Chevallier Baptiste
email: baptiste.chevallier@utc.fr

Istrate Dan

Zalc Vincent

Vera Nicolas

Labrousse Christophe

Physiological data recording in VR simulator for sleepiness detection during driving

Keywords: Augmented reality, Heart Rate Variability, PPG, EEG, signal preprocessing

Drowsy driving is a major issue in road safety. In this paper, we propose a description of an experimental data collection to develop a drowsiness detection model. The objective of this data collection was mainly to gather physiological data of individuals in simulated driving situations. We designed a realistically annoying scenario to induce fatigue while staying close to real driving conditions. The experiment was run on an augmented reality platform called CAVE. The need for contextualization came early in the design of the experiment. Therefore, in addition to physiological data, we added much more data sources, from driving habits to driving behaviour in addition to self-assessment of fatigue levels and the gold standard (EEG). As a result, this experience helped us create a data set of physiological data completed by elements of context and driving behaviour. Thus allowing us to perform a very rich analysis of these physiological data.

INTRODUCTION

Drowsy driving is one of the deadliest causes of accidents [START_REF] Board | Evaluation of us department of transportation efforts in the 1990s to address operator fatigue[END_REF]). Yet it is really difficult to estimate the part of drowsiness among other causes of accidents because fatigue isn't easy to measure after an accident. While drug use can be measured in blood, speeding can be evaluated from structure deformation but the equivalent analysis is impossible with drowsiness.

Therefore, industrial [START_REF] Friedrichs | Drowsiness monitoring by steering and lane data based features under real driving conditions[END_REF]) and political (EuropeanCommission, 2021) actors are actively trying to find solutions to detect drowsiness and alert drivers while he is still awake. From a broader perspective, monitoring driver attention on the driving task will be a major challenge for future vehicles. Autonomous driving cars is a very popular topic and major car companies are trying to make this a reality. For the next generation of vehicles to come, the autonomous level will be at 3, which means the driver isn't required to keep his hand on the wheel but should be able to take back control at any time. Therefore drowsiness and attention monitoring will be key, as the car should ensure the driver will be able to take that control back.

Our vehicles are becoming more of computers on wheels. They are full of sensors gathering data on the road, on the driver, or on the weather. Our approach is to replicate the type of information available in a modern car and use the combination of this data to detect drowsiness. In this study, we tried to gather data used in a multitude of systems. We record driving behaviour-related data, video of the face, and physiological signals, thus covering the three main solutions developed to detect drowsy driving.

Doing that we set two important constraints for our experiment. First, it should be immersive for the subject. Being able to offer a driving environment closer to reality will help to record more relevant data as the subject will have close-to-reality reactions. The second, constraint is to limit the invasiveness of sensors. We thought that sensors used in the experiment should be able to be used in real driving situations by everyone. This is why we chose small Bluetooth sensors which didn't interfere with the subject driving actions.

In this paper, we will describe the used hardware and explain how we set up the experimental scenario. We will then go through all the collected data and how we processed them in order to create a clean and rich database. We will also give the results of our first analysis. The experiment took place in France, in order to record data from subjects we have obtained an agreement with the ethical research committee of Sorbonne University (CER-SU) on protocol n°CER-2021-018.

RELATED WORK

Many studies have been conducted to develop drowsiness detection systems [START_REF] Sahayadhas | Detecting driver drowsiness based on sensors: a review[END_REF]. We can divide them into three major categories.

The first category is the analysis of driving behaviour using vehicle information like steering wheel angle or lane departure detection. Datasets have been recorded by car manufacturers in real driving conditions [START_REF] Friedrichs | Drowsiness monitoring by steering and lane data based features under real driving conditions[END_REF] but most commonly in simulated conditions like [START_REF] Chai | Drowsiness monitoring based on steering wheel status[END_REF]. Using the first approach you aim to develop a system that can easily be embedded in a vehicle. The latest approach aims to gather the maximum data possible to find out which are the most important signals. Models have been developed to anticipate behaviour that might be dangerous on the road such as [START_REF] Kim | Prediction of driver's intention of lane change by augmenting sensor information using machine learning techniques[END_REF] work. Other models use this information to provide personalised help to the driver [START_REF] Hori | Driver confusion status detection using recurrent neural networks[END_REF].

The second category uses cameras to analyse driver faces, especially eye closure or blinking like in [START_REF] Mckinley | Evaluation of eye metrics as a detector of fatigue[END_REF] and [START_REF] Abe | Detecting deteriorated vigilance using percentage of eyelid closure time during behavioral maintenance of wakefulness tests[END_REF]. The latest approaches in this domain use deep learning methods to process images and show good results in both detection and anticipation of drowsy events [START_REF] De Naurois | Detection and prediction of driver drowsiness using artificial neural network models[END_REF] The third approach is based on physiological signal analysis. It may be based on Electroencephalogram (EEG) and Electrooculogram (EOG) but these approaches are tough to use on real driving conditions due to vehicle vibration, static electricity and limited embeddability of devices. Cardiac signals like Electrocardiogram (ECG) and Photoplethysmoraphy (PPG) also seem to carry enough information and are easier to implement in real cars with more consumerfriendly sensors. Additionally, PPG provide an easy set-up and a non-intrusive driving experience compared with EEG and EOG.

Paper Contribution :

In this paper, we present a multi-source dataset for drowsiness detection. Our approach aims to bring simulated driving experiments to a new level, not by using cutting-edge technologies but through sensors and signals that can realistically be measured in real driving conditions for direct use in ecological conditions.

DATA COLLECTION PROCESS

Inclusion phase

According to ethical criteria and constraints related to the study, subjects were exclusively recruited within Université de Technologie de Compiègne (UTC). They were either students, professors, researchers or members of the administration that were contacted thanks to internal weekly communication. Subjects were invited to read the description of the experiment and answer a few questions about themselves. This questionnaire helps us to filter subjects on driving experience, gender and age in order to ensure diversity within our database. We also make sure no subjects were taking any medication or drug which could possibly modify heart rate or heart rate variability.

Lastly, since the experimentation would take place in front of a screen we also asked them about their tendency to feel motion sickness. If selected, subjects were then contacted to schedule an experiment time.

Participants

97 participants volunteered to participate in our study. 4 were rejected due to inclusion criteria. 33 were selected from the remaining, the other were put on a waiting list.

Simulation platform

The experiment took place in a Cave Automatic Virtual Environement (CAVE). CAVEs are augmented reality platforms where a subject is surrounded by glass panels [START_REF] Cruz-Neira | Surround-screen projection-based virtual reality: the design and implementation of the cave[END_REF]. The virtual environment is projected through these panels thanks to projectors placed outside the cube. Subjects can move freely within the cube while being surrounded by the virtually created environment. In this specific experiment, we placed a seat with a wheel and pedals, thus reproducing the usual driving commands. The projected environment reproduced the point of view from the driver's seat of a car, showing the car structure, infotainment system and the road through the windscreen.

Sensors

For data collection, we used sensors available on the shelf. Three devices were selected to study their ability to provide a good signal in driving situations. These devices measured three signals: Heart Rate Variability (HRV) with ECG, HRV with PPG and EEG. EEG is recorded using Dreem headband [START_REF] Arnal | The dreem headband as an alternative to polysomnography for eeg signal acquisition and sleep staging[END_REF]. This headband was developed to analyse sleep quality for daily usage. It is, therefore, a very light and easy-to-wear sensor. It records a 6 channel EEG at 250Hz. The device shape and electrode placement are described in figure 2. We used two different techniques to measure HRV. The first sensor is an elastic band with electrodes attached to it with the ability to communicate via Bluetooth. The interval identification technique is based on ECG and consists of the identification of the R peak in QRS complexes, to then measure the time between two peaks. The identification is performed directly on the device. We used Cardiosport TP5 Heart Rate Monitor (Cardiosport, 2022) to perform that measure. This device has an integrated Bluetooth processor that can send data in live conditions. The second technique uses PPG to measure the time between two blood waves by analysing the opacity of the veins [START_REF] Allen | Photoplethysmography and its application in clinical physiological measurement[END_REF]. We used Garmin Venu SQ (Garmin, 2022) which is a smartwatch made to be used all day long with light and comfortable materials. This device connects to a mobile application to send live HRV data.

Simulation scenario

The simulation scenario proposed to all subjects was identical. It consists of a fifty kilometres left-hand loop starting in an urban zone, then going through a forest with varying tree density. Along the road, various left and right turns were created to reduce the feeling of going in circles. Subjects were alone on their side of the road to avoid unwanted collisions with other cars that may force the simulation to stop too early. On the other side of the road, groups of cars were placed to improve the immersion and reduce the emptiness of the environment. Subjects were asked to drive when possible with cruise control activated and set at 100km/h. They had a button on the steering wheel specifically dedicated to that function. Two events were added to the scenario to measure the subject's reaction in drowsy conditions. A previous study proved this approach to be efficient to induce and measure stress [START_REF] Zontone | Supervised Learning Techniques for Stress Detection in Car Drivers[END_REF]. The first event was placed after fifteen minutes of driving. We choose this moment as we observed in precedent measures that drivers tend to have their first drowsy event after 15 min on task. The event is composed of a set of trucks and lights, simulating road work on the right side, forcing the driver to change lanes to avoid the collision. The second event is an animal crossing the road. With no lights and no previous indications, this object is harder to anticipate and requires much more attention. It's placed after 45 minutes of experience in the middle of a straight line, which is the most annoying section of the circuit.

For the simulated environment, we choose to simulate clear weather at night just before dusk so that rain doesn't impact the experiment.

Experimental protocol

Here is how a standard measure goes :

1. Welcome the subject on the platform.

2. Ask the subject to fill in a questionnaire on his sleeping habits.

3. Start and install physiological sensors on the subject.

4. Install the subject in the CAVE.

5. Start a training loop until the subject feels at ease with the commands.

6. Last briefing on what is expected from the subject during the experiment.

7. Auto-evaluation formation, explain what is expected from them in order to record KSS.

8. Synchronisation of all signals.

9. Driving can start.

10. After completing the two loops, the driving stops.

11. Subject is invited to leave the CAVE 12. Subject is asked to fill in the last questionnaire on his feeling during the experiment.

