Muhammad Salman Shahid

Benoît Delinchant

Béatrice Roussillon

Frédéric Wurtz

Daniel Llerena

Adélaïde Fadhuile

Nils Artiges

Designing and Experimenting Nudge Signals to Act on the Energy Signature of Households for Implementing Indirect Energy Flexibility

To maintain energy balance in the grid, energy flexibility is entailed at consumer side. Generally, the participants of demand response experiments are offered economic incentive with historic or normative feedback on their energy consumption. In this article, we present an energy flexibility experiment concerning residential sector, which is based on nudge signals with indirect feedback and no monetary incentive. The results show that nudge signal can serve as an important tool to implement energy flexibility without hindering consumer's comfort. This study is effective to implement energy flexibility on local energy communities while offering no direct economic incentive.

Key Innovations

 Load curtailment and load shifting alerts are conceived for the residential buildings based on the day ahead forecasted condition of national grid.  Nudge cocktail (a collection of nudge signals) is devised for sending alerts to the participants. The participants may respond to each alert according to their degree of flexibility without loss of comfort.  Reference load curve is formulated for each participant. An image of reference load curve superposed on measured load curve is sent to the subjects as indirect feedback.

Practical Implications

The study is significant for energy flexibility of residential sector to mitigate forecasted day ahead energy imbalance in the grid. The load shifting alerts are based on the historic consumption of same sector, which enables the participant to implement energy flexibility according to their degree of flexibility without any loss of comfort.

Introduction

Electrical energy has become a necessity for mankind since its worldwide deployment through national grids in 20 th century. However, the urge for decentralized renewable energy production leads to new challenges in the electric grid management. Constraints like network congestion and intermittent renewable production require energy flexibility to maintain balance in the grid. Network congestion may occur due to disconnection of a circuit or change in energy demand owing to the variation in temperature. This results in load shedding, therefore loss of comfort for residential consumers. The renewable energy production is intermittent in nature, therefore to avoid high cost energy storage, the renewable energy must be consumed during the period of production. At consumer end, demand response serves to shift the demand pattern so that it can better match electricity supply. Direct load control enables the demand response operator to switch the shiftable loads at remote end. It can be effective for the industrial sector, however, the remote switching cause loss of comfort in residential sector. Alternatively, sending occasional alerts prompt the residential consumer to manage energy consumption in accordance with their comfort and degree of flexibility. These alerts tend the consumer to either implement upward flexibility (valley filling during the interval of renewable production) or downward flexibility (curtailing partial load during peak hours). This article deals with an experiment regarding energy consumption behaviour of households. Several aspects can be studied to evaluate the efficiency of the nudge strategy, however this article only deals with the first aspect along with the statistical analysis of the results.  Effectiveness of nudge cocktail to induce upward and downward flexibility.  Degree of Flexibility in participant's household keeping in consideration equipments present in the house and the composition of the household.  For each household, the distinct degree of flexibility (in terms of committed appliances) for upward modulation and download modulation.

State of the Art

This section presents state of the art of energy flexibility and nudge tool. In addition to that, it also presents suitable types of feedback of the earlier experiments conducted worldwide.

Energy Flexibility

The energy crisis in 1970s forced North America to start experimenting different modes of energy flexibility. [START_REF] Ehrhardt-Martinez | Advanced Metering Initiatives and Residential Feedback Programs: A Meta-Review for Household Electricity-Saving Opportunities[END_REF] ). Incentive based programs allow the operator to remotely shut down consumer equipment; whereas the price based programs impel the consumers to manage their consumption according to the dynamic pricing [START_REF] Albadi | Demand Response in Electricity Markets: An Overview[END_REF]. These programs achieve energy flexibility at the cost of consumer comfort. [START_REF] Hatton | French electricity system: estimation of residential customers' load shedding[END_REF] studied 20 energy flexibility experiments worldwide which were based on time of use (TOU), real time pricing (RTP) and critical peak pricing (CPP). EDF (Electricity of France) has introduced two colour coded critical peak pricing mechanisms and sends day ahead notifications to its residential subscribers [START_REF] Bivas | Load shedding production: how to offer electricity savings to millions of households (in french: La production d'effacement : comment offrir des économies d'électricité à des millions de foyers)[END_REF]. The demand response is steered at the grid operator level while obliging the consumer to act upon it.

It is intrusive, costly and takes from 10 seconds to 30 minutes to execute demand side management for the intended period (as illustrated in red box in figure 1).

Figure 1 : Flexibility solutions relevant to intermittent renewable production (IRENA, 2018) Another important aspect in energy flexibility is the type of feedback. In case of direct feedback, the demand response operator is obliged to give feedback to its customers in real time. Contrary to this, an indirect feedback is given to the consumer after the flexibility period is finished. It is either historic (comparing the consumption of household with the past consumption), or normative (comparing household energy consumption with that of a group of similar households) [START_REF] Wang | Impact Analysis of Customized Feedback Interventions on Residential Electricity Load Consumption Behavior for Demand Response[END_REF]. It is normally presented in numerical form e.g. kWh, cost, CO2 emissions [START_REF] Fischer | Feedback on household electricity consumption: a tool for saving energy?[END_REF], in the form of clustered baseline load curve of identical households [START_REF] Abreu | Using pattern recognition to identify habitual behavior in residential electricity consumption[END_REF] or as average daily load curve [START_REF] Ozawa | Determining the relationship between a household's lifestyle and its electricity consumption in Japan by analyzing measured electric load profiles[END_REF]. Figure 2 presents a spectrum of different feedback mechanisms.

Figure 2: Feedback mechanisms [START_REF] Neenan | Residential Electricity Use Feedback: A Research Synthesis and Economic Framework[END_REF] In a number of experiments, a control group is created with similar characteristics of treated group. "The control group is not subjected to any treatment and serves as a baseline to measure the effort of treated group" [START_REF] Lesgards | Residential Electricity Demand Management: A Review of 30 Years of Global Experiments (in french :La gestion de la demande résidentielle d'électricité: retour sur 30 ans d'expérimentations mondiales[END_REF]. A matching method is used to place the individuals in control group and treated group based on the socio-economic characteristics of households. The matching method is not effective if the number of participants are unequal in both groups. Alternatively, a weight can be assigned to average load curve of control group with respect to each subject of treated group; The energy flexibility can be observed by difference of two load curves [START_REF] Heckman | Matching As An Econometric Evaluation Estimator[END_REF]. "Difference in difference" is another method to measure the energy flexibility. With the assumption that the evolution of consumption in both groups is identical, the difference in difference method eliminates the temporal effects and bias selection between two groups [START_REF] Bode | Incorporating residential AC load control into ancillary service markets: Measurement and settlement[END_REF]. Another method is to create profile load curve for each subject. In this method, one selects the measured load curve of a number of previous days (of energy flexibility day 'D'), taking average of these load curves and then adjust the reference load curve with respect to a defined coefficient; the coefficient can be calculated by taking the difference or ratio of the average value of measured load curve and profile load curve [START_REF] Goldberg | Protocol Development for Demand-Response Calculations: Findings and Recommendations[END_REF]. In this article, an alternative demand side management technique is presented, which is non-intrusive towards the end user, have low cost and takes from a few hours to certain days (as illustrated in the green box in figure 1). A reference load curve is created based on the historical consumption data of household and serves as indirect feedback to respective household of treated group. Nudge "Nudge is an aspect of the choice architecture that alters people's behaviour in a predictable way without forbidding any options or economic incentives." [START_REF] Thaler | Nudge: Improving decisions about health, wealth, and happiness[END_REF]. "The choice architecture refers to the practice of influencing choice by organizing the context in which people make decisions" [START_REF] Shafir | The Behavioral Foundations of Public Policy[END_REF]. Social norms remained effective during the study of nonprice based energy flexibility experiments. The pilot nonprice nudge field study was performed in USA. In collaboration with energy utility companies, OPOWER analysed the energy consumption of households and sent Home Energy Reports (HER) to respective household consumers periodically. The energy consumption of a household for a period of time is compared with the energy consumption of energy efficient neighbours and all neighbours. This comparison is presented in graphical form along with energy conservation tips in the report, and is considered as the "descriptive norm". An "injunctive norm" is also added in the report by giving a rating in the form of "efficiency standing". This efficiency standing categorized the household as "Great," "Good," or "Below Average". Multiple models predict that the social comparison module would nudge the households to decrease their energy consumption if they found in their home energy report that they have consumed more than the norm (i.e. their neighbours); and the case is opposite for those households for whom the social comparison module would nudge to increase their energy consumption if they found in their home energy report that they have consumed less than their neighbours [START_REF] Allcott | Social norms and energy conservation[END_REF]. It has also been found that the provision of (indirect) feedback to customers on home energy usage with a focus on peer consumption decreased energy consumption by 1% to 2% [START_REF] Ayres | Evidence from Two Large Field Experiments that Peer Comparison Feedback Can Reduce Residential Energy Usage[END_REF]. Through literature review, it has been observed that the nudges in the past experiments were price incentive (as in price based demand response programs, reward or penalty), competition based or environmental propagative. The price based nudges tend the consumer to either gain or avoid loss monetarily. The competition based nudges tend the consumer to win only and therefore are effective during the duration of the competition. In case of unlimited duration of competition, the consumer might abandon its efforts after a period of time. Thus these type of nudges does not remain sustainable. "The results suggest that environmental nudges are most effective in relatively liberal communities" [START_REF] Costa | Energy Conservation "Nudges" and Environmentalist Ideology: Evidence from a Residential Electricity Field Experiment[END_REF] In this article, we coined a term "nudge cocktail". The reason for coining this term is that the conceived nudge for the experiment includes behavioural insight of the households and is a combination of multiple nudges. It is used to keep the households engaged within the experiment and measuring the effort of energy efficiency. This nudge cocktail does not include any social norm, rather it keeps a nudge based on the energy consumption of the household during alert period. It is presented in detail in the following section.

