibration sets and the external validation set (either in saline or 5% dextrose) were averaged. Finally, statistical analysis was performed on two homogeneous groups of 36 physically and statistically comparable results.

A c c e p t e d M a n u s c r i p t

Results and Discussion

Spectral signatures generated by RS

Exposure of objects to the laser beam was both direct and through the primary packaging (Fig. 1 and2); this is safe for both operators and their working environment. Mastering the tool allowed us to systematically maintain a total acquisition time of 1 min; this value is dependent on the type and geometry of the device and its content. The RIC allows for the optimization of the focal length by repeating the measures applied to a device, filled, for example, with a hydroethanolic solution (5:95, v/v). The setting results in a focal length of 0.5 mm between the extremity of the probe and secondary packaging, i.e., a polycarbonate envelope in the present case. This focal length reflects the optimal ratio (signal of the therapeutic solution/signal of the device). Figure 3 depicts the Raman signatures of the portable pump studied under four conditions and without 5-FU. The polyisoprene chamber was filled either by normal saline, 5% dextrose, sterile water, or ambient air. The Raman signatures were obtained by scanning between 100 and 3400 cm -1 at 21°C. Figures 4 and5 show the signatures of the portable pumps filled with 5-FU (concentrations from 1.5 to 50 mg/mL) in normal saline or 5% dextrose.

The comparison of the RS signatures generated with and without the API allows for the definition of a PLS (Partial Least Square) regression interval between 700 and 1400 cm -1 . Within this interval, there is minimal variation in response to the matrix. In contrast, the signature of 5-FU is intense between 740 and 800 cm -1 . RS signatures are highly specific of a TO and are an assembly of rigid layers (the container) and liquid layers (the content). This assembly is both the main limiting factor of the RS performance (see LOQs in Table 2) and one of the main assets of the method. Analysis can be applied to an object while maintaining its integrity. This illustrates the major importance of a rigorous selection of spectral bands for both the characterization and quantification of an API. Thus, the quantification step is the result of an adjustment process; it is also an empirical compromise between many parameters, including An optimal number of 12 PLS factors were chosen for both matrixes in order to minimize the RMSECV. As seen in Table 3, the RMSEC (root mean square error of calibration), RMSECV and RMSEP (root mean square error of prediction) values are low and thus confirm the quality of the models. However, those criteria do not allow the assessment of the ability of the model to accurately quantify over the entire concentration range. Therefore, the performance of the predictive model was evaluated with accuracy profiles computed on the external validation results.

Method validations

Figure 6 displays the accuracy profiles computed with the external validation set results. For the reference method, the expectation tolerance limits are fully included within the ±10% acceptance limits. For the RS in both saline and 5% dextrose, the expectation tolerance limits are included between the range from 7.5 to 40 mg/mL within the ±10% acceptance limits.

The ICH Q2 (R1) validation criteria obtained for both methods (HPLC and RS) are summarized in Table 2. As shown on the accuracy profiles, the bias is less than 3% except for RS in dextrose, where it is 7.3% at a concentration of 2.5 mg of 5-FU per mL. The precision of each method was estimated by measuring the repeatability and intermediate precision at the 5 concentrations levels. The dispersion of the results was below 4% from 7.5 to 40 mg/mL (Fig. 6). The precision of the RS is less satisfactory at the 2.5 mg/L concentration level, particularly in 5% dextrose. This leads to larger LLOQs, i.e., 3.8 and 6.1 mg/L, respectively, in saline and in 5% dextrose vs. 2.5 mg/L for HPLC in both cases. To verify the linearity, each model was fitted on the back calculated concentrations of the validation standards for all series as a function of the introduced theoretical concentration. The slope and intercept are close to 1 and 0, respectively, confirming the absence of a proportional and constant systematic error in each model. The linearity of the models were between the range from 7.5 to 40 mg/mL for RS and in A c c e p t e d M a n u s c r i p t 14 the entire range of concentration levels tested for HPLC because the absolute β-expectation tolerance limits were within the absolute acceptance limits (Fig. 6 andtable 2). The range of linearity was smaller by RS compared to HPLC; however, it covers the entire range of concentrations encountered in clinical practice, especially when using a portable pump. This is also true for the FOLFOX and FOLFIRI protocols, which are commonly prescribed to children presenting with a BSA of approximately 1 m² and with a dose reduction of 50% (Table 1).

