Emile Hohnadel
email: emile.hohnadel@inria.fr

Joël Marthelot

Ignacio Andrade

Thibaut Metivet

Olivier Pouliquen

Flo- Rence Bertails-Descoubes

Frictional three-point bending test: disentangling the role of friction through real and numerical experiments

Keywords: thin elastic rods, dry frictional contact, numerical simulation

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

The three-point bending test is a classical test, widely used to determine the bending modulus of a rod. However, the role of friction on this single test has been scarcely studied [START_REF] Van Paepegem | Effect of friction on the hysteresis loops from three-point bending fatigue tests of fibre-reinforced composites[END_REF]. Our objective in this work is therefore to investigate the role of friction in this archetypical test in both the small and large deflection regimes by combining experimental and numerical studies.

On the one hand, we design a three-point bending experimental setup with fixed -non-rollingsupports, with precision measurements of the forces applied at the deflection point together with the corresponding displacement of the fiber along one of the two supports. On the other hand, thanks to our carefully validated numerical model coupling a rod model to frictional contact [START_REF] Romero | Physical validation of simulators in Computer Graphics: A new framework dedicated to slender elastic structures and frictional contact[END_REF], we manage to predict accurately the geometry and forces of the system in the full nonlinear regime.

By comparing the numerical results with the experimental ones and expanding on a wider range of parameters, the role of friction is quantified and analysed, extending the usual rolling three-point bending test. A mathematical study is also conducted, based on the numerical observations to complement the results. Finally, we demonstrate that the frictional three-point bending test provides a simple way to measure the friction coefficient of a slender structure.

Frictional

  three-point bending test: disentangling the role of friction through real and numerical experiments Émile Hohnadel, Joel Marthelot, Ignacio Andrade-Silva, Thibaut Métivet, Olivier Pouliquen, Florence Bertails-Descoubes To cite this version: Émile Hohnadel, Joel Marthelot, Ignacio Andrade-Silva, Thibaut Métivet, Olivier Pouliquen, et al.. Frictional three-point bending test: disentangling the role of friction through real and numerical experiments. European Solid Mechanics Conference ESMC 2022, Jul 2022, Galway, Ireland. hal-

Fig. 1 :

 1 Fig. 1: Left : Picture of the experimental manipulation. Center: illustration of one arbitrary step of the simulation, showing the forces applied on the indented fiber (arrow colors indicate the stick (red) or slip (green) regimes). Right: plot of the deflection force as a function of the indentation for a full indentation cycle, computed with our simulator.


Guillaume Dessevre

Cléa Martinez

Franck Fontanili

Liwen Zhang

Christophe Bortolaso

SIMULATION AND ANALYSIS OF DISRUPTIVE EVENTS ON A DETERMINISTIC HOME HEALTH CARE ROUTING AND SCHEDULING SOLUTION

Due to the aging of populations and a desire to relieve the growing demand on medical structures in recent years, the demand for home health care services has been increasing, and the Home Health Care Routing and Scheduling Problem (HHCRSP) is now among the most intensely studied optimization problems. However, most studies on the HHCRSP are based on deterministic models that do not consider any disruptions that may compromise the execution of the schedules. In this paper, we analyze the impact of different sources of disturbances on a deterministic schedule : delays at the start of the route, variability of travel time, and variability of service processing time. Simulation has been chosen because it helps to easily model and analyze complex environments with several sources of variability. Graphical representations and an analysis of variance are presented to interpret the results, leading to several managerial insights and openings for future research.

INTRODUCTION

Thanks to the progress of science, the life expectancy of humans is constantly increasing. Thus, there are more and more people living longer lives. In France, for example, people over 60 years old represented around 25% of the population in 2018, compared to only 20% in 2000[START_REF] Brutel | La population de la France métropolitaine en 2050 : un vieillissement inéluctable[END_REF] predicts more than 30% in 2050. In addition, there is a desire to reduce the demand on medical structures (such as hospitals), pushing people to return to their homes as quickly as possible. Consequently, the demand for services and home care has increased sharply in recent years, as have scientific studies on the subject [START_REF] Di Mascolo | Routing and Scheduling in Home Health Care: A Literature Survey and Bibliometric Analysis[END_REF].

The Home Health Care Routing and Scheduling Problem (HHCRSP), derived from the Vehicle Routing Problem (VRP) which has been studied for decades [START_REF] Dantzig | The Truck Dispatching Problem[END_REF], consists in assigning tasks to staff members of an HHC agency, planning care visiting hours for patients at home, and designing the caregivers' routes. Many studies focus on HHCRSP, since several parameters can be considered: the objective function (cost minimization, maximization of stakeholder satisfaction, etc.), the constraints of the model (consideration of time windows, a matrix of feasibility between caregivers and services or patients, the workload rate of caregivers), the horizon studied (day, week, or month), the resolution approach or tool, and the stochasticity of the environment, etc. This last point is one of the least studied, and that is why in this article, we measure and analyze the impact of three different sources of disturbances on a deterministic schedule coming from a HHCRSP literature paper. Discrete-event simulation has been chosen because it easily allows complex environments with several sources of variability to be modeled and analyzed.

The paper is organized as follows: section 2 presents a brief literature review and concludes with the research question, section 3 introduces the use case and the methodology, section 4 presents the results, and section 5 is the conclusion and openings for future research.

LITERATURE REVIEW

There are many studies on the HHCRSP which have been recently reviewed in [START_REF] Cissé | OR problems related to Home Health Care: A review of relevant routing and scheduling problems[END_REF][START_REF] Di Mascolo | Routing and Scheduling in Home Health Care: A Literature Survey and Bibliometric Analysis[END_REF][START_REF] Grieco | Operational Research Applied to Decisions in Home Health Care: A Systematic Literature Review[END_REF]) and which explore a large range of problems presenting numerous and various features. As a result of the number of publications on the subject, we present in this section a non-exhaustive review of what has been studied to raise a relevant research question. We approach the literature review according to three criteria: objective function, resolution approach, and variability modeling.

The Objective Function

In the literature, the main objective function is cost minimization: [START_REF] Begur | An Integrated Spatial DSS for Scheduling and Routing Home-Health-Care Nurses[END_REF] The other widely studied optimization criterion is the maximization of stakeholder satisfaction. For patient peace of mind, this essentially involves minimizing violations of time windows [START_REF] Bertels | A Hybrid Setup for a Hybrid Scenario: Combining Heuristics for the Home Health Care Problem[END_REF]Trautsamwieser et al. 2011), and improving continuity of care, which is generally interpreted as assigning a unique caregiver to each patient (Trautsamwieser and Hirsch 2011) or minimizing the number of different caregivers [START_REF] Wirnitzer | Patient-Based Nurse Rostering in Home Care[END_REF]. For the satisfaction of caregivers, [START_REF] Cappanera | Home Care Optimization: Impact of Pattern Generation Policies on Scheduling and Routing Decisions[END_REF] consider workload balancing, [START_REF] Zhang | Stakeholders' Tolerance-Based Linear Model for Home Health Care Coordination[END_REF] work on balancing the difficulty of services and [START_REF] Rest | Daily Scheduling of Home Health Care Services Using Time-Dependent Public Transport[END_REF] minimize overqualified work.