Experimental Design

This section demonstrates the experimental design. The experiment was conducted for a period of 1 year. The orange alerts were sent in winter during the months of November 2019 and March 2020. The green alerts were scheduled to be sent between April 2020 and September 2020. However due to the lockdown caused by COVID-19, the green alerts were rescheduled between July 2020 and September 2020. Architecture For this experiment, GAEL (Grenoble Applied Economics Laboratory) recruited 175 households (equipped with LINKY smart energy meter) in a French agglomeration. LINKY transmits the daily measured load curve of the consumer at a sampling period of 30 minutes to ENEDIS (French distribution system operator) server [START_REF] Duplex | A better knowledge of electricity consumption for residential customers through the Linky smart meter[END_REF]. G2ELab (Grenoble electrical engineering lab) receives the daily measured load curve of each household from ENEDIS in encrypted form. An automatic script decrypts and anonymizes the data as per GDPR consent signed with each households. The households are distributed into control group and treated group. The control group comprises of 79 households and treated group comprises of 96 households. The control group represents as a reference for electrical consumption of households in treated group. It ensures that the energy consumption of treated group is only influenced by the nudge during alert day. The treated group receives a set of SMS as nudge signal for each alert day. Alerts are not triggered for weekend and holidays. Two types of alerts are devised to send nudge signal towards treated group. Green alert (GA): The purpose of this alert is to nudge the treated group for shifting their partial load from evening to the duration between noon and 3:00 PM on alert day 'D'. Following is the criteria to send a green alert:

 The nebulosity on alert day 'D' in the said French agglomeration should be zero. i.e. the sky will be clear and the solar production will be maximum.  Based on the forecasted French national load curve of residential sector, a coefficient is calculated. The forecasting model is briefly discussed in next subsection. To trigger a green alert, this coefficient should be greater than 1 i.e. the forecasted afternoon consumption of next day should be lower than the forecasted evening consumption. The coefficient is mathematically given in equation 1.

𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝐺𝐴 = ∑ 𝑃 𝑐𝑜𝑛𝑠𝑢𝑚𝑚𝑒𝑑 8 𝑃𝑀 6 𝑃𝑀 𝑡 1 ⁄ ∑ 𝑃 𝑐𝑜𝑛𝑠𝑢𝑚𝑚𝑒𝑑 3 𝑃𝑀 12 𝑃𝑀 𝑡 2 ⁄ (1)
Where 𝑡 1 and 𝑡 2 are number of hours during the considered period. Their values are 2 and 3 respectively. Orange alert (OA): The purpose of this alert is to nudge the treated group for curtailing their partial load between 6:00 PM and 8:00 PM on alert day 'D'. The orange alert is based on the day ahead announcement of PP1/PP2 (Peak Period 1 and 2). These days correspond to high electricity consumption determined by RTE (French electric Transmission System Operator). ). The data is sampled at 30 minutes and hereafter termed as national load curve. For our study, we selected "dynamic profile coefficient" of category "RES11_BASE". This category consists of the residential consumers which have contracted power ≤ 6 kVA. Most of the French households subscribes this contract and normally does not have electrical heating in their home. ENEDIS does not periodically update this data, therefore a prediction model is created that predicts the next day "D+1".

ENEDIS also provides the national temperature of France via another API. The national temperature is calculated by a weighted aggregation of measured temperature for 32 French cities (RTE France, 2020). Since we only have data until 'D-2' from ENEDIS API of temperature, therefore we need the weighted aggregation of forecasted temperature of 32 French weather stations. For this purpose, we use the API of CLIMACELL to gather the forecasted temperature data. The data is sampled by 1 hour. Using the method given in (RTE France, 2020), the aggregated temperature of 32 French cities is calculated.

Figure 4: Prediction of 4 future days of French residential load curve by random forest regression By using the data obtained from the APIs given above and adding certain lag features and temporal features (e.g. hour of day, day of week etc.), a random forest regression is performed on the French national load curve of residential sector. Figure 2 illustrates the prediction of French national load curve of residential sector versus the actual curve. The execution of model yields a mean absolute percentage error of 2.52%.

Elements of Nudge Cocktail

There are multiple elements of the nudge cocktail that are implemented for each alert day 'D'. For each alert day 'D', 4 sms are sent to each subject of treated group. The information in each type of sms is given below.  Alert SMS: Energy production and its environmental impact i.e. elevated production of thermal power plants for orange alert and maximum use of renewable energy production for green alert.  Commitment SMS: A customized set of advice for each subject of treated group about how to optimize energy consumption with his pre-defined commitment. The subject may change their predefined commitment for each alert.  Reminder SMS: A reminder sms is sent in the morning of alert day 'D' to all the subjects of treated group.

 Image visualization SMS: An sms is sent to all the subjects of treated group so that they can view the result of their effort during the period of action on alert day 'D'. The participants of treated group signed a commitment form, stating the appliances that they will use or not use in response to the alert. The commitment form consists of a list of all the appliances present in subject's household and the timeslots during which these appliances are used. For each alert day 'D', the subjects must commit the appliances that they will use (or not use) during period of action. For this purpose, a URL is added in the commitment message that permits the subjects to modify their default commitment on day 'D-1'. Regular feedback to the subjects in the form of an image of the measured load curve superposed by reference load curve for alert day 'D' is sent to the subjects of treated group. The aim of this sms is to positively reinforce the subjects to continue acting on the nudge signals. Timeline  A potential alert is registered in database on day 'D-1' at 6:00 PM.  At 6:45 PM on day 'D-1', alert sms is sent to treated group. Following this, customized commitment sms is also sent to each subject of treated group.  The subjects of treated group are sent a reminder sms on alert day 'D' at 7:30 AM.  The period of action on alert day 'D' depends upon the type of alert. For green alert, the period of action is from noon to 3:00 PM during which load shifting is expected. For orange alert, the period of action is from 6:00 PM to 8:00 PM during which load curtailment is expected.  At 3:00 PM on day 'D+2', the measured load curve of all the subjects of both groups is received on G2ELab server. The measured load curve of each subject is anonymized with respective subject code as per GDPR consent and is stored in the database.

Figure 5: Timeline of each alert of experiment  At 3:30 PM on day 'D+2', an image file is generated for each subject of treated group in which the measured load curve of alert day 'D' is superposed by reference load curve for alert day 'D' (reference load curve will be briefly discussed in a later section). These images are stored on a FTP server. The images are picked up by GAEL later the same day and is placed on the personal account of each subject for visualization.  At noon on day 'D+3', a sms is sent to all the subjects of treated group so that they can visualize their effort of alert day 'D' on their online account. Reference Load Curve A reference load curve has an important role in this study. It helps in scientific evaluation of the efficiency of nudge signal. Besides, the reference load curve is itself a nudge. A reference load curve is in fact an expected load curve on a normal day. The difference of reference load curve (i.e. expected load curve on non-alert-day) with flexibility driven measured load curve gives energy flexibility on alert day 'D'. Practically, it is important to select the method that does not underestimate or extremely overestimate the effort of energy flexibility on alert day "D". Currently, the following methods are used.

Mean [PD-1 & { Min (PD-2 : PD-5)}] :

For an alert day 'D', a reference load curve is created by taking average of measured load curve of previous day 'D-1' and the measured load curve having lowest energy consumption between day 'D-2' and 'D-5'. This method is used for presenting the energy flexibility for load curtailment. Figure 6 illustrates the reference load curve superposed on measured load curve. The selected methods take into account the temporal effect and indirectly take in to account the temperature factor for load curtailment alerts. The methods take into account the evolution of energy consumption with respect to time as it includes the energy consumption of day 'D-1'. Besides, it does not nullify the effect of minimum (or maximum) energy consumption occurred at any day D-n (where 2≤ n ≤ 5).

Comparison of energy consumption of control group and treated group during normal days

A control group is created in order to find out if any external factor affect the experiment. The control group does not receive any treatment. Ideally, the average energy consumption of both group should be identical. For the sake of experiment, the period between noon and 3:00 PM is significant for load shifting on alert day 'D' (i.e. implementing green alert). Similarly, the period between 6:00 PM and 8:00 PM is significant for load curtailment on alert day 'D' (i.e. implementing orange alert). Therefore it is essential to compare the energy consumption of both groups during these periods on normal day (i.e. non alert day). Figure 7 represents the distribution of energy consumption of both groups between noon and 3:00 PM during normal days, whereas figure 8 represents the distribution of energy consumption of both groups between 6:00 PM and 8:00 PM during normal days. It is interesting to see that the energy consumption pattern of both groups during the intended period of study is identical. The median difference between treated group and control group in figure 7 is 54 Wh, whereas the median difference between treated group and control group in figure 8 is 16 Wh; which is very small.

Statistical comparison between the two groups

A statistical comparison of the data distribution of two groups gives us an idea whether the consumption of two groups is similar or different during the period of action.

Through the visualization of data during the period of action on alert day 'D', it has been found that the data is asymmetric (i.e. not normally distributed) and is skewed towards left. Therefore a non parametric test called Mann-Whitney U test is chosen to find the statistical significance of each alert. The following hypothesis are tested using the Mann-Whitney U test.