Considering the ranges of linearity, the relative expanded uncertainties are not higher than 6% and 7%, respectively, for HPLC and RS (Table 2). This means that for both techniques, and with a confidence level of 95%, the unknown true value is located within a maximum of ±7% around the measured results. The two methods are satisfactory for the key criteria of trueness, precision and accuracy in the entire range of concentrations encountered in current clinical practice. The chromatographic method remains more powerful; both the precision RSD and the accuracy relative to the -expectation tolerance limit are lower with the HPLC method than with the vibrational spectroscopic method. Analysis conducted by RS can be described as contextual, i.e., the combined effects of matrixes and packaging (Fig. 1 and3) in addition to the vibrational spectroscopic response of the API.

Correlation study

Considering the 36 averaged samples, i.e., means of each concentration level (from 1.5 to 50 mg/mL) by day and for three consecutive days, the values of ρ (Spearman test) and τ (Kendall test) were all greater than 0.93. Thus, the hypothesis H0, by which the ranks are independent, was rejected with a lower risk than 2.2.10 -16 with both Spearman and Kendall tests and in both matrices (lowest p-value provided by the statistical software). According to Bland and Altman [START_REF]Eurachem/Citac Guide, Quantifying the Uncertainty in Analytical Measurement[END_REF], we found in both matrices a) that points are homogeneously distributed along the line of equality; this finding indicates that the two methods are well correlated; b) that the dispersion on both sides of the line of equality is homogeneous and there is no measurement bias; and c) that the dispersion is greater on the x axis (analysis by RS); this result A c c e p t e d M a n u s c r i p t demonstrates higher variability of the measurements performed by RS. The variability of measurements was also greater when 5-FU was in 5% dextrose. The average of the differences in the concentrations [CLHP -RS] (mg/mL  SD), limits of acceptability (LoA, mg/mL) and limits of acceptability weighted by the repeatability of the analytical techniques (LoAP, mg/mL) were, respectively, 0.15  0.42, [-0.9 -1.2] (LoA), [-2.5 -2.8] (LoAP) in normal saline and, 0.07  0.50, [-1.2 -1.3] (LoA), LoAP [-3.2 -3.3] in 5% dextrose (Fig. 7 and8).

To simplify the development of the method, we did not take into account the range of concentrations. Thus, the difference in the concentrations [HPLC -RS] examined side-by-side vs. the average value increased with the same average concentration. Whatever the mixture, clouds of points were homogeneously distributed in terms of LoAP, whereas differences of LoAs were reasonably low in the considered range of concentrations, i.e., from 1.5 to 50 mg 5-FU per mL. The dispersion of the differences for both measurements and the LoAPs (and their variability) were higher in 5% dextrose. Considering a) the highly statistical significance of the two rank tests (Spearman and Kendall tests), b) the strong graphic correlations and c) the homogeneous distribution of the differences for both the LoAs and LoAPs, there was a strong correlation in the results (5% statistic risk) between the two methods under the experimental conditions used. The correlation tests and the statistical studies performed on the graphs confirmed that the RS gave satisfactory results vs. the standard HPLC method. We also identified the functional limit of RS, which becomes less accurate and less powerful when the matrix is dextrose in water. The spectral signature of this matrix is much more intense than that obtained in saline. In the context of AQC, this leads to the following recommendation: unless the use of dextrose is necessary (which is rare to our knowledge), it is preferable to use a saline matrix.

