Amel Hedhili
email: amel.hedhili@inrae.fr

Samuel Lubbers

Elias Bou-Maroun

Francine Griffon

Ebenezer Akinyemi

Florence Husson

Dominique Valentin

Moringa Oleifera supplemented biscuits: nutritional values and consumer segmentation

Keywords: Moringa Dried Leaves (MDL), Hedonic test, Consumer segmentation, Open-ended questions, In vitro digestibility, Proximate analysis

Moringa oleifera is a nutrient-rich plant, known as a miracle tree, and commonly used as a food supplement. Despite its popularity, there are scant empirical findings on its real nutritional benefits and acceptance among consumers when added to food. To fill this gap, we added Moringa Dried Leaves (MDL) to biscuits. A consumer test was implemented to study the sensory properties of the biscuits. Nutritional properties, including in vitro protein digestibility, and physical properties were also investigated.

Global liking indicates the segmentation of consumers into two clusters and confirmed heterogeneity. Cluster 1 consumers disliked the supplemented biscuits and cited dark green color and texture as the main reasons for dislike. Conversely, cluster 2 consumers, who were much younger, liked the supplemented biscuits due to their adventurous taste for novel products. Nutritional analysis revealed that the incorporation of MDL to biscuits increased their iron and proteins but led to incomplete protein digestion especially for biscuits with high supplementation. In addition, vitamin A derived from MDL was degraded during baking. The biscuit with the highest acceptability and digestion (C1) would increase protein intake only slightly but provide essential amino acids, which are deficient in wheat flour. These findings, confirm that there is a limit to further increasing the amount of MDL added to foods in order to provide more nutrients. In addition, it is recommended that Moringa supplemented products should be advertised with caution in order not to mislead the consumers.

Introduction

The Moringa oleifera tree is universally known as a miracle plant. This plant derived its name from the fact that all its parts (leaves, seeds, flowers etc.) can be used as nutritional supplement, medicine, water purifier and animal fodder [START_REF] Daba | Miracle tree: A review on multi-purposes of Moringa oleifera and its implication for climate change mitigation[END_REF].

Native to northern India, Moringa oleifera Lam. (Moringaceae) is now cultivated in many subtropical regions in Africa, tropical America, Mexico, Malaysia, and the Philippines [START_REF] Adeyemi | Influence of drying methods on the proximate and phytochemical composition of Moringa oleifera Lam[END_REF][START_REF] Fahey | Moringa oleifera: A review of the medical evidence for its nutritional, therapeutic, and prophylactic properties[END_REF]. Several studies have shown that Moringa oleifera leaves are a rich source of certain macro and micronutrients. [START_REF] Sánchez-Machado | Nutritional quality of edible parts of Moringa oleifera[END_REF] reported that Moringa plant contains a high percentage of essential amino acids in green leaves. While [START_REF] Siddhuraju | Antioxidant properties of various solvent extracts of total phenolic constituents from three different agroclimatic origins of Drumstick tree (Moringa oleifera Lam.) leaves[END_REF] and [START_REF] Sreelatha | Antioxidant activity and total phenolic content of Moringa oleifera leaves in two stages of maturity[END_REF] have also reported antioxidant properties of Moringa oleifera leaves. The leaves of Moringa have also been found to contain important amounts of calcium, potassium, magnesium, vitamin A, C and E [START_REF] Hekmat | Sensory evaluation of locallygrown fruit purees and inulin fibre on probiotic yogurt in Mwanza, Tanzania and the microbial analysis of probiotic yogurt fortified with Moringa oleifera[END_REF]. Witt's (2008) meta-analysis of 49 scientific articles summarizes the nutritional composition of Moringa dried leaves (MDL). It shows that in 100 g of MDL there are 24 ± 5.8 g of proteins, 36 ± 9.2 g of carbohydrates, 6 ± 2.5 g of fat, 20.6 to 28.6 g of fiber, 32.5 ± 10.8 mg of iron, and 3639 ± 1980 µg of vitamin A.

Currently, the use of Moringa oleifera as a nutrient-rich plant for food supplementation is getting much attention. It was first used in India before it was later exported to African countries where it was incorporated in traditional foods such as amala, a starchy meal in Nigeria and Ghana [START_REF] Oyeyinka | Moringa oleifera as a food fortificant: Recent trends and prospects[END_REF]. In developed countries, for instance in Europe, Moringa oleifera is marketed as a "superfood" for a wide range of health benefits such as high level of antioxidant activity [START_REF] Bruins | Considerations for secondary prevention of nutritional deficiencies in high-risk groups in high-income countries[END_REF]. The importation of Moringa to Europe was estimated between 100 and 200 tons in 2017 and the main market destinations are the United Kingdom, Germany, and France (CBI, 2019).

Many scientific studies have shown that the supplementation of staple foods such as bread, cheese, yoghurt, and biscuits with MDL improve their nutritional properties [START_REF] Dachana | Effect of dried Moringa (Moringa Oleifera Lam.) leaves on rheological, microstructural, nutritional, textural and organoleptic characteristics of cookies[END_REF][START_REF] Hekmat | Sensory evaluation of locallygrown fruit purees and inulin fibre on probiotic yogurt in Mwanza, Tanzania and the microbial analysis of probiotic yogurt fortified with Moringa oleifera[END_REF][START_REF] Salem | Enhancement of nutritional and biological values of Labneh by adding dry leaves of Moringa oleifera as innovative dairy products[END_REF][START_REF] Sengev | Effect of Moringa oleifera leaf powder supplementation on some quality characteristics of wheat bread[END_REF].

Biscuits is one of the most popular bakery products in the human diet due to many characteristics such as palatability, convenience, ready-to-eat, affordability and longer shelf-life in comparison to the other bakery products [START_REF] Arshad | Nutritional assessment of cookies supplemented with defatted wheat germ[END_REF][START_REF] Nagi | Effect of storage period and packaging on the shelf life of cereal bran incorporated biscuits[END_REF]. It is also widely accepted and consumed in many countries, which makes it a viable supplementation vehicle for nutritional improvement of vital nutrients like protein, dietary fibers and functional ingredients [START_REF] Sulieman | Rheological and quality characteristics of composite gluten-free dough and biscuits supplemented with fermented and unfermented Agaricus bisporus polysaccharide flour[END_REF].

In previous studies, MDL were incorporated in biscuits with levels varying from 3% to 15% and results showed that this supplementation increased protein, fiber, bcarotene [START_REF] Dachana | Effect of dried Moringa (Moringa Oleifera Lam.) leaves on rheological, microstructural, nutritional, textural and organoleptic characteristics of cookies[END_REF][START_REF] Mouminah | Effect of dried Moringa oleifera leaves on the nutritional and organoleptic characteristics of cookies[END_REF], and minerals (Fe, Ca, Mg, P and K) composition of biscuits [START_REF] Abdel-Samie | Effect of Moringa oleifera leaves (Moringa oleifera Lam.) on some physico-chemical and sensory properties of wheat flour cookies[END_REF]. The incorporation of Moringa also has an impact on the physical and sensory properties of biscuits.

Physical properties such as diameter and thickness changed depending on the amount of MDL added and breaking force significantly increased with the concentration of Moringa [START_REF] Dachana | Effect of dried Moringa (Moringa Oleifera Lam.) leaves on rheological, microstructural, nutritional, textural and organoleptic characteristics of cookies[END_REF]. Previous studies that focused on sensory evaluation showed that biscuits were acceptable up to 9% or 10% of Moringa supplementation respectively [START_REF] Abdel-Samie | Effect of Moringa oleifera leaves (Moringa oleifera Lam.) on some physico-chemical and sensory properties of wheat flour cookies[END_REF][START_REF] Dachana | Effect of dried Moringa (Moringa Oleifera Lam.) leaves on rheological, microstructural, nutritional, textural and organoleptic characteristics of cookies[END_REF]. [START_REF] Lee | A comparison of the flavor of green teas from around the world[END_REF] revealed that the typical leafy flavor and slightly bitter taste decreased the consumer acceptance of a product supplemented with leaves. Furthermore, [START_REF] Dachana | Effect of dried Moringa (Moringa Oleifera Lam.) leaves on rheological, microstructural, nutritional, textural and organoleptic characteristics of cookies[END_REF] observed that the addition of MDL to cookies resulted in darker samples, which can lead to a lower consumer acceptance. This finding is in agreement with [START_REF] Ramota | Proximate, mineral and sensory qualities of 'Amala' prepared from Yam flour fortified with Moringa leaf powder[END_REF] who state that MDL has a deep green color, which may be attributed to its high chlorophyll content and may strongly mask the color of original foods.

In contrast, a study carried out by [START_REF] Ramaroson | Studying the nutritional beliefs and food practices of Malagasy school children parents. A contribution to the understanding of malnutrition in Madagascar[END_REF] in Madagascar showed that the Moringa green color is not always a problem when added to food. Cassava root cakes were supplemented with MDL and presented to children who had to score their overall liking of the samples. At the end of the experience, children chose one of the products as a reward for their participation. Results showed that the product containing the highest proportion of Moringa received high liking score and was chosen as reward by a majority of the children despite its greener color, which demonstrated that color was not a barrier to children acceptance in the study. This result suggests that there might be inter-individual difference between consumers in terms of acceptance.

Previous studies investigated consumer preferences without examining the underlining heterogeneity that might exist among consumers due to individual peculiarity [START_REF] Abdel-Samie | Effect of Moringa oleifera leaves (Moringa oleifera Lam.) on some physico-chemical and sensory properties of wheat flour cookies[END_REF][START_REF] Dachana | Effect of dried Moringa (Moringa Oleifera Lam.) leaves on rheological, microstructural, nutritional, textural and organoleptic characteristics of cookies[END_REF][START_REF] Rathnayake | Utilization of Moringa oleifera leaves as a functional food ingredient in bakery industry[END_REF]. Hence, the first objective of this study was to implement sensory analysis in order to gain understanding of heterogeneity in consumer preferences of Moringa supplemented biscuits by looking at inter-individual differences among the study participants.