 Null Hypothesis: The statistical distribution of energy consumption data of the treated group is same to the statistical distribution of energy consumption data of the control group during the period of action.  Alternate Hypothesis: The statistical distribution of energy consumption data of the treated group is different to the statistical distribution of energy consumption data of the control group during the period of action. The test was performed using the function of Python's SciPy package (scipy.stats.mannwhitneyu()). If the resulting p-value of any alert is less than α=0.05, the alternate hypothesis is validated (ie. both groups are statistically dissimilar over the period of action on alert day 'D').

Mann Whitney U Test for Orange Alerts

Table 1 presents the mean and standard deviation of both groups while table 2 presents the statistics, p-value and statistical significance (validation of the alternate hypothesis) of each orange alert by doing a comparison between control group and treated group. It has been found that for 7 orange alerts out of 9 orange alerts, the pvalue is less than α, i.e. the difference between the population's mean of control group and treated group is statistically significant. In other words, the energy consumption of the treated group during the period of action on alert day is different than the energy consumption of control group for these 7 orange alerts. The aggregated result of both tables indicate that globally the orange alerts tended the subjects of treated group to implement load curtailment. The difference of the averages between control group and treated group in table 1 yields an average load curtailment of 133 W/30 minutes (or 266 W/h); which is significant if considered for a single household during peak hours of residential consumption. This is further validated with a 0 p-value for aggregated alerts in table 2. Among these orange alerts, the 7 th orange alert performed better as compared to the others. The difference of the averages between two groups for orange alert no. 7 is 225 W/30 minutes (or 450 W/h). The average consumption load curve of both groups for orange alert no. 7 is presented in figure 9. It can be observed that the average energy consumption of treated group during the period of action is less than control group. The case is inverse for day 'D-1' and day 'D+1'. It suggests that the nudge signal had an impact on the households to implement load curtailment during period of action on day 'D'.

Figure 9: Average consumption load curve of both groups for 7 th orange alert Another important result to check is whether the subjects of treated group having electric heating have same or different energy consumption distributions as compared to the subjects having no electric heating. Except for orange alert no. 2, it is observed that there is a significant difference in the mean of both types of treated subjects. Figure 10: Average consumption load of both groups for 6 th green alert It should be noted that the results of some green alerts are affected with lack of retrieval of measured load curve of certain subjects due to expiration of annual GDPR consent signed with the subjects. However, most of the data is retrieved for 5 th and 6 th green alerts and the results of these two green alerts are less affected with the impact of lack of data. As given in table 5, the difference of mean of both groups is small except for green alert no. 6, in which we observe a difference of 178 W/30 minutes (or 356 W/h). Figure 10 presents the average load curve of control group and treated group for 6 th green alert. It can be observed that the average energy consumption of treated group during the period of action is more than control group. However, it needs further investigation about which electrical loads remained significant for achieving load shifting.

Discussion and Conclusion

The traditional demand response techniques either ask for direct load control or offer price based incentives to the residential customer. These techniques are however intrusive and may be costly. The price based incentives keeps the consumer in loop as long as the offer is in place. Alternatively, demand side management can be achieved by social competition. The OPOWER experiment in USA is an example of social competition which induced a sense of load curtailment through self-evaluation and comparison of load consumption with neighbours. Yet, the impact of such experiments is for limited time. An alternative mechanism is proposed in this article, in which nudge signals are sent to the households of treated group with indirect feedback and no price incentive. The purpose of this experiment and specifically nudge signals is not to tend the subjects to implement energy flexibility for any monetary gain or competition, rather they are based on the forecasted condition of the electrical grid to avoid network congestion or consume elevated renewable energy production on day 'D'. In an experiment, a hypothesis is tested that whether the forecasted information of grid condition could nudge the residential consumers to implement indirect energy flexibility. The challenge of energy flexibility is connected with energy transition objectives, as it can leverage a better integration of intermittent production. Most of the subjects that are participating in this experiment are sensible about environment and react to nudges in this perspective. A comparison of the impact of nudge is done between control group and treated group. The comparison of energy consumption of both groups reveals that the proposed nudge signal cocktail has an impact on the households for most orange alert days demanding downward flexibility. The behavior for alert day is found different than the day 'D-1' and day 'D+1'. The impact for upward modulation on alert day 'D' is not clear, possibly due to lack of sufficient data, and requires further investigation. A similar procedure called "mon-ecowatt" is currently implemented by RTE. RTE sends SMS signal to the subscribers for curtailing load on peak consumption days. The future prospects of this work includes (but not limited to) measuring whether a habit of implementing energy flexibility is formed over the course of time. It is also interesting to measure how the socio-economic characteristics of each household affects their degree of implementing energy flexibility. Also, it will be interesting to know which time of the day is more impactful/reliable for implementing energy flexibility. Furthermore, the potential appliances for implementing indirect energy flexibility could be explored by measuring the impact of individual appliances.

Figure 3 :

 3 Figure 3: Schematic Diagram of project "EXPESIGNO" Forecasting the French national load curve of residential sector In order to forecast a day ahead French national load curve of residential sector, certain third party APIs are used to obtain daily updated data. Two of these APIs are related to ENEDIS. ENEDIS constructs national profiles of the energy consumption sectors in France. A profile represents average behaviour of a group of users and reflects how an average individual in the group consumes

Figure 6 :

 6 Figure 6: Superposition of reference load curve over measured load curve to visualize load curtailment Mean [PD-1 & { Max (PD-2 : PD-5)}] : For an alert day 'D', a reference load curve is created by taking average of measured load curve of previous day 'D-1' and the measured load curve having highest energy consumption between day 'D-2' and 'D-5'. This method is used for presenting the energy flexibility for load shifting.

Figure 7 :

 7 Figure 7: Distribution of energy consumption of both groups between noon and 3:00 PM

Table 1 :

 1 Mean and standard deviation of energy consumption of control group and treated group for orange alerts

	Orange	Control Group		Treated Group
	Alert	Mean	Standard	Mean	Standard
	No.		Deviation		Deviation
	1	703	810		659	1263
	2	623	818		460	443
	3	825	1012		631	845
	4	707	899		534	735
	5	734	917		557	626
	6	630	770		616	779
	7	689	843		464	623
	8	611	782		473	589
	9	660	800		587	948
	Aggregated	687	854		554	798
	Table 2: Mann Whitney U Test between Control group and
		treated group for orange alerts
	Orange Alert No.	Statistics	p-value	Significance
	1	49266		0.001		True
	2	52209.5	0.097		False
	3	48381		0.001		True

Table 3 :

 3 Mean and standard deviation of energy consumption of subjects having or not electrical heating for orange alerts

	Orange	Subjects having	Subjects not having
	Alert	electrical heating	electrical heating
	No.	Mean	Standard	Mean	Standard
			Deviation		Deviation
	1	887	1676		431	535
	2	450	397		470	481
	3	758	840		513	835
	4	698	831		387	601
	5	733	724		388	457
	6	803	943		444	537
	7	645	806		303	318
	8	624	698		338	430
	9	811	1132		388	689
	Aggregated	714	967		407	564
	Table 4: Mann Whitney U Test between the subjects of treated
	group having electric heating and those who have not electrical
		heating in their house
	Orange Alert No.	Statistics	p-value	Significance
	1	12684,5	0		True
	2	15424		0,225		False

Table 5 :

 5 Mean and standard deviation of energy consumption of control group and treated group for green alerts

	Green	Control Group	Treated Group
	Alert	Mean	Standard	Mean	Standard
	No.		Deviation		Deviation
	1	341	451	412	587
	2	306	363	495	696
	3	402	421	396	443
	4	349	419	412	555
	5	347	575	392	469
	6	231	310	409	571
	Aggregated	326	436	420	568

Table 6 :

 6 Mann Whitney U Test between Control group and treated group for green alerts

	Green Alert No.	Statistics	p-value	Significance
	1	86783	0,07	False
	2	65250,5	0,001	True
	3	27909,5	0,243	False
	4	92615,5	0,133	False
	5	83942	0,004	True
	6	76617	0	True
	Aggregated	2571333	0	True

Acknowledgment

This work has been supported by the Auvergne Rhône-Alpes region, with "Pack Ambition Recherche 2017 -Expesigno projet" (17 01110301) and the "OREBE" project. This work has also been partially supported by the CDP Eco-SESA receiving fund from the French National Research Agency in the framework of the "Investissements d'avenir" program (ANR-15-IDEX-02).


domain: chim phys

text:
Sourav Marik

Deepak Singh

Bruno Gonano

Fabien Veillon

Denis Pelloquin

Yohann Breard

Yohann Bréard

Long range magnetic ordering and magneto-(di) electric effect in a new class of high entropy spinel oxide