RS as a tool for routine control of TOs

We now examine where RS has potential for routine AQC. The main advantage of RS is to allow rapid and safe contextual analysis of the TO. In fact, for routine control of TOs, it's not This major benefit could be considered as a relative disadvantage by some professionals. We proceed with the simultaneous analysis of at least four entities: a) an API (5-FU in the present case), b) a dilution matrix, c) an immediate packaging whose geometry may vary over time, i.e., a flexible elastomeric (polyisoprene) shape memory reservoir, d) a secondary packaging, i.e., a rigid polycarbonate shell in the present case, and sometimes, e) a plastic overwrapping, i.e., a plastic film or a polyethylene soft bag. This contextual variability might require new analytical validations if one of the four entities change. Such work might also be necessary in the case of a change of supplier, either for the medical device or for the drugs it contains. Conversely, this relative disadvantage could be another benefit of RS; in the near future, the gradual construction of a spectral database could help us to optimize the choice of the products that we use.

In view of our objectives, and including the AQC of a therapeutic solution of 5-FU in portables infusion systems, Raman technology presents a number of attractive benefits. First, we showed that with the addition of an RIC, it was possible to qualitatively and quantitatively explore TOs of various geometries, without any intrusion or destruction to the material. In addition, we identified multiple benefits: a) operator safety is guaranteed at all times, i.e., during the production step as well as in the laboratory, b) the complete elimination of disposables, c) the elimination of analysis waste is a precious guarantee of protection to the working environment, d) a fast analytical response of less than 2 minutes (compatible with the rejection of a non-compliant and a fast reshaping of the TO), e) the ability of RS to discriminate and identify the solubilizing phase of an API, f) a lower risk of errors vs. HPLC, which requires stages for withdrawal and often dilution of samples, g) negligible maintenance costs, which is not surprising because the machine does not contain any mechanical moving parts, and h) reduction in the budget dedicated to technician training. In total, we demonstrated that contextual analysis by RS allows for efficient AQC, especially for complex and non-withdrawal therapeutic objects, e.g., autonomous infusion systems or small syringes.

Conclusions

We demonstrated the potential of RS as an effective tool to perform non-intrusive AQC of complex TOs, especially its non-inferiority vs. HPLC, to determine the concentration of a widely used anticancer drug, such as 5-FU. From a practical point of view, the selection of bands for the characterization and quantification by RS was the result of a gradual adjustment process combining the matrix effects. Our results confirmed the potential of this option for future applications, owing to its capability to explore therapeutic objects with any type of geometry and its contributions to the safety of the medication circuit. This method also contributes to the protection of caregivers and their working environment. List of the major chemotherapy protocols that include a continuous infusion of 5-FU and their main parameters of use. LV2, SV2, and LV5 are brand names of Baxter Healthcare.

Table 2.

Trueness, precision, accuracy, lower and upper limit of quantification, and uncertainty, obtained with HPLC vs. RS in saline and 5% dextrose. 3. Raman signatures of the portable pump (Infusor ® SV2 system) studied in different circumstances and without 5-FU. The polyisoprene chamber was filled either by normal saline, 5% dextrose, sterile water, or ambient air. Raman signatures were obtained after scanning between 100 and 3400 cm -1 at 21°C. Insert: the research interval, between 300 and 1850 cm -1 . Fig. 4. Raman signatures obtained after scanning between 100 and 3400 cm -1 of an elastomeric portable pump (Infusor ® SV2 system) filled with 5-FU in saline (concentration range between 1.5 and 50 mg/mL). Insert a: selected band of PLS regression, i.e., 700-1400 cm -1 . Insert b: chemical structure of fluorouracil (5-FU), i.e., 5-fluoro-1H-pyrimidine-2,4-dione. Fig. 5. Raman signatures obtained after scanning between 100 and 3400 cm -1 of an elastomeric portable pump (Infusor ® SV2 system) filled with 5-FU in 5% dextrose; the concentration range is between 1.5 and 50 mg/mL). Insert: selected band of PLS regression, i.e., 700-1400 cm -1 . Fig. 6. Accuracy profiles from both techniques, HPLC vs. Raman spectroscopy (5-FU in saline and 5% dextrose). The plain red line is the relative bias, the blue dashed lines and the black dotted lines are, respectively, the β-expectation tolerance limits and the acceptance limits. The