Another potential limitation of the use of Moringa for food supplementation is that most of the reported evidence do not take into account the effect of processing on nutritional compounds and/or of the bio-availability of these compounds. Furthermore, the few studies which explored this last point are far from being consensual. For example, a study carried out by [START_REF] Teixeira | Chemical characteristics and fractionation of proteins from Moringa oleifera Lam. leaves[END_REF], showed that the in vitro protein digestibility (IVPD) of MDL was 33.29% whereas a previous study comparing the IVPD in thirteen plants species reported a value of 74.2% of IVPD of MDL [START_REF] Ly | Nutritional evaluation of tropical leaves for pigs: Pepsin/pancreatin digestibility of thirteen plant species[END_REF]. The second goal of this study was to investigate the level of nutritional improvement of biscuits due to Moringa supplementation.

To achieve these objectives, our study asked and offered answers to four questions, namely: (1) Did the incorporation of MDL in biscuits improve their nutritional properties and affect their IVPD? (2) What is the contribution of biscuits containing MDL in recommended daily requirement? (3) Did the incorporation of MDL in biscuits affect the physical properties of biscuits? (4) What is the effect of supplementation with MDL on sensory properties of biscuits and consumer acceptance?

Materials and methods

Biscuit preparation

All ingredients (Wheat flour T-45, sugar, shortening, salt and baking powder) used to produce the biscuits were purchased from local supermarket Carrefour®, Dijon, France. MDL were purchased in Dijon, France.

Three experimental biscuits (C1, C2, and C3) were prepared by supplementing a control biscuit (C0) with different amounts of MDL. The control biscuit was made of 100 g wheat flour, 30 g sugar powder, 30 g shortening, 2.5 g baking powder, 0.5 g salt, and water. A proportion of 10%, 20% and 30% of MDL, respectively was added to the base recipe to obtain supplemented biscuits C1, C2 and C3, respectively.

Wheat flour and MDL were sieved before mixing with shortening until homogeneous lumps were formed. Then, sugar, salt and baking powder were added. The mixture was mixed at low speed with a pastry robot for 10 min with a stop every 2 min. Water was added gradually and mixed for 2 min at low speed. The dough was wrapped in stretch film and refrigerated at 4 °C for 20 min. After 20 minutes, the dough was placed on a lightly floured biscuit sheet. The prepared dough was rolled to a thickness of 4mm and cut using a circular shape of 3 cm in diameter. The biscuits were baked at 180 °C for 20 min. After baking, the biscuits were cooled down to room temperature and kept in airtight food plastic boxes. Fig. 1 shows the control biscuit (C0) and the biscuits supplemented with the three levels of MDL (C1 to C3).

Proximate analysis

All reagents and chemicals used for the proximate analysis were purchased from Sigma Aldrich® (France) and were of analytical grade. Biscuit samples were analyzed in triplicate for moisture, proteins, vitamin A and iron. Moisture content was determined according to AOAC (2011). Crude proteins were determined according to Kjeldahl method. The proteins content was obtained using the conversion factor 4.4 (factor used for tropical plant samples) [START_REF] Ramaroson | Studying the nutritional beliefs and food practices of Malagasy school children parents. A contribution to the understanding of malnutrition in Madagascar[END_REF]. Vitamin A content was determined using the method of vitamin A (Retinol) in foods (AOAC, 2001). Iron content was obtained following the method of determination of trace elements by atomic absorption spectrometry (French standard 14082, 2003).

In vitro protein digestibility (IVPD)

Pepsin (from porcine stomach mucosa, >2500 U/mg protein), pancreatin (from porcine pancreas, 4 x USP), casein sodium salt from bovine milk (C-8654) and TAME (p-Toluene-Sulfonyl-L-arginine methyl ester; T4626) were purchased from Sigma-Aldrich (France). In vitro digestibility was carried out according to the method of [START_REF] Minekus | A standardised static in vitro digestion method suitable for food -an international consensus[END_REF] with some modifications. Analysis was done in duplicate. In addition, 1 g of MDL or 1 g of biscuit was prepared in 10 mL of solution then 8 mL of simulated gastric fluid (SGF) electrolyte solution was added. To this mixture 1.6 mL of porcine pepsin solution (25.000 U/mL) and 5 µL of 0.3 M CaCl2 were added. The pH of the mixture was adjusted to 3.0. The solution was incubated for 120 min at 37 °C under continuous stirring at 170 rpm. After gastric digestion, gastric chime was mixed with 11 mL of simulated intestinal fluid (SIF). To this solution, 736 mg of the pancreatic enzyme and 40 µL of 0.3 M CaCl2 were added and the final volume was completed to 40 mL by SIF solution. The pH of the mixture was adjusted to 7.0. The final solution was incubated for 120 min at 37 °C with stirring. To determine the nitrogen release in the samples, the trichloroacetic acid (TCA) precipitation method was used. Aliquots of 10 mL of the withdrawn digestion mixture were mixed with 10 mL of 10% TCA solution. The mixtures were mixed and then centrifuged (8000 g, 10 min). The nitrogen content of the resulting supernatants was determined by the Kjeldahl method. The percentage of soluble nitrogen released during the digestion process was calculated using the following equation [START_REF] Teixeira | Chemical characteristics and fractionation of proteins from Moringa oleifera Lam. leaves[END_REF].

% Enzymatic Hydrolysis (%EH) =

! " # * 100

The percentage of digestibility of the proteins was deduced from the digestibility of the casein considered as standard (100%) [START_REF] Teixeira | Chemical characteristics and fractionation of proteins from Moringa oleifera Lam. leaves[END_REF].

Physical characteristics of biscuits

Diameter, thickness and spread ratio

Diameter (mm), thickness (mm) and spread ratio of samples were measured in triplicate following the method of [START_REF] Ganorkar | Effect of flaxseed incorporation on physical, textural, sensorial and chemical attributes of cookies[END_REF]. To determine biscuit diameter, six biscuits were placed edge to edge and the total diameter was measured in mm by a Vernier caliper. Then biscuits were rotated at an angle 90° for triplicate measure. The average diameter was reported in mm. Six biscuits were placed on top of one another to determine thickness. The total height was measured and the average was presented in mm. Spread ratio was calculated as: spread ratio = Average diameter / Average thickness * 10.

Breaking force

A three-point bend test was used to estimate the biscuits breaking force as an indicator of hardness using a texture analyzer TA-TX2 equipped with a 25 kg load cell. The peak breaking force (N) of biscuits using the force in compression was recorded. Biscuit samples were placed on base beams with a distance of 1.8 cm between the two beams. A three point-bending rig was used with an HDP/3PB, knifeedge probe. The analyzer was set at a return-to-start cycle with a pretest speed of 2 mm/s, a test speed of 2 mm/s, and a post-test speed of 10 mm/s. The trigger was 20 g and distance of 10 mm. Analysis was done in triplicate.

Color measurement

Color attributes of biscuits supplemented with MDL (L*, a* and b*) were measured in triplicate using Hunter Lab color analyzer (HunterLab Color Flex EZ, USA). The L* value (lightness index scale) ranges from 0 (black) to 100 (white) while, a* value indicates the redness (+a*) or greenness (-a*) and the b* value refers to the yellowness (+b*) or blue (-b*). The petri dish containing sample was placed directly on the colorimeter sensor.

Sensory evaluation 2.5.1. Consumers

The consumer panel consisted of 91 students and staff members from the University of Burgundy (73.63% Women -26.37% Men; 74.63% <30 years and 25.27% >30 years). To ensure a larger generalizability of the results no constraint was placed on the nationality of consumers: 75.82% were French, 10.99% were African, 5.49%

were European other than French and 7.69% Asian.

Experimental conditions

Consumers were provided with information about the study, following which they completed an informed consent form in keeping with French ethical requirements.

The consumers tasted the samples in a sensory evaluation room at Agrosup Dijon.

The biscuits were served in covered white plastic cups coded with a three-digit random number. Two series of four samples (C0, C1, C2, and C3) each were presented on a tray. Different random codes and different presentation orders were used for the two series. The presentation order followed Williams' Latin squares.

Consumers were not aware that the biscuits in the two series were the same. Bottled water was provided for palate cleansing. The questionnaire was written in French language and explained in English when necessary.

Procedure

The consumer test included two steps. During the first step, consumers were instructed to taste the first series of samples from left to right. They had to rate the overall liking of each sample on a structured scale ranging from 1 (I do not like at all) to 7 (I like it a lot) with 4 being anchored as neither like nor dislike. Before proceeding to the next samples, consumers were asked to write down what they liked and what they disliked about the sample [START_REF] Symoneaux | Open-ended questions[END_REF]. During the second step, consumers were then asked to taste the second series of biscuits and evaluate the appearance, odor, taste and texture of the samples using 7-points hedonic scales. Consumers could answer either in French or in English as they wished.

Throughout tasting, consumers were told to drink the water provided to ensure palate cleansing.

Statistical Analysis

Chemical composition

Data were analyzed using one-way Analysis of Variance (ANOVA) with sample as fixed factor and protein, moisture, iron, vitamin A, thickness, diameter, spread ratio, breaking force, a*, b*, L*, as dependent variables. When a significant sample effect was obtained, a Student Neuman-Keuls pair comparison test was applied (α = 5%).

Sensory evaluation

Principal Component Analysis (PCA) was performed on the consumer x biscuit global liking scores to evaluate the agreement among consumers' judgments. Consumer segmentation was then obtained by performing a Hierarchical Cluster Analysis (HCA) of the coordinates of the consumers on the first two dimensions of the PCA. A

Euclidean distance and a Ward aggregation criteria were used for the HCA.