Keywords: High Entropy Oxides, Spinel, Magneto-(di)electric effect

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Development of advanced materials with novel functional structures and improved -tailorable functionalities is the key to the continuous progress of materials science. In this context, the advent of a new materials design strategy namely high entropy stabilization route, which is evolved with the discovery of high entropy alloys [START_REF] Miracle | A critical review of high entropy alloys and related concepts[END_REF][START_REF] Ye | Highentropy alloy: challenges and prospects[END_REF][START_REF] Yeh | Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes[END_REF], opens the possibility to stabilize the phases by high configurational entropies, and have drawn intense research interest in recent times [START_REF] Miracle | A critical review of high entropy alloys and related concepts[END_REF][START_REF] Ye | Highentropy alloy: challenges and prospects[END_REF][START_REF] Yeh | Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes[END_REF][START_REF] Koželj | Discovery of a superconducting high-entropy alloy[END_REF][START_REF] Marik | Superconductivity in a new hexagonal highentropy alloy[END_REF][START_REF] George | High-entropy alloys[END_REF][START_REF] Biswas | Designed materials with the giant magnetocaloric effect near room temperature[END_REF][START_REF] Rost | Entropy-stabilized oxides[END_REF][START_REF] Sarkar | High-entropy oxides: fundamental aspects and electrochemical properties[END_REF][START_REF] Sarkar | High entropy oxides for reversible energy storage[END_REF][START_REF] Zhang | Long-range antiferromagnetic order in a rocksalt high entropy oxide[END_REF][START_REF] Anand | Phase stability and distortion in high-entropy oxides[END_REF][13][START_REF] Witte | High-entropy oxides: An emerging prospect for magnetic rare-earth transition metal perovskites[END_REF][START_REF] Ye | First-principles study, fabrication and characterization of (Zr0.25Nb0.25Ti0.25V0.25)C high-entropy ceramics[END_REF][START_REF] Jiang | A new class of highentropy perovskite oxides[END_REF][START_REF] Lei | Development of advanced materials via entropy engineering[END_REF][START_REF] Harrington | Phase stability and mechanical properties of novel high entropy transition metal carbides[END_REF][START_REF] Lederer | The search for high entropy alloys: A high-throughput abinitio approach[END_REF][START_REF] Liu | Synthesis of superfine high-entropy metal diboride powders[END_REF]. The key point of the highentropy design strategy is the use of the combination of a five or more number of cations in equiatomic or near equiatomic ratio. The high mixing entropic contribution (∆Smixing) to the decreased Gibbs free energy stabilizes disordered solid solution phases in a simple structure and overcome the usual enthalpy driven phase separation generally observed in heavily doped systems.

High entropy oxides (HEOs) are the extension of the concept of high-entropy alloys (HEAs) to entropy-stabilized oxides [7 -14]. In 2015, Rost et al. [START_REF] Rost | Entropy-stabilized oxides[END_REF] discovered the first HEO [(Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)O] having five different cations, in equiatomic ratios. Such oxide materials, stabilized by high configurational entropy are located at the centre of a multinary phase diagram. This domain of materials composition is seldom studied, and therefore unexpected multifunctional properties can be anticipated. Recently, investigations into this new class of oxide systems have resulted in several intriguing discoveries. Examples include superior Li storage capacity retention capabilities [START_REF] Sarkar | High-entropy oxides: fundamental aspects and electrochemical properties[END_REF][START_REF] Sarkar | High entropy oxides for reversible energy storage[END_REF][START_REF] Wang | Multi-anionic andcationic compounds: new high entropy materials for advanced Li-ion batteries[END_REF], room temperature Li+ superionic conductivity [START_REF] Bérardan | Room temperature lithium superionic conductivity in high entropy oxides[END_REF], catalytic properties [START_REF] Chen | Entropy-stabilized metal oxide solid solutions as CO oxidation catalysts with high-temperature stability[END_REF], colossal dielectric constants [START_REF] Bérardan | Colossal dielectric constant in high entropy oxides[END_REF], narrow and adjustable band gaps [START_REF] Sarkar | Multicomponent equiatomic rare earth oxides with a narrow band gap and associated praseodymium multivalency[END_REF] and long-range magnetic ordering [START_REF] Zhang | Long-range antiferromagnetic order in a rocksalt high entropy oxide[END_REF]13]. Nevertheless, the field of HEOs is at its early stage, and many of the materials are remain to be explored.

Herein we report synthesis, structure and physical properties of a new class of high entropy spinel oxide with composition (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4. For the last two decades, chromium-based spinel materials (ACr2O4) have been a fertile playground for experimental and theoretical investigations on the physics of geometrical frustration [START_REF] Das | Density functional theory based comparative study of electronic structures and magnetic properties of spinel ACr2O4 (A = Mn, Fe, Co, Ni) compounds[END_REF][START_REF] Lee | Local spin resonance and spin-peierls-like phase transition in a geometrically frustrated antiferromagnet[END_REF][START_REF] Chung | Statics and dynamics of incommensurate spin order in a geometrically frustrated antiferromagnet CdCr2O4[END_REF][START_REF] Tomiyasu | Magnetic shortrange order and reentrant-spin-glass-like behavior in CoCr2O4 and MnCr2O4 by means of neutron scattering and magnetization measurements[END_REF][START_REF] Yamasaki | Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide[END_REF]. At the same time, they are considered of significant interest for a range of potential applications [START_REF] Kim | Application of spinel-type cobalt chromite as a novel catalyst for combustion of chlorinated organic pollutants[END_REF][START_REF] Wen | Device application feasibility of single-crystal CdCr2Se4, a ferromagnetic semiconducting spinel[END_REF][START_REF] Cui | Sol-gel synthesis of nanoscaled spinels using propylene oxide as a gelation[END_REF]. The octahedrally coordinated Cr atom form a three-dimensional network similar to a pyrochlore lattice. The high geometrical frustration in this pyrochlore lattice originates intriguing physical effects (such as multiferroics, Spin-Peierls-like phase transition, quantum magnetic frustration) as a correlation of structural and spin degrees of freedom. A-site cations, on the other hand, occupy the eightfold tetrahedral sites. Materials with nonmagnetic cations in the A site are geometrically frustrated in nature and facilities studies of these highly degenerate ground states [START_REF] Bérardan | Colossal dielectric constant in high entropy oxides[END_REF][START_REF] Sarkar | Multicomponent equiatomic rare earth oxides with a narrow band gap and associated praseodymium multivalency[END_REF]. Magnetic A 2+ cations introduce different crystal fields and therefore, can provide exciting aspects of magnetism and magnetoelectric effects [START_REF] Bérardan | Colossal dielectric constant in high entropy oxides[END_REF][START_REF] Das | Density functional theory based comparative study of electronic structures and magnetic properties of spinel ACr2O4 (A = Mn, Fe, Co, Ni) compounds[END_REF][START_REF] Lee | Local spin resonance and spin-peierls-like phase transition in a geometrically frustrated antiferromagnet[END_REF][START_REF] Chung | Statics and dynamics of incommensurate spin order in a geometrically frustrated antiferromagnet CdCr2O4[END_REF]. Here, utilizing the high entropy stabilization route, we have synthesized a new class of high entropy spinel oxide with composition (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4. A detailed study on the structure, microstructure and physical properties of this new material are presented here. Due to existence of several magnetic and nonmagnetic cations with different electron configurations and their random distribution in the structure a robust structural disorder is anticipated, and, one may at a glance expect a spin-glasslike magnetic state. However, on the contrary, the present HEO material exhibits long-range AFM ordering.

The sample with composition (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4 was synthesized by the standard solid-state reaction route, using the stoichiometric amounts of MgO (99.9%), Co3O4 (99.9%), NiO (99.9%), CuO (99.9%), ZnO (99.9%) and Cr2O3 (99.9%). The stoichiometric amounts of the precursors were carefully mixed and pressed in the form of bars. The sample was then heated at 1100°C for 24 hours followed by the water quench. This step was repeated twice. X-ray diffraction patterns were collected at room temperature in an X'pert Pro diffractometer and D8 diffractometer working with the CuKα radiation. Energy Dispersive X-Ray Spectroscopy (EDS) mappings are carried out on ZEISS SUPRA 55 scanning electron microscope (SEM). The high-angle annular dark-field (HAADF), annular bright field (ABF) scanning transmission electron microscopy (STEM), and EDS analyses were performed on a JEOL ARM-200F cold FEG probe image aberration corrected microscope operated at 200 kV and equipped with a large solid-angle CENTURIO EDX detector. Direct current (dc) magnetic measurements were performed by using a Quantum Design superconducting quantum interference device (MPMS, Quantum Design). Alternating current (ac) susceptibility measurements (ac excitation = 10 Oe, dc magnetic field = 0 Oe) were carried out using the ac Measurement System (ACMS) attachment in a Physical Properties Measurement System (PPMS, Quantum Design). Specific heat measurement was performed by the two tau timerelaxation method using the PPMS in zero magnetic field. The dielectric measurement were carried out as a function of temperature and magnetic field for various frequencies using an LCR meter (Agilent 4284A) with a home-made sample insert for a Physical Properties Measurement System (PPMS, Quantum Design). Silver paint was used to make the parallel plate capacitor of a pressed rectangular shaped polycrystalline sample.