Resolution Approaches

Derived from VRP, HHCRSP is NP-hard, so numerous exact or approximate approaches have been developed to tackle the problem, such as Mixed-Integer Linear Programming (MILP) [START_REF] Cheng | A Home Health Care Routing and Scheduling Problem[END_REF], a branch and price algorithm [START_REF] Liu | A Branch-and-Price Algorithm for the Home-Caregiver Scheduling and Routing Problem with Stochastic Travel and Service Times[END_REF], dedicated heuristics [START_REF] Fathollahi-Fard | A Set of Efficient Heuristics for a Home Healthcare Problem[END_REF], and a variable neighborhood search [START_REF] Nasir | Solving a More Flexible Home Health Care Scheduling and Routing Problem with Joint Patient and Nursing Staff Selection[END_REF], etc. Even though the majority of the articles have developed a centralized approach to routing and scheduling caregivers, some studies prefer distributed approaches. [START_REF] Marcon | A Multi-agent System Based on Reactive Decision Rules for Solving the Caregiver Routing Problem in Home Health Care[END_REF] propose an agentbased model to dynamically re-route caregivers according to a set of decision rules. [START_REF] Alves | Scheduling of Home Health Care Services Based on Multi-Agent Systems[END_REF] use multi-agent simulation to deal with the perturbations due to vehicle problems and to re-schedule interventions. In [START_REF] Viana | Optimizing Home Hospital Health Service Delivery in Norway Using a Combined Geographical Information System, Agent Based, Discrete Event Simulation Model[END_REF], the impact of various demand patterns is evaluated through an agentbased model and discrete-event simulation.

Variability Modeling

Fikar and Hirsch (2017) highlight the importance of taking uncertainties into account when solving the HHCRSP. Variability can come from many sources of disturbance, and can be modeled in several ways. The first source of disturbance comes from the patients who may change their time slot [START_REF] Lin | Jointly Rostering, Routing, and Rerostering for Home Health Care Services: A Harmony Search Approach with Genetic, Saturation, Inheritance, and Immigrant Schemes[END_REF], their frequency of visit [START_REF] Mosquera | Flexible Home Care Scheduling[END_REF], or cancel services [START_REF] Yuan | Disruption Management for the Real-Time Home Caregiver Scheduling and Routing Problem[END_REF]. Caregivers can also disrupt the system: for example, they may fall ill and change their availability [START_REF] Xie | A Periodic Repair Algorithm for Dynamic Scheduling in Home Health Care Using Agent-based Model[END_REF]. The most widely studied source of variability is variations in travel time, due to traffic [START_REF] Yalçındağ | The Patient Assignment Problem in Home Health Care: Using a Data-Driven Method to Estimate the Travel Times of Care Givers[END_REF], breakdowns, parking and driving skills [START_REF] Shi | A Robust Optimization for a Home Health Care Routing and Scheduling Problem with Consideration of Uncertain Travel and Service Times[END_REF], and variations in service time [START_REF] Yuan | A Branch-and-price Algorithm for the Home Health Care Scheduling and Routing Problem with Stochastic Service Times and Skill Requirements[END_REF].

Two main approaches have been used to consider these disturbances. The first one is to predict the variations to obtain a robust solution that remains feasible even when the schedule is disturbed. Variability is then modeled either by a discrete set of scenarios [START_REF] Cappanera | Demand Uncertainty in Robust Home Care Optimization[END_REF][START_REF] Rodriguez | Staff Dimensioning in Homecare Services with Uncertain Demands[END_REF], or by intervals of values [START_REF] Mosquera | Flexible Home Care Scheduling[END_REF][START_REF] Carello | A Cardinality-Constrained Robust Model for the Assignment Problem in Home Care Services[END_REF], and the values are arbitrarily uniformly or normally distributed.

Conclusion and Research Question

As a conclusion of this review, it is known that (i) there are many studies on the HHCRSP, that (ii) the minimization of travel distances is the most widely studied criteria, inherited from the VRP, but more and more studies are considering stakeholder satisfaction (patients and caregivers), that (iii) there are many tools and methods that have been developed over the years in the literature to solve the HHCRSP, but that (iv) the variability of the systems has only been studied for a few years without analyzing its impact on the performance of the solutions. One question thus arises: What are the impacts of disruptive events on the satisfaction of HHCRSP stakeholders?

To answer this question, we propose to study a short-term deterministic solution coming from a HHCRSP literature paper that considers stakeholder satisfaction, to model several sources of disturbances and variability using discrete-event simulation, and to analyze the impacts on performance measures.

METHODOLOGY

Our research strategy is based on the study of a use case inspired by [START_REF] Zhang | Stakeholders' Tolerance-Based Linear Model for Home Health Care Coordination[END_REF]. In this paper, we follow the procedure recommended by [START_REF] Montgomery | Design and Analysis of Experiments[END_REF] for designing and analyzing experiments (Figure 1). The objectives of the experiments are to measure and quantify the impacts of different sources of schedule disruptions, including two sources of variation.

Figure 1: Steps of the methodology applied to our case study.

Discrete-event simulation has been chosen as the method because it allows complex environments with several sources of variability to be easily modeled and analyzed (Mourtzis 2020), and a lack of studies on the impact of the variability on deterministic schedules has been highlighted in the literature review.

Use Case and Deterministic Solution Representation

The chosen use case for experimental purposes comes from [START_REF] Zhang | Stakeholders' Tolerance-Based Linear Model for Home Health Care Coordination[END_REF], where the objective is to provide a solution to the HHCRSP on a daily horizon. The data set was extracted from an existing HHC institution.

For the demand side, 28 patients are included in this case. Fourteen of them require only one care service, while the others have between 2 and 5 services during the day. For each care service, patients specify a one-hour arrival starting time window (from case study data), corresponding to the window during which the caregiver must come to start the service (the service can be finished after this time window). Fifty-five care services are requested by 28 patients. There are three types of services according to the temporal criteria: 15-minute short services, 30-minute medium services, and 60-minute long services.

For the offer side, there are 4 caregivers (who have undergone training in caregiving) to be dispatched to perform the 55 care services (refer to nursing care or home health aide services), hence the 4 different routes in Figure 2. The maximum workload is 10 hours per day for each caregiver.

Based on the MILP model described in [START_REF] Zhang | Stakeholders' Tolerance-Based Linear Model for Home Health Care Coordination[END_REF], we obtain the optimum solution generated by CPLEX for our experimental use case. In this model, several specific parameters have been considered, such as the difficulty of care services and a feasibility matrix between caregivers and services. Furthermore, a series of soft constraints aimed at considering the satisfaction of all the stakeholders (patients and caregivers) have been taken into account: (i) for patients, the beginning of a service has to be scheduled as closely as possible within the requested time windows, and in the case of more than one care service requested by the same patient, the temporal interval between two successive services should be greater or equal to the requested inter-service time; (ii) for caregivers, the duration of a working round for one caregiver should be respectful of his/her allowed maximum working hours, and the set of rounds should be balanced according to the level of difficulty. Regarding the optimal and deterministic solution obtained by executing the described MILP-based model, the average workload rate of caregivers is 83% (between 76% for the least busy and 93% for the busiest). The workload rate includes travel time and care service time, divided by the 10 hours of work per day. In this case, travel time represents about one-third of service time. Travel time is calculated by taking the Euclidean distances (i.e., as the crow flies, Figure 2) between each patient, and dividing it by the average speed of 20 km/h. Finally, we must emphasize that the exact method-oriented MILP-based model described in Zhang et al. ( 2021) is a deterministic model, under two assumptions in terms of temporality: deterministic travel time and the operation time of each care service. In this paper, we propose to study the impact of variability on these times on the schedule. In addition, we study the impact of the delay of caregivers at the start of their routes.