For each consumer cluster generated by the HCA, an ANOVA was performed on all hedonic scales (global liking, appearance, odor, taste, texture) considering consumer as random factor and samples as fixed factor. When a significant effect of sample was obtained a Student Neuman-Keuls (SNK) pair comparison test was applied with an alpha risk of 5%.

The open-ended question was analyzed by grouping terms with similar meaning.

This was done by two researchers. For each cluster, we computed the number of consumers who used each term to describe what they liked and disliked in each biscuit. Only terms used by more than two consumers were considered in the rest of the analysis. A correspondence analysis was performed to visualize the relationship between the samples and the descriptions.

Results

Biscuits characterization

Proximate analysis

Protein, iron, vitamin A content and moisture of raw MDL and MDL supplemented biscuits are presented in Table 1. The analysis of the raw MDL revealed a content of 4.48 g of moisture, 20.7 g of protein, 11.77 mg of iron, 0.14 mg of vitamin A in 100 g of powder. These results are within the range of the percentage of protein (18.2 -29.8 g/100 g of MDL) reported in Witt's meta-analysis. However, the percentage of iron content is lower than the values given by this meta-analysis (21.72 -43.28 mg / 100 g of MDL). The vitamin A content in C1, C2 and C3 are below the detection limit.

This result suggests that vitamin A was degraded during baking.

The ANOVA result showed a significant effect of MDL concentration on moisture (F Finally, the addition of MDL increases significantly the biscuit iron content from 0.85 mg/100 g (biscuit C1) to 2.46 mg/100 g (biscuit C3). The pair comparison shows a significant difference between all biscuits.

In vitro protein digestibility (IVPD)

The percentage of enzymatic hydrolysis (%EH) of casein is 92%, which corresponds to the expected 100% of IVPD of casein and thus validates our protocol. For raw MDL we obtained 57% of IVPD. The IVPD of biscuit C1 (84%) was higher than the control biscuit C0 (47%). Then, the IVPD decreased from C1, to C2 (58%), to C3 (54%).

Biscuit physical properties

The analysis of the physical characteristics of the supplemented biscuits is presented in Table 1. The ANOVA indicates that there is a significant difference between biscuits for all parameters. A significant decrease in thickness was observed with the increase in MDL concentration (F (3; 8) = 162.88; p <0.0001). The biscuit containing the highest concentration of MDL (C3) exhibited the lowest thickness of 6.72 ± 0.19 mm, whereas the control biscuit (C0) showed the highest thickness of 9.44 ± 0.10 mm.

The diameter of the C3 biscuit was significantly higher (F (3; 8) = 35.45; p <0.0001) than the diameter of the control sample while no significant difference was observed among C0, C1 and C2 samples. The spread ratio also increased significantly as the level of MDL added to the biscuit increased (F (3; 8) = 113.86; p <0.0001).

The breaking force increased significantly with the concentration of MDL (F (3; 8) = 160.05; p <0.0001). A weight of 15.44 kg was necessary to break the biscuit with the highest MDL concentration (C3), whereas, only 3.08 kg was necessary to break the biscuit without MDL. The pair comparison test showed no significant difference between samples C1 and C2.

The impact of incorporation of MDL on biscuit color parameters is presented in Table 1. The ANOVA showed a significant effect of MDL on L* values (F (3; 8) = 227.01; p <0.0001). The SNK test showed that the lightness parameter significantly decreased

Sensory evaluation results

Consumer segmentation

The first two Principal Components (PC) of the PCA explain 74.9% of the total variance of the overall liking scores (Fig. 2a and2b). All four samples load positively on the first PC (53.4%). Consumers that are positively correlated with this component tend to like better the supplemented biscuits than other consumers. The second PC (21.5%) opposes samples C0 and C3. Consumers that are positively correlated with this PC preferred sample C3 to sample C0 and conversely, consumers negatively correlated with this PC preferred sample C0 to sample C3.

The HCA separated the consumers into two clusters (Fig. 2b). Consumers from cluster 1 (N=49) tend to like the biscuits less than consumers from cluster 2 (N=42).

The two clusters differ significantly in term of consumers' age (F (1; 89) = 5.53; p <0.0209. Consumers in cluster 2 are much younger (median age = 24.5) than the consumers in cluster 1 (median age = 26). No significant difference was observed in term of nationality (khi2 = 1.33) or gender (khi2 = 0.26). Consumers from cluster 1 (Fig. 3a) accepted only the control biscuit C0 (median = 5).

Seventy-five percent of consumers rated the C1 biscuit between 2 and 4 with a median of 4.3. For C2 and C3 products, all scores were below 4 with a median of 3 and 2 respectively. Consumers from cluster 2 (Fig. 3b) liked better the biscuits containing MDL than consumers from cluster 1 (average score > 4). For the C0 product, 75% of consumers had liking scores greater than 5 with a median of 6. For product C1 and C2, 50% of consumers had scores between 5 and 6 and 4 and 5 with medians equal to 6 and 5 respectively. The liking scores for C3 were more variable with some consumers clearly disliking this biscuit (scores close to 1) and other liking it (scores equal to 6).

Effect of Moringa content on overall, appearance, texture, smell and taste liking scores

ANOVA and pairwise comparison tests were carried out separately for each cluster and each rating scale (Table 2). A sample effect was observed in both clusters for each rating scale. This effect is, however, stronger in the first cluster than in the second one. In both clusters, appearance is the factor that affects the liking of the biscuit the most (R 2 = 0.76 and 0.71 for cluster 1 and 2 respectively). In the first cluster, texture is the factor that has least effects on the liking of the biscuit. The other scales have comparable effects. In the second cluster, texture influences the liking scores more than taste and odor, which is the least impacting factor.

The pair comparison indicates that for both clusters and all liking scales the control biscuit is significantly preferred to the MDL supplemented biscuits. In the first cluster, C2 and C3 are not significantly different for global liking, odor, and texture scale. A significant difference was observed for appearance and taste. In the second cluster, we observe significant differences between all samples for all scales but odors.

Analysis of open-ended question

We represented the frequencies of positive and negative terms as word clouds separately for each cluster (Fig. 4). For cluster 1, (consumers who liked less the Moringa supplemented biscuits) the most frequent word used to describe what consumers liked in the four samples is a texture term: crunchy. Consumers liked also the taste, especially the sweetness of the control sample as well as its color. On the negative side, they found it bland. Color was the most frequently used term to describe what consumers disliked in the samples supplemented with MDL. The term too hard was also mentioned for samples C2 and C3 followed by vegetal. For sample C3, terms frequently mentioned include odor, spinach, unpleasant, too strong, and bitter.

For Cluster 2, (consumers who liked more the MDL supplemented biscuits) crunchy was frequently used to describe the positive aspects of the four biscuits as for cluster 1. Sweet and color were also mentioned frequently for C0 whereas new terms appear to describe what consumers liked in the MDL supplemented biscuit such as taste, sweet, color and crispy for sample C1. Cluster 2 consumers also appreciated the originality of the MDL supplemented biscuits, especially in sample C3. Finally, the term vegetal was mentioned among the positive aspects of sample C2. For the negative side, as in cluster 1, consumers cited the term bland for sample C0. For the other samples, color was much less cited than in cluster 1. For sample C1 the most frequent term was vegetal. After-taste and spinach were also important for this sample. C2 was characterized mostly by the term too hard, followed by color, vegetal and bitter. C3 was perceived as having a taste that is too strong in addition to being vegetal and bitter. Color was also cited but in a lesser extent than for samples C2 and C1.

Fig. 5 shows the first two dimensions (71.5% of the variance) of the CA carried out on the term frequency counts. For both clusters, the first dimension (55.5%) opposes the control sample to the MDL supplemented samples. In both clusters, the control sample is positively perceived except for the term bland whereas the MDL supplemented samples have negative global perception among consumers. The second dimension opposes the two clusters. The difference between the clusters increases with the proportion of MDL included in the biscuit. In cluster 1, the MDL supplemented biscuits attracted mostly negative terms, whereas in cluster 2 some positive terms were associated to these biscuits. Sample C1 attracted terms such as pleasant and balanced and samples C2 and C3 were positively associated with terms such as vegetal and original. Consumers in this group diverge somewhat in their appreciation of sample C3. While some consumers liked its originality and its vegetal character, others were less positive and associated it with negative surprise, bitterness and find its taste too strong.

Discussion

The first objective of this work was to implement sensory analysis in order to gain understanding of heterogeneity in consumer preferences of Moringa supplemented biscuits. Secondly, this study also investigated nutritional enrichment of biscuits supplemented with Moringa.

Effects of MDL supplementation on biscuits nutritional properties and IVPD

Although raw MDL contain vitamin A, this compound was degraded during the baking process. In order to avoid this loss, one solution could be to incorporate MDL after the cooking process (e.g. soup, sauce) or in raw products (e.g. salad). However, this solution may lead to nutritional or sensory related problems. Findings from the sensory analysis revealed that MDL had a pronounced vegetal taste, which is unpleasant when eaten raw. Previous studies showed that heat processing was an effective method to inactivate anti-nutritional factors of most tropical legumes. The inactivation of trypsin inhibitor, for example, makes protein more susceptible to enzymatic digestion [START_REF] Akande | Effect of processing methods on some antinutritional factors in legume seeds for poultry feeding[END_REF]. Therefore, another solution could be to use cooking processes with low heating impact in order to find a trade-off between all these criteria.