The figure 1 As illustrated in Fig. 1 (c), EDS mapping confirms the stoichiometric chemical composition and highlights that all elements are uniformly distributed at the micrometre scale in the sample. The The Rietveld refinement of the XRD pattern (collected using a D8 diffractometer, figure S3 and table S1 in the SI) is shown in the supporting information (SI) file. Almost full occupancy of the Cr site (B site of the ABO4 type spinel, fractional occupancy = 0.98 (2), table S1) is observed in the Rietveld refinement of the XRD pattern. As Co, Ni, Cu, Zn have a similar electronic configuration it is not possible to get accurate information about the fractional site occupancies for these elements from the XRD. Hence, we fixed the fractional occupancies (0.2 as observed from the EDS mapping) for these elements (A site of the ABO4 structure) during the refinement. Also, considering a large amount of disorder within the system and the small ionic radii of some of the cations the possibility to have some inter-mixing (between the A and B sites of the ABO4 type spinel) can not be discarded. Nevertheless, Co,Mg,Zn,Cu,Ni have been chosen for purpose due to their highest capability to adopt a nonspherical configuration in comparison to Cr. Therefore, the inter-mixing between the A (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2 for the present case) and B (Cr) sites is less favorable (also supported by the XRD refinement). Further site-sensitive measurements are required to get accurate information about the fractional occupancies of the elements in different sites. Figure 2 shows STEM -ABF and HAADF images of the (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4 material. Also, the EDS analysis performed on numerous crystallites during the STEM studies shows good compositional homogeneity and confirms the stoichiometric cationic compositions at the nanoscale. The STEM images shown in figure 2 are consistent with the expected spinel structure along [110] zone axis. Inset in figure 2(c) highlights the electron diffraction (ED) on the same crystallite. The brightest reflections in the ED patterns can be indexed on a cubic unit cell with the cell parameters determined from the room temperature powder XRD pattern. These reflections are typical for a spinel structure. Also, the observed lattice parameter (8.4 Å) from STEM images matched well with the value found from the XRD refinement. Figure 3 (a) shows the temperature variation (5 -300 K) of the dc -magnetic susceptibility data measured at 1 T. The field cooled (FC) and zero field cooled (ZFC) magnetic susceptibility do not show any irreversibility down to 25 K. However, a clear peak indicative of an antiferromagnetic (AFM) transition is observed at 35 K in both the FC and ZFC measurements. It is noteworthy that up to 35 K, the magnetic susceptibility continues to increase with lowering the temperature, and this is somewhat expected for a strongly disordered system. Similar behavior is recently observed in the HEO material (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)O below its AFM (TN = 113 K) ordering temperature [START_REF] Zhang | Long-range antiferromagnetic order in a rocksalt high entropy oxide[END_REF]13]. The Curie-Weiss [χ = C/(t -θCW), C= Curie constant, θCW = Curie-Weiss temperature] fitting in the high-temperature region (150 -300 K) of the inverse of the FC magnetic susceptibility measured at 1 T leads to an effective paramagnetic (PM) magnetic moment (μeff) of 6.03 μB. We have subtracted the core diamagnetic contributions of all the elements from the susceptibility plot. The observed paramagnetic moment shows an excellent match with the expected theoretical values calculated on the basis of spin only contributions of all the transition metal elements (μtheoritical = 5.93 μB). The negative sign of Curie-Weiss temperature (θCW = -459 ± 1 K) highlights the predominant AFM type spin correlations. The high value of θCW indicates very high frustration (frustration index f = │θCW│/TN ~ 13) in the system. Magnetization measurements as a function of the magnetic field (M -H) at different fixed temperatures are shown in figure 3 (b). Typical unsaturated AFM type hysteresis loops are observed. A small coercive field, indicating the magnetic frustration in the material is observed in the M-H loop measured at 5 K. Besides the high frustration index observed in the Curie-Weiss fitting, due to existence of several magnetic and nonmagnetic cations and their random distribution in the Asite of the crystal structure, one may at a glance expect a spinglass-like magnetic state. Also, it has been already shown that the doping in the A site of the chromium spinel leads to the spin glass type magnetic behavior [START_REF] Martinho | Magnetic properties of the frustrated antiferromagnetic spinel ZnCr2O4 and the spin-glass Zn1-xCdxCr2O4 (x=0.05,0.10[END_REF]. Therefore, to know the exact nature of the magnetic interaction and to verify the possibility of the spin-glass transition, we have carried out the temperature dependence of the ac susceptibility measurements at different ac frequencies. The temperature variation of the real (χ') and imaginary (χ'') part of the ac susceptibility measured at various frequencies is shown in the supporting information (SI, figure S1) file. Similar to the dc susceptibility measurements, a peak is observed at 35 K in the real part of the ac susceptibility data. However, no peak is observed in the imaginary part near this transition. Also, no frequency-dependent shift of the peak is observed in the ac susceptibility data. All these observations unambiguously indicate a long-range antiferromagnetic order and absence of a spin glass type freezing. It is important to note here that, all the chromium spinels having magnetic cations in the A site of the structure shows long range ferrimagnetic (FIM) ordering (for instance, CoCr2O4 shows FIM at 97 K [START_REF] Yamasaki | Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide[END_REF], for NiCr2O4 TC=75 K [START_REF] Suchomel | Spin-induced symmetry breaking in orbitally ordered NiCr2O4 and CuCr2O4[END_REF], for CuCr2O4 TC = 120 K [START_REF] Suchomel | Spin-induced symmetry breaking in orbitally ordered NiCr2O4 and CuCr2O4[END_REF]). Quite interestingly, the present material, despite of having a disordered A site (and therefore various A -O -Cr interactions) and having the effect of different crystal fields on Cr site shows predominant AFM ordering at 35 K. The irreversibility between FC and ZFC susceptibility observed at 20 K could be due to the spin reorientation or lock-in transition (the crossover from incommensurate to commensurate phase) commonly observed in spinel structure [START_REF] Bérardan | Colossal dielectric constant in high entropy oxides[END_REF][START_REF] Yamasaki | Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide[END_REF][START_REF] Cui | Sol-gel synthesis of nanoscaled spinels using propylene oxide as a gelation[END_REF]. However, further experimental and theoretical studies (such as neutron diffraction, inelastic neutron scattering and pair distribution function calculations) are required to know the exact nature of the spin structure of this interesting high entropy system. Further, we have performed temperature dependent heat capacity measurement in the absence of an external magnetic field to investigate the magnetic ordering. As shown in figure S2, in an agreement with the magnetic measurements, a hump like peak is prominent ~35 K and this confirms the long range nature of the magnetic transition. Figure 4 shows the temperature variation of the dielectric constants for (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4 measured below 100 K. The very low value of tanδ (dielectric loss) reveals highly insulating nature of the sample. Both the dielectric constant and loss show that the frequency dispersion started above 60 K. This indicates the growing Maxwell-Wagner type relaxation or another source of conductivity above 60 K and the dielectric constants are intrinsic below this temperature. Interestingly, a clear peak at the AFM ordering is observed in the dielectric data, indicating the possibility of magneto-electric coupling at this temperature. Magneto-electric coupling due to the incommensurate spin-spiral structure at low temperature is already observed in the chromium based spinel samples at low temperature (for instance, in CoCr2O4 at 26 K) [START_REF] Yamasaki | Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide[END_REF]. In such cases, at spiral magnetic transition, the inverse Dzyloshinskii-Moriya (DM) interaction (Dn,n+1•Sn×Sn+1, Dn,n+1 is the Dzyaloshinskii vector) due to the spiral spin ordering breaks the inversion symmetry at neighboring sites of non-collinear spins and produces ferroelectricity [START_REF] Yamasaki | Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide[END_REF][START_REF] Lawes | Dielectric anomalies and spiral magnetic order in CoCr2O4[END_REF]. Also, in the presence of a magnetic field, the dielectric constant for the present materials starts to decrease near the AFM temperature, and a negative magnetocapacitance effect is observed below this temperature.

In conclusion, we have synthesized and studied a new high entropy spinel oxide. The SEM-EDS elemental mapping, Xray diffraction, and STEM ABF and HAADF measurements show that the sample crystallizes in a cubic spinel structure with an excellent chemical homogeneity at the nanoscale. The dc, ac magnetometry and specific heat show a long range antiferromagnetic ordering at 35 K in this highly disordered single-phase material. It is remarkable that the present material, despite of having a disordered A site (and therefore various A -O -Cr interactions) and having the effects of different crystal fields on Cr site shows long range magnetic ordering at 35 K. Magnetic measurements highlight a high magnetic frustration (f = │θCW│/TN ~ 13) in the system. The disorder (both magnetic and structural) and the presence of Jahn-Teller active cations (Cu and Ni) in the structure could be the reason of the magnetic correlations in this material remain frustrated, however, with a long-range magnetic ordering at 35 K. A peak in the dielectric measurement likely due to the possible magneto-electric effect is observed at the AFM ordering temperature. Further investigations (both theoretical and experimental) on this new material are warranted in order to underpin the exact nature spin configuration correlation and mechanism of MD coupling in this disordered material.

  (a) shows the Le Bail profile fitting of the room temperature (RT) powder X-ray diffraction patterns (XRD) for (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4 and indicates that the material can be isolated as single-phase crystallizes in a cubic spinel structure (space group Fd -3m) with a =b =c = 8.3233 (1) Å. The crystal structure is shown in the figure 1 (b). The octahedrally coordinated Cr atom occupy the B site of the structure. Mg,Co,Ni,Cu,Zn occupy the eightfold tetrahedral A sites. Figure 1 (c) illustrates the representative SEM image of the material. To determine the chemical composition, corresponding distribution and chemical homogeneity, we have carried out EDS elemental mapping.

Figure 1 .

 1 Figure 1. (a) Le Bail profile fit of the room temperature powder X-ray diffraction pattern and (b) crystal structure for the (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4 material. (c) A representative SEM image and EDS elemental mapping results for the same material.

Figure 2 .

 2 Figure 2. Room temperature (a) STEM-ABF and (b) STEM-HAADF images along [110] zone axis for (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4 material. Inset in figure (b) shows the electron diffraction pattern on the same crystallite along [110] zone axis. Enlarged views of both images are shown in (c) and (d).

Figure 3 .

 3 Figure 3. (a) Temperature variation of the magnetic susceptibility (left axis) and the inverse of the FC magnetic susceptibility (right axis) measured at 1 T magnetic field for (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4 material. (b) Magnetic field variation of the magnetization at different fixed temperature for the same material.

Figure 4 .

 4 Figure 4. Real part of dielectric constant (ε') as a function of temperature for (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4 material. Lower inset shows the loss part (tanδ). Magnetic field dependence of the dielectric constant for the same material is shown in the upper inset of the figure.