13. Sensors are removed.

14. End of the measure.

A simplified and schematic version of the protocol is represented in Figure 3.

For the synchronisation part, we asked subjects to hold their hand in front of the camera, blocking the view, while turning the steering wheel on the right. Meanwhile, the operator was on the computer doing a countdown from 3 to 0. At 0, the subject releases the steering wheel and unblocks the camera view, and the operator presses the starting key at the same time. Software developed for the experiment record the timestamp of the key press.

In order to ensure synchronisation between systems that could have a small variation in clock we used UNIX timestamps from a remote server on every device.

As a result, we have a hand movement on the camera, a common timestamp between the computer and smartphone combined with a peak in simulator signal due to steering at the same time. This is our synchronisation point.

Personal context

During the inclusion process and before the experiment, subjects were asked to answer a few questions about themselves. There were two main subjects covered by these questions, the first one being drivings habits and the second one being sleep health.

We selected only people that obtained their driving license at least one year ago and who are driving frequently since. We asked subjects more precise questions about their driving habits regarding long and night trips when drowsiness is more likely to appear. Regarding the sleep health topic, we asked subjects to describe their sleep quality, and how many hours of sleep they had the days before.

These data will help to detect trends amongst the measured population. The first analysis shows that experienced drivers, which often drive for a long time are less affected by the simulation. It's also really useful to analyse the correlation between the sleepiness of a subject and the length of his previous nights.

Physiological data

Physiological sensor record two different types of information. Firstly we have EEG signals measured on eight channels with a sample rate of 250Hz. EEG is the gold standard signal in sleep scoring. This signal will be used for data annotation and analysis.

Secondly, we have two sensors gathering heartrelated data. More specifically, these sensors measure beat-to-beat intervals.

The frequency of these data is variable as both these sensors send new data every time they detect a new beat. This data will later be used to develop a classification model.

Driving behaviour

The simulation software is able to record many signals while the simulation progresses. We choose to filter signals that were relevant to our simulation scenario, as well as signals that proved their importance in the literature.

The set of signals is composed of :

• Position of the Centre Of Gravity (COG) of the vehicle on the map.

• Speed of the COG of the vehicle.

• Acceleration of the COG of the vehicle.

• Wheel angle and rotation speed.

• Pressure on the brake and acceleration pedals.

• Activation state of cruise control.

• Distance between COG centre of the nearest lane.

These signals were recorded with a sampling frequency of 100 Hz.

Auto-Evaluation

Fatigue is a continuous state which isn't perceived the same by everyone. It is a physiological reality but also a personal feeling. Depending on whether we feel physical fatigue or psychological fatigue, our perception of our fatigue level is quite different and can greatly vary. To normalise the definition of drowsiness levels, a scale going from 1 (Very Alert) to 9 (Very sleepy) has been determined and is used in a vast majority of studies [START_REF] Kaida | Validation of the karolinska sleepiness scale against performance and eeg variables[END_REF] and is also the reference scale for European Union (EU).

Therefore we implemented the assessment of this scale in the experiment. As for the technical solutions we chose to ask the participants to press a numerical key on a Numpad every five minutes. This gap was selected according to EU technical requirements on Karolinska Sleepiness Scale (KSS) rating protocol (EuropeanCommission, 2021).

However, note that measuring drowsiness with this scale has many flaws. First of all, it requires the subject to make a cognitive effort in order to answer the question. While the scale is not overly complex it still requires some time to adapt and understand how to correctly rate ourselves. That is why a great part of the briefing is focused on explaining KSS. Secondly, this auto-evaluation is, in essence, subjective. People tend to over and/or under-estimate their drowsiness level all the time. Therefore auto-evaluation has a bad impact on the experiment and we have to take the result with care, taking into account potential bias.

Labelling data

Labelling our dataset is a key part of our study since we aim to use it for supervised machine-learning applications. The objective is to develop a system which is able to detect drowsiness states in opposition to awake states. It is a binary classification problem.

We can use three different pieces of information to label data :

1. EEG : EEG is a gold standard signal used, in combination with EOG and ECG, for sleep scoring method by sleep specialists. This method consists on the analysis of 30 seconds segments of signal and the association of a tag : sleep or no-sleep. This tagging method requires a qualified set of professional reviewers. While being the most precise on sleep detection, this method isn't as efficient to detect rapid drowsy event. That is a major issue, because while driving subject won't fall completely asleep. Their drowsy events will more likely be short moments of absence which aren't easily recognisable on polysomnographic records.

KSS :

KSS gives a subjective assessment of a fatigue level. While this scale has 9 levels we can divide them in two categories : 1 to 7 for awake and 7 to 9 for drowsy. However using this information directly as a training target can have many flaws. As it is a subjective information we can't be sure if the level associated with the situation really corresponds to the true definition of the level. Also, we can't normalise levels among participants as an eight for someone can mean a six for another.

Video :

Lastly, we can use the video of the face and the point of view of the driver to identify drowsy behaviour and driving mistakes caused by drowsiness. The method first consists of the definition and the selection of a list of observable events that may be interesting to annotate. The list has been defined by studying literature and observing subjects in driving simulators. The result is a list of seven events which are: Yawning, Change of position, Long blink, Face/Neck scratch, Loss of Control, Accident and Sleep. The next step is reviewing conjointly both of the videos and select-ing tags as they occur during the measure. The reviewing process is done by two different people. Then a third one validates every event. This process ensures no events can be missed and no event can be falsely tagged.

Dataset

The final dataset content is summarised in table 1. It is composed of three synchronised physiological signals as well as nineteen behaviour-related signals, an autoassessment drowsy scale based on KSS, a video feed of the face of the driver and a video feed of the point of view of the driver, lastly it is composed of personal and driving habits data on the subject.

Each signal can be used for direct interpretation, annotation or classification purposes. Some examples are presented in this table but the possible applications are not limited to this.

PRELIMINARY ANALYSIS

In this section, we will perform a preliminary analysis of our data. As our objective was to record drowsiness we should ensure that we have sufficient drowsy drivers and drowsy events. Since we determined different methods of annotation the proportion of drowsy drivers may slightly vary from one to another. The proportions are pictured in figure 4. In these graphics, Heavy fatigue corresponds to either KSS > 6 or a video tag of clear loss of control. Light fatigue is for 7 > KSS > 4 or a video tag of early external signs of fatigue. No fatigue is for 5 > KSS and no video tags. From this figure, we can conclude that these methods give significantly different results. Subjects tended to overestimate their fatigue level and were globally able to drive even though they graded their drowsy state as > 6. We can also conclude we have been able to record a significant amount of fatigue events considering subjects were not sleep deprived.

Driving behaviour

Early analysis of behaviour signals extracted from the simulator show which one will be the most important. We observed three principal features that were particularly affected during drowsy events, namely: Distance to the middle of the road, angle of the wheel, and rotation speed of the wheel. Figure 5 shows an example of these signals. In this graphic, we can see three seconds where there was no wheel activity while the car was going away from the centre of the lane. Then the driver starts a trajectory correction to replace the vehicle closer to the centre.

If we look at the maximum values reached during drowsy and standard measures, we can see a drowsy driver going far away from the centre line and having spike activation of the wheel more critical than the average driver (Table 2).

With these features from behavioural signals, we can characterise the difference in behaviour between two populations. The subsequent development would improve these parameters and test their relevance in a machine-learning model.

Physiological signal processing

The first physiological data processing shows a great quality difference between our sensors. For example, with the PPG watch, we have an average recording time of 3646 seconds (standard deviation of 100 s), while the ECG belt has 2927 seconds average with a standard deviation of 1396 s.

We discovered the Bluetooth connection between the belt and the computer failed many times, thus creating very short records for some subjects. Thankfully this behaviour only impacted six people.

Signal

Drowsy Awake

Distance from lane centre (m) (MAX then AVG on population) 6.2 2.5 Wheel rotation speed (rad.s -1 ) (MAX then AVG on population) 8.8 6.7

Table 2: Difference between a drowsy and awake driver on some signals

POTENTIAL LIMITATIONS

During this experiment and while we performed our first analysis, we noted some limitations of our work that should be disclaimed. However, the limitations aren't limited to the ones listed after that.

Even if finding differentiating characteristics to identify events is essential for the analysis, we can't be sure these characteristics can be generalised. Our model should apply to many people and shouldn't be helpful only for one type of driver.

Also, it is difficult to evaluate how different the subject's physiological state would be in actual driving conditions. Therefore, the principal solution would be to record even more subjects to get the most heterogeneous data set possible, thus covering the most physiological responses imaginable.

Finally, the quantity of data is critical when developing a machine-learning algorithm. While having a lot of drowsy events, this data set remains quite unbalanced between awake and fatigued states. Different techniques can be used to answer that issue, like data augmentation.

CONCLUSIONS

In this research, we developed an experimental protocol to record the data from subjects in simulated driving conditions. Considering many previous studies, we added a large variety of sources. The objective was to induce fatigue by gathering the subject's states when they were about to fall asleep.

The experimental protocol has been validated with self-assessment and video annotation, which makes it reliable for machine learning developments. With one-third of people having at least one tired event during their measure, this data set presents enough positive events to be detected. In addition, the population measured is quite diverse in terms of age, gender, driving and sleep habits, making our data set a powerful resource for developing a model.

The data set could be used differently to study the correlation between physiological signals and drowsiness in a mono-modal or multi-modal approach. It could also be used to compare data sources between them, for example, comparing the signal from ECG band and Garmin smartwatch.

From the early analysis, we can find differentiating characteristics for some drowsy events. The following work will determine if a predictive drowsiness model can be developed on this database. This will be possible by finding ways to generalise the characteristics of our population. Developing features and implementing some based on the literature is also an extensively considered approach. Another perspective would be to use this protocol, which has proven to be efficient, on longer measures to gather more drowsy events.