A c c e p t e d M a n u s c r i p t 2 ABSTRACT

 2

  and validation parameters of the methods, external validation TOs and calibration TOs were produced and analyzed 6 and 3 times per campaign, respectively.

  expectation tolerance limit. The parameter was calculated from each determination of the external validation TOs, i.e., six measurements per day for three days. d) Precision is the closeness of agreement among measurements from multiple samplings of a homogeneous sample. It gives information about the average value of the results and variances (expressed in relative standard deviation, RSD). The intra-series variance leads to repeatability variance, whereas the intra-and inter-series variances sum leads to the intermediate precision variance. The precision was obtained from the six replicate determinations under the prescribed conditions for each external validation TO per day for three days. e) Trueness refers to the A c c e p t e d M a n u s c r i p t 10 closeness of agreement between a conventionally accepted value or a reference value vs. a mean experimental value. It provides information on systematic error. The parameter is expressed in terms of relative bias (%) at each concentration level of the external validation

[

  23]. Data analysis was primarily graphic and based on following the H1 hypothesis: concentrations measured for each sample by HPLC and by RS are strictly identical. According to H1, the measurements displayed on a graph are distributed according to the concentrations of 5-FU measured by HPLC vs. those measured by RS; they should be positioned on the line of y = x, with y and x the concentrations determined, respectively, by HPLC and RS. According to H1, a second graph will show the differences in concentrations of 5-FU measured, either by HPLC or by RS for each matched sample (y = [HPLC -RS]) vs. the concentration average for the same sample determined via the two methods ([HPLC + RS]/2). These differences are A c c e p t e d M a n u s c r i p t 11

  packaging. PLS regression was performed with the calibration set. Crossvalidation based on random subsets was performed to select the model number of PLS factors.

A

  c c e p t e d M a n u s c r i p t necessary to recalibrate the instrument and the established calibrations are sufficient to proceed to the AQC of the TO in a unique spectroscopic analysis.

Fig. 1 .

 1 Fig. 1. Elastomeric portable pump diagram (Infusor ® SV2 system, ref 2C1702KD, Baxter

Fig. 2 .

 2 Fig. 2. Configuration of the Raman bench used for the AQC of the TOs. The laser source is

Fig.

  Fig. 3. Raman signatures of the portable pump (Infusor ® SV2 system) studied in different

A

  c c e p t e d M a n u s c r i p t 23 green dots represent the relative error of the back-calculated concentrations; they are plotted with respect to the targeted concentrations.

Fig. 7 .

 7 Fig. 7. Average values for the measurements obtained by both techniques vs. the differences in

Fig. 8 .

 8 Fig. 8. Average values for the measurements obtained by both techniques vs. the differences in

A c c e p t e d M a n u s c r i p t

A c c e p t e d M a n u s c r i p

Figure 1 A c c e p t e d M a n u s c r i p

 1 Figure 1

Figure 2 Page

 2 Figure 2

Figure 3 A c c e p t e d M a n u s c r i p

 3 Figure 3

Figure 4 Page

 4 Figure 4

Figure 5 A c c e p t e d M a n u s c r i p

 5 Figure 5

Figure 6 Page

 6 Figure 6

Figure 7 A c c e p t e d M a n u s c r i p

 7 Figure 7

Figure 8

 8 Figure 8

Table 1 .

 1

Table 3 .

 3 Spectral range, spectral pre-treatment, number of PLS factors, r² of validation, RMSEC, RMSECV and RMSEP of the Raman spectroscopy model.

Table 1 .

 1 Ct° max (recommended): upper limit of concentration into the infusion system for a BSA (Body Surface Area) of 2 m². b Ct° min (recommended): lower limit of concentration into the infusion system for a BSA of 1.3 m² and a dose reduction of 50%.