Although, in agreement with previous work [START_REF] Dachana | Effect of dried Moringa (Moringa Oleifera Lam.) leaves on rheological, microstructural, nutritional, textural and organoleptic characteristics of cookies[END_REF][START_REF] Mouminah | Effect of dried Moringa oleifera leaves on the nutritional and organoleptic characteristics of cookies[END_REF][START_REF] Rathnayake | Utilization of Moringa oleifera leaves as a functional food ingredient in bakery industry[END_REF], the addition of MDL increased protein and iron content of biscuits, only a percentage of these proteins were digested. Moreover, with respect to the IVPD of biscuits, the results showed that the biscuit sample which had the lowest concentration of MDL (C1), had the highest IVPD of 84%. Beyond this concentration, the IVPD decreases when the protein concentration in biscuits increases. This decrease of digestibility could be explained by an incomplete enzymatic hydrolysis of proteins due to insufficiency of digestion time or enzyme concentration. Nevertheless, [START_REF] Boisen | Prediction of the apparent ileal digestibility of protein and amino acids in feedstuffs and feed mixtures for pigs by in vitro analyses[END_REF] confirmed that in vitro digestibility can predict in vivo ideal digestibility. Thus, the appropriate solution is maybe to avoid incorporating a fairly large amount of MDL in the biscuit in order to optimize their digestibility and their benefits.

Contribution of supplemented biscuit to recommended daily requirement

In order to determine the contribution of biscuits containing MDL to the recommended daily requirement, we chose the C1 biscuit, which is the best digested and the most widely accepted by consumers. So, 100 g of biscuit C1 (10%MDL; 84%IVPD) /day provide about 0.85 mg of iron and 5.11 g of proteins. Compared with the recommended daily requirement of adults (11 mg of iron /day and 0.83 g of protein/kg/day (ANSES, 2016), the consumption of 100 g of biscuits C1/ day would provide 7.7% of the iron. For protein, this consumption provides just 8.5% of the protein after digestion (for an adult weighting 60 kg). Despite this rather low percentage of protein intake, the leaves of Moringa contain the eight essential amino acids among which the most abundant is leucine and the least abundant is methionine [START_REF] Ramaroson | Studying the nutritional beliefs and food practices of Malagasy school children parents. A contribution to the understanding of malnutrition in Madagascar[END_REF]. Wheat protein have a lower nutritional quality since they are deficient in essential amino acids such as lysine and threonine [START_REF] Dewettinck | Nutritional value of bread: Influence of processing, food interaction and consumer perception[END_REF][START_REF] Ndife | Evaluation of the nutritional and sensory quality of functional breads produced from whole wheat and soya bean flour blends[END_REF]. Combining MDL with wheat flour products can improve essentials amino acids composition.

Effects of MDL supplementation on physical properties of biscuits

The incorporation of MDL in biscuits impacts also the physical properties of biscuits, as thickness decreases. This change is due to the reduction of the percentage of gluten contained in the blend. It has been reported by [START_REF] Sengev | Effect of Moringa oleifera leaf powder supplementation on some quality characteristics of wheat bread[END_REF] that partial replacement of wheat flour with non-glutinous flour results in lower bread volumes. Gluten is the main structure-forming protein in flour. It is responsible for the elastic and extensible properties needed to produce good quality bread [START_REF] Greene | Macroscopic and sensory evaluation of bread supplemented with sweet-potato flour[END_REF]). In addition, the breaking force increases when the percentage of MDL incorporated in the biscuits increases. This explains why the texture of the supplemented biscuit was affected by the addition of MDL. This result is in line with [START_REF] Galla | Nutritional, textural and sensory quality of biscuits supplemented with spinach (Spinacia oleracea L.)[END_REF] who show that the increase of leafy spinach in biscuits increases hardness and breaking strength. All of these changes and constraints confirm that there is a limit to further increasing the amount of MDL in the biscuit in order to provide more nutrients.

Effects of MDL supplementation on biscuit sensory properties and consumer acceptance

The results of this study show that the global liking of biscuits containing MDL was not homogenous. Some consumers (cluster 2) tended to like biscuits containing MDL whereas, other consumers did not accept them (cluster 1). When considering the different sensory modalities, the appearance was the factor that affected the most the global liking of biscuits for both consumer groups. The open-ended question suggests that color is the main visual driver of rejecting biscuits supplemented with MDL: color was clearly disliked by consumers of cluster 1 but less so by consumers from cluster 2. Consumers in cluster 2 were younger than consumers in cluster 1.

This age difference perhaps implies that younger consumers are more willing to accept the supplemented biscuit due to their curiosity to test novel products as attested by the high frequency of the term original in this cluster. This interpretation is in line with the study of [START_REF] Ramaroson | Studying the nutritional beliefs and food practices of Malagasy school children parents. A contribution to the understanding of malnutrition in Madagascar[END_REF] carried out in Madagascar.

Concerning cluster 1, color hampers consumer's acceptance of MDL supplemented biscuit. This might be explained by the fact that consumers in this cluster were not familiar with the green color brought by MDL. The rejection of MDL supplemented biscuits by these consumers could thus be interpreted in terms of food neophobia, which is the avoidance of, or reluctance to consume novel foods [START_REF] Aldridge | The role of familiarity in dietary development[END_REF]. Texture was also one of the most important drivers of biscuit rejection. The main problem was the hardness of the biscuit: the force needed to break the biscuit sample that had the highest concentration of MDL (C3) was five times higher than the force needed to break the control biscuit. In line with this interpretation, the term too hard was frequently evoked in the open-ended question for MDL supplemented biscuits.

Conclusion

The present study showed that the incorporation of MDL in food products like biscuits would encounter several obstacles to consumer acceptance and affect physical properties especially in terms of color (green) and texture (hardness). For nutritional benefits, this fortification can enhance nutritional values such as iron and protein compounds but many constraints and negative effects appear following this incorporation. Protein provided by these biscuits were not completely digested.

Besides, due to baking processes, some of the nutrients from Moringa such as vitamin A can be lost. Therefore, incorporating a high concentration of MDL in biscuits is constrained by a lot of limits as previously explained.

In conclusion, Moringa oleifeira could be a proper source to enhance nutritional compounds in foods. In addition, some advice can be given to food producers who are interested in food supplementation: it is essential to choose the appropriate product in which to incorporate Moringa leaves to benefit from these dietary advantages with the right quantity without influencing the technological and sensory properties of products, mainly texture and appearance.

Declaration of Competing Interest:

The authors declare no conflict of interest. Means with the same letter are not significantly different at an alpha risk of 5%. Only terms used by at least 10% of consumers have been kept. Sample descriptions obtained for consumers from cluster 1 are denoted by CL1 before the code of the samples and sample descriptions obtained for consumers from cluster 2 are denoted by CL2 before the code of the samples

Figure Captions

  (3; 8) = 129.99, p <0.0001), protein (F (3; 8) = 79.57, p <0.0001) and iron (F (3; 8) = 708.63, p <0.0001) composition of biscuits. The pair comparison test indicates that the control biscuit C0 is significantly different in moisture content from the biscuits containing MDL. The amount of moisture increases with the concentration of MDL but the pair comparison test shows no significant difference between C1 and C2. The gradual increase of MDL concentration added to biscuits also caused a gradual increase in protein content. The pair comparison test, revealed a significant difference between the control C0 and all other biscuits. Thereby, a substitution of wheat flour with MDL (from 10 to 30%) increases the protein content in biscuit by plus 10, 17, and 21% (for C1, C2 and C3 respectively) based on the control biscuit.

(

  from 75.06 to 41.67) with increase in MDL concentration: The more the quantity of MDL added to the control sample, the darker the biscuits. The a* value parameter also reflects a significant effect (F (3; 8) = 141.71; p <0.0001) on biscuits containing MDL. The increase of MDL concentration moved biscuits from the red color area (+a*) to the green color area (-a*). For C0, an a* value of +1.9 was observed, while the a* values of C1, C2 and C3 were respectively -0.13; -0.27; -1.53. The pair comparison test shows no difference between C1 and C2 in term of a*. The ANOVA showed that the b* value decreased significantly (F (3; 8) = 192.37; p <0.0001) from C0 to C3 (21.43 to 7.25) indicating that with the addition of MDL, biscuits had a dark blue color.

Fig

  Fig 3a and b represent the global liking score distributions for cluster 1 and 2.

  With our IVPD protocol (gastric digestion 2h; intestinal digestion 2h), 57% of the proteins of raw MDL was digested. This value is within the range of IVPD values reported by Teixeira et al. (2013) (33.3%) and Ly et al. (2001) (74.2%). This difference in percentage of IVPD can be explained by the difference in experimental conditions where, for example, for Teixeira et al. (2013) the gastric digestion takes 3h and the intestinal digestion takes 1h.

Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5

 12345 Fig. 1 Photographs of control biscuit (C0) and Moringa supplemented biscuits (C1,

Table 2

 2 One-way repeated measure ANOVA with consumers as a random factor, 663 samples as a fixed factor and liking scores as dependent variables.

	664
	Cluster 1	F	P	R 2	C0	C1	C2	C3
	Global liking 66.10 0.0001 0.65 4.9 a 3.7 b	2.6 c	2.4 C
	Appearance 94.70 0.0001 0.76 5.6 a 3.9 b	3.0 c	2.3 d
	Odor	45.69 0.0001 0.65 4.5 a 3.2 b	2.6 c	2.4 c
	Texture	30.90 0.0001 0.60 5.3 a 4.7 b	3.4 c	3.4 c
	Taste	69.20 0.0001 0.67 5.2 a 3.8 b	2.6 c	2.2 d
	Cluster 2
	Global liking 24.60 0.0001 0.47 6.0 a 5.3 b	4.6 c	4.0 d
	Appearance 54.97 0.0001 0.71 5.7 a 4.7 b	3.7 c	3.1 d
	Odor	17.98 0.0001 0.48 5.2 a 4.0 b	3.7 bc 3.3c
	Texture	30.70 0.0001 0.61 6.0 a 5.4 b	4.1 c	3.9 c
	Taste	27.39 0.0001 0.56 5.9 a 5.1 b	4.3 c	3.7 d

Acknowledgements

The authors would like to thank AgroSup Dijon and Embassy of Tunisia in France for the financial support of this work. We gratefully thank Bernadette Rollin, Anne-Sophie Viaux and Christine Rojas for their assistance with the laboratory work. Catalina Onofrei is particularly acknowledged for English proofreading.