Figure 1 :

 1 Figure 1: Subject being installed in the CAVE.

Figure 2 :

 2 Figure 2: Electrode placement for Dreem EEG sensor.

Figure 3 :

 3 Figure 3: Schematic experimental protocol

Figure 4 :

 4 Figure 4: Proportion of trips with drowsy drivers according to KSS (left) and video (right)

Figure 5 :

 5 Figure 5: Behaviour signals during drowsy events

Table 1 :

 1 Dataset content summary

ACKNOWLEDGEMENTS

The authors would like to thank all the subjects for their patience and time. Also, thanks to Heudyasic laboratory, which gave us the opportunity to use their platform and to develop the scenario as we wanted. More specifically authors would like to personally thank Mr Bouvet Yohan for his crucial help and commitment to the realisation of the study.

ETHICS DECLARATIONS

All volunteers gave their informed written consent following approval and in accordance with the CER-SU Review Board.


Olivier Pilmis

Escaping the Reality Test. How Macroeconomic Forecasters Deal With 'Errors' 1

The success of this saying makes it difficult to trace its precise origins.

4 Although tackling issues of legitimacy and critique, the expression 'reality test' does not, here, strictly match 'pragmatic' conceptions (Boltanski and Thévenot 1991, 40-42; Boltanski 2009, 103-107). 5 In order to underline that a statement will be here considered 'erroneous' with respect to how actors define it, the nouns 'error' and 'mistake', as well as the adjectives 'right', 'wrong' and so on will be kept in quotes throughout the chapter.

Introduction

'Why did no one see it coming?' H.M. Queen Elizabeth II reportedly asked during a visit to the London School of Economics in November 2008. 2 The question echoes the criticisms economic forecasters often face for not having 'anticipated' the emergence of a particular economic crisis. The 2008 subprime mortgage crisis and its aftermath were no exception and gave birth to an important literature that takes the inaccuracy of forecasts as its starting point. Springing from sociology [START_REF] Fligstein | Why the Federal Reserve Failed to See the Financial Crisis of 2008: The Role of 'Macroeconomics' as a Sense-Making and Cultural Frame[END_REF], economics [START_REF] Galbraith | The End of Normal. The Great Crisis and the Future of Growth[END_REF], popular science [START_REF] Orrell | Economyths. Ten Ways Economics Get It Wrong[END_REF] or the media [START_REF] Turin | Le bal des aveugles [The Ball of the Blind[END_REF], critical assessments of macroeconomic forecasters' records rejuvenate the well-known saying: 'economists are experts who know tomorrow why the things they predicted yesterday didn't happen today'. 3 N. N. Taleb's best-selling book The Black Swan goes further and calls 'predictions' a 'scandal' (Taleb 2007, 137-164).

Whatever their sources, criticisms of forecasting usually present a mirror image of praise for whistleblowing: economists and forecasters are blamed for being overly optimistic and consequently failing to warn of future crises. These criticisms endorse a systematic comparison between 'what actually happened' and 'what had been predicted' as the only 'reality test' 4 possible to warrant forecasts' accuracy and eventually pronounce them 'right' or 'wrong'. 5 Repeated experiences seem to have brought clear-cut evidence that predicting future economic reality is impossible. The mere existence of an activity such as forecasting therefore turns out to be puzzling: how do forecasters manage to fend off criticisms and persuade themselves and others of their own credibility and that of their activities?

This attention to the relationship between beliefs and practices on one hand, and 'reality' on the other is reminiscent of early anthropologists' discussion of magic, religion, and science, all of which have been defined as belief-based practices. Building bridges between anthropology, economics, and sociology, Durkheim's enduring conception of belief offers an understanding of the persistence of forecasting despite recurring 'errors'. The Durkheimian ground of economic conventions and fictions has long been emphasized in both heterodox economics and sociology: while Orléan (2011, Chapter 5) has shown that following Keynes's track eventually leads back to Durkheim, Beckert (2016, 192-204) demonstrates how Durkheim's notion of totem and mana [START_REF] Durkheim | The Elementary Forms of the Religious Life[END_REF]) sheds light on the kind of fictionality that consumption encapsulates. However, the issue of whether beliefs are still held in adverse situations encourages us to turn to Hubert's and Mauss's seminal theory of magic. As disciples of Durkheim, they claim that the authority of magic and magicians originates in collective forces, so much so that beliefs and confidence in magic are a priori rather than evidence-based. Prior confidence in magic arises from the collective need to find explanations to phenomena that would otherwise remain inexplicable. Thus, magical beliefs stand firm when challenged. Moreover, the 'will to believe' is the origin of magicians' belief in magic: at the very least, they keep faith in their own ability to perform magic because they believe in the magic of others [START_REF] Hubert | A General Theory of Magic[END_REF].

In the case of macroeconomic forecasting, a similar somewhat functionalist argument posits that forecasting has more to do with coordination than with prediction. When uncertainty prevails, actors' decisions are necessarily anchored in 'fictions', requiring actors a priori to 'suspend disbelief' and adopt an 'as if' convention. When the future has yet to be created and cannot be known at present (Shackle 1972(Shackle [1992]]; and the introduction to this volume), economic actors can base their action only on 'fictional expectations'-that is, 'pretended representations of a future state of affairs' (Beckert 2013, 226) drawing upon actors' imagination. In this perspective, fictional expectations may be supported by 'instruments of imagination', such as forecasts or economic theories, but a 'right' forecast is one that is shared within a large community, thus enabling economic action. The ex post judgment of the accuracy of ex ante forecasts does not matter, as forecasts are judged according to their practical credibility at the time made [START_REF] Beckert | Imagined Futures. Fictional Expectations and Capitalist Dynamics[END_REF]. The notoriously poor track record of macroeconomic forecasting does not put its legitimacy at risk, because actors need forecasts anyway to design strategies. A rather provocative Hughes-inspired insight might even suggest that forecasters are to a certain extent hired by economic actors to 'make their mistakes for them' (Hughes 1951, 321).

But a series of 'failures' may lead to the persistence, or return, of disbelief. 'Fiction in economic contexts is vulnerable to contradictory experiences in the real world' (Beckert 2013, 225). Such tension within the forms of beliefs in which future-oriented activities engage is shared by both macroeconomic forecasting and magic. The belief may vanish if the expected benefits from magical acts do not come 'true'. Magic, like religion, is viewed as a totality; either you believe in it all, or you do not. … Conclusions are immediately generalized, and a belief in a single case of magic implies the belief in all possible cases. Conversely one negative instance topples the whole edifice; magic itself then comes under suspicion. We have examples of obstinate credulity and deeply rooted faith crumbling before a single experience. (Hubert and Mauss 1902, 113) Even though Hubert and Mauss pay little attention to it, they implicitly suggest a distinction between faith in 'general' and 'singular' beliefs-that is, between magic as a whole and local magical acts, or between forecasting per se and some forecasts or forecasters.

Their work also stresses that, in some circumstances, a 'will to believe' does not suffice and that 'make-believe' practices are needed. Magical acts thus encompass 'simulation' a notion, the authors remark, which should not be confused with that of 'fraud', especially as it applies not only to the public or clients of magicians, but also to magicians themselves. Magicians' practices and discourses are consequently aimed at convincing both others and themselves. In this chapter, a similar inside approach is proposed for the case of forecasting 'errors'. Indeed, while forecasters freely acknowledge that 'errors' and 'mistakes' are their bread-and-butter, they also devote significant time to replying to critiques, sometimes even highlighting them in public6 or making fun of them.

After we met, the interviewee walks me back through the building. We come across another economist who, I am told, joined the Institute in the 1980s. I am encouraged to benefit from his long experience: 'Didn't you [the other economist] tell me [the interviewee] that, in the 80s, forecasts were as right as they are today?' The other instantly replies: 'You mean I said "as wrong"?' Both laugh.

(Institute, Observation, 1 September 2015) Forecasters' discourses in practice question the relevance of a 'reality test' in its most commonsense form. Because fully endorsing such a test would jeopardize the whole project of forecasting, forecasters' justifications often design alternative definitions of forecasting 'rightness' that rely on the procedures it follows rather than its substance. Scrutinizing how 'errors' are dealt with internally provides insights into forecasters' activity and the organization of the forecasting world. This shift implies a move from front stage, where forecast clients stand and public discussions take place, to back stage, wherein lie interpretative and discursive processes, as well as the actual production of forecasts [START_REF] Reichmann | Epistemic Participation. How to Produce Knowledge about the Economic Future[END_REF]. It underlines the role of key features found in both magic and macroeconomic forecasting, such as rituals, professional identity, and representations of causal mechanisms. Ultimately, forecasters' de facto replies to criticisms delineate a singular 'regime of veridiction'; that is, 'the set of rules enabling one to establish which statements in a given discourse can be described as true or false' (Foucault 2004, 35).

Paying attention to insiders' perspective on this issue also makes it possible to understand how forecasters remain motivated to perform an activity that is bound to be 'mistaken', if its purpose is to depict correctly future economic reality. Competing definitions of 'rightness' are connected to differing representations of 'errors': one is defined externally, and the other internally. In line with Hubert's and Mauss's argument that magicians truly believe in their magic, including their own, even if it involves simulation to some degree, forecasters' discourse should not be considered to be merely an expression of dishonesty-even though excluding bad faith a priori would obviously pose mirroring methodological problems. In a market for symbolic goods, actors' justifications are for the most part rooted in sincere beliefs as to the worth of what is done, rather than solely expressing denial or concealing 'real' economic motivations (Bourdieu 1977, 5, 21-22). 7 Going 'back stage' allows us to shed light on forecasters' reflections on their own craft and their judgments on their own performance. These reflections and judgments revolve around three major arguments: the ontological indeterminacy of economies, the constructivist epistemology of forecasting, and the claim of professionalism.