ACKNOWLEDGMENT

SM acknowledges the financial support of the University Caen Normandy for this work. The authors acknowledge the financial support of the french Agence Nationale de la Recherche (ANR), through the program "Investissements d'Avenir"(ANR-10-LABX-09-01), LabEx EMC3.

AUTHOR INFORMATION

Corresponding Author *soumarik@gmail.com, soumarik@thapar.edu

The authors declare no competing financial interests.


Arif Badrou

Nicolas Tardif

Philippe Chaudet

Nathan Lescanne

Jérome Szewczyk

Raphaël Blanc

Nahiene Hamila

Anthony Gravouil

Aline Bel-Brunon
email: aline.bel-brunon@insa-lyon.fr

Jérôme Szewczyk

Nahiène Hamila

Simulation of multi-curve active catheterization for endovascular navigation to complex targets

Keywords: Aorta, Endovascular navigation, Shape Memory Alloy, Catheter, Modeling

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Introduction

There has been a development of endovascular treatments in recent years.

The introduction of minimally invasive surgery has led to reduce mortality and morbidity rates compared with open procedures [START_REF] Verhage | Minimally invasive surgery compared to open procedures in esophagectomy for cancer: A systematic review of the literature[END_REF]).

The development of such techniques has been accompanied by more and more numerical simulations for decision support [START_REF] Gindre | Patient-Specific Finite-Element Simulation of the Insertion of Guidewire During an EVAR Procedure: Guidewire Position Prediction Validation on 28 Cases[END_REF]; [START_REF] Perrin | Patient-specific simulation of stent-graft deployment within an abdominal aortic aneurysm[END_REF]; [START_REF] Auricchio | Patient-specific aortic endografting simulation: From diagnosis to prediction[END_REF] or as training tools [START_REF] Westwood | Medicine Meets Virtual Reality 13: The Magical Next Becomes the Medical Now[END_REF]; [START_REF] Nesbitt | The role of simulation in the development of endovascular surgical skills[END_REF]; [START_REF] Alderliesten | Simulation of minimally invasive vascular interventions for training purposes[END_REF]; [START_REF] See | Evidence for Endovascular Simulation Training: A Systematic Review[END_REF]). Among them, few are related to the navigation of tools, i.e., guidewires and catheters, in the aorta to reach the target to treat. In [START_REF] Mouktadiri | Aortic endovascular repair modeling using the finite element method[END_REF]; [START_REF] Gindre | Patient-Specific Finite-Element Simulation of the Insertion of Guidewire During an EVAR Procedure: Guidewire Position Prediction Validation on 28 Cases[END_REF]; [START_REF] Mohammadi | A Numerical Preoperative Planning Model to Predict Arterial Deformations in Endovascular Aortic Aneurysm Repair[END_REF]; [START_REF] Kaladji | Prediction of deformations during endovascular aortic aneurysm repair using finite element simulation[END_REF]; [START_REF] Roy | Finite element analysis of abdominal aortic aneurysms: geometrical and structural reconstruction with application of an anisotropic material model[END_REF]) models were developed to predict arterial deformations during surgical tools navigation in the framework of aortic aneurysm. In [START_REF] Menut | Chirurgie endovasculaire virtuelle pour patient-spécifique : Application au traitement de l'anévrisme de l'aorte thoracique[END_REF] the simu-lation of navigation tools was adapted to the thoracic aorta. [START_REF] Vy | Patient-specific simulation of guidewire deformation during transcatheter aortic valve implantation[END_REF] developed a patient-specific model to predict guidewire deformation on the first stage of a transcatheter aortic valve implantation.

These works involve passive tools where their curvature only depends on their interactions with the aortic wall. The use of such passive devices is adequate in most cases, but in 20% of endovascular therapies, the areas to treat are so-called complex due to large tortuosities, e.g., at the Supra-Aortic Trunks (SATs) level, and the navigation may fail [START_REF] Madhwal | Predictors of Difficult Carotid Stenting as Determined by Aortic Arch Angiography[END_REF]; [START_REF] Macdonald | Towards Safer Carotid Artery Stenting[END_REF]; [START_REF] Lam | The impact of increasing age on anatomic factors affecting carotid angioplasty and stenting[END_REF]).

Recently, in order to reach complex targets, active devices have been developed. These steerable devices can be made of Shape Memory Alloys (SMAs) [START_REF] Wayman | An Introduction to Martensite and Shape Memory[END_REF]; [START_REF] Ali | First Expert Evaluation of a New Steerable Catheter in an Isolated Beating Heart[END_REF]; [START_REF] Haga | Small diameter active catheter using shape memory alloy[END_REF]), but other magnetic or electrostrictive materials are also used to curve the guidewires [START_REF] Ganet | Development of a smart guide wire using an elec-trostrictive polymer: option for steerable orientation and force feedback[END_REF]; [START_REF] Hwang | A review of magnetic actuation systems and magnetically actuated guidewire-and catheter-based microrobots for vascular interventions[END_REF]).

An active guidewire composed of a SMA was designed to facilitate the access to complex areas including SAT in an interventional neuroradiology context [START_REF] Couture | Design and Experimental Validation of an Active Catheter for Endovascular Navigation[END_REF]; [START_REF] Szewczyk | Active Catheters for Neuroradiology[END_REF][START_REF] Szewczyk | Process for Manufacturing a Flexible Elongate Structure Having an Orientable End[END_REF]). It was made of a long steel shaft and a blade-shaped distal tip on which a Nitinol wire was attached. The combination of wire and blade is called an active part. By applying an electric current, the wire heats up by the Joule effect. The Shape Memory Effect (SME) inherent to SMAs thus causes the wire to shrink [START_REF] Lagoudas | Shape Memory Alloys[END_REF]; [START_REF] Maynadier | Thermo-mechanical description of phase transformation in Ni-Ti Shape Memory Alloy[END_REF]) forcing the distal tip to bend. This controlled curvature facilitates the navigation through tortuous endovascular paths.

The insertion of the guidewire is followed by the insertion of a Distal Ac-cess Catheter (DAC) [START_REF] Spiotta | The Versatile Distal Access Catheter: The Cleveland Clinic Experience[END_REF]) that generally exhibits a rigidity gradient along its length to ease its navigation [START_REF] Gindre | Patient-Specific Finite-Element Simulation of the Insertion of Guidewire During an EVAR Procedure: Guidewire Position Prediction Validation on 28 Cases[END_REF]; [START_REF] Mouktadiri | Aortic endovascular repair modeling using the finite element method[END_REF]). The success of navigation is driven by the mechanical behavior of the inserted tools and their co-manipulation.

The aim of the present study was to develop a numerical simulation of the navigation of the active guidewire and DAC towards complex targets.

Our success criterion is the ability to catheterize the left carotid. The model was confronted with phantom experiments on three complex patient-specific cases. Based on existing studies on endovascular navigation, the main contributions of this work concerned: (i) active navigation to complex targets leading to original navigation scenarios, including the simulation of snapping, and (ii) measurements of clinical gestures thanks to an original bench test.

Herein, we first detail the navigation features observed and measured on a dedicated set up. Then, the numerical model of this navigation is described.

Finally, results are presented and discussed.

Characterization of the endovascular navigation on phantom aorta

Navigation towards complex targets is an elaborated combination of gestures and co-manipulations of tools. To get a better insight in this procedure and build the navigation model, this section presents observations and measurements of navigation features performed on a test bench.

The test bench

We aimed at simulating the navigation of the devices in the same conditions as those on the test bench at the French company BaseCamp Vascular (BCV) that developed the active guidewire. The test bench consisted of a module with two boxes: one containing the aortic arch, the other comprising a cylinder representing the descending aorta (see Fig. 1). Any phantom of aortic arch can be mounted in the first box.

Descending aorta

Cameras

Hemostatis valve Catheter

Aortic arch phantom The vascular structure was immersed in a mixture of washing liquid and water. A flow of 250L/h was imposed inside the aorta to represent the blood stream, which is rather low and constant compared to the pulsed flow occurring in reality [START_REF] Hashimoto | Pulse Pressure Amplification, Arterial Stiffness, and Peripheral Wave Reflection Determine Pulsatile Flow Waveform of the Femoral Artery[END_REF]; Sochi (2013)).

Active navigation and snapping effect

The navigation goal was to enter the aortic arch through the descending aorta (assuming femoral access) and to hook the left carotid artery which leads to the brain. The aforementioned active guidewire was used with the combination of the Navien A+ intracranial catheter and the introducer Neuron MAX. Fig. 2 displays the guidewire with two activated moduli showing the S-curvature used to facilitate the navigation through aortas. Active navigation involves different movements including:

1. Pushing, pulling and rotating the guidewire;

2. Activating the distal active flexions;

3. Pushing the DAC to reach the target area.

During navigation, clinicians often use a buckling phenomenon called snapping, which can be described as follows: when the distal part of the guidewire is in contact with the aorta, the activation of both the distal and the proximal active parts, accompanied by a rotation gesture operated by the handler, leads to a sudden rotation of the entire guidewire around its own axis. Thus, the hook formed by the guidewire changes direction and points in the opposite one, as illustrated in Fig. 2. This technique, relying on a S-shaped active double curve at the distal tip, appears to be an efficient maneuver to stabilize the device within the aortic arch and point into a selected SAT ostium.

Gestures by the clinician

As explained, in the case of navigation with active devices towards complex targets, clinicians perform many movements including rotations in addition to distal tip actuation. To correctly simulate the insertion of surgical tools, we aimed at determining an order of magnitude of the velocities applied to the devices.