	Protocol name	Dose (mg/m²)	Time of infusion (h)	Volume (mL)	Infusion system brand name	Ct° max (mg/mL) a	b Ct° min (mg/mL)
	TPF	3750	120	240	LV2	31.3	10.1
	GORTEC	2400	96	192	LV2	25.0	8.1
	VOKES	4000	120	240	LV2	33.3	10.8
	CDDP-5-FU C225 4000	96	192	LV2	41.7	13.5
	LOHP 5-FU	5000	120	240	LV2	41.7	13.5
	FOLFOX or FOLIRI 2400	46	96 230	SV2 LV5	50.0 20.9	16.3 6.8
	FOLFOX or FOLIRI pediatric use c	2400	46	96	SV2	50.0	12.5

a c Ct° max and Ct° min: recommended values for a BSA of 1 m² and a dose reduction of 50%.

Table 2 .

 2

	Relative bias (%)

Table 3 RS

 3

	model	Selected parameter NaCl 0.9%	Selected parameter G5%
	Spectral range selected (cm-1)	700-1400	700-1400
	Spectral pre-treatment	First derivative + Mean Center First derivative + Mean Center
	Number of PLS factors	12	12
	R2	0.995	0.999
	RMSEC (mg/mL)	0.001	0.001
	RMSECV (mg/mL)	0.787	0.482
	RMSEP (mg/mL)	1.13	0.397


Arthur Gontier

Charlotte Truchet

Charles Prud'homme

. However, for the algorithm to run on global constraints, there is still a need to specify for each of them the explanation rules. This is a huge obstacle on its standardisation in off-the-shelf solvers. In this paper, we propose a method to automatically generate explanation rules from any constraint decomposition.

Introduction

Conflict analysis consists in preventing a solver from repeating the same failures during the search. In SAT solvers, Conflict Driven Clause Learning (CDCL) [START_REF] Moskewicz | Chaff: Engineering an efficient sat solver[END_REF] showed great improvement in the solving efficiency. When a fail occurs, SAT solvers can learn new constraints in the SAT format, i.e., clauses, which encapsulate the combination of literals leading to the failure. These learnt clauses are used later in the search process to prune the search space. In Constraint Programming (CP), conflict analysis has been an active research topic since the 90's, with, among others, constraint explanations [START_REF] Prosser | Hybrid algorithms for the constraint satisfaction problem[END_REF][START_REF] Jussien | The versatility of using explanations within constraint programming[END_REF]. Several adaptations of the CDCL method where proposed for CP [START_REF] Stuckey | Lazy clause generation: Combining the power of sat and cp (and mip?) solving[END_REF][START_REF] Veksler | A proof-producing csp solver,a proof supplement[END_REF], offering significant improvements. This is also a necessary first step to provide user information, (such as certificate checking). However, explaining constraints is still a challenge, as the constraint format is much richer than the SAT clauses. Global constraints must be analysed separately in order to derive fair and accurate inference rules. Our contribution aims at reducing this burden, by deriving explanations rules automatically from global constraint decompositions.

The principle of the algorithm presented in [START_REF] Veksler | A proof-producing csp solver,a proof supplement[END_REF] is as follows. During CP solving, constraints filtering algorithms, or propagators, remove values from the domain of variables. These removals are called events and are stored in an implication graph. When a conflict occurs, the algorithm looks for a set of events responsible for this conflict in the implication graph. Then, a clause based on these events is built and added to the set of constraints to prevent finding back the same conflict. To do so, the algorithm needs to be able to find how each propagator generates their events upon a conflict in order to derive the explaining events. This knowledge is the core of an explanation rule, written explaining events explained event [R rule name ] in the following. Finding all these rules could be tedious or difficult for global constraints. This is being studied for instance in [START_REF] Richaud | Outillage logiciel pour les problèmes dynamiques[END_REF][START_REF] Downing | Explaining alldifferent[END_REF][START_REF] Schutt | Explaining time-table-edge-finding propagation for the cumulative resource constraint[END_REF]. To address this problem, we rely on global constraints decompositions. A decomposition expresses the semantic and syntax of a global constraint with atomic constraints, namely lower arity constraints. Several such decompositions exist in the literature [START_REF] Narodytska | Reformulation of global constraints[END_REF]. We assume that the inference rules of atomic constraints are already known or easy to define. Our proposal consists in combining these inference rules through the implication graph deduced from the decomposition of a global constraint to explain the events that the latter generates. In other words, the global constraint is used to filter values from the domain of variables and a decomposition of it is used to explain those events. This paper is organised as follows. In Section 2 we introduce the background material and propose a simple constraint decomposition formalism and the explanation rules for these equations. Section 3 presents the algorithm that uses these last two to generate an explanation rule for the prime constraint and we gives an execution example in section 4. Finally, in Section 5 we present the questions raised by the solver usage of these generated explanation rules.