Tables

 Table 1 Physico


domain: spi stat

text:
Xiaoyan Xie
email: xiaoyan.xie@enpc.fr

Fabien Leurent

Yazi Zhu

Mining passenger's regional intermodal mobility from smartcard data

Keywords: Intermodality, Activity based trip-chain model, Machine learning, AFC data, Park and Ride

Park & Ride (P&R) enables railway users to access the transit network by means of their own cars. Its usage at the regional level can be analyzed on the basis of Household Travel Surveys (HTS). To overcome the HTS limitations in sample size and refreshment, this paper is aimed to combine such HTS for learning the car2rail intermodality phenomenon of individual mobility, with an Automated Fare Collection (AFC) database for inferring it over a very large set of individual trips. The approach involves three steps: (i) the HTS-based featuring of Origin-Destination (O-D) trips; (ii) the treatment of the AFC dataset using the dynamic path search and ad-hoc rules based on General Transit Feed Specification (GTFS) data, to yield AFC rail O-D trips; and (iii) the supervised machine learning of P&R usage based on the HTS and AFC data, considering three methods (Support Vector Machine, Decision Tree and Artificial Neural Network). Application to the Paris -Ile-de-France region with 2010 HTS and 2019 AFC data revealed three types of intermodal trips by an unsupervised machine learning algorithm, two of them at morning peak hours with either short or long rail distances, and the last one after the evening peak.

Introduction

In big cities endowed with railway lines for mass passenger transit, Park & Ride (P&R) is a well-known travel strategy to make use of the railway network by accessing to it using one's car [START_REF] Kimpton | Parking Behavior: Park 'n' Ride (PnR) to encourage multimodalism in Brisbane[END_REF]. P&R facilities are purported to build up such travel practices and make full use of the rail network and its environmental advantages over the car mode. In the Paris -Ile-de-France region, 46 P&R facilities were labeled by the Region using Public Transport (PT) smartcard Navigo in 2018, and it is scheduled to label 34 other car parks by 2021 [START_REF] Idfm | D'ici 2021, 80 Parcs Relais pour faciliter le stationnement aux abords des gares[END_REF].

Up to now, it has been costly to monitor P&R usage. Parking surveys would be required on all sites, notably to make a distinction between plain car parking and intermodal trips. Household Travel Surveys (HTS) at the regional level are adequate tools to gain a statistical understanding of the intermodal phenomenon, e.g., the Paris -Ile-de-France region [START_REF] Leurent | Quelques éclairages sur la mobilité des Franciliens[END_REF]; yet these tools are limited in sample size and refreshment, thereby missing spatial details. As Automated Fare Collection (AFC) data of smartcards have become widely available over the past decade, it is thus tempting to use them to depict an almost comprehensive picture of rail usage in the territory under scrutiny. Among previous research on that topic, the works by [START_REF] Alsger | Public transport trip purpose inference using smart card fare data[END_REF][START_REF] Alsger | Validating and improving public transport origin-destination estimation algorithm using smart card fare data[END_REF][START_REF] Zhou | Mining regional passenger mobility activity using multiple data sources: A case study in Paris area[END_REF] have succeeded to generate Origin-Destination (O-D) trips between stations on the public transport network and to infer the trip purposes by machine learning based on an HTS, but only monomodal O-D trips on the regional RER network in Paris -Ile-de-France [START_REF] Zhou | Mining regional passenger mobility activity using multiple data sources: A case study in Paris area[END_REF].

This paper develops this line of analysis by studying intermodal rail usage as a phenomenon of individual travel, on the two datasets, HTS and AFC dataset. Special care is taken to rebuild individual rail O-D trips, by involving not only the AFC-monitored tap-ins and tap-outs, but also a GTFS model of railway services, dynamic path search and ad-hoc rules to delimit and feature out O-D trips in terms of utilized stations, passage times and travel time. Our methodology is devised to study the P&R travel practice in the Paris -Ile-de-France region. Special attention is given to the officially labeled P&R facilities -the 46 such facilities as of 2018 are taken here as a spatial filter to focus on a sub-population of trips. The resulting sub-populations of trips coming from the HTS and the AFC dataset, respectively, are subjected to machine learning in order to extract meaningful information from the HTS dataset and make P&R inference based on the AFC dataset.

The body of the paper is in 5 sections. After introducing the study case and the multiple data sources (Section 2), a three-step methodology is developed: (i) O-D trip map-matching from the HTS, with selection in relation to the P&R labeled sites (Section 3), (ii) O-D trip generation from the AFC dataset, with feature reconstitution involving GTFS dataset, dynamic shortest path search and ad-hoc rules (Section 4), (iii) supervised machine learning (Section 5). Its results will be taken to reveal three types of intermodal rail trips using the k-means algorithm (Section 5). The last Section brings about conclusions and suggests some directions for further research (Section 6).

Study case of Paris -Ile-de-France region and data sources

In France, the "Île-de-France" region encompasses the greater Paris conurbation: about 10,6 million inhabitants as of 2010, spread over about 12,500 km², with 80% of people living in 30% of the regional space (OMNIL, 2012). The region is endowed with three main systems of rail transit (IdFM, 2019): firstly, 14 metro lines (M1-14) constitute a semi-closed system equipped with tap-in gates only. Secondly, the regional railways include 8 "Transilien" suburban lines (Train H, J, K, L, N, P, R, U) and 5 RER (Regional Express Network) lines (RER A, B, C, D, E), along which most stations are equipped with both tap-in and tap-out gates, save for some suburban stations that only have tap-in machines on their platforms Thirdly, there are 11 tramway lines (T1-11) that constitute a semiclosed system equipped with on-board tap-in machines. A transfer inside any one of the 3 systems requires neither tap-out nor tap-in, with the exception of in-tapping on boarding a tram. On transferring from one to another of the three sub-modes, the tap-out is only required after alighting from a train-RER, but all tap-ins are required.

We availed ourselves of five datasets, namely: (1) the AFC data as of 2019, (2) the Household Travel Survey (HTS) data as of 2010, (3) the transit network geo-locations as of 2019; (4) the vehicle timetable data under General Transit Feed Specification (GTFS) as of 2019; (5) the list of officially labeled P&R facilities as of 2018. In the first stage of the study, we filtered the data, especially for AFC and HTS datasets.

The regional AFC system stems from fare integration at the regional level: there is a unique smartcard called Navigo. Our AFC dataset, provided by the regional mobility authority IdFM, contains the anonymous data of all Navigo smartcards on Monday 11th February 2019, about 13.6 million records. There are 12 attributes in the raw data: card ID (anonymous number maintained over 3 months), tap instant, tap date, station ID, station name, tap-gate ID, tap type (access, egress, transfer), vehicle ID, run ID, transit mode, route ID, and operator. As those data include not only the rail transit data (the blue parts in Fig. 1a) but also the bus service data (the grey part in Fig. 1a), the AFC records of bus are filtered. The number of taps per card is depicted in the Fig. 1b. As there are some abnormal data, e.g. more than 100 taps per card per day, we keep only the cards which have 2-20 taps each per day. We got about 97.10% of the records. The distributions of tap-in records (blue bars) and tap-out records (orange bars) per rail station are shown in Fig. 1c. There are large numbers of taps in suburban stations, but more stations in the central area -Paris city. As for HTS, IdFM supplied us with the EGT2010 (Enquête Globale Transport in 2010), which is the only survey on the individual mobility of all region residents for all modes of transport and purposes. The survey was obtained by face to face interviews for 18 thousand households totaling 43 thousand people and 140 thousand trips per day as of 2009 [START_REF] Omnil | Enquête globale transport La mobilité en Île-de-France[END_REF]. Three household samples were independently drawn from the built property file: 15 thousand on a weekday, 1,500 for a Saturday and 1,500 for a Sunday. The survey files include 4 distinct sheets:

• Households. It contains the characteristics of the household: the type of housing occupied, the equipment of the household for means of transport (cars and two-wheeled motor vehicles) and their level of income. • Persons. Each person in the household is described in terms of age, gender, level of education, main occupation, whether or not they had a driver's license, a public transport subscription or shared bikes.

• Trips. For all persons aged 5+ who traveled the day before the interview, all trips made are recorded in terms of the times and places of origin and destination, as well as purposes (work, studies, errands, leisure, etc.).

• Means. The travel modes used in each trip are described sequentially; modal legs ends are timestamped and geo-located using a 100 m x 100 m grid. The weekday sample of EGT2010 is considered. It was drawn so that at least 4,000 people were interviewed in each of the 8 administrative districts composing the region ("departments"). There were about 120 thousand O-D trips. Their destinations are mapped in Fig. 2 [START_REF] Alsger | Validating and improving public transport origin-destination estimation algorithm using smart card fare data[END_REF][START_REF] Alsger | Use of Smart Card Fare Data to Estimate Public Transport Origin-Destination Matrix[END_REF][START_REF] Xie | Chapter 5 Passenger trajectory generation using modern datasets, in: Book "Towards Sustainable and Economic Smart Mobility: Shaping the Future of Smart Cities[END_REF], where a trip-leg is a journey between one pair of O-D stations along a single transit line.