Data and Method

The material drawn upon in this chapter consists of interviews and observations from ongoing research on macroeconomic forecasting that focuses mainly, but not exclusively, on France (that is, macroeconomic forecasts produced about France). Thirty-six interviews have been conducted since June 2014 (average duration: eighty minutes) with economists and forecasters from public (either national or international) and private (banks, insurance companies, and so on) institutions. Among them, ten interviews were conducted with members of the same prominent French forecasting institution, which will be referred to here as the Institute, and where data from observation have been collected upon four successive forecast-production cycles between 2015 and 2017. During the interviews interviewees were encouraged to describe the actual practice of forecasting, rather than just expressing their own views about it in its most abstract aspects. The observations used in this chapter include those obtained at twenty-two work meetings (around three hours each), two press conferences (one hour each), and two debates during which the newly-produced forecasts were discussed by a pair of economists from other French institutions (two hours each).

The purpose of work meetings varies along with the process of forecasting, within which three stages may be roughly identified: post-mortem (the analysis of 'errors' in previous forecasts and of recent economic trends) and scenario and point forecasting. A 'forecast' indeed comprises two distinct elements. One is the 'point forecast', a precise figure depicting the value an economic variable may take in the future (for example, 'next year's GDP growth rate will be x %'), and whose calculation relies on econometric modelling and economic expertise. The 7 For example, Tetlock's analysis of political forecasts regards forecasters' justifications as mere belief defence strategies (Tetlock 2005, 129-137). While stressing similar mechanisms to those that are tackled in this chapter, Tetlock incorporates them as elements for testing forecasters' reliability in a psychology-inspired positivist perspective. However, the distinction he makes between 'Getting it Right' and 'Thinking the Right Way' undoubtedly applies to macroeconomic forecasters as well, as will be shown in this chapter. other is the 'scenario' -a narrative that exhibits a set of causal mechanisms leading from the present to the forecast horizon (the next quarter, semester, year, and so on), established through the combination of national accounts and judgmental assessments.8 Often considered a summary of the 'scenario', the 'point forecast' is determined at the end of the process, once a scenario is agreed upon. It attracts public attention, if only because it fits formats in use in the media, such as newspaper headlines.

Is It Even Possible to Know? The ontological Indeterminacy of Economies

A first line of argument proffered by forecasters seeking to absolve themselves from forecasting 'failure' is related to the nature of economic reality and the tools forecasters use to apprehend it. The unknowability of the future is a constraint on economic decision-making and gave rise to the profession of forecasting. But uncertainty is also a resource for forecasters when facing contradiction. Their poor results in the context of a reality test may be qualified as consequences of the shortcomings of econometric models rather than as 'errors'. By combining equations, models reflect the relationships between major economic variables (prices, exports, imports, public spending, employment, and so on) and describe the behavior of 'representative' economic agents (Evans 1999, 50-76) in a way that is taken to be symbolic of the whole economy. In this respect, models hold a position in the world of forecasting similar to that of instruments and tools in magical rituals: specifically, they belong to the 'class of objects which appear to be used for their own sakes by virtue of their real or imaginary properties, or … because they coincide with the nature of the rite' (Hubert and Mauss 1902, 59).

By definition, models focus only on chosen variables: completeness is not an option. It is thus no surprise that a significant part of the economic literature devoted to macroeconomic forecasting conveys a statistical representation of forecast 'errors' through the notions of 'residuals', 'error terms', or 'loss functions' (see, for example, [START_REF] Elliott | Macroeconomic Forecasting[END_REF]. Residuals capture all elements left outside the equations, such as the unexpected events (such as surprising weather conditions or accidents) that dramatically change the course of events and render the former assumptions, reasoning, and hence forecasts obsolete. These shocks are treated as external or 'exogenous' to the system-and therefore as legitimate excuses for forecasting 'errors'. In practice, though, at least some of these shocks-the 2008 financial crisis for example-are 'endogenous', as they originate from innovations and other features within the economy [START_REF] Bronk | Uncertainty, Modelling Monocultures and the Financial Crisis[END_REF]). More importantly still, although economists discuss plausible stock market movements and possible changes in central bank policies, most, if not all, econometric models do not include the financial sector and its impact on the real economy: this is a consequence of the dominance of a macroeconomic framework within which the 'real' and the 'financial' spheres of the economy are unconnected [START_REF] Goodhart | Macro-Modelling, Default and Money[END_REF][START_REF] Fligstein | Why the Federal Reserve Failed to See the Financial Crisis of 2008: The Role of 'Macroeconomics' as a Sense-Making and Cultural Frame[END_REF].

All shocks or decisive factors not captured by models are treated in the same way, whether endogenous or exogenous. Obviously, the further out the forecast horizon, the greater the odds that shocks will occur. Whereas macroeconomic forecasting, along with other activities such as credit rating [START_REF] Carruthers | From Uncertainty toward Risk: the Case of Credit Ratings[END_REF], purports to turn uncertain futures into calculated probabilities (or 'risks'), to put it in classical terms [START_REF] Keynes | A Treatise on Probability[END_REF][START_REF] Knight | Risk, Uncertainty and Profit[END_REF], shocks ensure the persistence of the very uncertainty that forecasting aims at reducing: the economy remains ontologically undetermined and the future remains open.

The dream of a perfect elimination of uncertainty can never be realized and forecasts can thus never be 'right' in a realistic sense. Forecasters' emphasis on radical uncertainty implicitly acknowledges that economic reality is non-ergodic, that is, non-stationary and not determined by the past. Because 'future outcomes are [not] merely the statistical shadow of past and current market signals' (Davidson 1996, 480; see also the introduction to this volume), forecastingoperation. As described in this paragraph, the first refers to the 'baseline scenario', namely the 'story' (to quote numerous interviewees) that forecasters tell once causal mechanisms are identified and a set of hypotheses is settled upon. Another refers to 'variants', that is, changes in the set of hypotheses and assumptions in order to build 'alternative scenarios' and fathom the risks associated with the baseline scenario (Carnot et al. 2005, 148-154). To avoid confusion between these two meanings, the word 'scenario' will be used in this chapter only in the sense of a baseline scenario or narrative.

which implies assessing economic regularities-is threatened at a microeconomic level by innovations, and at a macroeconomic level by shocks. A review of the ECB Survey of Professional Forecasters (SPF),9 for example, relates the 'errors' panel members made regarding the inflation rate to the various unexpected shocks that affected the newly created eurozone (Garcia 2003, 16).

Economic crashes have a special place among such shocks. The case of the Great Recession, regularly evoked by forecasters in the interviews, illustrates this, all the more as the crisis exploded at the end of a forecasting process. Since forecasts are produced on a quarterly (end of March, June, September and December) or biannual (end of March and September) basis, the collapse of Lehman Brothers on 15 September 2008 took place when point forecasts had been settled. 'Error' then brings into play both the shock itself and the organization and timing of the forecasting process, eventually making forecasts and forecasters 'run off the road', to quote a French economist.

We had our scenario frozen on September 15 th , 2008. The very same day Lehman Brothers collapsed! The forecast was not published yet, but the numbers were set: actually, to be released around October 15th, numbering has to be frozen earlier, next comes a phase of writing and harmonizing. […] We actually had ended up, by mid-September 2008, with a growth scenario that was pretty much settled on and stated 'well, there is a crisis, a liquidity crisis and a rather severe financial crisis' but, back then, it seemed to us that ... Big mistake we made was thinking the economy would be more or less resilient and there wouldn't be another shock like this. So, what happened that day is that we didn't change our forecasts. We are committed, though unofficially: people expect us to release our forecasts around mid-October and, at that moment, it was impossible to start all over again and make a brand new scenario. ... We decided to go public anyway but said we'd make new forecasts by the end of the year. We warned our readers that the forecasts had been made before [the Lehman Brothers collapse] and would be updated. ... Indeed, one bank going bankrupt is not enough for us to say that our scenario for growth in the Eurozone is 'minus 4 %', '4 % recession'. It needs the bankruptcy and a set of later developments. But it was embarrassing because we knew we were going to release something that ran off the road.

(Economist, Institute, 28 April 2015)

The ontological indeterminacy of economies is a key issue for forecasters, who regard it as a major cause of 'errors' and 'mistakes'. External critics argue that this brings discredit on forecasting per se. 'Black Swans'-that is, highly improbable events with devastating consequences-underline experts' inability to accurately predict what departs from the ordinary (Taleb 2007, 206-214). But for most economists, either orthodox or heterodox, the 'Black-Swan theory' is merely a wake-up call that emphasizes the limits of forecasters' reasoning and modelling in the face of indeterminacy (Galbraith 2014, 4). Significantly, even ninety years after the Great Crash, the economic literature continues to address the possibility of being able to predict it, sometimes leading to posthumous reassessments of the importance and significance of economists with respect to their 'prescience' [START_REF] Irwin | Who Anticipated the Great Depression? Gustav Cassel versus Keynes and Hayek on the Interwar Gold Standard[END_REF]. For instance, Dominguez and her colleagues (1988) argue that the Great Depression could not have been foreseen either by contemporary forecasters (the then competing Harvard Economic Service led by Warren Persons and the team Irving Fisher directed at Yale10 ) or, more interestingly, by forecasters making use of late 1980s methods and data. In the same breath, the authors thus both refute the assertion that Harvard forecasters actually had anticipated the Crash (Bullock and Crum 1932, 137;[START_REF] Schumpeter | History of Economic Analysis[END_REF]Schumpeter , 1131) ) and exculpate all forecasters from any period, on the grounds that 'error' is the consequence of unexpected events outside all models.

On this line of reasoning, the number of 'mistaken' forecasters serves as a proxy measure of the historical uniqueness of an event, and hence of its unexpectability. As McGoey (2012, 563-571) argues, collective ignorance offers an 'alibi' that forecasters use to deflect individual accountability: the wider the extent of ignorance, the more easily 'mistakes' are denied. The very fact that no expert knew about or understood what was coming proves it was impossible to know. Collective ignorance does not make the reality test ineffective as such but it makes forecasters immune to its verdict as they are not accountable for not having predicted what was unpredictable: forecasts were 'wrong' but no error was made.