3.2

Experimental Protocol

Statement of the Problem

In Zhang et al. ( 2021), the MILP-based model has been used to determine the optimal solution, which is a deterministic daily schedule. This solution does not consider any variation that could occur during the day (heavy traffic, car breakdowns, services taking longer than expected, etc.). Figure 3 presents the optimal schedule (due to limited space and the need for legibility, the afternoon schedule has not been shown), as well as the detailed routing results for the first caregiver (with time windows to respect for each patient).

The routes are shown in Figure 2. Note that the execution of this schedule will be the baseline scenario for the design of the experiments, and it already includes several early arrivals (in yellow, Figure 3) and late arrivals (slashed and encircled in red). Data and calculated values are deterministic, i.e., they are considered to be fixed, without variation. For example, at 20 km/h, a 10 km trip will always take 30 minutes. The duration for performing a care service is also the fixed time. However, many unforeseen events can happen and disrupt the schedule, deteriorating its performance related to stakeholder satisfaction. Therefore, we propose to model different sources of variability and analyze their impacts on this deterministic schedule.

Selection of the Response Variables

Since we are interested in the satisfaction of all stakeholders involved in HHC, and we assume that the sources of variability introduced into the model may disrupt the schedule by shifting the care services, then the response variables are the total number of late arrivals and the total number of early arrivals.

A late arrival occurs when a caregiver arrives after the one-hour time window requested by the patient, and an early arrival occurs when a caregiver arrives before the time window. In the latter case, the caregiver has to wait for the start of the time window before entering the patient's home and then beginning the care service.

A tolerance of one minute early or late is considered. For example, if a caregiver arrives 15 seconds later than the end of the time window, this is not considered a delay.

Choice of Factors, Levels and Ranges

The choice of factors reflects the events that could modify the initial schedule and degrade the performance of the solution. Consequently, three sources of disturbances are considered in the model:

1. The delay at the start of the caregiver's daily working round (start time delay). This delay may be due to a car/bike breakdown, an unexpectedly difficult de-icing, a sick child to be looked after, etc. 2. The variability of travel time. It is important to highlight that in real life, travel times fluctuate constantly due to traffic congestion, traffic jams, accidents, etc. 3. The variability of service processing time. Two of the same care services never take exactly the same amount of time to be carried out, especially when considering the various human characteristics of caregivers and their proficiency when performing the same care services under different contexts on site. Care service processing time is highly variable and it is difficult to model these temporal events based on unpredictable human factors.

To assess the impacts of these different sources, four levels of variability have been designed: a deterministic one where there is no variation (as modeled in the reference paper), and three levels where values are uniformly distributed, as shown in Table 1. Deterministic Uniform(0.9:1.1) Uniform(0.7:1.3) Uniform(0.5:1.5) Service time Deterministic Uniform(0.9:1.1) Uniform(0.7:1.3) Uniform(0.5:1.5)

For the start time delay, the three ranges for each uniform law are 0 to 10, 0 to 30, and 0 to 60, corresponding respectively to an average departure delay of 5, 15 and 30 minutes. We do not consider the case where a caregiver leaves early from home, since in this case the caregiver just has to wait before leaving. For the travel and service times, the three ranges correspond to ±10%, ±30%, and ±50% around the mean value of the deterministic model, to model different degrees of variability (low, medium, high). Therefore, with a range at ±50%, a 10-minute ride will be uniformly distributed between 5 and 15 minutes, and a 60-minute care service will be uniformly distributed between 30 and 90 minutes. The choice of uniform laws comes from the literature [START_REF] Naji | A Robust-MILP for Synchronized-mTSPTW: Application to Home Health Care under Uncertainties[END_REF][START_REF] Rodriguez | Staff Dimensioning in Homecare Services with Uncertain Demands[END_REF].

Choice of Experimental Design and Performing the Experiments

The design of the experiments is composed of 4x4x4 = 64 scenarios.

The scenarios are compared to the baseline, which corresponds to the case where the caregivers start on time, and the travel and care service times are deterministic. The baseline is the solution obtained by running an MILP-based model developed in CPLEX. Each scenario is simulated with 100 replications (except for the baseline, which is deterministic and needs only one replication), and each replication lasts one day. The model being empty in the initial state, there is no warm-up period.

The modeling and simulation were performed with Arena software, version 16.10. A simplified version of the simulation model process flow is shown in Figure 4: the caregivers, entities of the model, are created (1); then they wait for a delay, depending on the simulated scenario, before getting their route information and making a first trip (2); the travel time is calculated according to a distance matrix and is subject to variability (3); the response variables are incremented if an early arrival (4) or a late arrival (5) occurs; finally, the care service is carried out by considering variability (6), and the caregiver moves on to the next patient until the end of the route has been reached.

RESULTS

Overview of Design of Experiment Results

The results of the 64 scenarios are represented in Figure 5: on the abscissa, the total number of early arrivals, and on the ordinate, the total number of late arrivals. Thus, the best scenarios are those at the bottom left of the graph. To differentiate the scenarios, the following legend has been used:

• The shapes (circle, square, triangle, rhombus) correspond to the different levels of the Start time delay (S) factor, • The fill colors (green, orange, blue, grey) correspond to the levels of the Travel time (T) factor, and • The border colors (same four colors but darker) correspond to the levels of the Care service time (C) factor.

The matches between shape, color and levels are shown in Figure 5. Moreover, each scenario has a specific name according to the level of its factors. For example, the scenario where the Start time delay (S) is between 0 and 10 minutes, the Travel time (T) is ±30% and the Care service time (C) is ±50% is named S10_T30_C50, and represented by a blue square outlined in dark gray. The scenario named S00_T00_C00 is the baseline.

For the baseline scenario, the total number of early arrivals is 5, and the total number of late arrivals is 4. It is the best compromise between a low number of early and late arrivals. By adding disturbance sources, the number of late arrivals increases to 20, and the number of early arrivals goes up to 8.

Graphic Visualization of the Effects of each Source of Disturbance

In order to better understand the effect of each factor on the number of early and late arrivals, Figure 6 presents three graphs where scenarios are grouped by color according to the level of each factor. The colors green, orange, blue and gray represent the different levels (deterministic and uniform distributions).

Figure 5: Total number of early arrivals and late arrivals for each scenario.

The start time delay increases the number of late arrivals but decreases the number of early arrivals: the more caregivers fall behind on their routes at the start of the day, the more they arrive late for services, thus reducing early arrivals. Moreover, the effect spreads throughout the morning: the caregiver is late for almost every morning service in Figure 7 (scenario S60_T00_C00). It is important to note that the lunch break (on the right, Figure 7) behaves as a time buffer, allowing the lateness of the morning to be absorbed, which thus has no impact on the afternoon care services (not represented), showing a solution for absorbing schedule variations.

Graphically, for the two sources of variability, variations in travel time mainly impact the number of early arrivals, while variations in service time affect the number of late arrivals for the caregivers (note that the axes of the graphs are not normalized). To mathematically confirm these observations, a two-way ANalysis Of VAriance (ANOVA) was carried out without considering any start time delay (S00).