Constraint decomposition and their explanation rules

We first briefly introduce some definitions that are necessary to the description of our method. For a more precise introduction of CP, we refer the interested reader to [START_REF] Rossi | Handbook of constraint programming[END_REF][START_REF] Montanari | Networks of constraints: Fundamental properties and applications to picture processing[END_REF]. Definition 1. A Constraint Satisfaction Problem is a triplet < X, D, C > with X variables, D their domains and C the set of constraints, which are logical formulas that define their relations.

There are different types of constraints [START_REF] Beldiceanu | Global constraint catalog[END_REF], some of them are global [START_REF] Bessiere | To be or not to be... a global constraint[END_REF]. The important point in the following is that a global constraint can be decomposed in multiple lower arity constraints [START_REF] Narodytska | Reformulation of global constraints[END_REF]. This is usually done using constraint reification [START_REF] Khong | Réification de contraintes tables[END_REF] (example in section 4) Definition 2. A reified constraint c is associated to a boolean variable b such that the truth state of b matches the satisfaction state of c. b is called a reified variable and we have c ⇐⇒ b.

Constraint satisfaction problem solving is a two-step process. The first step is to remove all the impossible values of the domain of variables. To do so, each constraint has a propagator, an algorithm to detect and remove values that cannot satisfy the constraint given the current state of the domains. This step can result in a solution, a conflict or an incomplete state. The latter triggers the second step: a decision is applied, i.e., a non-assigned variable is selected and its domain is reduced to a singleton. This modification must be verified by the application of step one. By this process, a tree called the implication graph is built. Its leaves contain either solutions, or conflicts. A conflict happens when a domain is emptied by a propagator. From our point of view, the inner nodes of the graph contain events. Definition 3. An event is a domain reduction written (X ≤ t, X ≥ t, X = t, X = t) in the following. It is caused by either propagation or decision [START_REF] Schulte | Finite domain constraint programming systems[END_REF].

Global constraints can often be expressed with simpler, lower arity constraints. To build their decompositions, some basic constraints are introduced below, along with their explanation rules. In the following, the events b = 1 and b = 0 on a boolean variable b are written b and ¬b. Rules3 (1)(2) are purely technical, they express the equivalence between the events of the global constraint and their corresponding reified variable.

(1) Equality:

X i = t ⇐⇒ b it ∀i ∈ 1, n ∀t ∈ 1, m X i = t b it [R = ] X i = t ¬b it [R = ] b it X i = t [R = ] ¬b it X i = t [R = ]
(2) Inequality:

X i ≥ t ⇐⇒ b it ∀i ∈ 1, n ∀t ∈ 1, m X i ≥ t b it [R ≥ ] X i < t ¬b it [R < ] b it X i ≥ t [R ≥ ] ¬b it X i < t [R < ]
Conjunction (3) and disjunction (4) are needed to build decompositions, their rules are deduced from the truth tables of their reified formulas.

(3) Conjunction:

( i∈ 1,n b i ) ⇐⇒ b b b i [R 1 ∧ ] ¬b b j ∀j = i ¬b i [R 2 ∧ ] b i ∀i b [R 3 ∧ ] ¬b i ∃i ¬b [R 4 ∧ ] (4) Disjunction: ( i∈ 1,n b i ) ⇐⇒ b b ¬b j ∀j = i b i [R 1 ∨ ] ¬b ¬b i [R 2 ∨ ] b i ∃i b [R 3 ∨ ] ¬b i ∀i ¬b [R 4 ∨ ]
To decompose cardinality constraints, sums of booleans variables (5)(6)(7) are added to the formalism. The sum rules are deduced from their saturated cases. For example, in the sum (5), when the sum reaches its limit, the other variables will be set to false so the explanation for a false variable is the fact that the others are true. The reasoning is inverted when the reified variable is false.