Contrary to mainstream economics, whose perfect-competition hypothesis assumes predictability as a methodological feature of reasoning, forecasting as a form of applied economics deals only with actual economic conditions and thus must cope with a reality that is partly indeterminate and uncertain. The activity of forecasting is, consequently, doomed to be at least a partial failure: by definition, it cannot capture ex ante what a dynamic and unstable 'reality' will be. This provides forecasters with a rationale to discard a supposedly stable 'reality' as a relevant benchmark to assess the accuracy of forecasts.

At the same time, acknowledging the difficulties of forecasting involves shedding new light on the process of forecast production and suggests methodological refinements. In this respect, 'errors' mark the shifting frontier of knowledge about the economic environment, the relationship between variables in an econometric model, and the values they are expected to take. Hence the statement that forecasts are usually 'erroneous' leads to the apparently paradoxical conclusion that forecasting methods and models should be improved rather than withdrawn once and for all [START_REF] Evans | Soothsaying or Science? Falsification, Uncertainty and Social Change in Macroeconomic Modelling[END_REF]. As part of a never-ending trial-and-error process, 'error' may then even be of some value by pointing towards the limits and flaws of forecasting models and reasoning.

What Is It All About? The Epistemology of Forecasting

Emphasizing the way in which forecasts are produced offers forecasters another argument for proclaiming the irrelevance of reality testing. Criticisms addressing macroeconomic forecasting usually adopt a 'realistic perspective': they focus on numerical outcomes to compare them ex post to the 'reality' they were supposed to anticipate 'correctly'. 'Mistakes' then come from mismeasurements [START_REF] Desrosières | The Politics of Large Numbers. A History of Statistical Reasoning[END_REF]. A stress on the nature and epistemological basis of forecasting helps forecasters to challenge this standpoint on two different, yet related, grounds: first, by focussing on the nature and consequences of forecasting as a practical activity based around scenarios; and secondly, because the adoption of a 'realist' perspective on forecasting is considered misguided, because the use of statistical data requires the adoption of a 'constructivist' [START_REF] Desrosières | Entre réalisme métrologique et conventions d'équivalence: les ambiguïtés de la sociologie quantitative[END_REF] or 'constructionist' [START_REF] Hacking | The Social Construction of What?[END_REF]) perspective.

To a large extent, narrative forecast scenarios matter more to forecasters than calculated point forecasts. Forecasters often describe the establishing of scenarios as the 'true' purpose of their activity. Macroeconomic evolutions and causal mechanisms are then described in relation to a statistical and qualitative assessment of the current macroeconomic situation. Qualitative information is distributed along a wide range of phenomena, from public policy announcements to scandals involving major firms, through elections, weather conditions, and geopolitical environment. Built from a set of assumptions and guiding the subsequent econometric modelling, narratives illustrate the blend of statistical data and judgment that characterizes macroeconomic forecasting. Scenarios rely on experience, expertise, and intuition, all of which are assumed to endow forecasters with an ability to spot economic processes as they unfold: while economic reality is too erratic for accurate point forecasts, it remains predictable enough for regularities to be discerned. Such scenarios comprise representations of causal mechanisms in the economy. As emphasized in the Durkheimian tradition, religion, science, and magic all rely on representations of causality: whether in Newtonian science, primitive religion, or magic, unexplained 'forces' ultimately operate as explanatory principles [START_REF] Durkheim | The Elementary Forms of the Religious Life[END_REF]. A more or less comprehensive analysis shows how scientific, religious, or magical actions can set these forces in motion in order to produce effects (Hubert and Mauss 1902, 75, 78). In macroeconomic forecasting, representations of causality deal only with the analysis of economic causes and consequences.

Differences between forecasts from different institutions, or from the same institution at different times are thus often related to differences between scenarios that, in turn, may be understood with reference to the various possible depictions of economies. Baseline scenarios remain interpretations of the present economic environment, and one of the key challenges facing forecasters is selection of the relevant information. Besides, scenarios are thoroughly discussed within forecasting institutions and among forecasters from different institutions. As Reichmann (2013, 857; see also [START_REF] Evans | Social Networks and Private Spaces in Economic Forecasting[END_REF] notes, 'economic forecasters are permanently negotiating their views with each other and with others to come to a certain view'. Since interpretations based on judgments and shaped through collective deliberation are central to scenarios, they are often revised as new information and elements are taken into account. In this way, they combine facts (what is known) and bets regarding developing situations in a way reminiscent of the way in which uncertainty is managed in the case of journalism [START_REF] Pilmis | Producing in Urgent Situations. The Management of Unpredictability in the World of Journalism[END_REF].

This can be illustrated by the case of 'Brexit'. Until the vote (23 June 2016), forecasters from the Institute bet that the United Kingdom would remain in the EU, in accordance with a common 'nothing changes' assumption, and hence Brexit was not regarded as a key issue for forecasting. By contrast, once the referendum results were known, Brexit gained major importance in the process of forecasting. This can be measured by the amount of time devoted to it: Brexit was not covered in any of the five observed meetings of the spring 2016 forecasting session, whereas the fall 2016 work meetings usually begin with Brexit, with up to two hours devoted to it. It may also be measured in terms of coverage in the published forecasts: some two and a half pages out of 180 in spring 2016 (with the word 'Brexit' appearing on ten occasions) as against twenty-one pages out of 206 in fall (with the word 'Brexit' appearing on sixty occasions).

Forecasters often present narratives as the 'real' forecasts, those that should be paid attention to rather than 'point' forecasts. In this perspective, forecasting has more to do with storytelling than with calculation. Whereas it seems easier to assess the accuracy of forecasts, and thus their 'errors', with reference to calculated numbers, the quality of storytelling is a more appropriate, though less convenient, test of forecasts. 11 To fellow forecasters, a 'good', or 'right', forecast 'correctly' describes macroeconomic progression in such a way that the 'story' matches the coming string of events, even if the anticipated figures are 'wrong'. The often-quoted expression 'being right for the wrong reasons, and being wrong for the right reasons' suggests that forecasting is not subject to simple falsification because it leads to assertions unsuited to a process of refutation. In short, forecasters argue for a more nuanced epistemological position in relation to their craft.

The partial construction by contingent theoretical frames of the data used in forecasts also introduces indeterminacy. This suggests that it is appropriate to adopt a constructivist rather than a realist epistemology, which deals with the work routines, deliberations, and conventions involved in the process of forecasting. Conventions characterize not only forecasting institutions but also those surrounding them. A detailed investigation of the principles according to which data are built and knowledge is produced is often described as a prerequisite for judging forecasting: the classical statement that data do not preexist their collection or gathering is a common caveat among forecasters. This is obviously the case for abstract notions, such as potential GDP or the output gap, with which actual economic performances are compared and whose estimations vary widely across forecasting institutions. It is also true of the more or less formal information forecasters collect from the economic actors they meet, as well as of the raw material statistical bureaus supply them with. Forecasting 'errors' may originate in misleading information or erroneous statistical data, as they may lead to 'inaccurate' depictions of the economy. The case of economic indices exhibits the constructivist point of view forecasters adopt: whereas they are regularly considered to be reliable measures of economic activity (as shown by their use as the unquestioned 'reality' against which forecasts are compared), their regular revisions have a strong impact on macroeconomic forecasting.

You need people with a bit of knowledge about public stat[istics], people who know how key figures, those everyone pays attention to, are constructed. When you've been in the public sector, you know in what condition figures are brought to you, because you have practiced their production, so you're a bit better than others since you know what may play. I, for instance, since I used to forecast inflation, I know that in May and December, revisions are large because basic welfare benefits rise. So, these two figures are a bit more important. I know that rises in the price of natural gas (by 2.3% as announced today) or transportation will have an impact on inflation on the following month… (Chief economist, insurance company, 13 February 2017) Statcan [Statistics Canada] is for me a model. And why does it work great? They estimate GDP monthly, and it is a very good proxy for the upcoming quarterly data, with few revisions. That's why I told you [earlier] that 'the [Japanese] data is no good'. Japanese data is tremendously 11 Forecasters regularly complain about what seems to them an excessive focus on numbers, leading to situations that are described as 'absurd': calling a 1.5% GDP growth rate forecast 'wrong' because the observed rate was 1.3% would just be a matter of the 'thickness of the line' (Economist, asset manager, 22 October 2015).

revised. And when you use a model to forecast GDP in the short run, you not only check the last statistical point, but also the preceding quarters. If the quarters are revised a lot, you'll be mistaken a lot. That's why I called them 'disastrous', because of the revisions.

(Economist, OECD, 9 November 2015)

Discussing the nature and purpose of forecasting gives forecasters the opportunity to dispute the reality test as a relevant assessment of quality. First, they argue that a focus on calculation misses the 'true' locus of forecasting, which consists in establishing scenarios. Though less apparent, scenarios are presented as a decisive outcome of forecasting. Secondly, forecasters' epistemological arguments make it possible to qualify the results of a reality test as consequences of the data used in the process of forecasting. As data come at the conclusion of a series of conventions and operations, they may not accurately measure today's economic situation; and, consequently, neither can forecasts envision tomorrow's situation. Like magical rituals, forecasting implies that 'the confection or preparation of [the] materials, the ritual ingredients, is a long and finicking business' (Hubert and Mauss 1902, 58). 'Error' springs not only from the centre of the universe of forecasting, but also from its margins, where raw data are produced at the earliest stage of the forecasting process. In any event, forecasters should not take the blame. The emphasis on using second-hand data and information to produce forecasts ultimately depicts the universe of forecasting as a 'social world', or as a segment of a broader 'social world of economic analysis'. Like the art worlds H. S. [START_REF] Becker | Art Worlds[END_REF] studied, the 'forecasting world' cannot be reduced to those who are located at its heart: beyond the most obvious practitioners (forecasters themselves), support personnel-such as statistical agencies or economic actors who 'epistemically participate' [START_REF] Reichmann | Epistemic Participation. How to Produce Knowledge about the Economic Future[END_REF] in the activity-have to be taken into account.