The P&R related rail HTS O-D trips are inferred by matching the HTS trips to the nearest rail transit stations of P&R facilities. This is achieved by a three-step algorithm:

Step 1: Extract the rail HTS O-D trips;

Step 2: Extract the nearest rail stations of P&R facilities by min( ), where is the Haversine distance between the geo-location of a P&R parking and the nearest rail station; Step 3: Match the rail HTS O-D trips to the nearest rail stations of P&R facilities by using the 100 m x 100 m cells, min( ), where is the Haversine distance between the center of a cell and the nearest rail station of the P&R parking. Among the P&R related rail HTS O-D trips, 22,231 are rail only and 1,254 are intermodal trips combining a car mode and a rail mode. Thus the full HTS weekday sample contains 1.01% intermodal trips, 17.9% rail only trips and 81.1% other trips (Fig. 3a). The distribution of intermodal trips per station is shown in Fig. 3b

Generation of P&R related rail O-D trips from smartcard data

An AFC record of a smartcard is either a tap-in or a tap-out. To reconstitute O-D trips from the AFC dataset, we need to concatenate all records of tap-in and tap-out for each card ID over the selected day. Two issues of missing information in the Île-de-France AFC data deserve special investigation: (i) the lack of tap-in or tap-out record; and (ii) the lack of transfer information between the branches of the same line or between different lines of a given submode. To cope for both issues, an Activity based Trip-chain Model (ATM) is developed for the semi-closed threemode network, extending our ATM for the closed mono-modal RER-only network in [START_REF] Zhou | Mining regional passenger mobility activity using multiple data sources: A case study in Paris area[END_REF]. Two main stages are involved: (1) the inference of O-D pairs, and (2) the inferences of transfers and O-D trips.

Inference of O-D pairs

Based on the properties of the AFC data in Île-de-France, the data are divided into three cases: Case a, Case b and Case c. The algorithm of the inference of O-D pairs for the three cases is as following:

Case a: A tap-in is followed by a tap-out + 1.

We get directly one O-D pair ( , + 1). Case b: A tap-in is followed by a tap-in + 1.

The tap-in station + 1 is taken as the missing tap-out station of tap-in station , while the tap-in stations and + 1 are different. If the tap-in staions and + 1 are the same, we pass to next tap-in until the tap-in staions are different: Tap-in , 1, -1 ≠Tap-in + , min 1, -=> Tap-out , 1, -1 =Tap-in + , min 1, -. where is the total number of taps of a card. Case c: There lacks the final tap-out of the day.

We suppose that the last trip of the day always returns to the starting station of the day.

Per card ID, the records are processed by a waiting queue algorithm under First-In, First-Out (FIFO) discipline to generate O-D pairs for the three cases. We got about 7.5 million O-D pairs (Fig. 4): most of the O-D pairs fall in Case b. As the travel times of the inferred O-D pairs are not checked in this stage, the inferred O-D pairs will be further adjusted in the next stage according to the PT supply. Three algorithms were considered to build SLMs in the TensorFlow environment: Support Vector Machine (SVM), Decision Tree and Artificial Neural Network. They were cross-compared according to the following model evaluation metrics: precision, recall, and F1-score: the higher the accuracy the better the model. In order to reveal typical usage situations, the intermodal rail AFC O-D trips were classified by an unsupervised learning algorithm of clustering analysis (K-means), based on five attributes per trip: train departure time at origin station, train arrival time at destination statin, travel time, distance between origin and destination, and total number of transfers. The number of clusters, K, can be determined according to the average silhouette value [START_REF] Rousseeuw | A graphical aid to the interpretation and validation of cluster analysis[END_REF] or the elbow method [START_REF] Thorndike | Who belongs in the family?[END_REF]. We thus obtained the following K = 3 types of intermodal trips:

• Class 1: Morning peak trips with long travel times, many transfers, and short travel distances. The origins and destinations are very close to Paris city center. • Class 2: Evening off-peak trips with short travel times, only one or two transfers, and long travel distances.

  Fig. 1. AFC records: (a) the distribution among the 4 transit sub-modes; (b) the distribution of validation times per card on the surveyed day, and (c) the distribution of tap-in records (blue bars) and tap-out records (orange bars) at each rail station.

  (violet dots) in relation to the RER stations (red dots). They are mainly concentrated in the central part (the Paris city).

Fig. 2 .

 2 Fig. 2. Geo-locations of the HTS O-D trips: destinations (violet dots) versus the RER stations (red dots). The GTFS data of Ile-de-France in 2019 are supplied as open source data by IdFM. The GTFS files contain the service routes and timetables, the transfer times and station geo-locations. Lastly, a file of the 46 officially labeled P&R geo-locations as of 2018 was available open data from IdFM.

Fig. 3 .

 3 Fig. 3. HTS data: (a) Distribution of HTS O-D trip types; (b) Distribution of intermodal trips per station: go-trips (orange) and back-trips (blue).

Fig. 4 .

 4 Fig. 4. Inferred O-D pairs.

Fig. 5 .

 5 Fig. 5. Inferred transfer (Vincennes) between Origin (Torcy) and Destination (Sucy-Bonneuil), and generated O-D trips. By applying Rule 1, when ∆ O-D pair " 2h, an O-D pair is used to find out an itinerary between the Tap-In and Tap-Out (TITO) times. Otherwise, ∆ O-D pair > 2h, two O-D trips are generated: one is based on the tap-in time, the tap-in station, the tap-out station, and ∆ O-D pair " 2h; and the other one is based on the tap-out time, the tap-in station, the tap-out station, and ∆ O-D pair " 2h. Furthermore, train run choice and route choice are both considered to find out a unique transfer between two successive trip-legs: this amounts to a dynamic passenger assignment involving Rule 2 for checking the transfer time and the transfer walking distance. All trip-legs of an O-D trip are concatenated as a chain. For example, Fig. 5 introduces the transfer inference between the O-D pair of Torcy (tap-in at 9h05) and Sucy-Bonneuil (tap-out at 9h58). The unique transfer occurs at the Vincennes station where two train runs arrive

  Fig. 6b shows that Decision Tree performed best in this study, so it was further used to predict the intermodal rail AFC O-D trips. Finally, we got 3 025 intermodal rail AFC O-D trips, about 8.64% of the P&R related rail AFC O-D trips.

Fig. 7 .

 7 Fig. 7. Types of the intermodal rail AFC O-D trips.

Acknowledgements

This research was supported by the Research and Education Chair on Territorial Mobility operated by ENPC in partnership with IdFM, to which the authors are grateful.

The origins are very close to Paris city center, but the destinations are relatively far from the city center.

• Class 3: Morning peak trips with long travel times, only one or two transfers, and long travel distances. The origins are far away from Paris urban area, but the destinations are in Paris urban area. The 3 Classes are illustrated in Fig. 7 by projecting the 5 attributes to a 3D graph (pca0, pca1, pca2) by the Principal Component Analysis (PCA): Class 1 (red), Class 2 (orange) and Class 3 (green).

Conclusions and perspectives

We developed a methodology to learn about P&R practices from an HTS and to infer it in a broader, more comprehensive way by using an AFC dataset in combination to a GTFS model of rail services, a dynamic path search algorithm and three ad-hoc identification rules. Data treatment at the trip level is a key methodological step to enrich the AFC dataset with information on the used stations, the passage times and the trip travel time. The resulting trip attributes enable us to "learn" about intermodal practice from the HTS and infer it from the enriched AFC dataset. Machine learning was implemented by testing three supervised learning algorithms, namely SVM, Decision Tree and ANN. Out of them, Decision Tree was selected to infer intermodality for rail trips in the AFC dataset. Furthermore, the resulting inferred trips were clusterized in three groups using the k-means algorithm.

The methodology may certainly be transferred and tailored to study other mobility phenomena based on both HTS and AFC. As for intermodal practice, further research might address a deeper characterization of O-D situations in terms of not only transit conditions but also car conditions on the main trip leg, as well as deeper characterization of feeding conditions such as the transfer walk distance and the average speed of the feeder mode around the rail station. As for the Paris -Ile-de-France case, on-going research involves the more recent HTS (2018) and addresses the full set of railway stations, with ad-hoc characterization of the parking conditions around the station. Lastly, more sophisticated Machine Learning (ML) methods can also be explored to improve the process of IIM, yet a local sensitivity analysis about K for user classification.


MD Liem Trinh
email: trinhdinhliem@gmail.com

MD, PhD Nacim Bouheraoua

MD Stanislas J Roman

MD François X Auclin

MD, PhD Antoine Labbé

MD, PhD Christophe Baudouin

Programmation au laser excimer de l'astigmatisme réfractif ou de l'astigmatisme cornéen antérieur en cas d'astigmatisme oculaire résiduel (ORA)

Keywords: Astigmatism programming in ocular residual astigmatism Conflits astigmatism, LASIK, excimer, cornea, ORA, cylinder, refractive surgery ± 0, 2 En cas de discordance entre astigmatisme manifeste astigmatisme, LASIK, excimer, cornée, ORA, cylindre, chirurgie réfractive

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

Résumé

Objectif: Déterminer la meilleure valeur à programmer dans le laser excimer entre l'astigmatisme réfractif manifeste (RA) et l'astigmatisme cornéen antérieur (CA) en cas de discordance entre les deux, appelée astigmatisme oculaire résiduel (ORA). Résultats: Sur un total de 104 yeux opérés de LASIK, 22 yeux de 12 patients (21,1%) avaient une ORA > 0,75 D et ont été inclus. L'ORA moyen était de 0,9 ± 0,2 D et le cylindre subjectif postopératoire moyen était de 0,45 D. La différence de vecteurs entre DV-DVRA était de 0,57