(

) Sum ≤ : i∈ 1,n b i ≤ c ⇐⇒ b ¬b ¬b j ∀j = i b i [R inf 1 sum ] b b j ∀j = i ¬b i [R inf 2 sum ] ¬b i ∀i b [R inf 3 sum ] b i ∀i ¬b [R inf 4 sum ] (6) Sum ≥ : i∈ 1,n b i ≥ c ⇐⇒ b b ¬b j ∀j = i b i [R sup1 sum ] ¬b b j ∀j = i ¬b i [R sup2 sum ] b i ∀i b [R sup3 sum ] ¬b i ∀i ¬b [R sup4 sum ] (7) Sum = : i∈ 1,n b i = c ⇐⇒ b b ¬b j ∀j = i b i [R sup1 sum ] b b j ∀j = i ¬b i [R inf 2 sum ] b i ¬b j ∀i = j b [R =1 sum ] b i ∀i ¬b [R =2 sum ] ¬b i ∀i ¬b [R =3 sum ] 5
3 Generation of explanations

To generate the explanation rule of an event for a global constraint, we build the implication graph of its decomposition until we find the explaining events of the global constraint. This is used once and for all for each constraint, as a preprocessing step. In the following algorithms (Algorithm 1 and Algorithm 2), the term constraint refers to decomposition constraint and Ctrs(e) is the set of the decomposition constraints that contains the event e.

The generation starts by calling the find function (Algorithm 1) with the event to explain, no previous constraint and an empty path. First, it checks if the event to explain, or its negation, has not been processed before, in which case the explanation is void. Then it looks for the event to explain in the decomposition, and calls the corresponding explanation rule function on each of its appearances. Finally, it adds a node in the explanation graph, labelled with an OR, to state the multiplicity of possible explanations. In Algorithm 2, an example of explanation rule function is depicted, here, the four rules of equation ( 3). The purpose of such a function is to apply the rules presented in Section 2. First, the rule that matches the input event is applied. If the explaining event belongs to the global constraint, it is added as a leaf of the explanation tree. Otherwise, i.e., if the event is internal to the decomposition, the find function is called on it. If the rule states multiples explaining events, the node is labelled with an AND. In addition to these two main mechanism, our system also features an index propagation system. In practice, many constraint decompositions are written using either operations on the variables indexes (e.g., X i+1 , X i-1 ...), or even sets of variables indexes (e.g., ∀j = i...).

To properly propagate the indexes appearing in a decomposition, we add to each event in the decomposition two index propagation functions (index propagate and index update). The first one implements the modification written in the decomposition equation, for example b i+1 will add one to the index i. The second one synchronises the current event index with the corresponding decomposition event index before any propagation. In the end, our system is capable of dealing with equalities and inequalities between indexes, addition or substraction by a given integer, and ∃ and ∀ quantifiers over a given integer set. This is, in practice, sufficient to deal with most of the decompositions, but the formalism is also expandable.

An example: the cumulative constraint

Consider the Cumulative({X 1 , . . . , X n }, {d 1 , . . . , d n }, c) constraint4 . This constraint expresses a capacity constraint in a scheduling problem. We use here the Cumulative's variant with fixed durations, and a fixed task height of 1. Starting time variables are written X, the durations d and the capacity c. For this constraint we have the following decomposition [START_REF] Schutt | Explaining time-table-edge-finding propagation for the cumulative resource constraint[END_REF]:

X i ≥ t ⇐⇒ b it ∀i ∈ 1, n ∀t ∈ 1, m (1)
(b i(t-di) ∧ ¬b it ) ⇐⇒ b2 it ∀i ∈ 1, n ∀t ∈ 1, m (2)
i∈ 1,n b2 it ≤ c ∀t ∈ 1, m (3)
The first constraint (1) reifies a domain modification of the cumulative variables.

The second constraint (2) and its reified variable b2 encodes the overlap of the i th task on time t. The last equation (3) constrains the number of overlapping tasks not to exceed the integer c.