What Makes a 'Good' Forecaster? Forecasters' Claims of Professionalism

The notion that forecasting is a 'social world' implies that it is ruled by a set of conventions according to which there is an established boundary between what ought to be done and what not, enabling cooperation between actors (Becker 1982, 28-34). Conventions delineate a set of rules and methods that 'professional' forecasters are expected to comply with. Although central bank staff are unlikely to be familiar with the sociology of professions and occupations, their actual definition of what the forecasting 'profession' might be when surveying 'professional forecasters' is noteworthy. They identify the implemented methods as a key feature of professionalism: in the case of the ECB-SPF, the selection and inclusion of panelists are delegated to each member country's central banks. The criteria applied include a 'formalized approach' (by which is meant the use of macroeconomic modelling), which is taken as crucial evidence that a given forecasting institution 'fits the … description [of] professional forecasters' (Economist, European Central Bank, 26 June 2014). Generally speaking, according to forecasters, a major aspect of 'professional' forecasting is consistency; that is, the mutual compatibility of all macroeconomic aggregates that are included in the analysis, whether it relies on narratives or statistical models. Specifically, macroeconomic forecasts have to fit national accounting principles, and for example make sure the total exports from all countries equal total imports. Some widely used terms, such as 'closure' (French: 'bouclage'), express this concern.

Both econometricians dealing with large-sized statistical models and economists who only make use of spreadsheets to implement small-scale models consisting of supply-use tables insist on the importance of consistency for forecasting. A national accounts basis for forecasting professionalism delineates the legitimate forms of forecasting and operates as a key criterion to judge the quality and validity of forecasts. Mavericks' claims to have foreseen what other forecasters missed is often met with skepticism, if not hostility, due to their perceived lack of professionalism: it is no surprise that they are regarded by 'professional' forecasters as mere outsiders whose reasoning lacks basic economic principles and who should be kept beyond the boundaries of the world of macroeconomics. The skills of economic 'visionaries' are regularly disputed. By stressing their lack of training in macroeconomics and challenging the outlined causal sequence, forecasters question the expertise of people who were probably just 'lucky'.

Sometimes you read something and think 'this is rubbish', because it doesn't fit, there is no closure with respect to macroeconomics. I do not pretend mine are always perfect but still… ... Actually a first simple closure is accounting identity: make sure national accounts are a closed system, which means one cannot see an increase in households saving rate and an increase in consumption if income is lower. Unfortunately, it happens sometimes. ... Well, it's a bit more subtle. If you take a look, you see the income doesn't rise enough to allow what has been reported. It's not that blatant, but still. Accounting identities have to be checked. Then another thing is … for example, if you report a decrease in growth in China, in the US, and in France, you cannot see a rise in the foreign demand for French goods. There is an identity at the international level which is actually pretty weighty because world demand has to be taken into account. (Economist, research institute, 23 October 2015) Predicting the worst is a good strategy because as time goes by … See, nowadays, X [another French observer who, the interviewee assures us, is a professor of finance and 'knows nothing of macroeconomic matters'] made a business out of it. He keeps repeating 'the crisis lies ahead'. And he is right: the crisis is ahead! Inevitably there will a crisis at some point. If you want to win the media, you have to say the crisis lies ahead because afterwards people think you should have been listened to. ... Last summer, X said (we know each other well, he is a nice guy by the way) 'there is a crisis ahead'. 'Sure, you're right, date it'. 'This summer.' And, once the Chinese thing occurred [the 2015 Chinese slowdown], he came back: 'See? I told you so.' 'No, you didn't say that. You said the stock markets would collapse in the United States and Europe for intrinsic reasons that had nothing to do with emerging countries'. (Economist, Institute, 7 September 2015) Conversely, forecasters who go by the book are exonerated of forecasting 'errors': they are not to be held responsible for 'mistakes' since none have been made. Forecasters advocate an approach to 'error' that relates it exclusively to the degree of compliance with internally-defined standard practices and formal rules. In line with the Durkheimian view that magicians represent an example of early professionals, forecasters' emphasis on procedures seem connected to their claim that their professional identity is first and foremost that of economists who shall be judged according to the narratives they set up rather than the calculations they end up with. Like other occupations, protection from blame is obtained by proving that the ritual of forecasting has been followed: insofar as the process has been correctly handled, there is no point in criticizing its outcomes and only 'professionals' are, consequently, authorized to assess that 'errors' have been committed (Hughes 1951, 324-325).

As noted in the case of magic, the general belief in forecasting remains to a certain extent immune to contradictory experiences because it may be argued that the dubious ritual was not properly executed, rendering it null and void. The conditions required for magic or forecasting to be successful are numerous 'to such an extent that it seems to be providing itself with loopholes, and often successfully', so that 'it is natural for a magician to take refuge behind questions of procedures and technicalities, to protect himself in case of failure of magical prowess' (Hubert and Mauss 1902, 62). Forecasters, then, like magicians, argue that all that really matters is that they follow due process.

The outcome can be that stage-front (public discussion) is dismissed as a place for disputing the accuracy of forecasts and that discussions remain confined to the back-stage area (the profession itself): while economic actors may provide forecasters with relevant information, debates and disputes are kept between 'professionals'. As mentioned earlier, that does not mean that forecasters do not acknowledge that forecasts are frequently 'erroneous' from a realist point of view, but a firm distinction is made between 'erroneous forecasts' and 'faulty forecasters'. As a social world based on shared conventions, the forecasting world also displays some of the properties of 'professional' ecologies. The combination leads to a representation of the world of forecasting as autonomous. Social boundaries protect forecasters both from competitors whose abilities are contested and from criticisms originating from outside the profession.

However, forecasting cannot achieve full autonomy, because it necessarily remains connected to the economy, which takes part in the process of forecasting and within which forecasters' clients are to be found. At some point, forecasters are bound to turn back to the external sphere and stage-front. Ironically, then, the distance that forecasters can put between themselves and the reality test should not be overestimated. Provided the general credibility of forecasting is maintained, the credibility of specific forecasts or forecasters can be questioned. Indeed, regarding its connection to the outside, the forecasting world shares features with a market within which actors compete with each other to access economically defined opportunities with clients and customers (Weber 1922, 635-640). Such competition necessarily takes place in the foreground and uses the 'reality test'-that is, the accuracy of ex ante forecasts-to assess forecasters' reliability: 'errors' may be put forward as 'evidence' that some forecasters are more trustworthy than others. The reality test is then commonly used to increase the symbolic capital or prestige of individual forecasters or forecasting institutions.

[At the end of the interview, the interviewee shows me a couple of files on his computer] I can't help the sweet treat: you'll get why. [He opens a spreadsheet: two tables display data from a dozen forecasting institutions -French government, OECD, IMF, research institutes and banks -for two different periods : 1999-2016 and 2013-2016]. So I look at what has been forecasted for Year y in September of Year y-1, then I look at the first GDP growth estimate for Year y, which is released in January of Year y+1. Obviously I consider the difference in absolute value. Here it is: our average difference for 2013-2016 is 0.15 point [he waves the computer mouse to stress this figure is lower than that of other institutions]. For example, we forecasted an average 1.15 GDP growth and it came out at 1. ... I fill the form myself. So, here is what my little fellows have marked for 2017 so, when it'll be January 2018, I will check it out. ... Everyone is convinced [they] have the best forecast except [he says it as if whispering a secret] that I have the evidence.

(Chief economist, research institute, 22 March 2017) Like many other social spaces, the forecasting world is not characterized by an opposition between symbolic and economic rewards: on the contrary, both coalesce to a large extent. Indeed, retaining clients and gaining new ones is a key concern for privately-funded institutions. In this perspective, the accuracy of forecasts exhibits 'evidence' of excellence in economic analysis, which 'clients remember' (Economist, private bank, 30 September 2015), even though they often value the narrative element of forecasting as well. Dismissed as being irrelevant to assess the quality of forecasts in general terms, the reality test remains the most commonly used instrument when specific macroeconomic forecasts come to be publicly debated.

Conclusion

The contradiction between what had been anticipated and what actually happened is a common challenge for all belief-based practices, and serves as the basis for comparing present-day macroeconomic forecasters to the magicians that Hubert and Mauss analysed in the early twentieth century. Rather than presenting the condescending claim that sophisticated macroeconometric models barely conceal primitive forms of reasoning, however, the aim of this chapter is to suggest that, though different, magic and forecasting share important traits. Both are activities whose results become apparent somewhere down the line, and in each case their performance relies on precise forms of representation, purposively designed materials, defined sets of procedures, and trained professionals.

The analysis presented in this chapter of the discourse forecasters use to legitimate 'errors' and preserve forecasting from a reality test that could endanger its very existence involves three arguments. Taken together, they serve to reduce the relevance of a comparison between ex ante and ex post figures to assess the 'quality' of forecasts and to mitigate the impact of forecasters' overall poor records in this respect.

In the first place, forecasters argue that forecasting focusses on narratives rather than on calculations: figures and numbers are thus discarded as the appropriate criterion by which forecasts should be judged. Instead, narratives identify the causal mechanisms through which economic processes unfold, and make representations about causality a key feature of forecasting. In this perspective, a 'reality test' based on estimating the accuracy of ex ante point forecasts is revoked.

The causal representations may also account, however, for the discrepancies between forecasts and 'reality' in order to dispute their qualification as 'errors'. Indeed, forecasters contend that many representations of 'reality' are misleading, as they assume that economies are more stable and predetermined than they actually are. The causal sequences economic theory posits, for example, are often pulled off track by contingent-hence unanticipated-phenomena. A proper appreciation of the indeterminacy of economic futures, consequently, absolves forecasters of blame for 'errors'.