Patients et Méthodes

Introduction

Excimer laser treatments, through photorefractive keratectomy (PRK) and laser in situ keratomileusis (LASIK), has proved to be one of the most accurate, safest and most predictable tools in refractive surgery for correcting astigmatism [START_REF] Tomita | Safety, efficacy, and predictability of laser in situ keratomileusis to correct myopia or myopic astigmatism with a 750 Hz scanning-spot laser system[END_REF][START_REF] Roszkowska | Long-term results of excimer laser procedure to correct astigmatic refractive errors[END_REF][START_REF] Costa | Photorefractive keratectomy for myopia and myopic astigmatism correction using the WaveLight Allegretto Wave Eye-Q excimer laser system[END_REF]. Manifest refractive astigmatism is mostly due to anterior corneal astigmatism. However, discrepancies between refractive astigmatism (RA) and anterior corneal astigmatism (CA) are common and are quantified by a vector difference between RA and CA known as ocular residual astigmatism (ORA) [START_REF] Alpins | Vector analysis of astigmatism changes by flattening, steepening, and torque[END_REF]. Several studies have shown that the correction of astigmatism is less predictable in cases of high ORA than in cases of low ORA [START_REF] Kugler | Efficacy of laser in situ keratomileusis in correcting anterior and non-anterior corneal astigmatism: comparative study[END_REF][START_REF] Archer | Comparison of the predictability of refractive cylinder correction by laser in situ keratomileusis in eyes with low or high ocular residual astigmatism[END_REF][START_REF] Bragheeth | Effect of refractive and topographic astigmatic axis on LASIK correction of myopic astigmatism[END_REF][START_REF] Qian | Influence of internal optical astigmatism on the correction of myopic astigmatism by LASIK[END_REF]. ORA results from posterior corneal, lenticular, vitreous and retinal astigmatism. Programming for RA is an obvious choice if preoperative RA corresponds to anterior corneal toricity. Indeed, excimer photoablation takes place on the anterior surface of the cornea and is more appropriate for the treatment of anterior corneal astigmatism. However, if RA is greater than CA, total RA correction by photoablation will create a new astigmatism on the cornea, due to corneal aberrations. Some studies have suggested that topographic astigmatism should be included in the treatment of patients with ORA, rather than pure manifest refractive cylinder [START_REF] Qian | Influence of internal optical astigmatism on the correction of myopic astigmatism by LASIK[END_REF][START_REF] Alpins | Clinical outcomes of laser in situ keratomileusis using combined topography and refractive wavefront treatments for myopic astigmatism[END_REF][START_REF] Frings | LASIK for spherical refractive myopia: effect of topographic astigmatism (ocular residual astigmatism, ORA) on refractive outcome[END_REF][START_REF] Ozulken | Comparison of wavefrontoptimized ablation and topography-guided contoura ablation with LYRA protocol in LASIK[END_REF].

In cases of discrepancy between RA and CA, a key question remains to be addressed: what is the best astigmatism value to use when programming the excimer machine, as excimer laser ablation acts solely by reshaping the anterior cornea.

The aim of this study was to determine whether RA or CA was closest to the ideal cylinder for laser programming. We retrospectively analyzed refractive results for patients undergoing LASIK with an ORA > 0.75 D by the Alpins method [START_REF] Alpins | A new method of analyzing vectors for changes in astigmatism[END_REF]. We performed a vectorial analysis to compare postoperative refractive outcomes with the gap between planned astigmatism and RA, and with the gap between planned astigmatism and CA, to determine which measurement should be used for planning to obtain the lowest level of residual astigmatism.

Patients and methods

In this retrospective analysis, we reviewed the data for consecutive patients who had undergone LASIK refractive surgery at the Quinze-Vingts National Ophthalmology Hospital, Paris, France, performed by a single surgeon (LT). This study was performed in accordance with the Declaration of Helsinki and patients gave their informed consent for collecting and analyzing their data. Patients treated for hyperopic or myopic astigmatism by LASIK were enrolled. The other inclusion criteria were: no history of ocular surgery or disease, age between 23 and 50 years, no cataract or dry eye disease, manifest sphere between -8.00 and +3.00 D, manifest refractive cylinder between -5.00 and 0,00 D, corrected distance visual acuity (CDVA) of 20/20 or better, a minimum postoperative follow-up of three months, and a difference between preoperative manifest refractive astigmatism and anterior corneal astigmatism > 0.75 D. The patients included had no contraindication for LASIK, such as forme fruste keratoconus, irregular and asymmetric astigmatism, or a calculated corneal residual bed of less than 300 μm after laser ablation.

Surgical technique

The same surgeon (LT) performed all surgical interventions. The programming of the excimer laser for astigmatism did not always correspond to RA, with modulation according to CA in some cases. Before procedures, 0.4% topical oxybuprocaine hydrochloride was applied three times to each eye. A corneal flap was created with an Intralase FS60© femtosecond laser (Johnson and Johnson Vision, Jacksonville, Florida, USA). The laser had a pulse frequency of 60 kHz, an energy of 0.75 μJ and a pulse duration of between 600 and 800 fs. Line and spot spacings were 8 μm. Superior hinged flaps were created. The intended flap thickness was 110 μm, and the side-cut angle was 90 degrees. The flap diameter was between 8.5 and 9 mm.

Once the flap had been lifted, excimer laser Wavelight© EX500 (Alcon Laboratories, Inc., Fort Worth, Texas, USA) treatment was performed on the stromal bed, with a 6.0 mm optical zone and 0.5 mm transition zone. The corneal stromal bed was irrigated with balanced normal salt solution before the flap was repositioned. After surgery, the patients were told to instill a combination of dexamethasone and tobramycin drops three times daily for one month.

Postoperative evaluation

Clinical results were assessed at a follow-up visit three months after surgery. Postoperative data included measurements of uncorrected distance visual acuity (UDVA) and CDVA, with a Snellen acuity chart at 5 m, and manifest refraction (sphere and cylinder).

Vectorial analysis

The vectorial analysis was performed by the Alpins method [START_REF] Alpins | A new method of analyzing vectors for changes in astigmatism[END_REF][START_REF] Alpins | Astigmatism analysis by the Alpins method[END_REF]. The aim of this study was to perform a retrospective analysis of postoperative refractive astigmatism and programmed astigmatism values, to determine whether the use of RA or CA to program the laser would have given the smallest postoperative residual cylinder. The amplitude and axis of ORA was defined with a double-angle vector diagram, as the difference vector between preoperative RA and CA (Fig. 1). The CA value was obtained by corneal topography (Pentacam©, Oculus, Wetzlar, Germany). The target induced astigmatism (TIA) vector corresponds to the preoperative RA with a 90° opposite axis, and the surgically induced astigmatism (SIA) vector is the difference vector between postoperative and preoperative refractive astigmatism values, corresponding to the actual change in astigmatism induced by surgery. The difference vector (DV) is the vectorial difference between TIA and SIA and represents the residual uncorrected astigmatism (Fig. 2). The index of success was calculated by dividing DV by TIA. The programming value of astigmatism (PRA) in the excimer laser was not always the preoperative RA, and was frequently influenced and partially modulated according to CA (Fig. 3). The vectorial difference between PRA and RA on the excimer laser (called DVRA) and the vectorial difference between PRA and CA on the excimer laser (called DVCA) were calculated (Fig. 4). Finally, we assessed vectorial differences between DV and DVRA, and between DV and DVCA (Fig. 5). The lowest value was used to determine whether DVRA or DVCA was closest to the DV actually measured, indicating which of RA and CA was the ideal value for programming purposes. DV measured the error of correction between the target correction and the achieved correction. If this error was closer to the difference between the programmed correction and RA (DVRA) than to that between the programmed correction and CA (DVCA), then RA would be the best value to use for laser programming, making it possible to obtain results closer to the target correction. Conversely, if DV was closer to DVCA, then CA would be more reliable than RA for achieving the target correction. We illustrate this with the example of a patient, to facilitate understanding (Table 1).

Statistical analysis

Results are presented as the mean ± standard deviation for continuous variables and as proportions (%) for categorical variables. Difference vectors were compared in Student's t test. A P value < 0.05 was considered statistically significant. Statistical analyses were performed with Excel 2011 software (Microsoft Corp).

Results

Of a total of 104 consecutive eyes undergoing LASIK surgery, 22 eyes from 12 patients (21.1%) had an ORA > 0.75 D and were included in this study. The mean age and sex of the patients, the preoperative refractive sphere and cylinder, preoperative anterior corneal cylinder and preoperative ORA are shown in Table 2.

Mean preoperative ORA was 0.95 ± 0.28 D, mean preoperative refractive astigmatism was 0.96 ± 0.59 D and mean postoperative refractive cylinder was 0.52 ± 0.25 D. Mean DV was 0.52 ± 0.3 D and the mean index of success was 0.52, indicating that 48% of the preoperative refractive astigmatism was treated. DVRA was 0.2 ± 0.22D and DVCA was 0.69 ± 0.23 D (P<0.05). Programmed astigmatism was significantly closer to RA than CA. The DV-DVRA difference vector was 0.57 ± 0.2 D and the DV-DVCA difference vector was 0.86 ± 0.44 D (P=0.02). RA gave the value closest to the ideal correction of astigmatism. The postoperative results are summarized in Table 3.

Discussion

In refractive surgery, ORA, defined as a difference between refractive and anterior corneal astigmatism, is not a rare clinical finding. Residual astigmatism can be attributed to the posterior surface of the cornea and internal optics, such as the lens, vitreous and retina, which are not assessed by usual corneal topography procedures. Many studies have reported a lower efficacy of treatments for astigmatism treatments in such cases than for patients with astigmatism located primarily in the anterior cornea [START_REF] Kugler | Efficacy of laser in situ keratomileusis in correcting anterior and non-anterior corneal astigmatism: comparative study[END_REF][START_REF] Archer | Comparison of the predictability of refractive cylinder correction by laser in situ keratomileusis in eyes with low or high ocular residual astigmatism[END_REF][START_REF] Bragheeth | Effect of refractive and topographic astigmatic axis on LASIK correction of myopic astigmatism[END_REF][START_REF] Qian | Influence of internal optical astigmatism on the correction of myopic astigmatism by LASIK[END_REF]. Laser surgery for astigmatism was much more effective when RA was concordant with CA. One of the explanations for this finding is that the location of the treatment is also the site of astigmatism. Indeed, as excimer laser ablation occurs on the anterior cornea, the cylindrical correction is more appropriate and accurate if this site is the principal location of the astigmatism. In cases of discordance between RA and CA due to internal optic-mediated astigmatism, photoablation guided by RA may induce iatrogenic corneal aberrations to compensate the internal astigmatism, thereby decreasing the quality of vision. The optical aberrations induced depend on the type of preoperative astigmatism, with-or against-the-rule. Correcting internal astigmatism by treating astigmatism at another site is not clearly logical. As excimer laser refractive surgery reshapes only the anterior corneal surface, we investigated whether RA or CA was the most appropriate value for the excimer laser programming in cases of discrepancy between these two values. Integrating CA, even only partially, into the programming of the laser for patients with ORA has been suggested by several authors [START_REF] Qian | Influence of internal optical astigmatism on the correction of myopic astigmatism by LASIK[END_REF][START_REF] Alpins | Clinical outcomes of laser in situ keratomileusis using combined topography and refractive wavefront treatments for myopic astigmatism[END_REF][START_REF] Frings | LASIK for spherical refractive myopia: effect of topographic astigmatism (ocular residual astigmatism, ORA) on refractive outcome[END_REF], and may better respect the location of photoablation treatment.