Two-Way ANOVA

An ANOVA is a statistical test used to analyze the difference between the means of different factors. A two-way ANOVA is used to estimate how the mean of a quantitative variable changes according to the levels of two categorical variables. In our case, the statistical test is used to measure the effect of the sources of variability in travel and service times that are observed in Figure 6. For the number of late arrivals, the results data are presented in Table 2, and the variance and F-value calculations are summarized in Table 3. Since the F-values are greater than 𝐹 9 3 (for alpha = 0.01) for both travel time and service time, they are both statistically significant, especially for the service time factor. The same statistical test has been performed for the total number of early arrivals, with F-values equal to 26.83 (for travel time) and 4.70 (for service time). Therefore, travel time is statistically significant but care service time is not. In conclusion, the variability of service time mainly impacts the number of late arrivals, while the variability of travel time mainly impacts the number of early arrivals.

As 100 replications were simulated for each scenario, a two-way ANOVA with replications has been performed to assess whether there is an interactive effect between the factors. For late and early arrivals, the F-values of the interactive factor are respectively 2.21 and 0.52, while 𝐹 1584 9 (for alpha = 0.01) is 2.41. We can conclude that the interaction factor is not statistically significant at alpha level 1%.

CONCLUSION AND OPENINGS

In this paper, we measure and analyze the impact of different sources of disturbances on a deterministic schedule coming from a HHCRSP literature paper. Three sources of disturbance have been modeled (delays at the start of the route, the variability of travel time, and the variability of service processing time), and the objective is to quantify their impacts on stakeholder satisfaction. Graphical representations and analyses of variances have been conducted, to conclude on the impact of disruptive events: this study emphasizes that it is unreasonable not to consider the variability of the HHCRSP environment when designing schedules.

To go further, it would be interesting to study what features of the model are affected by disturbances. For example, in our case study, travel time represents a third of service time: in another case, will the impacts of the sources of disturbances be different? Thus, we could create robust solutions depending on system features. Note that in our case study, although some patients require several services on the same day, there is no case where the delay of a caregiver leads to an overlap of services, further disrupting the schedule and its performance indicators.

The next step is to collect user data (patients and caregivers) to analyze whether the modeled disturbances are relevant, and to better understand stakeholder behavior.

Finally, several solutions (some of which already exist in the literature) can counteract the variability of the environment and disruptive events. Among the interesting solutions to study and explore, there are:

• Providing margins on travel time and service time. But how to optimize their sizing? Where to place them? What degree of conservatism for the robust solution?

Figure 2 :

 2 Figure 2: Routes of the model's four caregivers.

Figure 3 :

 3 Figure 3: Start of the schedule determined by Zhang et al. (2021).

Figure 4 :

 4 Figure 4: Simplified simulation model process flow.

Figure 6 :

 6 Figure 6: Effect of each factor on performance measures.

Figure 7 :

 7 Figure 7: Execution of the schedule for scenario S60_T00_C00.

Table 1 :

 1 Levels and ranges for each source of disturbance.

	Source of disturbance	Ø	Low	Levels and ranges Medium	High
	Start time delay	Deterministic	Uniform(0:10)	Uniform(0:30)	Uniform(0:60)
	Travel time

Table 2 :

 2 Results data of late arrivals and means calculation.

	Late arrivals	Deterministic	Travel time factor Uniform(0.9:1.1) Uniform(0.7:1.3)	Uniform(0.5:1.5)	Mean
		Deterministic	4.00	4.06	5.12	5.86	4.76
	Service time factor	Uniform(0.9:1.1) Uniform(0.7:1.3) Uniform(0.5:1.5)	4.77 7.27 8.83	5.03 6.88 8.72	5.86 7.16 8.98	6.42 7.40 9.36	5.52 7.18 8.97
		Mean	6.22	6.17	6.78	7.26	6.61

Table 3 :

 3 Variance and F-value calculation for late arrivals.

	Source of variability	Sum of Squares (SS)	SS / SS(Total)	Degrees of freedom	Mean SS	F-value	𝑭 𝟗 𝟑 (𝟗𝟗%)
	Travel Service	3.19 42.06	7% 90%	3 3	1.06 14.02	7.19 94.92	6.99
	Residual	1.33	3%	9	0.15
	Total	46.58

  • Rescheduling caregivers' routes in real time based on disruptions. But what tools to use? Which indicators? What are the consequences for patients?

AUTHOR BIOGRAPHIES

GUILLAUME DESSEVRE is an postdoctoral researcher in the Industrial Engineering Center from IMT Mines Albi (France). He earned his PhD in the Department of Mathematics and Industrial Engineering at Polytechnique Montreal. His research interests include organizational engineering for health, stochastic simulation design and analysis, and optimization simulation. His e-mail address is guillaume.dessevre@mines-albi.fr.

LIWEN ZHANG is a research engineer at Berger-Levrault and an invited researcher in the Industrial Engineering Center at IMT Mines Albi. He holds a PhD degree in Industrial Engineering and Computer Science from IMT Mines Albi. His research interests include Combinatorial Optimization, Model-Driven Engineering, and Discrete-Event Simulation, applied to engineering application areas including Home Health Care systems, Computerized Maintenance Management Systems and Academic Scheduling and Routing. His e-mail address is liwen.zhang@berger-levrault.com.

CLEA MARTINEZ received the PhD degree in Industrial Engineering from Université Grenoble Alpes, France. She is currently working as an assistant professor at IMT Mines Albi, France. Her research interests lie in the areas of operations research, scheduling and optimization applied to healthcare systems. Her e-mail address is clea.martinez@mines-abi.fr. CHRISTOPHE BORTOLASO has a PhD in Computer Science, and he has contributed for more than 10 years to numerous research and software development projects in France and Canada, in various sectors such as defense, culture, energy, public and health. Now head of research in the industry at Berger-Levrault, he coordinates a team of researchers in multiple domains ranging from software engineering to human-machine interaction, to artificial intelligence and natural language processing. His e-mail address is christophe.bortolaso@berger-levrault.com.

FRANCK FONTANILI is an Associate Professor at the Industrial Engineering Department of the University of Toulouse IMT Mines Albi, France. His research activities focus on the use of the discrete event simulation-based digital twin in industry 4.0, the supply chain and healthcare fields. The aim of his research work is to help in the design, analysis, diagnosis and improvement of organizations. He has performed several industrial studies and research projects using discrete event simulation and associated tools such as BPM, Real-Time Location Systems, Process and Data Mining. His e-mail address is franck.fontanili@mines-albi.fr.


Audrey Hault-Dubrulle
email: audrey.hault@univ-valenciennes.fr

Frederic Robache
email: frederic.robache@univ-valenciennes.fr

Marie-Pierre Pacaux
email: marie-pierre.lemoine@univ-valenciennes.fr

Herve Morvan
email: herve.morvan@univ-valenciennes.fr

Determination of pre-impact occupant postures and analysis of consequences on injury outcome. Part I: A driving simulator study

Keywords:

This paper considers pre-impact vehicle maneuvers and analyzes the resulting driver motion from their comfort seating position. Part I of this work consists of analyzing the driver behavior during a crash. The study is conducted using the LAMIH driving simulator and involves 76 participants. The emergency situation is created by a truck emerging from behind a tractor on the opposite side of the road and tearing along the participant. The driver positioning throughout the simulation is recorded via five video cameras allowing view of the front scene, the driver face, feet and pedals, hands on the steering wheel and global lateral view. Data related to braking force, seat pressure, muscular activity for major groups of muscles and actions on the steering wheel are also collected.