The materials used to produce forecasts pose a second set of challenges. Whether they are made up of qualitative information or statistical data, they are considered a possible source of 'error'; namely, as the result of the conventions involved in their construction. While, on an ontological level, economic 'reality' is regarded as shaped by events over which forecasters have no control, this epistemological argument suggests that attention should be paid to the series of operations leading to the depiction of such 'reality'. The implication, again, is that forecasters should not necessarily be held responsible for 'errors'. A reality test is not, in this case, dismissed in principle, but its results are framed in such a way that they may not be qualified as 'errors'.

A third argument puts forward the notions of ritual and profession. Forecasters claim that they are mostly, if not exclusively, accountable for their compliance with sets of standards and practices. In this perspective, the process of forecasting matters more than its results: provided forecasts are produced according to the proper methods, they may not be considered faulty. A 'professional' representation of the forecasting world disputes the relevance of an external adjudication of the reality test: instead of the test being part of a public debate, the emphasis on professionalism tends to confine discussions about forecasting 'quality' within the limits of the forecasting world. Another shared feature between magic and forecasting is thus their separation from the ordinary, or 'profane', world. Ontological, epistemological, and professional claims resonate to challenge the appropriateness of the reality test in general.

Nevertheless, forecasting cannot stand entirely apart from the rest of the economic world. Stage-front does not lie so far away from back-stage. Since its actual purpose remains to guide economic actions, forecasting takes part in a division of labour that makes it necessary for forecasters to engage in relations with 'outsiders'. Moreover, while forecasts are regularly used to depict the future evolution of the economy, especially in the private sector they are also used competitively to assess the quality of economic analysis and gain clients. Forecasts and forecasters' credibility thus remain at stake. Despite forecasters' efforts to frame 'errors' as an issue solely for insiders, the reality test cannot be dismissed once and for all. But the resurgence of a reality test presupposes the narrowing of its scope: maintaining a general belief in forecasting is a prior condition for disputing particular forecasts and forecasters.

In early 2017, the chief economist of the Bank of England provided an example of the necessity for forecasters to address public criticisms (Phillip Inman, 'Chief economist of Bank of England admits errors in Brexit forecasting', The Guardian, 5 January 2017. https://www.theguardian.com/business/2017/jan/05/chief-economist-of-bank-of-england-admits-errors, retrieved 11 January 2017).

In the world of forecasting, two kinds of 'scenario' may be distinguished, along with two different kinds of

The ECB-SPF is a quarterly survey of expectations concerning inflation rates, real GDP growth, and unemployment in the euro area for several horizons. Explicitly inspired by a similar survey carried out in the United States in 1968 by the American Statistical Association and the NBER, and taken over by the Federal Reserve in Philadelphia in 1990, the ECB-SPF was launched in 1999 to coincide with the introduction of the euro.

This early period of forecasting in the United States has been vividly recounted by W. A.[START_REF] Friedman | Fortune Tellers. The Story of America's First Economic Forecasters[END_REF].


Benjamin Delbos

Rémi Chalard

Federico Di

Arnaud Lelevé

Richard Moreau

Multimodal Haptic Simulation for Ventriculostomy Training*

Freehand ventriculostomy is a frequent surgical procedure and is among the first ones that junior neurosurgery residents learn. Although training simulators exist, none has been adopted in the clinical routine to train junior residents. This paper focuses on a novel multimodal haptic training simulator that will lift the limitations of current simulators. We thus propose an architecture that integrates (1) visual feedback through augmented MRIs, and (2) a physical mock-up of the patient's skull to (3) active haptic feedback.

I. INTRODUCTION

Ventriculostomy is one of the most frequent procedures in neurosurgery [START_REF] Amoo | Common trajectories for freehand frontal ventriculostomy: A systematic review[END_REF]. It consists in the insertion of a catheter into the brain to relieve pressure due to the accumulation of CerebroSpinal Fluid (CSF) in the ventricles. The procedure is prescribed through diagnostic imaging, which is used to evaluate the size, shape, and position of the ventricles. In many cases, patients require emergency intervention, and the Freehand Ventriculostomy (FV) technique is preferred to assisted procedures [START_REF] Brenke | High accuracy of external ventricular drainage placement using anatomical landmarks[END_REF]. In FV, neurosurgeons blindly insert the catheter through the parenchyma, aiming for the Anterior Horn of the Ventricle (AHV). The burr-hole is placed at the Kocher's point using external anatomical landmarks, namely the nasion, the eyeballs, the External Auditory Canal (EAC), and the coronal suture [START_REF] Brenke | High accuracy of external ventricular drainage placement using anatomical landmarks[END_REF]. To guide their trajectory, surgeons usually aim for the foramen of Monroe, an internal structure joining ventricles [START_REF] Clemens | Virtual reality-based simulation training for ventriculostomy[END_REF]. In these conditions, an accurate understanding of the internal anatomy of the patient is required. Indeed, neurosurgeons need to map their mental representation of internal structures to external landmarks and thus need to combine different types of information. Proprioceptive information related to the palpation of the skull, haptic information related to the progression of the needle, and the graduation of the catheter are all taken into account to successfully puncture the ventricle. An illustration of the FV procedure is provided in Fig. 1.

Despite its high prevalence, the accuracy of the FV technique is still a controversial topic. Numerous image-assisted procedures, e.g. neuronavigation, have been proposed, but the additional efforts required are not always perceived as worth it by surgeons [START_REF] Bijlenga | External ventricular catheter placement: how to improve[END_REF].

Even though this gesture seems simple, insufficient training causes additional trauma and increases the risk for the patients [START_REF] Bijlenga | External ventricular catheter placement: how to improve[END_REF]. It is the first surgical act that neurosurgery junior residents are trained for, but some surveys have shown that they still need more passes than senior residents to arnaud.leleve@insa-lyon.fr successfully puncture the ventricle [START_REF] O'neill | A survey of ventriculostomy and intracranial pressure monitor placement practices[END_REF], highlighting the limits of current training procedures. To tackle these issues and adapt to new regulations, simulators have been developed to help in the training of ventriculostomy. We distinguish three categories of haptic simulations approaches [START_REF] Rangwala | Ventriculostomy Simulation in Neurosurgery, ser. Comprehensive Healthcare Simulation[END_REF] (onlycomputer-based simulation has been discarded as the training of such a gesture requires haptic feedback [START_REF] Våpenstad | Perceiving haptic feedback in virtual reality simulators[END_REF]):

1) Physical simulation (with cadavers or manikins) enables palpation of external landmarks important in ventriculostomy procedures, but suffers from low reusability and variety [START_REF] Rangwala | Ventriculostomy Simulation in Neurosurgery, ser. Comprehensive Healthcare Simulation[END_REF], as haptic feedback is reproduced by the insertion of a real catheter into a limited set of physical elements that wear and tear over time. 2) Virtual Reality (VR) based simulation, associated with Active Haptic Feedback (AHF), is not subject to the same limitations. It enables training on various anatomies [START_REF] Clemens | Virtual reality-based simulation training for ventriculostomy[END_REF], [START_REF] Lin | A novel virtual reality simulation training system with haptic feedback for improving lateral ventricle puncture skill[END_REF], but its important drawback is its high cost and the lack of anatomical landmarks [START_REF] Rangwala | Ventriculostomy Simulation in Neurosurgery, ser. Comprehensive Healthcare Simulation[END_REF]. 3) Although Mixed Reality (MR) simulation associates physical simulation (3D-printed materials) with VR to enhance learning efficiency, it still suffers from the same downsides of material degradation over time.

Due to design compromises, these simulators all lack part of the multi-modal (visual, kinesthetic, and touch) feedback required in the daily practice of the FV gesture. For this reason, experienced neurosurgeons from the Hospices Civils de Lyon have not used any of the aforementioned training tools for the junior residents' clinical practice to date.

In this paper, we introduce a ventriculostomy simulator that provides multi-modal feedback associated with AHF, virtual medical imaging, and a tangible setup. This association is unprecedented in ventriculostomy training. Rendered haptic feedback was designed from needle insertion models found in the literature. The parameters of these models could not be found in the literature and were experimentally tuned in collaboration with partner neurosurgeons.

This paper is organized as follows. Section II exposes components of the simulator and their synchronization. In Section III, force rendering of the catheter-brain interaction is discussed with experimental results introduced in Section IV.

II. MATERIAL AND METHODS

To enhance training efficiency, we propose a multi-modal simulator that permits both tangible and motorized haptic feedback and visual feedback. It features a physical manikin of a patient's head that does not wear out, and a real catheter handled by the user to enter the manikin. They both permit palpation and dual-hand handling to provide tangible haptic and direct visual feedback. The variety of patient anatomies and tissue properties is handled by numeric simulation that renders haptic feedback through a motorized haptic device mechanically connected to the end of the catheter. The trainees can view, in real time, virtual medical imaging of the internal anatomies of the patient and the position of the catheter inside, synchronized with their gestures.

A. Tangible Haptic and Visual Feedback

To reproduce realistic interactions between the hand of the trainee and the patient's head, a 3D-printed skull, (see Fig 5), was designed based on an arbitrary set of MRIs. It features mostly used external landmarks. To allow passage of the catheter through the manikin, the printed skull is opened behind the right eyeball and before the EAC. Although the burr-hole would typically be small enough to let the catheter pass, the aperture was made sufficiently large to allow trainees to choose different entry points, and mimic the positioning of the Kocher's point. To replicate clinicalpractice conditions, a usual graduated catheter is guided by the trainee into the skull.

B. Rendered Haptic Feedback

The minimal Degrees of Force Feedback (DoFF) required for the haptic simulation of needle insertion have not been established yet in the literature [START_REF] Corrêa | Haptic interaction for needle insertion training in medical applications: The state-of-the-art[END_REF]. 1 to 3 DoFF could be sufficient for the simulation of a "single region". However, 5 DoFF are advised to simulate an insertion in "arbitrary regions" [START_REF] Corrêa | Haptic interaction for needle insertion training in medical applications: The state-of-the-art[END_REF]. To provide efficient training scenarios, by enabling the placement of the entry point and choosing the needle's direction, we determined that at least 5 DoFF were necessary:

• 1 DoFF to render axial forces (F A );

• 2 DoFF to render lateral forces (F L ); • 2 DoFF for moments around orthogonal axes (moment around the shaft is not required in the FV). A Virtuose 6D Desktop (Haption) is chosen as haptic device, enabling 6 DoFF to render interactions between the catheter and a virtual patient brains.