This study was original in that we retrospectively analyzed patients undergoing LASIK with an ORA greater than 0.75 D, to determine whether RA or CA gave the best refractive astigmatism results, assuming that the excimer laser is equally precise for all values and axes of astigmatism. We addressed this question, by calculating the DV -DVRA and DV -DVCA difference vectors. The value closest to zero identified the most reliable cylinder for use in programming of the laser to obtain the best postoperative refractive results. We obtained a DV -DVRA difference vector of 0.57 ± 0.2 D, which is significantly lower than the DV -DVCA difference vector of 0.86 ± 0.44 D. DV was thus closer to DVRA than to DVCA, indicating that the magnitude of surgically induced error was very close to the difference between programmed astigmatism and RA. We can therefore deduce that RA is a more appropriate value for the programming of the refractive procedure than CA. A prospective study should be set up to confirm these preliminary results, in which two groups should be compared, one with programming according to RA and the other with programming according to CA, to determine which of these values gives the best postoperative results. The other results of our study are consistent with published findings. Alpins described an ORA greater than 1.00 D in 34% of eyes [START_REF] Alpins | New method of targeting vectors to treat astigmatism[END_REF], and Archer and coworkers reported that 21% of patients had a high ORA (ORA/refractive astigmatism ≥1.0) [START_REF] Archer | Comparison of the predictability of refractive cylinder correction by laser in situ keratomileusis in eyes with low or high ocular residual astigmatism[END_REF]. In our series, patients with an ORA > 0.75D accounted for 21.1% of the patients undergoing LASIK surgery. The index of success (DV/TIA) in our study was 0.52, a value similar to those reported in other studies.

For example, Kugler and coworkers reported an index of success of 0.50 in the high-ORA group [START_REF] Kugler | Efficacy of laser in situ keratomileusis in correcting anterior and non-anterior corneal astigmatism: comparative study[END_REF], Archer and coworkers reported an index of success of 0.37 in the high-ORA group [START_REF] Archer | Comparison of the predictability of refractive cylinder correction by laser in situ keratomileusis in eyes with low or high ocular residual astigmatism[END_REF] and Qian reported an index of success of 1.75 (indicating overcorrection) [START_REF] Qian | Influence of internal optical astigmatism on the correction of myopic astigmatism by LASIK[END_REF]. As previously shown in all these articles, efficacy was moderate in our case series, with preoperative astigmatism reduced by only half. Nevertheless, our statistical analyses confirmed that RA gave better postoperative results than CA and should therefore be used to program the excimer machine. The results obtained remain unsatisfactory, as the astigmatism remains only half-corrected. However, attempting total RA correction on the corneal surface, when CA is less than RA, would induce additional astigmatism and new corneal aberrations with deleterious effects on the final results. Logically, reshaping of the anterior cornea with an excimer laser should target only anterior corneal astigmatism, whereas astigmatism due to internal optic defects should be treated by intraocular refractive surgery. Integrating topographic astigmatism into the programming of correction to modulate RA is clearly the path to follow. Arbelaez and coworkers used the vector planning method incorporating corneal and refractive astigmatism [START_REF] Arbelaez | Clinical outcomes of laser in situ keratomileusis with an aberration-neutral profile centered on the corneal vertex comparing vector planning with manifest refraction planning for the treatment of myopic astigmatism[END_REF], but the results obtained were similar to manifest refraction correction.

Modern topography-guided treatments, such as Wavelight Allegro Contoura (Alcon Laboratories), convert anterior corneal aberrations to generate an ablation profile [START_REF] Stonecipher | Comparing wavefront-optimized, wavefrontguided and topography-guided laser vision correction: clinical outcomes using an objective decision tree[END_REF]. The topography-modified refraction (TMR) protocol used in Wavelight Allegro Contoura topography-guided treatment modifies the programmed cylindrical refraction to match the value and axis of topographic anterior corneal astigmatism [START_REF] Kanellopoulos | Topography-modified refraction (TMR): adjustment of treated cylinder amount and axis to the topography versus standard clinical refraction in myopic topography-guided LASIK[END_REF][START_REF] Kanellopoulos | Topography-guided LASIK versus small incision lenticule extraction (SMILE) for myopia and myopic astigmatism: a randomized, prospective, contralateral eye study[END_REF]. Comparisons between anterior corneal astigmatism correction (in topography-guided ablation) and manifest refractive astigmatism correction have yielded conflicting results. Kanellopoulos reported superior postoperative residual astigmatism outcomes in the TMR group [START_REF] Kanellopoulos | Topography-modified refraction (TMR): adjustment of treated cylinder amount and axis to the topography versus standard clinical refraction in myopic topography-guided LASIK[END_REF]. Wallerstein and coworkers reported results similar to our own, with superior refractive outcomes for clinical manifest refractive astigmatism than for topography-guided treatment based on anterior corneal astigmatism [START_REF] Wallerstein | Primary topography-guided LASIK: treating manifest refractive astigmatism versus topography-measured anterior corneal astigmatism[END_REF]. Another study concluded that there was no significant difference in refractive and visual outcomes between the two types of correction, but that there were fewer higher-order aberrations (HOAs) in topography-guided LASIK [START_REF] Kim | Topography-guided versus wavefront-optimized laser in situ keratomileusis for myopia: Surgical outcomes[END_REF].

Topography-guided treatment may be an interesting way forward in the future, for the treatment of astigmatism, particularly in cases of ORA. Further studies are required to determine the exact proportion of CA to incorporate into laser programming for the treatment of astigmatism in topography-guided ablation, to obtain the most suitable compromise between postoperative residual refractive cylinder and corneal aberrations.

Disclosure of interest:

The authors declare that they have no competing interest.

Vector diagram representing preoperative manifest refractive astigmatism (RA), anterior corneal astigmatism (CA) and the vectorial difference between the preoperative RA and the CA, known as ocular residual astigmatism (ORA).

Figure 2

Vector diagram representing preoperative manifest refractive astigmatism (RA), postoperative refractive astigmatism (PA), the surgically induced astigmatism vector (SIA) corresponding to the difference vector between RA and PA, the target-induced astigmatism vector (TIA), and the difference vector between TIA and SIA (DV).

Figure 3

Vector diagram representing preoperative manifest refractive astigmatism (RA), anterior corneal astigmatism (CA), programming value of astigmatism (PRA) in the excimer laser, target-induced astigmatism vector (TIA), and the difference vector between TIA and SIA (DV).

Figure 4

Vector diagram representing preoperative manifest refractive astigmatism (RA), anterior corneal astigmatism (CA), programming value of astigmatism (PRA) in the excimer laser, target-induced astigmatism vector (TIA), and the difference vector between TIA and SIA (DV). The vectorial difference between PRA and RA in the excimer laser (called DVRA) and the vectorial difference between PRA and CA in the excimer laser (called DVCA) were calculated.

Figure 5

Vector diagram representing preoperative manifest refractive astigmatism (RA), anterior corneal astigmatism (CA), programming value of astigmatism (PRA) in the excimer laser,

:

  Les patients opérés de chirurgie LASIK présentant une discordance entre le cylindre manifeste et le cylindre cornéen (astigmatisme résiduel oculaire ORA) > 0,75 D ont été inclus rétrospectivement dans cette étude. Le vecteur d'astigmatisme induit cible (TIA), le vecteur d'astigmatisme induit chirurgicalement (SIA), la différence de vecteurs entre l'astigmatisme programmé dans le laser excimer et RA (DVRA), la différence de vecteurs entre l'astigmatisme programmé sur le laser excimer et CA (DVCA) et la différence de vecteurs entre TIA et SIA (DV) ont été calculés par la méthode d'Alpins. Les différences vectorielles entre DV et DVRA, et entre DV et DVCA ont été calculées pour déterminer lequel de RA ou CA donnait la valeur la plus proche du cylindre idéal à programmer sur le laser.

target-induced astigmatism vector (TIA), the difference vector between TIA and SIA (DV), the difference vector between PRA and RA in the excimer laser (called DVRA) and the difference vector between PRA and CA in the excimer laser (called DVCA).

The DV -DVRA, and DV -DVCA difference vectors were calculated. The lowest difference vector was used to determine whether RA or CA was the closest to the measured DV, i.e. the ideal programming value.

DV -DVRA < DV -DVCA Table 1: Example of the calculation of difference vectors for one patient

In this example, DV -DVRA is lower than DV -DVCA, so DVRA is closer to DV than DVCA.

We can deduce that, for this patient, RA was a more reliable value than CA for excimer laser programming.

TIA: Target induced astigmatism; SIA: Surgically induced astigmatism; DV: Difference vector between TIA and SIA; DVRA: Difference vector between programmed astigmatism (PRA) in the excimer laser and refractive astigmatism (RA); DVCA: Difference vector between programmed astigmatism (PRA) in the excimer laser and anterior corneal astigmatism (CA)