These velocities were established thanks to a set-up added to the existing test bench presented in Fig. 3.

It consisted of two bearings sliding on a 500 mm rail. One of them was attached to the catheter, and the other to the proximal part of the guidewire. Targets were stuck to the bearings and a camera was able to track the movements on both the catheter and the guidewire. For the rotation of the guidewire, a stained token was attached to the shaft with adhesive tap. An other camera tracked the rotations. The frequency of the two cameras was 10Hz. Two additional cameras recorded the navigation through the aorta. As the activation of the guidewire consisted of applying a current, a last camera focused on an LCD screen displaying the electric current injected in the proximal and the distal moduli as well as the hands of the clinicians.

Several navigations with the goal of reaching the left carotid artery were filmed. Sequences were sorted and we computed an average velocity for the various phases as presented in Tab.1. All the measurements were performed on the same phantom (named PY aorta for the anatomy of the patient PY, see Fig. 7). Rotating guidewire 210.9 ± 80.4 RotG

Methods

Once the main features of navigation as performed by surgeons were characterized, we built a numerical model based on the Finite Element Method (FEM) to simulate this navigation and validate it against observations on the test bench. The full length of the different tools was not modelled. Indeed, due to a narrow entrance of the descending aorta visible in Fig. 1, we assumed in the case of simulating the experimental navigation, that the length outside the box had no effect on the navigation itself. A sufficient length was adjusted to allow the navigation to the left carotid.

Mesh. The FEM was chosen to simulate the navigation. We used Hughes-Liu beam elements in Ls-Dyna (Ansys / LST, CA., USA, 1976) for the guidewire.

The wire and the blade (distal tip) were meshed with a 1-mm beam. Beam elements of 2 mm were chosen for the shaft. The mesh size for the tools and the aorta was determined based on a convergence analysis on aorta PY, see Supplementary Material. One integration point was used for the Nitinol wires in order for them to act as bar elements and the overall rigidity of active parts was borne by the blade in green.

The catheters and the introducer were meshed with fully integrated shell elements to avoid Hourglass modes. Belytschko-Tsay shells which are of the type Reissner-Midlin were preferred for the introducer. The number of integration points was fixed to three which was clearly enough for the thickness of the elements.

Material law. Because of the complex composition of the catheters, some parts (mainly the distal one) exhibited a viscoelastic behaviour modeled by a generalized Maxwell formula with one element [START_REF] Herrmann | A Numerical Procedure for Viscoelastic Stress Analysis[END_REF]):

G(t) = G ∞ + (G 0 -G ∞ )e -βt
Here, G ∞ and G 0 were respectively the long and short time shear modulus, and the parameter β was a constant expressed per unit of time.

The other parts were assumed to be elastic. Tab.2 lists the material parameters for the Navien catheter, the introducer and the guidewire components depending on their elastic or viscoelastic behavior.

Table 2: Mechanical properties along the surgical tools: areas A to D are related to those in Fig. 4. As discussed previously, the guidewire was an active steerable device, and its curvature could be controlled thanks to the SME. To model this particular behavior, we implemented a 1D law described by [START_REF] Tanaka | Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys[END_REF] in Ls-Dyna, following studies previously conducted by [START_REF] Ianucci | The Development of a User Defined Material Model for NiTi SMA Wires[END_REF]. To represent the actuation of the Nitinol wires, we implemented a 1D law described by [START_REF] Tanaka | Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys[END_REF] in Ls-Dyna, following studies previously conducted by [START_REF] Ianucci | The Development of a User Defined Material Model for NiTi SMA Wires[END_REF]. The description of the law is given in Appendix. We used this law in a simplified way: we were interested in the guidewire curvature (corresponding to the maximum recoverable strain of the wire ϵ L ) as well as activation / deactivation times (t a and t d respectively). Therefore, we identified parameters ϵ L , t a and t d using the experiments presented in [START_REF] Badrou | Characterization of Surgical Tools for Specific Endovascular Navigation[END_REF]. Then, in the simulation, we imposed to the Nitinol wires a temperature load T as a linear function of time between 37°C and 65°C. The time intervals from one temperature to the other were defined to respect t a and t d . The wire model provided a longitudinal strain leading to the device bending, until reaching ϵ L . This way of using Tanaka's law is equivalent to drive the wire strain by displacement; however, we used Tanaka's law so that our model is easily adaptable to a full description of SME. From [START_REF] Badrou | Characterization of Surgical Tools for Specific Endovascular Navigation[END_REF], we determined that ϵ L = 0.0347 and t a = t d = 1.7s for the guidewire design tested in this paper.

We indeed observed experimentally that, due to the blade elasticity which brings the wire back to its initial configuration at deactivation, the activation and deactivation times are very similar. ϵ L is a design parameter that can be tuned to adapt to the considered patient as we will see in section 4.2.

Aortic phantoms modeling

Geometry. Three phantoms were available for the test bench, based on patient cases (patients PY, LP and FM). The same geometries were used in the model. They were classified by surgeons in our group as "complex" because the insertion point in order to reach the left carotid was difficult to access (see Fig. 7). These are typically complex anatomical cases in which navigation with passive tools would most probably fail. Indeed, for the aorta PY, the anchor point for hooking the carotid artery is low compared to the dome of the aortic arch. The aorta FM has a bovine arch: the innominate artery shares its origin with the left carotid. The origin of the carotid in the aorta LP is narrow and is not aligned with the insertion points of neighbouring arteries.

Mesh. The different geometries were meshed based on a mesh sensitivity analysis. We chose to use Belytschko-Tsay triangular shell elements. Since we were interested in hooking the left carotid we decided to finely mesh the areas near the SAT to catch the tortuosities. The chosen mesh size was 0.5 mm on these areas. A transition area with a mesh size of 1 mm was applied and the rest of the aorta was meshed with 2-mm elements for contact management. The thickness of the aortas varied from 2 to 4 mm on the BCV test bench. We decided to fix an average thickness for the overall aortas of 3 mm.

Material law. The aortas were assumed to be rigid. Nodes of the catheter and introducer in area 5 were fixed in displacements in X and Y and in rotation around the X and Y axis. These particular conditions were due to the narrow entrance (see Fig. 1) that constrained the devices. The proximal end of the catheter (nodes of areas 3) was constrained in all directions when the guidewire was moving. Nodes of area 4 were fixed.

Boundary conditions and numerical parameters

Indeed these ends were assumed to be held by the handler. The end of the guidewire (area 1) was presumed to move only along the Z axis and rotate around it. A rotation speed was applied on nodes of area 2 and a linear velocity command on those of area 1, their amplitude is given in Tab.1. Regarding the contact between the materials, frictional forces were assumed to be present both between the tools themselves and between the tools and the aorta. We used a penalty method to represent the contact and a friction coefficient of 0.2 was set by default except between the guidewire and the aorta and between the catheter and the introducer where the friction coefficient was set to 0.3 and 0.1, respectively. Mass scaling was employed with a given time step of 5.10 -6 s. To stabilize the active guidewire during the navigation, Rayleigh damping was used by playing of the mass proportional damping coefficient. We see in Fig. 7 that damping energy as kinetic energy are low compared to internal energy which confirms the validity of the damping and mass scaling levels adopted for this study.

Results

Validation

In order to validate the simulation of the endovascular navigation through phantom aortas, we simulated the insertion of the surgical tools into the aorta PY with regard to the experimental navigation. The inputs followed the path-based gestures of the clinicians. Validation was conducted on passive sequences (back and forth movements were applied to the guidewire without any activation), and on active sequences in which the device was actively bent. Attention was paid to several actions and phenomena occurring in reality:

Passive navigation: by pushing, pulling or rotating the devices without any activation;

Activation of the active parts: the distal tip of the guidewire curves in a multi-curve way;

Snapping.

We tried to correctly represent these phenomena in simulation. Fig. 6 compares the guidewire position between simulation and real navigation on the test bench during both passive and active sequences. For active sequences, we also followed the tip of the guidewire and recorded its coordinates with the camera plane of the test bench. The results show good agreement between the two datasets, a slight position deviation can be seen on the guidewire just after snapping but it did not affect the final position. The model parameterization made it possible to reproduce the various phenomena observed experimentally: snapping, active curvatures, interactions between the tools. Now that navigation within a phantom could be reduced, we wanted to make use of this simulation as a design assistance tool to find a combination of guidewire design parameters that would make it possible to hook the left carotid in different anatomies.

Application: simulation of endovascular navigation in two additional complex aortas

For the PY aorta, "clinical" gestures were measured and combinations of sequences could be reproduced. For the two other aortas, we relied on the previously validated simulator to find appropriate navigation parameters and guidewire design specifications to hook the left carotid.

The parameters on which we acted were the lengths L p , L d , e and the maximum recoverable strain ϵ L . The latter parameter concerned the ability of the Nitinol wire to contract exhibiting a change in the current intensity or in the grade of SMA. The values used to achieve hooking were determined by trial and error.

For the navigation into the PY and FM aorta, the boundary conditions were quite similar: the guidewire was pushed until the distal tip was in the ascending aorta, the parts were activated and the guidewire was snapped.

The device was then pulled in order to hook the left carotid. Regarding the LP aorta, the active parts did not overlap (blade only) and the distance between them, e, was long. No snapping was used in this case. The proximal modulus helped to curve the distal part of the guidewire and the distal modulus made it possible to point to the entrance of the carotid.