C. Visual Feedback

Visual feedback consists of a direct view of the aforementioned skull and catheter. We also render diagnostic images (MRI scans) projected in the sagittal, axial, and coronal planes and sliced at a specific dynamic position. To match clinical practice, the trainees can browse through MRIs and evaluate the shape of the ventricles using a dedicated Human-Computer Interface (HCI). During the first stage of training, the trainees will also be able to visualize the current position of the catheter tip on MRI slices to stimulate their understanding of directionality and spatiality. As the trainees progress, the "interactive-time" visualization of the trajectory is removed to match clinical practice conditions.

D. Synchronization

To provide realistic and immersive simulation, the catheter-brain interaction must be consistent in every modality of the simulator. As the skull can be freely oriented by the trainee (as the head of a real patient in practice), its position and orientation are tracked using an Inertial Measurement Unit (IMU) attached to its inner side. They are expressed in the reference frame of the robot R Robot .

Two different patient brains have been selected for training purposes. They are derived from real MRIs, chosen to match the printed skull (R Skull ). On the one hand, they are displayed on a screen, associated with the R MRI frame. On the other hand, they have been segmented and rescaled to be used in a 3D collision software engine to render interaction forces by way of the haptic device connected to the catheter tip. This collision model is associated with the frame R Virtual . The consistency of these three modalities is ensured by the real-time knowledge of the transformations (depicted in Fig. 2) between each frame.

To visualize the trajectories of the catheter projected onto MRI slices, positions need to be expressed in R MRI through the following transformation:

MRI T Robot = MRI T Virtual * Virtual T Skull * Skull T Robot (1)

III. CATHETER INSERTION FORCE FEEDBACK

As the catheter is relatively rigid compared to the tissues, we consider its insertion to be similar to that of a needle in human tissues. Needle insertion is a ubiquitous act in medicine [START_REF] Corrêa | Haptic interaction for needle insertion training in medical applications: The state-of-the-art[END_REF]. It is generally divided into 3 stages: (1) deformation of the tissue before puncture, (2) penetration, and (3) retraction [START_REF] Barbé | Needle insertions modeling: Identifiability and limitations[END_REF]. In this work, we consider a deformationbased approach in which forces due to interaction with soft tissues are divided into three subforces [START_REF] Okamura | Force modeling for needle insertion into soft tissue[END_REF]. As shown in Fig. 3, these components relate to anatomical layers crossed during insertion:

• At first, the catheter pushes against the outer membranes of the brain (meninges), and stiffness forces ( ⃗ f s ) are generated as a response to elastic deformation. • Once a predetermined force threshold is reached, the meninges breach. Then, cutting forces ( ⃗ f c ) are applied to the tip of the catheter as it cuts the brain parenchyma. • As the needle advances, its surface of contact with the tissues increases, thus friction forces ( ⃗ f f ) are raising.

Parenchyma Ventricle Meninges

Fig. 3: Axial forces exerted on the needle during different stage of the catheter-brain interaction.

A. Stiffness force

Although in the case of a ventriculostomy, the outer layer of the meninges is cut and cauterized to facilitate passage of the catheter, the inner layers still oppose penetration. A small resistant force is thus felt before puncture, corresponding to ( ⃗ f s ) in [START_REF] Okamura | Force modeling for needle insertion into soft tissue[END_REF]. To render contact before puncture, linear functions [START_REF] Corrêa | Virtual reality simulator for dental anesthesia training in the inferior alveolar nerve block[END_REF], as well as polynomials [START_REF] Daniel | Development of haptic simulator for practicing the intraarticular needle injection under echography[END_REF] or exponential [START_REF] El-Monajjed | Analysis of surgical forces required to gain access using a probe for minimally invasive spine surgery via cadaveric-based experiments towards use in training simulators[END_REF] have been used. As the force threshold to puncture the meninges F r was estimated quite low (around 0.6 to 0.8 N) by expert neurosurgeons, ⃗ f s is at first modeled using a linear spring.

B. Cutting force

The cutting of soft tissues ideally results in constant cutting forces [START_REF] Okamura | Force modeling for needle insertion into soft tissue[END_REF]. In [START_REF] Daniel | Development of haptic simulator for practicing the intraarticular needle injection under echography[END_REF], the tracking wall algorithm is introduced to render a constant cutting force without chatter. This algorithm also reproduces the elastic behavior of soft tissues surrounding cutting interactions (repulsion forces [START_REF] Maurin | In vivo study of forces during needle insertions[END_REF]). According to feedback from experienced surgeons using our simulator, cutting of the brain parenchyma occurs at around 0.5 N, resulting in a constant cutting force of norm F c during the steady-state phase of the insertion.

As soon as the tip of the needle penetrates the ventricle, the cutting force applied at the needle tip drops to zero, resulting in a sudden loss of force, which is often the signal awaited by surgeons to stop.

C. Friction force

Friction forces ⃗ f f have been modeled using stick-slip models [START_REF] Okamura | Force modeling for needle insertion into soft tissue[END_REF] or Lugre model [START_REF] Daniel | Development of haptic simulator for practicing the intraarticular needle injection under echography[END_REF].

Due to the high softness of the brain [START_REF] Bilston | Brain Tissue Mechanical Properties[END_REF], it was assumed that static friction would induce an elastic behavior of the brain. As such, the aforementioned tracking wall algorithm has been reworked to render cutting and friction forces. This enables overcoming chatter issues in rendering friction at near-zero velocities. As described in [START_REF] Azar | Estimation of the fracture toughness of soft tissue from needle insertion[END_REF], friction forces ⃗ f f are proportional to insertion depth. In the event of a puncture of the ventricle, however, these forces are capped to a maximum value F f as the maximum contact area with the parenchyma is reached. This value depends on the insertion depth at which the ventricle is reached.

D. Overall Forces

Pressure on the needle shaft due to the displacement of soft tissues [START_REF] Kataoka | Measurement of the tip and friction force acting on a needle during penetration[END_REF] gives rise to lateral forces ⃗ f l and moments ⃗ m, as the user strays from the insertion direction. As inspired from [START_REF] Barnouin | A real-time ultrasound rendering with model-based tissue deformation for needle insertion[END_REF], these efforts vary with insertion depth as the needle becomes more constrained by surrounding tissues.

Thus, the global force ⃗ f g expressed in R Robot is:

⃗ f g = ⃗ f s + ⃗ f c + ⃗ f f + ⃗ f l (2)
IV. RESULTS

Two trajectories obtained from a failed (red) and a successful (green) puncture of the ventricle are compared to the ideal trajectory (dashed line from Kocher's point to Monroe's foramen) in Fig. c) profiles differ due to the puncture of the ventricle in the successful attempt resulting in a sudden drop of force. Following this event, the friction force, which was increasing with depth, is capped at the value of F f . In the failed attempt, the friction force is not capped as the needle keeps progressing into soft tissues. At an insertion depth of around 7 cm, the trainee decided to retract, as by that depth the ventricle should have already been punctured. As the needle is retracted, forces due to elastic deformation at the needle tip gradually diminish. During retraction, friction force progressively decreases as the surface of contact between the needle and the tissues decreases (see Fig. 4). Haptic parameters to render forces could not be found in the literature, as models used in ventriculostomy simulators lack clear descriptions. The values used in the current simulator were chosen according to feedback from expert neurosurgeons using this simulator. These values are illustrated in Fig. 4, and correspond to F r = 0.8 N to rupture the meninges and F c = 0.5 N to cut the parenchyma. The stiffness of the meninges was tuned to a value of around 133 N/m. As friction is very low in the context of FV, properties were hard to tune. At the moment, a friction coefficient of 1.6 is used, resulting in a maximum value F f ≈ 0.1 N at the moment of puncture. These values vary slightly between patients due to inter-patient variability.

The simulator resulting from the association of elements described in Sec. II is illustrated in Fig. 5. Currently, two

V. CONCLUSION

Current ventriculostomy simulators fail to offer a sufficient set of feedback required to train the multi-modal technique of Freehand Ventriculostomy. In this work, a multimodal approach is introduced, offering the trainees haptic and visual feedback using tangible elements (the catheter and patient skull) and virtual ones (synchronized medical imaging and catheter-brains interaction force feedback). The tangible elements help render realistic manual palpation and dual-hand handling of the tool, while the virtual ones bring the variability of rendered medical cases and the flexibility of customization for a richer training experience. In future works we will investigate registration algorithms to enable preoperative patient-specific simulation. The usage of more advanced force models will also be explored, in accordance with the evaluation of content, construct, and face validity of the simulator through trials with novice and expert surgeons.

Fig. 1 :

 1 Fig. 1: Overview of the freehand ventriculostomy: (I) the catheter; (II) palpation of anatomical landmarks; (III) the burr-hole place at the Kocher's point; (IV) the AHV.

Fig. 2 :

 2 Fig. 2: Reference frames and transformations. A T B is the transformation matrix from reference frame R A to R B .

4 .

 4 Corresponding force profiles are plotted as a function of time in Fig 4(b), and of insertion depth in Fig 4(c). Both insertion and retraction were performed by the trainee, resulting in a closed-loop force profile in Fig 4(c). In both Fig 4(b) and (

Fig. 4 :

 4 Fig. 4: Two experimental trajectories succeeding (green) and failing (red) to reach the ventricle, projected on a slice of the MRI (a). Corresponding force plots are given; (b) as a function of time, (c) as a function of insertion depth.

Fig. 5 :

 5 Fig. 5: Freehand Ventriculostomy Simulator: I) Catheter, II) Printed Skull, III) Haptic Device, and IV) MRI Visualization.