The typical response to this type of emergency event is to brace rearward into the seat and to straighten the arms against the steering wheel, or, to swerve to attempt to avoid the impacting vehicle. While turning the steering wheel, the forearm can be directly positioned on the airbag module at time of crash which represents a potential injurious situation.

These positions are used in Part II to determine scenario of positions for numerical simulation of a frontal collision.

Introduction

In order to assess restraint systems effectiveness, crash tests are performed with ATDs (Anthropometric Test Devices) positioned in a standardized seating posture. Nevertheless, it is widely accepted that vehicle occupants do not maintain exactly the same posture as crash ATDs during normal driving, nor under stressful conditions (vehicle pre-impact maneuvers, emergency braking). Consequently, their posture at the time of impact may significantly differ from those used for restraint system development and evaluation.

Since passenger cars have been widely equipped with airbags, a lot of organizations have reported on the airbag effectiveness for saving lives and reducing serious injuries in frontal crashes. How-ever, there is still a controversy about serious occupant injuries caused by airbag deployment, mainly attributed to the airbag interacting with the occupant in out-of-positions (OOP).

Common injury situations are encountered when drivers, who are fairly short, position themselves close to the steering wheel. During a crash, as a result of deceleration forces, they move even closer to the steering wheel and can be injured by the airbag punchout. Another common type of injury occurs when pre-impact braking places unbelted or improperly belted child near the airbag at the time of deployment, or, when a rear-facing child restraint system is installed on the front passenger seat [START_REF] Kamiji | Study of test procedure to evaluate airbag deployment force[END_REF].

In order to evaluate airbag deployment injuries, OOP have been tested. They correspond to extreme postures such as passengers with their feet on the dashboard, unbelted children in close contact with the deploying passenger airbag or unbelted short-stature females sitting very close to the steering wheel (chin on airbag module) [START_REF] Tylko | Static out-of-position test methodologies: identifying a realistic worst case for small stature female drivers[END_REF]. However, these cases are not fully representative of real world occupant postures.

Furthermore, until the 90s, restraint devices remained nonadaptive, and their functionality was limited to a fixed operation mode related to a fixed value of occupant anthropometry and collision characteristics. Nowadays, many new vehicles offer adaptive or 'smart' restraint systems. These smart restraint systems adjust the force applied to occupant according to information sent to the computer from sensors located for example in the seat belt retractors and front seats (Occupant Classification Systems (OCS)). Smart restraint systems, which account for occupant characteristics, require assessment of occupant state parameters, including both time-invariant properties like stature and mass as well as time-variant states such as the postural orientation and muscle bracing level.

Accident data provide good information on injuries sustained in specific cases, however it is rare that the pre-impact posture is known or can be determined.

Numerous studies demonstrated that driving simulators are effective tools for road safety research such as investigation on driving speeds [START_REF] Bella | Driving simulator for speed research on two-lane rural roads[END_REF], lateral positions [START_REF] Auberlet | The impact of perceptual treatments on lateral control: a study using fixed-base and motionbase driving simulators[END_REF][START_REF] Briand | Impact of perceptual treatments on driver's behavior: from the driving simulators studies to the field tests-first results[END_REF], and driving assistant systems [START_REF] Abe | The influence of alarm timing on braking response and driver trust in low speed driving[END_REF][START_REF] Chang | Driving performance assessment: effects of traffic accident location and alarm content[END_REF]. Driving simulators have several positive features such as efficiency, low expenses, safety, experimental control and ease of data collection. Previous simulation experiments on driver responses facing an imminent collision demonstrated that it is possible to provoke realistic avoidance behaviors [START_REF] Morvan | Pre-crash investigation using a driving simulator and numerical analyses to determine the influence of the arms positions[END_REF][START_REF] Van Schijndel-De Nooij | APROSYS: advances in secondary safety research[END_REF][START_REF] Couper | Driver dynamic response study, Report R4B of PRISM project[END_REF][START_REF] Morris | Occupant behaviour during pre-impact braking-car passengers, Report R4C of PRISM project[END_REF] and that driver behavior in a virtual driving situation is similar to a real one [START_REF] Perron | Active experiments with common drivers for the specification of active safety systems[END_REF][START_REF] Briand | Impact of perceptual treatments on driver's behavior: from the driving simulators studies to the field tests-first results[END_REF]. Thus, an alternative approach to identify pre-crash postural orientation of car occupants is to simulate crashes using a driving simulator.

The objective of this research is to analyze the driver position changes during an emergency situation and to investigate the pre-collision driver posture effects on injury outcome during a collision. The study is split in two parts. This first part reports a driving simulator study aiming at determining how drivers behave during pre-impact events. The second part reports numerical and experimental studies performed to estimate the effect of pre-crash occupant posture on injury outcome; it also proposes a technical solution to reduce driver injury risk in OOP situations.

This first part of the two-part paper begins with a short description of the LAMIH driving simulator and the presentation of the experimental protocol. Then, the results of the experimental drive are presented. Finally, the paper ends with a discussion about the postural changes from comfort driving in such a frontal collision and the determination of pre-crash postures for numerical simulation in Part II.

Driver dynamic response study

LAMIH driving simulator, SHERPA

The study was conducted using the driving simulator of the University of Valenciennes, SHERPA (French Acronym for 'Simulateur Hybride d'Etude et de Recherche de PSA Peugeot Citroen pour l'Automobile') (left-hand drive simulator vehicle and manual gear box) (Fig. 1a). It consists of an interactive motion-base driving simulator fitted with a whole Peugeot 206. The car is positioned in front of three angled projection surfaces. The central projection surface is located 3.3 m in front of the driver with two peripheral surfaces connected to the central surface at angles of 60 • . The entire projection image produces a 180 • horizontal × 45 • vertical front view of the simulated roadway from the driver position at a resolution of 1280 × 1024 pixels. The central rear view mirror and both wing mirrors are replaced with three small color LCD screens (with resolutions of 800 × 480 pixels). The image refreshment rate is 60 Hz.

The controls include the steering wheel, the manual gearbox and the pedals (brake, accelerator and clutch) of the original car. Accurate speed and engine data are displayed on the vehicle's dashboard. A force feedback steering wheel is used. The car is equipped with speakers mimicking engine, road tyre and passing traffic noises.

The SHERPA driving simulator uses a 6 degree-of-freedom hexapod motion system. The bump experienced in crash was simulated via this motion system.

Route and traffic scenario (simulation scenario)

Routes selected for this simulation included rural roads, villages, main roads and highways. Weather and lighting conditions were optimal.

The complete trial began with a 27-km portion on a highway with a 130 km/h speed limit, followed by a 5-km section on a state highway with a 90 km/h speed limit. A regular traffic flow was reproduced so that participants were incited to respect the Highway Code and to adapt their driving to the presence of other cars. Unpredictable events were produced to investigate participant driving behavior (human error, especially traffic rules violation) such as a vehicle cutting up the participant's car on the highway or a slow-driving vehicle on a 2-lane road separated by a white line.