Xi ≥ t bit OR AND b i(t-d i ) Xi ≥ t -di ¬b2it b2 i t AND b i (t-d i ) ¬b i t X i ≥ t -d i X i < t b2 i(t+d i ) ? R ≥ R 2 ∧ R 2 ∧ R 1 ∧ R ≥ R inf 2 sum ? R 3 ∧ R 3 ∧ R ≥ R< Fig. 1.
Lower bound event explanation generation

The explanation rule generation is started on a chosen event, for example X i ≥ t. It is found only in the first equation [START_REF] Beldiceanu | Global constraint catalog[END_REF], thus the node b it is generated. The rule that has been used is written on the arrow and the first algorithm is then applied on b it . It appears three times in the decomposition, one in [START_REF] Beldiceanu | Global constraint catalog[END_REF] and two in (2), therefore, there are three possible explanations. The first constraint is forbidden because it was used to get b it . The two other possibilities are labelled by an OR node. The explanation by the negative variant of b it will generate an AND node as explained by R 2 ∧ . The generation will continue until we have no inner decomposition events in the leafs. At the end of this example, there is three leaves in the upper branch and none in the lower one because in this case, there are no rules for a positive variable in a sum less than an constant c with a reified variable set to true (a non reified constraint is implicitly reified to true).

We implemented the generator5 in the OCaml language. With the decomposition formalism we defined, we can parse the OCaml explanation rule in L A T E X for them to be read. For example the following generated explanation rules for the Cumulative constraint has been produced by our tool:

X i ≥ t t = t -c i , X i ≥ t t = t -c i , ∀i , i ∈ D, i = i, i ∈ D, X i < t ∀i , i ∈ D, i = i, i ∈ D, X i ≥ t X i < t t = t+c i , X i ≥ t t = t -c i , t = t+c i , ∀i , i ∈ D, i = i, i ∈ D, X i < t t = t + c i , ∀i , i ∈ D, i = i, i ∈ D, X i < t

Conclusion

We have presented a generation method for explanations of global constraints, that takes advantage of the constraint decomposition. This method automatically expands an implication graph that is run to generate an explanation of an event triggered by the global constraint. The resulting rules can then be encoded within any event-based CDCL-like CP solver. This is still a work in progress, and we plan to explore several questions which are still open. First, we have to extend our implementation to more global constraints, in particular cardinality constraints for which several decompositions exist. We also plan to compare both the expressiveness and the practical efficiency of our generated explanation, compared to the state of the art. The fact that we use a decomposition, which may filter less than the global constraint, may lead to weak explanations, and we will investigate this case. Finally, we already propose a LaTeX generated expression of the explanation in order to help the user refine his/her model. Yet, we have to improve the presentation of this output to obtain a more concise, userfriendly explanations. Since our method is generic, we plan to build a catalog of global constraints explanations as a way to systematically compare different explanations frameworks.

Algorithm 1 : 3 Add e in path p 4 c 7

 1347 find(e=event, ctr=previous ctr, p=path)1 if e or ¬e not already in path p then 2 for c ∈ Ctrs(e), c = pre do p=path)1 slf : current ctr 2 if e = bi then 3 find(b, slf , p)// [R 1 ∧ ] 4 else if e = ¬bi then5 find(¬b, slf , p) 6 find(bj ∀j = i, slf , p) Label node(AND)// [R 2 ∧ ] 8 else if e = b then 9 find(bi ∀i, slf , p)// [R 3 ∧ ] 10 else if e = ¬b then 11 find(¬bi ∃i, slf , p)// [R 4 ∧ ]

Recall that an explanation rule is defined as explaining events explained event [R rule name ].

http://sofdem.github.io/gccat/gccat/Ccumulative.html

https://github.com/ArthurGontierPro/Explanations-by-constraint-decomposition. git

Acknowledgements

The work presented in this article was funded by the French National Research Agency as part of the DeCrypt project (ANR-18-CE39-0007).

Conflict analysis in CP solving: Explanation generation from constraint decomposition