Fig. 7 shows that we were able to hook the left carotid for all cases despite their complexity, demonstrating the potential of the simulation to provide guidance into navigation gestures and device design. The navigation sequences were similar for the other aortas.

Discussion

Main results

This article describes the developement of a numerical model of endovascular navigation involving an active guidewire and catheters to cerebral targets. To the best of our knowledge, this is the first simulation combining an active steerable device, a catheter and their interactions with the vascular environment. In order to create the model, a complete characterization of the navigation was conducted. This work enabled (i) a better overview of the effects occuring during active navigation, such as snapping, and (ii) measurements of the velocities imposed by the clinicians to the surgical tools thanks to an original set-up.

Indeed, during endovascular navigation many movements are imposed on the tools. It is thus crucial to have an order of magnitude of the velocities for pulling, pushing and rotating the tools as well as for the sequences.

Thus, an additional set-up was added to the phantom aorta test bench and several navigations from experienced handlers were recorded. In particular, experimental analysis was carried out of the snapping phenomenon. Through observation and simulation we investigated the reasons of this buckling in rotation and we found that snapping occurs when the proximal active modulus is directly connected to the shaft and activated after the guidewire contacts the aorta distally.

Regarding the experimental point of view, we performed a 3-point bending test on a portion of the phantom aorta and found a Young modulus of 4.3

MPa. The idea was to confirm the hypothesis of a rigid aorta in our model.

Therefore, we compared the final position of the guidewire's distal part when navigating into the PY aorta between a rigid vs deformable aorta (phantom).

The difference in position was computed using the Modified Hausdorff Distance (MHD) [START_REF] Dubuisson | A modified Hausdorff distance for object matching[END_REF]). A value of MHD less than 1 mm was obtained and the assumption of a rigid aorta was therefore considered acceptable. Of course, this assumption can be questioned when it comes to real patient data and a probably less stiff aortic wall, but this present work only focused on simulating a phantom aorta test bench.

We could thus create the endovascular navigation model based on this result and the experimental characterization. The model was validated with regard to the experimental navigation into a complex aorta and particular attention was paid to the representation of experimentally observed phenomena such as the activation of the guidewire, passive navigation or the snapping effect.

Once our model was set-up, we demonstrated that hooking the left carotid was partially driven by the guidewire design. Among the various parameters, we acted on five parameters specific to the guidewire. Thanks to different configurations we succeeded in hooking three highly complex anatomies.

Among these design parameters, ϵ L is probably the most challenging as it reflects both material (Nitinol grade) and activation (current intensity) features. It is also affected by fatigue. Hence, preliminary tests would probably be necessary to reach the targeted value of ϵ L during design.

Study limits

The blood flow in the aortic arch is pulsed and considered to be turbulent [START_REF] Menut | Chirurgie endovasculaire virtuelle pour patient-spécifique : Application au traitement de l'anévrisme de l'aorte thoracique[END_REF]). This particular flow may have an impact on navigation. The flow applied to the test bench was low compared to real conditions and in simulation and the bloodstream was not taken into consideration at all in the simulation. Moreover, navigation tests on animals were conducted by the team and it was observed that blood flow and aortic wall deformations could probably be neglected because of their small influence on the guidewire position.

Concerning the geometries of the surgical tools involved in the simulation, we did not represent the total lengths of the devices. We can consider that it did not have any consequences related to the gestures of the clinician:

during experimental navigation, handlers navigate near the hemostatis valve to reduce the risk of buckling when it comes to linear movements. But the rotations are applied close to the proximal end of the shaft whereas in our model they are applied near the valve. This difference resulted in a shorter turnaround time in simulation but did not affect the navigation itself.

Regarding the experimental results on the measurement of the clinician gestures, the uncertainties were large due to a low amount of data and to movements that were difficult to repeat (especially the rotations). However, the success of navigation was not limited to a few speed values but rather allowed for a wide range of speeds. For our simulations, we considered average velocities.

The simulation was performed on the same patient-specific geometries as the ones used to create the phantoms for validation purposes. However, the geometries slightly differ. Indeed, the Supra-Aortic Trunks (SATs) and the ascending aorta are shorter in the numerical model. Manufacturing phantoms also generates small inaccuracies, that can be visible at the junction between the SATs and the aortic arc and in the descending aorta for instance.

However, we consider that the experimental and simulation geometries are close enough to ensure a satisfactory validation of the navigation related to this study.

A rigid aorta clearly differs from real aorta modeling [START_REF] Labrosse | Mechanical behavior of human aortas: Experiments, material constants and 3-D finite element modeling including residual stress[END_REF]). The simulations were therefore not transferable to a clinical situation. But in reality, the aortic arch is quite rigid, thus, the position of the guidewire should not be too far from the one obtained with a simulation on a rigid aorta. Nevertheless, this requires further validation against patient data.

Validation was performed in different configuration based on displacements only. It showed that the passive behaviour of the guidewire is mechanically reasonable as the guidewire deformation due to contact with the aortic walls is accurately simulated. However, concerning activation as previously discussed, the constitutive law used to represent the wire behaviour is equivalent to a displacement-driven one. Therefore, in the simulation, the curved guidewire would impose its motion to its environment and generate very high reaction forces; this is obviously not realistic and unfit for validation. We anyway used this model as it was shown both on phantom experiments and animal experiments that the activated guidewire is indeed very stiff compared to the surrounding tissue and tools.

Conclusion

This paper presents a numerical model of active endovascular tools navigating towards complex targets. It is based on patient specific anatomies and experimental characterization of both the tools and the praticians's gestures.

Now that is has been shown that complex anatomies can be successfully navigated on the test bench and in simulation, two main perspectives can be drawn:

1. For design purposes and surgeons training, the numerical model could be generalized to a larger cohort of anatomy using for example learning or reduced order modeling approaches (Lu et al. (2017a); Lu et al.

(2017b));

2. For clinical application purposes, the model could be adapted to real patient cases provided some assumptions regarding for example material models, boundary conditions or effect of blood flow are further questioned.

Acknowledgements

The French National Research Agency (ANR) partially supported this work through the DEEP project: Devices for augmEnted Endovascular navigation in complex Pathways (grant n°ANR-18-CE19-0027-01).

Conflict of interest statement

The authors declare that there are no conflicts of interest.

10. Supplementary material Figure 9: Results of the mesh convergence analysis for the catheters, the aorta and the guidewire. For these three parts, distinct studies were conducted involving endovascular navigation. The position of the guidewire was compared between the different configurations and a reference configuration (fine mesh) using Mean Hausdorff Distance. For the aorta and the active guide, 4 different mesh sizes were investigated. As the dimensions of the catheters were small, only two configurations were considered for the catheters as the mesh intended to preserve the tools geometry.

Figure 1 :

 1 Figure 1: Overview of the phantom aorta test bench used at BCV.

Figure 2 :

 2 Figure 2: Focus on the activation of the guidewire and illustration of the snapping effect: (a) activation of a so-called double-deck guidewire: two active parts are visible in the figure, the wires of the active parts are arranged on both sides of the blade so that the double activation tends to snake the guide, (b) illustration of the snapping effect: 1) The guidewire is in contact with the aorta distally 2) Both moduli are activated and a rotation is imposed at the shaft 3) The snapping occurs and the distal part of the guidewire points to the opposite side.

  distal and proximal part Remote control to activate the guidewire

Figure 3 :

 3 Figure 3: Additional set-up to measure clinician movements during navigation: instrumentation of the BCV bench.

3. 1 .Figure 4 :

 14 Figure 4: (a) Devices dimensions of the model: active guidewire and catheters used in our case. For each tool, the colors describe various portions having their different mechanical properties. Each portion is identified by a letter (from A to D) which refers to Tab.2 presenting the properties of the devices. (b) Visualization of the guidewire distal tip when activated: when the Nitinol wires are heated, they shrink making the blade (green parts) bend. (c) Assembly of the different tools (introducer + catheter + guidewire) in the PY aorta for the endovascular navigation.

Fig. 5

 5 Fig.5 depicts the boundary conditions at the entrance of the descending aorta model for the surgical tools.

Figure 5 :

 5 Figure 5: Boundary conditions applied on the devices during endovascular navigation. PushC, PushG, PullG and RotG are related to Tab.1 defining the different movements and their value.

Figure 6 : 1 O

 61 Figure 6: (a) Validation of the active navigation into the phantom aorta PY at different stages. (b) Guidewire tip coordinates during endovascular navigation in the camera plane: comparison between numerical (top) and experimental (bottom) data. The guidewire navigation begins at the top of the aortic arch in 1 O until it contacts the descending aorta

Figure 7 :

 7 Figure 7: Hooking of three complex aortas with details of the guidewire configuration used in each case. ϵ L is the maximal recoverable strain. CPU times using six Xeon 2.30 GHz cores are indicated. Graph of energies are plotted for the navigation into the PY aorta: the active guidewire first crosses the aortic arch until it is located nearby the left carotid artery. The two moduli are activated and the snapping effect occurs (kinetic energy peak). The active guidewire is pulled and the proximal modulus is deactivated. The left carotid is hooked and the Navien catheter slides on the guidewire to reach the carotid.

Table 1 :

 1 Mean velocities of the clinician gestures during active navigation.

	Movement	Speed values	Description
		(mm/s and °/s) (see Fig.5)
	Pushing guidewire 21.4 ± 5.1	PushG
	Pushing catheter	-13.5 ± 4.2	PushC
	Pulling guidewire	12.3 ± 4.6	PullG

Calculation of the martensite volume fraction

Heating phase Cooling phase

Calculation of the applied stress by Newton-Raphson algorithm