Then the participant drove along a main road crossing a small village with a 50 km/h speed limit. Few meters after entering the village, a car emerged out of a junction on the right-hand side of the road and jumped the stop, thus surprising the participant. This situation was designed to remind participants that unpredictable events might happen at any time as in real life.

Finally, the experimental drive ended with a portion of a rural road and the simulated collision (Fig. 1b). The road was composed of two lanes separated by a white line. The collision occurred in a large bend. Trees along the curving road and an isolate farm concealed the long-rang visual information needed to predict the path of the road ahead and to anticipate future events. In the turn, a lane of trucks, a tractor followed by 2 trucks, appeared in the opposite lane. The truck just behind the tractor pulled out suddenly to overtake, such that the scenario could not be expected by the participant.

Trees along the road side and trucks on the opposite lane lessened the collision avoidance (Fig. 1b). To improve the realism, a real physical impact was added. At the time of the virtual crash, a large foam rubber block (Fig. 2) impacted the windscreen, a truck horn was emitted and the car body was jerked to simulate the bump experienced in a crash.

The foam rubber block was initially hidden in front of the vehicle, such that it could not be seen by the driver during the experiment. A mechanism fixed on the side of the vehicle produced the motion of the foam rubber block.

The route was 34.3 km long. The participants needed approximately 30 min to complete the scenario depending on the participant's speed.

The participants believed they were participating in a study in ergonomics so they could not predict the occurrence and the location of the collision. Each participant encountered one emergency traffic event during the experimental drive so they could not anticipate the simulated crash.

Experimental procedure

Participants firstly provided personal information-gender, age, and driving experience. They all read and signed an informed con-sent document. Experiment directions and safety rules regarding driving tasks and the simulator use were provided.

After a short training session designed for familiarization with the simulator, the true experiment was conducted. No specific requirements were made; participants were asked to drive as they would do in the same real world situation and to adapt their speed to the driving conditions.

At the end of the experimental drive, drivers were asked to fill in questionnaires evaluating their driving characteristics (behavior patterns), their reactions to each separate situation and the realism of the experiment.

Measurements

Camera set-up

The driver position was recorded throughout the experiment via five video cameras allowing views of the front scene, the driver face, feet and pedals, hands on the steering wheel and a global lateral view (Fig. 3).

Collected data

Data related to braking force, seat pressure and actions on the steering wheel were collected thanks to load cells (Fig. 4).

Data related to muscular activity were recorded for major groups of muscles of the upper and lower limbs (triceps brachii, biceps brachii, trapezius, wrist extensor, quadriceps, soleus muscle, tibialis anterior, ischio) and will be used later in modeling activities. * The participant obtained the driving license from some months.

The driver-vehicle-environment interaction parameters were measured, such as impact velocity, time of crash, steering wheel position, state of the pedals, gear lever position and vehicles' position on the road.

Volunteer data

Participants were students and staff at the University of Valenciennes and people recruited locally.

Participants were asked to own a valid driving license and to have a normal or corrected vision. No selection criteria were made in terms of gender, age, height or weight in the participant selection.

Two people already used the driving simulator before but not in a similar experiment.

Table 1 lists the participants' demographic and driving information.

The sample was composed of 20 women and 56 men, with and average age of 26.8 years (18-52, SD 7.3). Seventy of the participants were under 40 years old and only 6 participants were over 40. The participants owned their driving license from few months to 29 years. The yearly kilometer average reported by the participants was 12,910 km, ranging from 300 to 40,000 km (SD = 9748 km).

Physical data

For each participant, anthropometric data were measured in a calibrated space to allow a postural reconstruction method [START_REF] Hetier | A new approach for safety crash test: using a genetic algorithm[END_REF][START_REF] Hetier | Experimental investigation and modelling of driver's frontal pre-crash postural anticipation[END_REF]. Table 2 provides the height and weight statistic data for all participants and for women and men separately.

An anthropometric survey was conducted on 3252 French drivers (1587 females, 1665 males) by [START_REF] Rebiffé | Laboratoire de physiologie et biomécanique de l'association Peugeot Renault[END_REF]. The main results in height and weight are reported in Table 3 for men and women.

From these results, it can be seen that the participants selected for the current study were quite representative of the French driver population.

Results

Simulation realism

Subjective and objective data were collected to evaluate the realism of the experiment. Subjective data included both the driver's verbalizations and their answers to questions evaluating their driving behavior and their reactions. Objective data included the time needed to release the accelerator, to brake, to engage the clutch, to change gears, as well as the amplitude of the braking and swerving maneuvers provoked by the truck passing. Regarding the results, it can be supposed that most of the participants have reacted as they would have done in the real life.

General driving characteristics

All participants reacted to the traffic accident by actions on pedals and/or steering wheel. Six persons avoided the frontal crash but hit the truck laterally or collided with trees. General driving performances are presented in Table 4. The participants who avoided the frontal collision with the truck were not included in these statistical data. Men and women had the same performance, so no distinction was made according gender.

The average speed in town was calculated from the host vehicle speed at 50 m after the town enter panel and its speed at 50 m before the town exit panel.

The accelerator release time corresponded to the period between the overtaking event and the release of the accelerator. The braking reaction time was defined as the time period between the overtaking event and application of the brakes. The collision occurred on a main road segment. The average driving speed of the participant vehicle was 76.3 km/h. The speed seems realistic, considering the type of road, which was the beginning of a wide turn. This speed was quite steady until the truck appeared in the opposite lane (the truck was visible at 150 m). When the truck pulled out, most of participants braked. The average deceleration rate was 1.6 m/s 2 . The mean overlap of the vehicles during the impact was 61.8% and the angle between the truck and the host vehicle varied from -18.8 • to 5.1 • .

3.3. Force analysis: pre-event and event data.

The Fig. 4 indicates the position and the direction of force sensors.

The forces applied on the seat (cushion and back), the seat adjustment rail, the steering wheel and brake pedal were recorded for 26 drivers only, due to technical problems with the acquisition system. The evolution of these forces from pre-event to event data was analyzed.

Four periods are defined 1. Quiet period: As the collision occurs in a wide turn, the tractor and the trucks are not immediately visible. The trees along the curving road and an isolate farm conceal the visibility of the road ahead.

The quiet situation corresponds to the time period before the tractor and trucks are visible.

The mean forces during the quiet situation are computed at a time interval going from -50 s to -5 s before the time that the trucks are visible. The time interval is chosen such that forces are constant for all drivers during this period. 2. 150 m before crash period: The reference time for this period is chosen as the time at which the driver arrives at a distance of 150 m from the crash location. This corresponds globally to the onset of visibility of trucks (tractor followed by trucks) on the opposite lane. It depends on the driving speed of the occupant.

The mean forces for this period are computed at an interval of 1 s centered on the reference time. 3. Truck overtaking period: The truck overtaking onset time corresponds to the time the truck crossed the white line.

The mean forces for the truck overtaking period are computed on an interval of 1 s centered on the truck overtaking onset time. 4. Crash period: This is the time period of the collision (the vehicle hit the truck).

The extreme values of forces are computed on an interval of 1 s centered on the collision time.

At the end of the experiment, when the simulation was stopped, participants were asked to push the steering wheel with hands placed in a 10 and 2 o'clock position, pushed back the upper torso against the backseat and pushed the pedals with maximal voluntary forces (Table 5). The forces measured in the seat, the steering wheel and the pedals were denoted Ffull. The same experiment was reproduced but with pulling the steering wheel. The values of Ffull were used to normalize forces measured during experiment. If the driver applied an axial compressive load on the steering wheel during the crash, the Ffull efforts measured during pushing out were used to normalize the values. If the driver applied an axial traction on the steering wheel during the crash, the Ffull efforts measured during the pulling on were used to normalize the values. This normalization allows the comparison among driver efforts independently of their morphological variability.

The normalized forces on the seat (cushion and back), rail, steering wheel and brake pedal are illustrated in Figs. 5, 6 and 7, respectively.

Drivers realized that a crash was imminent when the truck crossed the white line. Until this moment, global positions of the drivers remained quite steady with some small perturbations due to the type of road; such that participants replacing their hands on the steering wheel at the beginning of the bend. Then, significant altering in postural orientation was observed at the moment of crash.

During the quiet situation, no force was applied on the brake pedal. At imminent collision, drivers braked suddenly. As a consequence of bracing and braking, the participants pushed the pelvis back into the seat and leant backward. Contact occurred between the seat back and the upper portion of the torso, around the shoulder area. An increase of seat back and rail seat forces and a decrease of seat cushion efforts were induced. Only one person pushed down in the cushion seat (increase of cushion seat force). Participants also strengthened arms and legs. Consequently, increased forces on the steering wheel and brake pedals were induced. Some people developed forces during crash over the maximum voluntary efforts. This can be explained by the fact that Ffull efforts are sustained efforts while driving efforts during crash are instantaneous efforts.

Postures: comfort posture to pre-crash posture

Videos were analyzed for the seventy participants who did not avoid the frontal collision. Results suggest that most of drivers had sufficient reaction time to anticipate the imminent collision that led to significant altering in postural orientation.

The typical response to this type of emergency event (frontal collision with a truck) was to brace rearward into the seat and to straighten the arms against the steering wheel and/or the gear lever, or, to turn the steering wheel to swerve around the vehicle.

Three positions during crash are highlighted in this part of this study illustrating video observations .

In Fig. 8, the bracing driver in pre-impact situation tended to extend elbow and knee joints, and consequently pushed the pelvis back into the seat and lean backward. A considerable straightening of the arms was observed but the elbows remained bent at approximately 90 • . This position accounted for 52.86% of participants.

In Fig. 9, the participant drove with the two hands on the steering wheel at the beginning of the turn. During the emergency event, he moved much further away and put his right hand on the gear lever. Considerable straightening of arms was observed. This position at impact was observed for 35.71% of participants.

In Fig. 10, the participant braced and gave a sharp turn of wheel to try to swerve around the truck during emergency event. This position was highlighted since in this configuration the forearm was placed in front of the steering wheel.

A particular attention is paid to arm and hand position on the steering wheel since airbags can inflict injuries when upper extremities are close to the air bag module at the time of impact [START_REF] Huelke | Upper extremity injuries related to airbag deployments[END_REF][START_REF] Marco | Bilateral Smith fracture of the radius caused by airbag deployment[END_REF].

Hand and arm positions

Videos were analyzed to establish drivers' hand location at the time of impact. Standard clock face nomenclature was used to describe the positions.

At the beginning of the experimental drive, participants adopted a 10 and 2 o'clock position or 9 and 3 o'clock position. Comfort positions were observed after only 20 min. For the left arm, participants often rested their arm by leaning their elbow on the window sill or the forearm on their thigh. For the right arm, drivers often rested their arm by laying their right hand on the gear lever or the forearm on their thigh. Participants regularly came through one comfort position to another one. Then, when drivers realized a crash was imminent, they modified their posture.

First, both hands were examined together. At the point of impact, the most common position (Table 6) for the drivers was to have both hands on the steering wheel (52.86%). The next common position for the driver was to have the left hand on the steering wheel and the right hand on the gear lever (35.71%). Five participants (7.14%) had the left hand on the steering wheel and the right hand off the wheel. This mainly corresponded to drivers that brought their right hand down from the steering wheel or thigh to the gear lever. Unusual cases were driver with the left hand on the wheel and the right hand on the handbrake or the thigh, and driver with the left hand off and the right hand on the wheel. Prior to impact, 100% of the participants braked and 54.26% declutched. This can be related with the fact that 35.7% of the participants had their right hand on the gear lever. Indeed, a strong braking is often associated with declutching.

Then, each hand position was examined separately. The distribution of hands' positions on the steering wheel is presented in Fig. 11.

In 17.2% of cases, the left hand was in a 1-5 o'clock position. For 2.8% of cases, the right hand was in a 10 or 11 o'clock position. These cases were due to participants giving a sharp turn of wheel in an attempt to swerve around the truck. The forearm or the hand was then in close proximity to the airbag module and was likely to sustain injuries during the airbag deployment.

Furthermore, the results showed that 21.4% of participants had their left hand in a 10 o'clock position, 11.4% had their right hand at 2 o'clock, but only 7.14% of participants were in a 10 and 2 o'clock position as the standardized hand posture of ATD in a frontal impact.

Conclusions and discussion

Changes in driver posture were determined during a simulated frontal collision on the LAMIH car driving simulator. It integrated a real vehicle (Peugeot 206, left-hand drive simulator vehicle and manual gear box); a 6 degree-of-freedom hexapod motion platform that generated motion experienced under normal acceleration, braking and steering; accelerator pedal, brake pedal and steering wheel with force feedback; a virtual reality-based visual and audio system.

The main conclusions from this study can be summarized as follows:

-An unavoidable crash was reproduced to provide insight on driver postural orientations during emergency vehicle maneuvers. The realism of the simulator study was verified to ensure the validity of the results for a frontal collision. Results from videos suggested that most drivers had sufficient reaction time to anticipate the imminent collision that led to significant altering in postural orientation.

-The typical response to this emergency event (frontal collision with a truck) was to brace rearward into the seat and to straighten the arms against the steering wheel and/or the gear lever, or, to turn the steering wheel to attempt to avoid the impacting vehicle. -Giving sharp turn of wheel led 20% of the participants to have one arm in front of the steering wheel at the time of crash. Since airbags are usually mounted in the hub, this may represent a rather risky position.

Based on these conclusions, an OOP is identified from this car driving simulator study based on incidence and potential severity. This OOP corresponds to a driver seating with the left arm in front of the steering wheel. Numerical simulations and experiments are then performed to investigate the influence of this identified driver pre-collision posture on injury outcomes. This is the object of the second part of this article.

However, a limitation of the study is that the participants are relatively young. While older drivers have become a larger part of the driving population and will continue to do so as the baby boomers reach retirement age [START_REF] Lyman | Older driver involvements in police reported crashes and fatal crashes: trends and projections[END_REF], the findings of the study cannot be applied to older drivers who may have slower reactions.

Fig. 1 .

 1 Fig. 1. (a) Dynamic driving simulator. (b) Scenario of the virtual crash.

Fig. 2 .

 2 Fig. 2. Impacting foam.

Fig. 3 .

 3 Fig. 3. Interiors views of video recording during the crash.

Fig. 4 .

 4 Fig. 4. Sensor positions.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Evolution of seat efforts for participants until crash. (a) Backseat and (b) cushion seat.

Fig. 7 .

 7 Fig. 7. Evolution of efforts for participants until crash. (a) steering wheel (compression) and (b) brake.

Fig. 8 .

 8 Fig. 8. Normal position to moving further, straightening arms.

Fig. 9 .

 9 Fig. 9. Normal position to moving further, touching gear lever.

Fig. 10 .

 10 Fig. 10. Normal position to moving further, steering.

Fig. 11 .

 11 Fig. 11. Percentage of participants' left and right hand positions on steering wheel.

Table 1

 1 Characteristics of participants.

		Driving simulator study
	Sample of participants	76
	Women	20
	Men	56
	Age (range)	18-52 years
	Average Age (standard deviation (SD))	26.8 (7.3)
	Driving experience (range) (years)	0

* -29 years Average kilometers driven per year (SD) 12,910 (9748) Kilometers driven per year 300-40,000

Table 3

 3 Height and weight of French drivers from[START_REF] Rebiffé | Laboratoire de physiologie et biomécanique de l'association Peugeot Renault[END_REF] study.

		Weight		Height
		Men	Women	Men	Women
	Mean	74.1	59.5	171.6	160.2
	Standard deviation	11.0	10.0	6.8	6.1
	5th percentile	58.2	46.5	160.7	150.7
	50th percentile	73.2	58.0	171.9	160.4
	95th percentile	94.6	78.0	183.0	170.5

Table 2

 2 Height and weight of simulator study participants (distinction men and women).

		Weight (kg)			Height (cm)
		All	Men	Women	All	Men	Women
	Maximum	122	122	100	190	190	176
	Minimum	46	49	46	156	158	156
	Mean	74	76.3	67.5	175.1	178.1	166.5
	Standard deviation	14.1	12.8	15.7	8.3	6.8	5.7
	5th percentile	52	55	46	160	168	156
	50th percentile	72.5	73	62	175	179	166
	95th percentile	99	96	92	188	188	175

Table 5

 5 Maximum voluntary efforts.

		Mean	Min	Max	SD
	Seat back	-811.90	-407.00	-1428.50	259.10
	Cushion seat	-509.85	-334.18	-834.41	104.46
	Rail seat	520.37	279.75	752.53	121.98
	Steering wheel	-175.34	-36.38	-561.14	152.16
	Brake pedal	529.03	207.47	979.63	241.55

Table 6

 6 Hand positions at the time of impact.

	Positions	Left hand	Right hand	%
	1	On the steering wheel	On the steering wheel	52.86
	2	On the steering wheel	On the gear lever	35.71
	3	On the steering wheel	Off a	7.14
	4	On the steering wheel	On the handbrake	1.43
	5	On the steering wheel	On lap	1.43
	6	Off	On the steering wheel	1.43

a For example when the participant tries to take the gearshift.

Acknowledgements

The present research work has been supported by International Campus on Safety and Intermodality in Transportation, the Nord-Pas-de-Calais Region, the European Community, the Regional Delegation for Research and Technology, the Ministry of Higher Education and Research, the National Center for Scientific Research, the Zodiac Automotive Company in France and the company IsI Automotive in Austria supplying us the cold gas inflator.

The authors gratefully acknowledge the support of these institutions.

The authors would like to thank all the members involved this work, and in particular Denis Lesueur, Rémi Delille and Hervé guillemot, for their hard work and continuing support.

Positions and opinions advanced in this paper are those of the authors and not necessarily their sponsors. The authors are solely responsible for the content of the paper.


domain: sde chim sdv

text:
Maëva Marimoutou
email: maeva.marimoutou@univ-pau.fr

Gilles Bareille

Mathieu Milhe-Poutingon

Patrick Baldoni-Andrey

Amiel Boullemant

Cecile Courreges

Clémentine Gelber

Sandra Mounicou

Hélène Tabouret

Séverine Le Faucheur

C Courrèges

Evaluation of the use of gastropod shells as bioindicators of metal contamination in rivers using mass spectrometry imaging techniques

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

Gasteropods are known to be sensitive to metal contamination and to have several characteristics to be a good bioindicator such as sessile, easy to collect and ubiquitous [START_REF] Amorim | Lymnaea stagnalis as a freshwater model invertebrate for ecotoxicological studies[END_REF][START_REF] Krupnova | Gastropods as potential biomonitors of contamination caused by heavy metals in South Ural lakes, Russia[END_REF]Rainbow, 2002). Up to now, most studies have focused on bivalves and the analysis of total metal concentrations in their soft bodies. Very few have explored their distribution or accumulation in shells. Mollusc shells grow throughout their life by integrating some of the chemical elements present in their environment, including metals. The objectives of this work are: 1) Assess the spatial distribution of metals within the shell using mass spectrometry imaging techniques 2) Determine how shell concentrations respond to metal chemistry in the environment For this purpose, mass spectrometry imaging techniques are currently optimized to explore the variability of metals in shells at different spatial scales: Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMSnanoscale) and Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICPMS -micrometer scale). Both methods are sensitive and provide the elemental (LA-ICP-MS) and molecular (TOF-SIMS) characterization of solids samples (Massonnet & Heeren, 2019;[START_REF] Russo | Laser ablation in analytical chemistry -a review. Massonnet P & Heeren RMA (2019) A concise tutorial review of TOF-SIMS based molecular and cellular imaging[END_REF].

For this purpose, 12 natives Radix balthica were collected in spring 2021 at different sites.

1 ) Pilots rivers (outdoor mesocosms) of TotalEnergies (Lacq, France) : water from the Gave de Pau (control).

2 ) Waste Water Treatment Plant (in the effluent, up-and downstream)

At each site, water was sampled (n=3) to be analyzed for their dissolved metal concentrations by ICP-MS, cations, anions and dissolved organic carbon . Also the physicochemical (pH,O 2, conductivity) were collected with a sensor HACH HQ40D.

Shell analysis (n=3 for each site and analysis)

Separation Ø Similar Pb concentration were found in the soft tissues of R. balthica collected at the 4 sampling sites ØNi concentrations were higher in WWTP upstream than at the other 3 studied sites ØComparable concentrations in soft tissues for both metals Ø Ni concentrations in shells were similar among studied sites ØPb concentrations were higher at the upstream site and effluent than at the PR and downstream site ØAt all studied sites, higher Ni concentrations than Pb in shells

MATERIALS AND METHODS INTRODUCTION

Internal surface

External surface

Figure 2 .

 2 Figure 2. Picture of the ablation of the shell after analysis (A) and imaging obtained by ImageJ for Ni and Pb distribution in the last growth streaks of shell by count per second (cps) at the different studied sites of WWTP (upstream (B), effluent (C), downstream (D)) analysed by LA-ICP-MS

Figure 1 .

 1 Figure 1. Metal concentrations in water, soft bodies and shells at the different studied sites : pilots rivers (PR) and at WWTP (upstream, effluent, downstream) analysed by ICP-MS.

Figure 3 .

 3 Figure3. Microstructure of shell mollusc composed of three layers from external to internal : periostracum, prismatic and nacre layer[START_REF] Checa | Physical and Biological Determinants of the Fabrication of Molluscan Shell Microstructures[END_REF]

Table 1 .

 1 Characteristics of shell analysed by LA-ICP-MS

	208 Pb

ACKNOWLEDGEMENT

We are grateful to Iktus for allowing us to collect organisms on their site. Stellia Sebihi helped with field preparation and sampling. Mathieu Milhe-Poutingon provided his precious helped with ICP-MS analysis.